r/EPA
United States
Environmental Protection
Agency
Office of Policy,
Planning, and Evaluation
(2122)
EPA 230-R-95-008
October 1995
The Probability of
Sea Level Rise
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This document has been reviewed in accordance with the U.S. Environmental Protection Agency peer
and administrative review policies and approved for publication. Mention of trade names or commer-
cial products does not constitute endorsement or recommendation for use.
Library of Congress Cataloging-in-Publication Data
Titus, James G.
The probability of sea level rise/by James G. Titus, Vijay K. Narayanan.
p. cm.
Includes bibliographical references.
1. Sea level. 2. Greenhouse effect, atmospheric. 3. Climate Change, atmospheric.
I.Titus, James G., 1955- II. Narayanan, Vijay K, (Vijay Kumar), 1958- III.Title
GC89.T57 1995
551.4'58-dc20 95-15973
CIP
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THE PROBABILITY OF SEA LEVEL RISE
James G. Titus
Vijay K. Narayanan
U.S. Environmental Protection Agency
Carol M. Browner, Administrator
Office of Policy, Planning, and Evaluation
David M. Gardiner, Assistant Administrator
Climate Change Division
Dennis A. Tirpak, Director
Adaptation Branch
Joel D. Scheraga, Chief
Recycled/Recyclable • Printed with Vegetable Based Inks on Recycled Paper (20% Postconsumer)
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SUMMARY
Many climatologists believe that increasing
atmospheric concentrations of carbon
dioxide and other gases released by
human activities are warming the Earth by a mech-
anism commonly known as the "greenhouse
effect." This warming effect appears to be partly
offset by the cooling effect of sulfate aerosols,
which reflect sunlight back into space. The Earth's
average surface temperature has risen approximately
0.6°C (1°F) in the last century, and the nine
warmest years have all occurred since 1980.
Climate modeling studies generally estimate
that global temperatures will rise a few degrees (C)
in the next century. Such a warming is likely to
raise sea level by expanding ocean water, and melt-
ing glaciers and portions of the Greenland Ice
Sheet. Warmer polar ocean temperatures could
also melt portions of the Ross and other Antarctic
ice shelves, which might increase the rate at which
Antarctic ice streams convey ice into the oceans.
Warmer polar air temperatures, however, would
probably increase annual snowfall, which would
partly offset the rise in sea level caused by warmer
temperatures. Along much of the United States
coast, sea level is already rising 2.5-3.0 mm/yr
(10 to 12 inches per century).
By ratifying the United Nations Framework
Convention on Climate Change, more than 120
countries have agreed to implement measures for
adapting to rising sea level and other effects of
changing climate. Because the design and location
of coastal structures involve decisions that cannot
be easily reversed, people responsible for these
activities must either plan now or risk losing
the opportunity for a meaningful response.
Nevertheless, the value of planning for sea level
rise depends upon the probability that the sea will
rise by a given magnitude.
This report develops probability-based pro-
jections that can be added to local tide-gauge trends
to estimate future sea level at particular locations.
It uses the same models employed by previous
assessments of sea level rise. The key coefficients
in those models are based on subjective probability
distributions supplied by a cross-section of clima-
tologists, oceanographers, and glaciologists. The
experts who assisted this effort were mostly authors
of previous assessments by the National Academy
of Sciences and the Intergovernmental Panel on
Climate Change (IPCC).
The estimates of sea level rise are somewhat
lower than those published by previous IPCC
assessments, primarily because of lower tempera-
ture projections. This report estimates that global
temperatures are most likely to rise 1°C by the
year 2050 and 2°C by the year 2100, that there is
a 10 percent chance that temperatures will rise
more than 4°C in the next century, and a 90 percent
chance that they will rise by at least the 0.6°C
warming of the last century. By contrast, IPCC
(1992) estimated that a warming of 2.8°C was most
likely. Our temperature estimates are lower
because (a) we assume lower concentrations of car-
bon dioxide; (b) we include the cooling effects of
sulfates and stratospheric ozone depletion; and
(c) our panel of experts included a scientist who
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doubts that greenhouse gases will substantially
increase global temperatures.
Based on the aforementioned assumptions,
which this report explains in detail, our results can
be summarized as follows:
1. Global warming is most likely to raise sea
level 15 cm by the year 2050 and 34 cm by
the year 2100. There is also a 10 percent
chance that climate change will contribute
30 cm by 2050 and 65 cm by 2100.
These estimates do not include sea
level rise caused by factors other than
greenhouse warming.
2. There is a 1 percent chance that global warming
will raise sea level 1 meter in the next lOOyears
and4 meters in the next200years. By the year
2200, there is also a 10 percent chance of a
2-meter contribution, and a l-in-40 chance
of a 3-meter contribution. Such a large rise
in sea level could occur either if Antarctic
ocean temperatures warm 5°C and Antarctic
ice streams respond more rapidly than
most glaciologists expect, or if Greenland
temperatures warm by more than 10°C.
Neither of these scenarios is likely.
3. By the year 2100, climate change is likely
to increase the rate of sea level rise by
4.2 mm/yr. There is also a l-in-10 chance
that the contribution will be greater than
10 mm/yr, as well as a l-in-10 chance that
it will be less than 1 mm/yr.
4. Stabilizing global emissions in the year
2050 would be likely to reduce the rate of
sea level rise by 28 percent by the year
2100, compared with what it would be
otherwise. These calculations assume that
we are uncertain about the future trajectory
of greenhouse gas emissions.
5. Stabilizing emissions by the year 2025
could cut the rate of sea level rise in half.
If a high global rate of emissions growth
occurs in the next century, sea level is
likely to rise 6.2 mm/yr by 2100; freezing
emissions in 2025 would prevent the
rate from exceeding 3.2 mm/yr. If less
emissions growth were expected, freezing
emissions in 2025 would cut the eventual
rate of sea level rise by one-third.
6. Along most coasts, factors other than
anthropogenic climate change will cause
the sea to rise more than the rise resulting
from climate change alone. These factors
include compaction and subsidence of
land, groundwater depletion, and natural
climate variations. If these factors do not
change, global sea level is likely to rise
45 cm by the year 2100, with a 1 percent
chance of a 112 cm rise. Along the
coast of New York, which typifies the
United States, sea level is likely to rise
26 cm by 2050 and 55 cm by 2100.
There is also a 1 percent chance of a
55 cm rise by 2050 and a 120 cm rise
by 2100.
m
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TABLE OF CONTENTS
METHODS
1. INTRODUCTION 1
Background and Organization 1
How Much of This Report is Worth Reading? 5
Approach 5
2. CONCENTRATIONS OF GREENHOUSE GASES 13
3. CLIMATE CHANGE 21
A. TEMPERATURE AND THERMAL EXPANSION 21
B. CHANGES IN POLAR PRECIPITATION 58
4. GREENLAND ICE SHEET 65
5. ANTARCTIC ICE SHEET 85
6. SMALL GLACIERS 115
RESULTS AND CONTEXT
7. RESULTS 123
8. PLACING THE RESULTS IN CONTEXT 135
9. HOW TO USE THESE RESULTS TO PROJECT LOCAL SEA LEVEL 143
APPENDICES 149
REFERENCING CONVENTIONS AND ACKNOWLEDGEMENTS 185
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TABLE OF CONTENTS (continued)
1. INTRODUCTION 1
Background and Organization 1
How Much of This Report Is Worth Reading? 5
Approach 5
Combining Reviewer Opinions 6
Correlations Between Parameters 9
Time Horizon 11
References 11
2. CONCENTRATIONS OF GREENHOUSE GASES 13
Anthropogenic Emissions 13
Concentrations and Radiative Forcing 14
Expert Judgment 15
Final Results 17
References 19
3. CLIMATE CHANGE 21
PART A: TEMPERATURE AND THERMAL EXPANSION 21
The Use of 1-D Ocean Models to Estimate Global Temperature and Thermal Expansion 21
Fixed Parameters 24
Allowing w to Vary 25
Parameter Distributions for the 1-D Model in the Draft Report 31
Climate Sensitivity 31
Diffusivity and Initial Upwelling Velocity 31
Probability that Upwelling Velocity Changes 32
Values of TI in the Fixed-w Case 32
Values of n and w in the Variable-w Case 32
Polar Climate: Subsidiary Equations 33
Equilibrium Polar Warming 34
Antarctic Air Temperature 34
Southern Hemisphere Circumpolar Ocean Warming 34
Greenland Temperatures 35
Adjustment Times for Polar Temperatures 35
Changes in Antarctic Sea Ice 36
Results for Initial Draft Assumptions: Temperature and Thermal Expansion 37
Expert Judgment 39
Climate Sensitivity 42
Baseline Stochastic Variability 42
vii
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TABLE OF CONTENTS (continued)
Ocean Model 44
Greenland Temperature 47
Antarctic Air Temperature 48
Circumpolar Ocean Warming 48
Sea Ice 49
Implications of Reviewer Comments for Projecting Sea Level 49
Final Results 50
PART B: CHANGES IN POLAR PRECIPITATION 58
Greenland 58
Antarctica 59
Expert Judgment 60
Final Results 61
Reference 62
4. GREENLAND ICE SHEET 65
Ablation 66
Scaling and Mass Constraint 68
Parameter Values 68
Refreezing 69
The Lag Due to Refreezing 69
Elevations Where All Meltwater Refreezes 70
Calving 71
Ice Sheet Dynamics and Changes in Profile 71
Draft Results 76
Expert Judgment 76
Final Results 78
References 82
5. ANTARCTIC ICE SHEET 85
Background 85
Approach 86
Basal Melting of Ice Shelves: Generalizing the Relations Expressed
in the Polar Research Board Report 90
Ross Ice Shelf 90
Other Ice Shelves 91
Vlll
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TABLE OF CONTENTS (continued)
Impact of Basal Melting on Grounded Ice 93
Simple Model Based on Melting (AM2) 93
The Thomas Model (AM3) 94
Ice Stream B 94
Scaling 97
Alternative Scaling of the Thomas Model 97
Disaggregating the Thomas Model into Different Ice Streams 98
Ross andRonne Filchner 98
Amery and Other Shelves 98
Antarctic Peninsula 100
Adjustment to Antarctic Precipitation if the Area
of the Ice Sheet Declines 100
Sensitivity Runs and Selected Simulations 100
Linearization of the Huybrechts and Oerlemans Model 102
Draft Results 102
Expert Judgment 104
Ice Shelf Assumptions 105
Ice Sheet Response to Shelf Thinning 108
Final Results 109
References 114
6. SMALL GLACIERS 115
Draft Results 117
Changes Made in Final Version 119
Final Results 119
References 121
7.RESULTS 123
Summary of Previous Chapters 123
Total Contribution of Climate Change to Sea Level 125
Comparison with IPCC (1990) 129
The Implications of Alternative Emission Rates 130
Sensitivity Analysis of Variation 132
Numerical Error of the Monte Carlo Algorithm 132
References 134
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TABLE OF CONTENTS (continued)
8.PLACING THE RESULTS IN CONTEXT 135
Revisions of Sea Level Scenarios 135
Lower Global Temperatures 135
Antarctic Contribution 138
How Should Sea Level Rise Scenarios Be Used? 138
Encouraging Additional Efforts 139
Engineering Design 139
Land Use: Planning and Regulation 140
Impact Assessments 141
References 141
9. HOW TO USE THESE RESULTS TO PROJECT LOCAL SEA LEVEL 143
The Approach Employed by Previous Studies 143
Recommended Procedure 144
Caveats 144
References 147
APPENDICES 149
Appendix 1: Cumulative Probability Distributions Underlying this Analysis 150
A. Results Reported in Chapters 2 through 9 151
B. Results From Sensitivity Analysis Using IPCC Scenario A 170
C. Results From Sensitivity Analysis Using IPCC Scenario E 173
D. Results From Sensitivity Analysis Using Alternative
Emissions Policies and/or Fixing Particular Parameters 176
Appendix 2:Historic Contribution from Various Sources According to IPCC (1990) ....181
Appendix 3:Miscellaneous Information Concerning Antarctic Ice Sheet Research 182
REFERENCING CONVENTIONS AND ACKNOWLEDGEMENTS 185
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CHAPTER 1
INTRODUCTION
Background and Organization
In the last several years, a steady stream of
reports has estimated that the rate of sea level rise is
likely to accelerate in the next century (EPA 1983;
NRC 1983; NRC 1985; IPCC 1990; Wigley & Raper
1992). As a result, coastal decisionmakers around the
world have gradually begun to consider how to
respond. In many cases, no immediate response is
necessary, because the time required to implement a
response is less than the time likely to pass before the
sea rises significantly (NRC 1987).
A number of important decisions, however, are
sensitive to sea level rise on time scales of a century or
so. In some cases, the cost of preparing for a large rise
in sea level is small compared with the costs that
would eventually be incurred if the sea rises more than
assumed in a project's design. In such a case, it is
rational to design for a relatively high scenario, even if
that scenario is unlikely. For example, the Dutch
flood-protection system is designed to endure the "ten
thousand year storm," which has only a 1 percent
chance of occurring in a given century (Goemans
1986). Thus, if a new dike is expected to last a cen-
tury, maintaining the desired level of safety requires
an explicit consideration of the probability distribu-
tion of sea level rise.
Similarly, if a state intends to protect its coastal
wetlands or the public's legal right to access along the
shore, the cost of anticipatory land use planning can
be less than 1 percent of the eventual cost of remedi-
al action (Titus 1991); thus, it can be rational to
implement these land use policies even for areas with
a low probability of inundation. A few states have
added restrictions to the development of coastal prop-
erty which essentially say that if sea level rises
enough to erode or inundate it, the property owner
must remove any structures that impede the landward
migration of natural shorelines.1 If other states con-
sider this option for protecting their tidelands, they
may wish to determine the resulting impact on coastal
property values.2 Doing so requires an explicit
assessment of the timing and likelihood of the sea ris-
ing enough to inundate a particular property.
In spite of the need for this information, previous
assessments of future sea level rise have not provided
probabilities, for both computational and conceptual
reasons. At the computational level, projections of sea
level rise require complex nonlinear functions. Hence,
even if we knew the distributions of the various uncertain
processes, probability theory would offer us no direct
"closed form" solution for estimating the probability
distribution of future sea level rise. Instead, one must
iteratively approximate the distribution by evaluating the
models with alternate values for the various unknowns.
But many models—particularly the "general circulation
models" used to assess the impact of greenhouse gases
on climate—cost too much to run for this to be possible.
Even where the computational problems can be
solved, estimating probability distributions seems to
involve more subjectivity.3 Existing measurements
may lead researchers to be confident that a particular
set of low, medium, and high scenarios are reasonable.
But ascribing probabilities requires an additional level
of specification, and current knowledge does not per-
mit this to be done with precision. For example, both
Meier (1990) and IPCC (1990) report the results of
committees that agreed to a high scenario in which the
Antarctic contribution to sea level rise is zero. The
committees did not, however, decide whether "no
Antarctic contribution" represents a worst-case sce-
nario or a scenario with some chance of being exceed-
ed. Had they decided upon the latter interpretation,
they would have faced the additional difficulty of esti-
mating the probability of such an exceedence, which
would have required more subjectivity.
The main reason to estimate probability distri-
butions is that decisionmakers need this information.
If the published literature does not provide a proba-
lE.g., South Carolina's Beachfront Management Act special per-
mits; Texas' Open Beaches Act; and Maine's Dune Rule 355.
2In some states, the common law allows the government to prohib-
it bulkheads; hence, allowing a bulkhead to be built provides a
windfall to a riparian owner, the value of which the state may wish
to consider. In other states, property owners have a right to build a
bulkhead; a rule prohibiting bulkheads would decrease property
values. In either case, a measure of the probability distribution is
necessary to determine the present discounted value of the proper-
ty being lost at some future date. See J.G. Titus (draft), "Rising
Seas, Coastal Erosion, and the Takings Clause."
3In reality, the subjectivity is no greater. Whether one picks low
and high values or ascribes a probability distribution, one must
subjectively interpret the literature.
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Chapter 1
bility distribution, then engineers, economists, and
decisionmakers must implicitly or explicitly develop
their own estimates, which are likely to be less accu-
rate than the results of expert panels.4
This report presents the methods and results of a
two-part effort to estimate the probability distribution
of future sea level rise implied by the expectations of
approximately twenty climate researchers. In the first
phase, we developed a simplified model for estimat-
ing sea level rise as a function of thirty-five major
uncertainties, derived probability distributions for each
parameter from the existing literature, and conducted
a Monte Carlo5 experiment using 10,000 simulations.
The first portions of Chapters 2 through 6 summarize
the model, distributions, and results of that "draft"
analysis:
Chapter 2—emissions, concentrations,
and atmospheric forcings of greenhouse
gases;
Chapter 3A—the use of a 1 -D ocean
model for estimating global temperatures
and sea level rise due to thermal expan-
sion of ocean water; and simple relation-
ships describing the dynamics of polar
air and water temperatures as functions
of global temperatures;
Chapter 3B—simple relationships
describing changes in polar precipitation;
Chapter A—the impact of wanner polar
temperatures and precipitation changes
on the contribution to sea level from the
Greenland ice sheet;
Chapter 5—several alternative models
relating polar warming to Antarctic ice
discharges; and
Chapter 6—our adaptation of the IPCC
model of the contribution to sea level from
small glaciers.
4Focusing on probability distributions may also foster scientific
cohesion by enabling scientific panels to avoid choosing sides in
matters of scientific uncertainty, and instead lend partial credence to
competing, contradictory viewpoints, until one or the other is dis-
proved. For example, unlike previous EPA reports, this study does
not reject out of hand the view of some "greenhouse skeptics" that
greenhouse warming will be negligible. As discussed in Chapter 3,
our simulations include the views of a representative skeptic.
5See Note 8, infra.
Figure 1-1 illustrates the relationships between
the various models we used and developed to project sea
level. Given the emissions projections, we used existing
gas-cycle models to project atmospheric concentrations
and the resulting radiative forcing (Chapter 2). We devel-
oped simple models of how upwelling may change,
based on the results of three-dimensional models.6 We
used an existing model to project the resulting tempera-
ture and thermal expansion estimates (Chapter 3). We
devised simple models for projecting changes in polar
climate and Antarctic water temperatures (Chapter 3),
as well as the impact of water temperatures on ice-shelf
melting (Chapter 5). We developed a simple model of
a possible fast-but-stable impact of ice-shelf melting on
the Antarctic ice sheet contribution, while using existing
models to simulate an unstable response and a stable-
but-slow response (Chapter 5). We developed a simple
model of how the runoff elevation in Greenland
responds to climate change, but used existing models to
project the actual contribution of the Greenland ice sheet
to sea level (Chapter 4). We used an existing model to
estimate the impact of small glaciers on sea level
(Chapter 6). To estimate relative sea level at a specific
location, one can combine tidal-gauge observations with
the estimated glacial and thermal expansion contribu-
tions (Chapter 9).
In the second phase of this study, we circulated
the draft report to a "Delphic" panel of experts7—
approximately two dozen climatologists and glaciolo-
gists, listed in Table 1-1. In each case, we directed their
attention to specific chapters, and asked them to review
our assumptions, and suggest the assumptions that they
would have used had they conducted the analysis. A
few of the researchers provided comments without
probability distributions; but twenty of the researchers
did give us their best assessment of the values of the
model coefficients most closely related to their own
research. Moreover, five researchers even provided
alternative model specifications. Given the probability
distributions specified by our Delphic panel of experts,
we reran the 10,000 simulations.
6Additional models were added in the second phase, based on the
expert reviews.
7Broadly defined, a Delphic assessment is an analysis based in part
on the opinions of experts. The origin of the term stems from the
oracles at Delphi in Greek mythology, who, among other things,
warned Oedipus that he would kill his father; they were also known
as oracles of Apollo, the god of prophesy. The expert opinions of
a Delphic assessment, like the pronouncements of the oracles at
Delphi, are presumed valid regardless of whether there is an expla-
nation supporting them. Nevertheless, in this report, the reviewers
generally do provide explanations.
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Introduction
Concentrations
Radiative
Forcing
Antarctic
Air AT
V
Antarctic
Precipitation
D
Exogenous Data
Variables Calculated
by Model
Previously Published
Models
^ Models Developed in
this Study
£ Summation
AT Temperature Change
Figure 1-1. Relationship Between the Various Models We Used to Project Sea Level.
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Chapter 1
TABLE 1-1
REVIEWERS WHO CONTRIBUTED TO THIS ANALYSIS
Global Climate and Polar Temperature Assumptions
Robert Balling
Francis Bretherton
Martin Hoffert
Michael MacCracken
Syukuro Manabe
David Rind
Stephen Schneider
Sarah Raper3
Tom Wigleya
Polar Precipitation Assumptions
Richard Alley
Michael Kuhn
Michael MacCracken
David Rind
Stephen Schneider
Jay Zwally
Antarctic Assumptions
Richard Alley
Anonymous
Charles Bentley
Robert Bindschadler
Stan Jacobs
Craig Lingle
Robert Thomas
CJ. van der Veen
T. Wigley and S. Raper3
Jay Zwally
Greenland Reviewersb
Walter Ambach
Robert Bindschadler
Roger Braithwaite
Mark Meier
Robert Thomas
T. Wigley and S. Raper3
Jay Zwally
Arizona State University
University of Wisconsin
New York University
Lawrence Livermore National Laboratory
NOAA/Princeton Geophysical Fluid
Dynamics Laboratory
NASA/Goddard Institute for Space Studies
Stanford University
University of East Anglia
University Corporation for
Atmospheric Research
Pennsylvania State University
Innsbruck University
Lawrence Livermore Nat. Laboratory
NASA/Goddard Institute for Space Studies
Stanford University
NASA/Goddard Space Flight Center
Pennsylvania State University
University Professor
University of Wisconsin
NASA/Goddard Space Flight Center
Lament Doherty/Columbia University
University of Alaska
NASA/Greenland Ice Core Project
Ohio State University
University of East Anglia
NASA/Goddard Space Flight Center
University of Innsbruck
NASA/Goddard Space Flight Center
Geological Survey of Greenland
University of Colorado
NASA/Greenland Ice Core Project
University of East Anglia
NASA/Goddard Space Flight Center
Tempe, AZ
Madison, WI
New York, NY
Livermore, CA
Princeton, NJ
New York, NY
Stanford, CA
Norwich, UK
Boulder, CO
Univ. Park, PA
Innsbruck, Austria
Livermore, CA
New York, NY
Stanford, CA
Greenbelt, MD
Univ. Park, PA
United States
Madison, WI
Greenbelt, MD
Palisades, NY
Fairbanks, AK
Washington, DC
Columbus, OH
Norwich, UK
Greenbelt, MD
Innsbruck, Austria
Greenbelt, MD
Copenhagen, Dmk
Boulder, CO
Washington, DC
Norwich, UK
Greenbelt, MD
aWigley and Raper provided a joint review based on their revisions to an unpublished analysis initiated by Richard Warnck. The Wigley &
Raper study is summarized in Wigley, T.M.L., and RD. Jones. 1992. "Detection of Greenhouse Gas Induced Climatic Change." Research
Proposal to U.S. Department of Energy. During the study, Wigley moved from East Anglia to University Corporation for Atmospheric Research.
bThe Greenland reviewers offered modeling suggestions but did not suggest independent parameter values, except for Wigley & Raper.
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Introduction
In the latter part of each of the following chapters,
we summarize the reviewer changes and present the
results of the Delphic Monte Carlo experiment. We dis-
cuss the draft and Delphic assumptions separately for
two reasons. First, the separate discussion helps to avoid
ambiguity with regard to which assumptions were devel-
oped by us and which were provided by the reviewers.
Second, and perhaps more importantly, in many cases
particular reviewers decided that the parameters from
the draft were reasonable enough. For example, based
on the commonly accepted 1.5 to 4.5 °C warming from a
CO2 doubling, we assumed that the most likely value is
2.6°C, which is the geometric mean of this range. All
but one of the researchers accepted this characterization.
Had we used the arithmetic mean of 3.0°C, most of the
reviewers may well have accepted that formulation as
well. Here and elsewhere, our initial specifications
almost certainly had a lingering effect on the results of
the analysis. By discussing the draft and the Delphic
analysis separately, we enable readers to (a) examine
how the reviewers changed our assumptions and (b)
thereby evaluate the extent to which our initial assump-
tions may have biased the analysis.
The last three chapters present our final results.
Chapter 7 summarizes the results of our analysis, focus-
ing on the likely impact of greenhouse gases on tem-
peratures and global sea level, and examining the sensi-
tivity of the results to alternative emissions scenarios
and other assumptions. Chapter 8 places the results in
context, examining both the reasons that sea level pro-
jections have been revised downward and the practical
uses to which sea level projections have been put.
Finally, Chapter 9 explains how to use our estimates to
project local sea level at specific locations.
How Much of This Report
Is Worth Reading?
We warn the reader at the outset that, for all but a
limited audience, most of this report is exceedingly
dry—particularly Chapters 3,4, and 5. The typical coastal
engineer, geologist, lawyer, or policy analyst may prefer
to read only Chapters 7, 8, and 9. For the more techni-
cal reader who is already familiar with the assumptions
underlying the IPCC and other sea level rise assess-
ments, it may be sufficient to read the sections entitled
"Expert Judgment," particularly in Chapters 3A, 3B,
and 5, along with the results reported in Chapter 7.
Those trying to understand how this analysis differs
from previous assessments should focus on the remain-
der of this Chapter and the "Expert Judgment" section
in Chapter 3.
The remainder of this chapter summarizes meth-
odological issues that are relevant to all of the chapters.
Approach
Our overall approach is to assume that
SL = M(a,b,c,...),
where SL is sea level,
M is the model, and
a, b, c,... are unknown coefficients.
We assume that the model would be true if we knew
the actual values of the coefficients. But because no
one knows their precise values, we must rely on esti-
mates, each of which is uncertain. Based on available
estimates and reasonable assumptions about the
shapes of the distributions, one can estimate a proba-
bility density function for each coefficient.
In the simple case, where SL=aX+bY and we
have data on X and Y, probability theory provides us
with a simple formula for estimating the distribution
of SL. Projections of sea level rise, however, are non-
linear: Even simple models must multiply uncertain
temperatures by uncertain melting-sensitivity para-
meters, and most models are far more complex.
Under these circumstances, solving for the distribu-
tion is too complicated to be practical.
Statisticians have shown, however, that one can
eventually converge on the distribution by randomly
selecting values of the coefficients, running the
model repeatedly, and treating the resulting estimates
as a sample. This procedure is known as "Monte
Carlo."8 Because we wanted to estimate the rise with
8The meaning of the term "Monte Carlo analysis" has evolved.
Originally, the term referred to the use of many trials to numerically
approximate a probability distribution—as opposed to analytically
solving the equations. As the use of Monte Carlo techniques
evolved, mathematicians have shown that the original approach of
randomly selecting the input values is not as efficient as nonrandom
sampling approaches such as Latin Hypercube. Although Latin
Hypercube is a Monte Carlo technique in the original sense of the
word, many authors use the term "Monte Carlo analysis" to refer
only to exercises that employ totally random samples.
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Chapter 1
a 1 percent chance of being exceeded, 10,000 trials
seemed to be sufficient.9
Table 1-2 lists thirty-five parameters used by the
draft report. In most cases, we characterized probabili-
ty distributions derived from the literature. In four
cases, however, the draft used alternative models; in
these cases, we specified n-nomial distributions based
on our best guess about the combined opinion of the
community.10 For example, if we have two alternative
models for estimating thermal expansion of ocean water,
we assume that there is a chance of p that SL=Mi(a,b,...)
and a chance of (1-p) that SL=M2(a,b,...). Although this
approach allows us to relax the assumption that a partic-
ular model is true, it still understates our uncertainty
because there is a chance that none of the models we
specify are either true or reasonably accurate summaries
of the likely response of the relevant processes.
Combining Reviewer Opinions. Once the review-
ers had reacted to our original draft by providing us with
their subjective probability distributions, we had to
decide (a) how to ensure that the insights of one review-
er would feed back onto the opinions of the other
reviewers, and (b) how to combine the reviewer opin-
ions to develop a probability distribution that fairly
incorporates the combined wisdom of all the reviewers.
Because of time and cost limitations, we followed the
simplest approach that we could devise. Our feedback
process primarily involved (1) circulating each of the
reviewer assessments to all of the reviewers of a partic-
ular chapter; (2) notifying each reviewer if another
reviewer questioned any aspect of his or her assessment;
and (3) giving each reviewer an opportunity to change
his or her subjective probability distributions based on
the assessments of the other reviewers. We also played
"Devil's Advocate" with each reviewer. For each para-
9The random Monte Carlo approach is not as efficient at estimating
the extremes of a cumulative distribution as the Importance Sampling
method. But the complex weighting required by the latter algorithm
would have required considerable time to implement. Moreover,
Importance Sampling might not have been very effective in our
case unless we ran millions of trials. Both Importance Sampling
and the Latin Hypercube methods require many more trials than we
conducted, before their superiorities emerge. As discussed below,
we have thirty-five parameters. Even if there were only eight para-
meters, with distributions divided into four segments for sampling,
the sample space would have 48 (i.e., 65,536) different areas that
had to be sampled; assuming that each required at least ten obser-
vations, one would require 650,000 simulations. See Morgan and
Henrion, 1990; Numerical Error of the Monte Carlo Algorithm,
Chapter 7, infra.
10This approach was extended in the final version, in two ways.
First, several reviewers provided additional models from which to
select. Second, our approach for incorporating the reviewer com-
ments essentially treated each reviewer's opinion as a separate
model from which to select.
meter, we would discuss the potential implications of
the reviewer's specified distribution to ensure that the
reviewer was providing a well-considered opinion.
Our final estimates reported in Chapters 7 and 9
are based on weighting each opinion equally. We con-
cede at the outset that there are more sophisticated
ways for combining reviewer opinions. For example,
we might have polled a second, independent group of
experts regarding the validity of the opinions of the
first group of experts, or we might have polled the orig-
inal group regarding the credibility of other reviewers
on specific parameters.11 Because such iterations were
not feasible,12 however, weighting the opinions equally
seemed justified under the circumstances.13 The review-
ers who participated represent a fair cross-section of
scientific opinion regarding the key areas of climate
sensitivity, polar temperature, polar precipitation, and
glacier sensitivity.
Recognizing that other researchers may wish to
weight the reviewer opinions differently,14 we report
all of the recommended probability distributions of
every reviewer. So that the reader of this report can
1 'To call these more iterative methods a "Delphi" approach is some-
what of a misnomer: the oracles at Delphi did not provide commentary
on the validity of the pronouncements of other oracles. Nevertheless,
these iterative approaches are generally referred to as "Delphi."
12So that other researchers might use this report for other purposes, we
wanted to keep this analysis "on the record," which would have been
impossible if the reviewers had to rate the expertise of other scientists.
A few reviewers had indicated at the outset that they would participate
only if each opinion was counted equally. Moreover, as we interviewed
most of the other researchers, we got the distinct impression that putting
probabilities on scientific processes that they had studied was already a
novelty, and that asking them to weight the opinions of other reviewers
was beyond what they wanted to do. (Two reviewers did, however,
indicate that they would have preferred to participate in a second iter-
ation concerning the relative expertise of the various reviewers.)
"Additional iterations would probably have been more important
were it not for the fact that obtaining the reviewer opinions was
already a second iteration for this study, the initial iteration being the
draft report we circulated, which was based on parameters obtained
from the literature.
14Theoreticians of decision analysis generally disapprove of the
practice of weighting all opinions equally. Nevertheless, Winkler
(1971) and Seaver (1978) "have found little or no difference in the
performance of various differential weighting schemes over equal
weighting...." (Morgan & Henrion (1990) at 167).
A more complex weighting scheme is possible only if there is a
group of experts ready and willing to assess the validity of the original
set of subjective probability distributions. If the political or monetary
cost of independently evaluating the experts is high relative to the cost
of obtaining the opinions in the first place, there may not even be a the-
oretical justification for the more complex weighting schemes. See
e.g., Morgan & Henrion at 167 ("The administrator of EPA, or his sur-
rogate, is likely to have difficulty publicly stating that he finds Dr.
Jones's views six times more credible than Dr. Smith's views....").
-------
Introduction
TABLE 1-2
INITIAL ASSUMPTIONS IN DRAFT REPORT
(Also used to represent some runs in the final report, where reviewer did not suggest changes)
Parameter
Parameter Distribution
Name Shape, Moments
CONCENTRATIONS OF GREENHOUSE GASES
Emissions
E Nordhaus & Yohe,
scaled
Value of
Moments
IPCC92 scenarios
for each gas
OCEAN MODEL PARAMETERS
Equilibrium ^2X lognormal, o limits
AT2XCO2
Diffusivity k lognormal, 2a limits
Probability of Cl binomial
Case A
Case A: Fixed Bottomwater Formation
Downwelling Ratio n lognormal, 2o limits
Upwelling Velocity w lognormal , 2a limits
Case B: Bottomwater Formation Declines with Temperature
Downwelling Ratio n Fixed
Upwelling Velocity
Initial w0 lognormal, 2(7 limits
Transient w w(AT)=w09AT
Sensitivity of w to 0 lognormal, 2a limits
Temperature
POLAR CLIMATE
Equilibrium Polar Amplification
Antarctic Summer PI lognormal, a limits
Antarctic Winter P2 lognormal, cr limits
Greenland Annual P7 lognormal, 2a limits
Circumpolar Ocean P3 lognormal, a limits
Adjustment Times (in addition to the global lag)
Circumpolar Ocean P4 lognormal, 2o limits
Antarctic Summer P5 lognormal, a limits
Antarctic Winter P6 lognormal, a limits
Greenland — Fixed
1.5, 4.5 °C
1000, 3000 m2/yr
Prob(Cl = 1) = 0.5
0.2, 1.0
2.0, 6.0 m/yr
0.2
2.0, 6.0 m/yr
0.852, 1.0
0.67, 1.5
1.0, 3.0
1.0,2.0
0.25, 1.0
20, 80 years
1,20
1,20
No Additional Lag
Correlation with
Other Parameters
perfect
correlation
none
w(l.O)
none
none
k(l.O)
none
k(l.O)
See function
none
P2 (0.5), P3
PI (0.5)
PI, P2 (0.5)
PI (0.75)
P5, P6 (0.5)
P6, P4 (0.5)
P4 (0.5)
-------
Chapter 1
Polar Precipitation
Antarctic P8
Greenland P9
TABLE 1-2 (continued)
lognormal, 2o" limits
See Table 3-3
(approx. 6%/°C)
lognormal, 2cr limits V(t)/V(0), (9%IAT = 1)
V'(t)/V'(0) (8.5%)
Antarctic Precip. P10 lognormal, 2a limits
Adjustment for Area
1/3, 2/3
ANTARCTIC ICE SHEET AND ICE SHELF ASSUMPTIONS
Ice Shelf Melt
0.05, 0.2
Seaice Sensitivity to P10 lognormal, 2a limits
Global Temperature
Sensitivity of Ross Ice 1+A1 lognormal, 2a limits
Shelf Warm Intrusions
Ross Melt Response A2
to Warm Intrusion
Probability of Undiluted C3
CDW Under Ross
Sensitivity of A3
Weddell Sea to Tcdw
lognormal, 2o~ limits
binomial
fixed
Ronne/Filchner
Basal Melt from
Weddel Warming
Threshold for Melt
Only Model
Ice Stream Model
A4 lognormal 2a limits
A7 Right Triangular
Initial Velocity VO
of Ice Stream B
Upstream Length, L
Shelf Backpressure
Calving C2
lognormal, 2o limits
lognormal, 2a limits
Trinomial
Fixed Calving
Reference Calving
Enhanced Calving
1,36
0.25, 1.0
min(0.05ATcdw, 0.25)
1.0
1.91,3.33
p(x) = 2x
F(x) = x2
100, 300 m/yr
100, 300 km
P(C2 = 2) = 0.7
P(C2 = 0) = 0.3
P(C2 = 1) = 0.0
P8 (0.5)
P7 (0.5)
none
none
none
none
none
none
none
none
none
none
NOTE: V(t) is the saturation vapor pressure at a particular time. V'(t) is
-------
Introduction
TABLE 1-2 (continued)
ANTARCTIC ICE SHEET MODEL SELECTION
Model Probability (%)
AMI, IPCC No Ice Sheet Response, Precipitation Only 10
AM2, Basal Melt Only 20
Thomas Ice Stream—Extrapolation Options
AM3, Continent Wide 5
AM4, Only to Streams that flow Through Shelves 10
AM5, Ratio of Ice Discharge to Melting 10
AM6, Ice Stream Specific Response 25
AM7, Oerlemans Model—Linearization 20
GREENLAND
Zero Ablation Line Gl
Response to AT
Calving Response G2
to Ablation
Response Time G3
Due to Refreezing
SMALL GLACIERS
Response Time T
Historic Contribution
Oerlemans Ml
Meier M2
Probability of the C4
Meier Estimate
lognormal, o limits
normal, 2o limits
lognormal, a limits
lognormal, o limits
normal, o limits
normal, a limits
binomial
111.1, 186.3 mfC
0, 1.14
12.5, 50 years
10, 30 years
0.515, 1.885 cm
1.2, 4.4
P(C4=1) = 0.5
none
none
none
none
none
none
none
gain a rough understanding of the results implied by
each reviewer's assessments, we also disaggregate
results by reviewer, where feasible. For example, for
each climate reviewer (Chapter 3A), we report global
and Greenland temperature estimates, as well as the
Greenland, Antarctic, and total sea level contribution.15
Because of the procedures we followed, our final results
must be viewed as conditional probability estimates—
conditional on the assumption that the participating
15The estimates of sea level contribution by climate reviewer, how-
ever, require assumptions regarding glacier parameters, for which
the climate reviewers generally expressed no opinion. For these
assumptions, we weight all nonclimatic reviewers equally. (The
Wigley & Raper assessment was an exception to this procedure, as
explained below.)
reviewers adequately represent the cross-section of
scientific knowledge on the parameters for which they
provided probability distributions.
Correlations Between Parameters. For a variety
of reasons, our uncertainty regarding one parameter
may be related to our uncertainty regarding another
parameter. As discussed in Chapter 3, for example, the
parameters k (diffusivity) and w (upwelling velocity)
used in ocean models are often viewed as being per-
fectly correlated, because the pattern by which ocean
water temperatures decline with increasing depth is
consistent with the assumption that k/w=500 meters.16
16See Chapter 3 for additional discussion of these parameters.
-------
Chapter 1
At least some of the factors that might lead Antarctic
winter temperatures to warm could also cause sum-
mer temperatures to warm (e.g., the latitudinal ocean
circulation); so there is some correlation between
summer and winter wanning, albeit less than perfect.
The draft accounted for some of these relationships
by generating random values of the parameters with
specified correlations.
The various reviewers of Chapter 3 suggested
several additional correlations. For example, because
reduced thermohaline circulation17 might imply a
weaker Gulf Stream with which to heat Greenland, one
researcher had a correlation of 0.5 between possible
changes in w and Greenland temperatures. Another
reviewer assumed that the warming of the Antarctic
circumpolar ocean will lag farther behind global tem-
peratures in cases where emissions grow more rapidly
or the climate sensitivity parameter AT2x is larger;
again a correlation of 0.5 was used.
The Delphic Monte Carlo analysis includes a
second type of correlation, designed to preserve the
internally consistent visions of the future implied by
particular reviewers' assumptions. For example,
although most reviewers of Chapter 3 did not specify a
correlation between it and changes in w, there was a
tendency for those who expected a low 71 to also expect
a decline in w, and for those who used high values of n
to consider w as less likely to decline. We preserve the
"consistent visions" by generating separate probability
distributions for each researcher, rather than by develop-
ing a single composite distribution for each parameter.
For the most part, these consistent visions apply
only to a particular chapter. The joint review provided
by Tom Wigley and Sarah Raper, however, provided
assumptions sufficient to estimate all of the contributors
to sea level. Therefore, we treat their consistent vision
as applying to the entire analysis; simulations repre-
senting their suggestions on wanning, for example,
are not combined with anyone else's assumptions
regarding Antarctica.
17Thermohaline circulation refers to ocean currents driven by dif-
ferent densities, which in turn result from different temperatures
and salinities. For example, evaporation over the Gulf Stream
increases the salinity level and thereby the density of ocean water,
enabling water to sink as it reaches the North Atlantic, forming
deep water. This sinking helps propel the circulation that causes
the Gulf Stream to flow north. Some climatologists expect warmer
global temperatures to cause more rainfall over the North Atlantic,
which would reduce salinity and deepwater formation, and thereby
slow the Gulf Stream.
Our procedure for preserving these conelations
is analogous to treating the reviews of each chapter as
a deck of cards. Separate groups of reviewers pro-
vided comments on the nonprecipitation climate vari-
ables (Chapter 3A), precipitation (Chapter 3B),
Greenland (Chapter 4), and Antarctica (Chapter 5).
Our procedure was as follows:
1. We divided the assumptions into six decks:
Deck 2: This deck has 10,000 cards, each
of which has a random value for
each parameter discussed in
Chapter 2.
Deck 6: Same as Deck 2, for Chapter 6.
Deck 3A: This deck is composed of eight
piles, each of which corresponds
to one expert reviewer, with the
first pile representing Wigley &
Raper. Each pile has 1250 cards,
each of which has a random value
for each of the nonprecipitation
climate parameters discussed in
Chapter 3. Each pile uses different
underlying distributions cones-
ponding to the distributions sug-
gested by the particular researcher.
Deck 5: Same as Deck 3A, for Chapter 5.
Deck 3B: Same as Deck 3A, except that only
six researchers provided distribu-
tions, so there are only six piles.
Deck 4: Same as Deck 3A, except that
seven of the eight piles are drawn
from the same underlying dis-
tribution. The first pile represents
the distributions specified by
Wigley & Raper. The remaining
seven piles are drawn from the
distributions accepted by the
glaciologists who reviewed
Chapter 4.
2. The top pile in each deck represents the sug-
gestions of Wigley & Raper, because their
joint review was the only review that sug-
gested parameters for the whole array of sea
level contributors. We remove the top pile
from each stack and set it aside temporarily.
10
-------
Introduction
3. We shuffle the remaining piles of Decks 3B
and 5. If we did not shuffle Deck 5, for
example, the simulations that use the sug-
gestions of the last reviewer of Chapter 3A
would only use the parameters specified by
the last reviewer of Chapter 5. By shuffling
the deck, the simulations using this last cli-
mate reviewer use the assumptions of all
the Antarctic (Chapter 5) reviewers in
roughly equal proportions. There is no
need to shuffle Deck 2 or 6, because they
are already randomly mixed, as are the
remaining seven piles of Chapter 4.
4. We put the Wigley & Raper piles back on
the top of each deck.
5. We draw the top card from each deck and
run a simulation using the parameter values.
We then draw the next card from each
deck and repeat the process for all 10,000
simulations.
Thus, the first 1250 simulations represent the con-
sistent vision of Wigley & Raper across all chapters. The
following 1250 simulations use the consistent vision of
the second climate reviewer but include a random
selection of parameters drawn from all other chapters.
Time Horizon. Like most previous assessments
of sea level rise, we focus on the year 2100. However,
we do not truncate our analysis at that date. We
extend our analysis farther into the future for both
technical and policy reasons.
On the technical side, several glacial modeling
efforts have suggested that impacts from Antarctica
will not be significant until after the year 2100 (e.g.,
Huybrechts & Oerlemans 1990). Yet the potential
impacts have long been discussed. To end our analysis
before Antarctica is likely to have a significant impact,
would lead our assessment to exclude consideration of
some of the most important research on the issue of
long-term sea level rise. If we could be certain that
Antarctica will not make a contribution within the rel-
evant time horizon, disregarding that research might
be warranted; however, no such certainty exists. In a
similar vein, examining longer time horizons helps to
provide a better understanding of the implications of
one's assumptions, and the impacts likely to occur over
longer periods of time are similar to the worst-case sce-
narios of what could happen in the next century.
On the policy side, no one has demonstrated
that impacts after the year 2100 are irrelevant. The
remoteness of the twenty-second century, we suggest,
can be better addressed by discounting the future than
by ignoring it completely. Policymakers concerned
with nuclear waste sites have considered potential
consequences thousands of years into the future. The
roads that are built today can determine the locations
of development for centuries into the future, even if
specific structures only last one-hundred years.
Although local planning commissions generally focus
on the next few decades, the civic groups that propose
policies often include churches and historic preserva-
tion groups with perspectives stretching back several
centuries. Finally, Cline (1992) argues that all cli-
mate impact assessments should extend two-hundred
years into the future, and at least one chapter of a draft
IPCC report has attempted to extend the analysis out
several centuries (Pearce et al. 1994).
Most officials will be more concerned with
"best-guess" estimates for the next few decades. But
the importance or lack of importance of very-long-run
and very-low-probability impacts can only be ascer-
tained if impact analysts have scenarios of these
remote contingencies.
References
Cline, W.R. 1992. The Economics of Global Wanning.
Washington, DC: Institute for International Economics.
Environmental Protection Agency. 1983. Projecting
Future Sea Level Rise. Washington, DC: U.S.
Environmental Protection Agency.
Goemans,T. 1986. "The Sea Also Rises: The Ongoing
Dialogue of the Dutch with the Sea." In: Titus, J.G.
(ed.). Effects of Changes in Stratospheric Ozone and
Global Climate. Washington, DC: United Nations
Environment Programme and U.S. Environmental
Protection Agency.
Huybrechts, Ph., and J. Oerlemans. 1990. "Response
of the Antarctic Ice Sheet to Future Greenhouse
Wanning." Climate Dynamics 5:93-102.
Intergovernmental Panel on Climate Change. 1990.
The IPCC Science Assessment. Cambridge: Cam-
bridge University Press.
11
-------
Chapter 1
Meier, M. 1990. "Reduced Rise in Sea Level." Nature
343:115-6.
Morgan, M.G., and M. Henrion. 1990. Uncertainty: A
Guide to Dealing with Uncertainty in Quantitative Risk and
Policy Analysis. New York: Cambridge University Press.
National Research Council. 1983. Changing Climate.
Washington, DC: National Academy Press.
National Research Council, Marine Board. 1987.
Responding to Changes in Sea Level. Washington,
DC: National Academy Press.
National Research Council, Polar Research Board.
1985. Glaciers, Ice Sheets, and Sea Level: Effect of
a C02-Induced Climatic Change. Washington, DC:
Department of Energy.
Pearce, D.W., W.R. Cline, R.K. Pachauri, P. Vellinga, S.
Fankhauser, and R.S.J. Tol. "Greenhouse Damage and
the Benefits of Control." June 1994 draft of Chapter 3
of the 1995 IPCC Assessment, Work Group 3.
Seaver, D.A. 1978. Assessing Probabilities with
Multiple Individuals: Group Interaction vs. Mathe-
matical Aggregation. Tech. Report SSRI-78-3. Social
Science Research Institute. Los Angeles: University of
Southern California.
Titus, J.G. 1991. "Greenhouse Effect and Coastal
Wetland Policy: How Americans Could Abandon an
Area the Size of Massachusetts at Minimum Cost."
Environmental Management 15:1:39-58.
Wigley, T.M.L., and S.C.B Raper. 1992. "Implications
for Climate and Sea Level of Revised IPCC Emissions
Scenarios." Nature 357:293-8.
Winkler, R.L. 1971. "Probabilistic Prediction: Some
Experimental Results." Journal of the American Statis-
tical Association 66:675-85.
12
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CHAPTER 2
CONCENTRATIONS OF GREENHOUSE GASES
Anthropogenic Emissions
This analysis is based on the IPCC assumptions
for emissions and concentrations, as updated by Wigley
& Raper (1992). That analysis considers seven green-
house gases (CO2, CH4, N2O, CFC-11, CFC-12,
HCFC-22, and HFC-134a) as well as three gases with
important indirect effects on climate (SO2, carbon
monoxide, and volatile organic compounds). For all
gases other than CFC-11, CFC-12, and HCFC-22, we
characterize (anthropogenic) emission rates through the
year 2100 using lognormal distributions, with the geo-
metric means and standard deviations calculated from
the six emission scenarios from IPCC (1992). For the
two CFCs, we used the IPCC scenarios directly.1
Figure 2-1 compares our probability density func-
tion for CO2 emissions with that of Nordhaus & Yohe
(1983). For the year 2100, Nordhaus & Yohe have a
median of about 14 gigatons (Gt) per year of carbon and
a geometric mean of 19 Gt/yr, while both our median
and geometric means are 16 Gt/yr. Our 68 percent con-
fidence interval (o range) extends from 8 to 34 Gt/yr,
while the 68 percent limits for Nordhaus & Yohe are 7
and 31 Gt/yr. Our 1,5, and 10%-high scenarios are 88.5,
53.6, and 41.3 Gt/yr, respectively. Nordhaus & Yohe
found similar uncertainty. Although the highest 7 per-
cent of their simulations are reported at around 52 Gt/yr,
this estimate presumably reflects a truncation of the dis-
tribution; their 10th percentile is approximately 43 Gt/yr.
Edmonds et al. (1985) found even more uncertainty:
Their 5%-high scenario is 80 Gt/yr, roughly equal to
our 2%-high scenario; and their 25%-high scenario of
28 Gt/yr is almost as great as our 16% (o-high) limit.
Figure 2-2 compares our projections of CO2 emissions
with the six IPCC emissions scenarios for the years
1990 to 2100.
For simplicity, we assume that emissions for the
various gases are perfectly correlated. This assumption
allowed us to draw from only one distribution to
'For CFC-l 1 and CFC-12, three of the IPCC scenarios assume that
emissions decline to zero. As a result, the geometric standard devi-
ation cannot be calculated. Therefore, we follow the procedure
outlined above for the three nonzero scenarios and draw from this
distribution one-half of the time. The other half of the time we
draw from one of the three zero-tending emissions scenarios. For
HCFC-22, two of the IPCC scenarios assume that emissions
decline to zero. Here again we follow a similar procedure, draw-
ing from a distribution 2/3 of the time and from one of the two
zero-tending scenarios 1/3 of the time.
020-|
0.18-
016-
014-
3
a
006-
004-
002-
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52
Emissions (Gt C/year)
0 10 20 30 40 50 60 70 80 90 100
Fossil Fuel Emissions (Gt C/year)
Figure 2-1. Probability Density of CO2 Emissions in the
Year 2100. (a) Nordhaus & Yohe (1983); (b) this analysis.
calculate all emissions, rather than from one distribu-
tion for each gas. In effect, we assume that the IPCC
scenarios were already designed to convey the com-
bined uncertainty of future emission rates.2 Moreover,
because economic growth and policies on emissions
reduction are the primary factors driving changes in
emission rates, emissions are highly correlated.
2This assumption is not as unreasonable as it might seem at first
glance. IPCC Scenario E, for example, which has the highest CO2
emission rate, assumes less emissions of HCFCs and methane than
assumed by Scenario F. Thus, assuming perfect correlation among the
scenarios is unlikely to overstate total uncertainty of radiative forcing.
13
-------
Chapter 2
.0H
1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Year
Figure 2-2. IPCC (1992) CO2 Emissions Scenarios.
a=IS92a,...f=IS92f. The shaded area shows the emis-
sions rates bounded by our a-low and a-high scenarios.
The scenario (i represents the geometric mean from our
analysis.
The IPCC projections did not extend beyond
the year 2100. While we would have liked to consid-
er subsequent changes in emission rates, the available
analyses after that year are rather sparse.3 Therefore,
our simulations assume that emissions are constant
after the year 2100. Temperatures and sea level will
continue to change, however, because the processes
determining atmospheric concentrations, climate,
thermal expansion, and glacial contributions each
take several decades to reach equilibrium.
Concentrations and Radiative Forcing
Given the emission rates, we calculate concentra-
tions using the same models as IPCC (1992), as modi-
fied by Wigley & Raper. For greenhouse gases other
than CO2, we explicitly consider uncertainties in atmos-
pheric lifetimes (unlike IPCC and Wigley & Raper).
Table 2-1 lists the atmospheric lifetimes employed by
Wigley & Raper, along with the uncertainty as estimat-
ed by various studies. In each case, we treat the ratio of
the high to the low value as representing the ratio
between the a-high and a-low scenarios.
3Cline (1992b) discusses results from the Nordhaus model. He
reports that the model projects about a 25 percent increase in emis-
sions during the 22nd century, but this scenario is based on the
assumption that per capita economic growth is only 0.1 percent per
year. When Cline modifies the model to allow for a 1 percent annu-
al economic growth, he finds that emissions could approximately
double during that time period.
The fate of CO2 is generally modeled as being
more complex than the fates of other greenhouse
gases. Wigley & Raper, for example, assume that
there are four independent sinks, with lifetimes of
1.6, 30, 80, and 330 years, and that, even in equilibri-
um, about 13 percent of the CO2 emitted remains in
the atmosphere.4 After one hundred years, only 1/e
(37 percent) of the carbon emitted in a particular year
remains, which is consistent with an atmospheric life-
time of one hundred years (i.e., an annual decay rate
of 1 percent). But after ten years, 25 percent of the
carbon has been removed, implying a much more
rapid adjustment at first; while after two hundred
years, 27 percent still remains, implying a slower
adjustment. Thus, the term "lifetime" when applied
to CO2 cannot be viewed as a shorthand for the entire
atmospheric decay function, but only as an estimate
of how long it takes for various sinks to absorb all but
1/e of the carbon emitted in a given year.
Table 2-1 suggests that the lifetime for CO2 is
less certain than the lifetime for the other greenhouse
gases. Nevertheless, we omit any consideration of this
uncertainty and simply adopt the set of parameters used
by Wigley & Raper. The complexities that we would
have to address are beyond the scope of this analysis
for two reasons: (1) there are many ways to alter the
carbon cycle model to convey the fourfold uncertainty
regarding the "lifetime" of CO2, and none could be
readily justified5; and (2) changes in temperatures,
oceanic circulation, and ecosystems are likely to alter
the underlying carbon cycle in ways that are not ade-
quately captured by any carbon cycle model that could
be readily adapted for our purposes.
The uncertainty surrounding future radiative
forcing is less than the uncertainty surrounding emis-
sions, for two reasons. First, concentrations represent
the cumulative impact of all past emission rates; thus,
they respond with a long lag to emission rates. For
example, the impact of a doubling or a halving of
emission rates after ten years would increase or
decrease concentrations of CO2 by less than 10 per-
cent; thus, our uncertainty about what emissions will
Concentrations respond to emissions of a unit of CO2 as follows:
Mass(t) = 0.13 + 0.22e-W30 + o.26e-f«> + 0.29e-«° + 0.01e-« 6.
5The most obvious way would have been to assume fourfold
uncertainty in all of the lifetimes, but such a result would imply
fourfold uncertainty for the initial response (e.g., first decade)
when, in fact, the short-term uncertainty is much smaller. We con-
sidered arbitrarily assuming that the two slower reservoirs of 80
and 330 years have fourfold uncertainty, but Tom Wigley con-
vinced us that such an assumption would probably be worse than
ignoring carbon cycle uncertainty.
14
-------
Concentrations of Greenhouse Gases
TABLE 2-1
PROBABILITY DISTRIBUTIONS OF ATMOSPHERIC LIFETIMES
OF GREENHOUSE GASES USED IN THIS REPORT
(years)
Gas
N2O
CFC-11
CFC-12
HCFC-22
HFC-134a
CH4
CO,
Wigley Point
Estimate
132
55
116
15.8
15.6
11.8
100
Range
110-168
42-66
104-113
13.5-17.7
N.A.
10-14
50-200
Uncertainty (ahigh/olow)
in simulations3
Source
WMO 1.53
WMO 1.57
WMO 1.09
WMO 1.31
WMO 1.31b
Vaghjiani (1991) 1.4
IPCC(1990) 1.0
"Calculated as the ratio of the high to low estimate under "Range."
bLacking a published estimate of uncertainty, we assume that the uncertainty for HCFC-134a is the same as that of HCFC-22.
NOTE: In all cases other than CH4 and CO2, the simulations use the Wigley & Raper point estimate for the median and "Uncertainty"
for the geometric standard deviation. In the case of CH4, the Vaghjiani & Ravishankara estimates of 10 and 14 years are treated as a
limits; i.e., the Wigley & Raper value is not used. In the case of CO2, we ignore uncertainties in the adjustment period.
do in the next decade has little impact on our uncer-
tainty regarding concentrations ten years hence.
Second, radiative forcing is proportional to the loga-
rithm of CO2 concentration, a functional specification
that inherently reduces uncertainty.
Figure 2-3 illustrates our draft estimates of the
increase in radiative forcing by the years 2030 and 2100.
Our median estimate of 6.2 watts per square meter
(W/m2) by the year 2100 was similar to the IPCC (1992)
estimate for radiative forcing under Scenario A, but
much less than the 7.5 W/m2 estimated by IPCC (1990).
Expert Judgment
Because of the extensive review of the IPCC sce-
narios, we did not develop reviewer-based probability
distributions for this chapter in the manner undertaken
for the next three chapters. Nevertheless, we did make
some changes due to the reviewer comments.6
The draft, like the IPCC (1990) and (1992)
reports, ignored the negative effects of sulfates and
ozone depletion. Several reviewers told us to include
those offsetting effects and we have done so, based on
the Wigley & Raper (1992) sulfate scenarios. CFC
emissions cause a long-term depletion of stratospheric
ozone, a greenhouse gas; this delayed effect eventually
offsets the warming from CFC emissions.7
Figure 2-4 illustrates the resulting estimates of
radiative forcing. Part (a) compares our uncertainty
for radiative forcing with the IPCC scenarios.
Ignoring the uncertainty in atmospheric lifetimes, our
o limits for the year 2100 are 3.9 and 7.1 W/m2,
slightly above the range implied by IPCC (1992) sce-
narios C and E. Figure 2-4b shows that including the
uncertainty surrounding non-CO2 atmospheric life-
times expands this range to 3.6 to 7.5 W/m2 in the
unlikely event that high and low lifetimes correspond
with high and low emission rates. The figure also
shows that the sulfates reduce radiative forcing by
about 8 percent in the median scenario.
The results also include the biological feedback
suggested by Wigley & Raper (1992). The draft had
used the same version of the carbon cycle model as
used by IPCC (1992), which resulted in a CO2 con-
6Subsequent chapters present the model as originally presented by
the reviewers, followed by the reviewer changes. Because the
reviewer changes are straightforward, this chapter only presents
the postreview version of our assumptions.
7On the other hand, CO and VOC emissions can result in reduced
atmospheric OH, which could in turn slow the rate at which
methane leaves the atmosphere.
15
-------
Chapter 2
7
6
5
4
3
2--
!••
Year: 2030
Median = 2.42 W/m2
Mean = 2.46 W/m2
c = 0.32 W/m2
P(forcing>mean+ o) = 18%
P(forcmg
-------
Concentrations of Greenhouse Gases
William Cline suggests that the few available
studies imply that emissions could continue to rise
after the year 2100. Cline (1992a) reports that Alan
S. Manne believes that a linear extrapolation of emis-
sion rates is reasonable, which implies that the Manne
& Richel (1990) estimates of CO2 emissions would
increase by about 0.6 percent per year from 27 Gt/yr
in 2100 to 712 Gt/yr in 2275. Cline (1992b) shows
that the Nordhaus (1992) model implies that emis-
sions would increase from 20 Gt/yr in 2100 to more
than 50 Gt/yr by 2275.
Both of those estimates focus on median scenar-
ios; it seems less likely that the 88 Gt/yr implied by
our 1%-high scenario would also continue at such a
growth rate. Yet, to assume that high emission rates
are more likely to stabilize or decline than the median
scenario implies that there is less uncertainty sur-
rounding emissions for the year 2200 than for the year
2100. This counterintuitive assumption should be
used, in our view, only if there is a physical or eco-
nomic constraint in the available supply of fossil fuels.
For purposes of our high scenario, such a con-
straint does not seem likely. Edmonds et al. (1985)
estimate that there is 5000 to 18,000 Gt of coal that can
be mined at $85/ton. If 70 percent is emitted as carbon,
this estimate implies that our 1 %-high scenario could be
sustained for 40 to 150 years at a price of $85/ton.
Because we are focusing on the high end of the range of
possible emission rates, the high end of the available
reserves is more relevant than the low end. Given the
lower emission rates likely to prevail during the twenty-
first century, the high scenario could be sustained until
at least the year 2200. Prices greater than $85/ton,
moreover, would increase the available coal and could
also make oil shale economical. Finally, new discover-
ies and better technologies would increase the amount
of fuels available at a given price. Therefore, we con-
clude that there is no physical constraint rendering it
impossible to sustain the high scenario for the period of
this analysis.
In light of the lack of knowledge regarding future
emission rates, it still seems most reasonable to keep
emissions fixed at the year 2100 level. Arguments can
be made for increasing or decreasing the median sce-
nario and for expanding or narrowing the range of
uncertainty for subsequent years. The assumption of
fixed emissions after the year 2100 is easier to under-
stand, allows us to avoid manipulating the IPCC (1992)
emissions scenarios, and at least hi the narrow sense
enables us to avoid additional speculation.8
Final Results
Table 2-2 illustrates our results for the increase in
radiative forcing for the period 1990 to 2100. Largely
because we included sulfates and the biological CO2
feedback, our final estimates of radiative forcing are
lower than reflected in previous IPCC assessments, as
well as our draft report. IPCC's (1992) scenario A was
about 6.2 W/m2 and IPCC's (1990) business-as-usual
scenario was 7.5 W/m2, whereas our median is only
4.9 W/m2.9 About 1 percent of our simulations have
higher forcing than the 8.5 W/m2 that IPCC (1992) esti-
mated for Scenario E,10 while about 20 percent have a
forcing less than the 3.5 W/m2 projected for Scenario C.
The table also shows our estimates for the year by which
radiative forcing will increase by 4.4 W/m2—the equiva-
lent of a CO2 doubling—over the 1990 level; the median
estimate is the year 2089, with a 10 percent chance that
the doubling equivalent will occur before 2068.
Our scenarios for radiative forcing are broadly
consistent with recent assessments. Our mean esti-
mate of radiative forcing (5 W/m2) is only slightly less
than the forcing estimate reported by Wigley &
Raper (1992). Although IPCC (1992) had a higher
forcing, the recent IPCC (1994) report on radiative
forcing has adopted scenarios that are much closer to
the Wigley & Raper estimates. Most importantly, the
IPCC has lowered the projected CO2 concentration
from 800 ppm to about 730 ppm by the year 2100.
See also Wigley (1993). Although IPCC (1994) did
not endorse a specific estimate of the average global
forcing effect of sulfates, it did acknowledge that sul-
fates have been offsetting global warming.11
We also show a selected set of 61 scenarios,
which we follow throughout the course of this report.
8In the broader and more realistic sense of the word, to assume no
change in a changing world is highly speculative. Nevertheless, the
convention of deeming such an assumption as not speculative is well
established. See e.g., IPCC (1990) (assuming that the contribution of
groundwater and Antarctic ice sheet changes to sea level will be zero
because the process is too difficult to model).
9Even though our analysis is based on Wigley & Raper (1992), our
median is less than their estimate for Scenario A (5.3 W/m2),
because Scenario A's emissions are greater than the geometric
mean of the six emission scenarios.
10About 20 percent of our simulations, however, have more forcing
than the 6.6 W/m2 estimated by Wigley & Raper for Scenario E.
11 As this report went to press, the IPCC was considering whether
and how the effect of sulfates should be incorporated into global
temperature projections for the comprehensive assessment due to
be published at the end of 1995.
17
-------
Chapter 2
TABLE 2-2
CUMULATIVE PROBABILITY DISTRIBUTION FOR
THE CHANGE IN CARBON DIOXIDE AND RADIATIVE FORCING
Year by Which
Cumulative
Probability (%)
O.lb
0.5b
1.0b
2.5b
5.0b
10
Forcing 1990-2100
(W/m2)
1.3
1.8
2.0
2.3
2.6
3.0
C02 by 2100
(ppmv)
405
427
439
462
482
511
CO2 Exceeds
600 ppmv
>2200
. >2200
>2200
>2200
>2200
>2200
Doubling Equivalent
for all Gasesa
>2200
>2200
>2200
>2200
>2200
>2200
20
30
40
50
60
70
80
3.6
4.0
4.4
4.9
5.4
5.8
6.4
554
591
633
680
729
792
878
2131
2103
2088
2078
2070
2064
2059
2151
2117
2099
2089
2081
2077
2073
90
95
97.5
99
99.5b
99.9b
7.2
7.8
8.2
8.7
9.0
9.4
1047
1204
1363
1614
1775
2364
2052
2048
2045
2042
2040
2037
2068
2066
2064
2062
2061
2059
Mean 5.0 738 N.A. N.A.
a 1.6 242 N.A. N.A.
N.A. = Not applicable.
a"Doubling equivalent" refers to the year by which radiative forcing increases by 4.4 W/m2 over 1990 levels, which is the radiative forcing
from a doubling of CO2.
These estimates are included for diagnosis purposes only. Because the focus of the analysis was on the risk of sea level rise rather than sea
level drop, less effort has gone into characterizing the lower end of the distribution.
Figure 2-5 shows a "spaghetti diagram" of radiative
forcing for these scenarios for the years 1990 to
2300. We selected these scenarios by ranking all the
scenarios according to the amount of sea level rise
for the year 2200. Figure 2-5 and all other spaghetti
diagrams in this report illustrate (from highest to
lowest) the following simulations: 1,2,5,10, 50,100,
200, 400, 600...9400, 9600, 9800, 9901, 9951, 9991,
9996, 9999, 10000. Thus, the top and bottom seven
simulations should be viewed as extreme (1 percent)
scenarios; otherwise, the simulations shown represent
equal levels of probability. We show a disproportion-
ate amount of extreme scenarios because (a) if unin-
tended model calculations are taking place, they are
most likely to occur and/or become noticeable in the
extreme scenarios; (b) risk assessments inherently
must focus on extreme scenarios; and (c) as a practical
matter, extreme scenarios tend to be more widely
spaced than the more typical scenarios, which makes
them more legible.
18
-------
Concentrations of Greenhouse Gases
1990
2300
Figure 2-5. Projections of Greenhouse Forcing:
Selected Simulations. This and all other spaghetti dia-
grams illustrate simulations 1,2,5, 10,20,50,100,200,
400, 600,..., 9400, 9600, 9800, 9901, 9951, 9981, 9991,
9996, 9999, 10000, where 1 and 10000 represent the
simulations with the highest and lowest estimates of sea
level rise for the year 2200.
The uncertainty in radiative forcing is fairly small
for the next 50 years, with virtually all scenarios show-
ing an increase between 2 and 3 W/m2. After the year
2050, however, IPCC scenarios C and D assume that
CO2 emissions decline or remain constant, while other
scenarios assume a continuing increase. As a result, the
range increases to about 2.5 to 8.0 W/m2 by 2100 and
2.6 to 13 W/m2 by 2200. The effect of Scenario C's
declining emissions can be seen in the bottom two
curves, which decline after around 2070. Even though
emissions are assumed to remain constant after the
year 2100, radiative forcing continues to increase
during the following two centuries for all but a
few of the scenarios, due to the long atmospheric
lifetime of CO?.
References
Cline,W.R. 1992a. The Economics of Global Wanning.
Washington, DC: Institute for International Economics.
Cline, W.R. 1992b. "Optimal Carbon Emissions over
Time: Experiments with the Nordhaus DICE Model."
(Unpublished Manuscript). Washington, DC: Institute
for International Economics.
Edmonds, J.A., J.M. Gardner, R.H. Gardner, and A.
Brenkert. 1985. Uncertainty in Future Global Energy
Use and Fossil Fuel CO2 Emissions: 1975 to 2075.
Washington, DC: Carbon Dioxide Research Division,
Department of Energy (report TR036).
Intergovernmental Panel on Climate Change. 1994.
Radiative Forcing of Climate Change. Report to the
IPCC from the Scientific Working Group. Cambridge
and New York: Cambridge University Press.
Intergovernmental Panel on Climate Change. 1992.
Climate Change 1992: The Supplementary Report to
the IPCC Scientific Assessment. Cambridge and New
York: Cambridge University Press.
Intergovernmental Panel on Climate Change. 1990.
Climate Change: The IPCC Scientific Assessment.
Cambridge and New York: Cambridge University Press.
Manne, A.S., and R.G. Richels. 1991. "Global CO2
Emissions Reductions: The Impacts of Rising Energy
Costs." The Energy Journal 12:1:88-107.
Nordhaus, W,D. 1992. "Rolling the DICE: An Optimal
Transition Path for Controlling Greenhouse Gases." (Un-
published Mimeograph). New Haven: Yale University.
Nordhaus, W.D., and G.W.Yohe. 1983. "Future Carbon
Dioxide Emissions from Fossil Fuels." In: Nierenberg
et al. (eds). Changing Climate 87-153. Washington,
DC: National Academy Press.
Vaghjiani, G.L., and A.R. Ravishankara. 1991. "New
Measurement of the Rate Coefficient for the Reaction
of OH with methane." Nature 350:406-9.
Wigley, T.M.L. 1993. "Balancing the Carbon Budget.
Implications for Projections of Futire Carbon Dioxide
Concentration Changes." Tellus 45B:409-25.
Wigley, T.M.L., and S.C.B. Raper. 1992. "Implications
for Climate and Sea Level of Revised IPCC Emissions
Scenarios." Nature 357:293-300.
World Meteorological Organization. 1992. Scientific
Assessment of Ozone Depletion: 1991. Global Ozone
Research and Monitoring Project. Geneva: World
Meteorological Organization.
19
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Chapter 2
20
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CHAPTER 3
CLIMATE CHANGE
Given the concentrations of greenhouse gases and
resulting radiative forcings during particular years, pro-
jections of sea level rise require two types of climatic
information: (1) estimates of the downward penetration
of heat for calculating the thermal expansion of ocean
water; and (2) estimates of polar air temperatures, water
temperatures, sea ice, and precipitation changes for cal-
culating the glacial contribution to sea level.1
Following the general convention, we use a
one-dimensional ocean model to simultaneously
calculate transient air temperatures and thermal
expansion of ocean water. We then employ sub-
sidiary equations to estimate changes in sea ice
and polar temperatures. After summarizing the
results from our initial draft assumptions, we pre-
sent the assumptions suggested by the expert
reviewers and the resulting estimates. Because a
different set of reviewers commented on our equa-
tions for polar precipitation, we present those
assumptions and results separately at the end of
this chapter.
PART A: TEMPERATURE AND
THERMAL EXPANSION
The Use of 1-D Ocean Models to
Estimate Global Temperature and
Thermal Expansion
Although three-dimensional models are generally
used to estimate equilibrium responses to greenhouse
gases, their cost is too great for undertaking analyses
that require many runs of a given model. Hoffert et al.
(1980) first proposed a one-dimensional upwelling-
diffusion model for analyzing global warming during
specific years; numerous studies have employed that
model and its descendants. The most widely used of
these descendants is the model by Wigley & Raper
(1987, 1992), which has been used to produce the
official temperature and sea level scenarios of the Liter-
governmental Panel on Climate Change. See e.g., IPCC
(1990, 1992). To be consistent with IPCC, we used the
Wigley & Raper model as well.2 The model requires us
to supply coefficients for (1) the equilibrium average
surface warming3 for a CO2 doubling (AT2X); (2) verti-
cal mixing/diffusion (k); (3) upwelling velocity (w); and
(4) the ratio of the warming of newly formed (polar)
bottom water to warming of surface water (71).
Like IPCC and Wigley & Raper, we ran the
model using historic concentrations of greenhouse
gases from a representative preindustrial starting point
(i.e., 1765) to the present. This procedure ensures that
when we project the model into the future, the resulting
estimates of thermal expansion and warmer tempera-
tures reflect the delayed impact of past emissions as
well as the impact of future emissions. While a single
historic simulation might be preferable,4 we follow the
convention of IPCC and Wigley & Raper by simulating
the model over the historic data for each of our simula-
tions. Figure 3-1 compares actual temperatures with
the projected temperatures using the Wigley & Raper
model under various scenarios. The model projects a
flattening out of the warming over the years 1955-70
because of the negative forcings associated with sul-
fates and CFC-related ozone depletion (see Chapter 2).
Unlike the original version by Hoffert et al.
(1980), this model treats the two hemispheres sepa-
1 Ideally, we would also like to know whether the precipitation in
polar areas is in the form of rain or snow. Because the models we
use for Greenland and Antarctica assume that all precipitation is
snowfall, this chapter does not address that question.
2Tom Wigley and Sarah Raper helped us adapt their model for our
purposes.
3Since at least 1979, studies of the greenhouse effect have focused
on the equilibrium impacts of a CO2 doubling, that is, an estimate
of how much the Earth's average temperature would rise if the con-
centration of atmospheric CO2 doubled and then remained at the
higher level indefinitely. See e.g., NAS (1979).
4For the reader familiar with one-dimensional modeling, we note that
this procedure may be analytically and computationally inferior to
simply running the historical simulation to 1990 once and starting
each of the 10,000 simulations at that point For example, if we
assume that temperature sensitivity is 4.5°C, the model estimates
much more historical warming than what actually occurred, which in
turn implies a greater temperature difference between the mixed layer
and the thermocline than actually exists. As a result, the model will
overstate the downward penetration of heat and thermal expansion
that ought to result from future greenhouse forcing. Conversely, for
low values of AT2x> the model understates thermal expansion.
A decline in upwelling also reduces the temperature difference
between the surface and the thermocline. As a result, the net effect of
simulating history each time is functionally similar to imposing a cor-
relation between low values of AT2X and declines in upwelling. But
see Chapter 9, Notes 6 and 7.
21
-------
Chapter 3
BAU
1850 1870 1890 1910 1930 1950 1970 1990 2010 2030 2050 2070 2090
Year
Figure 3-1. Comparison of Historic Temperatures
and Projections of the Wigley & Raper Model.
Curves (i) and (ii) use the medium assumptions and
IPCC scenario IS92a emissions of greenhouse gases;
(ii) also includes the offsetting forcings from sulfates
and CFC-induced ozone depletion. Curves (iii) and
(iv) are the same as (ii), except for AT2X values of 1.5
and 4.5°C. Curve BAU is the same as (i), except that
it uses the IPCC (1990) "Business-as-Usual" emis-
sion scenario. The jagged curve that stops in the
1990s represents historic temperatures.
rately. Thus, it would be possible to supply the model
with Northern and Southern Hemisphere values for k,
7t, and w. Nevertheless, we follow the convention of
previous studies and run the ocean model based on
the assumption that these parameters have the same
values for both hemispheres.5
Previous assessments of sea level rise have
assumed that the values of these parameters are fixed. In
reality, however, the three-dimensional processes that n,
k, and w approximate are all likely to change. The
importance of allowing for such changes depends on the
purpose to which the model is likely to be put, e.g.,
whether the principal goal is to project transient surface
temperatures or sea level. Regardless of the values of jt,
k, and w, the transient air temperature will eventually
approach AT7X if CC«2 is held fixed at twice its pre-
industrial concentration; those parameters merely
determine how rapidly temperatures adjust to their
equilibrium. IPCC (1990) showed that temperature is
not extremely sensitive to these parameters, especially
after the first few decades of a model run.
Sea level rise, by contrast, is very sensitive to these
parameters, particularly in the long run. For a given rise
in global surface temperatures, the oceanic expansion
depends on the resulting rise in water temperatures at
every depth. The upper (mixed) layer warms almost as
much as the Earth's average surface temperature, but
the bottom water only warms by n times that amount.
Intermediate waters initially warm less than the bottom
water, but eventually warm more than the bottom and
less than the surface.6
Figure 3-2 illustrates the sensitivities of the Wigley
& Raper model to a CO2 doubling, holding k and w
constant at the median values described below, for
7t=0, 0.2, and 1.0, and AT2X=2.5°C.7 Surface tem-
perature change is about 18 percent less for 7C=1 than
for 7t=0 after the first 100 years, and 16 percent less
after 500 years. Thermal expansion, however, is 40 per-
cent greater after 100 years, 90 percent greater after
200 years, and over three times as great after 500 years.
This difference occurs because even after 500 years, the
deep ocean (e.g., depth of 2 km) warms only 0.05°C for
7t=0, while for 7t=l it warms by approximately 1°C.
During the first century, most of the thermal expansion
takes place in the mixed layer and upper thermocline,
which warm by about the same amount for Jt=0 and
Jt=l. During later centuries, however, the majority of
expansion comes from the thermocline and deep ocean.
Even though both the warming and the coefficient of
expansion are much greater for the mixed layer than for
the thermocline and deep ocean, there is far more water
to expand in those lower layers; hence they ultimately
contribute the majority of thermal expansion.
Figure 3-2 also illustrates the impact of an instan-
taneous 50 percent decline in deepwater formation (w)
with no change in greenhouse gas concentrations (the
relevance of which is discussed below).8 Such a change
in ocean circulation would warm the thermocline
(Figure 3-2b) substantially. Assuming that 7C=0.2, a
50 percent decline in deepwater formation would
5We occasionally refer to hemisphere-specific values for these para-
meters as part of the conceptual justification for the global values that
we use, but all model runs use the same values for both hemispheres.
6This model artifact probably does not correspond to reality. See
Figure 3-5 and accompanying text, infra.
7The significance of these parameter values is described below. We
remind the reader that the assumption 7t=l implies that the water that
sinks toward the bottom in polar regions warms as much as the glob-
al average warming; 71=0 implies that the water sinks at the same
temperatures as today. For a given amount of heat, warmer sinking
water means that the water remaining at the surface is colder.
8The paramater literally represents the average rate of upwelling
throughout all portions of the ocean other than those where down-
welling occurs. Because the amount of deepwater formation is
proportional to the upwelling velocity, we mean both "deepwater
formation" and "upwelling velocity" when referring to w.
22
-------
Climate Change
a
30 -i
g 10-
Surface Temperature Change
n=0.0
n=02
lt=0 2, Aw=-50%
0 100 200 300 400 500 600 700
Years
b Thermocline (500 m depth) Temperature Change
0 100 200 300 400 500 600 700
Yean
C Deep Ocean (2000 m depth) Temperature Change
Thermal Expansion
0 100 200 300 400 500 600 700
lt=02, Aw=-50%
lt=0 2, Aw=-50%
lt=0.2
)t=00
0 100 200 300 400 500 600 700
Years
Figure 3-2. Impact of CO2 Doubling or 50 Percent Reduction in Deepwater Formation: Evolution Over Time.
Impacts on (a) surface temperature; (b) thermocline temperature at 520 m depth; (c) deep ocean temperature at 2020
m depth; and (d) ocean expansion, resulting from one-time doubling of CC>2 or halving of deepwater formation, with
AT2x=2.5°C, as projected by the Wigley & Raper model. The first three curves assume a CO2 doubling with climate
sensitivity of 2.5°C, with n equal to (i) 0, (ii) 0.2, and (iii) 1.0. The fourth curve (iv) holds greenhouse gases con-
stant but cuts the upwelling velocity from 4 m/yr to 2 m/yr, with 7t=0.2.
raise sea level about as much as a CO2 doubling
(Figure 3-2d).
When using an upwelling/diffusion model to
estimate thermal expansion, the sinking water ampli-
fication parameter n serves two purposes, which tend
to suggest vastly different values. The direct function
of the parameter is to indicate the rise in the temper-
ature of newly formed deep water as a fraction of the
warming of globally averaged surface temperature.
For a given value of the upwelling velocity parameter
w, however, n represents the equilibrium ratio of the
warming of all deep water to the warming of the sur-
face temperatures. Because the Earth will not warm
enough to measure n for several decades, this para-
meter must be picked based on theory and judgment,
not measurement. This judgment would be substan-
tially helped, however, if three-dimensional modeling
studies would report the temporal evolution of n—
preferably for both hemispheres.
23
-------
Chapter 3
Previous assessments have generally picked w
and k based on direct measurements and the fact that
the existing temperature-depth profile is determined by
a given ratio of k/w. By contrast, n cannot be measured
directly; thus, it is picked so that the one-dimensional
model has desirable properties. A value of 7t=l allows
the model to assume that, in equilibrium, the shape of
the temperature-depth profile does not change; this
assumption is a reasonable default because no one
knows whether the difference between temperatures of
deep and surface water will increase or decrease. A
value of 7i=0 allows the model to reflect the fact that
most deep water is formed by the creation of sea ice,
which will always occur at the same temperature,
unless sea ice changes substantially.9
The initial simulations we distributed to the
reviewers were split evenly between runs in which we
employed (a) fixed values of the three parameters and
(b) those in which we allowed w to change in response
to global temperatures.
Fixed Parameters (OM1)
One can pick n based on either (1) a reasonable
assessment of the warming of polar sinking water or (2) on
desired equilibrium properties of the model. Most deep
water is formed by the freezing of surface sea water:
The salt is separated from the ice, leaving a brine that is
denser than surrounding sea water due to its higher
salinity and perhaps its colder temperature as well.
Because global warming will not change the tempera-
ture at which saltwater freezes, the deep water that is
formed would logically be no warmer than it is today,
implying that 7C=0. The assumption of 7t=l is more rea-
sonable for areas where deep (or intermediate) water is
formed as a result of evaporation-driven salinity
increases, as in the North Atlantic and Mediterranean
regions. If one assumes that 7ESIf=0 for the 80 percent
of bottom water formed through salt rejection in the
Antarctic, but that 71^=1 for the 20 percent that is
formed from evaporation in the Northern Hemisphere,
the average global value of n is 0.2.
One consequence of using a low value of n in
thermal expansion calculations is that most of the
ocean is assumed to warm much less than the surface,
even in equilibrium. As a result, total thermal expan-
sion estimates are lower than would be the case if all
of the ocean warmed uniformly, especially in the long
run.10 In the absence of a strong theoretical explana-
tion for how the shape of the temperature profile
might change, a reasonable default assumption might
be to assume no change. Thus, for example, IPCC
(1990) assumes that 7t=l; as Figure 3-3 shows, the
temperature-depth profile flattens if 71=0, while largely
retaining its current shape if 7t=l.
A possible problem with ;c=l is that such an
assumption, at least superficially, implies that the
newly formed polar bottom water warms 1:1 with the
global average surface temperature. Many researchers
find this assumption unlikely because of the role of sea
ice; see e.g., Wigley & Raper (1991). Others believe
that, in the long run, the downwelling water could
warm as much (and perhaps more) than the global
average warming, but that initially the warming will be
less because Antarctic warming will lag behind global
warming. As a result, the initial value of nSH is close
to 0, but it gradually increases to (and perhaps even
beyond) a value of l.O.11
Schlesinger & Jiang (1991), for example, ran
their coupled ocean/atmosphere model for twenty
years, after which time polar ocean temperatures are
projected to warm between 0.004 and 0.57 times the
global average warming, with a depth-averaged value
of 0.14. They suggested that with a longer run, the
depth-averaged value would probably be closer to 0.4;
accordingly, they suggested that it would be appropri-
ate for analyses employing simpler models to assume
that 7t=0.4.
The analogy between three-dimensional and one-
dimensional models is less than perfect. Most impor-
tantly, 7t does not literally represent polar warming; a
1-D model does not even have latitude. Instead, n rep-
resents the amount of additional heat conveyed by
downwelling to the deep ocean, expressed as a fraction
of the amount of heat that would be conveyed if green-
house forcing warmed the downwelling water by as
much as it warms the average surface temperature.
Therefore, 7t=ATpolai/ATglobal only if AT^ is aver-
aged only over the regions and seasons in which
downwelling takes place. Because the Schlesinger &
Jiang calculations do not refer directly to the warming
of the downwelling region, their suggestion that 7t=0.4
is somewhat ad hoc, but it is probably as reasonable as
other procedures for picking the value of 7t.
9The relationship between TC and seaice formation is described
further, below.
10ln the very long run, it is even theoretically possible for the bot-
tom water to warm more than the surface—especially if bottom-
water creation due to seaice formation were to decline.
11 See Expert Judgment, infra for a discussion of the wide diver-
gence of opinion on the value of rt.
24
-------
Climate Change
-2000-
-3000-
-4000
n=0
-1000-
e,
S -2000
-3000-
00 25 50 75 10.0 125 150 175 200
Temperature (°C)
7t=0.2
t=750
00 25 5.0 75 100 125 15.0 175 200
Temperature (°C)
-1000 -
|j_ -2000 -
&
-3000 -
-4000
Tt=l
-1000 -
TC=0
Step function w
00
75 100 125 150
Temperature (°C)
17 5 20 0
75 100 12.5
Temperature <°C)
15.0
Figure 3-3. Impact of CO2 Doubling or 50 Percent Reduction in Deepwater Formation: Depth-Temperature
Profiles. These profiles correspond to Figure 3-2; i.e., instantaneous CO2 doubling in 1990 with (a) Ji=0, (b) 71=0.2,
and (c) 71=1.0; and (d) no change in CO2 but 50 percent reduction in upwelling velocity. Each box shows profiles
for years 0, 250, 350, and 750.
An alternative approach is to pick the value of n
that comes closest to duplicating temperature or ther-
mal expansion estimates from a 3-D coupled ocean
model. As we discuss below, for example, Figure 3-6
shows that a value of ji=0.6 approximates the 25 cm of
thermal expansion projected over a 95-year period by
the GFDL model; a value of 0.13 approximates the
Southern Hemisphere surface warming.
Allowing w to Vary (OM2)12
As long as the three parameters are fixed, the
value of n determines the amount of heat reaching the
deep ocean. Thus, other than by sheer coincidence, it is
impossible to pick a specific value of n that both (1) con-
forms to the narrow definition Tr^AT™^ sinking /ATglobal
and (2) functionally represents a desired assumption
regarding the long-term evolution of ATsurface - ATdeep.
The approach, endorsed by Wigley & Raper and
Schlesinger & Jiang (1991) focuses on the former—
which is at least arguably "measurable" from 3-D
transient experiments—and accepts whatever result is
12We remind the reader that by "fixed w," we mean that w=w0
throughout a given simulation, not that all simulations use the same
value for w.
25
-------
Chapter 3
implied regarding equilibrium deep ocean tempera-
tures (and thus thermal expansion). The approach
followed by IPCC (1990), by contrast, (a) constrains
the calculations to a reasonable default assumption
that in the long run the middle and deep oceans warm
as much as the surface, and (b) accepts the implied
assumption that the bottomwater-formation tempera-
ture rises by ATglobal, even though the freezing point
of water stays relatively constant.13
If one allows w to vary over time, by contrast,
one can assume that sea water will continue to freeze
at the same temperature, without having to assume
that, in equilibrium, there will be a large increase in
the temperature difference between bottom and surface
waters; by contrast, when 7t=0 and w is fixed, this
assumption is unavoidable. Thus, our second approach
is to assume that in the Southern Hemisphere, Jt=0, but
that WSH declines in proportion to the decline in annual
Antarctic seaice formation that accompanies warmer
temperatures. Because Northern Hemisphere deep water
is generally not formed by freezing, we assume that
%H=1. This case also assumes that WNH declines,
albeit for a different reason: increased precipitation
prevents salinity in the Gulf Stream from rising as
much as today, thereby reducing downwelling in the
North Atlantic. See Manabe & Stouffer (1993).
Figure 3-4 compares the (OM2) case where
K=0.2 and w declines geometrically by 15 percent per
degree Celsius (C) of surface warming, with three
OM1 cases (fixed w) where rr. is set to 0, 0.2, and 1.0.
The figure illustrates warming at (a) the surface and
depths of (b) 520 m and (c) 2000 m, as well as (d)
thermal expansion. Radiative forcing is based on the
IPCC (1990) "Business-as-Usual" scenario through
the year 2100, and constant thereafter, with
AT2X=2.5. For the first century, the surface tempera-
ture of the OM2 (variable-w) case is within 1 percent
of the OM1 (rc=l) case, while thermal expansion is
somewhat less. During subsequent centuries, thermal
expansion diverges markedly.
The rough equivalence in thermal expansion
estimates is largely coincidence. Given the similarity of
surface temperatures, both cases have about the same
amount of expansion in the mixed layer. In the variable
w case, however, the thermocline (Figure 3-4b) warms
13At prevailing salinities, the freezing point is typically about —1.9°C.
Although lower salinity would raise the freezing point somewhat, it
cannot warm by more than 1.9°C, and even that would require an
unrealistic 99.9% decline in ocean salinity. Thus, for any significant
value of AT, AT^^ smkmg will be well below AT, unless the deep
water is formed by a process other than seaice creation.
more rapidly due to the declining rate at which colder
bottom water upwells to this depth. The deeper layers
of the ocean warm much more rapidly in the ?t=1.0
case because, by definition, the very bottom warms as
much as the surface. With w=4 m/yr, a depth 200 m
above the bottom receives water that downwelled
fifty years previously. Warming at this depth by the
year 2100 is equal to the 2050 surface warming,
ignoring any diffusion from the surface (which is
negligible at this depth). Thus, the cases differ in that
the declining w allows more downward diffusion over
time, while the n=l allows for a gradual warming of
the deep ocean by directly replacing the coldest
remaining layer in each time step with water that has
warmed as much as the surface.
The variable-w case is more realistic than n=l in
many ways. As Figure 3-5 shows, the one-dimensional
model with n=l yields an odd depth pattern of temper-
ature changes: Not only do deep layers warm more than
the surface and intermediate layers (Figure 3-5g), but a
fairly substantial inversion also results (Figure 3-5c).
This odd result stems from the fact that the model
assumes that all downwelling conveys water to the
very bottom (as opposed to distributing this water to
various layers). By 2100, the bottom (4000 m) reaches
a temperature of 2.8°C, compared with the 1.2°C that
prevails at 3000 m; by 2500, the bottom reaches 5.0°C,
compared with 3.1 °C at 2000 m. By contrast, in the vari-
able-w case, the inversion is trivial even after 500 years:
1.36°C at 4000 m and 1.33°C at 3000 m. This anomaly
should not lead one to automatically disregard the rel-
atively high thermal expansion estimates of Jt=l; the
inversion probably diminishes the thermal expansion
estimates. A more sophisticated 1-D model might
avoid the inversion by distributing the additional heat
due to downwelling at various depths. Because these
warmer depths are accompanied by higher expansion
coefficients, the resulting sea level rise would be some-
what greater.
Nevertheless, the variable-w assumption creates
a number of risks. Like setting nSH at zero in the
fixed-w case, allowing w to decrease may satisfy a
narrow criteria: the parameter in the one-dimensional
model corresponds to reasonable expectations of how
the 3-D variable would change. But it may do so at the
expense of causing unintended dynamic model prop-
erties. Furthermore, intended reasonable "default"
properties may not in reality be correct, or they may be
overwhelmed by other changes that we cannot foresee.
For example, a decrease in seaice formation would
seem to imply less bottom water and hence a decline in
w. Yet the 1-D models were designed and calibrated to
26
-------
Climate Change
3-
2-
variable w
n=l
1950 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500
Year
b
4 n
3 -
53
2050 2100 2150 2200 2250 2300 2350 2400 2450 2500
Year
2.5-,
20-
1 0-
0.5-
1950 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500
Year
200-
175
150
125
100
75
.
25-
1950 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500
Year
Figure 3-4. Impact of IPCC Business-as-Usual Scenario Over Time. Impacts on (a) surface temperature; (b) thermo-
cline temperature at 520 m depth; (c) deep ocean temperature at 2020 m depth; and (d) ocean expansion, assuming that
greenhouse gas concentrations increase through 2100 as projected by the IPCC (1990) Business-as-usual scenario, and
remain constant thereafter. The first three graphs assume that climate sensitivity is 2.5 °C for a CO2 doubling, and that K
equals (a) 0, (b) 0.2, and (c) 1.0; (d) also assumes that 7t=0.2, but that upwelling velocity (w) declines 15 percent per
degree (C) of surface warming. In all cases, the initial 1990 conditions are derived by running the model from 1765 to
1990 using historic concentrations.
deal with the way the ocean circulates today; there is no
guarantee that either (1) Antarctic bottomwater forma-
tion will change in proportion with the reduction in
seaice formation or (2) that a decline in bottomwater
formation will change thermocline temperatures in the
same fashion as a 1-D model would suggest.
Although these uncertainties caution us against tak-
ing any of the results too seriously, they do not necessarily
imply that the resulting thermal expansion estimates are
less reliable than for the (OM1) case where w=w0 and
71=0.2 (7tSH=0). For example, if sea ice declines and deep-
water formation does not decline or declines less than pro-
portionately, it seems reasonable to assume that the down-
welling water must be significantly warmer, which would
imply a relatively high value for n. Presumably in this
case, deep water formed by processes other than salt
rejection must (at least partly) offset the reduction in
bottom water formed by sea ice, and such downwelling
generally would take place at a higher temperature.
27
-------
Chapter 3
-4000
10 15 20
Temperature (°C)
-4000
10 15 20
Temperature (°C)
25
-1000 -
-2000 -
-3000 -
-4000
71=1
d
o-\
-1000-
e,
•5 -2000-
I
10 15
Temperature (°C)
20
10 15
Temperature (°C)
Figure 3-5. Impact of IPCC Business-as-Usual Scenario on Temperature-Depth Profile. These profiles corre-
spond to Figure 3-4; i.e., IPCC (1990) increases in greenhouse gas concentrations with (a) 71=0, (b) n=0.2, (c) 7C=1.0;
and (d) 71=0.2 along with upwelling velocity declining 10 percent per degree (C) of surface warming. Absolute tem-
continued on page 29
One theory for expecting downwelling not to
decline as sea ice declines is that thermohaline circula-
tion is driven by equatorial upwelling, as well as polar
downwelling. To this extent, elimination of seaice
formation need not lead to a proportional reduction in
the forces that cause water to downwell. Moreover,
increased evaporation in the tropics might further
increase the tropical force contributing to down-
welling. Because the circumpolar ocean is 3°C warmer
than the in situ freezing point of sea water and may be
wanner in the future, the replacement downwelling
water would presumably be at least 3°C warmer than the
bottomwater formed by sea ice. Thus, if the assumption
that w declines in proportion with the decline in sea ice
is an overestimate of the actual decline in w, we also are
underestimating 7tSH by assuming it to be zero—it could
be much higher, implying that TC could be closer to one.
How should we pick the rate at which w changes?
Just as 71 can be picked either to satisfy expected changes
in polar water temperatures or to satisfy desirable long-
term dynamic properties, so can w be picked based
either on estimates of circulation changes or to satisfy
dynamic properties. In the case of w, the literature
28
-------
Climate Change
-1000-
I
f -2000 H
V
Q
-3000-
-4000
TC=0
year 2100-year 1990
year 2500-year 1990
7C=0.2
year 2100-year 1990
year 2500-year 1990
00 05 10 1.5
20 2.5
AT C
30 35 4.0 45
00 05 10
20 25 3,0
AT(°C)
35 40 4.5
-1000-
-2000-
TC=1
year 2100-year 1990
year 2500-year 1990
00 05 10 1.5 20 25 30 35 40 4.5 50
AT (°C)
year 2100-year 1990
year 2500-year 1990
peratures are shown for the years 1765, 1990, 2100, and 2500. Note that the inversions in box c for 1990 and 2100
are unreported results from IPCC (1990). The post-1990 changes in temperatures corresponding to boxes a-d are
shown in boxes e-h, respectively, for the years 2100 and 2500.
offers both (a) estimates of how seaice formation might
respond and (b) 3-D model estimates of total changes in
circulation. The most obvious dynamic property to
watch is the ability of the model to duplicate thermal
expansion estimates from 3-D models.
Figure 3-6a compares projected thermal expan-
sion over a 95-year period using the 1-D model for
various sensitivities of n and w, with the results from
the Geophysical Fluid Dynamics Laboratory (GFDL)
model reported by Manabe et al. (1991). For a value
of Jt=0, w must decline by slightly more than 25 per-
cent per degree (C) to duplicate the 25 cm of thermal
expansion; if 7t=0.2, w declines 15%/°C; if Jt=0.4, w
declines about 5%/°C; and if 71=0.6, a fixed w slightly
overpredicts the GFDL estimate of thermal expansion.
Figure 3-6b shows the surface wanning for the same
combinations of TC and w. All of the combinations that
provide good fits for thermal expansion underestimate
the 2.7°C Southern Hemisphere wanning projected by
the GFDL model, with the high values of n (which are
accompanied by low sensitivities of w) coming closer.
As Figure 3-6c shows, the GFDL coupled ocean model
suggests approximately a one-third reduction in overall
29
-------
Chapter 3
30 -i
26-
22"
20
u
a
b
2.8 -I
2.6-
24-
a
I 20H
GFDL model
thermal expansion
5 10 15 20 25
Percent decline in w per 1°C warming
GFDL model
temperature change
5 10 15 20
Percent decline in w per 1°C warming
90N 60
30 60 90S
Figure 3-6. Using the GFDL Coupled Atmosphere-Ocean Model to Derive a Reasonable Value of How Upwelling
Velocity Responds to Global Warming. Given various values of jt, (a) shows thermal expansion as a function of the
upwelling sensitivity. The GFDL estimates of thermal expansion can be duplicated by combinations in which upwelling
sensitivity is approximately equal to 0.25-71/2, at least for 0<7t<0.6. Unfortunately, these combinations do not duplicate
Southern Hemisphere temperatures, as shown in (b). Nevertheless, the derived value of w-sensitivity is further supported
by (c) GFDL's estimate of the change in stream functions over a seventy-year period: A one-third decline in circula-
tion is evident between the S (baseline) and G (CO2 doubling) simulations; similarly, a 50 percent reduction in CO2
would increase mixing by about 1/2, as shown in the D-simulation.
SOURCES: Manabe et al. (1991) for three-dimensional results; see text for 1-D results.
30
-------
Climate Change
upwelling after seventy years (by which time global
temperatures rise 3°C).
The impact of warming on annual seaice formation
also is an indicator of changes in downwelling.
Parkinson & Bindschadler (1982) estimated a 50 percent
reduction in Antarctic seaice formation for a 5°C warm-
ing in Antarctic air temperatures, which corresponds to a
decline of 14.8%/°C. Although the sensitivity in that
analysis referred to Antarctic (rather than global) tem-
peratures, the implied sensitivity is broadly consistent
with that suggested by comparing 1-D with 3-D models.
Parameter Distributions for the
1-D Model in the Draft Report
We now present our reasoning behind the initial
set of parameter distributions employed in the draft
Monte Carlo analysis that was circulated to the
reviewers. As discussed below, the reviewers used
these initial distributions as a starting point in select-
ing the distributions used in the simulations.
Climate Sensitivity (AT2X)
Since the 1979 National Academy of Sciences
report CO2 and Climate: A Scientific Assessment, the
consensus estimate has been that a CO2 doubling will
warm the Earth's average surface temperature 1.5 to
4.5°C in equilibrium. That report and a second panel
(NAS 1982) stated that 3°C was the most likely value.
Subsequent reports such as NAS (1983) and IPCC
(1990) concluded that the most likely value is 2.5°C.
Wigley & Raper (1991) employed their one-dimen-
sional model to estimate that historic warming is con-
sistent with a value of about 3.3°C. They have subse-
quently concluded that they may have overestimated
the impact of historic aerosols, which would imply a
sensitivity closer to 2.5 °C. On the other hand, their
analysis assumed that 7T,=0.2 and that w remains con-
stant; allowing w to decline or a higher value of TC
would result in a higher sensitivity estimate. Overall,
their analysis does suggest that the historic record thus
far is consistent with the consensus estimate of AT2X.
Nevertheless, this range has not met with uni-
versal acceptance. Patrick Michaels, the State of
Virginia's climatologist, estimated that the warming
is likely to be about 1°C (Michaels et al. 1992); and
Sherwood Idso of the U.S. Agricultural Research
Service in Tempe, Arizona, has long argued that the
warming is likely to be much less than the consensus
assumes. Idso & Balling (1991), for example, esti-
mated a sensitivity of only 0.35°C. At the other end
of the spectrum, Lashof (1989) estimated that the
warming could be as high as 8 to 10°C, particularly if
the anthropogenic doubling induces biological feed-
backs to release additional greenhouse gases.14
The combined picture that these studies paint is
that our uncertainty is a skewed distribution that can be
roughly described as lognormal. The draft report
assumed that AT2X is lognormally distributed with a
geometric mean of 2.6°C and a limits of 1.5 and 4.5°C.
This distribution has a mean of 3.0°C and a 2 percent
chance of exceeding Lashof's 8°C estimate, as well as
a 5 percent chance of falling below Michael's 1°C.
Diffusivity (k) and Initial Upwelling Velocity (w0)
The parameters k and w determine how rapidly
the ocean reaches its new equilibrium. Diffusivity (k)
represents the rate at which heat is transported from the
relatively warm surface layers of the ocean downward
to the colder thermocline and deep ocean. The para-
meter represents conduction and local-scale mixing, as
well as the diffusion that its name suggests. Sarmiento
et al. (1976) used measurements of the distribution of
radium and radon isotopes to estimate upper and lower
bounds for k as a function of depth. IPCC (1990)
accepted the Hoffert et al. (1980) calculations that the
depth-averaged value of k implied by Sarmiento et al.
is between 1000 and 3000 m2/yr, and used the inter-
mediate value of 2000 m2/yr.
The upwelling velocity parameter w can be lit-
erally interpreted as the speed at which ocean water
flows upward, averaged over the entire ocean except
for those areas where ocean water is sinking. Because
the total water that sinks must equal the total water
flowing upward, and because the region over which
ocean water sinks is relatively small, this parameter is
estimated as the ratio of global deepwater formation
divided by the area of the ocean.
In picking the current upwelling velocity w0, a
primary consideration is to ensure that when combined
with the value for k, the ocean model duplicates
14Both Michaels et al. and Lashof included nonclunatic factors in
their estimates. Michaels et al. included the expected correlative
increase in aerosol concentrations; Lashof included possible bioiog-
ical feedbacks that might increase natural greenhouse gas emissions.
31
-------
Chapter 3
today's temperature-depth profile. IPCC assumed that
k/w=500 m, implying that w=4 m/yr. This value is
consistent with existing literature: Perry & Walker
(1977) estimated the total bottomwater formation to be
35 to 55 million cubic meters per second. Averaged
over the entire (nonbottomwater-forming) area of the
ocean, this range implies an average upwelling velocity
of 3.3 to 5.2 m/yr.
We used a lognormal distribution for k and w0 to
avoid negative values. As a result, we had to choose
between using the IPCC values as the medians of our
distribution and using the ranges derived from previous
studies; we opted for the former.15 Thus, the draft
assumed that k has a median of 2000 m2/yr with 2a
limits of 1333 and 3000. Given the assumption for
k/w, w0 had a median of 4 m/yr with 2a limits of 2.67
and 6.0; the a limits of 3.3 and 4.9 m/yr were thus con-
sistent with the Perry & Walker estimates.16
Probability that Upwelling Velocity Changes
Under OM1, the ocean model treats w as fixed
and draws n from a distribution described below. For
OM2, by contrast, the ocean model allows w to change
over time. Lacking analysis favoring one model over
the other, the draft assumed that each of these cases
were equally likely; that is,
Prob(OMl) = Prob(OM2) = 0.5.
Thus, half of the simulations assumed that w=w0 and
half assume that w changes.
Values of n in the Fixed-w Case
Under OM1, the draft used a lognormal distribution
for both hemispheres, with 2a limits of 0.2 and 1. The
high end is justified by its use in IPCC (1990) and by the
fact that, without additional information, the simplest
assumption is that in equilibrium the various layers of
the ocean warm by the same amount. The low end is
justified by its use in Wigley (1992) and the fact that
without additional information it might be reasonable to
assume that the temperature at which the nonfreezing
bottom water (20 percent) forms would rise by the global
average, while the water forming due to freezing (80 per-
cent) would continue to occur at the same temperature.
l5With 2a limits of 1000 and 3000, a normal distribution implies a
median (mean) of 2000, but a lognormal distribution implies a
median (geometric mean) of 1732.
16We remind the reader that k/w=500 m refers to the current situ-
ation. Thus, in the cases where w declines as temperatures rise, we
have to pick an initial value for w]765 such that when the simula-
tion reaches the year 1990, w=w0.
Values of n and w in the Variable-w Case
Ideally, we would treat the two major sources
of deepwater formation differently: (a) in the North
Atlantic, where bottom water is caused by evaporation,
we would assume that n=l and allow w to change as
indicated in various studies reporting declines in North
Atlantic bottomwater formation17; (b) in the Southern
Hemisphere, where bottom water is created by freez-
ing, we would assume that freezing still occurs at the
same temperature (i.e., 7CSH=0), but that it (and thus
WSH) declines as described below.
Because the Wigley & Raper one-dimensional
model does not fully account for heat transfer between
the hemispheres, we must run the model using global
values for w and n. Thus, we set 71=0.2, which is con-
sistent with the assumption that 7iNH=1.0 and rtSH=0.0.
The literature provides two possible ways to
estimate how w might change as temperatures rise:
(1) assume a direct relationship between global (or Ant-
arctic) temperatures based on coupled-ocean models;
and/or (2) estimate the decline in seaice formation result-
ing from warmer temperatures and assume that WSH
declines proportionately. The GFDL coupled-ocean
model run reported by Manabe et al. (1991) projects
about a 30 percent decline in deepwater formation by the
time global temperatures rise 3°C. As described above,
the Wigley & Raper model most closely approximates
the thermal expansion estimates generated by GFDL
when w declines 5 and 15 percent per degree (C) of sur-
face warming, for 7t=0.4 and 0.2, respectively. Parkinson
& Bindschadler (1985) estimated that a 5°C uniform
Antarctic warming would cause a 50 percent decline in
sea ice, which would decrease w by 40 percent (because
80 percent of deep water is formed in Antarctica).
At first glance, the estimates from seaice reduc-
tion and 3-D modeling results are fairly consistent.
However, the Manabe et al. projections coincide with
a warming of only about 1 °C in Antarctica, implying
a sensitivity three times greater than that implied by
Parkinson & Bindschadler.
The draft assumed that both w and sea ice
decline as temperatures warm. We define the para-
meter 0 to describe how w changes:
w = w0 9AT.
17Seaice formation in the North Atlantic is relatively minor.
Although seaice formation in the Arctic Ocean is significant, the
mixing between the Arctic and the other oceans is sufficiently
small for it to be safely ignored in a one-dimensional model.
32
-------
Climate Change
The draft assumed that 9 has a lognormal distribution
with a median of 0.85, consistent with the results
shown in Figure 3-6. To allow for some possibility of
increased upwelling, the draft assumed that the o limits
for 9 are 0.852 (i.e., 0.72) and 1.0.
Polar Climate: Subsidiary Equations
The one-dimensional model estimates only one
of the components of sea level rise directly: thermal
expansion. As we discuss in Chapter 6, the models
for projecting the alpine contribution to sea level rise
are simple enough to require only a projection of
global temperature change, which is also provided by
the 1-D model. But 99 percent of the world's land-
based ice rests on the polar ice sheets of Antarctica
and Greenland. Thus, for estimating future sea level
rise, the impact of greenhouse gases on polar climate
could be as important as its impact on the worldwide
average change in temperatures.
Early climatic assessments (e.g., NAS 1979) sug-
gested that polar temperatures were likely to warm two
to three times as much as the global average. This result
was based on both paleoclimatic evidence and the
results of mixed general circulation models. Because of
these projections, the relationship between global and
polar temperatures is commonly known as the "polar
amplification parameter." As Table 3-1 shows, many
general circulation model studies with mixed-layer
oceans suggest a considerable polar amplification. On
the other hand, more recent studies (with deep-ocean
models coupled to atmospheric models) suggest that the
polar amplification may be less than 1.0.
Moreover, the annual average change in tem-
peratures is not the best indicator for the impact of
climate change on these ice sheets. Greenland is tens
of degrees below freezing during winter, so a winter
warming would not induce melting; the impact on
summer temperatures is far more important. Antarctica
is so cold that surface melting is trivial throughout the
year. Ice flows gradually toward the oceans in the form
of ice streams that are buttressed in part by floating ice
shelves, most of whose bases are melting. If warmer
climate is going to induce a significant contribution of
Antarctic ice, it may do so through warmer water
intruding beneath the ice shelves. Such warm intrusions
could be enhanced either by warming the circumpolar
ocean or by reducing the amount of sea ice. Finally,
warmer temperatures could increase precipitation in
polar areas, offsetting the potential contribution to sea
level. Because most polar precipitation occurs during
TABLE 3-1
GREENLAND WARMING ESTIMATED BY
VARIOUS CLIMATE MODELS
Model Year
Coupled Ocean
Season
Warming (°C)
Greenland Global
GFDL
GFDL
GFDL
MPI
NCAR
UKMO
60-80
60-80
60-80
56-65
31-60
65-75
winter
summer
annual
annual
annual
annual
3-5
1.0-1.5
3-4
2-5
1
1-2
2.3
2.3
2.3
1.3
0.5
1.7
Equilibrium Mixed-Laver Ocean
GFDL
GFDL
CCC
CCC
UKMO
UKMO
2XC02
2XC02
2XCO2
2XCO2
2XC02
2XC02
winter
summer
winter
summer
winter
summer
8-18
2-6
4-8
2-6
0-4
2-4
4.0
4.0
3.5
3.5
5.2
5.2
SOURCE: IPCC 1990, 1992.
the warmer months, summer temperatures are more
important than winter temperatures.18
Although several studies have reported the likely
equilibrium impact of a CO2 doubling on polar air tem-
perature changes, relatively few have reported time-
dependent projections. Fewer still have examined the
likely changes in polar ocean temperature changes.
Therefore, the draft used the simplest procedure:
assume that (1) in equilibrium the temperature change
is a constant times the global change, but that (2) at
least in the Southern Hemisphere, the polar tempera-
ture change lags behind the global change.
This section describes the draft report's assump-
tions for polar temperature and seaice changes.
Because different reviewers were involved, we defer
discussion of precipitation changes until the final sec-
tion of this chapter. Conceptually, our projections
require two tasks: (1) estimating the relationship
between global warming and equilibrium polar tem-
peratures; and (2) specifying the dynamics and
adjustment times by which polar temperatures respond
to global warming.
18See Chapters 4 and 5 for more details on Greenland and Antarctica.
33
-------
Chapter 3
Equilibrium Polar Warming
Our projections of the equilibrium conditions
toward which polar temperatures would tend required us
to specify parameters for Antarctic air temperatures, Ant-
arctic water temperatures, and Greenland air temperatures.
Antarctic Air Temperatures. The draft report assumed
that, in equilibrium, the summer surface air warms Pj
times the global average surface warming. Pj was
lognormally distributed with a median of 1.0 and 2a
limits of 0.67 and 1.5, based on IPCC (1992).
The draft assumed that winter temperatures would
be more sensitive. (As Table 3-1 shows, most modeling
studies have reached this result as well.) Sea ice would
decline as a result of the increased radiative forcing from
greenhouse gases, even if temperatures did not warm;
summer wanning also reduces sea ice. Where sea ice is
removed, air temperatures will be much warmer during
winter because the exposed ocean can keep the air at
around the freezing point, rather than tens of degrees
below freezing. Because seaice retreat will allow these
warmer areas to advance inland, temperatures over the
coastal portions of the continent will be warmer as well.
We assumed that, in equilibrium, the winter surface air
warms P2 times the global average. The draft report
assumed that P2 is lognormal with 2a limits of 1.0 and
3.0. See EPCC (1992).
We also considered the correlation between winter
and summer Antarctic warming. Uncertainties regard-
ing polar amplification in summer and winter must be
correlated, because changes in ocean circulation and sea
ice would affect both. The correlation must be less than
1, however, because it is unlikely that all the processes
that affect summer and winter temperatures would affect
them in the same proportions.19
Because the correlation must be greater than zero
but less than one, the draft assumes that ppi p2=0.5.
Southern Hemisphere Circumpolar Ocean Warming.
The draft expresses the equilibrium change in cir-
cumpolar ocean temperatures as P3 times the average
equilibrium surface warming of the Earth.
As mentioned above, climate modeling studies
suggest that the winter warming of Antarctic air tem-
peratures does not result from warmer ocean tempera-
tures as much as from the decline in sea ice, which
enables oceanic heat to escape and warm the cold
Antarctic air. By contrast, during summer, the surface
air and the surface water should warm by about the
same amount (although the change in water tempera-
tures at ice-shelf depths may be different). This rea-
soning suggests that the summer Antarctic air temper-
ature increase would be a better indicator of Antarctic
ocean warming than the average annual warming of
Antarctic surface temperatures, which would imply a
warming of 0.67 to 1.5 times the global warming.
Coupled ocean-atmosphere models suggest that
ocean waters will warm by less than the global aver-
age warming, at least for the first century. As dis-
cussed below, Manabe et al. (1991) estimated that the
polar ocean may warm by only about 25 percent as
much as global temperatures after one hundred years.
Fitting a simple differential equation to those results
suggests that the long-run warming would be only
about 1/2 the global warming.20
The draft report assumed that P3 is lognormal
with a median of 0.5. As discussed below, such an
assumption yields results that are consistent with the
Manabe et al. (1991) results. Moreover, if extrapolated
backwards in time, this assumption implies that during
the last ice age, the circumpolar ocean temperature
would have been hovering at about the freezing point.21
Somewhat arbitrarily, we assumed a fourfold uncertainty
(i.e., a limits of 0.25 and 1.0) and a 0.75 correlation
with summer equilibrium warming. Thus, in only about
15 percent of the simulations would the circumpolar
"Note that the radiative effect of seaice retreat is positive in the sum-
mer but zero during the polar night. On the other hand, convection of
heat from ocean to air is much more enhanced during winter, when
the air is much colder than the water, than during summer, when they
are both at approximately the same temperature.
20More recently, Manabe & Stouffer (1993) report that after 500 years,
the circumpolar ocean warms as much as the global average tempera-
ture; i.e., ATcdw=AT. Manabe himself suggests that the Antarctic
ocean temperatures should warm as much as the global average, but
with a 100 to 300 year lag. See Expert Judgment, infra.
21The current circumpolar ocean temperature is about 1.9°C above the
in situ freezing point. A more realistic approach might have been to
assume that cfT^^/aT is low, as long as there is permanent sea ice, but
that it increases as the area of sea ice, ice shelves, and icebergs decline.
Such an assumption would resolve the inconsistency between the pos-
itive polar amplification that climatologists have long expected for a
CO2 doubling equilibrium and the fact that such an amplification can-
not be extrapolated backwards without freezing much of the southern
ocean. Lacking an objective basis for describing how this marginal
rate of polar amplification might increase, we retained the proportion-
al assumption. But see Hoffert's suggested distributions under Expert
Judgment, Circumpolar Ocean Warming, infra.
34
-------
Climate Change
deep water (CDW) warm by more than the global
average—even in equilibrium. For the most part this
would happen along with scenarios in which summer
Antarctic warming is also greater than the global aver-
age warming (and thus where precipitation increases
are significant as well).
Greenland Temperatures. IPCC (1990) assumed that
Greenland warms 1.5 times the global average. As
Table 3-1 shows, coupled ocean-atmosphere models
suggest that Greenland warming will be between one
and two times the global average warming. As with
Antarctica, GFDL suggests that the summer warming
will be less than the winter warming, as does the equi-
librium mixed-layer run by the Canadian Climate
Center (CCC). Although the United Kingdom Meteor-
ological Office (UKMO) mixed-layer run suggests that
summer warming will be greater than winter warming,
the summer warming is still less than global average
equilibrium warming. The draft report assumed that
annual temperatures in southern Greenland rise Py
times the global average, with P7 being lognormal with
two a limits of 1 and 2. Because existing models for the
Greenland contribution to sea level rise only consider
annual temperatures, we follow suit.
Adjustment Times for Polar Temperatures
Manabe et al. (1991) employed a coupled ocean-
atmosphere model with a linear time trend in forcing.
They estimated that average global temperatures even-
tually follow a linear trend, after an initial "startup" of a
few decades; such a temporal pattern could be approxi-
mately described by the first-order differential equation:
dT
dt
= a(Teq-T),
where Te(, is the equilibrium temperature implied by
atmospheric forcing at a given time, and I/a is the
e-folding time. Because T^ follows a linear time
trend, the trajectory for transient temperatures would
be approximately:
4JL =a(Bt-T),
where B represents the annual trend of equilibrium (also
called "committed") warming (i.e., climate sensitivity
expressed as the sensitivity to a CO2 doubling, divided
by the number of years CO2 takes to double). If b=aB,
4L =a(Bt-T),
and the only solution through the origin is:
T - -b- p-at + b ct _ K
1 ~ a? e + a lt aj-
The GFDL results seem to suggest that the
adjustment time for Antarctic temperatures may be
much longer than for average surface warming, as
shown in Table 3-2. Solving for a and B suggests that
the e-folding times for global surface temperature,
Antarctic air, and circumpolar water are nine, twenty-
nine, and fifty years, respectively. Even so, the long-
term warming trend for water temperatures is only
about half that of air temperatures.
The simple linear first-order differential equation
is only a rough summary of the dynamics.22 A possi-
ble alternative approach for summarizing the dynamics
would be to use higher order differential equations, and
estimate the coefficients by fitting a nonlinear regres-
sion of their solutions through the annual (or at least
decadal) time series. At least for surface air tempera-
tures, a second-order equation seems likely to more
accurately describe the dynamics: The first-order equa-
tion assumes that the difference between the equilibri-
um and the actual value declines exponentially; second-
order equations, by contrast, can capture a response that
declines as the sum of two declining exponentials.
Given the evidence that the mixed layer adjusts in a
matter of decades while the deep ocean takes centuries,
such a functional form would seem applicable. On the
other hand, the simplified version may be preferable for
purposes of a Monte Carlo analysis, since each para-
meter clearly represents a particular issue.
A further problem remains with the simple dif-
ferential equation: We are already using a one-
dimensional upwelling-diffusion model to capture the
dynamics of the global surface temperature adjust-
ments. Different values of Ji, k, and w lead to different
adjustment times and "shapes" of the adjustment func-
tion. Therefore, to use the lag functions derived from
GFDL results for Antarctic air and water temperatures
would leave us with the risk that for some combina-
tions the temporal pattern of adjustment for the polar
temperatures would be inconsistent with that of the
global temperatures.
22Consider transient surface air temperatures: the fit we obtain implies
an equilibrium warming (for 2XCO2) of only 2.6, while the 2XCO2
equilibrium run by Manabe et al. with a mixed-layer ocean suggests
4.2. If we fit the simple differential equation using the equilibrium val-
ues, we obtain much longer e-foldmg times of 38 and 300 years for
average and Antarctic air temperatures, respectively
35
-------
Chapter 3
To prevent such an inconsistency, we assume:
TABLE 3-2
LINEAR FIRST-ORDER DIFFERENTIAL
EQUATIONS FIT TO GFDL TRANSIENT
ESTIMATE OF GLOBAL AND POLAR
TEMPERATURES
Year
15
25
35
45
50
55
65
70
75
85
90
95
Global
Surface
0.3a
0.7
1.1
1.4
1.5
1.6
2.0
2.3b
2.5
2.9
3.1
3.3a
Change in Temperatures
500 m-deep South
75°S Air Circumpolar Greenland
0.1 — —
0.2 — —
0.3 — —
0.5a — —
0.5 —
0.5
0.4
1.0
1.5
1.5
— 2.0
— 3.15-3.8b
0.75a —
1.0a
4.6
2.0a'b —
Fitting equation to (a~l years
a
B
e-fold
AT2X
Fixing B based on equilibrium run and fitting to year b
a 0.02646 0.005 — 0.022-0.031
0.1147
0.0382
8.7
2.66
0.0356
0.0221
28.1
1.54
0.0202
0.0206
49.5
1.44
B 0.0603 0.115
e-fold 38.7 200
AT2X 4.2 8.0
0.0912
31^4
6.1
aYears employed in solving for a and B in the equation
-------
Climate Change
TABLE 3-3
CUMULATIVE PROBABILITY DISTRIBUTION
OF GLOBAL WARMING BASED ON
ASSUMPTIONS FROM THE
DRAFT REPORT (°C)
Global Mean Surface Temperature Change
Cumulative
Probability (%)
1
5
10
20
30
40
50
60
70
80
90
95
97.5
99
99.5
Mean
a
2030
0.35
0.51
0.6
0.75
0.88
0.97
1.1
1.2
1.3
1.5
1.75
1.95
2.1
2.4
2.5
1.1
0.45
2100
0.85
1.2
1.5
2.0
2.3
2.7
3.1
3.5
3.9
4.6
5.6
6.5
7.3
8.3
9.1
3.3
1.6
2200
1.05
1.9
2.24
3.1
3.6
4.2
4.8
5.6
6.3
7.5
9.3
10.9
12.6
14.7
16.4
5.4
2.9
1990 2050 2100 2150 2200 2250 2300 2350 2400
Year
Figure 3-7. Selected Scenarios of Global Warming:
Draft Report. See Figure 2-5 and accompanying text
for explanation.
Results for Initial Draft Assumptions:
Temperature and Thermal Expansion
Table 3-3 illustrates the probability distribution of
global warming for selected years given the initial draft
assumptions for concentrations (see Chapter 2) and the
climate variables described above. As the table shows,
our median estimate for the year 2100 was 3.1°C,
10 percent higher than IPCC's 2.8°C best estimate for
the IS92a scenario. Our 90 percent confidence interval
was also somewhat higher than the IPCC range: IPCC's
low estimate for the IS92a scenario of 1.8°C is 20 percent
greater than our 5%-low estimate of 1.5°C, while IPCC's
high IS92 estimate of 4.2°C is 35 percent less than our
5%-high estimate of 6.5°C. The draft report's estimates
for the year 2100 are somewhat higher than the EPCC pro-
jections principally because our lower values of TI allow
for a more rapid adjustment of surface temperatures.
Figure 3-7 illustrates temperature estimates for
selected simulations through the year 2400.23
Although temperatures increase throughout the simu-
lation period for most runs, a few runs show a peak
around the year 2075; that result stems from the declin-
ing emission rates assumed in IPCC scenario IS92c.
Figure 3-8 shows the corresponding probability densi-
ties for 2100 and 2200.
The importance of the lower values of n is further
affirmed when one compares our thermal expansion
estimates (Figure 3-9 and Table 3-4) with those of IPCC
(1990). For the year 2100, our median draft estimate of
30 cm was about 25 percent less than IPCC's "best esti-
mate," even though our estimated temperature was
about the same (the IPCC 1990 report had slightly
higher temperatures than the 1992 report). Similarly,
our 60 percent confidence interval (20 to 44 cm) was
about 25 percent lower than the range spanned by the
IPCC low-to-high range of 26 to 58 cm. Only 5 percent
of our simulations exceed the IPCC high estimate, while
35 percent of them fell below the EPCC low estimate.
23See Figure 2-5 and accompanying text for a discussion of the
selection criteria for this and other spaghetti diagrams.
37
-------
Chapter 3
01 II 21 31 41 51 61 71 81 91 101 HI 121
3 15 --
0 15 3 45 6 75 9 105 12 135 15 165 18 195 21 225 24
AT (°C)
Figure 3-8. Probability Density for Surface Warming: Draft Report. Estimated probability density of surface
temperature warming between 1990 and (a) 2100 and (b) 2200.
325 1325 2325 3325 4325 5325 6325 7325 8325 93251032511325
Thermal Expansion (cm)
0 20 40 60 80 100 120 140 160 180 200 220 240
Thermal Expansion (cm)
Figure 3-9. Probability Density for Thermal Expansion: Draft Report. Estimated probability density for sea
level rise due to thermal expansion between 1990 and (a) 2100 and (b) 2200.
38
-------
Climate Change
TABLE 3-4
CUMULATIVE PROBABILITY DISTRIBUTION
OF THERMAL EXPANSION BASED
ON ASSUMPTIONS FROM THE
DRAFT REPORT (cm)
Cumulative
Probability (%)
1
5
10
20
30
40
50
60
70
80
90
95
97.5
99
99.5
Mean
a
2030
2.8
4.0
4.8
5.8
6.8
7.5
8.4
9.3
10
11
13
15
—
18
—
8.8
3.3
2100
8.7
13
16
20
23
27
34
38
44
52
60
78
—
113
—
32
15
2200
16
23
30
39
46
53
61
71
79
93
115
137
161
193
215
68
36
175--
2400
Figure 3-10. Thermal Expansion for Selected Simu-
lations for the Period 1990-2400: Draft Report. See
Figure 2-5 and accompanying text for additional
explanation.
Figure 3-10 provides a spaghetti diagram of
thermal expansion for the period 1990-2400. All sce-
narios show increasing expansion, including the few
scenarios for which temperatures decline after 2075.
The slight drop in temperatures would result in thermal
contraction of the mixed layer; but because tempera-
tures would still be about 1.5 C warmer than today, the
deep layers of the ocean would continue to warm and
expand, more than offsetting contraction at the surface.
Figure 3-11 shows the warming of Greenland,
Antarctic air temperatures, and circumpolar deep
water for selected simulations. Please note that seven
of the curves shown are from the upper 1 percent of all
simulations. In spite of the occasional extreme simula-
tion, for example, the 1%-high scenario resulted in a cir-
cumpolar ocean warming of about 6.5°C during the next
200 years, less than half the 1 %-high for global warming.
Expert Judgment
Our final results are based on the subjective distri-
butions provided by expert reviewers for the various
parameters; Table 3-5 lists the eight expert reviewers
who examined the draft report and provided distributions
for the climate assumptions other than precipitation.
Even though this final report is based on reviewer-
specified distributions, we have focused on the initial
distributions of the draft report for two reasons. First,
the reviewers were reacting to an initial draft; so those
desiring to scrutinize the methods and results of this
report can only do so by considering the initial specifi-
cations to which the reviewers were reacting. Second,
the initial distributions retain a residual relevance. In
several cases, a given reviewer would find that, for a
given parameter, our specifications were adequate: that
is, while the reviewer would not have selected precisely
the same values that we specified, she did not believe
that her specifications would have been sufficiently dif-
ferent for alternative specifications to be worthwhile.
All but one of the reviewers were participants in
the IPCC (1990) Science Assessment. Our reasons for
selecting these reviewers were that we wanted (a) repre-
sentatives from the major general circulation models and
(b) those with experience using one-dimensional models
39
-------
Chapter 3
COW Temperature Change
Greenland Surface Warming
53'
2 -
1990 2050 2100 2150 2200 2250 2300 2350 2400
Year
£
1990 2050 2100 2150 2200 2250 2300 2350 2400
Year
Antarctic Summer Warming (°C)
25 T
HiiiiiiniiiiiiiimrTfTrriTiiiiiiii iiiiiiiiiiiiiiiiiiiniwi
1990 2050 2100 2150 2200 2250 2300 2350 2400
Figure 3-11. Polar Wanning for Selected Simu-
lations for the Period 1990-2400: Draft Report
These spaghetti diagrams illustrate waiming of
(a) circumpolar deep water, (b) Greenland air tem-
peratures, and (c) Antarctic air temperatures. (See
Figure 2-5 and accompanying text for explanation.)
40
-------
Climate Change
TABLE 3-5
EXPERT REVIEWERS OF CHAPTER 3 (excluding precipitation)
Robert Balling
Francis Bretherton
Martin Hoffert
Michael MacCracken
Syukuro Manabe
David Rind
Stephen Schneider
Sarah Raper
Tom Wigley
Arizona State University
University of Wisconsin
New York University
Lawrence Livermore National Laboratories
NOAA/Princeton Geophysical Fluid
Dynamics Laboratory
NASA/Goddard Institute for Space Studies
National Center for Atmospheric Research
Climate Research Unit, University of East Anglia
University Center for Atmospheric Research
Tempe, AZ
Madison, WI
New York, NY
Livermore, CA
Princeton, NJ
New York, NY
Boulder, CO
Norwich, UK
Boulder, CO
to project transient climate change. All of the major
modeling groups were invited to participate, as were all
of the authors of the IPCC chapter on time-dependent
climate change. Almost all of the U.S. scientists con-
tacted agreed to participate. We were less successful in
securing the reviews of foreign modeling experts, with
two notable exceptions: Tom Wigley and Sarah Raper
from the University of East Anglia24 provided a set of
probability distributions based on a probability analysis
that they had performed but not published. John Church
from CSIRO in Australia offered to provide simulations
from his model of thermal expansion, an offer that our
time and budget constraints unfortunately prevented us
from implementing.
There is an important difference between the
ways that scientific assessments (e.g., NAS 1979; IPCC
1990) and Delphic probability analyses choose models
and parameter values. Scientific "assessments" usually
are more than passive assessments; they often attempt
to forge a consensus. As a result, in addition to provid-
ing a guide to policymakers, they have a feedback on
the evolution of science. In a Delphic probability
analysis, by contrast, we take the science as we find it.
If the experts disagree, we make no effort to broker a
compromise or pick the theory that is most likely to be
correct—we simply try to ensure that the simulations
reflect the fact that there is a difference of opinion.
Thus, while the need to forge a consensus tends to dis-
courage assessment panels from including those with
dissenting views, such inclusion is essential in a
Delphic analysis, lest the results artificially "compress
the tails of the distribution" (i.e., lest we mislead the
reader regarding how certain the future really is).
For purposes of this chapter, the most important
group of dissenting scientists are those who believe that the
"mainstream" drastically overestimates the likely warming
resulting from greenhouse gases. Since the original NAS
(1979) assessment was published, Sherwood Idso of the
U.S. Department of Agriculture in Tempe, Arizona has
published dozens of publications disputing the estimate
that a doubling of CO2 would warm the Earth 1.5 to
4.5°C. The second NAS (1982) assessment devoted
about 10 percent of the main body of its report to taking
issue with the findings of Idso and other dissenters.25
Nevertheless, there is a group of rational scientists
that rejects the consensus view that the Earth will warm
1.5 to 4.5°C from a CO2 doubling and who (1) have
an internally consistent theory for rejecting the con-
sensus view, (2) are continually analyzing empirical
data on the question, and (3) have a theory that will be
impossible to completely prove or disprove for at least a
decade. Two dozen of them met in 1990 and developed
24Tom Wigley subsequently relocated to the University Corporation
for Atmospheric Research in Boulder, Colorado.
25Our own studies of climate impacts (e.g., Earth & Titus 1984;
Titus 1986; Titus 1991; Titus et al. 1991; Titus 1992) have general-
ly attributed little information content to the dissenters; but our rec-
ommendations for coastal policies have always assumed that there
is a substantial chance that the rise in sea level will be negligible.
41
-------
Chapter 3
a proposed research agenda (Balling et al. 1990).
Therefore, we asked Robert Balling of Arizona State
University to review the draft report and provide com-
ments reflecting the viewpoints of this important
group of "greenhouse skeptics."
What is the most reasonable way of combining
the different distributions suggested by the reviewers? It
depends on where one draws the boundaries of "exper-
tise." If we had been able to incorporate the judgments
of fifty or sixty reviewers of this chapter, we might have
defined "expert" on a parameter-specific basis. Thus,
for example, the estimate for n might have been based
primarily on the judgments of one-dimensional model-
ers such as Martin Hoffert and Wigley & Raper, while
the estimates for AT2xco2 would be based on the opin-
ions of three-dimensional modelers such as David Rind
and Syukuro Manabe. With only eight reviewers, how-
ever, such a procedure would leave us with only one or
two opinions for most of the parameters.
At the other extreme, we might have secured the
opinions of each reviewer for every parameter in the
entire study; but such an approach would go too far in
the other direction. Therefore, we divided the reviews
by chapter and weighted the assessments of each
reviewer equally; for example, there are 1250 simula-
tions drawing from the distributions preferred by each
of the eight reviewers listed in Table 3-4. When the
reviews came in, it became apparent that some of the
glaciologists reviewing Chapters 4 and 5 had expertise
regarding polar precipitation changes, while several of
the climate reviewers chose not to comment on pre-
cipitation. Therefore, precipitation is considered sep-
arately later in this chapter.
We now describe the probability distributions
requested by the expert reviewers. Table 3-6 summa-
rizes the most important assumptions.
Climate Sensitivity
With the exception of Robert Balling, all of the
reviewers accepted the 1.5 to 4.5°C range as the equi-
librium surface warming from a CO2 doubling; most
reviewers accepted our initial characterization of this
range as a limits. Wigley & Raper suggested treating
this range as a 90 percent confidence interval (i.e., 1.5
and 4.5°C are 1.65a limits) due to the information that
has accumulated since the original NAS (1979) report.
Manabe agreed that 1.5 to 4.5 °C is a reasonable estimate
of a 90 percent confidence range for how a randomly
chosen general circulation model would respond to CO2
doubling. However, because the future response of the
actual atmosphere is less certain than the response of a
climate model, Manabe suggested that we retain the
assumption that 1.5 and 4.5 °C represent o limits, not
the 90-percent confidence interval. MacCracken
agreed with Manabe's assessment, largely because the
general circulation models do not currently include
mode switching or ozone chemistry.26
Robert Balling concluded that, based on Idso &
Balling (1991), AT2X should be normally distributed
with a mean of 0.35 and a limits of 0 and 0.7. Balling
was also concerned that the draft report suggested that
there was no chance that the Earth would cool. Because
a negative climate sensitivity is impossible given the
scheme of a one-dimensional upwelling/diffusion
model, we set negative values equal to zero. Neverthe-
less, we incorporated the possibility of cooling by
adding to all simulations a stochastic component, which
we discuss below.
We also had to make a nonstandard interpretation
of climate sensitivity to faithfully incorporate Balling's
suggestions. One-dimensional models assume that the
initial forcing from a CO2 doubling is 4.4 W/m2 regard-
less of climate sensitivity—enough to warm the Earth
1.2°C in equilibrium—and that the remaining forcing
results from climate feedbacks that increase linearly
with temperature. As a result, to the extent that the deep
oceans delay the warming from an increased forcing,
they also delay the increased forcing associated with
those feedbacks, further delaying the actual warming in
high scenarios. For climate sensitivities less than 1.2°C,
however, the effect is the opposite: negative feedbacks
increase with temperatures. Thus, the model would
show an initial increase in radiative forcing followed by
a decline in forcing over time. The Idso & Balling
study, however, is based on the assumption that climate
warming has at most a trivial delay.27 To be consistent
with this assumption, our Balling simulations adjust
direct forcing downward and assume no long-term tem-
perature-driven feedback; in the extreme case where
climate sensitivity is zero, we simply assume no change
in greenhouse forcing.
Baseline Stochastic Variability
In response to Balling's comments, we also polled
the various reviewers on the best way to characterize a
26However, MacCracken did suggest that we truncate the distribu-
tion at an upper limit of 9°C, given the lack of evidence that the
warming could be greater.
27In effect, Idso & Balling assume that the negative feedbacks
occur rapidly (e.g., the feedbacks are forcing-dependent).
42
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Climate Change
TABLE 3-6
GLOBAL CLIMATE AND POLAR TEMPERATURE ASSUMPTIONS
Balling Bretherton/ Hoffert MacCracken Manabe
Draft
GLOBAL CLIMATE PARAMETERS
AT
2X
o-low
c-high
i
2o-low
2o-high
71
O.On-'°
0.7n
0.2d
1.0d
1.5
4.5
0.2d
1.0d
1.5
4.5
0.2,PGreen
l-0,PGreen
W/WQ given AT = 4°C (in cases where w changes)
2o-low 0.27d 0.27d 0.27,0.075
2o-high 1.0d 1.0d 1.0,0.445
1.5
4.5t9
0.04
l.O'1
0.27
1.0
1.5
4.5
0.2
0.2
0.4
0.4
Rind
1.5
4.5
Poreen.0-0
0.2
1.8
Schneider
1.5
4.5
0.2
1.0
0.27, 0.2
1.0, 1.8
PROBABILITY OF ALTERNATIVE SPECIFICATIONS OF CHANGES IN UPWELLING
OM1
OM2
OM2.1
OM3
OM4
OM5
OM6
50d
50d
0
0
0
50d
50d
0
0
0
50
0
0
0
0
50
0
35
35
0
30
0
0
0
0
0
0
100
80
5
5
5
5
50
20
15
10
5
Wigleyc
& Raper
1.86=
3.62"
-0.04C
0.58"
N.A.
N.A.
100
0
0
0
0
POLAR TEMPERATURE CHANGES
o-low
o-high
p
r cdw
O-low
O-high
tcdw (years)
o-low
o-high
p
r Greenland
2o-low
2o-high
0.67d
0.25d
1.0d
20d
80d
1.0d
2.0d
0.67d
1.5d
0.25d
1.0d
20d
80d
1.0d
2.0d
2.38C
3.36e
1.0-2.0h
57C
131C
1.0-2.0h
1.0-4.0h
0.5"
1.5"
0.25d
1.0d
20d
80d
0.5
2.0
0.67d
1.5d
1.0
1.0
100
300
0.5
1.0
i.63c
2.45C
1.0
3.0
80
90
1.0
3.0
0.5
2.0
0.5
2.0
20
80
0.5
3.5
0.62'
1.21C
N.A.
N.A.
N.A.
N.A.
0.93C
2.15°
OM1- The original Wigley & Raper (1992) specification with fixed w=w0 and specified distribution of n.
OM2: w declines geometrically: w=w0(l-6)AT; 6>Q
OM2.1: w increases geometrically: w=w0 (l-QY^; 6<0.
OM3: w declines suddenly by 80 percent when AT exceeds a threshold Tw. The threshold is between 1 and 4°C, with the higher values more likely; the
cumulative probability distribution is: F(Tw)=(Tw-l)2/9 for 1<^TW<4.
OM4: w increases suddenly by 80 percent when AT exceeds the threshold Tw, whose distribution is the same as in OM3.
OM5 w and 71 are fixed for the first 1°C of warming, after which w declines linearly to 0.05 w0 by the time AT reaches a threshold Tw. it increases linearly
from its initial value to the (transient) polar amplification parameter by the time T reaches Tw. Tw is uniformly distributed between 4 and 6°C.
OM6 TC is fixed at 0.2, and w declines linearly with temperature: w=(l-0.15AT) w0 for 06.
P — P
rGreen ~~ r Greenland
c Reviewer's estimate was a "round number" but specified with respect to a different probability level than O or 2a used here.
d Did not disagree with the draft's suggested value, but did not explicitly endorse parameter value either.
— Reviewer did not consider OM5 and/or OM6; those options were proposed sua sponte by Hoffert and Manabe, respectively.
h Hoffert assumes that P=l for AT<1. For 1
-------
Chapter 3
baseline nongreenhouse forcing. IPCC (1990) points
out that there has been a variation of about 0.3°C on a
century time scale, and that another 0.3°C variation
could result from anthropogenic aerosols.
Comments forwarded by the Dutch Delegation
to the IPCC suggested that we use the autoregressive-
moving average (ARMA) approach popularized by
Box & Jenkins (1976). For example, the Dutch noted
that Tol & Vos (1993) fit the following model:
AT = -4.6 + 0.015 CO2(t - 20) + e(t),
where
e(t) - 1.07 e(t-l) + 0.18 e(t-2)
= w(t) - 0.68 M(t-l) - 0.67 K(t-2),
u(t) is random noise with au=0.11°C, and (t) repre-
sents the average value of a particular variable during
the year t.
There are two ways to fully implement this
model: (1) use the ARMA model estimated by Tol &
Vos or (2) fit a one-dimensional model to the historic
data while simultaneously estimating an ARMA
model of the residuals. We lacked the time to do the
latter, which in any event might have required a dif-
ferent ARMA model for each value of n and AT2X-
We also decided not to use the Tol & Vos parameter
estimates directly: Their model implies a decadal
variation of 0.16°C, which only increases to about
0.176°C for time scales of a century and longer, which
is too small.28
Therefore, we adopt a simpler approach: A first-
order autoregressive model describing a random compo-
nent that we add to the mixed-layer temperature calculat-
ed by the 1-D model at the end of each time period:
noise(t) = 0.9975 noise(t - 1) + «(t),
where
-------
Climate Change
25
Figure 3-12. Surface Temperatures 1765-2065, With and Without an Illustrative Serially Correlated Nongreen-
house Forcing. The shaded area illustrates the a limits of the nongreenhouse forcing; variation increases from 0.1 °C on
a decadal time scale to 0.4°C on a century time scale. All scenarios are based on IPCC (1992) emissions scenario A.
the initial values in the draft report were close enough
to what they would have chosen. Thus, they decided
that additional specification on their part would not be
worthwhile. The other six reviewers had extensive
comments on both the model specifications and the
actual parameters employed.
Model Specifications. While the draft report switched
between two alternative specifications, the expert reviewers
suggested a total of seven different ocean models:
OM1 The original Wigley & Raper (1992)
specification with fixed w=w0.
OM2 Like the draft report's variable-w model,
that is, w changes geometrically: w=w0 0AT.
But unlike the draft report, where 71=0.2,
71 is also drawn from a distribution.
OM2.1 The same as OM2, but 0 is greater than
1 .0 and thus upwelling increases.
OM3 w declines suddenly by 80 percent when AT
exceeds a threshold Tw. The threshold is
between 1 and 4°C, with the higher values
more likely; the cumulative probability distri-
bution is: F(Tw)=(Tw-l)2/9 for
OM4 w increases suddenly by 80 percent when
AT exceeds the threshold Tw, whose
distribution is the same as in OM3.
OM5 w and n are fixed for the first 1°C of
warming, after which w declines linearly
to 0.05 w0 by the time AT reaches a
threshold Tw. n increases linearly from
its initial value to the (transient) polar
45
-------
Chapter 3
amplification parameter by the time
T reaches Tw. Tw is uniformly
distributed between 4 and 6°C.
OM6 Very similar to the draft report's
variable-w model, n fixed at 0.2, and
w declines linearly with temperature:
w=(l-0.15AT)w0 for 06.
We discuss the specifications from each of the reviewers
in turn.
Wigley & Raper recommended that we run their initial
specification (OM1) for all of the simulations. While
acknowledging the possibility that w would change
over time, they did not believe that such an assumption
would improve the projections. They suggested high-
er values of k (and hence w0): median of 1 cm2/sec
(3154 m2/yr) with 90 percent (L65a) limits of 0.5 and
2.0 cm2/sec (1576 and 6307 m2/yr). For reasons dis-
cussed in Wigley & Raper (1991), they believe that low
values of TC are appropriate even with a fixed upwelling
velocity. They recommend a shifted lognormal distrib-
ution, in which ic+0.4 is lognormal with a median of 0.6
and 1.650 limits of 0.4 and 0.9; the net effect of this
assumption is that (a) the median is 0.2 and (b) 90 per-
cent of the observations are between 0 and 0.5.
Syukuro Manabe also favors low values of n, but
believes that downwelling is likely to decline. He rec-
ommends that we use a value for re of 0.2 and assume
that w would decline as suggested by a graph published
in Manabe & Stouffer (1993). We fit a linear regression
equation of downwelling on transient temperature,
which yielded a coefficient of 15 percent per degree (C),
down to the point where downwelling has declined by
90 percent. We refer to this set of assumptions as OM6.
Michael MacCracken was the first of several reviewers
to note the possibility of a sudden decline in bottom-
water formation, suggesting that the probability of
such a switch would rise to about 30 percent for a 4°C
warming; he accepted David Rind's functional specifi-
cation regarding the uncertainty of the threshold Tw,
i.e., OM3, discussed below. MacCracken assumed that
the fixed-w specification OM1 and the variable-w
specification OM2 should each be used 35 percent of
the time. For all three models, TC has a median of 0.2
and 2a limits of 0.04 and 1, with the distribution trun-
cated at 1. For OM2, MacCracken retained the initial
assumptions of the draft report that 0 has a median of
0.85 (i.e., w declines 15%/°C) and 2o limits of 0.722
(i.e., 0.852) and 1.
MacCracken also explicitly assumed a 0.5 corre-
lation between TC and 0, which implies that lower values
of TC are accompanied by a greater decline in down-
welling. This assumption was motivated in part by com-
paring his own comments with those of David Rind. He
observed that there appear to be two schools of thought
on what will happen with deepwater formation.
Some scientists, such as MacCracken and Manabe,
believe that decreased Antarctic sea ice or increased
high latitude precipitation could cause a decline in deep-
water formation. The water that does sink will warm
much less than the global average because (a) down-
welling in the Southern Hemisphere continues to be
caused largely by seaice formation, and (b) the North
Atlantic Deep Water cannot sink if it warms too much
(compared with the temperature of the thermocline).
This view implies that TC is low and that upwelling is sen-
sitive to temperature.
Others view the downwelling as driven by a
conveyor that is influenced by the equatorial up-
welling, which could conceivably increase due to the
enhanced evaporation at higher temperatures. Thus,
polar waters could continue to sink even at higher
temperatures. This view implies a higher value of n
but a lower decline—and possibly even an increase—
in downwelling.
David Rind preferred to assume a fixed w (OM1)
80 percent of the time. He divided the remaining 20 per-
cent of simulations equally between (a) OM2, with a
gradual decrease in w, using a median and 2o~ limits
for B as specified in the draft report; (b) OM2.1, with
its gradual increase in w, using a median and 2a limits
equal to the reciprocal of those specified for OM2;
(c) OM3, with its sudden 80 percent decrease in up-
welling; and (d) OM4, with its sudden 80 percent
increase in upwelling. Rind's justification for the 80 per-
cent change in upwelling was that deepwater formation
apparently was 80 percent less during the last ice age.
For both OM3 and OM4, he suggested that the proba-
bility density of a sudden change in upwelling should
increase linearly from zero, for a warming less than
1°C, to a maximum which is reached at 4°C—hence
the quadratic cumulative distribution function.
Unlike the previous reviewers, Rind recom-
mended relatively high values for n. In the Northern
Hemisphere, TCNH is perfectly correlated with the polar
amplification parameter and lognormally distributed
with 2a limits of 1 and 3; in the Southern Hemisphere,
TCSH is uniformly distributed between 0 and 1. Because
only 20 percent of the downwelling occurs in the
46
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Climate Change
Northern Hemisphere, the net effect is that the global n
has a median value of about 0.75.
Stephen Schneider made structurally similar rec-
ommendations, although he allocated the probabilities
differently: OM1—50%; OM2—25%; OM2.1—10%;
OM3—10%; and OM4—5%. For all cases, he used the
initial distribution that the draft report applied for OM1;
for example, n had a lognormal distribution with 2a
limits of 0.2 and 1.
Martin Hoffert favored devoting 50 percent of the
simulations to OM1, using the initial assumptions of the
draft report for all of the ocean model parameters. Based
on Hoffert (1990), he allocated the remaining 50 per-
cent to OM5. This model assumes that jt and w are
fixed for AT<1°C. For 1TW, w remains fixed at 7.5 percent of its initial
value w0.31 Although Hoffert (1990) suggested that
TW=4°C, for purposes of this study Hoffert suggests
that Tw is uniformly distributed between 4 and 6°C.
Hoffert also assumes a gradual increase in the
value of n. For AT<1°C, 71=1.0. For AT>TW, Hoffert
sets n equal to the transient polar amplification; i.e.,
sinking water warms by the same amount as circum-
polar ocean water. For 1
-------
Chapter 3
less than P7. To be consistent with Hoffert (1990), he
suggested that the amplification factor is 1.0 for the first
degree of warming. He treats P7 not as an equilibrium
amplification factor, but rather as what the amplification
factor would be once AT>TW. He then assumes that as
AT increases from 1.0 to Tw, the polar amplification fac-
tor increases linearly from 1.0 to P7. For example, if
Tw=5 and P7=3, then AT=1,2, and 3°C imply amplifica-
tion factors of 1,1.5, and 2, resulting in AT,^,^^!, 3,
and 6°C, respectively. Thus, Hoffert's assumptions
imply a Greenland warming similar to the projections of
Manabe for the first degree, Wigley & Raper for the sec-
ond degree, and Rind for the third degree. After that
point, Hoffert's assumptions imply much greater wann-
ing for Greenland than any of the other reviewers.
Antarctic Air Temperatures
The Antarctic contribution to sea level depends on
changes in both air and water temperatures. As discussed
in Chapter 6, the melting of Antarctic ice shelves is
assumed to respond to both declines in sea ice and warmer
water temperatures. Warmer air temperatures contribute
both to declines in sea ice, discussed in the previous sec-
tion of this chapter, and the countervailing impact of
increased precipitation, discussed in Chapter 3B.
Most of the reviewers focused on the more impor-
tant Antarctic water temperatures and let stand our initial
draft assumptions for the equilibrium southern polar
amplification and the speed at which the adjustment takes
place. MacCracken suggested that declines in Antarctic
sea ice could possibly allow summer air temperatures to
cool; therefore, he suggested that we use a normal distri-
bution with a limits of 0.5 and 1.5 for the summer ampli-
fication parameter Pj, which implies a 2 percent chance
that Antarctic summers will cool if global temperatures
warm. Wigley & Raper also suggested a range of 0.5 to
1.5, albeit for a lognormal distribution and 90-percent
limits. Schneider retained our initial assumptions for
winter warming; he thought that summer warming was
most likely to be equal to average global warming, but
suggested 2o limits of 0.5 and 2 times the global warm-
ing. Hoffert, by contrast, suggested 2o limits of 2 and 4,
consistent with his Northern Hemi-sphere assumptions.
Rind assumed a median amplification of 2, with 2a lim-
its of 1.33 and 3.
Hoffert and Wigley & Raper were the only review-
ers to change the simple first-order linear adjustment by
which Antarctic temperatures respond to transient global
temperatures. Hoffert adopted the specification that he
employed for Greenland temperatures. Wigley & Raper
assumed no additional lag.
Circumpolar Ocean Warming
The reviewers generally agreed with the draft
report's assumption that circumpolar ocean temperatures
will respond more slowly than Antarctic and Greenland
air temperatures. Three of the reviewers suggested no
change to our initial assumptions of an amplification (P3)
with a limits of 0.25 and 1.0, along with an adjustment
time (P4) with 2o limits of 20 and 80 years. Manabe sug-
gested that the circumpolar ocean will eventually warm as
much as the global average warming, but with an adjust-
ment time of 100 to 300 years (a limits). For the year
2100, this assumption yields about the same circumpolar
warming as our initial median assumptions.
Three of the reviewers, however, suggested sub-
stantially higher sensitivities than reflected in the initial
draft report. Schneider agreed with Manabe that the
most likely long-term amplification would be 1 but
retained our initial assumptions regarding the likely lag.
He also suggested a relatively wide uncertainty range,
involving 2a limits of 0.5 and 2. While agreeing with the
initial adjustment times from the draft report, he added
that the adjustment would be (relatively) slower in cases
where the warming is more rapid. Therefore, he sug-
gested a 0.5 correlation between the adjustment time and
both emissions and temperature sensitivity.
Rind and Hoffert both suggested that circumpolar
ocean temperatures should warm more than the global
average, in equilibrium. Rind suggested 2a limits of 1
and 3, the same as his suggested range for air tempera-
tures. He noted, however, that the North Atlantic deep
water tends to stabilize both sea ice and circumpolar
water temperatures, so that very little warming could
occur until warmer North Atlantic water arrived. Based
on Broecker & Takahashi's (1981) estimate that it takes
80 to 90 years for deep water to arrive from the North
Atlantic, Rind specified an absolute lag of 80 to 90 years;
i.e., rather than assuming a linear adjustment in which
some wanning occurs immediately, he assumed that the
global warming in a given year alters the circumpolar
ocean temperatures 80 to 90 years later.
Hoffert also suggested that the impact of global
warming on water temperatures could eventually be as
great as the impact on air temperatures. As with polar air
temperatures, however, he assumed that the amplification
factor starts out at 1 and rises with temperatures up to a
maximum value of P3, as AT rises from 1 to Tw; P3 has
2a limits of 2 and 4. However, unlike air temperatures,
where the amplification factor is the ratio AT^^/AT, for
water temperatures this amplification factor represents
the derivative dTcdw/(fY. For example, for his median
48
-------
Climate Change
assumptions of P3=3 and Tw=5, and using values of
AT=1,2, and 3°C, his assumptions imply derivatives of
1,1.5, and 2, and ATcdw=l, 2.25, and 4"C, respectively.
For a warming of 5°C, however, Hoffert's median
assumptions imply equilibrium circumpolar ocean
warming of 7°C. Thus, Hoffert assumes that for each
degree of global warming, the circumpolar ocean warms
in equilibrium by less than the polar air temperatures,
until AT=TW. At this point, Hoffert assumes that per-
manent sea ice would disappear, removing the primary
process that prevents the circumpolar ocean from warm-
ing as much as polar air temperatures. Hoffert assumes
that the circumpolar ocean warming lags behind global
warming with a linear adjustment. He assumes a medi-
an e-folding time of 86 years, with 3o limits of 25 and
300 years, which implies 2a limits of approximately 40
and 200 years. Thus, Hoffert, Rind, and—to a lesser
extent—Manabe expect greater equilibrium warming of
the polar ocean than assumed in the draft report; but they
also expect a slower adjustment.
Sea Ice
Only two of the reviewers recommended a change
in our sea ice assumptions. Rind suggested that, for the
most part, the Parkinson & Bindschadler (1982) study
(i.e., a 5°C warming causes a 50 percent reduction) over-
estimated the response of sea ice, because it omitted the
stabilizing influence of North Atlantic Deep Water. He
therefore suggested that it would be more appropriate to
assume that the decline is only one-half as great as
assumed in the draft report. In the (10 percent) cases
where deepwater formation declines, however, this sta-
bilizing influence would be diminished, and thus the ini-
tial draft assumptions would be more appropriate.
Hoffert, by contrast, thought that the Parkinson &
Bindschadler study understated the decline in sea ice.
Hoffert (1990), for example, suggested that a 4°C glob-
al warming would eliminate all of the permanent sea ice.
However, because the Antarctic models employed in
Chapter 5 depend on annual seaice formation, not the
total extent of sea ice, we used the Parkinson &
Bindschadler sensitivities for the Hoffert simulations.
Implications of Reviewer Comments
for Projecting Sea Level
The net effect of the comments from the review-
ers of Chapter 3 is to substantially widen the uncertain-
ty range compared with the initial report. At the low end
of the spectrum, the incorporation of Robert Balling's
comments ensures that approximately one-eighth of the
simulations assume temperature sensitivities (AT2x)
well below the low end of the consensus range adopted
by the NAS (1979), IPCC (1990), and others. The net
effect is that the median and mean values of AT2x are
2.4 and 2.7°C (as opposed to 2.6 and 3.0°C in the
draft), with 25 percent of the simulations using values
below 1.5°C.
At the high end of the spectrum, the reviewer
comments tend to slightly depress projections of future
temperatures. Three of the eight reviewers—Balling,
MacCracken, and Wigley & Raper—compressed the
upper end of the distribution in some fashion, but the
overall effect is relatively small, with 13 percent of the
simulations having values of AT2X that exceed 4.5°C,
and 5 percent exceeding 6°C.
The reviewer comments for n and w have a
greater impact at the high end of the range: The com-
bined comments of Manabe, Hoffert, Rind, Schneider,
and MacCracken imply that w declines by at least 80
percent for about one-fifth of the simulations in which
warming eventually exceeds 5°C (in addition to the
more modest declines that occurred in about half the
simulations in the draft report). Given the 0.5 to 0.75°C
cooling that Figure 3-4 shows for the more modest
decline in upwelling, this greater decline reduces warm-
ing by about 1°C by the year 2100. In addition, two
reviewers suggested substantially higher values of n.
For a small warming, the Rind and Hoffert comments
imply that about 20 percent of the simulations have a
value of n exceeding 0.6, with about 15 percent having
a value greater than 1.0. As Figure 3-4 shows, this high-
er value could decrease warming by about 0.5°C in the
median temperature scenario.33
The slower warming, however, is offset by the
increased thermal expansion implied by reduced
upwelling. As Figure 3-4 shows, even a modest decline
in w results in a one-third increase in the warming at a
depth of 500 m; and the resulting expansion of the ther-
mocline more than offsets the reduced expansion of the
mixed layer that results from the smaller surface warm-
ing. Higher values of n enable the deep ocean to warm
more; a value of Tt=l results in 20 percent more expan-
sion after 100 years than a value of 0.2. Thus, five of the
eight reviewers increased the upper estimates of thermal
expansion for a given level of atmospheric forcing by
about 15 percent. Of the remaining reviewers, the
33The 1%-high temperature estimate for the year 2050 from
Schneider's assumptions is almost twice the estimate implied by
Manabe's assumptions. The only material difference in their assump-
tions are the values for jc and w: Schneider allows thermohaline cir-
culation to increase in some scenarios, while Manabe has a substan-
tial decrease. See Appendix 1 and Figure 3-13, infra.
49
-------
Chapter 3
Balling and Wigley & Raper assumptions both implied
substantially lower 1%-high estimates. All of Balling's
estimates had low sensitivities, and because of their nar-
rower range for AT2X Wigley & Raper also had a down-
ward impact. But these moderating assumptions had a
small impact on the high end of the range for the over-
all assessment, for two reasons. First, these comments
removed only about 10 percent of the high-temperature
simulations. Second, the mathematics of, for example,
a normal distribution are such that even if half of the
reviewers eliminated all of their high-scenario esti-
mates, the overall 1%-high estimates would rise if the
other half of the reviewers increased o by 15 percent.
Perhaps most important, the reviewers expanded
the high end of the uncertainty range regarding the
polar temperature estimates that the Greenland and
Antarctic models use in Chapters 4 and 5. Three of the
reviewers substantially increased the high estimates of
Greenland temperature sensitivity, outweighing any
downward impact on the high end from the revisions
suggested by Manabe and MacCracken; the low end of
the range was also broadened.
Similarly, half of the reviewers suggested that
eventually, the Antarctic circumpolar ocean is likely to
warm as much as the Earth's average temperature
warms, with three of the reviewers suggesting that the
polar water could warm twice as much. Even assuming
a lag on the order of one hundred years, such a sensi-
tivity suggests that the Antarctic ocean could warm by
6 to 8°C in the next two centuries. By comparison,
studies of the potential sensitivity of Antarctica have
assumed only a 1°C circumpolar ocean warming (see
Chapter 6). If, as the reviewers suggest, there is a sig-
nificant risk that circumpolar ocean temperatures could
warm 4 to 8°C, recent assessments of the vulnerability
of Antarctica may have overlooked the most plausible
scenario by which a disintegration of the West Antarctic
Ice Sheet could occur.
Final Results
Table 3-7 and Figure 3-13 summarize the cumu-
lative probability distribution for thermal expansion and
global temperatures. The net effect of the reviewer sug-
gestions was to lower the median estimate of global
warming from 3.1°C in the draft report down to 2.0°C.
A small part of this lowering resulted from including
the Balling estimates; but even when his assumptions
are excluded, the median estimate is 2.2°C. The prima-
ry reason the reviewer assumption lowered our estimate
is that our median forcing estimate for the year 2100
was 4.9 W/m2, 20 percent less than the median value
from the draft report. At the high end of the spectrum,
the temperature estimates are also about one-third
lower. As a result of the random forcing, the low end of
the distribution includes a 2 percent chance that tem-
peratures will decline.
The median thermal expansion estimates were
also lowered by about one-third as a result of the
reviewer assumptions. At the high end of the spectrum,
however, the reviewer assumptions only decrease the
estimate slightly: In those cases, the lower forcing and
temperature estimates are mostly offset by the large
declines in thermohaline circulation, which enables the
thermocline to warm more.
The importance of the different assumptions for n
and w increases over time. By 2100, the Manabe
assumptions imply a median thermal expansion 27 per-
cent greater than the Schneider median, which is
depressed by an assumed 20 percent chance of
increased upwelling; by 2200, this ratio grows to 37
percent. The difference is reversed for the upper tails of
the distribution because some of Schneider's runs have
large declines in w and high values of n, which increase
thermal expansion. Wigley & Raper's low values for n
and 6—as well as a narrower range for AT2X—result in
the least risk of a large thermal expansion. The global
temperature projections show small variation across
reviewers other than for Balling and Wigley & Raper.
Figures 3-14 and 3-15 illustrate the dynamics of
thermal expansion and global temperatures for selected
simulations. Between 2060 and 2090, three of the sim-
ulations include a sudden decrease in deepwater forma-
tion, which results in a global cooling of about 1.5°C
over a ten-year period. For the next century, the rates of
warming are mostly between 0 and 0.3°C per decade;
but 5 to 10 percent of the simulations warm more than
0.5 °C during at least one decade. After the year 2100,
temperatures continue to rise in all but a few cases; but
the rate of warming is less than 0.25 °C per decade in all
but a handful of cases. The rates of thermal expansion,
by contrast, do not exhibit the deceleration evident for
the rate of global warming.34
The polar temperature estimates (Figures 3-16 and
3-17) show considerably more variation across review-
ers than global temperatures and thermal expansion.
Manabe's suggested lag of 100 to 300 years, for example,
implies that, for the year 2100, Prob(ATcdw<1.0)=75%
and Prob(ATcdw<2.0)=98%. By contrast, Schneider's
^See Figure 3-4 and accompanying text for an explanation.
50
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Climate Change
TABLE 3-7
CUMULATIVE PROBABILITY DISTRIBUTION OF GLOBAL WARMING
AND THERMAL EXPANSION OVER 1990 LEVELS
Cumulative
Probability (%)
Change In Temperatures (°C)
2050 2100 2200
Thermal Expansion (cm)
2050 2100 2200
la
5a
10
20
30
40
50
60
70
80
90
95
97.5
99
99.5a
99.9a
Mean
o
-0.13
0.12
0.31
0.55
0.73
0.88
1.0
1.2
1.4
1.6
1.9
2.2
2.5
2.9
3.1
5.0
1.08
0.66
-0.12
0.26
0.57
1.0
1.4
1.7
2.0
2.4
2.7
3.2
4.0
4.7
5.4
6.3
6.9
8.7
2.2
1.4
-0.17
0.37
0.84
1.6
2.2
2.8
3.4
4.0
4.8
5.8
7.4
9.1
10.9
12.7
14.1
18.5
3.9
2.7
-0.5
1.1
2.5
4.7
6.2
7.4
8.6
9.8
11
13
16
18
21
23
25
32
9.7
3.4
-0.8
2.3
5.1
10
14
17
20
23
26
31
38
45
50
58
64
73
21
13
-1.6
3.8
9.9
20
28
36
44
52
62
76
99
120
139
163
181
215
50
36
"These estimates are included for diagnosis purposes only. Because the focus of the analysis was on the risk of sea level rise rather than sea level
drop, less effort has gone into characterizing the lower end of the distribution.
more rapid response implies that Prob(ATcdw>1.0)=80%
and Prob(ATcdw>4.0)=5%. Although Hoffert and Rind
believe that, in equilibrium, ATcdw could be two to four
times AT, their long adjustment times keep their estimates
of ATcdw from exceeding those of Schneider until after
2100. Combining all the distributions, the median esti-
mate of ATcdw for the year 2100 is 0.85°C; and 6 per-
cent of the simulations had values greater than 3°C. The
variation for Greenland temperatures is even greater.
Combining all the assumptions, the median estimate for
^Greenland K 2.5°C, but Green-land temperatures rise
more than 10°C in 2.5 percent of the simulations.
Because the reviewers all assumed that Green-
land warming would be a simple multiple of global
warming, the dynamics of Greenland temperatures fol-
low the same overall pattern as that of global tempera-
ture change (Figure 3-16a). Thus, temperatures in
Greenland decline 1.0 to 1.5°C for the three simula-
tions where deepwater formation declines suddenly.35
The dynamics of circumpolar ocean temperatures, by
contrast, are very different from that of global temper-
atures as a result of the 50-to-100-year adjustment peri-
od (Figure 3-17a). The net effect is to smooth the
"bumpy" changes in global temperatures, except for
those simulations representing the Rind assumptions.36
35Our simple approach implies that the decline in Greenland tem-
peratures (resulting from a shutdown in deepwater formation)
depends on the amount of global warming. A more realistic model
might make the polar-equator temperature difference depend on
deepwater formation for a given global temperature.
-^Rind's assumed fixed lag implies that the bumps in Greenland tempera-
tures are reproduced 80 to 90 years later m CDW.
51
-------
Chapter 3
95 —
90 ^
70 —
•g 50 -
o —
°- 30 -
10 -^
05 —
-0
99
,95 —
90 ^
.70 —
ni 50 —
30 —
.10 -»
.05 —
m
-1
, • i ;. , • K, i * f ^
Balling/'' ***?///
' / J'
/ • '// - - - - - Hoffert
> / r ' MacCracken
' / /
/ ' i / Schneider
/ -- / '/' Total
/' , // / A
1 ' 1 1 ' V 1 1 1 I
50 1 2 34567
Average Surface Warming, 1990-2100 (°C)
•••'/•'•'• v" x^r
/ Balling / /^
/'"'' / //•
i / Wigley/' ///
1 //?
I V
1 // '
1 &' '
\ $
! ///
' / W
! {(•:< Hnffbrt
1 / !•! MarTrarttan
\ 1 1// Schneider
; / /'/
00 10 20 30 40 50 60
X
"?•
—
•<:
T;
—
7
^
—
^ •*
i
* ^
> -z
—
0
/ Wigley /'' ^ ^
Balling/ \ / ^ /
\; //' /
^ ^ ^
I /,/
.fi ~
,' , // Hoffert
// Schneider
/ /// T°tal
/. //
i ' V i
10 56 10 15 1
Average Surface Warming, 1990-2200 (°C)
I / I I *•' I ^- •• — -"^
/Balling Wigley /' ,'/• ^
\/ \/ //
> 1 //
/ ,'' ^^" ^
1 t' ^-^ -^ —
/ S j, /
1 / ' / / '
1 / /
/ ,fi ]
' / / •'
1 ///.''
/ /'.-' —
*> ( ' /I Hnffart ~?
1 ' *
' / // Schneider
,'/ //
i i i
00 50 100 150 1
95
>90
70
50 (0
-Q
O
30
^ 10
05
6
95
^90
70 £
50 ^
.30
>10
.05
iO
Thermal Expansion, 1990-2100 (cm)
Thermal Expansion, 1990-2200 (cm)
Figure 3-13. Cumulative Probability Distributions of Surface Warming and Thermal Expansion by Reviewer.
Several curves were removed for clarity. The Rind estimates generally track Schneider because both include the pos-
sibility of both increased and decreased upwelling, along with high values of K. The Bretherton and Manabe estimates
generally track MacCracken, but Manabe's thermal expansion estimates are closer to those of Hoffert due to the large
decline in upwelling both researchers expect.
52
-------
Climate Change
1990
2050
-!•- I- t—|--f—1 —I- f— -I- -I 1 -I—
2100 2150 2200
Year
Figure 3-14. Spaghetti Diagrams of Thermal Expansion. Selected simulations for (a) thermal expansion and
(b) rate of thermal expansion for the years 1990-2300. See Figure 2-5 and accompanying text for additional expla-
nation of the scenarios selected.
53
-------
Chapter 3
1990
2050
2100
Year
2150
2200
Figure 3-15. Spaghetti Diagrams of Global Warming. Selected simulations for (a) global temperatures and
54
-------
Climate Change
0.75 +
0.25
0.25
-0.5
2000
2050
2100
2150
Year
2200
2250
2300
(b) rate of global warming through 2300. See Figure 2-5 and accompanying text for additional explanation of the
scenarios selected.
55
-------
Chapter 3
2!
O
2 H I ---I—f 1 —I 1- -I
b •*»
Balling /
V
/ // / x
Hoffert
MacCracken
Schneider
Total
.01
-0.5 01235 10 12
Greenland Warming, 1990-2100 (°C)
Figure 3-16. Greenland Warming, (a) Selected simulations for the period 1990-2300 and (b) cumulative proba-
bility distribution by the year 2100 for various reviewer assumptions.
56
-------
Climate Change
1990
2250
2300
Balling/
\/Manabe/ Hoffert - ^
I V YS t
I ////
- MacCracken
Rind
Total
T
234
CDW Warming, 1990-2100 (°C)
Figure 3-17. Circumpolar Ocean Warming, (a) Selected simulations for the period 1990-2300 and (b) cumula-
tive probability distribution of circumpolar ocean warming by the year 2100 for various reviewer assumptions.
57
-------
Chapter 3
7 -
2050
Figure 3-18. Spaghetti Diagram of Antarctic Air
Temperatures. Selected simulations showing the
change in Antarctic air temperatures for the period
1990-2300. See Figure 2-5 and accompanying text for
additional explanation of the scenarios selected.
PARTB: CHANGES IN POLAR
PRECIPITATION
Chapters 4 and 5 show that warmer temperatures
could increase the rates of melting in Green-land and
Antarctica and thereby contribute to sea level. These
contributions could be offset, however, by the increased
snowfall that would probably accompany warmer tem-
peratures—particularly in Antarctica. If nothing else
changed, a doubling of precipitation over Greenland
would lower sea level 1.3 mm/yr (Cf. Ohmura & Reeh
1991); a doubling over Antarctica would lower sea level
4.2 or 5.6 mm/yr (Bentley & Giovinetto 1990), depend-
ing upon whether one includes the precipitation that
falls onto the ice shelves.37
Greenland
Previous assessments of the likely impact of
global warming (e.g., Huybrechts & Oerlemans 1990)
''Precipitation on the floating ice shelves does not directly lower
sea level; however, several of the models used in Chapter 5 assume
that thinning of the ice shelves eventually affects sea level by
increasing the rate at which ice streams flow into the shelves.
have modeled changes in precipitation based on
changes in the saturation vapor pressure V(T) (i.e., the
amount of water vapor held by a saturated atmosphere
at a given temperature and pressure). The simplest
approach is to assume that precipitation is proportion-
al to saturation vapor pressure:
Precipt = V(Tt)/V(T0) PreciPo
(A).
If snowstorms release all (or a fixed portion) of the
water vapor in an air mass, such a representation is
reasonable. On the other hand, if rainstorms involve
cooling of a fixed number of degrees N, then precipi-
tation should be proportional with the change in satu-
ration vapor pressure that results from this cooling:
Huybrechts & Oerlemans (1990) use a similar
specification, which is equal to the limit of equation
(B) as N approaches zero:
= V'(Tt)/V'(T0)Precip0
(C),
where V'=dV/dT.
The draft assumed that precipitation changes
are lognormally distributed, with equations (A) and
(C) treated as the 2a limits and T representing air
temperatures at sea level. Following the conven-
tion of IPCC (1990) among others, we based pre-
cipitation changes on TGreeniand, rather than on
Tglobal- In cases where Greenland temperature
warmed less than the global temperature, however,
we used global temperature. The primary justifica-
tion is that the circumstances most likely to cause
Greenland to warm less than the global average
would involve declines in the formation of North
Atlantic Deep Water, caused by increases in North
Atlantic precipitation.38
These representations are crude, failing to allow
for seaice retreat and the resulting increase in moist
convection, possible changes in the lapse rate, and
other changes in meridional circulation. Some of these
38The practical significance of this assumption is that it allows for
the possibility of an increase in the Greenland Ice Sheet, when sig-
nificant increases in precipitation caused by a general rise in glob-
al temperatures coincide with a small increase in melting caused by
a smaller rise in Greenland temperatures. In the final results, this
is most likely to happen in the Manabe-based simulations and the
5 percent of the time that Rind projects a drastic decline in
upwelling, as well as some of the MacCracken runs.
58
-------
Climate Change
TABLE 3-8
INCREASES IN ANTARCTIC ACCUMULATION WITH 1°C WARMING
(GigatonsfC)
Using Saturation Vapor Pressure
Absolute Derivative
Interior
Coastal
Shelf
61.6(7%)
60.0 (6.4%)
18.4 (6.5%)
57.1
55.5
17.0
95%-Low
43.6
-9.2
23.7
Regression
Mean
50.2 (5.7%)
21.1 (2.2%)
32.8(11.4%)
95%-High
56.8
51.4
41.9
SOURCE: Fortuin & Oerlemans (1990).
TABLE 3-9
ANTARCTIC PRECIPITATION BASINS EMPLOYED IN THIS REPORT
Regions Employed Herein
W. Antarctic ice shelves
Antarctic Peninsula
West Antarctica
East Antarctica
SOURCE: Fortuin & Oerlemans (1990).
Corresponding Grouping
from Oerlemans Analysis
Ice Shelves
Escarpment
Antarctic Interior
Antarctic Interior
Accumulation
(km3/yr)
286.9
937.4
106.5
773.5
changes are addressed by general circulation models
(GCMs); future studies should compare their results
with the implications of these assumptions.
Antarctica
As with Greenland, previous assessments have
assumed that precipitation will change with saturation
vapor pressure. However, Fortuin & Oerlemans (1990)
have done more empirical work on the relationship,
with a cross-sectional analysis of 876 annual surface
mass balance measurements and 927 temperature mea-
surements. Because the analysis used cross-sectional
regression rather than time series, it is possible that it
incorrectly assumed that temperature differences are
responsible for differences in accumulation rates that
are, in reality, caused by other factors such as proximi-
ty to the coast. Nevertheless, we follow IPCC's (1990)
convention of using this analysis.
The draft did not seasonally disaggregate precip-
itation changes. Because winter precipitation is gen-
erally much less than summer precipitation, the use of
an annual average tends to overstate precipitation
increases in regions where winter warming is greater
than summer warming.39
Superficially, the Fortuin & Oerlemans Antarctic
work also differs from the Huybrechts & Oerlemans
Greenland study in that the former use the temperature
of the "free atmosphere" (i.e., the altitude below which
air temperatures increase with increasing altitude in the
stable Antarctic atmosphere). However, because they
assume that Tfree=0.67Tsurface-1.19, rather than using
independent measurements, die regressions are mathe-
matically equivalent to using surface temperatures.
Table 3-8 compares the results from the regression with
those obtained using saturation vapor pressure or its
derivative with respect to temperatures.
The draft assumed that the regression equations
and the equations based on saturation vapor pressure
have equal validity. Therefore, we sampled (a) 50 per-
cent of the time from a distribution whose a limits are
the results obtained from the saturation vapor pres-
sure and the derivative of saturation vapor pressure
and (b) 50 percent of the time from the distribution
implied by the Fortuin & Oerlemans (1990) regression
equations, treating their 95 percent confidence interval
as 1.96o limits in a lognormal distribution. We divided
the continent into four regions, as shown in Table 3-9.
39Because P!>P2 most of the time, this will generally be the case
for our scenarios of Antarctica.
59
-------
Chapter 3
0 30 60 90 120 150 180 210 240 270 300 330 360 390
Years
Figure 3-19. Antarctic Precipitation for Selected
Scenarios in the Draft Analysis. A doubling of pre-
cipitation would lower the rate of sea level rise by 4.2
to 5.6 mm/yr, holding everything else constant.
Because disaggregation should not diminish our
uncertainty about total precipitation, the draft also
assumed that the uncertainties regarding precipitation
changes for the four regions were perfectly correlated.
Figure 3-19 illustrates the draft precipitation results for
selected simulations.
Expert Judgment
We did not set out to have a different set of review-
ers for the precipitation portion of this chapter. The
alternative set resulted from reviewer self-selection.
Most of the climate modeling reviewers of Chapter 3
chose not to provide comments on the precipitation
portion of this chapter. On the other hand, three of the
glaciology reviewers chose to provide comments on
polar precipitation even though we had originally
assumed that they would confine their recommendations
to Chapters 4 and 5. Although projecting polar precipi-
tation is, in principle, a climate modeling question, it is
clearly a greater practical concern to glaciologists and
others who study the polar regions (see Table 3-10).
The climate modelers did not substantially change
the precipitation scenarios. Schneider and MacCraken
were satisfied with our initial specifications; Rind's only
comment was to use the saturation vapor pressures
for both hemispheres. One of the polar researchers,
Michael Kuhn, endorsed the approach of relying on
absolute saturation vapor pressure, noting that regres-
sions may yield results based on synoptic anomalies.
The other two polar researchers, by contrast, sub-
stantially widened the uncertainty range. Richard Alley
suggested that relying on thermodynamic relations such
as saturation vapor pressure may overstate precipitation
changes by at least a factor of two. He argued that many
years of Danish work (e.g., Clausen et al. 1988) have
shown empirically that precipitation increases by only
5 percent per degree (C) rather than the 10%/°C implied
by saturation vapor pressure. Moreover, he noted that
during the Holocene, the sensitivity may have been as
low as 1%/°C (Kapsner 1994; Kapsner et al. 1993). We
Richard Alley
Michael Kuhn
Michael MacCracken
David Rind
Stephen Schneider
Jay Zwally
TABLE 3-10
REVIEWERS OF PRECIPITATION ASSUMPTIONS
Pennsylvania State University
Innsbruck University
Lawrence Livermore National Laboratories
NASA7Goddard Institute for Space Studies
National Center for Atmospheric Research
NASA/Goddard Space Flight Center
University Park, PA
Innsbruck, Austria
Livermore, CA
New York, NY
Boulder, CO
Greenbelt, MD
60
-------
Climate Change
Alley
Kuhn
Zwally
Total
234
Greenland Precipitation, 1990-2100 (mm/yr)
5 53
Figure 3-20. Changes in Greenland Precipitation,
Sea Level Equivalent. Cumulative probability dis-
tribution for the year 2100, assuming that the current
rate is 1.33 mm/yr; the Rind, MacCracken, and
Schneider precipitation assumptions were essentially
the same as those of Kuhn.
treated these observations as a limits for the sensitivity of
Greenland precipitation (see also Kapsner et al. 1995).
For Antarctica, Alley views the thermodynamic
sensitivity of 10%/°C as a bit more reasonable than for
Greenland, but suggests that it is probably on the high
side; we treat it as his 1/2 o-high limit. He also states
that the o-low should be no higher and possibly
lower than 5%/°C; we treat 4%/°C as his a-low limit.
Assuming a normal distribution, Alley's assumptions
imply a median of 8%/°C and a o-high limit of 12%/°C.
Jay Zwally suggested even more uncertainty
regarding future precipitation changes. In Zwally (1989),
he showed in a footnote that the existing literature sup-
ports sensitivities ranging from 5 to 20%/°C. Since that
time, however, ice core data has been published sug-
gesting a sensitivity of about 3%/°C. Therefore, Zwally
recommends 2a limits of 3%/°C and 20%/°C for both
Greenland and Antarctica.
Final Results
The combined assumptions imply a 50 percent
chance that, by 2100, Greenland precipitation will
increase 20 percent, and a 5 percent chance that it will
double, as shown in Figure 3-19. Figure 3-20 shows that
the changes in Antarctic precipitation follow a similar
1990 2050 2100 2150 2200 2250 2300
1990 2050 2100 2150 2200 2250 2300
Figure 3-21. Spaghetti Diagram for Polar Precipitation,
Sea Level Equivalent Changes in (a) Greenland and (b)
Antarctic precipitation for selected simulations, 1990-2300.
Current rates of precipitation lower the rate of sea level
rise by 1.3 and 4— 5 mm/yr for Greenland and Antarctica,
respectively. See Figure 2-5 and accompanying text for
an explanation of the scenarios illustrated.
61
-------
Chapter 3
pattern. As discussed in Chapter 5, the increased pre-
cipitation in Antarctica more than offsets the melting
effect of warmer temperatures for most scenarios. In
Greenland, by contrast, the precipitation is small
compared with the increased melting.
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63
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Chapter 3
64
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CHAPTER 4
GREENLAND ICE SHEET
If the Greenland Ice Sheet melted completely,
sea level would rise 7.6 meters (Hollin & Barry 1979).
Even with today's climate, the ice sheet is melting at a
rate greater than the annual snowfall in places where
the surface is within about fifteen hundred meters of
sea level. This elevation, where melting and snowfall
are equal, is known as the "equilibrium line." The ice
sheet continues to exist because most of the ice sheet is
above the equilibrium line.
For about one hundred meters above the equi-
librium line, ice melts and runs off to the sea, albeit at
a rate less than the annual accumulation rate. Above
this elevation, known as the "runoff line," some melt-
ing occurs, but all of the water refreezes in place.
Consider the land-based analogy: Small storms and
small springs form puddles and ponds whose water
does not run off to the sea, while larger storms and
springs form floods and rivers whose water does flow
to the sea. Analogously, unless the amount of melting
exceeds a certain level, the melt water will not form
the conduits necessary to reach the surface and sub-
terranean "streams" that extend up to the runoff line.
As we discuss below, melt water appears to run off
only where annual melting is at least 58 to 70 percent
of the annual snowfall. Finally, about one hundred
meters above the runoff line is the "melt line," above
which there is typically no melting.
Greenland would have to warm about 15 to 20°C
to place the entire ice sheet below the equilibrium line.
Nevertheless, a more moderate warming will increase
both (1) the elevation below which melting and runoff
take place and (2) the rate of melting in areas where
melt water is already running off into the sea.
Counteracting those effects, warmer temperatures
could increase precipitation rates. Like previous stud-
ies, this analysis concludes that enhanced melting will
probably exceed the increased precipitation.
IPCC (1990) cites four models of the sensitivity
of the Greenland Ice Sheet to warmer temperatures.
We base our model on the earliest of those models,
Bindschadler (1985). For most practical purposes,
the results would not be substantially different had
we used the other models.1 The model characterizes
Greenland's cross-section as a parabola. It assumes
that, below the runoff line, annual melting and runoff
is a linear function of altitude and that accumulation in
the form of snowfall is constant throughout the ice
sheet. Thus, the impact of warmer temperature sce-
narios from Chapter 3 is a higher runoff line, which
implies increased melting at all elevations below that
line; the impact of precipitation changes (also from
Chapter 3) offsets some (and in some cases all) of that
increased runoff. The model assumes that all precipi-
tation is in the form of snowfall; hence, it does not con-
sider the direct runoff or accelerated melting that might
result if warmer temperatures changed the physical
state of precipitation from snow to rain.
We make four modifications to Bindschadler's
model to (1) allow for ablation (mostly melting2) and
runoff in areas where melting is less than precipita-
tion; (2) explicitly constrain the mass implied by the
model to the actual mass of the Greenland ice sheet;
(3) consider the lag between warming and runoff due
to refreezing; and (4) adjust the profile of the glacier
after each timestep.
'Aside from being the earliest model, the Bindschadler model is per-
haps the simplest. In a review of the draft manuscript, Roger J.
Braithewaite of the Geological Survey of Greenland in Copenhagen
states:
The Bindschadler model...is very simple, but later and sup-
posedly better models do not give dramatically different results.
The best model of Greenland's contribution to sea level is by
Huybrechts et al. (1991), which combines ablation, dynamics, and
bedrock in a 3D distributed grid. This was developed in Germany
but also uses information and ideas from [the Geological Survey
of Greenland]. Our approach is to collect new data sets from
Greenland, in cooperation with other European groups, to remedy
shortcomings in the model rather than simply tinkering with it....
The Huybrechts model has whistles and bells so even with a
CRAY-2 you don't have much room [to consider other process-
es]....In the meanwhile, under the European Ice Sheet Modelling
Initiative, Niehls Reeh of the Danish Polar Centre is developing a
more portable version of the ablation part of the Huybrechts
model. When finished, it will be used to calculate the short-term
response of the surface balance to climate sce-narios without the
longer term dynamic response....Sadly for [this EPA report,] this
model is not available yet....
2Ablation includes melting, sublimation, and evaporation. We
focus on melting because (1) the change in ablation resulting from
climate change is likely to result mostly from increased melting,
and (2) to the extent that sublimation and evaporation are signifi-
cant, the impacts of warmer temperatures are roughly proportion-
al to the impact on melting.
65
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Chapter 4
Ablation
Bindschadler treats Greenland's cross-section
as a parabola whose altitude is described as:
y = Hpeak(l-x/L)l/2
with Hpeak=3250 m representing the altitude of the
glacier and L representing the distance from the apex
to the coast, a variable for which he solves.3
Bindschadler assumes that annual (net) ablation
(b) is a linear function of altitude:
b = d (He - y) for y < He
= 0
a = 0.35 m/yr
= 0
for
for
for
y>He
yHe + a/d(i.e.,y>1729m).
The only functional difference between Bindschadler's
approach and ours is that the former assumes that abla-
tion (and hence runoff) declines linearly with altitude
up to the equilibrium line where it equals accumulation,
beyond which it drops to zero. Our approach, by con-
trast, assumes that runoff continues to fall off linearly
above the equilibrium line until it reaches zero at the
runoff line (1729 m). (We return to this distinction
below, when we discuss the delay caused by refreezing.5)
Following Bindschadler, we calculate B, the total
ablation for a given cross-section, by integrating over
areas where there is ablation—in our case values of x in
which y
-------
Greenland Ice Sheet
4000
Runoff Line
Equilibrium
Line
MELTING
Runoff Line
Equilibrium
Line
'•^—Initial Profile
V* V- After Ablation
MELTING
-Initial Profile
-After Ablation
500
4000
Runoff Line
Equilibrium
Line
ACCUMULATION
4000
Runoff Line
Equilibrium
Line
ACCUMULATION
Initial Profile
After Ablation
', Ablation and
7" Accumulation
4000
Runoff Line
Equilibrium
Line
ADJUSTMENT
4000
Runoff Line
Equilibrium
ADJUSTMENT
New Profile = Initial Profile
Figure 4-1. Two-Dimensional Schematic of the Greenland Ice Sheet. The profiles in (a) show the framework
employed by Bindschadler; (b) shows our modification. In each case, the first diagram shows the initial profile (dot-
ted) and a new profile (solid) after one period's melting. Note that the Bindschadler scheme assumes no runoff above
the equilibrium line, implying a slight discontinuity; this is the main difference between the two approaches. The
second diagram shades the accumulation that takes place, with the solid line showing the net impact of ablation and
accumulation, and the dashed curve showing only the effect of ablation. The final diagram's solid line shows the
profile adjustment after each time period. Bindschadler's model does not have a mass constraint (i.e., the profile
simply returns to its position at the previous time period). This analysis adjusts the profile by calculating a new
parabola whose area is reduced by the net of ablation and accumulation.
67
-------
Chapter 4
Figure 4-2. Schematic of Bindschadler (1985) Model.
Extrapolating the 2-D model to three dimensions by a scal-
ing factor of 5000 km is equivalent to assuming two para-
bolic cylinders back-to-back, with transverse (longitudinal)
length of 2500 cm. Greenland is drawn to the same scale.
Scaling and Mass Constraint
At this point, we must discuss a second way by
which we depart from Bindschadler's approach. Because
the circumference of Greenland is approximately 5000 km,
Bindschadler scales the two-dimensional model to three-
dimensional reality by multiplying all results by 5000 km.
Implicit in this assumption is that the Greenland ice
sheet can be viewed as two parabolic cylinders back-to-
back with a transversal length of 2500 km, as shown in
Figure 4-2. The volume of such an ice sheet would be
3.85 million cubic kilometer, which is 28 percent more
than the 3 million cubic kilometer of ice found on the
continent (Hollin & Barry 1979).6 Because Bind-
schadler did not adjust the mass after each timestep to
6The effect of this assumption is to assume that the base of the ice
sheet is a plane tangent to the Earth's surface at sea level. In
reviewing the draft manuscript, Robert Bindschadler told us that
this is a reasonable assumption. Even if, for example, there are
occasional mountains intruding upward into the ice sheet, the net
effect of this assumption does not change total potential sea level
rise because the volume is still constrained to 3 million km3.
reflect the net contribution to sea level, the volume
implied by his assumptions was irrelevant.
We adopt a different procedure for two reasons.
First, as we discuss below, this exercise keeps track of
mass changes, so it is necessary to impose a meaningful
mass constraint. Second, scaling by 5000 km implies
that Greenland's current accumulation is 695 km3, which
is (coincidentally) 28 percent greater than the 535 km3
annual flux suggested by recent observations (Ohmura &
Reeh 1990). Thus, reducing our scaring factor to 3850
enables our assumptions to duplicate both the current
rate of accumulation and the current volume of the ice
sheet; so we adopt this scaring factor, which we call LL.
Parameter Values
Following Bindschadler, we assume that calving
is 0.04 km2/yr for each cross-section (i.e., 0.04 km3/yr
per km of shoreline). Assuming that the estimated
equilibrium-line elevation refers to a period when the
entire Greenland Ice Sheet was neither growing nor
shrinking,7 accumulation equals ablation plus calving:
A = B + C;
and we solve for L as follows:
3Hpe:
ale
Given the values for the parameters suggested by Bind-
schadler, L=397.86 km. To check our value of LL
against the mass constraint, we consider LL*, defined as
the value of LL that satisfies the mass constraint. LL*
can be calculated as the volume of the ice sheet divided
by the cross-sectional area. The cross-sectional area
under the parabola is simply 2/3 L Hpeak=862 km2; thus,
LL*=3,000,000 km3/862 km^^Okm, which is rea-
sonably close to our scaring factor of 3895 km.
Using estimates of the other parameters, our equa-
tions for current ablation and accumulation become:
Accumulation = LL A = 397.86 LL a/1000
0.00153 397.86 LL Hzb3
Ablation = LL B =
3 Hpeak2
7Future reports could solve for the distribution of L implied by the dis-
tribution of uncertainty regarding the recent mass balance of Greenland.
68
-------
Greenland Ice Sheet
where Hzj,=He+a/d, that is, the altitude of the zero-abla-
tion line, which is 1729 m under current conditions.
Given the equation explaining current runoff, the
sensitivity to warmer temperatures shows up as the
sensitivity of the zero-runoff line (Hzb) to warmer tem-
peratures.8 Bindschadler analyzes two scenarios based
on previous estimates of the warming required to raise
the equilibrium line by 100 m: 1.12°C and 0.6°C. This
study employs these sensitivities as a limits. Note,
however, that because accumulation increases with
warmer temperatures, the equilibrium line rises less
than the runoff line. We estimate the change in the
runoff line by assuming that a 0.6°C warming would
increase the baseline accumulation rate (35 cm/yr) by
1.8 cm/yr, and that a 1.1 °C warming would increase
precipitation by 3.4 cm/yr.9 Assuming that d=1.53 m
of ablation per year for each kilometer of elevation, the
runoff line would rise 100 m + 11.8 m for the 0.6°C
warming and 100 m + 22.2 m for the 1.1 °C warming,
implying that dHzbA^Greenland has a limits of 111.1
and 186.3 m per degree (C); we call this parameter Gj.
These values imply that, in areas where there is
melting, a 1°C warming increases annual melting by 17
to 28 cm. By contrast, even with the highest suggested
precipitation sensitivity (see Chapter 3B) of 20 percent
per degree (C), the model suggests that precipitation
would only increase by about 6 cm/yr. Nevertheless,
only about one quarter of the ice sheet is assumed to
be below the runoff line of 1729 m10; thus, an addi-
tional 6 cm of precipitation would add about the same
amount of mass as a 24 cm increase in the melt rate.
Therefore, the increased precipitation could more
than offset the increased melting in some of the
extreme scenarios.
Substituting our equation explaining the eleva-
tion of the runoff line,
Hzb = 1729 m + G AT
8Although the equation for ablation includes the equilibrium line
elevation, the presence of the constant term in the linear equation
implies that the term for equilibrium-line elevation is merely an
intuitively appealing way to present the equation. Equilibrium ele-
vation is, in fact, derived from existing data on elevation versus net
ablation. Thus, the term refers to equilibrium elevation given cur-
rent accumulation rates, not the equilibrium elevation that might
occur from alternate changes in precipitation. Assuming increased
precipitation, the actual equilibrium line will probably rise less
than would be expected given the current lapse rate, but this is
immaterial for estimating net ablation, since accumulation shows
up directly in the model.
9See Chapter 3B for a discussion of the impact of warming on
Greenland precipitation. These assumptions are based on the mean
of the results from assuming that precipitation changes in proportion
with the saturation vapor pressure or the derivative of the saturation
vapor pressure.
10This assertion follows from the parabolic form: y=3250(l~x/398)1/:z.
Setting x equal to 0,285, and 398 gives elevations of 3250,1729, and 0.
Greenland
into the previous equation, we have:
. , , . 0.00153 397.86 LL (1729 m + G, AT)3
Ablation = - - 1 — '-
6 Hpeak •
Thus, ablation is a cubic equation in temperature,
with AT showing up raised to the 1, 2, and 3 powers.
The linear term reflects the fact that once an area is
within the ablation zone (i.e., the area where net abla-
tion is greater than zero), the rate of ablation is linear
in temperature. The higher order terms reflect the fact
that additional areas of the glacier are brought within
the ablation zone: Had the glacier's profile been linear,
ablation would have been a quadratic; because the area
within the ablation zone is a quadratic, total ablation
becomes a cubic.11
Refreezing
The impact of refreezing is important for two rea-
sons: (1) after a part of the ice sheet is warmed, it
would take time to form a conduit by which the water
can flow to the sea; and (2) in areas where there is rela-
tively little melting, all of the melt water may refreeze.
For over a decade, glaciologist Mark Meier has warned
that by neglecting refreezing, estimates of the sea level
contribution from the Greenland Ice Sheet may be over-
stating the initial impact of global warming; we use the
results of an analysis by Meier and his colleagues at the
University of Colorado (Pfeffer et al. 1991).
The Lag Due to Refreezing
Suppose that the Greenland Ice Sheet warms and
new areas are brought within the melting zone. If the
ice sheet was a solid block of ice, the melt water would
run off into the ocean and contribute to sea level. But
there are many pores in the ice. Therefore, the initial
effect of bringing new areas within the melting zone
would not raise sea level at all; rather, the surface ice
would melt, and the water would percolate downward
and refreeze. Eventually, enough of the pores will be
filled and frozen to enable melt water to flow to the sea
through conduits formed by crevasses in the ice, rather
than simply flowing downward into the ice.
"Because G, is small compared with the initial elevation of the
zero-melt line, the effect of cubing the sum leaves the impact of the
cubed term smaller than the linear term until the warming exceeds
15°C, even for high values of Gj.
69
-------
Chapter 4
Pfeffer et al. (1991) considered models with
minimum and maximum delays due to refreezing.
Their minimum model represents, for practical pur-
poses, a near instantaneous formation of an "imper-
meable horizon 'perched' above the [ice sheet] which
remains permeable even after the establishment of
runoff."12 This model implies essentially no lag
between warming and runoff.
The maximum model, by contrast, assumes that
no runoff takes place until pores between the ice are
filled13 between a depth of approximately 70 m and
(for practical purposes) the surface. "This is an unreal-
istic requirement but results in a calculation of fill-in
time that is longer than any other process and as such
gives an upper limit on the time required to establish
runoff at some new elevation."14
In testing these models, Pfeffer et al. assumed that
the initial zero-runoff elevation is 1680 m (close to the
elevation we used). They considered the impacts of a
scenario in which temperatures warm linearly 4°C and
precipitation increases by 10 percent over the course of
a century, and remains constant thereafter. The mini-
mum model results in the zero-runoff elevation rising by
240 m after a century; the maximum model results in the
runoff line rising 150 m after 100 years and 190 m after
150 years.15 Simplifying the dynamics of the maximum
model implies an e-folding adjustment time of 50 years
for the maximum model.16 We assume that the
runoff line responds with an adjustment time of 63.17
12Pfeffer et al. at 22,120.
l3The pores only need to be filled to a "close-off density" of 83 g/cm3.
Id.
14W. at 22,119.
^Seeld. at 22,121, Figure 2.
16The equilibrium elevation of the zero-runoff line rises linearly
with temperature. Assuming that the transient elevation H^.^
adjusts linearly to its equilibrium value H2b,
Hpeak(t) = HpeakO - 1) + C [Hzb(t) - Hpeak(t-l)],
and 1/c is the e-folding time. A value of c=0.02 would imply ele-
vation changes of 140 and 202 m after 100 and 150 years, which
represent roughly equal under- and overestimates of the Pfeffer et
al. estimates of 150 and 190 m for those years.
1 ignoring refreeze, we calculate runoff by integrating the melt rate from
sea level up to the elevation where there is no melting, H^. When
refreeze is incorporated, the integrand remains the same; i.e., melting in
areas below the old runoff line (which equalled the zero-melt line)
increases by the same amount regardless of the impact of refreeze. The
upper limit of integration, however, is reduced: We now integrate from
sea level only up to the runoff line, which lags behind the zero-melt line.
Based on the Pfeffer et al. maximum model, the 2a
high limit is 50 years. For our median, we use 25
years, which is the average of the minimum and max-
imum models. Thus, our 2a low is 12.5 years.18
Even with the 2a lag of 50 years, the impact of
refreezing is not large for a small warming. Figure 4-3d
shows that for an instantaneous warming of 1°C, this
delay reduces the initial Greenland contribution by less
than 7 percent. Refreezing has no impact on areas that
were already below the runoff line; because the new
area brought into the melting zone is small compared
with the area where melt water was already running off,
the area of refreezing is small. For a faster wanning, by
contrast, the area brought within the melting zone con-
stitutes a greater portion of the total area where melting
is taking place, and the consideration of refreeze has a
greater proportional impact. Nevertheless, even for the
extreme assumption of an instantaneous wanning of
4°C, refreeze reduces the initial contribution by only
about 25 percent.19
Elevations Where All Melt Water Refreezes
In equilibrium, our calculations do not distin-
guish between the melt line and the runoff line; the lat-
ter simply approaches the former. Several authors,
however, point out that even in equilibrium, the upper
limit for runoff is below the zero-ablation line.20
Moreover, the original incarnation of the Bindschadler
model implicitly assumed that the runoff line is where
melting is 100 percent of precipitation.
Failing to make this distinction could lead a
model to overstate runoff for two reasons. Most
directly, a model will tend to overestimate the eleva-
tion of the initial runoff line and, hence, annual runoff.
Pfeffer et al. suggest that the Ambach & Kuhn (1989)
model overstates runoff even without a change in cli-
mate; this systematic overstatement accounts for
about 75 percent of the impact of refreeze they identify
18This estimate is slower than the instantaneous response implied by
the Pfeffer et al. minimum model. Although that model is clearly
unrealistic, we may have added a slight downward bias to some of
our higher simulations.
"These estimates are consistent with the differences that Pfeffer et
al. showed between the maximum and minimum models.
Pfeffer et al. (1991) (runoff line is elevation where melting
equals 70 percent of precipitation); Huybrechts et al. (1991) (60
percent). Reviewer Roger Braithwaite (Greenland Geological
Survey) adds: "I recently spent two years working on the meltwa-
ter refreezing problem and managed to refine Huybrechts 0.6 to
0.58, which is not a very impressive result...."
70
-------
Greenland Ice Sheet
in the first 100 years of their simulation. Because the
Bindschadler model uses an estimate of current
runoff to solve for the model parameters, however,
the impact of overestimating the elevation of the
runoff line is offset by a lower initial melting rate at
other elevations. In any event, our assumed initial
runoff elevation of 1740 m is only slightly higher
than the 1680 m elevation employed by Pfeffer et al.
The second consideration is that precipitation
changes and refreeze could interact to decrease the
sensitivity of the runoff line to increases in tempera-
ture. If precipitation increases, for example, the zero-
runoff line would rise by less than the zero-melt line,
even in equilibrium. Moreover, given the parabolic
shape, the total portion of the glacier between these
two lines would increase by a greater proportion than
the vertical elevation differences. For both of these
reasons, the area of Greenland that our model erro-
neously assumes to be contributing to sea level would
increase.21 Although the initial overstatement of melt
area is counteracted by the model parameters, the
increase is not. Given that the total impact of refreeze
in the Pfeffer et al. paper is 4.3 cm over 150 years,
however, the impact of our overstatement is unlikely to
be more than 1 cm.22
Calving
No models have been developed showing how
Greenland calving would respond to global warm-
ing. In the absence of any model, two reasonable
assumptions would be (a) no change and (b) calving
increases proportionately with melting. Bind-
schadler notes, however, that Sikonia (1982) found
empirically that calving increases with the 0.57
power of ablation.
The draft assumed that calving increases with
ablation raised to the G2 power, with 62 following a
normal distribution with a mean of 0.57 and 2a lim-
its of 0 and 1.14.
21At least until the entire ice sheet is within the ablation zone, after
which the area would decrease.
22According to the Pfeffer et al. analysis, 75 percent of the error from
ignoring refreeze stems from overstating the initial runoff elevation,
for which our parameter-selection compensates. Moreover, the
adjustment-time difference between the maximum and minimum
models accounts for at least half the remaining impact. Thus, the pre-
cipitation effect would be only one-eighth of the total impact of
refreezing, that is, about 0.6 cm.
Ice Sheet Dynamics and Changes
in Profile
Bindschadler's calculations kept the profile con-
stant over time, because for the 100-year period he
considered, changes in the profile seemed unlikely to
make much difference. Nevertheless, the altitude
dependence of ablation implies that Hpeak would
increase, while L would decrease. Over longer periods
of time, however, changes in ice sheet flow would at
least partly offset any steepening of the glacier.
The current version of the draft ignores ice sheet
dynamics and seeks merely to approximate the change
in profile shape resulting from the differential ablation
rate. Therefore, after the change in mass has been cal-
culated, the values of L and Hpeak are adjusted for
each time period as follows:
o Hpeak is increased by a(t)-a(0). Assuming
that the ice sheet is currently in equilibrium,
its height will increase only by the extent to
which future accumulation rates exceed the
current value.
o L is decreased to account for the change in
mass and the adjustment to Hpeak, i.e.,
(t) 3Amass
"t+1 Hpeak(t+l) 2Hpeak(t+l)
Figure 4-3 compares projections of (a) the equi-
librium line altitude; (b) the sea level contribution; and
(c) the rate of sea level rise from the median, a-low,
and o-high scenarios, assuming that precipitation and
calving do not change and that Greenland temperatures
rise 6°C per century for the next two hundred years and
remain constant thereafter.23 During the first century,
the total contribution in the median scenario is 10 cm;
during the following century the contribution is 48 cm.
Note that the equilibrium line reaches an elevation of
3200 m, bringing almost the entire glacier within the
area of net melting. Once temperatures stabilize,
Greenland's contribution to the rate of sea level rise
tapers off slightly because the decline in the ice sheet's
area leaves a slightly smaller surface on which melting
can take place. Under the low scenario, however, the
contribution is only 5 and 23 cm during the first and
second centuries, roughly the magnitude of potential
precipitation changes.
21This temperature assumption is consistent with the IPCC (1990)
assumption of a global warming of 4°C and a Greenland amplifi-
cation of 1.5.
71
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Chapter 4
a
4500 -i
s
•s
C
175 -\
150
Years
+0
+O
d
0035 -i
e
0200 -I
J 0075 •
no lag
lag due to refreeze
40 60
Years
no lag
lag due to refreeze
40 60 80 100
Years
I
•s
-O
150 200 250
Years
Figure 4-3. Impact of Alternate Assumptions About
Equilibrium-Line Sensitivity. The diagrams on the left
show (a) the equilibrium line altitude; (b) the cumulative
Greenland sea level contribution; and (c) the annual sea
level contribution for alternative equilibrium-line sensi-
tivity assumptions, assuming no refreeze, fixed precipi-
tation and calving, and that Greenland temperatures rise
6°C per century for the next two hundred years and
remain constant thereafter. The diagrams on the right
show the delay in equilibrium-line adjustment due to
refreeze. The annual contribution to sea level is shown
for instantaneous warmings of (d) 1°C and (e) 4°C, com-
paring no lag to the 20-high assumption of 50 years.
72
-------
Greenland Ice Sheet
The calving and precipitation assumptions have
a substantial net downward impact on these projec-
tions. Figure 4-4 shows that when median values24
are employed, calving increases the total contribution
by about 20 percent, while precipitation reduces it by
about 45 percent. The net effect is to lower the
impact during the first century to 7.5 cm and during
the second century to 36 cm.25 Because increased
precipitation in the median scenario is sufficient to
lower sea level 5 cm during the first century and 18 cm
during the second century, it has the potential to com-
pletely offset the Greenland contribution if equilibrium
sensitivity proves to be at the low end of the range.
Moreover, some of the high precipitation sensitivity
assumptions imply almost twice the increase assumed in
the median scenario; on the other hand, in about 10 per-
cent of the simulations, precipitation barely increases at
all (see Chapter 3).
The sensitivity analyses shown in Figures 4-3
and 4-4 suggest that our model is broadly consistent
with the sensitivity of the IPCC assumptions,
although we have a wider uncertainty range. Figure
4-4c shows that the IPCC estimates for the year 2100
were 2.9, 11.6, and 27.7 cm. Using the median
assumptions but excluding refreeze, we get a rise of
11.9 cm for the 110th year. Our low and high
assumptions in Figure 4-3b show rises of 8 and 33 cm
by 2100; subtracting the 4 cm net downward impact
due to calving and precipitation yields low and high
estimates of 4 and 29 cm, implying that the uncer-
tainty is slightly greater than sevenfold. The IPCC
uncertainty is ninefold in part because its estimates
were based on a Greenland warming of 4 to 9°C; for
a given warming, the IPCC uncertainty is only five-
fold.26 Thus, our model assumes a slightly greater
24For precipitation, we use the initial median assumption (see Table 1-1)
rather than the lower median that we obtain when we include the lower
projections of precipitation implied by Dr. Alley's review.
25The downward impact of precipitation in the median simulation,
however, is somewhat less: Because one of the expert reviewers of
Chapter 3 believes that precipitation is far less sensitive than we
assumed initially, the median precipitation increase in the simula-
tions is about 15 percent less than the median assumption shown in
this sensitivity analysis.
26See IPCC at 276 (Greenland contribution is 1 to 5 mm/yr per
degree (C).
uncertainty than does the IPCC analysis27; our uncer-
tainty range is further expanded by the impacts of the
polar temperature and precipitation uncertainties dis-
cussed in Chapter 3.
The long-term dynamics implied by our model
are illustrated in Figure 4-5. All scenarios shown
make the extreme assumptions of no increase in pre-
cipitation and o-high ablation sensitivity, along with
fixed calving; the same pattern would emerge for
more moderate assumptions, but over a longer time
period. Curve i illustrates a 6°C warming, with the
temperature staying at that level thereafter. The rate
of sea level rise reaches a maximum of 4.2 mm/yr in
the one-hundredth year and declines by about 4 per-
cent in each of the following centuries; the rise in the
equilibrium line has a lasting impact of bringing more
of the ice sheet within the ablation zone, while the
rate declines only slightly as the retreat of the ice
sheet diminishes the total area.
Curves ii and iii examine the model's stability
with respect to small and large changes in tempera-
tures. In scenario ii, temperatures rise 6°C during
the first century and fall back to today's tempera-
tures during the third century. For this relatively
small initial sea level contribution (75 cm), the
model is fairly stable, with a small persistent contri-
bution of 0.02 mm/yr resulting from the fact that the
melting during the first 300 years lowered the sur-
face of the ice sheet, and thereby brought a greater
portion of the glacier within the melting zone. By
contrast, in scenario iii, we test a larger change, in
which temperatures rise 6°C per century for three
centuries, remain constant for 350 years, fall back to
today's temperatures over the next 300 years, and
stay constant thereafter. A relatively high rate of sea
level rise persists, illustrating the potential instabili-
ty of the glacier for a large warming: The warming
brings most (in this case all) of the glacier within the
area of net melting; after several centuries, the ele-
vation of the glacier is reduced to the point that,
even after temperatures return to normal, more (or
all) of the glacier is below the equilibrium line; thus,
it continues to disintegrate.
27These estimates apply when holding calving and precipitation
fixed at their median values. The uncertainty is approximately
ninefold when those uncertainties are also included.
73
-------
Chapter 4
(i) and (ii)
b
3350-
3325-
(iii)
.5 2750 -
f '
I
•a 2000-
.2f
100 150 200 250 300
(i) and (ii)
50 100 150 200 250 300
300
Figure 4-4. Impact of Alternate Calving and
Precipitation Assumptions. Impact on (a) equilibri-
um line altitude; (b) the altitude of the glacier's apex;
and (c) the sea level contribution assuming the median
equilibrium-line sensitivity. Assuming no refreeze, the
curves show (i) fixed calving and fixed precipitation; (ii)
median calving with fixed precipitation; and (iii) medi-
an calving and median precipitation. IPCC (1990) esti-
mates are included in (c) for comparison. Because the
runoff line exceeds the height of the apex after year 180
in scenarios (i) and (ii), melting takes place over the
entire ice sheet and hence the height of the apex
declines in b.
74
-------
Greenland Ice Sheet
H
•3
(in)
(ii)
100 200 300 400 500 600 700 SOO 900 1000 1100
Years
(ill)
100 200 300 400 500 600 700 800 900 1000 1100
Years
1
I
•8
a
200 -
175 -
150
125 •
050 -
025 -
000 -
-025
0
(iii)
100 200 300 400 500 600 700 800 900 1000 1100
Years
i
I
•s
I
d
5000-1
(Hi)
(U)
100 200 300 400 500 600 700 800 900 1000 1100
Years
(i) and (ii)
(iii)
0 100 200 300 400 500 600 700 800 900 1000 IIOO
Years
Figure 4-5. Long-Term Impact of Extreme
Scenarios. Impact on (a) temperature; (b) sea level
rise; (c) rate of sea level rise; (d) equilibrium line ele-
vation; and (e) apex, assuming fixed precipitation,
fixed calving, and a-high equilibrium-line sensitivity.
Scenario i assumes a 6°C warming over one century,
with the temperature staying at that level thereafter;
scenario ii assumes that temperatures rise 6°C during
the first century and fall back to today's temperatures
during the third century; scenario iii assumes that tem-
peratures rise 6°C/century for 300 years, remain con-
stant for 350 years, fall back to today's temperatures
over the next 300 years, and stay constant thereafter.
75
-------
Chapter 4
o
045 6.45 1245 1845 2445 3045 3645 4245 4845 5445 6045 6645
Sea Level Rise (cm)
0 20 40 60 80 100 120 140 160 180 200
Sea Level Rise (cm)
Figure 4-6. Probability Density of the Greenland Contribution to Sea Level: Draft Report. Contribution between
1990 and (a) 2100 and (b) 2200.
Draft Results
Figure 4-6 and Table 4-1 illustrate the frequency
distribution for the draft's 10,000 simulations.
Comparing these results with those of IPCC suggests
that our results for the year 2100 have tracked the
IPCC range quite closely. For example, the median
estimate of 6.9 cm was 39 percent lower than the
IPCC best guess of 11.65 cm; the 5%-low estimate
was 25 percent less than the IPCC low (2.9 cm), and
the 95%-high was 23 percent less than the IPCC high
estimate (27.7 cm). Only 3 percent of the draft simu-
lations exceeded the IPCC high estimate, while over
10 percent of the simulations fell below IPCC's low
estimate for the year 2100. Figure 4-7 provides the
corresponding spaghetti diagrams.
Expert Judgment
The expert reviewers are listed in Table 4-2.
Because we only have three parameters, the basic
model selection was as much an issue for reviewers as
was the particular parameter values. The initial draft
assumed that Gj (melt-line sensitivity) would have 2o
limits of 111.1 and 186.3 based on two independent
measurements. One reviewer suggested that these two
estimates should be viewed as o limits; no reviewer
took issue with that suggested change. The initial draft
did not incorporate refreeze. Two reviewers suggested
that it should be included, and it was. Nevertheless, this
mechanism was not incorporated with the level of detail
that we would have employed had it been part of the
original design. In particular, we would like to have
explicitly assumed no runoff where melting is less than
58 to 70 percent of precipitation. Although the mass bal-
ance of the Bindschadler model helps to minimize the
impact on errors regarding the initial elevation of the runoff
line, such improvements would be conceptually more
appearing. As the section on refreezing discusses, how-
ever, the results would probably not be much different.
The reviewers generally indicated that the Bind-
schadler model is adequate for our purposes. One
reviewer, however, questioned why we did not disag-
gregate geographically. Our answer is that none of the
authors of the more elaborate models were ready to pro-
vide us with the necessary computer code, and devel-
oping such a model ourselves would have required
more resources than we had. Moreover, another
reviewer noted that a portable and improved model of
Greenland should be available relatively soon, but that
76
-------
Greenland Ice Sheet
750 -F
TABLE 4-1
DRAFT CUMULATIVE PROBABILITY 70° '
DISTRIBUTION OF GREENLAND eso
CONTRIBUTION TO SEA LEVEL
600 -
550-
Cumulative
Probability (%)
la
5a
10
20
30
40
50
60
70
80
90
95
97.5
99
Mean
0
2030
0.15
0.25
0.3
0.4
0.5
0.6
0.7
0.8
1.0
1.2
1.5
1.8
2.1
2.6
0.82
0.49
2100
1.4
2.2
2.8
3.9
4.8
5.7
6.9
8.1
9.9
12
17
21
26
34
8.6
6.5
2200 5°° "
450-
4 I 400 -
u
7 3 350-
10 ^300-
14 1 250-
18 200-
22
*•** 150 '
26
100 -
32
50 -
40
0 -
52 o
76
100 Fi
126 Se
ac<
163
36 rev
32 P31
aThese estimates are included for diagnosis purposes
only. Because the focus of the analysis was on the
risk of sea level rise rather than sea level drop, less
effort has gone into characterizing the lower end of
the distribution.
the more elaborate models seem to yield essentially the
same results anyway. Finally, one reviewer suggested
that the initial equilibrium line may be on the high side;
the possible implications of that observation, if valid,
are discussed in the section on refreezing.
Unlike the previous chapter on ocean modeling and
the next chapter on Antarctica, the reviewers did not pro-
vide divergent assessments of the magnitude and uncer-
tainty surrounding the possible impact of temperature and
precipitation changes on Greenland. Therefore, we did
not develop separate distributions for each of the expert
30 60 90 120 150 180 210 240 270 300 330 360 390
Years
Figure 4-7. Draft Greenland Contribution for
Selected Simulations, 1990-2400. See Figure 2-5 and
accompanying text for description of these simulations.
reviewers. For all but one-eighth of the simulations, the
parameter values in Table 1-1 completely define the dis-
tributions employed by our analysis of the response of the
Greenland Ice Sheet to changes in climate.28
One-eighth of our simulations for Chapters 3,
4, 5, and 6 represent the assumptions proposed by
Wigley & Raper.29 Their proposed model for Green-
land was the IPCC (1990) equation:
= PG ATG
reenland,
where (3G has a mean of 0.3 and 1.65o limits of 0.1
and 0.5, and dSL/dt is measured in mm/yr.
28We remind the reader, however, that the precipitation scenarios
used in the sensitivity analyses of this chapter were based on our
initial assumptions that precipitation will change with saturation
vapor pressure or its derivative. One reviewer of Chapter 3, how-
ever, has done field research suggesting that precipitation may be
much less. Including his assessment in our distributions has the net
effect of lowering the projections of future precipitation increases.
^See Correlations Between Assumptions, Chapter 1, supra.
77
-------
Chapter 4
Walter Ambach
Robert Bindschadler
Roger Braithwaite
Mark Meier
Robert Thomas
Jay Zwally
TABLE 4-2
EXPERT REVIEWERS OF CHAPTER 4
University of Innsbruck
NASA/Goddard Space Flight Center
Geological Survey of Greenland
University of Colorado
Greenland Ice Core Project
NASA Headquarters
NASA/Goddard Space Flight Center
Innsbruck, Austria
Greenbelt, MD
Copenhagen, Dnmk
Boulder, CO
Washington, DC
Greenbelt, MD
Final Results
Figure 4-8 illustrates the cumulative probability
distributions from the Greenland analysis. Combining
the reviewer assumptions with the nonlinear Bind-
schadler model implies a median Greenland contribu-
tion of only about 2.9 cm by 2100, much less than the
7.5 cm implied by the linearity assumptions favored
by Wigley & Raper. However, the 95 percent confi-
dence range implied by the combined assumptions is
-0.37 to 19 cm, while for Wigley & Raper it is 2.5 to
15 cm. By the year 2200, the assumptions imply a
median contribution of 12 cm, but a 10 percent chance
of a 50 cm contribution. Table 4-3 summarizes the
cumulative probability distributions for 2050, 2100,
and 2200.
The final median estimate is about half the esti-
mate from the draft report, primarily for two reasons:
(1) the revisions to atmospheric forcing (Chapter 2)
resulted in lower estimates of global warming, as dis-
cussed in Chapter 3; and (2) two of the climate review-
ers expect Greenland to warm 0.5 to 1.0 times the glob-
al warming, rather than 1.5 times the global wanning
assumed by IPCC (1990) and the draft median scenario.
The delay due to refreeze also has a negative, but small,
downward impact on the median estimate.
At the high end of the range, the final results are
only slightly lower than the draft results. Although
the reviewer assumptions resulted in a lower median
estimate of Greenland warming, the 5%-high esti-
mate of 8.06°C by the year 2100 is as high as
assumed in the draft report.
At the low end of the range, the reviewer assump-
tions imply a 5 percent chance that Greenland will have
a negative contribution to sea level through the year
2100. Such a decline is possible for two reasons. First,
in approximately 2 percent of the simulations, Green-
land temperatures (and thus the annual rate of melting)
decline, while in the draft, Greenland temperatures
were projected to rise in all cases. Second, the Zwally
precipitation assumptions (Chapter 3B) increase the
risk of a very large increase in snowfall.
The spaghetti diagrams in Figures 4-9 and 4-10
illustrate the dynamics of the Greenland contribution.
Because temperatures increase steadily throughout the
period, so does the annual contribution to sea level; the
median contribution rises from about 0.2 mm/yr in
2050, to about 0.6 mm/yr in 2100, to more than 1 mm/yr
after about 200 years. Moreover, in about 15 percent of
the cases, the annual contribution exceeds 3 mm/yr
within the next two centuries.
In one simulation, however, the Greenland contri-
bution peaks at about 0.3 mm/yr in 2100, but subse-
quently reverses, becomes negative, and drops off the
bottom of the scale by 2270. This scenario is possible
largely because precipitation rises exponentially with
temperature, while annual melting is mostly linear.30 At
the high end of Zwally's assumptions, precipitation
increases 20 percent per degree (C). Thus, the first
degree increases precipitation from 1.33 to 1.59 mm/yr
(sea level equivalent)—an increase of 0.26 mm/yr—
30As discussed above, melting is modeled as a cubic of tempera-
ture, but the linear term dominates.
78
-------
Greenland Ice Sheet
,yy —
.95 -
.90 -z
—
>> 7° ~
£
15
03 50 —
.Q
O _
30 —
-
10 -5
05 —
01 —
Balling /
v
/ //' X' -^ "^
/ / / /
> / Manabe; / // /
v-/// //-,-••• ^
/
/ X^ -" —
. " /V7 H
/ . x
/ / ,
/ / / -
' / X -
1 : ',/ /-
I • js / . -
1 / / ,
/ • X / • '
1 f / S ' '
> 1 ''" {(''' '
1 ; ••'//' /Wigley
; 7/ ti' '*''
i • ' ' i •
-05 0 1 2
/ // •
' //• ""
//'
/
—
Hoffert
MacCracken
Schneider
A
v
-
•?
—
T
—
—
—
-
—
-
^ ^
X'' ,''/
L ,-'/ ,./
/ '>-*" —
X' ' —
; X '
' // ~
i // —
1 /' Alley
/ !/l '
\ /'•' Kuhn
*/' •?
'ii' Zwally
u Tot^l ~
/ t \JlCli
A
1 ' ' ' ' ' IV 1 1 1
95
>90
70
50
30
^10
05
01
35 10 12 13 2 3 4 553
Greenland Warming, 1990-2100 (°C) Greenland Precipitation, 1990-2100 (mm/yr)
c
99 —
95 —
90 ^
>< 70 ~~
•*t^
(0 50 —
.Q
O
30 —
-
10 -z
05 —
01 —
A
1 1 1 1 1 ^"\ IV
Balling /
\/ Manabe .
> /
/"
d
A
///X 1
''X" "?
/ .- x'// -
' X '3
' ••' ' x'"
' ' / X/
' .'' /
I / /' '
'•' //^ -''
> /•' ,^ Wigley/'
/ ' / ' ^
//'' /''
t'J// / A
1 1 1 1 1 i (V
-20 5
.
/
/
—
—
Hoffert
MacCracken
Schneider
Total
-
•^
i i i
-
> ^
_
—
—
-
=• ^
^^^ • ' ' ** ^^
Balling/ .' / / , / •- ' ~
\ i Manabe .' '/ / /
> /' >•••' // - '-- -• -<
/ ••' ' i ^ . •
i ^-7 - :
/ .* / '/'
./-''/
X X><;
' • / /x .
', : /X -• /
1 • / / l
'.'//, /
;.'' /,' /' Hoffert
i)/:'..,. . /' MacCracken ^
' /.y . Wigley '
//'' \/ Schneider
,'n ' / - — Total
^ '// i A
1 1 1 V 1
99
95
>90
70
50
30
>10
05
01
10 20 30 40 -8 0 20 100 150
Greenland Contribution, 1990-2100 (cm)
Greenland Contribution, 1990-2200 (cm)
Figure 4-8. Climate Change in Greenland. Cumulative probability of (a) warming by the year 2100; (b) sea level
equivalent of annual precipitation in 2100, assuming that the current rate is 1.33 mm/yr; and Greenland contribution to
sea level through the years (c) 2100 and (d) 2200. The Rind, MacCracken, and Schneider precipitation assumptions were
essentially the same as those of Kuhn. The contribution to sea level attributed to Wigley (and Raper) is based on their
assumptions regarding both Greenland climate and the sensitivity of the ice sheet to warmer temperatures; all other esti-
mates are based on the named reviewers' Greenland temperature assumptions, the precipitation reviewer assumptions,
and the Bindshadler (1985) model employed with the consensus assumptions adopted by the glaciology reviewers.
79
-------
Chapter 4
10 -T-
u
s
I
•d
2100
1 1 1—H 1 1 1—
2150 2200
1 -- 1 - 1 - 1
1 - 1 - 1 - 1
2250
0.5 -i-
- -4—I 1 1 1 1 1—
1990
1 1 1 1 1
2250 2300
Figure 4-9. Spaghetti Diagram of Change in Greenland Climate. Increase in (a) temperatures and (b) precipita-
tion over the Greenland Ice Sheet.
80
-------
Greenland Ice Sheet
1
u
2000
2050
2100
2150
50 -
§
I
§
U
•o
O
-10 H -H
1990
2050
2100
2150
2200
Figure 4-10. Spaghetti Diagram of Greenland Contribution to Sea Level. Selected simulations of (a) the rate of
sea level contribution 1990-2300 and (b) total contribution 1990-2200. See Figure 2-5 for additional explanation
on the scenarios chosen for this and other spaghetti diagrams.
81
-------
Chapter 4
TABLE 4-3
FINAL CUMULATIVE PROBABILITY
DISTRIBUTION OF GREENLAND
CONTRIBUTION TO SEA LEVEL
2050
2100
2200
Cumulative
Probability (%)
O.la
0.5a
la
5a
10
20
30
40
50
60
70
80
90
95
97.5
99
99.5a
99.9a
Mean
a
aThese estimates are included for diagnosis purposes
only. Because the focus of the analysis was on the risk of
sea level rise rather than sea level drop, less effort has
gone into characterizing the lower end of the distribution.
while the fourth degree of warming increases precipita-
tion from 2.3 to 2.76 mm/yr—an increase of 0.46 mrn/yr.
Because Greenland melting in this scenario increases
by about 0.4 mm/yr per degree (C), wanning causes a
net contribution for the first few degrees; but after a
warming of about 3°C, each additional degree increas-
es the precipitation by more than it increases the melt-
ing. By the time the warming exceeds 5°C, the
increased precipitation exceeds the increased melting
and the annual contribution becomes negative.
-0.9
-0.4
-0.3
-0.2
-0.1
0.0
0.2
0.3
0.5
1.0
1.3
1.9
2.8
3.7
4.5
5.7
6.7
12.5
1.1
1.6
-4.2
-1.3
-0.8
-0.1
0.2
0.8
1.3
2.0
2.9
4.0
5.4
7.3
10.3
13.8
18.6
27.2
36.1
64.9
4.6
6.3
-11.4
-5.8
-2.7
-1.1
0.9
2.9
5.3
8.2
12.3
17.2
23.0
31.2
50.0
77.0
109.9
150.9
190.2
237.0
21.4
29.8
Although our simulations illustrate two mecha-
nisms by which the Greenland contribution might be
negative,31 they are both based on our simplistic para-
meterization of Greenland climate. We ignore two other
possibilities that may be equally important and could
change the Greenland contribution in either direction.
First, an increase in sulfate concentrations may have a
greater impact on Greenland temperatures compared
with the global impact. As a result, global temperatures
could continue to rise while Greenland temperatures
fall, which has been the pattern over the last fifty years
(Karl et al. 1995). On the other hand, if SO2 control in
the United States reduces sulfate concentrations, the
warming effect on Greenland could be greater than the
effect on the global average temperature.
Second, changes in North Atlantic deepwater for-
mation could cause Greenland to cool, and thus cause
melting to decline, without necessarily causing precipi-
tation to decrease as well. As discussed in Chapter 3,
Manabe and others have suggested that deepwater for-
mation could decline as a result of increased precipita-
tion over the North Atlantic. Under such a scenario,
precipitation may increase over Greenland as well,
while the decline in deepwater formation slows the Gulf
Stream, cools Greenland, and reduces melting. On the
other hand, if precipitation barely increases around
Greenland, as projected by Alley, the increased North
Atlantic evaporation could strengthen thermohaline cir-
culation and cause Greenland to warm much more than
the global average warming.
References
Ambach, Wv and M. Kuhn. 1989. "Altitudinal Shift of
the Equilibrium Line in Greenland Calculated from Heat
Balance Characteristics." In: Oerlemans, J. (ed). Glacier
Fluctuations and Climatic Change. Kluwer (Dordrecht).
Bindschadler, R.A. 1985. "Contribution of the Green-
land Ice Cap to Changing Sea Level: Present and Future."
In: Meier, M.F. et al (eds). 1985. Glaciers, Ice Sheets, and
Sea Level. Washington, DC: National Academy Press.
31In addition to precipitation exceeding melting, global and hence
Greenland temperatures cool in a few cases.
82
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Greenland Ice Sheet
Hollin, J.T. and R. G. Barry. 1979. "Empirical and
Theoretical Evidence Concerning the Response of the
Earth's Ice and Snow Cover to a Global Temperature
Increaase." Environmental International 2:437-44.
Huybrechts, P.A, A. Letreguilly, and N. Reeh. 1991.
"The Greenland Ice Sheet and Greenhouse Warming."
Palaeogeography, Palaeoclimatology, Palaeoecology
(Global and Planetary Change Section) 89:399-412.
Intergovernmental Panel on Climate Change. 1990.
Climate Change: The IPCC Science Assessment.
Cambridge: Cambridge University Press.
Karl, T.R., R.W. Knight, G. Kukla, and J. Gavin. 1995.
"Evidence for Radiative Effects of Anthropogenic
Sulfate Aerosols in the Observed Climate Record." In:
Charlson, R,. and J. Heintzenberg (eds). Aerosol Forcing
of Climate. Dahlem Konferenzen: John Wiley and Sons.
Ohmura, A., and N. Reeh 1990. New Precipitation
and Accumulation Maps for Greenland. Journal of
Glaciology 37(125): 140-8.
Pfeffer, W.T., M.F. Meier, and T.H. Illangasekare.
1991. "Retention of Greenland Runoff by Refreezing:
Implications for Projected Future Sea Level Change."
Journal of Geophysical Research 96:C12:22,117-24.
Sikonia,W.G. 1982. Finite Element Glacier Dynamics
Model Applied to Columbia Glacier, Alaska. U.S.
Geological Survey Professional Paper, 1258-B.
83
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Chapter 4
84
-------
CHAPTER 5
ANTARCTIC ICE SHEET
Background
Because of Antarctica s potential importance and
the many processes by which it might contribute to sea
level, our analysis of this ice sheet is somewhat more
detailed than those employed by the previous EPA and
IPCC assessments of future sea level rise. Studies not
designed to forecast sea level in specific years, however,
have employed several models at various levels of
complexity. We briefly summarize previous efforts.
National Research Council (1985) estimated that
warmer water temperatures could increase melting
under the Ross Ice Shelf by about 1 to 3 m/yr (com-
pared with 17 cm/yr today). The NRCs Polar
Research Board adopted as its high scenario a model
result reported in an appendix by Thomas (1985), in
which the Antarctic contribution to sea level by the
year 2100 is about 100 cm.1
Thomas (1985) employed two models to test the
sensitivity of Antarctic ice sheets to scenarios in which
the rate of basal shelf melting increases linearly by
1 m/yr or 3 m/yr by 2050 and remains constant there-
after. In the first model, the increased flow of ice
from ice streams into the shelf exactly balances the
increased basal melting. As a result, sea level rises
about 30 and 90 cm by 2100 for the two scenarios.
The second model was an ice-stream model,
which Thomas used to estimate the resulting discharge
of ice from Ice Stream B, before extrapolating the
results to all of Antarctica. The model assumes that
higher ice-stream velocity and the resulting flow of ice
shelves would increase total calving even if the seaward
margins of the shelves remained in their present loca-
tions. Under the 1 m/yr and 3 m/yr shelf-melt scenarios,
the model gave results of 13—30 cm and 55—130 cm.
'The NRC summary table explanations are somewhat inconsistent
with the Thomas results on which it relies. On page 64, note 10 of
the table states that the calculation assumed that the Ross Ice Shelf
melts 3 m/yr and that all the ice in Antarctica responds as ice
streams B and E, resulting in a 1 m contribution. However, Thomas
gets aim contribution from either (1) assuming 1 m/yr and all ice
behaving as ice stream B or (2) assuming 3 m/yr and only enough
glacial discharge to equal the melting that results. When Thomas
uses both the 3 m/yr and the assumption that glacial discharge
equals basal melting, he gets 2.2 m. Therefore, we interpret the
table on page 64 of the NRC report as consistent with either (1) or
(2), not both.
Thomas also considered an enhanced calving sce-
nario with ice fronts calving back to a line linking
adjacent areas of grounded ice in the 2050s. These
assumptions result in a rise of 92—239 cm and
121—295 cm by 2100, for the 1 m/yr and 3 m/yr sce-
narios, respectively.
Lingle (1985) used the same scenario of shelf
thinning, but applied a model of Ice Stream E. The
model suggests that for a 10 percent thinning of the ice
shelf, the ice sheet/shelf system is stable. However, if
the shelf thins 50 percent, it is unstable; i.e., reduced
backpressure from the shelf enables the ice stream to
accelerate. The greater acceleration results in calving,
rather than a (negative feedback) buildup of ice shelf
mass. Complete disintegration of the West Antarctic
Ice Sheet takes 660 years. However, for a 1 m/yr thin-
ning rate, the contribution to sea level is only 3 to 5 cm
over a 100-year period.
Huybrechts & Oerlemans (1990) analyzed the
sensitivity of Antarctic mass to climate change and
ice-shelf thinning. Given a scenario in which Ant-
arctic annual temperatures rise 4.2BC over a 250-year
period, they estimated that sea level would fall 6 cm.
Given current climate and an instantaneous increase
in shelf thinning of 1 m/yr, they estimated a cumula-
tive rise of 2, 5, 12, 20, and 30 cm after each of the
next five centuries.
MacAyeal (1992) examined the impacts of cli-
mate change on the Antarctic ice sheets assuming that
the ice-shelf basal melting remains constant. The analy-
sis was based on ice stream bed frictional changes
resulting from (a) warmer ambient temperatures and
(b) precipitation changes. His analysis suggests that
the loss of ice mass could be enough to raise sea level
60 cm or lower it on the order of 10 cm, with the latter
condition being sufficiently more likely than the former
so as to leave an expected change of about zero. He
argued that, in principle, it would be possible to collect
sufficient data on the stream bed characteristics (initial
conditions) to establish which response is most likely,
but that such data may be prohibitively expensive.
IPCC (1990) concluded that the Antarctic con-
tribution (including increased precipitation) will be
between zero and a decline in sea level of 0.6 mm/yr
per degree (C) wanning.
85
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Chapter 5
Drewry & Morris (1992) modeled the response
of Antarctica to climate change by disaggregating it
as (i) the interior of the ice sheet; (ii) the maritime
margin of the continent; and (iii) the Antarctic penin-
sula. Their model indicates that for a 26C warming in
mean annual surface temperature over a 40-year period,
the peninsula is likely to make a net contribution of
0.5 mm to sea level.
To the extent that these models each represent
how some researchers believe the Antarctic ice sheet
could respond, the most desirable approach would be to
run all the available models and assign probabilities to
each. However, some of these models are too expensive
to undertake several runs: MacAyeal s model, for exam-
ple, takes tens of hours on a Cray computer.
Therefore, we are left with three models of the
continent-wide contribution:
1. The IPCC model, which essentially assumes
that the Antarctic contribution is zero (aside
from changes in precipitation). We call this
model AMI.
2. The ice-shelf basal melt rate model
developed by the Polar Research Board
report (NRC 1985).
3. The Thomas ice stream model.2
All of these models have important limitations:
In a recent letter to the IPCC, the authors of the PRB
report noted that the assumption of no ice-sheet
response is a very poor characterization of the exist-
ing uncertainty range, even though it may not be a bad
median estimate (see Appendix 3).
The estimate of basal melting, by itself, does
not provide a sea level rise estimate, because the ice
shelf is already floating. To estimate sea level rise
requires an assumption regarding the response of the
ice sheet to the shelf thinning. The simplest approach
is to ignore this distinction by assuming that the melt-
ing reduces the backpressure of the shelves, allowing
ice to flow from the sheet into the shelves until the
shelves reach their original size; i.e., the contribution
to sea level equals the basal melting. At least in the
short run, this simple model overstates how rapidly
so? level rises by implying that the adjustment is
2We can also at least summarize the Oerlemans results with a func-
tion expressing the relationship between shelf melting and ice
stream contribution. See infra.
instantaneous. Over long periods of time, however, it
may understate sea level rise by assuming that the rate
of calving does not increase.
Criticisms of the Thomas model fall into two
categories: First, it may overstate the response of Ice
Stream B to ice-shelf thinning, because it assumes
that ice-shelf backpressure is the only force prevent-
ing Ice Stream B from reaching a maximum velocity
of 20 km/yr. Second, the response of Ice Stream B to
ice-shelf thinning is not typical of all Antarctic ice
discharge. Ice streams account for a large fraction of
ice discharge, but the streams that feed the major ice
shelves account for only about 20 percent of the dis-
charge. Since ice-shelf thinning would accelerate
only those streams for which shelf backpressure is a
major impediment to stream velocity, extrapolating to
the entire continent overstates ice discharge.
Approach
Our overall approach is to consider the impacts of
climate change on shelf melting, precipitation, and the
flow rates of ice streams (see Figures 5-1 and 5-2). We
divide the continent into seven regions: East Antarctica,
the Antarctic Peninsula, the rest of West Antarctica
(which is marine-based), and the Ross, Filchner/Ronne,
Amery, and other ice shelves. Relying primarily on data
compiled by Bentley & Giovenetti (1990), we use the
annual mass balance estimates shown in Table 5-1,
which reports accumulation, calving, melting, and the
quantities of ice that the ice streams convey from the
grounded ice sheets to the floating ice shelves. The table
suggests that calving and basal ice-shelf melting almost
balance accumulation and that ablation/runoff from
grounded ice is negligible. As a result, the mass of the
ice sheet is increasing enough to lower sea level 0.1 to
1.1 mm/yr; we incorporate this slightly positive mass
balance into our background assumptions. Table 5-2
reports the mass and area of the four major regions into
which Antarctica s ice can be divided: East Antarctica,
West Antarctica, Antarctic Peninsula, and ice shelves.
Warmer temperatures will probably increase the
amount of precipitation falling on Antarctica (see
Chapter 3), which would tend to increase the rate at
which mass enters the ice sheet. We consider three
ways by which the rate at which ice leaves the conti-
nent might accelerate:
(1) warmer circumpolar ocean water accelerates
the melting of ice shelves, which increases
the rate at which grounded ice flows into
these shelves;
86
-------
Antarctic Ice Sheet
Ronne Filchner Basin
George VI
IceSheK
-SOW
Pine Island and
Thwaites Glaciers
1000
km
Western Ross Basin
Eastern Ross Basin
180°
Figure 5-1. The Antarctic Basins Used in This Report.
A=91
A=77
0152
M=73
A=500
Antarctic Peninsula
East Antarctica — Lamb
Amery Ice Shelf
Amery Ice
Shelf
90°E-
Key
Ice shelf
Marine Based Ice Sheet
| | Land Based Ice Sheet
A=147.4
A=916
West Grounded
Figure 5-2. Schematic of the Antarctic Mass Flows Used in This Report.
0314
• S=246
C=259
87
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Chapter 5
TABLE 5-1
ANNUAL MASS BALANCE OF ANTARCTICA
(in gigatons)
Accumulation3
Specific Basins
Calvingb
Ronne/Filchner
Western Basin
Eastern Basin
Ice Shelf
Ross
Western Basin
Eastern Basin
Ice Shelf
147.4
91.6
82
91
77
75
Other Parts of West Antarctica
151
152
Stream0
147.4
44
191.4
99
51
150
Meltd
122.4
73
Antarctic Peninsula 500 500
West Other 257 146
East Antarctica
Lambert Glacier 18
Amery Shelf 4 20
East Other 143 131
Other Shelves 455 195.4
SUBTOTAL 1941 1295.4
Excluded Grounded6 203 203
West 20.3 20.3
East 182.7 182.7
TOTALf 2144 1498.4
Regions Used in This Analysis
East Groundeds 512 314
Ant Peninsula 500 500
West Marine Grh 516 259
Shelves, Misc' 616 425
R/F Shelf 82 151
Ross Shelf 75 152
Amery Shelf 4 20
Other Shelves 455 102
Accumulation = Precipitation — sublimation over an area
Calving = Discharge of icebergs from an ice shelf
11
11
352.4
106
0
246
353
191
150
11
0
93
-5
0
259.6
543
0
0
0
543
0
0
0
543
122
73
-5
353
Stream = Amount of ice conveyed from grounded area to ice shelf
Melt = Melting
Mass Balance = Accumulation — Stream — Melt, for grounded areas
= Accumulation + Stream — Melt — Calving,
for ice shelves
Mass Balance
0
47.6
0
-8
26
0
0
18
7
0
12
0
102.6
0
0
0
102.6
93
0
10
0
0
0
0
0
-------
Antarctic Ice Sheet
TABLE 5-1 (continued)
"From Bentley & Giovenetto (B&G) where possible. We allocate their estimates of accumulation in Ronne/Filchner (R/F) Basin between the shelves
and grounded ice by assuming the same accumulation rate per unit area for that shelf as for Ross, and that the remaining accumulation is divided
between east and west in the same proportions as would have been listed in B&G Table 3 had the typo been corrected for Eastern Ronne, which
should say 123. West Other (WO) consists of Thwaites and Pine Island from Table 1 and George VI and Brunt from Table 3. East Other (EO) con-
sists of Jutulstraumen, E. Queen, E. Enderby, and W. Wilkes from Table 1. AP is from Drewry (1992). Total and total shelf are from Jacobs et al.
1992; Other shelf is the difference between total shelf and those listed and thus includes George VI. Unmodeled represents areas not included by
B&G other than the Antarctic peninsula and is the residual between total and those listed.
bCalving is from B&G outflow estimates for EO, WO, Ross, Amery, and Ronne/Filchner. For Antarctic Peninsula (AP), we assume that calving equals
accumulation. For other shelves, we calculate calving rate necessary for shelf balance given calculated melt and inflow rates. For unmodeled, we
assume that calving equals accumulation. For total, we add the various contributors, which gives the same result as calculating calving rate necessary
for total continental mass balance to equal the mass balance of the modeled area, given accumulation and melt rates.
cModeled stream outflows from B&G except for Western Ronne/Filchner, where we assume that the grounded ice in the basin has zero mass balance,
which is consistent with B&G Table 3 s assertion that such an assumption is reasonable. By contrast, for the Eastern portion, where the assumption
is viewed as unreasonable, we assume that flow is equal to the measured outflow for the basin, which results in a positive mass balance implied by
B&G Table 3 s assertion that zero net balance is not reasonable. However, we do allow for enough melting to offset the precipitation over the shelf.
dGenerally from B&G. WO is from Table 3, measured for Larsen at 1 m/yr and derived by B&G for George VI. For Ronne/Filchner, melt rate equals
those derived and verified as reasonable by B&G for western region, plus a fraction of that derived and rejected for the eastern region. This latter
fraction represents a melt rate sufficient to balance the eastern region of the shelf while leaving the grounded portion with the imbalance implied by
the accumulation and outflow listed by B&G. Total melt from Jacobs et al. 1992. Other shelves estimate derived from Total minus those listed.
"Excluded area calculations based on the difference between subtotals from B&G data and totals from Jacobs et al. Arbitrary 90/10 division between
east and west is based on the inspection of Figure 5 of B&G.
'Total Accumulation and Ice Shelf melting from Jacobs et al. Net balance is calculated based on conservative assumptions from Bentley; that is, mass
balance outside of the area they studied is zero. Calving set consistent with those assumptions.
eConsists of E. Ross, E. R/F, E. Other, and E. Amery Lambert.
hConsists of W. Ross, W. R/F, and WO, except that the 93 Gt/yr shelf melting that takes place in the WO basins is subtracted here and added back
into shelves, below. To keep a balance, this 93 is added to calving. Similarly, 93 GT/yr is subtracted from calving for shelves.
'Consists of Ross, R/F, Amery, and other shelves. In addition, includes the shelf melting otherwise listed under West Other.
TABLE 5-2
VOLUME, AREA, AND THICKNESS ASSUMPTIONS FOR ANTARCTICA
East Antarctica
Antarctic Penin.
West Antarctica
Shelves (total)
Ross
Ronne/Filchner
Other0
Volume
(106km3)
25.92
0.18
3.22
0.79
0.21
0.23
0.35
Sea Level
Equivalent3
(m)
65.78
0.45
8.17
2.01b
0.53
0.58
0.89
Area
(106km2)
9.86
0.98
1.36
1.62
0.40
0.40
0.80
Thickness
(m)
2630
180
2370
490
525
575
450
a394,000 km3 of ice would contribute 1 m to sea level at a density of 917 kg/m3.
bMelting ice shelves would not raise sea level because they are already floating.
'Includes Amery Ice Shelf.
SOURCE: Menard, H.W., and S.M. Smith 1966. Hypsometry of Ocean Provinces. Journal of Geophysical Research, 71, 4305-25.
89
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Chapter 5
(2) the increased temperatures in the Antarctic
Peninsula increase the rate at which its ice
flows toward the oceans; and
(3) increased (or decreased) mass of grounded
ice increases (decreases) the forward
pressure under which ice flows toward
the ocean.
Because the Polar Research Board (NRC 1985)
provided substantial analysis of how the first matter
can be simplified, we focus primarily on that mecha-
nism. We rely essentially on relationships presented
in the summary report and appendices by Jacobs and
Thomas, but formally generalize them in a common
analytic framework. We first present the equations
we use to operationalize the PRB s shelf melting
assumptions. Next, we discuss several alternative
models for describing the impact of shelf melt on
Antarctic mass, along with two procedures by which
we calculate the impact on mass without directly esti-
mating the change in the shelves. Finally, we display
the results for the Antarctic contribution to sea level.
The PRB approach consisted of two parts: (1) esti-
mating the impact of warmer temperatures on shelf
basal melt rates; and (2) estimating the resulting impact
on the discharge of grounded ice into the ice shelves.
We consider each in turn.
Basal Melting of Ice Shelves:
Generalizing the Relations Expressed
in the Polar Research Board Report
Ross Ice Shelf
Like the PRB, we started by employing the sug-
gestion by Jacobs (1985) that net melting under the
shelf results from warm intrusions that are currently
0.56C above the in situ melting point; i.e., ~~1.4BC.3 We
treat this warm intrusion as a 5:1 mixture of shelf
water at ~t.9BC and circumpolar deep water (CDW)
(currently at +1.1BC). Thus,
Reformulating the equation to allow for alternative sen-
sitivities of the warm intrusion to CDW temperature,
T = Tcdw—1.9 DILUTE
warm 1+DILUTE
where 1/(1 + DILUTE) represents the sensitivity of
warm intrusion temperature to CDW temperature.4
If seaice formation declines, less shelf water
will be created each year. (See Chapter 3 for our
assumptions regarding seaice formation.) Therefore,
we could assume that
DILUTE = 5 seaice(t)/seaice(0).
However, because the 5:1 assumption is merely
an artifact of the observed temperatures, we have no
reason to believe that it will persist, or even that mix-
ing is the explanation for why the warm intrusions are
2.56C below the CDW temperature, which suggests:
1 +
SEAICE
SEAICE
where SEAICE=seaice(t)/seaice(0) and Aj allows for
alternative ratios of dilution. We assume that the medi-
an of the distribution of A] is 5.0. There is no a priori
reason why the warm intrusion could not warm as much
as the CDW, which occurs if Aj=0; by contrast, the
equation explodes if A^-l. Therefore, we assume that
(Aj+1) is lognormal, with a mean of 6 and 2o limits of
1 and 36. The right hand of this distribution implies that
the warm intrusions are very insensitive p e r h aps unre-
alistically insensitive t o warming of CDW. Given our
desire to use simple functions for probability distribu-
tions, we saw no way to avoid this situation.
However, this equation has to be modified, because it
implies that the warm intrusion today has a temperature of
3/Cl+AjSEAICE) above the in situ melting temperature
when, in fact, the temperature is 0.56C above the in situ
melting temperature, regardless of the value for Aj.
Therefore, we subtract S/O+A^EAICE)— 0.5. This
adjustment is in turn multiplied by SEAICE; as
1+5
3As discussed below, Jacobs now believes that colder, deeper high-
salinity water, which is approximately 0.5BC above the in situ
freezing point at the base of the ice shelf, is more likely to be the
explanation. See Jacobs et al. (1992).
4This formulation assumes that as CDW warms, there will not be
additional cool shelf water to offset the impact of the warming.
This linear specification effectively assumes that the portion of the
excess heat (conveyed by the warm intrusion) that is transferred to
the ice via melting will remain constant. As discussed in Expert
Judgment, infra, one reviewer suggested that increased circulation
between the circumpolar ocean and the subshelf cavity could result
in a nonlinear response.
90
-------
Antarctic Ice Sheet
the dilution declines, so must the differences between
the temperatures of CDW and the warm intrusion.
Tcdw —
SEAICE
1 + A SEAICE ~~
_ 3 SEAICE
1 +Aj SEAICE
+ 0.5 SEAICE
The PRB also notes that there is a possibility that
undiluted CDW would enter beneath the ice shelves,
independent of the decline in dilution associated with
decreased sea ice. Unfortunately, PRB specifies neither
the probability of such an occurrence nor how that prob-
ability might change as a function of changing climate.
In the above formulation, such an assumption implies
that DILUTE=0.
In the absence of any such model, we assume
that in the scenario analyzed by the PRB (" Tcdw=l),
the probability of such an occurrence is 5 percent.
Moreover, we assume that the probability increases
linearly with the warming of circumpolar ocean up to
(the unlikely) warming of SBC, past which the proba-
bility of such a dilution remains at 25 percent no mat-
ter how much the Earth warms.
The PRB provides several indications of how
much melting would take place with warmer intru-
sions. Assuming that net melting is proportional to the
excess heat provided by the warm intrusion tempera-
ture, a 1BC warming would triple the melt rate from
0.17 m/yr to 0.51 m/yr. The PRB report also suggests
that a 38C warming associated with undiluted CDW
flowing beneath the shelves would increase the thin-
ning rate by 2 m/yr, but that the additional 1BC warm-
ing could increase basal melting to 3 m/yr. Based on
these observations, one could assume:
Melt = A2(Twarm+ 1.4)
where Melt refers to increased basal melting above
the baseline, and A2 is lognormal with a median of
0.34 and 2a limits of 0.17 and .68.
Figure 5-3 illustrates the CDW temperatures and
resulting shelf-melt rates for alternate scenarios of
global temperatures. The scenarios in the left half of
the figure are based on the assumption that global tem-
peratures rise for 100 years and are steady thereafter;
those on the right side (other than scenario 3) involve
global temperatures rising for 200 years. The relation-
ships between the input temperature scenarios, as well
as a few other scenarios that are used elsewhere in this
chapter, are described in Figure 5-4 and Table 5-3.
Scenarios 3 and 4 both keep precipitation fixed,
assume that global temperatures rise 46C per century,
and employ median values for (a) the magnitude and
timing of the CDW response to global temperatures;
(b) the response of warm intrusion temperature to
CDW; and (c) the response of basal shelf melting to
warmer water temperatures. The only difference is
that global temperatures stabilize after 100 years in
scenario 3 and 200 years in scenario 4. Both scenar-
ios imply that CDW warms 1.7BC after 100 years;
after 250 years the warming is 3.0BC and 5.6BC for the
two scenarios, respectively. In both scenarios, the
melt rates more than double in the first century from
the current 0.17 m/yr to 0.421 m/yr; after 250 years
they rise to 0.52 rn/yr and 1.15 m/yr, respectively.
Thus, for the next two centuries our median assump-
tions imply shelf-thinning rates well below the 1 m/yr
generally viewed as a threshold for significant ice
sheet responses even when we assume a 4BC/century
global warming, which is almost twice our median
temperature projection.
Only when we test the high-sensitivity sides of
the distributions of our uncertainties do we obtain rela-
tively high shelf thinning. Scenario 5, for example,
assumes that the warm intrusion water will warm as
much as CDW warms, even without the impact of
declining SEAICE, allowing the shelf-thinning rate to
exceed 1 m/yr after year 70; scenario 7 assumes that
undiluted CDW penetrates the shelf after year 60,
which increases the melt rate to 1.85 m/yr. Finally, sce-
nario 10 is similar to scenario 5, except that (a) global
temperatures warm for 200 years; (b) CDW is assumed
to warm in equilibrium as much as the global wanning,
rather than only 3/4 as much; (c) the response time of
CDW to global temperatures is assumed to be 20
instead of 40 years; and (d) the (offsetting) impact of
increased precipitation is included. Given these plausi-
ble but unlikely assumptions, CDW warms 3.26C after
100 years and 7.96C after 250 years, leading to shelf-
thinning rates of 5.9 and 10.6 m/yr, respectively.
Other Ice Shelves
Jenkins (1991) suggests that the average melt
rate of the Ronne/Filchner Ice Shelf would increase
by 3.333 m/yr per degree (C) wanning of the Weddell
Sea, while a previous study by the same researcher
suggested that the melt rate would only increase by
1.91 m/yr. We use these rates as the 2
-------
Chapter 5
3 4.0-
20 -
15 -
10
0 25 50
Scenario 2
Scenario 3, 5, 6 and 7
75 100 125 150 175 200
Years
B 8-
S 7-
g
0
Scenano 10
Scenano 9
/ ,-*' Scenario 4 and 8
Scenario 3
0 50 100 150 200 250 300 350 400
Years
1
C
10 -I
25 50
100 125
Years
150 175 200
d
100-:
i
Scenano 10
Scenano 9
...-•;'--•'" Scenario 4 and 8
Scenano 3
100 150 200
Years
250 300 350 400
Figure 5-3. Circumpolar Deepwater Temperatures and Shelf Melt Rates for Various Scenarios. Scenarios
defined in Table 5-3 are shown (a) for the first two hundred years and (b) for the first four hundred years. The cor-
responding shelf-melt rates are shown in (c) and (d). Scenario 3 is shown for comparison purposes in both the right
and left sides. Note that this report assumes that the current rate of shelf melt is 0.17 m/yr, rather than the 0.25 m/yr
used by the PRB report.
92
-------
Antarctic Ice Sheet
lognormal distribution. We assume that the Weddell
Sea warms the same as circumpolar ocean.
The Amery Ice Shelf currently appears to have
net basal freezing, as shown in Table 5-1. Lacking any
better information, we assume that its melt rate would
increase by 1 m/6C warming of the circumpolar ocean.
Other shelves have varying melt rates. Most
noteworthy are the Larsen and George VI ice shelves,
which appear to have basal melt rates of 1 to 2 m/yr.
Because most of these other ice shelves are relative-
ly exposed to the circumpolar ocean, we assume that
their melt rates would increase in proportion to the dif-
Linear meltrate increase
Fixed Calving
Same as A but v
calving model
Same as A but with linear
increase in Antarctic air
temperature for 300 years
Scenario 2
Linear increase in TCDW for 100
years and then constant
Median sensitivity of Twarm to COM
and melting response to warm
intrusions
Scenario 3
Same as # 2 but except TCDW u
driven by " T global which rises
linearly for 100 years and then
stays constant P4=40 years
P3=0751C
Scenario 5
Same as #3 but Al=0 instead of 5
Scenario 6
Same as #3 but A2=l instead of 0 5
Scenario 7
Same as #3 except thai undiluted CDW
intrudes beneath the shelves
when' TCDW$(XjlC
Scenario 4
Same as #3 except that" T
global increases linearly
for 200 years and stays constant
thereafter.
Same as #4 but includes
precipitation changes
Same as # 8 but fast
response
Same as #9butAl=Oand
high scenario for for CDW
response.
Figure 5-4. The Relationships Between the Sensitivity
Runs.
ference between circumpolar temperatures and the
surface in situ freezing temperature of ~19BC. Thus,
1BC would increase melting by about 33 percent.
Impact of Basal Melting on
Grounded Ice
The draft employed five different models to
describe the impact of ice-shelf melting on the ice stream
contribution to sea level. We discuss each in turn.
Simple Model Based on Melting (AM2)
The simplest approach is to ignore the impact of
ice streams and possible increased calving. Ice-shelf
melting does not raise sea level, but a reasonable first
approximation would be to assume that it does at
least eventually. In the most optimistic of cases, the
increased melting comes entirely at the expense of
decreased calving; in a pessimistic case, the thinner
shelf permits faster ice flow and easier iceberg for-
mation, and thereby increases calving. Lacking good
models, the assumption that calving stays fixed is
intuitively appealing.
Even in such a situation, the initial impact on
sea level would be negligible because ice-shelf retreat
would not automatically accelerate the ice streams.
Nevertheless, even if the shelf exerted negligible
backpressure on the ice streams, it does presumably
exert backpressure on the part of the ice sheet immedi-
ately next to the ice shelf. Thus, if the shelf retreated
to the grounding line, some grounded ice would flow
onto the shelf to prevent the shelf from vanishing
entirely. Therefore, even in the melt-only model,
one can reasonably assume that the melt rate will con-
tinue after total melting has exceeded the current
mass of the ice shelves.
Thus, the draft melt-only model assumed that
shelf melt would make no contribution to sea level rise
until A7 percent of the shelves have melted, after
which point the contribution is 1:1. We assume that
A7 follows a right-triangular distribution between 0
and 1 in which pd(A7)=2A7, where pd is the proba-
bility density function; that is, F(A7
-------
Chapter 5
TABLE 5-3
SCENARIOS USED FOR SENSITIVITY RUNS IN THIS CHAPTER
A. Ice shelf melt rate increases from 0 to 1 m/yr during first 50 years and remains 1 m/yr thereafter. Calving is
fixed at current levels.
B. Same as A, but with Thomas s (nonenhanced) calving model.
1. Same as A except that Antarctic air and Antarctic summer temperatures rise 46C per century for first 300 years
and remain constant thereafter, resulting in increased precipitation according to median scenario.
2. Tcdw rises 0.03BC/yr for first 100 years and stays constant thereafter. Median scenarios for sensitivity of warm
intrusion temperature to CDW (ApS.O; i.e., holding SEAICE constant, intrusions warm 1/6 as much as CDW)
and melting response to warm intrusions below the shelves (A2=0.5 m/[6C yr]). Undiluted CDW does not pen-
etrate ice shelves. No change in precipitation.
3. Same as #2, except that Tcdw is driven by global temperatures, which rise 0.04BC/yr for 100 years and stay con-
stant thereafter. Adjustment time in excess of global adjustment time: P4=40 years. Equilibrium CDW warm-
ing per degree of global warming: P3=0.756C.
4. Same as #3, except that temperatures rise for 200 years and stay constant thereafter.
5. Same as #3, but AL=0 instead of 5.
6. Same as #3, but A2=l instead of 0.5
7. Same as #3, except that undiluted CDW intrudes beneath the shelves as soon as CDW warms 0.56C.
8. Same as #4, but includes precipitation changes.
9. Same as #8, but fast response for CDW (i.e., P4=20)
10. Same as #9, but (a) Aj=0 (i.e., ignoring changes in sea ice, the warm water intruding beneath the shelves warms
as much as CDW; as sea ice declines, the warm intrusion temperature approaches the CDW temperature) and
(b) high scenario for total CDW response (i.e., P3=l).
The Thomas Model (AM3)
Thomas (1985) modeled Ice Stream B
extrapolated the results to the entire continent.
and
Ice Stream B. This two-dimensional model assumes
that there is a single ice stream feeding an ice shelf.
The two dimensions considered were altitude (i.e.,
thickness of ice shelf) and longitude (i.e., distance
from grounding line to ocean/ice margin). The model
parameters for ice-stream velocity and mass discharge
were based on measurements for Ice Stream B. The
distances from the grounding line to ice rises (pinning
points) and to the ice margin, as well as the ice shelf s
thickness, were based on the Ross Ice Shelf. The
mass of the ice shelf was assumed to account for all
the backpressure constraining the current ice-stream
velocity. Thomas then picked an assumed velocity for
a point about 200 km upstream of the grounding line,
which provides the strain of the ice stream necessary
to duplicate the observed velocity at the grounding
line, given all the other parameters.
For a given acceleration in the rate of ice-shelf
melting, the Thomas model calculates the resulting
contribution to sea level, which we can view as:
" ice stream discharge =" melting +" calving + " shelfjnass.
94
-------
Antarctic Ice Sheet
-10
1 1 contribution after 5%
of the ice shelves melt
Scenarios 4 and 8
50 100 150 200 250 300 350 400
Years
800-
700-
600-
-. 500-
| 400-
^ 300-
200-
100-
0
-100
0
Scenario 10
1 1 contribution to sea level after
5% of the ice shelves melt
50% of the ice shelves melt
95% of the ice shelves melt
50 100 150 200 250 300 350 400
Years
Figure 5-5. Antarctic Contribution for the Draft Melt-Only Model. Sea level contribution for (a) scenarios 3, 4,
8, and 9 (see Table 5-3), given the assumption that (A7)1/2 (the fraction of the ice sheet that must melt before melt-
ing contributes to sea level rise) is equal to 0.05, and (b) scenario 10 with A7 equal to .05, 0.5, and 0.95.
A greater rate of ice-shelf melting initially thins the ice
shelf, which reduces shelf backpressure, which in turn
increases the ice-stream velocity. In Thomas s sug-
gested formulation of the model, the ice front/calving
margin remains in its current location. The higher
stream (and shelf) velocity means that (1) the total
area5 of the ice shelf discharged in the form of ice-
bergs in a given year is greater, but (2) the ice shelf is
thinner, which implies that the icebergs do not draw as
much water. Because shelf mass is proportional to the
thickness of the ice shelf,
calving = velocity X shelfjnass,
and thus,
calvingj _ velocityj shelfjnassi
calvingp velocityo shelf_mass0
Because the velocity increases while the shelf mass
decreases, it is not obvious a priori whether this
model would project calving to increase or decrease.
Thomas also specified an enhanced calving sce-
nario, in which the ice front retreats several hundred
5Area is represented by length in this 2-D model.
kilometers after shelf melting exceeds a threshold. Such
a scenario might be explained, for example, because
thinner ice is more easily broken off into icebergs.
Our draft report added a more conservative scenario,
for several reasons. First, as shown in Figure 5-6c,
Thomas s calving model implicitly embodies an instabil-
ity by which any sustained increase in the shelf-melt rate
leads to a continued thinning and gradual elimination of
the ice shelf, with the ice-stream velocity increasing all
the while. Second, as Figures 5-6a and 5-6b show, the
Thomas model projects that the Antarctic sea level con-
tribution is greater than the contribution from melting,
which implies that for every one cubic kilometer of ice
that melts, more than one cubic kilometer of ice will
flow into the shelf. Thus, the model implicitly assumes
that the (mass) calving rate must incre a s e even though
there is a thinner ice shelf.
Our more conservative fixed-calving scenario, by
contrast, assumed that the ice shelf is stable. If the rate
of shelf melt increases, the acceleration in ice-stream
velocity contributes to the mass of the ice shelf, rather
than to calving. This partial replacement of the mass
loss due to increased melting serves as a negative feed-
back on melting. Over time, the ice shelf approaches
a new equilibrium mass, and the rate of sea level rise
95
-------
Chapter 5
a
50-i
50 100 150 200 250 300 350 400
b
012 -i
f
I
0 50 100 150 200 250 300 350 400
Years
"Z 55 -
JS
a 50-
"8 45-1
§ '
S-' 40 -
& 35-
*» 30'
g 20-
I M
50 100 150 200 250 300 350 400
Years
| 400-
2
0 50 100 150 200 250 300 350 400
Years
S
£
e
30 n
50 100 150 200 250 300 350 400
Years
Figure 5-6. Contribution to Sea Level from Ice
Stream B and Antarctica Predicted by Thomas
(1985). These scenarios assume that the Ross Ice
Shelf melt rate accelerates from 0 to 1 m/yr linearly in
the first 50 years and is constant thereafter, (a) Sea
level equivalents of (i) Ice Stream B contribution, (ii)
corresponding ice-shelf melting assumed by the
Thomas model; and (iii) Ross shelf-wide melting
implied by the same melt rates, (b) Rates of rise corre-
sponding to (a), (c) Mass of Ross Ice Shelf, (d) Same
as (a) but (i) and (ii) are scaled for all of Antarctica as
in original Thomas model and (iii) shows melting of all
ice shelves, (e) Rates of rise corresponding to (d). All
runs use reference calving.
96
-------
Antarctic Ice Sheet
approaches the contribution due to melting. The
Thomas model with fixed calving is essentially a melt-
only model: sea level rise lags behind melting, and the
functional form of the lag is based on the physics of Ice
Stream B rather than the simple linear adjustment we
have used elsewhere (i.e.,
-------
Chapter 5
Ronne/Filchner Ice Shelves. Therefore, model AM4
assumes that the appropriate extrapolation is to assume
a coincident acceleration of only the streams that feed
the Ross and Ronne/Filchner Ice Shelves. This
assumption implies scaling the Ice Stream B results by
a factor of 10.1. As Figure 5-7 shows, the reference
calving scenario would imply an acceleration of 1.67
mm/yr if the shelves thin 1 m/yr.
This assumption also provides a lower estimate
of the amount of melting that is driving the model.
Unfortunately, it understates melting by a factor of 2.8.
AM5. The other way of addressing the same problem
is to view the Thomas model as showing how mass
flux lags (or leads) basal melting. Instead of assuming
that all (or some) ice streams accelerate by the same
fraction as Ice Stream B, AM5 assumes that the conti-
nent-wide ratio of mass flux to basal melting is the
same as that calculated in the Thomas model. S rep-
resents the ratio of continent-wide melting to melting
of the hypothetical shelf scaled by Ice Stream B, a fac-
tor of approximately 28. Thus, the model is driven by
an actual estimate of the continent-wide melt rate.
The propriety of this assumption depends in
part on whether one is using the fixed or reference
calving scenario. In the fixed calving scenario, we
have two offsetting oversimplifications. On the one
hand, we effectively assume that capacity of ice
streams feeding the relevant ice shelves is SAMS (i.e.,
28) times that of Ice Stream B, whereas it may be only
SAM4 (i.e., 10) times that of Ice Stream B (unless
streams outside of the Ross and Ronne/Filchner
Basins would also respond to shelf melt). On the
other hand, this overstatement also applies to the neg-
ative feedback caused by adding ice to shelves. Thus,
in the fixed-calving scenario, any over- or underesti-
mate of ice-stream capacity has an impact on the
speed at which ice-shelf mass (and thus sea level)
adjusts to shelf melting, but not on the equilibrium
rate of sea level rise toward which the system tends.
For the reference calving scenario, by contrast,
the system is not adjusting to an equilibrium.
Therefore, any implied over- or understatement of ice-
stream capacity will translate all the way through to
the projections of the rate of equilibrium sea level rise.
Disaggregating the Thomas Model
into Different Ice Streams (AM6)
The preceding discussion highlights the fact
that if we merely scale up the results of a two-dimen-
sional model, we must either (1) understate the
amount of underlying shelf melting or (2) overstate
the amount of ice-stream capacity.
Fortunately, we need not make this Hobbesian
choice: Data is available for other ice streams as well,
as shown in Table 5-1. As a result, one can employ
the Thomas ice-stream model without resorting to
continent-wide scaling.
AM6 divides Antarctica into the regions shown in
Figure 5-2, using the ice streams summarized in Table 5-1.
Several aspects of this approach need explaining. Most
importantly, AM6 does not arbitrarily scale up the results
reached in one basin; rather, it conservatively assumes
no change in processes that are not explicitly modeled.
Ross and Ronne/Filchner. AM6 assumes that the Thomas
approach applies only to the Ross and Ronne/Filchner
Basins. It allows for several ice streams feeding the
Ross and Ronne/Filchner Ice Shelves. In response to
thinning of the ice shelf at time tj, each stream is mod-
eled separately; and its contribution is added to the ice
shelf at the end of the period, so that at time t2, the
apparent thinning of the shelf will be equal to the basal
melting minus the combined contributions during tj of
(a) precipitation and (b) all the modeled ice streams.
Thus, the impact of having several streams is to increase
the speed at which mass flux responds to shelf thinning;
but because the flux from each stream builds back the
shelf, the long-term impact of extra streams is relatively
small. Since all of the major streams (plus a category
for other streams ) are included, no scaling is neces-
sary. Thus, with respect to the Ross and Ronne/Filchner
Ice Shelves, AM6 considers both the actual area of ice
shelf (like AM5) and the existing ice-stream capacity
(likeAM4).
Amery and Other Shelves. AM6 also has features of
AM4 and AM5 in the handling of other shelves.
While the former assumes no contribution and the lat-
ter assumes that the contribution will respond in pro-
portion to shelf melt, AM6 makes an intermediate
assumption: the shelves will melt entirely with no
contribution to sea level, after which point melting
adds to sea level on a 1:1 basis.
Effectively, this approach assumes that the lack
of backpressure exerted by the shelves will enable
shelves to thin substantially, but that the area of melt-
ing near the grounding line will retain its configuration.
Thus, the shelf does exert backpressure on the ice
immediately inland, so that if it thins past a point,
enough ice will flow into it to prevent the forming of a
98
-------
Antarctic Ice Sheet
§ 125-
50 100 150 200 250 300 350 400
Years
0 50 100 150 200 250 300 350 400
Years
Figure 5-7. Antarctic Contribution to Sea Level According to Model AM4. Same as Figure 5-6 (d) and
(e), except based on AM4; i.e., Ice Stream B results scaled by the contribution of ice streams feeding Ross and
Ronne-Filchner Ice Shelves.
50 100 150 200 250 300 350 400
Years
i and i
50 100 150
200 250
Years
300 350 400
Figure 5-8. Antarctic Contribution to Sea Level According to Model AM5. Same as Figure 5-6 (d) and
(e), butforAMS.
99
-------
Chapter 5
vertical wall and commensurate decline in melting
(which would require us to explain what happens to the
additional heat).
Antarctic Peninsula. The model by Drewry & Morris
(1992) suggests that for a 2BC warming, the total con-
tribution to sea level is only 1 to 2 mm. Because this
is not significantly different from zero, we assume
that the net contribution from the Antarctic Peninsula
is zero (i.e., that ablation and ice sheet flow counter-
balance the increase in precipitation over the conti-
nent). Future reports should explicitly include the
Drewry model, to account for possible ablation from
extremely warm scenarios and to uncouple ice flow
from precipitation changes.
Adjustment to Antarctic Precipitation if the Area of the
Ice Sheet Declines. This adjustment only becomes
relevant in the latter years of the extreme scenarios.
If ice shelves or ice sheets in West Antarctica
retreat, snow that would otherwise fall on the conti-
nent will fall into the sea. The draft assumes that East
Antarctica and the Antarctic Peninsula will maintain
their current area, but that the areas of the other two
regions will decline as their mass declines:
Area, = Area0 (Volumet/Volume0)p9.
No studies are available to provide values for
P9. To get a sense of possible values, consider a cube
melting along various sides. If the cube melts evenly
along the x-y, x-z, and y-z planes, the x-y area (which
determines snowfall) declines with the 2/3 power of
volume. If the cube melts only along the x-z, y-z, or
both planes, then x-y area declines with the 1.0 power.
If the cube melts along the x-y and either the x-z or y-z
planes, area declines with the 1/3 power.
The draft assumed that P9 is lognormally dis-
tributed with 2(7 limits of 1/3 and 2/3. This adjust-
ment is negligible in all but a few runs.
Sensitivity Runs and Selected Simulations
Figure 5-9 compares the four variations of the
Thomas model. Scenario A, using the disaggregated
AM6, implies a sea level contribution only slightly
greater than AM5, mostly because several ice streams
would allow a faster response than would a single ice
stream. The projections are below those for AM3 and
AM4, because those formulations (in our view)
overextrapolate by assuming that all the ice, or all the
ice leaving through the major ice shelves, respond as
a
1000-a
I .0,
0 50 100 150 200 250 300 350 400
Years
3
1!
0 50 100 150 200 250 300 350 400
Years
Figure 5-9. Comparison of Alternate Scalings of
the Thomas Model. Estimates of (a) total sea level
and (b) rate of sea level rise contribution from
Antarctica, for the various extrapolations of the
Thomas model (AM3, AM4, AM5), as well as our
more disaggregated version (A=AM6 with fixed calv-
ing, and B=AM6 with Thomas s reference calving).
All scenarios assume that the rate of shelf-thinning
increases 2 cm/yr2 for 50 years, after which it remains
constant at a rate of 1.17 m/yr (i.e., 1 m/yr greater
than the current rate for the Ross Ice Shelf).
100
-------
Antarctic Ice Sheet
Ice Stream B would respond if it were the only ice
stream feeding the Ross Ice Shelf. The use of
Thomas s calving model conies close to doubling the
sensitivity of AM6.
Figures 5-10 and 5-11 illustrate the cumulative
and annual Antarctic contribution to sea level result-
ing from the climate forcing scenarios described pre-
viously in Table 5-3. The scenario combinations in
Figure 5-1 Ob correspond to the scenarios examined in
the previous section on shelf-melt rates. The scenar-
ios in the left half of the figure are based on the
assumption that global temperatures rise for 100 years
and are steady thereafter; those on the right side
(other than scenario 3) involve global temperatures
rising for 200 years.
As before, scenarios 3 and 4 both keep precipi-
tation fixed, assume that global temperatures rise 46C
per century, and employ median values for (a) the
magnitude and timing of the CDW response to global
temperatures; (b) the response of warm intrusion tem-
perature to CDW; and (c) the response of basal shelf
melting to warmer water temperatures. The only differ-
ence is that global temperatures stabilize after 100 years
in scenario 3 and 200 years in scenario 4. Scenario 8
is like scenario 4, except that it also considers the medi-
an estimate of increased precipitation; thus, scenario 8
represents our true median scenario. Both scenarios 3
and 4 take about 170 years before climate change can
offset the existing negative contribution to sea level
rise implied by Bentley s mass balance estimates.
Scenario 8 shows a sea level drop of 3.8 cm for the first
100 years and a negative Antarctic contribution for the
foreseeable future. Thus, unlike the previous effort by
Thomas—but consistent with previous efforts by IPCC
and Huybrechts & Oerlemans—our median scenario
shows a negative contribution to sea level from
Antarctica. This is hardly surprising, when one
recalls that the shelf-melt rate only increases from
the current 0.17 m/yr to 0.42 m/yr in one hundred
years and takes two centuries to reach 1 m/yr, which
is generally viewed as a threshold for significant ice
sheet responses.
Only when we test the high-sensitivity sides of
the distributions of our uncertainties do we obtain rela-
tively high shelf thinning. Scenario 5, with the shelf-
thinning rate exceeding 1 m/yr after 70 years, provides
a positive contribution to sea level after about 90 years;
nevertheless, the total contribution after 200 years is
only 16 cm. Scenario 10, with its much greater shelf-
thinning rates, contributes about 5.6 mm/yr by the
a
04-i
2 02-)
"aJ
5
Scenario B
Scenario A
Scenario 2
Scenario 1
25 50 75 100 125 150 175 200
Years
50 75 100 125 150 175 200
Figure 5-10. Antarctic Contribution to Sea Level
According to Model AM6. Total contribution and
rate of sea level rise for scenarios A, B, 1, and 2.
100th year, and about 12 mm/yr after 200 years. This
scenario, however, is very unlikely because it would
require the temperature of the water intruding beneath
the ice shelves to warm more than 46C by 2100 and
almost 96C by 2200.8
^But see the comment by Thomas in Expert Judgment, infra.
101
-------
Chapter 5
a
05i -i
ooo -
Scenario 7
75 100
Years
Scenario 3
125 150 175 200
Scenario 7
Scenario 5
0 25 50 75 100 125 150 175
Scenario 10
50 100 150 200 250 300 350 400
Figure 5-11. Sensitivity Analysis of Model AM6. Cumulative and annual Antarctic contribution to sea level (a and
b) for scenarios 2, 3, 5, 6, and 7, and (c and d) for 3, 4, 8, 9, and 10.
Linearization of the Huybrechts
& Oerlemans Model
Huybrechts & Oerlemans (1990) estimate that
with a 1 m/yr rate of shelf-thinning, sea level rises 2, 3,
7, 8, and 10 cm during each of the next five centuries,
respectively. We adopt the simplest way of generalizing
these results: the first 100 m of shelf-thinning causes a
2 cm rise, the next 100 m, a 3 cm rise, etc. This assump-
tion oversimplifies the dynamics of their model.
Additional runs from those researchers would enable us
to determine whether we overstate or understate the
likely impact of scenarios with greater melt rates.9
Draft Results
Figure 5-12 illustrates the draft probability den-
sity of the Antarctic contribution; Figure 5-13 illus-
"Our simplification effectively assumes that if the rate of basal melt-
ing doubles, the response time is cut in half, but that a given shelf-
thinning produces a given rise in sea level regardless of its timing. In
the short run, this assumption probably overstates sensitivity; a 100 m
shelf-thinning over the course of a single year would not cause the fall
2 cm rise in that year. In the long run, this assumption may understate
the impact. For example, the implication that a rapid 500 m thinning
would cause only a 30 cm rise is far more optimistic than Lingle
(1985), which suggested that such a thinning could cause an irre-
versible disintegration of the West Antarctic Ice Sheet.
102
-------
Antarctic Ice Sheet
s
12-
10-
8-
6-
4-
2-
l
J
b
* B
-f
1
b2
JL_ ^
J
lll|j||.lr ... .
-2 -16 -12 -0.8 -04 0 0.4 0.8 1 2 1.6 2
Sea Level Rise (cm)
-12 -7-23 8 13
Sea Level Rise (cm)
18 23 25
-475 -35 -22.5-10 25 15 27 5 40 52.5 65 775 90 102.5 115
Sea Level Rise (cm)
Figure 5-12. Probability Density of the Antarc-
tic Contribution: Draft Report, (a) 1990—2030;
(b) 1990—2100; (c) 1990—2200.
103
-------
Chapter 5
Years
Figure 5-13. Spaghetti Diagram of Antarctic Contribu-
tion to Sea Level: Draft Report Antarctic contribution
for selected simulations. See Figure 2-5 and accompany-
ing text for additional explanation.
TABLE 5-4
CUMULATIVE PROBABILITY DISTRIBUTION
FOR ANTARCTIC CONTRIBUTION TO
SEA LEVEL: DRAFT REPORT
Cumulative
Probability (%)
1
5
10
20
30
40
50
60
70
80
90
95
97.5
99
99.5
Mean
a
2030
—12
—95
—86
-=75
-&
—55
—.15
—07
.02
.65
.80
1.2
2.1
—02
0.7
2100
—56
—36
-^29
—19
—16
—12
—10
0.0
1.5
2.1
2.9
5.0
8.2
16.0
21.7
0.3
4.0
2200
-£
-g
-5
-2
0
2
3
4
5
10
25
42
67
102
137
6.1
20.3
trates for selected simulations; and Table 5-4 summa-
rizes the draft cumulative probability distribution of
the Antarctic contribution to sea level. As expected,
the median contribution was negative. There was also
a 1 percent chance of a 16 cm contribution through
2100 and aim contribution by the year 2200. Almost
all of the high projections resulted, however, from the
500 simulations that used AM3.
Expert Judgment
The nine expert reviewers who provided com-
ments are listed in Table 5-5 (with the exception of
one reviewer who preferred to remain anonymous).
With the exception of Stan Jacobs and Craig Lingle,
all of the reviewers provided probability distributions
for at least some of the parameters. Lingle, however,
provided scenarios for what the Antarctic contribution
might be without a greenhouse warming.
Both Lingle and Jacobs took issue with our
assumption that, in the absence of additional climate
change, Antarctica would increase its mass and thereby
lower sea level 0.1 to 1.1 mm/yr. Indeed, IPCC (1990)
estimated that the historic contribution has been
between +0.5 and -0.5 mm/yr. Lingle (1989) devel-
oped three baseline scenarios ranging from ~1.5 cm to
+ 16 cm, with a rise of 5 cm most likely for the year
2100. We summarized these projections with a normal
distribution with a mean of 0.5 mm/yr and CT limits of
~f).l and +1.1 mm/yr. These baseline assumptions are
invoked 25 percent of the time; the ~Q.l to ~i.l mm/yr
range is invoked the rest of the time.10
As discussed in Chapter 1 ( Correlation Between
Assumptions ), one-eighth of the simulations reflect
Wigley & Raper s suggested assumptions for each of
'"Neither we nor Lingle were able to devise a reasonable way to
incorporate the results of Lingle (1985) into this analysis.
104
-------
Antarctic Ice Sheet
Richard Alley
Anonymous
Robert Bindschadler
Roger Braithwaite
Stan Jacobs
Craig Lingle
Robert Thomas
C.J. van der Veen
Jay Zwally
TABLE 5-5
EXPERT REVIEWERS OF CHAPTER 5
Pennsylvania State University
University Professor
Goddard Space Flight Center NASA
Geological Survey of Greenland
Lament Doherty Earth Observatory
Columbia University
University of Alaska
Greenland Ice Core Project
NASA Headquarters
Byrd Polar Research Center
Ohio State University
Goddard Space Flight Center NASA
University Park, PA
United States
Greenbelt, MD
Copenhagen, Dnmk
Palisades, NY
Fairbanks, AK
Washington, DC
Columbus, OH
Greenbelt, MD
Note: Wigley & Raper did not review this chapter; but they did provide their own expectations based on previous work, which we
employ as the linear model AM 1.1.
the major contributors to sea level rise. In the case of
Antarctica, their assumptions are a slight mod-ifica-
tion of AMI the IPCC (1990) assumptions in that
they allow for the possibility that melting would offset
some of the increase in precipitation:
dSL
'Antarctica.- ft - 7-
j, — -PA L Antarctica'
i
. I
where p\ has a median of —0.2 and a standard devia-
tion of 0.135, and dSL/dt is measured in mm/yr.
Because seven other researchers provided us
with process-specific assumptions for Antarctica,
each set of assumptions accounts for 1250 simula-
tions. We discuss the comments on ice shelves and
ice stream response separately.
Ice Shelf Assumptions
Most of the reviewers focused on our ice stream
models, that is, our assumptions regarding how much
mass would be transferred from Antarctica to the
oceans for a given thinning of the ice shelves; only
three provided comments on shelf melting. The lack
of comments does not imply a judgment that our
assumptions regarding ice shelf melt are more reli-
able. If anything, it indirectly suggests that they are
less reliable: The absence of ice shelf data and mod-
eling made it difficult for reviewers to improve on our
specific assumptions, so most chose not to comment.
The exceptions were Robert Thomas, Stan
Jacobs, and Robert Bindschadler. Although Jacobs
was unable to suggest alternative assumptions, his
comments provide a suitable caution:
It is probable that net melting under the Ross
Ice Shelf results from warm intrusions that are cur-
rently around 1.48C. However, we have learned a
few things since 1984, one of which is that the Ross
Sea warm intrusion is apparently divided into an
inflow and outflow, with relatively little net transport
of heat beneath the ice. This does not invalidate [the
assumption that the rate of melting is based on a]
temperature differential [between the temperature of
the warm intrusion and the in situ freezing point], in
part because of an interesting coincidence. That is,
the primary deep thermohaline circulation beneath
the large ice shelves is now believed to begin with
water at the sea surface freezing temperature
(approximately —1.9BQ which is approximately
0.5BC above the in situ freezing point at a depth of
about 700 m.
The issue of present-day warm intrusions and
how they might change with time is still an open
and thorny question. The impact of warm water is
best documented beneath the George VI Ice Shelf
105
-------
Chapter 5
(Potter and Paren 1985), where the basal melt rate
appears to be an order of magnitude higher than
beneath the Ross. It is not clear how readily this
Bellinghausen Sea type circulation could spread to
other regions of the continental shelf. In particular,
present circulation beneath the Ross Ice Shelf may
be protected by the strong offshore winds that gen-
erate large amounts of sea ice and high salinity shelf
water in that sector. The winds may not be as strong
in the Weddell Sea, but there the Antarctic Peninsula
and Weddell Gyre keep the deep water cooler. This
makes some of the Jenkins estimates look a bit on
the high side to us, at least on the near term.
[The current report assumes] that dilution of
the warm intrusion by shelf water is proportional to
annual sea ice formation. Maybe so, but there are
several problems with that assumption, aside from
what s noted above. [The] dilution applies only
to temperature, whereas the salinity and volume
changes may be more important. At low tempera-
tures, salinity exerts the primary control on density
and the resulting thermohaline circulation. Further,
the dilution of interest occurs only over the con-
tinental shelf, which occupies <20% of the winter
sea ice extent. It might thus be argued that ice
cover could change substantially without much of
an impact on the shelf circulation. It has also been
hypothesized that a warmer and wetter atmosphere
will effectively cap vertical heat flux from the deep
water, allowing sea ice to grow thicker (Manabe et
al., 1991). However, so far the intuition fits the
evidence, in that higher air temperatures are nega-
tively correlated with sea ice extent.J1
Jacobs concludes that our model was an improve-
ment over those assessments that simply assume that the
Antarctic contribution is a multiple of thermal expan-
sion (e.g., Hoffman et al. 1983) or of temperature (e.g.,
IPCC 1990). Nevertheless, his comments show that our
assumptions substantially oversimplify the processes
that will determine shelf melting.
Robert Thomas suggested specific changes to
the model for Ross Ice Shelf melting. The draft
assumed that a fixed dilution coefficient A} deter-
mined the extent to which CDW warming translates
into warmer water intruding beneath the ice shelves,
holding annual seaice formation constant, and that
changes in sea ice result in proportional changes in
this dilution. Thomas preferred to remove sea ice
from the model and to allow the dilution to change
linearly with Tcdw:
Twarm = Tcdw/dilution_factor,
where dilution_factor=6—" Tcdw for " Tcdw<5 and 1.0
thereafter in the median scenario, and temperatures
are measured with respect to the in situ freezing point.
Alternatively,
Twarm = Tcdw^6— " Tcdw) for " Tcdw<5;
= Tcdw for " Tcdw^5-
That is, Twarm = min{Tcdw, Tcdw/(9—Tcdw)},
where all temperatures are measured with respect to the
in situ freezing point. Generalizing, Thomas would
allow the dilution ratio to fall linearly from its initial
value of (1+Ai) to a value of 1 for a warming of A,6C:
T
T — min/T *CdW
1warm -mmUcdwi .A ""
A "T" i~Vl
cdw
Adjusting for the fact that the initial Twarm=0.5 when
Tcdw=3.0, we have
, = min{Tcdw,
T
1cdw
1 + A! — T
cdw
"Stan Jacobs, Lamont Doherty Earth Observatory, Columbia
University. Letter to James G. Titus. August 12, 1993 (quoting the
draft report).
where all temperatures are expressed in degrees above
the in situ freezing point of saltwater. This equation is
similar to the equation used in the draft, except that (a)
the impact of the variable SEAICE on the dilution fac-
tor is replaced by a simpler function of temperature and
(b) the existence of Tcdw in the denominator requires us
to explicitly prevent Twarm from exceeding Tcdw.
Because Thomas functional specification leads Twarm to
catch up with Tcdw more rapidly than our draft assump-
tions, Thomas employs a narrower range for Aj, retaining
our median value of 5 but using 2a limits of 2.5 and 10.
Perhaps more important, Thomas also models the
response to warm intrusion as a quadratic rather than as
a linear function of temperature, based on MacAyeal
(1984). He assumes that the response becomes linear
once the rate of shelf melting exceeds the 3 m/yr that he
examined in Thomas (1985). Thus, we have
Melt - 2 A2 Twarm2 + .25 (1 — 2A2)
for Twarm < [(2.75 + 0.5A2)/2A2]1/2, and
Melt = 3 + 4A2(Twarm — [(2.75 + 0.5A2)/2A2]l/2)
forTwarm > [(2.75 + 0.5 A2)/2A2] "2.
106
-------
Antarctic Ice Sheet
TABLE 5-6
COMPARISON OF SHELF MELT RATES FOR DRAFT AND THOMAS ASSUMPTIONS
Thomas Assumptions
Median Assumptions
Draft Assumptions3
Fixed Sea Ice
Median Sea Ice
"I,
cdw
0
1
2
2.7
3
4
5
6
cdw
3
4
5
5.7
6
7
0.5
0.8
1.25
1.73
2.00
3.5
8.0
9.0
melt
rate
0.25
0.64
1.56
3.00
3.53
6.53
15.53
17.53
0.5
0.66
0.83
0.95
1.00
1.17
1.33
1.5
melt
rate
0.25
0.33
0.42
0.47
0.5
0.58
0.67
0.75
seaice
rate
1
0.85
0.72
0.64
0.61
0.52
0.44
0.38
0.5
0.70
0.97
1.22
1.34
1.77
2.29
2.92
melt
rate
0.25
0.35
0.48
0.61
0.66
0.88
1.15
1.46
g-High Assumption for A
0
1
1.93
2
3
3.55
4
5
6
3
4
4.93
5
6
6.55
7
l
0.5
0.97
1.73
1.81
3.75
6.55
7
0.25
0.94
3.00
3.16
7.05
12.64
13.53
15.53
17.53
0.50
0.91
1.28
1.31
1.72
1.95
2.13
2.54
2.94
0.25
0.45
0.64
0.66
0.86
0.97
1.06
1.27
1.47
1
0.85
0.73
0.72
0.61
0.56
0.52
0.44
0.37
0.50
1.07
1.69
1.74
2.51
2.96
3.35
4.28
5.27
0.25
0.54
0.86
0.87
1.23
1.48
1.68
2.14
2.64
aThese calculations use the draft assumptions for the shelf-melt parameters. The temperature assumptions are arbitrarily specified. The
assumption that sea ice declines 15 percent per degree (C) is the median scenario for the final results; although the simulations base the
calculation on " T, this table uses " Tcdw for simplicity.
Table 5-6 compares the resulting estimates of
shelf-melt rates for both the draft and Thomas
assumptions, using the median and o-high values of
Aj. For the median value, the draft did not project the
shelf-melt rate to exceed 1 m/yr until Tcdw has
warmed by over 5BC12; by contrast, the Thomas
assumptions suggest that such a rate would occur with
a circumpolar ocean warming of about 1.56C.13
The potential for high rates of shelf melting is fur-
ther illustrated by the second half of the table. Using the
draft o-high assumption for Aj implies a shelf-thinning
rate exceeding 1 m/yr with a circumpolar ocean warm-
ing of about 36C; Thomas s o-high assumptions imply
a similar melting rate with a warming of only 16C.
12Except for cases where undiluted circumpolar ocean water
intrudes beneath the shelves, in which case the shelf-melt rate
accelerates immediately to about 1.5 m/yr.
Moreover, for a 2BC warming, Thomas s o-high
assumption implies a melt rate of over 3 m/yr. For a
warming in excess of 3.56C, his o-high assumption
implies melt rates in excess of 10 m/yr!
Do Thomas s assumptions imply unreasonably
high rates of ice shelf melt? We think not, especially
in light of the fact that they represent only one-eighth
of the simulations employed in this analysis. A shelf-
melt rate of 3 m/yr is certainly high, but in the median
13Recall from Chapter 3 that most of the climate modelers proposed
median assumptions in which Tcdw warms about 1BC by the year 2100.
Schneiders median assumptions, however, implied a warming of
about 1.56C after the year 2080. Thus, substantial contributions from
Antarctica before the year 2100 seem most likely to result in cases
where Schneider and Thomas assumptions coincide. Because Hoffert
and Rind have greater equilibrium polar amplification factors albeit
with longer lag times post-2100 contributions will be greatest when
Thomas assumptions coincide with either Hoffert or Rind.
107
-------
Chapter 5
case, Thomas does not assume that it would occur
unless the circumpolar ocean warmed 2 to 46C.14
Comparable rates of shelf-thinning have been observed
in areas where the water beneath the ice shelves is 2 to
SBC warmer than found under the Ross Ice Shelf.
The possibility that the ice shelves might even-
tually melt by 10 m/yr seems even more extraordinary,
since such a rate implies a fortyfold increase in the
currently observed rate. But the physical basis is not
implausible: A 4BC warming would imply an eightfold
increase in the temperature differential and hence
potential melt rate if the amount of circumpolar
ocean water intruding beneath the shelves remained
constant; if that water was not diluted by the colder
shelf water, its temperature would be 76C above the in
situ freezing point, and thus the differential would be
fourteenfold greater than today. Even assuming lin-
earity, a three- to fivefold increase in the amount of
water intruding beneath the ice shelves along with a
46C warming would appear to have the potential to
cause a melt rate of 10 m/yr. The comments of Stan
Jacobs highlight the fact that circulation may not
increase it could even decrease.
These high shelf rates are unlikely in the next
century, because they require the coincidence of two
unlikely events. First, the high half of Thomas s
assumptions account for only 8 percent of our simula-
tions; his a-high assumptions account for about 2 per-
cent. Second, only 15 percent of the simulations
involve CDW warming of 2BC in the next century, and
only 4 percent involve a 3.56C warming.15
Compared with the Thomas assumptions,
Robert Bindschadler s proposed revisions were fairly
minor. He generally agreed with the assumptions
employed by the draft but proposed a minor change to
the sensitivity of the Ronne/Filchner Ice Shelf to
warmer temperatures of the Weddell Sea. Because the
Jenkins estimate of 3.33 m/yr per degree (C) is a more
recent estimate, he suggested that this estimate should
be the median sensitivity, with the old estimate of 1.91
becoming the lower o~ limit.16
Ice Sheet Response to Shelf-Thinning
Aside from the aforementioned changes sug-
gested by Thomas, the assumptions proposed by the
14From the Thomas a-low assumption, not displayed.
lsSee Chapter 3, supra.
l6The draft had used both estimates as 2<7 limits.
Antarctic researchers generally conformed to the ana-
lytic structure of the draft report. One exception was
our melt-only model (AM2). The reviewers were
unanimous that this model should simply assume a
linear adjustment similar to those employed exten-
sively in Chapter 3. That is,
Shelf_Mass*(t) = Shelf_Mass0
- Shelf Mass(t) = Shelf_Mass*(t)-Shelf_Mass(t-l),
A8
where A8 represents the e-folding time of the response
of the ice shelf to net melting; Shelf_Mass* is the
equilibrium toward which the mass of the ice shelf is
tending at any point in time; and Sheet_Mass is the
mass of all Antarctic glacial ice. For small changes in
the mass of the ice shelf, the ratio at the right-hand side
of the first equation can be ignored. Thus, if melting
reduces the ice shelf s mass by one kilogram, AM2
assumes that eventually one kilogram of ice will be
transferred to the ice shelf, but that in the first year only
1/A8 kilograms will be transferred.
All but two of the reviewers suggested that the
response-time constant A8 should have a median of 100
years with 2a limits of 10 and 1000. Zwally suggested
that 2o limits of 50 and 200 would be more appropriate.
Thomas suggested a more rapid response time with a
median of 10 years and 2o~ limits of 1 and 100 years.
Having made this change in the melt-only
model, the reviewers unanimously rejected our fixed
calving assumptions by which we had proposed to
force the Thomas model to assume stability. The rea-
soning was simple enough: the Thomas model was
designed to yield an unstable ice stream response.
Thus, when reviewers voted to use this model, they
were voting for an unstable response; when they wanted
a stable response, they had the melt-only model AM2.
Thomas also suggested that some of the runs should
employ the Thomas (1985) enhanced calving sce-
nario based on a retreat of the calving front. For a one
degree (C) warming in " Tcdw, all scenarios use refer-
ence calving. From that point on, however, the proba-
bility of a retreat of the calving front increases linearly
with temperature by 10%/BC. Thus, a SBC warming
would imply, for example, a 20 percent chance of the
Thomas enhanced calving.
Coincidentally, the combined assessment of the
reviewers was fairly similar to the assumptions employed
108
-------
Antarctic Ice Sheet
in the draft, as show in Table 5-7. The low-response
models AMI and AM7 received 30 percent of the allo-
cation in the draft and 34.1 percent from the reviewers.
The addition of AM 1.1, however, brought the total
probability of low-response models up to 46.7. In the
original draft, 35 percent of the simulations had a stable
equilibrium response roughly equal to the total melting
(the Thomas models with fixed calving) and 20 percent
had a response equal to a fraction of the total melting (the
old AM2). The revised version, by contrast, has 32 per-
cent of the simulations based on a stable response rough-
ly equal to total melting (new AM2). Finally, 15 percent
of the simulations in the original draft involved an unsta-
ble response (the Thomas models with reference calv-
ing ), while 21 percent of the simulations in the current
version involve an unstable response.
At the high end of the simulations, the draft used
AM3 for 5 percent of the simulations; the reviewers sug-
gested that this scaling of the Thomas model only be
used 1 percent of the time. However, Thomas proposed
a modification of AM4 with results that are 60 percent as
great. Our original AM4 scaled the AM3 results down-
ward by a factor of 20 percent because only 20 percent
of the ice leaves through the Ross and Ronne/Filchner
Ice Shelves. Thomas reasoned that a more appropriate
scaling would be 60 percent, the portion of ice leaving
through any form of ice stream; we call this assumption
AM4.1. Coincidentally, this assumption gives the same
result scalar as AM5.
Figure 5-14 compares the revised versions of AM2
with the various scalings of the Thomas model. The por-
tion of reviewer-suggested simulations involving the highly
sensitive, unstable versions (AM3, AM4.1, and AM5) is
about half as great as the portion involving AM3 and AM5
in the original draft. Given that (1) all the simulations of
the Thomas models involve the assumption of instability,
while (2) the draft employed a stable version of the
Thomas model 70 percent of the time, the net impact of
the reviewer comments is to expand the uncertainty range
concerning the sensitivity of ice streams to ice-shelfmelting.
Final Results
Figures 5-15 and 5-16 illustrate our estimates of
the rate of Ross Ice Shelf melting. Because the cir-
cumpolar ocean warms by less than 16C in most of the
TABLE 5-7
REVIEWER ALLOCATION OF PROBABILITIES BETWEEN THE ALTERNATIVE ANTARCTIC MODELS
(percent)
Draft Bind- Bentley Alley Van der Zwally Thomas Anony- Wigley Total
Used schadler Veen mous
AMI
AM1.1
AM2
Thomas
AM3
AM4
AM4.
AM5
AM6
AM7
NOTE:
10
20
50
5
10
1
10
25
20
AMI
5
60
20
0
0
5
15
15
25
25
25
0
0
0
25
25
10
30
37
1
1
5
30
23
30
30
10
0
0
0
10
30
10
40
35
1
24
5
5
15
0
45
30
5
0
25
0
0
25
AMI = Precipitation only (IPCC).
AM1.1 = Wigley & Raper (1992) model.
AM2 = Precipitation + melt-only model.
AM3, AM4, AM4.1, AM5, and AM6 = Thomas (1985) model.
AM7 = Huybrechts & Oerlemans (1990) model.
0
25
25
1.11
3.98
3.98
2.39
13.53
50
100
10
12.5
31.9
22.75
1.02
3.65
3.65
2.08
12.32
24.1
109
-------
Chapter 5
50 100 150 200 250 300 350 400
350 400
Time
50 100 150 200 250 300 350 400
50 100 150 200 250 300 350 400
Time
Figure 5-14. Revised Models of Antarctic Contribution, (a) Temperature changes using median response time
assumptions, (b) The resulting annual shelf-melting, precipitation, and Antarctic contributions to sea level implied
by the stable melt-only model AM2, using median and 2o-high assumptions for shelf-melt sensitivity, and median
assumptions elsewhere, (c) Annual sea level contributions for the unstable models AM3, AM4, AM5, and AM6. The
sensitivity of the median assumptions from IPCC (1990) is shown for comparison, (d) Total Antarctic contribution
110
-------
99
i i
95 —
.90
.70 —
50 —
.30 —
.10
.05 —
/
/
01
Thomas
All Other Reviewers
Total
Shelf Melt Rate (m/yr), 2100 (cm)
Figure 5-15. Ross Ice Shelf Melt Rates: Cumulative Probability Distribution.
i i i i i i i i i i i i i i NTI i i i i r
1 2 5
10
Antarctic Ice Sheet
1990
2050
2150
2300
Figure 5-16. Ross Ice Shelf Melt Rates. Selected simulations for the period 1990-2300. See Figure 2-5 and
accompanying text for the source of the simulations selected.
Ill
-------
Chapter 5
a
4!
a
200 —
175 --
H 125
c
£ 100
•c
50 -
-25
H h
H 1 1 1 1 1 1 1 1-
2150
2000
2200
2300
Figure 5-17. Spaghetti Diagrams for Antarctic Contribution, (a) Annual and (b) cumulative Antarctic contribu-
tion for selected simulations. See Figure 2-5 and accompanying text for explanation of scenarios illustrated.
112
-------
Antarctic Ice Sheet
runs, the median shelf-melt rate is less than 0.5 m/yr
by 2100; and almost 90 percent of the simulations
project melt rates less than 1 m/yr. In the following
century, however, shelf-melt rates accelerate as cir-
cumpolar temperatures begin to rise at rates compara-
ble to the rate of global warming. In a few cases,
shelf-melt rates accelerate rather suddenly due to the
possibility of a switch in which undiluted circum-
polar deep water intrudes beneath the Ross Ice Shelf.
The resulting impact on the Antarctic contribu-
tion to sea level is illustrated in Figure 5-17 (previous
page). For virtually all scenarios, the increased precip-
itation associated with warmer temperatures dominates
at first, both because Antarctic air temperatures (and
hence precipitation) are assumed to respond more
rapidly than water temperatures (and hence shelf melt-
ing), and because the ice streams take another century
to respond to shelf melting. Thus, by the year 2050,67
percent of the scenarios show a net negative sea level
contribution; this percentage declines to 62 percent by
2100, and 50 percent by the year 2200 (see Table 5-8).
Even though most scenarios show a negative
contribution, the analysis suggests that there is a small
chance of a very large positive Antarctic contribution.
In the upper 10 percent of the scenarios, Antarctica
contributes approximately 10 cm during the 21st cen-
tury, 30 cm during the 22nd century, and 50 cm during
the 23rd century. In about 1 percent of the simulations,
Antarctica contributes 30—40 cm during the 21st century,
150—200 cm during the 22nd century, and 3—4m during
the 23rd century. Most of the scenarios show an initial
negative contribution due to the rapid response of
Antarctic precipitation, followed by an eventual positive
contribution due to the greater but slower impacts
resulting from the ice stream responses to warmer
Antarctic ocean temperatures.
Compared with the draft analysis, the reviewers
generally had a negligible impact on our median esti-
mate. For the year 2100, the median estimate is a drop
of 1.45 cm, barely different from the 1 cm drop projected
by the draft analysis (compare Table 5-8 with Table 5-5).
But the reviewer assumptions did increase the uncer-
tainty, compared with the draft analysis. At the low end,
the most important contributor was Zwally s (Chapter
3-B) assessment that Antarctic precipitation could, in
the extreme case, double with a 46C warming. Rind,
Schneider, and Hoffert also expanded the low end of the
spectrum by suggesting that Antarctic air temperatures
might warm by more than we had originally assumed,
which would result in more precipitation. These cli-
mate reviewers also expanded the high end of the range
TABLE 5-8
CUMULATIVE PROBABILITY DISTRIBUTION
ANTARCTIC CONTRIBUTION
Cumulative
Probability (%)
O.la
0.5a
1.0"
2.5"
5"
10
20
30
40
50
60
70
80
90
95
97.5
99
99.5a
99.9a
Mean
0"
Contribution Between 1990 and:
2050
—524
—320
—25.7
—167
—109
-67
—37
—24
—16
-09
—04
0.2
1.9
4.8
7.0
8.8
10.7
13.2
21.2
1.08
0.66
2100
—522
—368
—268
—189
—116
-68
—27
— L4
—03
+1.9
5.8
11.3
16.5
21.3
30.1
36.6
51.9
—LI
11.1
2200
—1356
—111.9
—899
—569
—379
—246
—130
—72
—33
-03
5.4
13.8
24.1
42.9
71.6
114.5
206.4
277.7
455.4
8.2
47.0
These estimates are included for diagnosis purposes only. Because the focus
of the analysis was on the risk of sea level rise rather than sea level drop,
less effort has gone into characterizing the lower end of the distribution.
by suggesting that circumpolar ocean waters are
likely to warm 1.0 to 1.56C by 2100, compared with
the 0.75BC implied by the draft assumptions.
The glaciology assumptions also increased the
uncertainty range. Surprisingly, the Thomas assump-
tions do not make much of a difference through the
year 2100. While Thomas (1985) suggested that a 30 cm
contribution was likely, and that a 1—2 m contribution
was possible, Thomas s assumptions now imply that
the contribution is as likely to be negative as positive
and that the chance of a 30 cm contribution is only
about 15 percent. Thomas s suggested shelf-melt
assumptions have little impact by the year 2100. His
lower estimates result primarily because our climatol-
ogy assumptions imply much less Antarctic warming
than was assumed by the 1985 National Academy
study to which Thomas had contributed.
Like the draft report, our final results suggest
that if Antarctica is going to have a major impact on
113
-------
Chapter 5
-e
o
ol
~T r~; 1 r
Wigley / f,
^/Bindschadler
Bentley
Van der Veen
Zwally
-- - Total
-50 -40 -30 -20 -10 0 10 20 3C 40
Antarctic Contribution, 1990-2100 (cm)
-100 -50 0 50 100 200 300
Antarctic Contribution, 1990-2200 (cm)
Figure 5-18. Cumulative Probability Distribution of
Antarctic Contribution to Sea Level by Reviewer. A few
curves have been removed for clarity: The distribution
implied by the Alley and Anonymous assumptions generally
tracked those of Bentley and Van Der Veen, respectively. For
the year 2100, the Thomas estimates are close to those of
Bindschadler; by 2200, however, they diverge markedly.
sea level, it will probably be after the year 2100. Even by
the year 2200, the median contribution is negligible. But
the reviewers estimate a 10 percent chance of at least a 40 cm
contribution, as well as 3 and 1 percent chances that the
contribution could exceed 1 and 2 m, respectively. As Figure
5-18 shows, the Thomas assumptions are largely responsible
for the upper end of the range. While most reviewers
estimate a 2—3 percent chance that the contribution through
2200 will be greater than 1 m, Thomas estimated a 10
percent chance of such a contribution, as well as 2 percent
chance that Antarctica could contribute more than 4 m!
References
C.R. Bendey and M.B. Giovinetto. 1990. Mass Bal-
ance of Antarctica and Sea Level Change. In: Inter-
national Conference on the Role of Polar Regions in
Global Change 481-8. Fairbanks: University of Alaska.
Drewry, D.J. and E.M. Morris. 1992. The Response
of Large Ice Sheets to Climatic Change. Phil. Trans.
R. Soc. London B338:235-42.
Huybrechts, Ph., and J. Oerlemans. 1990. Response of
the Antarctic Ice Sheet to Future Greenhouse Warming.
Climate Dynamics 5:93-102.
Jacobs, S.S. 1985. Oceanographic Evidence for Land
Ice/Ocean Interactions in the Southern Ocean. In:
National Research Council. Glaciers, Ice Sheets, and
Sea Level. Washington, DC: National Academy Press.
Jacobs, S.S., H.H. Hellmer, C.S.M. Doake, A. Jenkins, and
R.M. Frolich. 1992. Melting of Ice Shelves and the Mass
Balance of Antarctica Journal ofGlatiology 38:(130) 375-87.
Jenkins, A. 1991. A One Dimensional Model of Ice
Shelf-Ocean Interaction. Journal of Geophysical
Research 96:C11:20,671-7.
Lingle, C. 1989. Estimate of the West Antarctic Con-
tribution to Observed Sea Level Rise. Solicited submis-
sion and comment on Chapter 9 of draft IPCC 1990.
Lingle, C. 1985. A Model of a Polar Ice Stream and
Future Sea-Level Rise Due to Possible Drastic Retreat of
the West Antarctic Ice Sheet. In: National Academy of
Sciences. Glaciers, Ice Sheets, and Sea Level. Mark Meier,
Chairman. Washington, DC: National Academy Press.
MacAyeal, D.R. 1984. Thermohaline Circulation
Below the Ross Ice Shelf: A Consequence of Tidally
Induced Vertical Mixing and Basal Melting. Journal
of Geophysical Research 89:597-606.
MacAyeal, D.R. 1992. Irregular Oscillations of the
West Antarctic Ice Sheet. Nature 359:29-32.
National Research Council. 1985. Glaciers, Ice Sheets,
and Sea Level. Polar Research Board, Committee on
Glaciology. Mark Meier, Chairman. Washington, DC:
National Academy Press.
Thomas, RH. 1985. Responses of the Polar Ice Sheets to
Climatic Warming. In: National Research Council. Glaciers,
Ice Sheets, and Sea Level. Mark Meier, Chairman.
Washington, DC: National Academy Press.
114
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CHAPTER 6
SMALL GLACIERS
Although most of the world's ice is found in
Greenland and Antarctica, small glaciers elsewhere
contain enough ice to raise sea level approximately
half a meter. Because most of the mass of these glac-
iers is on snow-capped mountains, for our purposes,
the terms "mountain glacier," "alpine glacier," and
"small glacier" are often used interchangeably.
IPCC (1990) estimated the contribution to sea
level from small glaciers with the following equation1
from Raper et al. (1990):
dz
dt
where z
z0
AT
P
. [-z + (z0-z)iPSAT]
= J T
is sea level contribution (cm),
is equal to 50 cm (initial ice mass
in sea level equivalent),
is mean global warming since 1880 (°C),
represents sensitivity of glacial
melt to temperature changes, and
is the adjustment time (years).
Note that the equilibrium condition is
— = P AT/(1 + p AT),
Z0
which means that it takes 3.5 times as much warming
to raise the sea 30 cm as it does to raise it 15 cm.
These diminishing returns will tend to compress the
right-hand tail of the distribution for the alpine sea
level contribution.
IPCC picked three values for T: 10, 20, and 30.
It then derived 0.45, 0.25, and 0.1 as values for P by
fitting the historic temperature trend to Meier's (1984)
estimate that the alpine contribution to sea level during
the period 1900-1961 was 2.8+1.6 cm. We adopted a
similar procedure, except that we use the actual tem-
perature record rather than the modeled values for
estimating the historic contribution of small glaciers to
sea level. We assume that T has a lognormal distribu-
tion with CT limits of 10 and 30; Figure 6-1 illustrates
the resulting distribution of P. The lower half of the
figure is based on the recent estimate of Oerlemans &
'We have added in the absolute value signs so that the model is rea-
sonable for negative values of p.
3 --
2.5 -•
2 --
-02-01 0 01 020304 0.5 06070809 1 1112
b
3.5 -r
1.5 --
0.5 --
-0.2 -012 -004 004 012 02 028 036 0.44 052 0.6
Figure 6-1. Probability Density of Assumed
Small-Glacier Sensitivity to Global Warming.
Distribution of P based on (a) IPCC/Raper et al. (1990);
and (b) scaled by Oerlemans & Fortuin estimate.
115
-------
Chapter 6
a
40 -i
35 -
I 25-
^
\
2 20'
1
J 15 -
High
Medium
Low
1990
1925 1950 1975 2000 2025 2050 2075 2100
Year
•8
§
b
10 n
09 -
"•"*>,
0.6 -
05 -
1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Year
C
25 1
as
•3 10 H
1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Year
d
0.30 -
0.25 -
! 020 -
010 -
1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Year
Figure 6-2. Characteristics of the Raper et al. Model of the Small Glacier Contribution. Sensitivity runs using
Raper et al. (IPCC) model and IPCC 1990 "Business-as-Usual" forcing, showing (a) IPCC (1990) estimates of the his-
toric and future small glacier contribution; and projections over the period 1990-2100 for (b) remaining mass of world
small glaciers (as a fraction of original); (c) contribution to sea level; and (d) rate of sea level contribution. The num-
bered scenarios in (b), (c), and (d) represent: 1—IPCC (1990) medium scenario (i.e., median AT2x> t and (3); 2—
same as (1) but using Oerlemans's rather than Meier's estimate of historic small glacier contribution; 3—same as
(1) but a-fast t; 4—same as (1) but o-slow T; 5—same as (4) but AT2X = 4.5.
116
-------
Small Glaciers
Fortuin (1992) that the small glacier contribution to
sea level has been only 1.2 cm.
In the draft, we were uncertain whether to
regard this new estimate as an additional piece of
information or a replacement for Meier's estimate; as
a result, we assumed that both had equal validity.
Thus, for 50 percent of the simulations, we derived P
on the assumption that Meier's estimates characterize
the mean and standard deviation of a normal distribu-
tion of the historic contribution to sea level from
small glaciers; for the other simulations, we used the
Oerlemans & Fortuin estimate for the mean, and
imputed a standard deviation of 0.69 cm, the same
percentage of the mean as published by Meier.2
Figure 6.2a illustrates the IPCC (1990) results.
Note that the medium is closer to the high than to the
low scenario. This results partly from the peculiar
functional form used by the Raper et al. model.
Moreover, the high scenario contribution for
1990-2100 is depressed because the IPCC calculations
assume that the moun-tain glacier contribution between
1900 and 1990 was about 15 cm (Figure 6-2b), rather
than the 4 to 5 cm that one would expect from extrap-
olating Meier's results for 1900-1960.3 Thus, IPCC
inadvertently compressed the range of future alpine
contributions to sea level: the high scenario assumes
that in 1990 there was about 10 cm less ice to melt
than assumed in the medium scenario; the same argu-
ment applies in reverse to the IPCC low scenario.
Draft Results
Figure 6-3 illustrates the estimated probability
density for the small glacier contribution to sea level
rise. Unlike the distributions of Greenland and Ant-
arctica, which are skewed to the right, this distribution
is squeezed on the right-hand side, for the same rea-
sons that explain the IPCC medium scenario being
closer to the high than to the low scenario. Given the
downward revision implied by the Oerlemans & Fortuin
2Based on the assumption that global temperatures rose linearly by
0.28°C during the 61-year period, we derived distributions for (3 with
means of 0.23 and 0.125 and standard deviations of 0.14 and 0.077
for the Meier and Fortuin & Oerlemans distributions, respectively.
3This happens because Raper et al fit the model to the actual tem-
perature data, but IPCC uses simulated temperatures for 1900-1990;
if the model was separately fit for each simulation, the historic pro-
jections would more closely correspond to the actual record.
TABLE 6-1
DRAFT CUMULATIVE PROBABILITY
DISTRIBUTION FOR CONTRIBUTION TO
SEA LEVEL FROM SMALL GALCIERS
Cumulative
Probability (%)
1.0a
5a
10
20
30
40
50
60
70
80
90
95
99
Mean
2030 2100 2200
-2.4
-0.4
1.5
2.8
3.8
4.6
5.5
6.6
7.8
9.2
10.9
11.8
13.1
5.7
3.6
-7.1
-1.4
4.4
7.9
10.3
11.9
14.0
16.0
18.0
19.5
21.8
23.3
25.7
13.4
7.1
-10.5
1.9
6.6
11.3
14.4
16.9
19.3
21.3
23.2
24.8
26.9
28.3
30.5
17.6
8.7
aThese estimates are included for diagnosis purposes only.
Because the focus of the analysis was on the risk of sea level rise
rather than sea level drop, less effort has gone into characterizing
the lower end of the distribution.
data, it is not surprising that our median estimate for the
year 2100 (14 cm) was less than the 18.5 cm estimate
of IPCC (1990). Thus, only 10 percent of our simu-
lations exceeded IPCC's 21.5 cm high estimate, while
20 percent were less than IPCC's 8.8 cm low estimate
(see Table 6-1).
Note also that about 4 percent of the time there
was an increase in the mass of small glaciers and, thus,
a negative contribution to sea level. This result stemmed
from the fact that Meier's estimate of 2.8±1.6 cm means
that, at the 95 percent confidence level, one cannot rule
out a negative historic contribution; the functional spec-
117
-------
Chapter 6
o.
-108 -88-68 -48 -28 -0.8 12 3.2 52 72 92 112 132
Sea Level Rise (cm)
-2412-1912-14.12 -9.12 -412 088 588 10.88 1588 2088 2588
Sea Level Rise (cm)
35 1
30 -
miTniixuxujjj nill'iL'L'
-295-24.5-19.5-14.5 -9.5 -4.5 0.5 55 105 155 205 25.5 305
Sea Level Rise (cm)
-5 - -
-15 -L
E~"r--£.-,« S g | 2 S S g 3 2 S g g S
Figure 6-3. Small Glacier Contribution: Draft Report. Probability densities for the periods (a) 1990-2030,
(b) 1990-2100, and (c) 1990-2200, along with (d) a spaghetti diagram of cumulative small glacier contributions
to sea level: See Figure 2-5 and accompanying text for explanation of the scenarios chosen.
118
-------
Small Glaciers
ification employed by the Raper et al. model assumes
that such an impact would continue. Although that func-
tional specification has limitations,4 it seemed reason-
able to retain the negative projections in light of the fact
that a few researchers believe that increased snowpack is
a possible result of global warming.
The spaghetti diagram (Figure 6-3d) shows a few
scenarios in which the small glacier contribution to sea
level would decline after the year 2075, which implies
a negative annual contribution after that year. The
declining annual contribution results from the decline in
temperatures shown by a few scenarios in the draft
analysis (see Figure 3-7 and accompanying text).
TABLE 6-2
FINAL CUMULATIVE PROBABILITY
DISTRIBUTION FOR CONTRIBUTION TO
SEA LEVEL FROM SMALL GALCIERS
Cumulative
Probability (%)
O.la
0.5a
1.0a
25a
5a
2050 2100 2200
-6.6
-3.7
-2.6
-1.2
-0.4
-10.9
-5.7
-3.9
-1.8
-0.3
-19.1
-9.3
-6.5
-2.5
-0.3
Changes Made in the Final Version
In the final draft, we base all of the simulations
on the Oerlemans & Fortuin estimate. Warrick (1993)
suggests that a consensus is emerging among the key
IPCC (1990) contributing authors that the next IPCC
assessment will "support the Oerlemans & Fortuin
downward revision in glacier sensitivity." Deriving (3
from Oerlemans & Fortuin implies a median of 0.12
with 10 percent of the values greater than 0.22 and 10
percent less than 0.032.
The final version also corrects the IPCC (1990)
simulations of past contributions: Regardless of the
historic warming estimated in a given simulation, we
assume that the historic contribution of small glaciers
to sea level was 1.2±0.69 cm.
4Both the Greenland and the small glacier specifications used in this
report impose a mass constraint to prevent the sea level contribution
from exceeding the amount of ice that exists. The Greenland specifi-
cation suffers from the assumption that altitude is the sole reason that
some parts contribute more than others; in fact, differences in latitude
are also important. A good aspect of that model, however, is that it is
capable of assuming that increased precipitation over a given area
builds up at first, but that as warmer temperatures expand the ablation
zone, that area may begin to lose mass. A consideration of the frac-
tion of precipitation falling as rain would improve this aspect.
By contrast, the mountain glacier equation implicitly assumes a
variation in latitude: As temperatures rise, higher latitudes fall within
the net annual ablation zone. The model assumes that the equilibri-
um impact increases at a decreasing rate with temperature, which is
consistent with the idea that because there is, for example, less land
between 75-80°N than between 70-75°N (or for that matter, less land
at 3000 m elevation than at 2000 m), each additional degree of warm-
ing brings less alpine snow within the net ablation area. The prima-
ry problem with the specification is that the equilibrium condition
z/ZQ=p*AT/(l+p*AT) appears to have no theoretical or empirical
basis. It is hardly self-evident, for example, that it should take 5.44
times as much warming to melt the second 17 cm as it takes to melt
the first 17 cm, yet the Raper et al. equation imposes that assumption
for all values of (3.
10
20
30
40
50
60
70
80
90
95
97.5
99
99.5a
99.9a
Mean
o
0.4
1.7
2.7
3.7
4.8
5.9
7.2
9.0
11.5
13.8
15.8
18.0
20.2
26.3
5.4
4.5
1.0
3.3
5.3
6.9
8.7
10.5
12.4
14.8
18.3
21.1
23.6
26.3
27.8
32.2
9.2
6.7
1.6
5.2
8.1
10.7
13.2
15.7
18.5
21.7
25.8
29.0
32.8
34.2
35.6
38.6
13.5
9.2
aThese estimates are included for diagnosis purposes only.
Because the focus of the analysis was on the risk of sea level rise
rather than sea level drop, less effort has gone into charactenzmg
the lower end of the distribution.
Final Results
Given these changes, Table 6-2 summarizes the
cumulative probability distribution for the small glacier
contribution to sea level. The median estimate is one-
third lower than in the draft version because of (a) the
lower historic glacial sensitivity and (b) the lower tem-
perature estimates.5 Nevertheless, small glaciers still
5Excluding the Balling temperature estimate, our median tempera-
ture estimate by the year 2100 is a warming of 2.25°C, rather than
2.02°C. This higher warming results in a median mountain glaci-
er contribution of 10 cm.
119
-------
Chapter 6
.e
I
V)
"§
•s
1
u
C3
5
e
3
1
-1 --
-2
1990
2050
2100
2150
2200
2250
2300
Figure 6-4. Spaghetti Diagrams of the Small Glacier Contribution: Final Results. Selected simulations for (a) cumu-
lative and (b) annual small glacier contribution. See Figure 2-5 and accompanying text for explanation of scenarios selected.
120
-------
Small Glaciers
would contribute 0.8 mm/yr—more than four times the
historic contribution estimated by Fortuin & Oerlemans.
Unlike the median estimate, the final 1%-high
estimate (26.3 cm) is actually higher than the 25.7 cm
estimated in the draft report. The higher estimate
results primarily from our downward correction of the
historic contribution—and thus an upward correction
in the current mass of small glaciers—in those scenar-
ios that assume a high degree of global warming.
Figure 6-4 displays spaghetti diagrams for the total
and annual contributions of small glaciers to sea level.
Unlike other potential contributors to sea level rise, the
annual alpine contribution is likely to decline after the
next century as the glacial ice available for melting is con-
sumed. In the case of some of the outlier scenarios, where
the alpine contribution in the next decade is estimated to
be over 4 mm/yr, the current contribution is unlikley to be
sustained for more than the next 10-20 years.
The spaghetti diagrams suggest a declining uncer-
tainty in the annual contribution to sea level. In percent-
age terms, however, the uncertainty does not decline.
Even in absolute terms, the decline in uncertainty is an
artifact of the model's assumption regarding the relation-
ship between temperature and equilibrium glacial mass.
References
Intergovernmental Panel on Climate Change. 1990.
Climate Change: The IPCC Scientific Assessment.
Cambridge and New York: Cambridge University
Press.
Meier, M. F. 1984. "Contribution of Small Glaciers
to Global Sea Level." Science 226:1418-21.
Oerlemans, J., and J.P.F. Fortuin. 1992. "Sensitivity
of Glaciers and Small Ice Caps to Greenhouse
Warming." Science 258:115-7.
Raper, S.C.B., R.A. Warrick, and T.M.L. Wigley.
1990. "Global Sea Level Rise: Past and Future."
In: Milliman, J.D. (ed), Proceedings of the SCOPE
Workshop on Rising Sea Level and Subsiding
Coastal Areas, Bangkok 1988. Chichester: John
Wiley and Sons.
Warrick, R.A. 1993. "Projections of Future Sea
Level Rise: An Update." IPCC Eastern Hemisphere
Workshop on Vulnerability Assessment to Sea-Level
Rise and Coastal Zone Management. Tsukuba,
Japan: Intergovernmental Panel on Climate Change.
121
-------
Chapter 6
122
-------
CHAPTER 7
RESULTS
If the experts on whom we relied fairly repre-
sent the breadth of scientific opinion, the odds are
fifty-fifty that greenhouse gases will raise sea level at
least 15 cm by the year 2050, 35 cm by 2100, and
80 cm by 2200.1 Moreover, there is a one-in-forty
chance that changing climate will raise sea level
35 cm by 2050, 80 cm by 2100, and 300 cm by 2200.
For the reader who skipped the chapters outlin-
ing our assumptions, we begin by outlining the key
results from those chapters. Next, we present our esti-
mates for the total rise in sea level resulting from cli-
mate change and compare them with the results of
other recent assessments. We then estimate the extent
to which emission policies might reduce the risk of sea
level rise. We close the chapter with a brief analysis of
the extent to which uncertainty might be reduced
through a better understanding of some key processes.
Summary of Previous Chapters
We now summarize the highlights of the previous
chapters on radiative forcing, global temperatures and
thermal expansion, polar temperatures and precipita-
tion, and the contributions to sea level from Greenland,
Antarctica, and small glaciers (see Table 7-1).
Radiative Forcing. Our emission projections
were based on IPCC (1992) scenarios A through F; and
we used the assessment by Wigley & Raper (1992) for
calculating the resulting concentrations of both green-
house gases and sulfate aerosols. As a result, our sce-
narios for anthropogenic radiative forcing2 are broadly
consistent with other recent assessments.3 Like those
^Because other factors also contribute to sea level, the total rise is
likely to be significantly greater, as we see in Chapter 9.
2That is, the amount of additional radiation striking the Earth's
surface as a result of human modification of the atmosphere.
3Our mean estimate of radiative forcing for the year 2100, 5.0
W/m2, is only slightly less than the medium forcing estimate by
Wigley & Raper (1992).
TABLE 7-1
IMPACT OF GREENHOUSE GASES ON KEY CLIMATIC VARIABLES BY THE YEAR 2100
mean
estimate
2.5%
Probability that Value Will Not Be Exceeded
10% 50% 90% 95% 97.5%
99%
Temperature Change (°C)
Greenland 3.1 0.0 0.6 2.5 6.3 8.1 10 14
Antarctic Ocean 1.2 0.0 0.16 0.86 2.5 3.3 4.0 5.0
Global Average 2.2 0.0 0.6 2.0 4.0 4.7 5.4 6.3
Sea Level Contribution (cm)
Thermal Expansion 21 0.6 5.1 20 38 45 50 58
Small Glaciers 9.2 -1.8 1.0 8.7 18 21 24 26
Greenland 4.6 -0.4 0.22 2.9 10 14 19 27
Antarctica -1.1 -27 -12 -1.5 11 16 21 30
Other Variables
CO2 Concentration (ppm) 738 462 511 680 1047 1204 1363 1614
Radiative Forcing (W/m2) 5.0 2.3 3.0 4.9 7.2 7.8 8.2 8.7
Greenland Precipitation 1.7 1.3 1.4 1.6 2.2 2.6 3.2 4.2
(mm/yr, sea level equivalent)
Rate of Melting, 0.7 0.22 0.25 0.37 1.3 2.1 3.2 6.2
Ross Ice Shelf (m/yr)
123
-------
Chapter 7
assessments, we generally project smaller anthro-
pogenic changes in forcing than assumed in some of
the older assessments.
Our median projection is that, over the period
1990-2100, radiative forcing will increase by 4.9 watts
per square meter (W/m2), which is equivalent to
increasing CO2 concentrations from 350 parts per
million (ppm) to 770 ppm. By contrast, the IPCC
(1990) "Business-As-Usual" scenario projected an
increase of 7.5 W/m2; and IPCC (1992) projected
6.2 W/m2 for Scenario A.4 About 1 percent of our
simulations have more forcing than the 8.5 W/m2
IPCC (1992) estimated for Scenario E,5 while about
20 percent have a forcing less than the 3.5 W/m2 pro-
jected by IPCC (1992) for Scenario C. Our median esti-
mate is that radiative forcing will increase by 4.4 W/m2
(equivalent to a CO2 doubling) by the year 2089, with
a 10 percent probability that the doubling equivalent
will occur by 2068.
Although we project less radiative forcing than
early IPCC assessments, our assumptions are consis-
tent with the IPCC (1994) report on radiative forcing.
That report has adopted scenarios that are much clos-
er to the Wigley & Raper (1992) assumptions on
which our scenarios are based. Most important, the
IPCC has lowered the projected CO2 concentration
from 800 ppm to about 730 ppm for the year 2100.
Although IPCC has not yet endorsed a specific esti-
mate of the average global forcing effect of sulfates,
it has acknowledged that sulfates offset a large frac-
tion of the historic greenhouse warming.
Global Warming. The reviewer assumptions
imply that there is a 90 percent chance that the next
century will see more than the 0.5°C warming expe-
rienced in the last century, a 50 percent chance that
the Earth will warm more than 2°C, and a 3 percent
chance that our planet will warm 5°C, which is more
than it has warmed since the last ice age. Although a
2°C warming is most likely by the year 2100, there is
a 7 percent chance that it will occur by 2050. Even if
emissions are constant after 2100, temperatures are
likely to rise about 0.15°C per decade throughout the
22nd and 23rd centuries.
4These estimates are equivalent to increasing CO2 by factors of 3.4
and 2.8, respectively. Note that IPCC (1990) also estimated that
radiative forcing increased by about 2.5 W/m2 through the year
1990, compared with the preindustrial level.
5 About 20 percent of our simulations, however, have more forcing than
the 6.6 W/m2 estimated by Wigley & Raper (1992) for Scenario E.
Thermal Expansion. As global temperatures
rise, the various layers of the ocean will warm and
expand. Especially in the long run, thermal expan-
sion depends on the extent to which the heat is able to
penetrate into the intermediate and deep layers of the
ocean. For example, a decline in deepwater forma-
tion would slow upwelling, allowing heat to penetrate
farther, and thereby increase thermal expansion.
Differences in opinions regarding ocean circulation
changes led to a 10 percent variation among the review-
ers regarding likely expansion. By the year 2100, the
most likely expansion is 20 cm, but there is a 2 1/2 per-
cent chance that expansion will exceed 50 cm.
Although global temperatures are projected to rise 25
percent less during the 22nd century than in the 21st,
thermal expansion is likely to be 20 to 40 percent
more, due to the delayed response of expansion to
higher temperatures.
Greenland Climate. The likely contribution of
Greenland to sea level will depend on the magnitude
of increases in precipitation and melting, both of
which would increase at higher temperatures.
Particularly if the Gulf Stream weakens due to a shut-
down in North Atlantic deepwater formation,
Greenland may warm less than the global average
warming—or perhaps even cool. Nevertheless, most
of the reviewers expect Greenland temperatures to
eventually warm by more than the global average.
Thus, we estimate that there is a 50 percent chance
that Greenland will warm at least 2.5 °C between
1990 and 2100, a 25 percent chance of a warming
greater than 4°C, and a 2 1/2 percent chance that the
warming will exceed 10°C. By contrast, Wigley &
Raper (1992) projected a best-guess warming of 3.8°C.
All but one of the reviewers expect Greenland
precipitation to increase about 8 percent per degree (C),
which is equivalent to a sea level drop of 0.1 mm/yr per
degree. In light of the projected warming of
Greenland, there is a 50% chance that by 2100 Green-
land precipitation will increase 20 percent, and a 5%
chance that it will double. At the low end of the spec-
trum, there is a 10% chance that precipitation will
increase by less than 5 percent.
Greenland Contribution. Our median estimate is
that Greenland will contribute 2.9 cm to sea level by
the year 2100. Our 95 percent confidence range is
-0.37 cm to 19 cm. For 2200, we estimate a median con-
tribution of 12 cm, but a 10 percent chance of a 50 cm
contribution. At the low end of the range, we estimate a
5 percent chance that Greenland will have a negative
124
-------
Results
contribution to sea level through 2100. Mostly because
our temperature estimates are lower, our median is less
than the 7.5, cm projected by Wigley & Raper (1992).
Antarctic Climate. Antarctic air temperatures
are likely to rise by approximately 2.5°C in the next
century, largely as a result of reduced sea ice. For
each degree (C) of warming, Antarctic precipitation is
likely to increase approximately 8 percent, equivalent
to a 0.4 mm/yr drop in sea level.
Unlike Greenland, Antarctica is colder than
freezing even during summer; so warmer air temper-
atures will not cause significant glacial melting.
Warmer water temperatures, by contrast, could
potentially increase melting of the marine-based West
Antarctic Ice Sheet and adjacent ice shelves. The
reviewers generally agreed, however, that any warm-
ing of the circumpolar ocean is likely to lag behind
the general increase in global temperatures by at least
fifty years, and perhaps by a few centuries. Thus, we
estimate that Antarctic ocean temperatures are most
likely to warm 0.86°C by the year 2100. Although a
3°C warming is likely by 2200, there is only a 6 per-
cent chance that such a warming will occur by 2100.
Antarctic Contribution. Warmer ocean tempera-
tures have about a 50 percent chance of doubling the
average rate at which the underside of the Ross Ice
Shelf melts, from 0.17 m/yr to 0.35 m/yr, by the year
2100. Although a doubling may seem significant,
most previous studies have suggested that the rate of
melting would have to increase to at least 1 m/yr to
have a significant impact on sea level. The reviewer
assumptions imply that there is only about a 10 percent
chance of such an increase in the next century. We also
estimate that there is a 5 percent chance that by 2100
the Ross Ice Shelf will be melting 2 m/yr, which is
similar to the melt rate that prevails today beneath the
George VI Ice Shelf.
Even with a large rate of shelf-melting, the
Antarctic contribution to sea level may be negligible.
Because ice shelves float and hence already displace
ocean water, shelf-melting would raise sea level only
if it accelerates the rate at which ice streams convey
ice toward the oceans. Several models suggest, how-
ever, that shelf-melting will not substantially acceler-
ate ice streams—and even the models that project
such an acceleration generally suggest a lag of a cen-
tury or so. Thus, through the year 2100, we estimate
a 60 percent chance that the sea level drop caused by
increased Antarctic precipitation will more than offset
the sea level rise caused by increased ice discharge;
this probability declines to 50 percent by 2200.
Our analysis suggests that if Antarctica is
going to have a major impact on sea level, it will
probably be after the year 2100. Even by 2200, the
median contribution is negligible; but the reviewer
assumptions also imply a 10 percent chance of a con-
tribution greater than 40 cm, as well as 3 and 1 per-
cent chances that the contribution could exceed 100
and 200 cm, respectively.
Small Glaciers. If all the small glaciers melted,
sea level would rise approximately 50 cm. We estimate
that a 9 cm contribution through the year 2100 is most
likely, with a 5 percent chance that the contribution will
be greater than 20 cm.
Total Contribution of Climate
Change to Sea Level
The reviewer assumptions imply that there is
a 1 percent chance that climate change will raise
sea level 42 cm by the year 2050, 104 cm by 2100,
and over 4 m by 2200. The most likely (median)
contribution, however, is only about one-third as
great: 15 cm by 2050, 34 cm by 2100, and 81 cm by
2200. Uncertainty increases over time: the ratio of
our 1%-high scenario to our median scenario is 2.8
for 2050, 3.1 for 2100, and 5.1 for 2200. Figure 7-1
illustrates the cumulative probability distribution of
the primary contributors to sea level for the year 2100.
Thermal Expansion
Small Glaciers
n r
-40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110
Greenhouse Contribution to Sea Level, 1990-2100 (cm)
Figure 7-1. Greenhouse Contribution to Sea Level.
The cumulative probability distributions show the con-
tribution to sea level from thermal expansion, small
glaciers, Greenland, and Antarctica for the period
1990-2100.
125
-------
Chapter 7
TABLE 7-2
YEAR BY WHICH VARIOUS THRESHOLDS ARE EXCEEDED3
Probability that Threshold Will Be Exceeded by a Given Year
97.5% 90% 70% 50% 30% 10% 5% 2.5%
1%
THRESHOLD
Climate Contribution to Sea Level
> 50 cm >2200
> 1 meter >2200
Sea Level along U.S. Coastb
> 1 ft 2169
> 3 ft >2200
> 5-ft contour on >2200
topographic maps
Other Variables
AForcing > 4.4 W/m2
CO2 > 600 ppm
AT> 1°C
AT > 2°C
>2200 >2200 2136 2108
>2200 >2200 >2200 2180
2099 2069 2058 2049
>2200 2194 2157 2131
>2200 >2200 >2200 2180
2083
2133
2038
2106
2141
2074
2118
2034
2097
2127
2066 2059
2108 2097
2031 2027
2090 2083
2117 2107
>2200
>2200
>2200
>2200
>2200
>2200
>2200
>2200
2103
2117
2069
2174
2089
2078
2048
2099
2064
2077
2034
2073
2068 2066 2064 2062
2052 2048 2045 2042
2022 <2020 <2020 <2020
2052 2046 2041 2031
"Compared with 1990 levels.
''Based on rate of sea level rise at New York City, which typifies the Atlantic and Gulf Coasts of the United States. See Chapter 9 for further details.
(As we discuss in the final chapter, the rise in sea level
along most of the U.S. Coast will be higher due to
nonclimatic contributors to sea level.) Table 7-2 illus-
trates the year by which sea level and a few other key
variables will exceed particular thresholds. Although
a 2°C warming is most likely to occur over the next
century, for example, there is a one percent chance
that such a warming could occur by the year 2031.
Figures 7-2 and 7-3 illustrate the cumulative
and annual contributions of climate change to sea
level for selected simulations. By the year 2100, cli-
mate change is most likely to add 4 mm/yr to sea level
(implying a rate of more than 6 mm/yr along most of
the U.S. coast). Moreover, there is a 10 percent
chance that climate change will add 1 cm/yr, and a 1
percent chance that it will add 2 cm/yr, by the end of
the twenty-first century.
The net effect of the reviewer assumptions is illus-
trated by Table 7-3, which compares our final reviewer-
based estimates with the draft estimates. The final median
estimates are approximately one-third lower than esti-
mated in the draft report, primarily because the median
estimate of warming over the next century was lowered
from 3°C to 2°C. At the high end of the range, by con-
trast, the final results are only one-fourth lower for the
year 2100—and they are actually higher for 2200, pri-
marily because of the potential contribution from
Antarctica. At the low end of the range, the final results
are much lower than the draft results, for three reasons:
(1) one reviewer expects global temperatures to rise
only slightly, if at all; (2) another reviewer suggested
that polar precipitation is very uncertain and could con-
ceivably increase by 20 percent for a 1°C warming; and
(3) the factors that cause a lower median temperature
also operate on the low end of the spectrum.
126
-------
Results
i
1990
2050
2100
2150
2200
2250
2300
Figure 7-2. Cumulative Contribution of Climate Change to Sea Level: Selected Simulations.
1
-5
2000
2050
2100
2150
2200
2250
2300
Figure 7-3. Annual Contribution of Climate Change to Sea Level: Selected Simulations. See Figure 2-5 and
accompanying text for description of these and other spaghetti diagrams.
127
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Chapter 7
TABLE 7-3
CUMULATIVE PROBABILITY DISTRIBUTION OF THE
CONTRIBUTION OF CLIMATE CHANGE TO SEA LEVEL RISE
Cumulative
Probability
lb
2.5h
5h
10
20
30
40
50
60
70
80
90
95
97.5
99
2030a
4.1
6.3
7.8
9.7
12
13
15
16
18
20
23
26
Draft Results
Sea Level Rise
(cm)
2100
15
22
28
35
40
46
52
58
65
73
88
101
31
131
2200
28
34
43
55
72
84
100
112
128
148
180
228
280
332
400
452
Final Results
Sea Level Rise
(cm)
2050a
2100
2200
-1.2
0.4
2.1
4.6
8.1
11
13
15
17
20
23
28
33
37
42
46
-1.2
1.7
4.9
10
19
24
29
34
39
45
53
65
77
88
104
115
-0.8
3.5
10
22
39
53
67
81
96
115
143
196
254
316
409
498
Rate of Rise
(mm/yr)
2100
-0.36
0.03
0.47
1.05
1.91
2.68
3.44
4.21
5.04
6.08
7.49
9.89
12.37
15.41
19.34
23.05
Mean
o
16
9
37
99
82
5.04
4.19
aAlthough the draft piovided results for the year 2030, we subsequent!} decided that the year 2050 would he more useful for the purposes of this
chaptei Budget constraints precluded us from recomputing the draft results for 2050.
hlncluded for diagnostic purposes only Neither the reviewers nor the modeling efforts focused on the risk of a sea level drop. Therefore, the
lowei end of the uncertainty range is much less reliable than the upper end.
NOTE: Because nonclimatic factors also contribute to sea level rise, these results should not be used to project sea level in spe-
cific locations. See Table 9-1 for results better suited for that task.
Because the reviewers represent a cross-section
of the scientific community, we have weighted the
^Some Delphic studies have asked the reviewers to assign an
appropriate weight to the opinions of each reviewer We decided
not to follow that approach, for reasons explained in Chapter 1
Among those reasons (a) we would have had to double the num-
ber of questions asked of each reviewer; (b) the reviewers" exper-
tise on individual physical processes does not necessanly imply an
expertise to assess the merits of other reviewers' opinions, (c) the
reviewers already self-selected out of parameters on which they
had no expertise, (d) we wanted to keep this analysis "on the
record," which would have been impossible if the reviewers had to
rate the expertise of other scientists, and (e) we would still have to
pick an appropriate weight for each reviewer's opinion of the other
opinions. See Chapter 1, Approach.
individual assessments equally.6 Nevertheless, the
variation of reviewer assessments may also be worth
considering. Figure 7-4 shows the variation in sea
level estimates resulting from the assumptions sug-
gested by the various climate reviewers (see Chapter
3). Even though their estimates for global temperature
change were similar, Schneider, Rind, and Hoffert pro-
jected much less warming for Greenland and
Antarctica than did Manabe or MacCracken. As a
result, the Manabe and MacCracken assumptions sug-
gest a 1 percent chance of a 3 m rise by 2200; the
Schneider, Rind, and Hoffert assumptions, by contrast,
imply a 7 percent chance of a 3 m rise and a 1 percent
chance of a 5 m rise over the next two centuries.
128
-------
Results
TABLE 7-4
CONTRIBUTION OF CLIMATE CHANGE TO SEA LEVEL 1990-2100
COMPARISON BETWEEN IPCC (1990) AND OUR RESULTS
Scenario
IPCC/lowa
1%
10%
IPCC/besta
Median
IPCC/higha
90%
99%
Thermal
Expansion
25.8
-0.8
5.1
38.7
19.7
58
38.1
57.5
Small
Glaciers
7.8
-3.9
1
18.5
8.7
21.5
18.3
26.3
Greenland
2.9
-0.8
0.2
11.6
2.9
27.7
10.3
27.2
Antarctica
-7.6
-37
-11.7
-5.36
-1.4
0
11
30
Total
29
-1.2
10.3
64
34.1
107.2
65.1
104
aIPCC results cited here are somewhat different from those of IPCC 1990 because they are with respect to a 1990 base, rather than IPCC's 1985
base. In addition, IPCC (1990) rounded some of its results.
NOTE: Because nonclimatic factors also contribute to sea level rise, these results should not be used to project seal level in spe-
cific locations. See Table 9-1 for results better suited for that task.
I I
0 50 100 300 500
Greenhouse Contribution to Sea Level, 1990-2100 (cm)
Figure 7-4. Greenhouse Contribution to Sea Level
by Climate Reviewer. These cumulative distributions
show the greenhouse contribution for the year 2200.
Wigley & Raper provided assumptions for Greenland
and Antarctica; otherwise, the displayed distributions
combine the reviewer's climate assumptions with ran-
dom samples of the assumptions suggested by the pre-
cipitation and Antarctica reviewers.
The assumptions of Wigley & Raper and Balling,
by contrast, suggest that the risk of a large rise is much
smaller. Because Wigley & Raper assumed a narrower
range of possible temperature projections than the other
"mainstream" reviewers, their range of sea level projec-
tions is also narrower. Finally, Wigley & Raper provided
their own assumptions for the ice sheet contribution to sea
level—assumptions that suggest lower risk than was sug-
gested by the glacialogy reviewers of Chapters 4 and 5.
Their median projection is also somewhat lower because
their ocean model assumptions did not imply as much
downward penetration of heat as the assumptions favored
by the other reviewers. Given Balling's assumption that
global temperatures are not sensitive to greenhouse gases,
his low projections of the sea level contribution are not
surprising. Nevertheless, he allowed for random fluctua-
tions in climate and accepted the other models used in this
report. As a result, his relatively optimistic assumptions
still imply that there is a 1 percent chance that changing cli-
mate will add 90 cm to sea level over the next two centuries.
Comparison with IPCC (1990)
For the last several years, the most widely cited
estimates for future sea level rise have been those reported
129
-------
Chapter 7
by IPCC (1990). As this report went to press, the IPCC
was revising its projections for a report to be released
later in 1995. Although we hope that this report satis-
fies the special information needs of coastal planners
and engineers, it seems reasonable to assume that more
general assessments of the climate change issue will
continue to use IPCC estimates. Therefore, we briefly
compare our results with those of IPCC (1990), as well
as Wigley & Raper, whose periodic assessments have
often provided useful interim indications of the direc-
tion in which scientific opinion is headed.
Table 7-4 compares our projections for the year
2100 with those of IPCC (1990). Although our median
estimate of 34 cm is fairly consistent7 with the Wigley
& Raper (1992) estimate of 48 cm, it is substantially
lower than the IPCC "best-guess" estimate of 64 cm.
Our downward revision (compared with IPCC's
medium estimate) is primarily driven by the lower tem-
perature estimates, which in turn resulted from lower
estimates of radiative forcing (i.e., lower concentrations
of greenhouse gases and inclusion of the offsetting
effect of sulfate aerosols).
Our draft results, however, show that the median
sea level estimate would have been lower than the IPCC
(1990) estimate even if our temperature estimates had
been as high as those of IPCC (1990). The draft and
IPCC (1990) both assumed a warming of about 3°C
over the 1990-2100 period, but the draft projected a sea
level contribution of only 51 cm. About half of this
downward revision (compared with IPCC) resulted
from lower thermal expansion estimates, which
stemmed from changes in ocean modeling assump-
tions.8 Our nonlinear model of the Greenland contri-
bution, combined with explicitly considering increased
precipitation, resulted in a much lower estimate of this
ice sheet's sensitivity to a warming of a few degrees (C).
Finally, we incorporated recent work suggesting that
small glaciers are less sensitive to global temperatures
than previously thought.
Although our median projection is a downward
revision compared with IPCC (1990), it is more diffi-
cult to say whether our estimates of the entire range
also constitute a downward revision. The terms "low
7As discussed in Chapter 9, if one assumes that the historic sea
level rise has been 1.8 mm/yr, then our median estimate of the total
rise in sea level (including nonclimatic contributors) by the year
2100 is 45 cm.
"The most important changes were lower values of the parameter
TC and a correction in the Wigley & Raper model regarding how
expansion was calculated.
scenario" and "high scenario" have no precise mean-
ing. The IPCC (1990) high scenario, for example,
involved a coincidence of high temperature sensitivity
and high values for the sensitivity of Antarctic,
Greenland, and small glaciers; but it was based on
best-guess estimates of future concentrations and
ocean mixing (although those assumptions are both at
the high end of the range we use here). Our results, by
contrast, do not explicitly include a coincidence of all
parameters reaching their "high values," both because
we randomly selected the parameter values and
because the normal and lognormal distributions do not
have fixed upper bounds.
Nevertheless, given the interpretation of "high"
and "low" as "worst-case" and "best-case" scenarios,
our final results reflect far more uncertainty than the
IPCC results. More than 40 percent of our simula-
tions project less sea level rise than IPCC's low sce-
nario of 30 cm by 2100; 15 percent of the simulations
suggest that climate change will contribute even less
than Wigley & Raper's (1992) estimate of 15 cm. At
the upper end of the range, about 0.75 percent of our
simulations suggest more sea level rise than IPCC's
high scenario (110 cm). Thus, while IPCC's high
scenario was 1.7 times its "best-estimate" scenario
for the year 2100, approximately 16 percent of our
simulations are more than 1.7 times our median esti-
mate; and our 1%-high estimate is 3.1 times our
median scenario.
The Implications of Alternative
Emission Rates
The preceding results were based on a mix of
emission scenarios. To the coastal decisionmaker,
future emission rates are but one of many sources of
uncertainty and are functionally no different from (he
various climatic and glacial process parameters. To the
climate policymaker, however, emission rates are (in
theory) a variable that can be fixed by policy. As a
result, climate policymakers may be more interested in
the conditional probability distribution of sea level rise
for a given emissions scenario, and the implications of
policies to reduce emissions.
Table 7-5 summarizes the results for a variety of
alternative emission scenarios. The left side of the
table compares the impacts of IPCC Scenarios A and
E. We also examine the potential benefits of freezing
emissions in the year 2025 or 2050, rather than 2100.
These scenarios use the full distribution of emission sce-
narios from the baseline analysis. The third, fourth, and
130
-------
Results
TABLE 7-5
IMPLICATIONS OF ALTERNATIVE EMISSIONS SCENARIOS
Assumptions
Emission Scenarios:
Emissions Fixed After:
Climate Sensitivity13:
E
2100
1.0-
4.4
A
2100
1.0-
4.4
Increased Forcing, 1990-2100 (W/m2)
median 6.6 5.5
10%-high
1%-high
Warming, 1990-2100 (
median
10%-high
1% high
Warming, 1990-2200 (
median
10%-high
1%-high
Sea Level Contribution
median
10%-high
1%-high
Sea Level Contribution
median
10%-high
1%-high
6.6
6.6
°C)
2.6
4.5
6.7
•C)
4.9
9.0
13.8
, 1990-2100
40
71
110
, 1990-2200
108
237
447
Annual Greenhouse Contribution to
median 6.2
10%-high
1%-high
12.0
21.2
5.5
5.5
2.3
4.0
6.0
4.0
7.4
11.5
(cm)
36
66
103
(cm)
91
200
385
Sea Level
4.8
9.7
17.8
Alla
2100
1.0-
4.4
4.9
7.2
8.7
2.0
4.0
6.3
3.3
7.4
12.8
34
65
104
81
195
409
by 2100
5.0
9.9
19.3
All
2050
1.0-
4.4
4.4
5.8
7.0
1.9
3.6
6.0
2.9
5.8
9.9
33
62
102
71
166
357
(mm/yr)
3.6
8.2
17.4
All
2025
1.0-
4.4
4.0
4.9
5.9
1.7
3.3
5.6
2.7
5.2
9.0
31
59
101
66
152
347
3.2
7.3
15.3
All
2100
2.6
fix
4.9
7.2
8.7
2.4
3.3
4.4
4.0
5.6
7.4
38
53
84
97
162
308
4.9
8.1
15.2
All
2100
4.0
fix
4.9
7.2
8.7
3.3
4.8
8.1
5.8
8.3
10.5
53
73
118
140
236
455
7.1
11.7
22.1
All
2050
4.0
fix
4.4
5.8
7.0
3.1
4.2
6.9
5.0
6.6
8.1
50
70
113
124
205
403
5.9
9.8
19.5
All
2025
4.0
fix
4.0
4.9
5.9
2.9
3.8
6.3
4.6
5.8
7.1
48
67
110
114
191
366
5.3
8.9
17.3
aThe column shows the result for the final analysis discussed throughout this report.
bThe a range is 1.0-4.4 rather than 1.5-4.5, due to the downward effect of the Balling assumptions.
131
-------
Chapter 7
fifth columns in Table 7-5 use a range for the climate's
sensitivity to a CO2 doubling, while the last three
columns use the relatively high value of 4.0°C suggested
by many three-dimensional general circulation models.9
The results suggest that if emission Scenario E is
likely to unfold, the initial benefit of emissions policies
would be modest. Moving society down to the scenario
A trajectory would decrease the median sea level contri-
bution from 40 cm to 36 cm; freezing emissions in the
year 2050, which is roughly equivalent to IPCC Scenario
D, would reduce the sea level contribution to 33 cm—
only 17 percent less than what would occur under
Scenario E. Over the next two centuries, however, freez-
ing emissions by 2050 would reduce the expected rise in
sea level by 35 percent (71 cm compared with 108 cm).
Using the uncertainty range developed in
Chapter 2, freezing emissions by 2050 would only
reduce the next century's sea level rise by about 3 per-
cent, compared with freezing emissions in 2100; freez-
ing emissions by 2025 would reduce the rise by about
10 percent. These results do not necessarily mean that
stabilizing emissions is not worthwhile, only that the
benefits of doing so would accrue over a long period of
time. The median rate of sea level rise would be one-
third lower by 2100 if emissions were frozen in 2050,
and 40 percent lower if emissions were frozen in 2025.
The median cumulative greenhouse contribution to sea
level through the year 2200 would be reduced by 12
and 18 percent, respectively, if emissions are frozen in
2050 and 2025; the 10%-high estimates would be
reduced by 15 and 25 percent.
Sensitivity Analysis of Variation
Given the large number of parameters used in this
analysis, one might reasonably ask: Which of these
parameters are superfluous and which contribute sig-
nificantly to our uncertainty? Although a complete
analysis of this question is beyond our current
resources, we briefly discuss four of the most important
processes: emissions, climate sensitivity, the response
of polar temperatures to global temperatures, and the
response of ice-shelf melting to changes in Antarctic
ocean water temperatures. We fix the parameter(s) con-
trolling these processes at roughly their median values
and examine the extent to which uncertainty declines.
9We include the scenario where climate sensitivity is fixed at 2.6°C
here for the reader interested in the resulting temperature projec-
tions, which are not displayed in Table 7-6.
As Table 7-6 shows, the climate sensitivity
parameter accounts for the most uncertainty, espe-
cially at first. For the year 2100, fixing this parame-
ter reduces the standard deviation of sea level rise
projections by 35 percent. Fixing the polar-tempera-
ture parameters or the ice-shelf-melt parameters, by
contrast, each reduces the standard deviation by about
4 percent; and fixing emissions equal to Scenario A
reduces the uncertainty by about 0.5 percent. For the
year 2200, however, fixing climate sensitivity only
reduces the standard deviation by 21 percent, while
fixing polar-temperature and ice-shelf-melt sensitivi-
ties reduces the standard deviation by 10 and 16 per-
cent, respectively.
The contributions of polar amplification and
shelf-melt sensitivity to total uncertainty is greater for
the year 2200, primarily because the contributions of
Antarctica and Greenland to sea level are likely to be
much larger during the 22nd century than during the
21 st century. Fixing temperature sensitivity or polar
temperature amplification reduces the standard devi-
ation for the Greenland contribution by about one-
third. For Antarctica, however, the ice-shelf-melt
sensitivity accounts for about half of the uncertainty;
polar temperature amplification accounts for about
25 percent of the uncertainty; and climate sensitivity
accounts for about 7 percent. The differences are
even greater when one focuses on the 1%-high pro-
jections: fixing the shelf-melt sensitivity reduces the
1%-high estimate of the Antarctic contribution by
more than two-thirds.
Numerical Error of the Monte
Carlo Alogorithm
As discussed in Chapter 1, we chose to calcu-
late the probability distribution of future sea level
rise using the basic Monte Carlo algorithm. The
Importance Sampling algorithm generally provides
more precise estimates of the tails of a distribution
for a given number of simulations, but implementing
it would have required additional work. We decide
that the increased numerical accuracy was not worth
the extra effort.
As a rough check to ensure that we had run enough
simulations, we divided our sample into eight subsets,
representing the first 1250 runs, the second 1250 runs, and
so on. For the climate contribution to sea level
(1990-2100), the 1%-high generally ranged between 101
and 107, with a mean of 104 and a standard deviation of
132
-------
Results
TABLE 7-6
ANALYSIS OF VARIANCE: CUMULATIVE PROBABILITY DISTRIBUTION OF SEA LEVEL
CONTRIBUTION WHEN CERTAIN PARAMETERS ARE FIXED AT THEIR MEDIAN VALUES
PARAMETER FIXED
None
(Baseline)
Parameter Set To:
Greenland Contribution. 1990-2200
1% low -2.7
10% low 0.1
median 12.0
10% high 50.0
l%high 150.0
mean 21.0
a 29.8
Emissions
Scenario
A
(cm)
-3.2
1 2
15.0
53.3
149.1
23.3
29.4
Climate
Sensitivity
2.6T
2.5
3.7
14.7
39.8
130.6
23.7
19.7
Polar
Temperatures
Median
Values
1.5
2.5
12.8
39.3
105.2
18.3
19.4
Ice Shelf
Meit Rale
Median
Valuer,
—
—
—
—
—
—
—
Antarctic Contribution, 1990-2200 (cm)
1% low -90.0
10% low -25.0
median 0.0
10% high 43.0
1% high 206.0
mean 8.0
a 47.0
-88.7
-24.4
-0.1
46.0
206.4
8.9
45.6
-80.7
-15.4
9.7
47.8
152.7
22.4
44.0
-88.3
24.2
-0.2
35.7
139.0
6.1
38.1
-92.5
-24.1
-0.3
25.2
62.7
4.2
23.4
Total Greenhouse Contribution, 1990-2100 (cm)
l%low -1.0
10% low 10.0
median 34.0
10% high 65.0
l%high 104.0
mean 37.0
a 22.3
-1.0
12.0
36.0
66.0
103.0
39.0
22.2
7.0
21.0
38.0
53.0
84.0
40.0
14.6
-1.0
10.0
33.0
62.0
102.0
36.0
21.5
-1.0
9.0
33.0
62.0
98.0
36.0
22.0
Total Greenhouse Contribution, 1990-2200 (cm)
1% low -1.0
10% low 22.0
median 8 1 .0
10% high 196.0
1% high 409.0
mean 99.0
o 82.4
Annual Greenhouse Contribution by
1% low -0.36
10% low 1.05
median 5.04
10% high 9.89
1% high 19.34
mean 5.04
o 4.19
-1.0
28.0
91.0
200.0
385.0
108.0
83.9
the Year 2 100
-0.27
1.54
4.84
9.70
17.82
5.43
3.79
26.0
5.0
97.0
162.0
308.0
111.0
65.5
(mm/yr)
0.48
2.20
4.90
8.10
1521
5.42
2.95
-1.0
22.0
76.0
180.0
309.0
92.0
73.8
-0.21
1.05
3.96
9.19
16.62
4.69
3.52
-2.0
21 0
770
171.0
293.0
90.0
69.2
-0.17
1 .06
4.07
9.34
16.18
4.77
3.71
133
-------
Chapter 7
2.7 cm (see Appendix 1). Thus, the standard deviation of
our estimate of the 1%-high estimate is 0.99 cm.10
For the purposes of this study, a standard numer-
ical error of 1 cm for the 1%-high is acceptable. This
result is not surprising, given that the 1%-high esti-
mate represents one hundred observations. Had our
intent been to characterize the one-in-a-million risk
common in environmental risk assessments, or even
the one-in-ten-thousand risk considered in the Dutch
flood control system, the use of algorithms that cap-
ture the tails of a distribution would have been more
important. We determined at the outset, however, that
our models and assumptions were not suited for such
unlikely risks.
References
Intergovernmental Panel on Climate Change. 1990.
Climate Change: The IPCC Scientific Assessment.
Cambridge and New York: Cambridge University Press.
Intergovernmental Panel on Climate Change. 1992.
Climate Change 1992: The Supplementary Report
to the IPCC Scientific Assessment. Cambridge and
New York: Cambridge University Press.
Intergovernmental Panel on Climate Change. 1994.
Climate Change 1994. Radiative Forcing of Climate
Change and An Evaluation of the IPCC IS92 Emission
Scenarios. Cambridge and New York: Cambridge
University Press.
Wigley, T.M.L., and S.C.B. Raper. 1992. "Implica-
tions for Climate and Sea Level of Revised IPCC
Emissions Scenarios." Nature 357:293-300.
10Recall from elementary statistics that the standard deviation of
an estimate of the mean is equal to the standard deviation of a sam-
ple, divided by the square root of the sample size. In this case, the
"mean" refers to the average value of the 1%-high of various data
sets, and the sample size is 8.
134
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CHAPTER 8
PLACING THE RESULTS IN CONTEXT
Revisions of Sea Level Rise Scenarios
Long-range projections of physical, economic,
and ecological systems often prove to be wrong,
because they involve combinations of assumptions with
varying degrees of certainty. Moreover, with a highly
visible public policy issue such as climate change, the
projections themselves can motivate people to take
actions that render early projections obsolete (e.g., pro-
jections of a 4°C global wanning could lead people to
reduce emissions so that the warming is only 2°C).
This report and other recent analyses suggest
that sea level is likely to rise less than estimated by
early reports on the subject (see Table 8-1).1 The
lower estimates have resulted from both a downward
revision of future temperatures and an emerging con-
sensus that Antarctica will probably not contribute to
sea level in the next one hundred years.
Lower Global Temperatures. In the last decade,
estimates of the global warming likely to occur by the
year 2100 have been approximately cut in half. The
1983 reports by EPA and the National Academy of
Sciences assumed that the radiative forcing equivalent
of a CO2 doubling was likely to occur by 2050.
During the mid-1980s, several reports suggested that
an effective CO2 doubling could occur by the 2030s
(see e.g., Villach 1985). Thus, the EPA reports
released in 1983 projected a warming of 3 to 9°C by
2100, with CC>2 and other greenhouse gases account-
ing for equal amounts of warming (Hoffman et al.
1983; Seidel & Keyes 1983). The NAS (1983) report
projected a warming of 1 to 5°C from CO2 alone and
was thus viewed as being consistent with the EPA
results (see e.g., Chafee 1986). EPA's 1989 Report to
Congress (Smith & Tirpak 1989) was based on similar
assumptions, as shown in Table 8-2. For the most part,
scenarios of sea level rise for the year 2100 were in the
50 to 200 cm range, with 100 cm being the most likely.
Unlike some recent assessments by IPCC (1990, 1992) and
Wigley & Raper (1992), this report still projects a significant risk
that sea level will rise more than one meter by the year 2100; i.e.,
our downward revision applies more to the "best estimate" than to
the high end of the uncertainty range.
TABLE 8-1
CLIMATE CHANGE CONTRIBUTION
TO SEA LEVEL PROJECTED
BY VARIOUS STUDIES
A. Total Greenhouse Contribution to Sea Level by
2100 (cm)
Low
56
50
50
30
EPA (1983)a
NAS (1985/1983b)
NRC (1987)
IPCC (1990)
Wigley & Raper (1992) 15
This Report0 -1
B. Contribution to Thermal Expansion by 2100 (cm)
Medium
175
100
100
65
48
34
High
345
200
150
110
90
104
EPA (1983)<>
NAS (1983)
NRC (1987)
IPCC (1990)
Low
28
24
26
Wigley & Raper (1992) 22
This Report0 -1
Medium
72
30
39
33
20
High
115
36
58
44
58
aEPA (1983) refers to Hoffman et al. 1983.
'Thermal expansion from NAS 1983; glacial contribution from
NAS 1985.
°Low and High refer to lower and upper 1 percent.
135
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Chapter 8
TABLE 8-2
GLOBAL WARMING PROJECTED BY VARIOUS STUDIES
A. Warming Over 1990
Report
EPA(1983)a
NAS (1983)b
NAS (1985)
EPA(1989)a
IPCC (1990)
IPCC (1992)c
Wigley &Raper(1992)c
This Reportd
Levels
Low
0.7
—
—
—
1.3
1.0
0.8
-0.1
B . Year by Which Temperatures
Temperature
Report
EPA(1983)a
NAS(1983)b
NAS (1985)
EPA(1989)a
IPCC(1990)
IPCC(1992)C
Wigley &Raper(1992)t
This Reportd
Low
2095
2050
—
2090
2105
>2100
>2200
2050
Medium High
2.4 4.5
— —
— —
3.0 —
1.6 2.5
1.4 2.2
1.2 1.7
1.0 2.9
Warm 2°C or 4°C
2°C
Medium High
2040 2017
2030 2020
2050
2035 —
2060 2040
2075 2045
2080 2060
2099 2030
2100
Low Medium
2.1 5.0
— 4.5
1.5 3.0
— —
2.3 3.7
1.8 2.8
1.7 2.5
-0.1 2.0
4°C
Low Medium
>2100 2085
— 2080
2050 >2100
— 2060
>2100 >2100
>2100 >2100
>2100 >2100
>2200 >2200
CO2 = 600 ppm
Doubling
High Date
9.0
—
4.5
—
5.7
4.2
3.8
6.3
High
2040
—
>2100
—
2085
2095
>2100
2065
2050
—
2085
2060
2060
2060
2060
2080
aEPA (1983) refers lo Seidel & Keyes (1983); EPA (1989) refers to Smith & Tirpak (1989).
kCO2 only. Analyses based on assumption of 2°C warming "a few decades into the 21st century" and 3 to 4°C by 2080.
4PCC (1992) and Wigley & Raper (1992) results use IPCC emissions scenario A.
''Low and High refer to upper and lower 1 percent.
136
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Placing the Results in Context
Recent reports have gradually lowered the projec-
tions of future warming, primarily for three reasons.
First, in the mid-1980s the fully halogenated CFCs were
perceived as potentially responsible for about one quar-
ter of the expected warming (Cf. e.g., Ramanathan et al.
1985). These CFCs are no longer considered likely to
contribute significantly to global warming by the year
21002: The Montreal Protocol phases out their produc-
tion. Moreover, the direct greenhouse effect from CFCs
in the troposphere is partly offset because CFCs deplete
stratospheric ozone, which is also a greenhouse gas.
Although the partially halogenated HCFCs have not yet
been regulated, IPCC has reduced its projections for
these gases as well. For example, IPCC (1992) estimated
that by the year 2100 the concentration of HCFC-22 will
be 1.4 parts per billion, less than half the IPCC (1990)
estimate of 3 ppb.3
Second, estimates of the concentrations of carbon
dioxide have also been revised downward because of
both lower emissions and revised carbon cycle models.
The EPA studies released in 1983 assumed that CO2
emissions were most likely to reach 70 gigatons per
year by 2100. The IPCC (1992) Scenario A, by con-
trast, estimates about 20 Gt/yr; and even the high sce-
nario E only projects 35 Gt/yr.4 Thus, the IPCC (1990)
and (1992) reports projected CO2 concentrations of 825
and 800 ppm, respectively, well below the 1000 ppm
projected by the early EPA studies.5
Recent revisions in carbon cycle models have also
resulted in lower estimates of carbon dioxide concentra-
tions. Wigley (1993) concluded that more carbon may
be absorbed by the terrestrial biosphere than previously
assumed; he estimated 678 ppm as the most likely sce-
2For example, under IPCC's emissions scenario A, CFC-11 and
CFC-12 are expected to contribute 0.2 W/m2 by the year 2100, about
3 percent of the total radiative forcing from anthropogenic greenhouse
gases. Because the current contribution of these two CFCs is about
0.22 W/m2, IPCC scenario A implies a slight decrease in radiative forc-
ing from CFC-11 and CFC-12. IPCC (1992) at 175.
^HCFC-22 is by far the most important partially halogenated chloro-
fluorocarbon. IPCC (1992) estimates that the radiative forcing due to
HCFC-22 will rise from close to zero today to approximately 0.2 W/m2.
4But see Energy Modeling Forum (1995). Out of eight models consid-
ered, four models project emissions greater than the 26.6 Gt/yr assumed
by IPCC's (1992) second highest scenario (F). Two of the models pro-
ject emissions greater than IPCC's highest scenario (E); and one of the
scenarios exceeds 55 Gt by the year 2090. See Id. at slide entitled
"Modeler's Reference Case, World."
5The EPA and IPCC reports all projected concentrations of about 600
ppm for the year 2060. Because of the lags in the various processes, the
divergence in assumptions for the post-2060 period has a modest effect
on projections of sea level rise for the year 2100.
nario for 2100 if emissions follow the trajectory of IPCC
(1992) Scenario A. IPCC (1994) applied several alterna-
tive carbon cycle models to IPCC Emissions Scenario A;
all of the models project a CO2 concentration between
650 and 725 ppm.6 Our median estimate is 680 ppm.
Finally, temperature projections have declined
because the early studies did not consider the cooling
effect of atmospheric sulfates and other aerosols result-
ing from human activities. Since 1850, aerosols appear
to have offset about one-third of the radiative forcing
from greenhouse gases.7 Because aerosols rapidly fall
out of the atmosphere while greenhouse gases may accu-
mulate for tens or hundreds of years, the relative contri-
bution of aerosols will probably be less in the next cen-
tury than it has been in the last century. Nevertheless, as
discussed in Chapter 2, the IPCC emissions scenarios
imply that sulfates are likely to offset about 8 percent of
the increased radiative forcing from greenhouse gases
over the period 1990-2100.8
In spite of the downward revisions in future tem-
perature projections, one potential downward revision
has not occurred: climatologists still generally accept
the NAS (1979) estimate that, in equilibrium, a CO2
doubling would raise global temperatures 1.5 to 4.5°C.
The cooling effect of aerosols offers a plausible explana-
tion for why global temperatures have not risen as much
as climate models would have suggested.9 Wigley &
^But see Craig & Holmen (1995) (applying four different models for
balancing the carbon budget to IPCC emission Scenario A results in
CO2 concentrations of 825, 725, 700, and 690 ppm for 2100).
1See IPCC (1994) at 167 (The direct radiative forcing from
anthropogenic greenhouse gases released since preindustrial
times is 2.4 W/m2 ±15%; the mean direct radiative forcing from sul-
fates is -0.25 to -0.9 W/m2; the mean direct radiative forcing from bio-
mass burning is between -0.05 and -0.6 W/m2).
*hrhe IPCC scenarios do not assume that any governmental policies
will be implemented to reduce SO2 emissions, other than those
already enacted before 1992. Just as the effects of SO2 on plants
and human health, and eventually acid rain, led the United States
and other industrial nations to implement policies to reduce SO2
emissions, developing nations may also choose to reduce their emis-
sions, in which case the cooling effect of sulfates will be less than
implied by the IPCC scenarios.
'The extent to which sulfates have offset greenhouse warming can
be displayed by comparing world maps showing temperature trends
with world maps showing estimated radiative forcing from sulfates.
For example, the world map of estimated sulfate forcing, published
in IPCC (1994) at 31, shows the greatest sulfate impacts over
Europe, China, and the eastern United States. A world map of tem-
perature trends shows that virtually all of the Northern Hemisphere
has warmed by more lhan 1°C in the last fifty years, except for
Europe, China, and the Eastern United States (Kerr 1995 (citing
Karl et al. (1995) at Figure 2)). See also Mitchell et al. 1995.
137
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Chapter 8
Raper (1992) showed that when sulfates are included,
the historic change in global temperatures has been
consistent with a climate sensitivity of 2.5 to 3.0°C,
which is near the middle of the 1.5 to 4.5°C range.
The net effect of the various revisions is that the
best-guess estimate for global warming by the year
2100 is about 2°C—half the warming that was expect-
ed during the mid-1980s. Thus, even if there were no
revisions in our understanding of the impact of global
warming on sea level, one might reasonably expect
the 50 to 200 cm greenhouse contribution to sea level
rise to be cut in half. That appears to have happened:
The Wigley & Raper estimate of 48 cm is almost
exactly one-half the earlier best-guess estimate of
1 m; and their range of 15 to 90 cm is only slightly
below the 25 to 100 cm range that would be expected
if the sea level contribution was proportional to warm-
ing. Our 1%-high estimate of 1 m also reflects such a
revision.
Antarctic Contribution. Changing projections
of future temperatures is not the only reason that sea
level projections have been revised. Estimates of the
likely contribution from Antarctica have also been
revised downward. A decade ago, NAS (1985)
projected that by 2100, Antarctica could contribute
anywhere from -10 to +100 cm, with a contribution in
the tens of centimeters most likely. More recent
assessments, however, have generally concluded that
the initial Antarctic contribution will probably be neg-
ative. Since NAS (1985), polar scientists have recog-
nized the possibility that increased snowfall could at
least partially offset any positive contribution to sea
level from the Antarctic Ice Sheet's response to
warmer temperatures. Since IPCC (1990), however,
most studies have suggested that the ice sheet's
response may be small and thus more than offset by
increased precipitation, at least for the next century.10
Although a significant positive Antarctic con-
tribution is not likely by 2100, such a contribution is
still a risk that must be considered, both for calculat-
ing the likely rise by the year 2200 and for examining
"'The downward revision of the estimated ice sheet response has
resulted partly from lower global temperature projections. The
NAS (1985) analysis assumed a 4°C global warming by 2050,
whereas a 1.0 to 1.5°C warming by that date now seems more like-
ly. Although there is some disagreement among glaciologists
whether a 4°C warming would cause ice streams to accelerate,
there is a general consensus that a 1°C warming by 2050 would
probably not cause a major impact by 2100.
the 1%-high scenario. In the last fifty years, the
Antarctic Peninsula has warmed 2°C, causing the
peninsula alone to contribute approximately 0.5 mm
to sea level. (Drewry & Morris 1992). The Wordie
and Prince Gustav Ice Shelves have largely disinte-
grated in the last few decades; around Larsen inlet, the
ice shelf has retreated 10 to 15 km. In early 1995, an
iceberg with an area of more than 2000 km2 (the size
of Rhode Island) broke away from the Larsen Ice
Shelf. Until recently, James Ross Island was con-
nected to the Peninsula by ice shelves; but now it is
circumnavigable.
No one has demonstrated that these recent
events around the Antarctic Peninsula were caused by
global warming, nor that these events are a precursor
to a disintegration of any of the other ice shelves.
Nevertheless, these events lend some credence to the
assumptions provided by the glaciology reviewers
(Chapter 5), which generally imply that the NAS
(1985) high estimate of a 100 cm contribution from
Antarctica still has some validity, albeit for the year
2200 rather than 2100. Our attempts to quantify this
risk should not obscure the primary reason for recog-
nizing it: The processes that determine warming of
the circumpolar ocean, the melting of ice shelves, and
the speed at which glaciers flow are very poorly
understood. The assessment that Antarctica will not
make a major contribution is based on the assumption
that the water intruding beneath the ice shelves will
warm less than 1 °C in the next century; until there is
a consensus among climate modelers on this point,
one cannot reasonably rule out the possibility of a sig-
nificant Antarctic contribution in the next century.
Changes in models of Greenland, mountain
glaciers, and thermal expansion have also led to minor
downward revisions of the sea level projections.
Their combined impact, however, is small compared
with the uncertainty regarding Antarctica and global
temperatures.
How Should Sea Level Rise
Scenarios Be Used?
In the last decade, coastal managers have
increasingly incorporated information on sea level
rise into decisionmaking. The gradual downward
revision has not substantially reduced the use of these
scenarios. Possible explanations include: the fact that
most decisionmakers did not believe the high
scenarios anyway; the existence of tidal gauge
measurements—and recent satellite observations—
138
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Placing the Results in Context
showing that sea level is rising11; an increasing
consensus that at least some sea level rise will result
from global warming; and increased understanding
among coastal scientists, engineers, and policy
makers that even a small rise in sea level can have
important consequences.
Sea level scenarios have been used to (1) encour-
age and guide additional research and modeling
efforts; (2) justify modifications of engineering
designs; (3) alter the land-use planning process to
accommodate rising sea level; and (4) develop impact
assessments to help national policymakers decide the
appropriate level of attention warranted by the global
warming issue.
Encouraging Additional Efforts. A draft by
Hoffman et al. (1982) was the first effort by EPA or
anyone else to estimate future sea level for specific
years for the purpose of encouraging coastal decision
makers to address rising sea level. A previous analysis
by Schneider & Chen (1980) had examined the poten-
tial implications of a 5 to 8 m rise in sea level due to a
collapse of the West Antarctic Ice Sheet, suggesting
that such an occurrence could conceivably occur with-
in several decades. But the purpose of that study was
to alert society to the risks of CO2 emissions, not to
motivate coastal officials to change their own policies.
The Hoffman et al. (1982) draft was sent to every
U.S. coastal state, as well as one hundred scientists.
That draft and the final EPA report quickly spurred
three panels of the National Academy of Sciences to
consider how to project sea level for specific years. In
the NAS Climate Research Board's 1983 report,
Changing Climate, Roger Revelle estimated that, in the
course of a century, Greenland and small glaciers could
each add 12 cm to sea level if the Earth warms 3 to 4°C;
he estimated that a 70 cm rise in one hundred years was
most likely. Two years later, the NAS Polar Research
Board, assisted by the U.S. Department of Energy, pro-
vided the first detailed assessment of the potential
glacial contribution to sea level (NAS 1985); that report
adopted EPA's convention of estimating sea level
through the year 2100. Recognizing the superior
expertise of the Polar Research Board, EPA impact
studies immediately adopted the 50 to 200 cm range
implied by the Polar Research Board report,12 suggest-
ing that aim rise was most likely.
Meanwhile, the National Academy of
Engineering's Marine Board commissioned a panel to
examine the engineering implications (NRC 1987),
assisted by the Army Corps of Engineers. The wide
range of uncertainty of the EPA scenarios led the
Marine Board panel to recommend that engineers
consider scenarios ranging from 50 to 150 cm by the
year 2100.
Engineering Design. Rising sea level may some-
times justify designing coastal structures differently
than would be appropriate if sea level was stable. In
1985, EPA examined the implications of accelerated sea
level rise for the beach at Ocean City, Maryland (Titus
1985). The report noted that while groins may curtail
erosion due to alongshore transport of sand, it does not
curtail erosion due to sea level rise. Therefore, because
sea level was already rising and was expected to accel-
erate, it would be advisable to shift from groins to plac-
ing sand onto the beach. That message was presented
at dozens of public meetings and private briefings of
state and local officials. Shortly thereafter, the State of
Maryland decided to shift from groins to beach nour-
ishment (see Associated Press (1985)).
The prospect of sea level rise was not the only
reason that the state chose to shift strategies. Many
geologists doubted that the groins would work anyway;
and the U.S. Army Corps of Engineers was already on
record as supporting beach nourishment. But sea level
rise helped to provide a political environment in which
the issue could be reconsidered. First, the issue
prompted a series of articles in a Baltimore newspaper,
which explained how barrier islands naturally respond
to rising sea level, and questioned the state's then-cur-
rent erosion control strategy. Second, the issue could
be viewed as "new information," which made it possi-
ble to advocate beach nourishment without impugning
the original decision to build groins.
Like many of the policy changes motivated by
the accelerated sea level scenarios, the shift to beach
nourishment was justified by current sea level trends.
Thus, the fact that the sea level scenarios were (in ret-
rospect) too high had little or no impact.
Chapter 9 for a sample of U.S. tide gauge trends. Recent
satellite estimates suggest that global sea level rose approximately
4 mm/yr over the last three years (Nerem 1995).
nSee Table 8-1, supra. After 1984, no EPA study used the
Hoffman et al. (1983) high scenario. A few studies that were initi-
ated before the NAS report but published later made reference to
the Hoffman et al. scenarios; but accompanying text generally
made it clear that the range of 50-200 cm was to be preferred. The
50-200 cm range was also used in a 1989 report to Congress
(Smith & Tirpak 1989) and in EPA-funded studies of Senegal,
Nigeria, Venezuela, Argentina, and Uruguay (e g., IPCC 1995).
139
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Chapter 8
More recently, a number of design standards
have added an extra 30 to 100 cm to account for
future sea level rise. By 1987, California's Bay Area
Conservation and Development Commission (BCDC)
was requiring an additional one foot of elevation on
any newly reclaimed land in San Francisco Bay,
based on a scenario of a one-foot rise in fifty years.
Perhaps if it had waited for improved scenarios, the
BCDC might have chosen to require only an addi-
tional nine inches of elevation; but given the long life-
times of land reclamation projects, it seems just as
likely that the Commission would have employed the
same standard while citing a longer time horizon.
Reclamation in Hong Kong also includes a safety
margin for accelerated sea level rise, as do the design
of new seawalls in eastern Britain and the Netherlands
(Nichols & Leatherman 1995).
Land Use: Planning and Regulation. The early
EPA studies helped to motivate two states to alter their
land use regulations in the coastal zone. ERA'S, first
case study (Earth & Titus 1984) examined Charleston,
South Carolina, and provided maps showing the areas
that would be permanently inundated or periodically
flooded with various sea-level scenarios ranging from
30 to 350 cm. At a conference presenting the results,
an official from the Chamber of Commerce stated that
he "wished EPA had studied Savannah [Georgia]
instead," fearing that the prospect of sea level rise
might scare away business. But businesses do not gen-
erally base relocation decisions on potential flooding
that might occur in the year 2100, especially in areas
that are currently vulnerable to hurricanes.
The State of South Carolina was concerned,
however, about its eroding beaches. The State
Legislature appointed a "Blue Ribbon Panel," which
examined the risks to the shoreline. Motivated in part
by EPA's projection that sea level could rise one foot
in the next thirty years, the panel recommended that
no new structures be allowed within the area most
vulnerable to erosion, which it defined as a line land-
ward of the primary dune by a distance equal to forty
times the annual erosion rate. The South Carolina
Legislature enacted these recommendations in a new
Beachfront Management Act.13
Shortly thereafter, a developer named Lucas,
whose lots were entirely seaward of the setback line,
challenged the law as an unconstitutional taking of
private property without compensation. In one of the
most celebrated cases on property rights, Lucas v.
South Carolina Coastal Council,14 the U.S. Supreme
Court agreed that he was entitled to compensation.
Meanwhile, Hurricane Hugo had prompted the
Legislature to slightly revise the law, so that the set-
back only applied to lots that had room for a house
landward of the setback line. People in Lucas' situa-
tion are now allowed to build, but subject to a "rolling
easement" or "special permit", which requires them
to remove their structure if the beach erodes enough
to put the house in harm's way.15
Did EPA's erroneously high estimate of a one-
foot rise in thirty years prompt the Legislature to
enact hasty legislation? There is little evidence that
this occurred. The forty-year setback is somewhat
less stringent than the sixty-year setback in neighbor-
ing North Carolina. Moreover, the Beachfront
Management Act was passed four years after the EPA
case study was published, and only after the extra
deliberative step of a Blue Ribbon Panel. Because of
the importance of Lucas, the Beachfront Management
Act has been analyzed by dozens of legal commenta-
tors, none of whom has suggested that any flaws in
the legislation resulted from unrealistically high sea
level scenarios.16 As with the Ocean City study, the
Blue Ribbon Panel's analysis was not precise enough
to distinguish between a one-foot rise in thirty years
and one foot over sixty years.17
Maine's regulations are more closely linked to
the sea level rise scenarios: The state's Coastal Sand
Dune Rules explicitly presume the mobility of any
structures that would interfere with the landward
migration of sand dunes or wetlands with a rise in
sea level of up to three feet.18 Considerable technical
14112 S.Ct. 2886, 34 E.R.C. 1897 (1992).
15For additional details on the "Takings" implications of policies in
response to sea level rise, see J.G. Titus, 1994, "Rising Seas,
Coastal Erosion, and the Takings Clause" (draft).
l6See e.g., Richard A. Epstein, "Lucas v. South Carolina Coastal
Council: A Tangled Web of Expectations", 45 Stanford Law Review
1369, 1377 (1993) ("The Court has provided an effective blueprint
for confiscation....").
»S. C. Code §48-39-250 el seq.
a more detailed discussion of the implications of sea level
rise for the South Carolina law, see J. G. Titus (1994), "Rising
Seas, Coastal Erosion, and the Takings Clause" (draft).
I8"If the shoreline recedes such that the coastal wetland.. .extends
to any part of the structure, including support posts, for a period of
six months or more, then the approved structure.. .shall be removed
and the site shall be restored to natural conditions within one year."
Coastal Sand Dune Rules. Code Me. R § 355(3)(B)(1) (1987). See
Part III for a discussion of the South Carolina statute, which also
uses rolling easements.
140
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Placing the Results in Context
discussions took place as the state debated whether to
use the EPA or NAS scenarios. This illustrates an
information-transfer problem: by the time the regula-
tions were issued in 1987, EPA was recommending
the use of the NAS scenarios anyway.
Do the lower scenarios (if accurate) imply that
even a three-foot rise was too much to plan for? As
discussed in the following chapter, our analysis sug-
gests a 7 percent chance that sea level will rise three
feet along the U.S. Atlantic coast by the year 2100, and
a better than fifty-fifty chance that such a rise will
occur during the next two hundred years. The benefits
of this regulation (if the sea does rise three feet) would
have to be greater than the cost of the restrictions,
which must be borne whether or not the sea rises.
Given the fact that movable structures are allowed
in this area, the additional cost of the restriction may be
small. The benefits depend both on (1) how soon the
shore reaches a house (or the location where it would
have been built without the regulation) and (2) the
reduction in the cost of moving the structure as a result
of having designed it to be moved (or the additional
time it takes to reach the structure because it was built
farther from the shore).19 Although evaluating the
impact of revised sea level rise scenarios on the regula-
tion is beyond the scope of this report, a recent study by
the State of Maine suggests that the regulation has
greater benefits than costs even if a 50 cm rise in sea
level is most likely (Maine 1995).
Impact Assessments. Finally, sea level scenar-
ios have been used to illustrate the implications of sea
level rise for policymakers and members of the gen-
eral public who need to know whether or not global
warming is important, as well as people who are sim-
ply curious. Our previous estimate of the cost of a
one meter rise in sea level was about twice as great as
the cost of a 50 cm rise in sea level (Titus et al. 1991).
Both estimates suggest that coastal communities will
eventually have to develop a stable mechanism for
funding coastal protection. But because the sole use
of those national estimates is to gain a rough feel for
the issue, not to set an appropriation, there is no prac-
tical difference between what must be done today if
we expect an eventual cost of $200 billion and what
we must do if the cost will only be $100 billion.
19The greatest cost savings of the regulation may be institutional cost
avoided. Abandoning neighborhoods to an eroding shore is politically
problematic. Without an advance understanding that such a retreat is
part of the rules of the game, it may be politically int'easible to pro-
hibit property owners from rebuilding; as a result, natural wetlands
and beaches may be replaced by bulkheads. See Titus (1991).
Finally, there have and will continue to be strong
reasons to consider the one meter sea level rise scenario. In
the United States, most maps show the 5 ft contour, which
is typically about one meter above high tide. Regardless
of which scenario one expects, impact analysis would be
much easier if finer-resolution topographic maps were
available in coastal areas. Nevertheless, it is wise to
analyze a wide variety of possible scenarios.
References
Associated Press. 1985. ''Doubled Erosion Seen for Ocean
City." Washington Post, November 14 (Maryland Section).
Barth, M.C., and J.G. Titus (eds). 1984. Greenhouse
Effect and Sea Level Rise: A Challenge for This
Generation. New York: Van Nostrand Reinhold.
Chafee, Senator John H. 1986. "Our Global Environ-
ment: The Next Challenge." In: Titus, J.G. (ed). Effects
of Changes in Stratospheric Ozone and Global Climate.
Washington, DC: U.S. Environmental Protection
Agency and United Nations Environment Programme.
Craig, S.G., and K.J. Holmen. 1995. "Uncertainties
in Future CO2 Projections." Global Biogeochemical
Cycles 9:139-52.
Dean, R.G., et al. 1987. Responding to Changes in Sea
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Response of Large Ice Sheets to Climatic Change."
Phil. Trans. R. Soc. London B338:235-242.
Energy Modeling Forum. 1994. "EMF14: Integrated
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Second Round Scenario Results Have Been Received
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Hoffman, J.S., et al. 1982 (draft). Projecting Future
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P) election Agency.
Intergovernmental Panel on Climate Change. 1995.
Global Climate Change and the Rising Challenge of the
Sea. Proceedings of the International Workshop Held on
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Chapter 8
Margarita Island, Venezuala, March 9-13, 1992. Silver
Spring, MD: National Ocean Service, U.S. Department
of Commerce.
Intergovernmental Panel on Climate Change. 1994. Climate
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Karl, T.R., R.W. Knight, G. Kukla, and J. Gavin. 1995.
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Maine, State of. 1995. Anticipatory Planning for Sea-
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Washington, DC: U.S. Environmental Protection
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National Academy of Sciences. 1983. Changing
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142
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CHAPTER 9
HOW TO USE THESE RESULTS
TO PROJECT LOCAL SEA LEVEL
The results presented in Chapter 7, like those
from previous sea level assessments, only account for
the global rise in sea level resulting from global cli-
mate change. They include neither the change in
global sea level resulting from other factors1 nor
changes in local sea level resulting from land subsi-
dence, compaction, and other factors.
The Approach Employed by
Previous Studies
Previous EPA studies on the impacts of sea level
rise have assumed that the nonclimate contributors to
sea level will remain constant.2 Based on the assump-
tion that global sea level rose 12 cm over the last cen-
tury, these studies assumed that the net subsidence at
particular locations was 1.2 mm/yr less than the
observed rate of relative sea level rise measured by
tidal gauges. With that assumption, estimates of local
sea level rise were calculated as follows:
local(t) = global(t) + (trend —0.12) (t—1990),
where local(t) is the rise in sea level by year t at a par-
ticular location, measured in centimeters; global(t) is
the global rise in sea level projected by a particular
scenario; and trend is the current rate of relative sea
level rise at the particular location. Because more
recent estimates suggest that global sea level may be
rising 1.8 mm/yr, some studies have replaced the
coefficient 0.12 with 0.18.
Implicit in this procedure was the assumption that
in the next century global warming will be the only net
contributor to global sea level. Some impact researchers,
by contrast, have developed local scenarios simply by
adding local trends to the projections of global sea level
lE.g., very long-term (glacial/interglacial) changes in climate, and
nonclimatic factors such as groundwater depletion and changes in
land use. Although nonclimatic sources have added at most a few
centimeters to sea level in the last century (Sahagian et al. 1994), no
one has thoroughly assessed the likely future contribution.
2This convention started with EPA s first sea level impacts assess-
ment (Earth & Titus 1984) and continued through EPAs final
assessment of U.S. impacts (Titus et al. 1991). The approach was
endorsed by the National Academy of Engineering (Dean et al. 1987).
More recent assessments have subtracted out a slightly higher esti-
mate of global sea level trends.
Manabe
Schneider
Wigley
Total
Greenhouse Contribution to Sea Level, 1880-1990 (cm)
Figure 9-1. Historic Greenhouse Contribution to
Sea Level, 1880-1990. The median estimate of the
greenhouse contribution (0.5 mm/yr) implied by the
reviewer assumptions is well below prevailing esti-
mates of global sea level rise (1 to 2.5 mm/yr). Unless
the nongreenhouse contributors are likely to change, it
is reasonable to assume that global sea level rise in the
next century will also be 0.5 to 2 mm/yr greater than
the greenhouse contribution.
rise.3 Implicit in that procedure is the assumption that
none of the historic sea level rise was caused by global
warming. As long as people were investigating the
implications of a 1 to 2 m rise in sea level, there was lit-
tle practical distinction between these two approaches.
But with sea level projections on the order of 50 cm, this
12 cm discrepancy is worth resolving.
.Which of these assumptions are correct?
Probably neither. As Figure 9-1 shows, the reviewer
assumptions with which we project future sea level
rise imply that sea level rose about 0.5 mm/yr over
the last century. This estimate is well below the
3This procedure is consistent with the approach used by Roger
Revelle in NAS (1983). Revelle explicitly added the historic trend
of 12 cm to his estimates of thermal expansion, Greenland, and
small glacier contributions to sea level.
143
-------
Chapter 9
1.8 mm/yr estimate of total global sea level rise.
Thus, it would appear that other factors are adding to
sea level. Possible explanations include groundwater
depletion (Sahagian et al. 1994), a delayed response
to the warming that has taken place since the last ice
age, and shifts in ocean basins. It is also possible that
tidal gauges cannot measure true global sea level rise
because coasts are generally subsiding.4
Until we know precisely why our models
underpredict historic sea level rise, it seems most rea-
sonable to assume that those factors that we have not
modeled will continue. Because this assessment (like
previous 1PCC assessments) only examines the sea
level rise induced by climate change, the results pre-
sented in Chapter 7 should be interpreted as estimat-
ing the extent to which climate change will accelerate
the rate of sea level rise, compared with what other-
wise would occur.
Those who require an estimate of sea level rise
at a particular location can simply add the normalized
projection to the current rate of sea level rise6:
localCt) •= normalized!t) + (t — 1990) X trend.
For example, according to Table 9-2, sea level at New
York City has been rising 2.7 mm/yr.7 This rate is
typical of the U.S. Atlantic and Gulf Coasts (Lyle& et
al. 1988). For the year 2100, the median and 1%-high
normalized projections are 25 and 92 cm for the year
2100. Because even current trends would result in a
30 cm rise, the total rise is most likely to be 55 cm
(about 2 feet); but it also has a 1 percent chance of
exceeding 122 cm (about 4 feet). Similarly, if one
assumes that average worldwide sea level has been
rising 1.8 mm/yr, then global sea level has a 50 per-
cent chance of rising 45 cm, and a 1 percent chance of
rising 112 cm, by the year 2100. (See Figure9—2.)
Recommended Procedure
The most realistic procedure, in our view, is
to extrapolate all trends other than those due to glob-
al wanning. Simply adding historic trends to pub-
lished projections of sea level rise doublecounts what-
ever portion of the historic local trend was caused
by global warming. We remove this doublecounting
by developing a set of normalized projections in
which the historic component of the greenhouse
contribution has been removed.5 The normalized pro -
jections estimate the extent to which future sea level
rise will exceed what would have happened if current
trends simply continued. Table 9-1 summarizes our
normalized results.
4For example, due to the additional mass placed on the continental
shelves from previous sea level rise.
-1990
5Each normalized projection was calculated as follows'
Normalized/!) = globally — |model,(1990>—model/ 1880)]
where globalj(t) is the greenhouse (and sulfale) contribution to sea
level ((e.. the result reported in Chapter 7) between 1990 and the
year t for the i"1 simulation; and modelj represents the historic
greenhouse contribution to sea level estimated by the Ith simulation
between 1765 and a particular year. Thus, the ilh normalized pro-
jection represents the extent to which the greenhouse contribution
by a particular year exceeds the contribution that would be expect-
ed by merely extrapolating the estimated historic greenhouse con-
tribution. Assuming that the nongreenhouse contributors remain
constant, the normalized projection also represents the extent to
which sea level rise will exceed the rise that would be expected
from extrapolating the historic rate of rise.
Caveats
Scenarios of sea level rise can be put to a vari-
ety of uses. In general, individual users know far
belter than we the most appropriate uses for these
scenarios. All we can do is convey what we know
about their limitations.
Most importantly, our probability estimates are
not based on statistics. Our estimates simply convey
what the probability of various rates of sea level rise
would be if one is willing to assume that the experts we
polled are each equally wise and that their collective
6This procedure is not the same a« simply adding a historic trend to
every element of the probability distribution, since Modelj will be
different for different simulations (see Note 5, supra). The overall
tendency will be for the normalized distribution to have a smaller
variance than the gieenhouse contribution; for example, a high
temperature sensitivity implies that historic thermal expansion was
greater than the mean estimate, and hence that the historic non-
greenhouse contribution was less than the mean estimate, for a
given estimate of total historic sea level rise
Notwithstanding our concern in Chapter 3, Note 4, the normalized
projections are probably improved somewhat by the fact that each
model run included a historic simulation If a particular set of para-
meters substantially overestimates the historic rate of sea level rise,
foi example, the net effect of our procedure is to adjust the future pro-
jection downward by the amount of the historical overestimate
7The National Ocean Service periodically publishes estimates of
the rate of sea level rise for several U.S cities. As this report went
to press, NOS was about to release its new estimates for sea level
trends The new report can be obtained from Steve Lyles, National
Ocean Service, SSMC4, Station 7601, 1305 East-West Highway,
Silver Spring, MD 20910-3233 Fax- 301-713-4435.
144
-------
How to Use These Results to Project Local Sea Level
Cumulative
Probability (%)
10
20
30
40
50
60
70
80
90
95
97.5
99
Mean
o
TABLE 9-1
ESTIMATING SEA LEVEL RISE AT A SPECIFIC LOCATION
Normalized Sea Level Projections, Compared with 1990 Levels (cm)
Sea Level Projection by Year:
2025
-±
I
3
4
5
6
8
9
12
14
17
19
5
6
2050
-4
3
6
8
10
13
15
18
23
27
31
38
11
10
2075
0
6
10
14
17
21
24
29
37
43
50
57
18
15
2100
1
10
16
20
25
30
36
44
55
66
78
92
27
23
2150
3
16
26
35
43
53
65
80
106
134
167
210
51
47
2200
5
23
37
51
64
78
98
125
174
231
296
402
81
81
NOTE: To estimate sea level at a particular location, add these estimates to the rise that would occur if current trends were to
continue. See Table 9-2 for historic rates of sea level rise. For example, if sea level is currently rising 3 mm/yr, then under cur-
rent trends, sea level will rise 26 cm between 1990 and 2075. Adding 26 cm to the normalized values in the Table, the median
estimate for 2075 is 43 cm, with a 1 percent chance of an 83 cm rise.
TABLE 9-2
HISTORIC RATE OF SEA LEVEL RISE AT VARIOUS LOCATIONS IN THE UNITED STATES
(mm/yr)
Atlantic Coast
Eastport, ME 2.7
Portland, ME 2.2
Boston, MA 2.9
Woods Hole, MA 2.7
Newport, RI 2.7
New London, CT 2.1
Montauk, NY 1.9
New York, NY 2.7
Sandy Hook, NJ 4.1
Atlantic City, NJ 3.9
Philadelphia, PA 2.6
Lewes, DE 3.1
Annapolis, MD 3.6
Solomons, Is., MD 3.3
Washington, DC 3.2
Hampton Roads, VA 4.3
Portsmouth, VA 3.7
Wilmington, NC 1.8
Charleston, SC 3.4
Ft. Pulaski, GA 3.0
Fernandina, FL 1.9
Mayport, FL 2.2
Miami Beach, FL 2.3
Gulf Coast
Key West 2.2
St. Petersburg, FL 2.3
Pensacola, FL 2.4
Grand Isle, LA 10.5
Eugene Island, LA 9.7
Sabine Pass, TX 13.2
Galveston.TX
Freeport, TX
Padre Island, TX
6.4
14.0
5.1
Pacific Coast
Honolulu, HI
Hilo, HI
San Diego, CA
La Jolla, CA
Newport, CA
1.6
3.6
2.1
2.0
1.9
Los Angeles, CA 0.8
Santa Monica, CA 1.8
San Francisco, CA 1.3
Alameda, CA 1.0
Crescent City, CA —06
Astoria, OR
Seattle, WA
Neah Bay, WA
Sitka, AK
Juneau, AK
-03
2.0
—LI
—22
—124
SOURCE: Lyles et al. 1988.
145
-------
Chapter 9
wisdom reflects the best available knowledge. In a sta-
tistical model, we would conduct an experiment at
least several dozen times and determine the variation
of outcomes. But within the time horizon of this pro-
ject, humanity can only conduct the experiment once,
which we are doing; so statistical estimates of proba-
bility are impossible. Our projections are less like a
statistical weather forecast and more like handicap-
ping a horse race.
As with a horse race, our inaccuracy results
more from our inability to quantify the relevant fac-
tors than from the random fluctuations within the
processes whose uncertainties we have described. We
have left out some factors; so our uncertainty is prob-
ably greater than we estimate it to be.
Finally, this particular exercise, like EPAs
1982—83 report projecting sea level rise (Hoffman et
al. 1983), is limited by the fact that the authors are
not experts about any of the particular processes that
contribute to sea level. Just as the 1983 report was
undertaken because no one else was estimating sea
level rise for specific years, this report was under-
taken because no one was estimating the probability
of sea level rise or factoring in the small-but-impor-
tant risk of a large Antarctic contribution. For the
foreseeable future, coastal decisionmakers should
view this prospect as a potentially important risk that
is poorly understood. Although Antarctica will
probably not contribute significantly to sea level in
the next century, the glaciology reviewers of this
report were unanimous that the research necessary to
rule it out simply has not been undertaken. (See also
Appendix 3.)
The reader should have no illusions about the
adequacy of the models used in this or any report pro-
jecting future sea level rise. Because a reasonable
person cannot confidently be certain that any partic-
ular group of experts knows the actual story, we have
attempted to incorporate every view that we could
obtain. We hope that these estimates of the probabil-
ity of sea level rise help coastal engineers, planners,
and legislators to determine whether and how to pre-
pare for the consequences of a rising sea.
99
I
0 50 150 250 350
Normalized Sea Level Contribution (cm)
2050
2150
2100
Years
New York Relative Sea Level Rise (cm)
2200
Figure 9-2. Normalized Contribution to Sea Level.
By netting out the historic greenhouse contribution, the
normalized estimates in (a) represent the projected accel-
eration in sea level compared with historic trends. One
can estimate local or global sea level by adding these
estimates to trends from tide guages. For example, in
(b) these estimates are added to New York s historic trend
of 2.7 mm/yr, which typifies the U.S. Atlantic Coast.
146
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How to Use These Results to Project Local Sea Level
References
Earth, M.C., and J.G. Titus (eds). 1984. Greenhouse
Effect and Sea Level Rise: A Challenge for This
Generation. New York: Van Nostrand Reinhold.
Dean, R.G., et al. 1987. Responding to Changes in
Sea Level. Washington, DC: National Academy Press.
Hoffinan, J.S., D. Keyes, and J.G. Titus. 1983. Projecting
Future Sea Level Rise. Washington, DC: U.S. Environ-
mental Protection Agency.
Lyles, S.D., L.E. Hickman, and H.A. Debaugh.
1988. Sea Level Variations for the United States
1855-1986.
Service.
Rockville, MD: National Ocean
National Academy of Sciences. 1983. Changing
Climate. Washington, DC: National Academy Press.
Sahagian, D.L., F.W. Schwartz, O.K. Jacobs. 1994.
Direct Anthropogenic Contributions to Sea Level
Rise in the 20th Century. Nature 367:54-7.
Titus, J.G. 1991. Greenhouse Effect and
Coastal Wetland Policy: How American Could
Abandon an Area the Size of Massachusetts at
Minimum Cost. Environmental Management
15:1:39-58.
147
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Chapter 9
148
-------
Cumulative Probability Distributions
APPENDICES
149
-------
APPENDIX 1
CUMULATIVE PROBABILITY DISTRIBUTIONS
Explanations and Suggested
Comparisons
This Appendix presents tables documenting
the cumulative probability distributions presented in
the body of the report. Due to their repetitious
nature, we present explanations and suggested com-
parisons at the outset, rather than repeating them in
each of the relevant tables.
Table 13: Wigley and Raper did not specify
parameter values for Circumpolar Deep Water.
Tables 14-17, 19-21, 27-29, 31-37, 41-42, and
45-50: With the exception of Wigley and
Raper, all projections include a random
cross-section of precipitation and ice sheet
parameters.
Tables 22-23: All projections include
background probability distribution as
modified from the draft based on Jacobs and
Lingle comments.
Table 39. This table provides statistics for 8
random subsamples. The 99 percentiles range
from 101.5 to 110.2, with a mean of 104.2 and
a variance of 8. The variance of the mean of
this series (i.e. the average estimate of the 99th
percentile) is 8/n, where n is the sample size of
8. Thus, the standard error is approximately
1.0 cm. As a result, additional simulations did
not seem worthwhile. Note also that the 99-
percentile tails do not appear to vary
(in percentage terms) any more than the mean.
Therefore, the Latin Hypercube algorithm,
with its bias toward better estimates of the
tails, would probably be of little use for our
purposes. See also. Numerical Error of the
Monte Carlo Algorithm, Chapter 7, supra.
Table 40: Compare to Tables 7 and 8.
Table 41: Compare to Tables 21.
Table 42: Compare to Tables 17.
Table 43: Compare to Tables 28 and 35.
Table 44: Compare to Tables 29 and 37.
Table 45: Compare to Tables 30.
Table 46: Compare to Tables 7 and 40.
Table 47: Compare to Tables 8 and 40.
Table 48: Compare to Tables 28 and 43.
Table 49: Compare to Tables 29 and 44.
Table 50: Compare to Tables 30 and 45.
Table 51: The "Fixed Emission 2100"
scenario refers to the range of emissions
scenarios developed in Chapter 2 and used in
Chapter 3 to generate temperatures. The other
two scenarios are based on the assumptions
that emissions remain constant after the year
2025 and 2050.
Table 52-59: To simplify the necessary
comparisons, these tables present results for
only one reviewer; arbitrarily, we picked
Schneider. Therefore, each of the tables
should be compared to the column reporting
Schneider values.
Table 52: Compare to Table 7.
Table 53: Compare to Table 8.
Table 54: Compare to Table 17
Table 55: Compare to Table 21
Table 56: Compare to Table 28
Table 57: Compare to Table 29
Table 58: Compare to Table 38
Table 59: The authors regret omitting the
breakout by reviewer in Table 30.
150
-------
Cumulative Probability Distributions
A. RESULTS REPORTED IN CHAPTERS 2 THROUGH 9
1. 2100 CO2 Concentration
2. Year by Which CO2 Concentration
Exceeds 600 ppmv
Cumulative
C02 (ppm)
Cumulative
Year
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
405.28
426.87
438.65
461.90
481.96
510.59
553.50
591.41
633.28
679.52
728.78
792.21
877.97
1046.68
1203.56
1362.93
1614.16
1774.73
2363.46
679.52
737.98
242.19
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
2037
2040
2042
2045
2048
2052
2059
2064
2070
2078
2088
2103
2131
2200
2200
2200
2200
2200
2200
151
-------
Appendix 1-A
3. Forcing: 1990-2100, all Reviewers (W/m2)
Cumulative
AQ1990-2
1990-2100
5. Equilibrium Temperature Change
for a Doubling of CO2, all Reviewers (°C)
Cumulative
AT2x
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
1.28
1.77
1.94
2.29
2.61
3.02
3.55
3.99
4.41
4.90
5.38
5.83
6.36
7.17
7.76
823
8.69
8.99
9.39
490
4.99
1.58
0.10
0.50
1.00
2.50
5.00
10.00
20.00
25.36
30.00
40.00
50.00
60.00
70.00
80.00
86.97
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
0.00
0.00
0.00
0.07
0.29
0.62
1.26
1.50
1.68
2.01
2.37
2.75
3.19
3.83
4.50
4.90
5.93
7.21
8.64
9.54
14.31
2.37
2.66
1.81
4. Year by Which Forcing Exceeds 4.4,
all Reviewers (W/m2'
Cumulative
Year
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
2059
2061
2062
2064
2066
2068
2073
2077
2081
2089
2099
2117
2151
>2200
>2200
>2200
>2200
>2200
>2200
152
-------
Cumulative Probability Distributions
6. Global Mean Surface Temperature Change by Reviewer, 1990-2050
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind
Schneider Wigley All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-0.44
-0.36
-0.32
-0.24
-0.18
-0.10
0.00
0.07
0.13
0.20
0.26
0.33
0.41
0.52
0.60
0.71
0.79
0.84
0.93
0.20
0.21
0.24
0.00
0.11
0.22
0.33
0.42
0.54
0.70
0.84
0.97
1.11
1.25
1.41
1.65
1.96
2.28
2.61
2.82
3.03
3.20
1.11
1.19
0.57
0.07
0.15
0.19
0.34
0.45
0.58
0.75
0.88
1.01
1.13
1.26
1.43
1.61
1.97
2.29
2.52
2.89
3.00
3.62
1.13
1.21
0.56
0.08
0.23
0.27
0.33
0.43
0.55
0.70
0.85
0.99
1.12
1.27
1.43
1.66
2.01
2.32
2.64
2.89
3.15
3.50
1.12
1.21
0.59
0.16
0.26
0.30
0.34
0.41
0.51
0.68
0.80
0.93
1.04
1.18
1.32
1.49
1.77
1.98
2.14
2.45
2.72
3.05
1.04
1.10
0.48
0.04
0.14
0.20
0.29
0.40
0.55
0.71
0.83
0.99
1.12
1.27
1.43
1.65
1.99
2.26
2.51
2.87
3.15
3.41
1.12
1.20
0.58
0.04
0.14
0.22
0.31
0.41
0.55
0.75
0.88
1.02
1.15
1.34
1.52
1.78
2.23
2.68
3.05
4.60
6.03
9.06
1.15
1.33
0.88
0.24
0.33
0.38
0.47
0.57
0.67
0.83
0.95
1.05
1.16
1.28
1.38
1.53
1.74
1.97
2.23
2.48
2.61
2.85
1.16
1.20
0.43
-0.36
-0.21
-0.13
0.00
0.12
0.31
0.55
0.73
0.88
1.03
1.18
1.35
1.55
1.89
2.19
2.52
2.87
3.15
4.96
1.03
1.08
0.66
7. Global Mean Surface Temperature Change by Reviewer, 1990-2100
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind
Schneider Wigley All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-0.58
-0.47
-0.43
-0.28
-0.19
-0.09
0.04
0.19
0.27
0.38
0.48
0.59
0.74
0.99
1.19
1.38
1.47
1.64
2.02
0.38
0.42
0.42
0.15
0.33
0.41
0.66
0.83
1.03
1.36
1.70
1.96
2.24
2.54
2.94
3.39
4.11
4.80
5.61
6.31
6.83
7.10
2.24
2.45
1.25
0.20
0.42
0.49
0.66
0.85
1.09
1.41
1.68
1.90
2.19
2.43
2.78
3.29
4.04
4.74
5.31
6.30
6.82
7.62
2.19
2.41
1.21
0.24
0.40
0.51
0.60
0.76
0.99
1.34
1.62
1.91
2.15
2.45
2.81
3.22
4.04
4.89
5.45
6.66
6.91
9.15
2.15
2.38
1.27
0.35
0.50
0.58
0.70
0.83
1.03
1.34
1.63
1.87
2.13
2.40
2.74
3.21
3.82
4.40
4.98
5.55
6.03
6.32
2.13
2.31
1.11
0.27
0.36
0.43
0.56
0.72
1.00
1.34
1.64
1.92
2.23
2.58
2.97
3.46
4.18
5.04
5.71
6.37
6.94
8.07
2.23
2.46
1.32
-0.60
0.17
0.32
0.50
0.72
0.99
1.37
1.68
1.96
2.31
2.70
3.16
3.82
4.78
5.74
6.54
7.62
8.67
11.87
2.31
2.66
1.63
0.25
0.63
0.73
0.88
1.05
1.32
1.60
1.86
2.08
2.34
2.64
2.92
3.28
3.80
4.28
4.6
5.16
5.52
5.93
2.34
2.47
0.98
-0.47
-0.24
-0.12
0.04
0.26
0.57
1.05
1.41
1.73
2.02
2.35
2.73
3.22
3.98
4.69
5.41
6.30
6.87
8.67
2.02
2.20
1.37
153
-------
Appendix 1-A
8. Global Mean Surface Temperature Change by Reviewer, 1990-2200
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind
Schneider Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-0.91
-0.62
-0.57
-0.40
-0.25
-0.10
0.11
0.25
0.41
0.58
0.74
0.94
1.23
1.65
2.02
2.28
2.57
2.78
3.37
0.58
0.68
0.69
-0.07
0.33
0.46
0.79
1.12
1.52
2.12
2.72
3.24
3.85
4.41
5.07
6.07
7.64
9.16
10.68
12.12
13.16
14.49
3.85
4.27
2.52
0.22
0.69
0.73
0.93
1.23
1.62
2.18
2.67
3.15
3.62
4.19
4.80
5.95
7.64
9.66
11.07
12.77
13.64
15.36
3.62
4.22
2.56
0.25
0.46
0.59
0.92
1.17
1.52
2.04
2.53
3.00
3.54
4.12
4.92
5.93
7.72
9.37
11.06
13.08
14.52
18.83
3.54
4.19
2.70
0.12
0.57
0.75
0.98
1.24
1.59
2.16
2.69
3.15
3.66
4.24
5.01
5.88
7.66
9.46
10.88
12.93
14.00
14.71
3.66
4.23
2.54
0.31
0.50
0.58
0.77
1.01
1.45
2.11
2.62
3.12
3.64
4.30
5.04
5.97
7.50
9.17
10.99
12.71
13.80
15.80
3.64
4.19
2.56
-0.02
0.34
0.45
0.77
1.01
1.43
2.10
2.64
3.22
3.86
4.75
5.67
6.88
9.27
11.32
13.06
15.53
16.81
21.14
3.86
4.73
3.28
0.40
0.73
0.94
1.21
1.52
1.93
2.59
3.02
3.48
3.97
4.50
5.13
5.92
7.18
8.14
8.95
9.80
11.19
12.00
3.97
4.29
2.02
-0.60
-0.31
-0.17
0.08
0.37
0.84
1.59
2.20
2.78
3.34
3.99
4.75
5.76
7.39
9.12
10.87
12.73
14.10
18.48
3.34
3.85
2.74
9. Thermal Expansion by Reviewer, 1990-2050
Cumulative Balling Bretherton Hoffert MacCracken Manabe
Rind Schneider Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-2.79
-2.28
-1.94
-1.30
-0.92
-0.39
0.21
0.68
1.08
1.53
1.96
2.42
3.03
3.84
4.54
5.27
6.11
6.65
8.23
1.53
1.64
1.69
1.63
2.02
2.54
3.27
3.94
4.96
6.17
7.22
8.47
9.63
10.78
12.03
13.97
16.55
18.77
21.05
23.83
26.11
29.39
9.63
10.23
4.67
0.77
2.18
2.62
3.31
4.11
4.86
6.12
7.47
8.50
9.59
10.81
12.14
13.87
16.78
19.42
21.97
23.88
24.98
30.65
9.59
10.36
4.78
2.00
2.28
2.50
3.18
3.74
4.68
5.94
6.78
7.77
8.84
10.05
11.40
12.68
15.26
18.30
20.26
21.84
22.71
25.48
8.84
9.55
4.29
1.49
2.57
2.94
3.71
4.28
5.29
6.78
7.84
8.93
10.10
11.23
12.56
14.30
17.05
19.02
21.23
24.58
27.55
30.73
10.10
10.71
4.65
1.48
1.77
2.06
2.78
3.57
4.78
6.19
7.37
8.45
9.54
10.62
12.04
13.71
16.77
19.04
21.41
24.03
26.21
29.91
9.54
10.20
4.78
-2.74
0.85
1.26
2.03
2.86
3.95
5.19
6.40
7.31
8.34
9.42
10.73
12.78
15.88
18.27
21.76
26.20
30.49
46.87
8.34
9.34
5.78
2.76
3.30
3.59
4.28
4.92
5.81
6.90
7.84
8.58
9.34
10.08
10.96
12.24
14.28
15.77
17.38
18.70
20.78
25.70
9.34
9.71
3.36
-2.09
-1.11
-0.54
0.19
1.05
2.50
4.71
6.18
7.41
8.61
9.78
11.14
12.82
15.56
18.19
20.58
23.19
25.49
31.71
8.61
8.97
5.22
154
-------
Cumulative Probability Distributions
10. Thermal Expansion by Reviewer, 1990-2100
Cumulative Balling Bretherton Hoffert MacCracken Manabe
Rind Schneider Wigley
11. Thermal Expansion by Reviewer, 1990-2200
Cumulative Balling Bretherton Hoffert MacCracken Manabe
Rind Schneider Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-4.58
-3.42
-2.66
-1.93
-1.25
-0.45
0.67
1.58
2.40
3.19
4.10
5.04
6.66
8.29
10.09
11.71
13.84
15.01
17.89
3.19
3.66
3.51
3.09
3.85
4.96
6.71
8.59
10.82
13.97
16.67
19.21
22.43
24.96
28.38
33.37
39.52
46.14
51.01
56.91
63.80
70.76
22.43
23.98
11.59
4.06
5.03
5.70
7.42
9.17
11.20
14.34
17.16
20.07
22.95
25.69
29.28
34.58
42.07
48.44
53.20
61.23
62.63
69.25
22.95
24.82
12.06
3.72
4.49
5.10
6.61
8.06
9.85
12.80
15.47
17.79
20.21
23.39
26.80
31.34
38.76
44.97
50.01
59.01
64.55
69.49
20.21
22.59
11.52
2.85
6.19
7.12
8.77
10.00
12.02
15.21
18.17
21.06
23.90
26.52
30.05
34.60
41.57
47.26
53.19
60.02
65.35
70.24
23.90
25.47
11.56
2.59
3.92
4.66
6.25
8.02
10.22
13.80
16.87
19.33
22.18
24.96
28.94
32.59
41 .47
47.70
53.24
61.74
65.72
75.49
22.18
24.15
12.21
-3.90
-0.24
0.59
3.36
5.27
7.78
10.90
13.92
16.30
18.83
22.41
25.99
31.04
40.62
47.74
55.41
66.63
70.06
94.04
18.83
21.89
13.71
5.23
6.33
7.38
8.83
10.54
12.36
15.12
17.39
19.02
21.37
23.15
25.85
29.33
33.91
37.53
40.65
45.33
48.43
52.35
21.37
22.23
8.31
-3.42
-1.55
-0.81
0.57
2.27
5.12
10.28
13.82
16.84
19.69
22.86
26.25
30.83
38.11
44.97
50.43
57.53
64.01
73.45
19.69
21.10
12.86
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-7.14
-6.48
-4.73
-3.29
-1.95
-0.42
1.40
2.93
4.69
6.50
8.38
10.85
13.46
18.39
22.23
26.44
31.24
35.42
42.25
6.50
7.88
7.72
3.29
5.92
7.95
12.49
16.14
20.58
28.89
35.91
42.90
49.08
57.96
66.18
80.13
101.30
121.86
136.76
164.15
175.70
209.72
49.08
56.39
33.04
8.10
11.21
11.60
14.73
17.95
22.88
30.74
39.17
46.01
54.22
62.32
72.46
88.56
110.06
135.93
151.33
170.18
189.70
202.95
54.22
61.60
35.79
2.06
6.73
8.48
11.32
14.53
18.21
26.35
32.61
39.65
46.41
56.93
69.35
82.89
105.57
122.24
139.16
173.97
181.44
235.23
46.41
55.92
35.39
4.72
10.87
13.99
17.08
20.42
24.46
32.57
40.03
47.91
55.13
62.23
73.04
85.02
107.94
125.01
145.24
162.45
178.65
201.13
55.13
61.04
33.16
2.53
6.34
8.46
12.33
15.76
20.66
29.17
36.80
43.78
49.99
59.50
69.12
81.41
104.47
130.06
148.80
179.39
195.42
219.68
49.99
58.46
35.73
-9.45
-7.56
-4.31
-0.18
5.78
11.88
20.72
26.84
33.85
40.27
50.20
61.25
78.05
106.72
129.67
151.43
179.23
194.71
217.16
40.27
50.97
39.03
6.67
10.58
12.60
15.16
18.77
22.71
29.76
35.38
40.50
45.20
50.75
57.85
67.47
80.97
93.18
103.17
120.22
125.59
132.26
45.20
49.27
22.97
-7.10
-3.27
-1.57
0.88
3.84
9.92
20.11
28.36
36.07
43.72
52.16
62.26
76.06
98.73
119.34
138.92
163.15
181.44
215.45
43.72
50.19
35.86
155
-------
Appendix 1-A
12. Greenland Temperature Change by Reviewer, 1990-2100 (°C)
Cumulative Balling Bretherton Hoffert MacCracken Manabe
Rind Schneider Wigley
13. Circumpolar Deepwater Warming by Reviewer, 1990-2100 (°C)
Cumulative Balling Bretherton Hoffert MacCracken Manabe
Rind
Schneider
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-0.78
-0.68
-0.59
-0.42
-0.28
-0.12
0.06
0.25
0.38
0.54
0.69
0.86
1.06
1.42
1.79
1.99
2.44
2.61
3.65
0.54
0.60
0.63
0.16
0.46
0.59
0.92
1.11
1.40
1.87
2.31
2.72
3.13
3.58
4.16
4.96
6.09
7.30
8.41
10.16
10.56
11.62
3.13
3.51
1.95
0.20
0.42
0.49
0.66
0.85
1.13
1.69
2.21
2.69
3.37
4.09
5.06
6.96
9.67
12.96
15.88
17.67
17.82
19.12
3.37
4.58
3.80
0.19
0.34
0.45
0.53
0.69
0.91
1.22
1.53
1.82
2.14
2.48
2.92
3.58
4.62
5.80
6.73
8.42
11.64
13.82
2.14
2.53
1.71
0.20
0.25
0.31
0.39
0.50
0.64
0.85
1.07
1.27
1.46
1.70
2.08
2.48
3.28
3.90
4.42
5.34
5.56
7.71
1.46
1.74
1.10
0.43
0.54
0.62
0.85
1.08
1.49
2.12
2.70
3.27
3.79
4.39
5.15
6.28
8.07
9.98
11.30
13.48
14.64
18.00
3.79
4.38
2.75
-0.77
0.08
0.32
0.50
0.77
1.02
1.53
1.96
2.43
2.94
3.54
4.36
5.62
7.80
10.45
13.02
16.74
22.06
23.10
2.94
3.91
3.47
0.32
0.71
0.91
1.16
1.46
1.78
2.22
2.63
2.96
3.37
3.73
4.21
4.84
5.83
6.51
7.22
7.99
8.29
9.63
3.37
3.59
1.57
-0.68
-0.34
-0.18
0.05
0.33
0.64
1.09
1.52
1.98
2.47
3.02
3.68
4.58
6.23
8.06
10.32
13.65
16.00
19.12
2.47
3.11
2.69
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-0.60
-0,33
-0.21
-0.14
-0.08
-0.03
0.02
0.05
0.08
0.13
0.18
0.24
0.33
0.50
0.69
0.87
1.40
1.56
1.98
0.13
0.19
0.28
0.05
0.07
0.10
0.12
0.18
0.25
0.38
0.49
0.63
0.79
0.98
1.24
1.63
2.39
3.08
3.98
5.30
5.99
6.91
0.79
1.10
1.01
0.06
0.15
0.20
0.26
0.35
0.44
0.59
0.71
0.84
0.99
1.15
1.39
1.68
2.25
2.81
3.40
4.23
4.87
5.45
0.99
1.21
0.83
0.06
0.08
0.11
0.16
0.19
0.26
0.38
0.52
0.65
0.78
1.00
1.26
1.59
2.29
3.26
3.96
5.30
6.49
7.16
0.78
1.12
1.04
0.03
0.10
0.14
0.17
0.23
0.29
0.39
0.48
0.57
0.67
0.77
0.90
1.08
1.39
1.69
1.92
2.40
2.81
3.13
0.67
0.77
0.47
-0.71
-0.11
-0.03
0.10
0.25
0.47
0.83
1.08
1.29
1.52
1.79
2.14
2.58
3.36
3.95
4.33
5.09
5.74
7.30
1.52
1.75
1.14
0.17
0.27
0.31
0.46
0.57
0.73
1.01
1.22
1.46
1.71
2.00
2.31
2.69
3.44
4.19
5.12
6.32
7.38
8.10
1.71
1.95
1.20
-0.35
-0.12
-0.06
0.00
0.06
0.16
0.33
0.50
0.68
0.86
1.09
1.39
1.79
2.52
3.26
3.97
4.99
5.74
7.38
0.86
1.16
1.06
156
-------
Cumulative Probability Distributions
14. Greenland Precipitation by Reviewer, 2100 (cm/yr sea level equivalent)
Cumulative Alley Kuhn MacCracken Rind Schneider
Zwally
15. Greenland Contribution to Sea Level, 1990-2050 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe
Rind Schneider Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
0.1301
0.1322
0.1325
0.1331
0.1334
0.1340
0.1351
0.1364
0.1377
0.1397
0.1422
0.1453
0.1511
0.1626
0.1777
0.2003
0.2607
0.3153
1.0348
0.1397
0.1478
0.0442
0.1279
0.1292
0.1312
0.1328
0.1357
0.1406
0.1463
0.1521
0.1586
0.1654
0.1735
0.1843
0.1975
0.2314
0.2800
0.3318
0.4252
0.5096
0.6711
0.1654
0.1807
0.0575
0.1274
0.1303
0.1316
0.1339
0.1373
0.1405
0.1460
0.1519
0.1567
0.1629
0.1703
0.1791
0.1925
0.2236
0.2647
0.3400
0.4325
0.4636
0.6425
0.1629
0.1777
0.0557
0.1147
0.1304
0.1314
0.1330
0.1359
0.1398
0.1465
0.1522
0.1568
0.1627
0.1692
0.1788
0.1951
0.2241
0.2570
0.3126
0.4077
0.5046
0.5544
0.1627
0.1765
0.0498
0.1289
0.1306
0.1314
0.1330
0.1361
0.1404
0.1467
0.1518
0.1569
0.1630
0.1696
0.1798
0.1934
0.2231
0.2631
0.3190
0.4157
0.4786
0.6001
0.1630
0.1773
0.0523
0.1231
0.1312
0.1318
0.1329
0.1356
0.1389
0.1443
0.1496
0.1544
0.1605
0.1683
0.1783
0.1950
0.2314
0.2811
0.3437
0.5210
0.6749
1.2871
0.1605
0.1809
0.0803
0.1278
0.1305
0.1318
0.1330
0.1343
0.1366
0.1417
0.1466
0.1522
0.1583
0.1656
0.1748
0.1894
0.2192
0.2590
0.3196
0.4217
0.5208
0.8940
0.1583
0.1750
0.0589
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-0.64
-0.60
-0.48
-0.38
-0.29
-0.20
-0.08
-0.03
0.03
0.09
0.16
0.23
0.32
0.48
0.65
0.85
1.06
1.19
1.64
0.09
0.13
0.30
-0.70
-0.06
-0.01
0.08
0.14
0.22
0.41
0.56
0.73
0.93
1.15
1.38
1.78
2.45
3.20
3.92
4.75
5.66
6.43
0.93
1.18
1.02
-0.63
-0.13
-0.08
0.00
0.08
0.17
0.30
0.42
0.54
0.66
0.81
1.04
1.36
1.88
2.45
3.22
4.10
5.31
12.19
0.66
0.91
0.98
-0.69
-0.19
-0.12
-0.05
0.00
0.08
0.20
0.31
0.42
0.55
0.73
0.94
1.22
1.75
2.40
3.12
4.39
4.86
8.34
0.55
0.80
0.89
-0.76
-0.41
-0.31
-0.19
-0.12
-0.06
0.01
0.10
0.17
0.25
0.35
0.47
0.64
0.96
1.34
1.72
2.13
2.63
5.45
0.25
0.38
0.55
-1.64
-0.52
-0.31
-0.01
0.11
0.27
0.46
0.72
0.94
1.15
1.43
1.82
2.22
3.19
4.08
4.99
6.49
7.51
12.46
1.15
1.50
1.44
-2.69
-0.36
-0.21
-0.06
0.00
0.11
0.26
0.43
0.63
0.83
1.08
1.41
1.94
2.86
3.94
5.56
9.75
12.87
28.51
0.83
1.39
2.99
-1.08
-0.39
-0.03
0.42
0.72
1.09
1.59
1.97
2.32
2.60
2.93
3.30
3.77
4.48
5.10
5.78
6.42
6.84
8.18
2.60
2.72
1.35
-0.87
-0.42
-0.31
-0.17
-0.07
0.02
0.18
0.31
0.47
0.68
0.95
1.32
1.88
2.83
3.74
4.52
5.73
6.69
12.46
0.68
1.13
1.60
157
-------
Appendix 1-A
16. Greenland Contribution to Sea Level by Climate Reviewer, 1990-2100 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider
Wigley
17. Greenland Contribution to Sea Level by Climate Reviewer, 1990-2200 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider
Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-1.40
-1.31
-1.12
-0.81
-0.56
-0.33
-0.09
0.08
0.25
0.42
0.62
0.88
1.18
1.68
2.34
2.95
4.07
4.51
6.14
0.42
0.60
0.95
-2.77
-0.16
0.08
0.42
0.67
1.06
1.72
2.31
3.05
3.77
4.53
5.68
7.46
10.31
13.75
18.46
23.41
28.34
40.72
3.77
5.03
4.77
-3.29
-0.75
-0.06
0.22
0.49
0.85
1.43
2.03
2.58
3.37
4.15
5.43
7.55
12.24
18.47
26.56
36.28
51.08
75.57
3.37
5.64
8.35
-2.39
-0.67
-0.41
-0.11
0.12
0.42
0.87
1.27
1.67
2.20
2.86
3.74
4.97
7.28
9.92
13.37
18.80
22.23
47.19
2.20
3.33
4.00
-2.76
-1.70
-1.10
-0.62
-0.36
-0.13
0.17
0.47
0.75
1.12
1.47
1.97
2.63
4.06
5.62
7.13
9.20
12.59
21.28
1.12
1.64
2.31
-4.29
-2.34
-1.24
-0.03
0.58
1.12
1.92
2.85
3.70
4.69
5.93
7.50
9.60
14.52
19.28
25.62
36.35
43.38
58.74
4.69
6.66
7.25
-3.98
-1.63
-1.01
-0.15
0.11
0.52
1.16
1.81
2.56
3.42
4.36
5.69
8.21
13.34
18.99
27.16
43.45
54.87
59.99
3.42
5.83
9.74
0.57
1.49
1.74
2.53
3.31
4.21
5.18
5.98
6.76
7.52
8.24
9.14
10.22
11.90
13.34
14.78
16.66
18.13
19.96
7.52
7.80
3.10
-4.19
-1.26
-0.81
-0.37
-0.10
0.22
0.77
1.34
2.00
2.87
3.99
5.37
7.30
10.28
13.75
18.56
27.16
36.11
64.94
2.87
4.57
6.28
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-3.87
-2.82
-2.65
-1.82
-1.20
-0.61
0.03
0.48
1.02
1.66
2.37
3.20
4.65
6.71
9.14
12.62
17.84
21.82
25.85
1.66
2.58
3.74
-11.23
-1.09
0.26
1.42
2.37
4.18
6.83
9.24
11.80
15.86
19.91
25.98
35.38
55.86
73.54
107.39
124.31
138.77
148.00
15.86
23.99
25.25
-9.20
-5.48
-2.36
0.77
2.11
3.86
7.03
10.73
14.86
20.63
27.42
41.74
61.10
100.23
134.93
180.65
223.86
239.40
247.76
20.63
38.57
47.28
-10.01
-3.38
-1.91
-0.34
0.46
1.63
3.22
4.73
6.51
8.64
11.44
15.14
21.22
36.38
54.03
69.02
93.06
111.11
194.39
8.64
15.01
19.63
-12.21
-8.62
-6.93
-2.51
-1.42
-0.43
0.71
1.91
3.07
4.57
6.18
8.30
11.96
19.83
28.70
38.18
55.32
71.50
94.99
4.57
7.74
11.49
-22.07
-10.19
-4.63
-0.25
1.72
4.03
7.26
10.88
15.29
19.78
25.99
33.77
46.38
76.50
105.79
135.58
192.18
195.45
205.66
19.78
31.44
35.50
-12.71
-9.80
-7.20
-1.23
0.46
1.87
4.31
6.88
10.17
14.45
19.90
26.24
38.80
68.68
105.33
135.70
184.60
198.79
240.72
14.45
26.79
35.98
4.80
6.43
7.49
8.91
11.19
13.90
16.84
18.92
21.74
24.25
26.77
30.07
33.43
38.96
44.49
48.02
53.22
59.61
64.74
24.25
25.47
10.14
-11.44
-5.81
-2.69
-1.08
-0.16
0.92
2.90
5.32
8.24
12.28
17.21
23.01
31.21
50.04
76.95
109.91
150.94
190.22
236.97
12.28
21.45
29.76
158
-------
Cumulative Probability Distributions
18. Ross Ice Shelf Melt Rate in the Year 2100 (m/yr)
Cumulative Thomas
All Other Reviewers
All Reviewers
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
0.020
0.226
0.236
0.247
0.259
0.281
0.327
0.382
0.447
0.549
0.724
0.986
1.690
3.138
5.954
9.769
16.629
22.608
36.955
0.549
1.541
3.331
0.021
0.137
0.178
0.215
0.230
0.245
0.259
0.280
0.311
0.352
0.415
0.515
0.683
1.071
1.586
2.360
3.684
5.101
9.568
0.352
0.581
0.780
0.020
0.139
0.186
0.219
0.233
0.247
0.263
0.289
0.323
0.372
0.443
0.557
0.764
1.252
2.068
3.208
6.203
9.464
19.918
0.372
0.718
1.489
19. Antarctic Contribution to Sea Level by Climate Reviewer, 1990-2050 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider
Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-58.58
-40.54
-35.09
-20.03
-11.04
-7.45
-4.02
-2.51
-1.64
-1.04
-0.42
0.42
2.30
5.18
7.12
8.77
10.68
11.76
21.12
-1.04
-1.64
7.12
-49.04
-34.02
-25.99
-17.82
-10.87
-6.97
-3.98
-2.50
-1.63
-0.88
-0.30
0.72
2.58
5.21
7.36
9.28
11.70
13.70
27.80
-0.88
-1.34
6.66
-47.74
-27.60
-20.38
-15.93
-11.55
-7.07
-3.82
-2.55
-1.64
-0.91
-0.35
0.62
2.64
5.39
7.63
9.12
11.16
14.77
22.48
-0.91
-1.19
6.14
-73.70
-30.89
-23.98
-16.34
-11.50
-6.92
-3.84
-2.33
-1.47
-0.85
-0.27
0.72
3.00
5.43
7.05
8.44
10.23
10.68
19.95
-0.85
-1.25
6.56
-42.61
-32.63
-27.35
-19.03
-13.76
-8.20
-4.16
-2.73
-1.79
-1.05
-0.55
0.23
2.27
4.83
6.96
8.63
11.61
13.51
16.61
-1.05
-1.75
6.63
-52.39
-44.61
-26.83
-19.90
-13.00
-7.99
-4.35
-2.89
-1.84
-1.04
-0.48
0.48
2.40
5.26
7.26
9.44
11.77
13.55
14.85
-1.04
-1.77
7.18
-62.04
-31.98
-26.67
-17.53
-11.63
-7.25
-4.04
-2.56
-1.55
-0.72
-0.14
1.12
3.15
5.63
7.97
9.66
11.68
16.63
25.77
-0.72
-1.19
7.04
-6.84
-5.66
-5.25
-4.31
-3.83
-3.03
-2.24
-1.64
-1.28
-0.95
-0.69
-0.46
-0.18
0.18
0.52
0.86
1.37
1.58
2.28
-0.95
-1.21
1.33
-52.39
-34.02
-25.70
-16.68
-10.90
-6.66
-3.67
-2.37
-1.55
-0.94
-0.44
0.22
1.93
4.84
6.96
8.77
10.73
13.16
21.23
-0.94
-1.42
6.35
159
-------
Appendix 1-A
20. Antarctic Contribution to Sea Level by Climate Reviewer, 1990-2100 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider
Wigley
21. Antarctic Contribution to Sea Level by Climate Reviewer, 1990-2200 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider
Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-28.62
-27.03
-24.00
-20.29
-16.60
-11.18
-6.37
-4.15
-2.65
-1.54
-0.35
1.93
5.68
10.72
14.93
18.96
22.66
25.76
33.49
-1.54
-0.87
9.02
-49.45
-45.02
-37.29
-26.50
-18.23
-11.53
-6.72
-4.07
-2.34
-0.77
0.56
3.47
6.88
12.08
16.87
21.98
32.25
48.72
61.00
-0.77
-0.37
11.63
-55.89
-41.53
-36.08
-29.02
-21.87
-13.23
-7.10
-4.56
-2.46
-0.99
0.21
3.22
6.67
11.87
16.29
20.83
31.45
36.20
53.84
-0.99
-1.03
11.70
-55.01
-43.99
-39.17
-29.44
-19.89
-12.40
-6.68
-3.68
-2.06
-0.93
0.54
3.51
7.69
13.06
17.49
21.47
29.80
36.70
70.43
-0.93
-0.39
12.00
-56.02
-48.08
-41.17
-32.53
-25.11
-15.02
-7.61
-4.69
-2.82
-1.58
-0.55
1.72
5.81
10.62
15.62
19.85
28.65
34.66
40.58
-1.58
-2.02
11.91
-55.02
-45.81
-42.18
-32.25
-21.78
-15.07
-8.22
-4.92
-2.78
-1.43
-0.12
3.10
6.80
12.50
18.33
22.73
33.15
36.21
46.49
-1.43
-1.37
12.42
-50.78
-47.90
-42.54
-28.15
-20.23
-11.92
-6.42
-3.55
-1.78
-0.35
1.95
5.48
9.32
15.77
22.28
27.75
37.19
43.46
53.36
-0.35
0.77
12.97
-15.92
-14.21
-13.66
-11.56
-10.07
-8.38
-6.22
-4.77
-3.76
-2.97
-2.22
-1.45
-0.67
0.47
1.51
2.43
3.80
4.22
6.13
-2.97
-3.45
3.51
-52.18
-43.84
-36.80
-26.83
-18.87
-11.65
-6.78
-4.32
-2.70
-1.45
-0.33
1.89
5.81
11.36
16.47
21.33
30.11
36.58
51.89
-1.45
-1.09
11.09
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-129.09
-119.02
-107.26
-59.75
-37.54
-24.90
-12.60
-7.35
-4.16
-1.93
1.03
7.78
15.43
25.56
35.67
45.71
69.13
79.17
100.44
-1.93
-1.03
25.98
-148.07
-113.68
-82.27
-58.15
-35.69
-21.55
-10.66
-5.34
-1.58
1.98
9.05
16.36
25.60
40.72
67.38
112.89
206.73
240.09
293.21
1.98
9.10
41.03
-135.00
-116.72
-96.57
-65.38
-48.10
-27.54
-11.73
-5.94
-1.57
2.99
10.73
19.16
28.90
51.96
81.63
120.62
216.99
289.64
326.23
2.99
10.87
47.37
-135.44
-108.46
-84.54
-51.00
-35.63
-21.85
-10.40
-4.26
-1.51
2.29
9.34
16.86
26.08
41.68
64.76
108.60
189.81
286.58
333.38
2.29
9.86
42.91
-126.19
-115.00
-93.78
-63.96
-46.96
-28.80
-12.92
-6.63
-2.98
-0.60
3.97
12.08
20.70
34.66
50.71
75.82
114.60
221.73
274.47
-0.60
3.34
35.80
-143.55
-124.69
-100.68
-63.54
-41.88
-25.35
-10.25
-3.24
1.01
7.29
15.80
24.94
38.23
70.09
121.80
188.76
320.09
424.31
536.76
7.29
20.17
64.16
-131.31
-97.63
-86.34
-55.38
-32.42
-18.18
-7.95
-2.39
1.63
8.88
18.18
27.04
44.26
77.63
124.71
203.09
356.47
486.92
635.87
8.88
24.74
69.09
-58.59
-52.31
-45.12
-38.63
-33.21
-27.87
-20.12
-15.52
-12.22
-9.57
-7.18
-4.80
-2.44
1.50
4.73
8.01
11.56
12.47
18.07
-9.57
-11.36
11.67
-135.63
-111.93
-89.93
-56.86
-37.93
-24.63
-13.02
-7.25
-3.26
-0.27
5.43
13.78
24.07
42.88
71.56
114.54
206.38
277.76
455.40
-0.27
8.21
46.98
160
-------
Cumulative Probability Distributions
22. Antarctic Contribution to Sea Level by Glaciology Reviewer, 1990-2100 (cm)
Cumulative Alley Anonymous Bentley Bindschadler Thomas Van der Veen
23. Antarctic Contribution to Sea Level by Glaciology Reviewer, 1990-2200 (cm)
Cumulative Alley Anonymous Bentley Bindschadler Thomas Van der Veen
Zwally
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-58.58
-52.15
-42.06
-32.89
-22.53
-14.96
-8.20
-5.30
-3.20
-1.64
-0.38
2.31
6.25
11.03
16.21
20.51
30.10
36.52
61.02
-1.64
-1.95
12.27
-55.01
-48.94
-43.55
-29.53
-21.73
-13.12
-7.26
-4.31
-2.76
-1.51
-0.38
1.26
5.78
10.27
15.67
21.72
30.11
36.20
53.37
-1.51
-1.64
11.63
-56.93
-51.45
-49.20
-37.41
-25.77
-13.46
-7.81
-5.19
-3.12
-1.74
-0.56
1.45
5.78
11.56
15.75
21.54
31.12
34.66
48.75
-1.74
-2.19
12.72
-59.83
-47.90
-44.57
-34.02
-20.81
-12.87
-6.81
-3.87
-1.96
-0.42
1.79
4.97
9.04
15.06
19.86
26.92
40.58
50.66
78.63
-0.42
0.31
13.77
-55.89
-46.02
-38.88
-27.72
-18.47
-10.64
-4.74
-2.37
-0.98
0.26
2.98
4.96
8.63
14.86
19.30
26.83
40.50
53.03
71.04
0.26
1.33
12.70
-56.72
-52.41
-49.29
-30.17
-20.65
-13.62
-7.18
-4.31
-2.57
-1.29
-0.20
1.96
6.69
11.51
16.12
20.00
24.02
32.44
53.84
-1.29
-1.60
12.04
-59.43
-48.13
-43.84
-32.18
-21.39
-13.44
-6.97
-4.03
-2.34
-1.06
0.22
3.23
6.69
12.17
17.18
22.41
29.41
39.76
54.23
-1.06
-1.04
12.50
Zwally
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-206.45
-137.93
-113.68
-65.38
-44.56
-29.77
-14.24
-7.76
-3.21
0.51
6.38
13.73
23.98
38.33
59.54
86.59
128.90
199.56
256.96
0.51
4.02
39.25
-121.36
-93.33
-80.94
-54.19
-38.52
-24.65
-11.27
-5.49
-2.05
0.90
6.32
13.01
20.60
37.30
57.58
84.63
149.06
181.81
210.65
0.90
5.69
34.20
-179.79
-143.84
-111.68
-73.96
-48.62
-26.56
-14.08
-8.23
-4.21
-1.33
2.92
10.64
20.85
36.40
61.11
91.96
131.16
164.38
239.23
-1.33
2.68
38.27
-184.04
-115.69
-83.68
-56.93
-38.61
-23.30
-9.56
-3.05
1.47
8.75
15.85
23.03
35.88
58.21
83.80
117.67
167.58
207.52
274.81
8.75
14.21
42.25
-168.28
-94.33
-76.97
-44.05
-24.81
-12.97
-4.23
-0.37
4.81
12.32
19.27
28.17
45.08
104.12
227.41
339.93
589.34
675.42
693.72
12.32
38.36
100.36
-143.55
-123.31
-99.12
-56.47
-39.19
-25.41
-12.48
-6.45
-3.07
-0.76
3.95
12.61
21.88
36.86
55.49
78.14
120.62
152.53
234.62
-0.76
4.09
34.04
-135.44
-117.30
-91.88
-62.96
-38.95
-22.93
-9.99
-4.93
-1.80
2.08
8.81
17.35
27.28
45.47
69.60
98.01
165.16
219.59
286.58
2.08
9.16
40.84
161
-------
Appendix 1-A
24. Small Glacier Contribution to Sea Level by Climate Reviewer, 1990-2050 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider
Wigley
25. Small Glacier Contribution to Sea Level by Climate Reviewer, 1990-2100 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.50
99.90
Median
Mean
StdDev
-5.56
-4.17
-3.31
-2.50
-1.40
-0.79
-0.26
0.11
0.53
0.94
1.49
2.01
2.68
3.81
4.85
5.70
7.35
9.26
0.94
1.22
1.97
-6.08
-4.18
-2.49
-0.73
0.23
1.09
2.34
3.35
4.28
5.20
6.25
7.56
9.26
11.97
14.54
16.36
20.44
22.93
5.20
5.93
4.37
-9.13
-3.88
-2.05
-0.83
0.18
1.10
2.44
3.64
4.47
5.38
6.45
7.94
9.69
12.21
13.93
15.73
19.37
22.84
5.38
6.09
4.38
-6.98
-3.12
-2.40
-0.94
0.21
1.19
2.37
3.26
4.30
5.29
6.45
7.78
9.61
12.29
14.64
16.38
20.83
26.26
5.29
6.07
4.53
-4.54
-3.26
-2.26
-0.78
0.20
1.01
2.18
3.23
4.07
4.99
6.15
7.38
8.83
11.11
13.10
14.71
17.50
19.05
4.99
5.61
4.00
-6.32
-3.34
-1.84
-0.78
0.27
1.07
2.24
3.36
4.41
5.45
6.64
7.88
9.37
11.86
13.68
15.58
19.56
21.10
5.45
5.99
4.28
-10.44
-4.07
-2.26
-0.94
0.23
0.99
2.40
3.57
4.61
5.67
6.77
8.38
10.17
13.17
15.69
18.39
26.92
32.49
5.67
6.51
5.11
-9.88
-2.99
-2.09
-0.90
0.19
1.18
2.57
3.66
4.76
5.84
6.72
7.95
9.43
11.77
13.53
16.84
18.31
21.42
5.84
6.12
4.16
-6.58
-3.72
-2.55
-1.23
-0.36
0.41
1.65
2.69
3.73
4.76
5.92
7.20
8.97
11.52
13.76
17.96
20.16
26.26
4.76
5.44
4.49
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-5.72
-4.90
-3.78
-2.10
-1.48
-0.68
0.01
0.48
1.11
1.73
2.48
3.39
4.36
6.23
7.53
9.00
10.61
11.26
13.11
1.73
2.23
2.84
-8.54
-7.34
-4.22
-1.53
0.59
2.34
4.68
6.56
8.13
9.82
11.47
13.16
15.38
19.22
21.72
23.85
26.81
28.55
31.27
9.82
10.19
6.50
-14.43
-6.46
-3.60
-1.44
0.69
2.50
4.83
6.68
8.16
9.47
11.31
13.21
15.14
18.43
20.83
23.17
25.94
27.77
31.37
9.47
10.11
6.36
-12.30
-5.64
-4.31
-1.70
0.53
2.40
4.69
6.28
7.94
9.47
11.27
12.76
15.41
18.92
21.70
24.40
27.28
28.91
33.20
9.47
10.07
6.57
-8.65
-5.36
-4.62
-1.54
0.60
2.44
4.60
6.11
7.95
9.42
10.93
12.71
14.86
17.78
20.50
22.37
24.77
27.23
29.87
9.42
9.72
6.10
-12.72
-5.73
-3.90
-1.04
0.66
2.37
4.85
6.62
8.09
9.70
11.32
12.98
15.70
19.04
21.95
24.14
26.17
27.53
28.90
9.70
10.21
6.50
-11.25
-6.76
-3.89
-1.81
0.63
2.51
4.64
6.67
8.30
10.14
12.06
14.10
17.06
20.44
23.75
26.13
29.54
32.34
33.61
10.14
10.82
7.22
-10.91
-5.70
-4.10
-1.73
0.70
2.92
5.40
6.94
8.73
10.28
11.74
13.63
15.66
18.49
20.90
22.59
24.87
27.04
27.83
10.28
10.45
6.17
-10.92
-5.72
-3.94
-1.76
-0.32
1.03
3.34
5.25
6.92
8.73
10.55
12.43
14.82
18.31
21.09
23.57
26.31
27.83
32.18
8.73
9.23
6.71
162
-------
Cumulative Probability Distributions
26. Small Glacier Contribution to Sea Level by Climate Reviewer, 1990-2200 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
27. Greenhouse Contribution to Sea Level by Climate Reviewer, 1990-2050 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-7.17
-4.71
-3.90
-2.47
-1.61
-0.62
0.12
0.86
1.70
2.66
3.78
5.08
6.80
9.51
11.83
14.15
15.72
17.17
19.87
2.66
3.59
4.21
-14.08
-11.28
-7.50
-2.39
0.93
3.95
7.50
10.20
12.46
14.90
17.60
19.82
22.65
26.32
29.08
31.08
33.94
35.45
38.28
14.90
14.91
8.81
-23.18
-10.29
-6.40
-2.52
1.22
3.99
7.70
10.31
12.47
14.61
16.70
19.49
22.09
26.19
28.80
31.79
33.99
35.66
38.68
14.61
14.74
8.73
-21.49
-8.08
-7.01
-3.25
0.92
3.90
7.32
9.89
11.78
14.03
16.35
18.87
21.72
26.93
29.82
32.89
35.23
37.96
39.20
14.03
14.56
8.95
-15.32
-9.92
-8.65
-2.89
1.06
4.02
7.46
9.61
12.50
14.66
16.90
18.96
22.22
25.52
29.16
32.03
34.24
35.77
38.41
14.66
14.61
8.70
-19.14
-10.50
-6.68
-2.03
1.09
3.77
7.20
10.14
12.29
14.63
16.67
19.09
22.04
26.16
29.76
31.87
34.14
34.91
36.31
14.63
14.68
8.72
-18.06
-11.19
-7.34
-2.43
1.14
3.68
7.26
10.13
12.70
15.21
17.53
20.64
24.09
28.41
31.80
33.58
35.79
37.90
39.05
15.21
15.50
9.62
-20.17
-9.26
-7.29
-3.16
1.40
4.69
8.28
10.79
13.00
15.37
17.63
20.33
22.87
26.05
28.55
30.01
32.49
34.53
37.85
15.37
15.26
8.52
-19.14
-9.28
-6.53
-2.54
-0.26
1.63
5.15
8.11
10.73
13.25
15.75
18.47
21.68
25.82
28.98
31.75
34.17
35.63
38.61
13.25
13.48
9.23
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-7.40
-5.89
-4.39
-3.19
-2.14
-0.95
0.43
1.40
2.24
3.02
4.06
5.13
6.57
8.71
10.16
11.96
14.05
16.78
21.60
3.02
3.54
3.90
2.37
2.90
3.75
5.12
6.26
8.09
10.50
12.54
14.63
16.43
18.84
21.48
24.92
30.62
34.82
38.59
43.47
46.49
49.49
16.43
18.08
8.79
1.01
2.53
3.41
4.94
6.16
8.09
10.56
12.28
14.46
16.84
18.98
21.28
24.34
29.85
34.53
37.88
42.55
45.99
59.04
16.84
17.90
8.69
1.92
3.21
3.82
5.31
6.51
7.79
10.06
11.85
13.64
15.36
17.52
20.21
23.81
27.98
33.39
38.08
41.75
44.81
55.46
15.36
17.06
8.38
1.83
3.20
3.80
4.93
6.15
7.85
10.40
12.16
13.90
16.02
18.31
20.78
23.53
27.97
32.57
35.57
41.80
45.81
56.52
16.02
17.25
8.19
1.28
2.52
3.12
4.62
6.25
7.95
10.48
12.80
14.99
17.08
19.38
22.07
24.70
30.06
34.29
38.64
43.16
45.83
53.18
17.08
18.22
8.78
0.55
2.05
3.48
4.36
5.53
7.22
10.14
12.09
13.84
16.06
18.48
21.38
25.10
30.70
35.94
41.52
52.54
57.99
80.20
16.06
18.01
10.01
2.53
3.39
4.24
6.18
7.57
9.05
11.34
13.11
14.75
16.29
18.22
20.29
22.96
26.79
30.11
34.02
36.31
37.97
48.37
16.29
17.34
7.06
-5.20
-2.52
-1.19
0.43
2.09
4.61
8.11
10.60
12.74
14.94
17.19
19.90
23.24
28.17
32.80
36.94
42.26
46.43
60.75
14.94
15.93
9.41
163
-------
Appendix 1-A
28. Greenhouse Contribution to Sea Level by Climate Reviewer, 1990-2100 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
29. Greenhouse Contribution to Sea Level by Climate Reviewer, 1990-2200 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider
Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-8.60
-6.96
-6.34
-4.35
-2.40
-0.57
1.78
3.49
5.10
6.96
8.94
11.05
14.40
18.85
22.72
26.85
32.15
38.07
60.01
6.96
8.34
8.34
4.83
6.82
8.69
12.02
15.09
18.44
24.47
29.66
34.03
38.57
43.72
51.20
58.13
69.84
82.99
95.05
107.06
116.66
131.51
38.57
42.27
21.05
5.98
7.46
8.95
11.74
14.73
18.98
24.37
29.27
33.76
39.06
43.96
49.65
56.93
71.81
84.05
95.52
113.19
131.19
186.09
39.06
42.59
22.48
3.77
6.50
8.74
12.00
14.33
17.41
22.66
27.00
31.11
34.86
39.65
45.78
53.45
64.86
75.94
86.18
104.23
112.42
130.81
34.86
38.80
19.67
4.13
8.75
9.80
12.61
14.74
18.16
23.16
27.61
31.81
36.07
40.70
45.83
52.44
62.65
71.21
81.32
92.03
104.83
122.68
36.07
38.88
18.14
4.17
5.71
6.99
11.35
14.19
18.25
24.90
29.90
34.62
39.81
45.13
51.32
59.90
72.10
85.10
98.16
1 10.62
122.28
171.37
39.81
43.42
22.71
0.99
4.03
7.00
9.27
12.61
17.08
22.57
27.37
32.13
37.70
43.68
50.54
60.86
76.31
87.52
101.58
118.24
135.23
157.18
37.70
42.59
24.34
6.25
9.69
11.32
14.86
17.36
20.72
24.99
28.67
31.82
35.47
39.31
43.05
48.64
55.87
61.07
68.23
75.92
78.92
87.63
35.47
37.04
13.85
-6.43
-3.06
-1.24
1.71
4.86
10.35
18.55
24.14
29.23
34.08
39.34
45.22
53.08
65.08
77.23
88.25
104.01
114.58
151.64
34.08
36.74
22.34
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-12.63
-11.35
-9.45
-6.45
-3.21
0.28
3.85
7.68
11.58
15.83
20.53
26.06
33.30
47.39
59.08
73.09
92.85
105.82
125.99
15.83
20.28
20.42
4.25
12.43
13.69
23.52
30.01
39.57
53.13
66.69
81.10
93.99
111.47
130.93
155.00
203.22
256.27
311.29
379.53
467.31
526.21
93.99
111.89
74.73
-6.46
9.68
15.62
22.32
29.67
39.76
57.49
71.88
87.87
105.27
125.52
150.58
189.60
258.16
331.03
395.84
502.49
568.02
608.11
105.27
131.66
97.50
1.76
13.23
15.28
21.57
28.85
36.01
48.62
61.10
71.86
84.24
97.44
118.64
144.03
187.07
236.12
277.53
354.39
484.99
549.11
84.24
102.04
70.96
-3.35
15.33
18.79
23.54
30.54
38.70
50.11
60.27
71.47
83.94
95.02
110.96
129.28
163.65
199.33
235.99
302.71
337.48
434.75
83.94
94.74
57.07
7.93
10.93
14.28
22.53
32.08
40.64
60.57
75.87
91.34
107.76
126.67
148.70
185.87
251.31
321.23
393.93
548.35
601.56
732.86
107.76
132.05
98.27
-0.13
6.12
10.96
18.45
26.10
34.59
49.92
62.52
76.85
97.19
1 15.04
144.17
182.17
250.99
304.86
383.57
540.44
587.61
724.72
97.19
124.05
100.67
10.32
13.48
20.81
26.16
32.58
39.09
48.50
57.49
65.34
74.59
82.64
93.37
107.09
123.13
142.48
160.06
180.43
184.77
203.49
74.59
78.63
34.24
-10.23
-4.77
-0.82
3.48
10.35
22.06
39.30
53.19
66.61
80.60
96.28
115.79
142.94
195.70
254.16
315.97
409.59
497.77
641.96
80.60
99.42
82.41
164
-------
Cumulative Probability Distributions
30. Annual Greenhouse Contribution to Sea Level in 2100, all Reviewers (mm/year)
Cumulative Rate (mm/yr)
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-1.21
-0.57
-0.36
0.03
0.47
1.05
1.91
2.68
3.44
4.21
5.04
6.08
7.49
9.89
12.37
15.41
19.34
23.05
33.63
4.21
5.04
4.19
31. Historic Greenhouse Contribution to Sea Level by Climate Reviewer, 1880-1990 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-6.80
-5.49
-4.86
-3.44
-2.46
-1.33
-0.10
0.84
1.68
2.37
3.10
3.93
4.96
6.13
7.16
8.23
9.53
11.13
14.33
2.37
2.42
3.03
-11.42
-9.20
-6.40
-3.91
-2.13
-0.32
2.11
3.68
4.95
6.35
7.75
9.30
11.35
15.03
18.47
21.64
25.01
27.48
31.61
6.35
6.96
6.28
-15.09
-10.90
-7.59
-5.03
-2.50
-0.60
1.74
3.39
4.82
6.15
7.86
9.78
11.89
15.85
18.79
20.79
25.47
27.56
34.17
6.15
6.94
6.64
-12.12
-7.81
-6.23
-4.09
-1.76
0.15
2.22
3.77
5.03
6.25
7.40
8.84
11.09
13.81
17.15
20.52
24.34
27.04
38.16
6.25
6.78
6.02
-11.37
-8.23
-6.56
-4.02
-2.67
-0.33
1.81
3.66
5.44
6.65
8.36
10.21
12.49
15.88
19.67
22.42
28.55
31.07
36.02
6.65
7.41
6.84
-9.42
-7.73
-6.45
-4.42
-2.65
-0.28
1.95
3.61
4.79
6.30
7.75
9.49
11.61
15.84
19.91
23.19
27.26
30.92
31.22
6.30
7.10
6.68
-12.49
-9.23
-6.75
-4.14
-1.74
0.22
2.08
3.25
4.45
5.60
6.93
8.65
10.43
13.89
16.43
19.64
25.52
32.77
38.01
5.60
6.43
6.09
-10.80
-7.99
-6.07
-3.64
-1.54
0.23
2.23
3.71
5.16
6.41
7.72
9.14
11.07
13.62
16.06
18.12
22.10
24.80
25.65
6.41
6.70
5.52
-12.09
-8.19
-6.42
-4.05
-2.29
-0.41
1.58
3.02
4.28
5.59
6.94
8.61
10.78
14.30
17.59
20.59
24.69
28.29
35.46
5.59
6.34
6.18
165
-------
Appendix 1-A
32. Normalized Greenhouse Contribution to Sea Level by Climate Reviewer, 1990-2025 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
33. Normalized Greenhouse Contribution to Sea Level by Climate Reviewer, 1990-2050 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-31.79
-24.44
-20.19
-10.68
-6.36
-4.53
-2.48
-1.48
-0.78
0.00
0.65
1.51
2.52
4.00
5.34
6.46
8.18
9.22
10.55
0.00
-0.40
4.49
-20.71
-13.39
-9.75
-5.45
-2.31
0.05
1.96
3.42
4.66
5.58
6.84
8.33
9.83
12.73
14.93
17.32
19.87
20.47
24.68
5.58
5.88
5.51
-12.80
-7.86
-6.74
-3.82
-1.94
0.08
1.99
3.46
4.57
5.72
6.94
8.46
10.25
12.14
15.03
17.46
20.22
21.25
27.12
5.72
6.11
5.35
-13.63
-11.91
-8.95
-3.96
-1.64
0.03
1.81
3.05
4.21
5.41
6.53
8.06
9.79
12.32
14.34
17.51
19.66
21.14
26.62
5.41
5.75
5.31
-16.31
-12.37
-10.43
-5.91
-2.96
-0.67
1.57
2.91
4.20
5.36
6.46
7.60
9.25
11.91
14.00
15.90
18.64
19.89
21.96
5.36
5.35
5.27
-25.32
-17.83
-11.02
-6.72
-2.23
0.11
1.98
3.14
4.37
5.57
6.63
8.27
10.18
12.57
15.06
16.93
19.63
21.13
27.26
5.57
5.75
5.72
-15.88
-12.84
-10.79
-5.76
-2.77
-0.21
1.80
3.01
4.31
5.64
7.04
8.59
10.18
13.18
15.52
18.47
21.33
23.42
27.78
5.64
5.96
5.84
-3.69
-1.01
0.29
1.21
2.05
2.94
3.89
4.95
5.88
6.76
7.69
8.77
10.16
12.39
14.17
16.05
18.30
19.77
22.03
6.76
7.23
3.83
-24.30
-13.20
-10.37
-5.83
-3.19
-1.05
1.10
2.57
3.85
5.06
6.29
7.69
9.47
12.04
14.42
16.56
19.34
20.97
26.99
5.06
5.21
5.64
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-52.57
-40.99
-33.66
-17.67
-10.99
-7.02
-3.92
-2.05
-0.79
0.37
1.53
3.13
4.91
7.40
9.81
12.03
13.72
16.87
23.68
0.37
-0.18
7.69
-33.41
-25.04
-15.25
-6.73
-2.00
1.35
4.99
7.49
10.04
11.90
13.83
16.23
19.56
24.76
28.96
32.07
35.11
37.78
41.67
11.90
12.18
9.74
-23.74
-14.44
-10.51
-5.64
-1.77
1.51
5.11
7.55
9.64
11.67
13.93
16.43
19.68
23.96
27.88
32.26
37.53
43.38
49.94
11.67
12.31
9.42
-22.08
-18.12
-13.87
-6.19
-1.94
1.57
4.60
7.01
9.19
10.84
12.88
15.77
18.69
23.48
27.26
31.52
34.54
36.24
41.39
10.84
11.58
9.19
-25.52
-19.21
-16.73
-8.31
-3.39
0.76
4.25
6.74
8.74
10.77
12.95
15.28
17.93
21.85
25.93
28.69
33.27
36.97
40.88
10.77
10.92
9.10
-40.37
-27.75
-17.39
-9.94
-1.91
1.50
4.96
7.36
9.49
11.60
13.79
16.64
19.63
24.94
28.56
31.47
35.63
38.34
53.69
11.60
12.03
10.11
-24.30
-23.51
-15.30
-7.07
-2.77
1.00
4.58
7.06
9.16
11.52
13.91
16.54
19.81
25.40
29.79
34.76
44.73
54.68
61.18
11.52
12.38
10.73
-0.80
0.89
2.02
4.06
5.20
6.60
8.40
9.94
11.55
12.98
14.44
16.26
18.28
21.85
24.95
26.83
30.77
32.97
36.10
12.98
13.62
6.03
-40.37
-23.39
-16.10
-8.91
-4.23
-0.73
3.18
5.97
8.31
10.39
12.65
15.14
18.12
22.78
26.84
30.56
34.77
38.23
52.63
10.39
10.60
10.00
166
-------
Cumulative Probability Distributions
34. Normalized Greenhouse Contribution to Sea Level by Climate Reviewer, 1990-2075 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
35. Normalized Greenhouse Contribution to Sea Level by Climate Reviewer, 1990-2100 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-53.99
-48.37
-45.88
-24.23
-15.06
-9.35
-5.29
-2.37
-0.68
0.98
2.69
5.33
7.71
11.23
15.22
18.06
21.23
23.80
25.66
0.98
0.47
10.45
-45.58
-33.06
-20.78
-8.76
-1.11
3.86
9.28
13.18
16.46
19.70
23.09
27.17
32.03
39.45
46.39
51.73
57.23
62.51
71.48
19.70
20.50
15.12
-33.26
-20.42
-13.65
-6.25
-0.33
3.75
9.34
13.04
16.18
18.98
22.86
27.07
31.47
38.48
46.35
53.05
61.27
69.35
82.54
18.98
20.57
14.66
-28.66
-20.27
-17.05
-7.55
-1.47
3.91
8.49
11.80
15.00
17.50
20.76
25.30
30.66
36.80
43.35
50.03
53.63
58.09
67.33
17.50
19.10
13.94
-31.64
-24.39
-20.44
-10.22
-1.99
2.70
8.09
11.54
14.86
17.79
21.22
24.43
28.29
35.11
40.52
46.57
53.01
56.49
64.43
17.79
18.17
13.61
-50.39
-36.63
-23.96
-9.63
-1.12
3.99
8.99
12.49
16.21
19.49
23.25
27.17
32.37
40.32
46.90
51.51
57.68
64.08
82.88
19.49
20.47
15.66
-32.53
-24.02
-16.01
-6.53
-1.55
2.80
8.40
11.95
15.11
18.87
22.57
26.99
32.90
41.93
50.04
56.49
71.48
79.55
90.39
18.87
20.82
16.53
-1.56
2.25
3.43
6.43
8.94
11.01
13.67
15.85
18.29
20.45
22.65
25.30
28.64
32.77
37.66
41.20
45.98
48.29
50.55
20.45
21.36
8.83
-48.37
-29.64
-20.76
-11.06
-5.06
0.00
6.08
10.32
13.83
17.10
20.52
24.42
29.35
36.51
43.32
49.71
56.49
64.08
80.14
17.10
17.68
15.30
All
0.10
0.50
1,00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-67.32
-59.92
-48.59
-30.96
-19.33
-12.02
-6.25
-2.73
-0.18
1.79
4.63
7.94
11.22
17.29
21.44
26.33
29.84
33.36
37.45
1.79
1.72
13.40
-62.83
-37.09
-24.61
-10.21
0.01
6.91
14.72
19.84
24.68
29.44
34.81
41.13
48.28
59.76
70.72
80.84
91.85
106.09
114.01
29.44
31.45
22.54
-34.21
-24.33
-16.07
-5.37
1.06
6.68
14.79
19.77
24.60
29.33
34.68
40.59
48.43
60.76
73.30
87.15
101.13
117.28
171.91
29.33
32.38
23.46
-30.28
-21.60
-17.46
-7.56
-0.74
5.61
13.12
17.45
22.07
25.70
30.55
37.88
45.59
56.90
64.31
75.43
89.28
102.92
113.28
25.70
28.82
20.85
-36.29
-30.56
-24.31
-11.36
-1.26
5.49
12.33
17.27
22.02
26.46
30.63
35.78
42.18
51.51
60.40
70.46
77.63
83.96
92.71
26.46
27.28
19.42
-44.81
-31.29
-27.45
-10.27
-0.60
6.93
14.42
19.62
24.19
30.40
35.01
41.88
49.18
61.86
72.38
85.11
98.05
105.35
111.47
30.40
31.98
23.13
-38.58
-19.79
-16.10
-7.96
-1.01
6.00
13.23
18.27
23.09
28.20
33.96
41.63
50.18
64.64
78.77
91.34
103.75
109.75
123.77
28.20
32.21
24.42
-2.15
2.95
4.27
9.13
12.68
15.10
19.03
22.45
25.63
28.82
32.11
36.16
40.79
47.36
53.04
58.45
63.41
65.88
70.85
28.82
30.20
12.72
-57.66
-33.83
-24.31
-13.11
-5.80
0.92
9.52
15.58
20.36
25.09
30.25
36.33
43.99
54.94
66.13
77.76
91.85
102.62
122.53
25.09
27.00
22.62
167
-------
Appendix 1-A
36. Normalized Greenhouse Contribution to Sea Level by Climate Reviewer, 1990-2150 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
37. Normalized Greenhouse Contribution to Sea Level by Climate Reviewer, 1990-2200 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-76.31
-61.92
-51.38
-39.67
-26.88
-17.25
-8.42
-3.28
0.41
4.47
8.37
14.03
19.24
29.52
37.85
45.87
53.95
63.79
69.55
4.47
4.89
19.77
-51.70
-37.26
-30.61
-11.92
1.28
12.63
25.08
33.40
43.26
52.35
62.88
74.05
88.23
112.20
137.33
172.12
199.91
251.06
282.43
52.35
58.81
44.76
-46.04
-37.70
-20.91
-4.74
2.58
14.05
26.02
35.68
44.39
55.02
64.73
79.54
97.74
134.56
170.00
208.04
244.81
272.13
343.67
55.02
65.82
53.12
-33.17
-28.81
-21.21
-9.97
-0.46
10.23
21.59
30.03
37.83
45.72
54.42
67.10
82.44
109.06
129.02
157.87
190.63
217.64
308.46
45.72
53.61
42.46
-49.45
-39.48
-30.46
-12.73
-0.19
9.86
21.01
30.30
37.15
44.71
52.22
62.70
74.11
92.86
113.98
130.31
162.16
177.56
258.94
44.71
48.68
36.35
-55.06
-46.04
-34.02
-12.75
2.53
14.27
25.87
35.62
45.18
56.06
66.15
78.89
96.25
126.02
157.94
191.66
237.31
311.97
381.32
56.06
64.49
52.24
-51.74
-42.79
-20.79
-5.45
1.55
10.04
22.11
32.69
40.59
49.96
62.44
76.99
100.87
132.65
165.19
204.05
258.06
295.95
515.84
49.96
64.00
57.56
-4.88
2.53
4.91
12.29
17.22
21.73
28.81
34.50
39.87
46.10
51.01
58.38
68.18
79.79
91.49
100.32
110.50
113.34
122.44
46.10
48.55
22.76
-55.06
-43.72
-32.30
-17.20
-6.94
3.02
16.16
26.26
34.94
43.41
52.86
65.14
80.27
106.43
134.03
167.68
209.68
250.84
342.20
43.41
51.10
46.99
All
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-84.75
-69.99
-61.69
-51.31
-34.58
-22.34
-10.51
-3.61
1.19
6.58
12.43
19.64
27.47
42.02
56.31
68.27
81.17
88.56
104.12
6.58
8.24
27.25
-59.94
-43.30
-39.42
-16.01
2.86
17.95
35.40
48.38
61.90
76.34
93.68
113.24
136.74
182.64
227.57
288.04
353.79
445.40
542.37
76.34
91.73
76.58
-53.65
-38.57
-29.52
-6.34
4.67
20.44
39.30
55.02
70.07
86.23
105.47
136.74
168.82
236.06
312.25
390.40
480.37
519.86
591.61
86.23
111.99
97.38
-47.00
-36.58
-25.74
-9.82
-0.28
14.14
29.96
42.92
55.05
67.54
81.37
101.59
125.28
171.10
214.07
264.64
332.04
447.65
550.16
67.54
83.01
71.84
-65.08
-51.03
-39.23
-18.89
-0.54
13.92
30.53
41.85
53.96
63.19
75.21
90.92
109.64
138.52
172.07
211.86
263.12
331.54
427.53
63.19
72.74
58.47
-60.30
-57.34
-39.82
-12.83
6.02
22.23
41.41
56.27
71.08
87.83
106.67
129.45
163.49
227.52
296.36
370.80
537.48
559.78
672.03
87.83
110.40
97.49
-64.37
-45.58
-27.93
-5.87
2.81
15.26
32.34
47.05
61.35
77.56
96.99
124.79
163.51
225.08
289.69
368.34
534.01
559.61
679.95
77.56
104.30
99.11
-9.20
0.02
6.38
14.24
20.83
28.07
36.75
45.23
53.42
60.86
68.84
79.01
92.91
110.52
128.29
142.13
156.07
164.33
172.98
60.86
65.63
32.83
-68.91
-51.95
-40.13
-21.44
-8.40
4.78
23.28
37.31
50.52
63.67
78.30
98.14
124.79
174.42
230.39
295.91
401.57
481.87
587.01
63.67
81.01
81.49
168
-------
Cumulative Probability Distributions
38. Year by Which U.S. Sea Level is Likely to Inundate 1-Foot, 3-Foot, and NGVD Contours
Cumulative
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Year US Sea Level rises
1ft (relative to 1990)
2019
2025
2027
2031
2034
2038
2044
2049
2053
2058
2062
2069
2079
2099
2127
2169
>2200
Year US Sea Level rises
3ft (relative to 1990)
2065
2078
2083
2090
2097
2106
2119
2131
2144
2157
2173
2194
>2200
>2200
>2200
>2200
>2200
Year US Sea Level rises
to NGVD 5ft contour
2086
2101
2107
2117
2127
2141
2162
2180
>2200
>2200
>2200
>2200
>2200
>2200
>2200
>2200
>2200
Note: NGVD is the National Geodetic Vertical Datum, which is approximately equal to mean sea level for the year
1929. Because sea level has been rising, the 5-foot (NGVD) contour on U.S. topographic maps is generally only
about 4.5 feet above sea level. These calculations assume that sea level is rising 2.7 mm/yr relative to the U.S. coast.
39. Greenhouse Contribution to Sea Level Rise for eight random subsamples (cm): 1990-2100
Cumulative Bin 1 Bin 2 Bin 3 Bin 4 Bin 5 Bin 6 Bin 7 Bin 8 All
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
Standard
-1.36
2.66
5.37
11.17
19.31
24.86
29.31
35.17
40.56
46.95
54.22
65.46
76.56
89.15
104.08
35.17
37.65
22.84
Error of l%high:
-0.57
1.83
4.63
9.59
17.99
23.68
28.80
33.78
39.41
45.30
53.36
64.86
74.14
86.19
107.04
33.78
36.51
22.79
0.99cm
-2.02
0.50
3.14
9.27
17.32
23.64
29.00
33.54
38.26
44.01
52.43
63.81
74.49
86.41
103.90
33.54
35.78
22.45
-2.89
0.50
3.69
8.15
16.37
22.22
28.31
32.70
38.66
44.57
51.96
65.55
78.90
95.05
1 10.22
32.70
35.95
23.72
0.44
3.77
6.99
13.51
20.03
25.06
30.03
34.46
39.79
46.06
54.17
67.29
79.65
87.27
101.54
34.46
37.76
21.57
-1.23
1.77
5.00
10.73
19.11
23.86
29.29
34.06
38.93
45.84
53.95
67.17
79.04
87.94
103.68
34.06
37.21
22.83
-2.29
0.91
3.94
9.87
18.39
24.38
29.65
34.47
39.75
45.62
53.51
64.53
77.31
92.01
106.72
34.47
36.90
22.76
-0.08
3.57
6.92
12.03
18.96
24.24
28.86
33.95
38.85
44.48
51.21
62.99
74.72
86.46
102.74
33.95
36.42
21.12
-1.24
1.71
4.86
10.35
18.55
24.13
29.23
34.08
39.34
45.22
53.08
65.08
77.23
88.26
104.23
34.08
36.77
22.53
The 10,000 simulations were randomly divide into eight sets of mutually exclusive sub-samples. Thus each column represents
1250 simulations. See Numerical Error of the Monte Carlo Algorithm, in Chapter 7, supra.
169
-------
Appendix 1-B
B. RESULTS FROM SENSITIVITY ANALYSIS USING IPCC EMISSIONS
SCENARIO A
40. Global Warming
Cumulative
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
1990-2100
°C
-0.460
-0.240
-0.110
0.070
0.310
0.700
1.300
1.670
1.980
2.270
2.560
2.900
3.320
3.980
4.650
5.290
5.980
6.530
8.680
2.270
2.349
1.315
1990-2200
°C
-0.580
-0.260
-0.120
0.140
0.510
1.180
2.260
2.910
3.460
3.980
4.550
5.210
6.060
7.420
8.680
9.960
11.520
12.430
16.230
3.980
4.236
2.471
41. Antarctic Contribution to Sea Level, 1990-2200 by Climate Reviewer (cm)
Cumulative Balling Bremerton Hoffert MacCracken Manabe Rind Schneider
Wigley
All
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
-91.50
-61.61
-39.90
-23.12
-12.07
-7.13
-4.21
-1.85
1.26
7.59
14.01
24.14
33.36
49.00
67.35
-1.85
-0.92
25.73
-91.58
-69.05
-42.57
-23.55
-11.08
-5.32
-1.69
1.81
8.81
16.15
25.99
47.80
72.45
103.61
187.54
1.81
9.74
39.71
-116.53
-72.93
-50.29
-28.85
-12.84
-5.75
-1.40
2.87
10.24
19.46
29.95
53.93
90.37
126.61
221.14
2.87
10.70
48.06
-93.50
-65.70
-39.03
-22.40
-11.16
-5.90
-1.97
1.40
8.42
15.97
24.89
45.58
72.00
114.86
175.70
1.40
9.51
42.87
-87.20
-58.97
-39.75
-24.18
-12.22
-6.19
-2.34
0.28
6.34
13.35
21.85
36.66
52.98
72.00
125.56
0.28
4.99
35.56
-111.37
-63.59
-45.72
-25.61
-10.66
-3.06
1.34
8.02
15.90
24.95
40.18
72.77
127.97
182.40
325.91
8.02
21.54
64.22
-62.09
-47.39
-31.08
-17.01
-6.61
-2.14
2.08
9.71
18.98
29.80
44.44
79.79
140.97
213.09
330.67
9.71
27.46
62.87
-45.18
-38.61
-34.02
-28.30
-21.36
-16.93
-13.47
-10.97
-8.49
-5.65
-2.71
1.58
5.14
8.96
13.42
-10.97
-12.17
10.92
-88.73
-58.83
-39.01
-24.46
-13.38
-7.46
-3.36
-0.13
5.84
13.73
24.51
46.02
74.34
119.72
206.38
-0.13
8.86
45.62
170
-------
Emissions Scenario A
42. Greenland Contribution to Sea Level, 1990-2200 by Climate Reviewer (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider
Wigley
All
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
-2.51
-1.84
-1.16
-0.48
0.19
0.68
1.29
1.91
2.48
3.52
4.82
7.24
9.39
12.78
15.20
1.91
2.72
3.47
0.81
2.32
3.75
5.62
8.25
11.29
14.91
18.93
24.04
29.57
38.35
55.99
80.46
103.45
142.37
18.93
26.64
24.87
-1.08
1.21
3.13
5.71
9.94
14.27
19.68
25.86
35.31
50.05
70.60
105.08
132.83
166.73
199.32
25.86
41.82
46.45
-2.99
-0.44
0.54
2.02
4.19
6.16
8.01
10.59
13.96
18.01
24.11
37.06
51.04
67.50
113.56
10.59
16.70
19.51
-5.82
-3.18
-1.62
-0.48
0.93
2.43
3.73
5.34
7.44
9.57
13.41
20.29
29.53
37.47
56.15
5.34
8.50
11.13
-5.58
-0.54
2.60
5.66
9.70
13.63
17.31
22.47
29.81
38.49
53.07
81.59
106.16
135.33
175.90
22.47
34.43
34.73
-6.84
-1.09
0.69
2.63
5.93
8.61
12.12
16.79
22.25
29.41
43.64
70.08
100.62
133.35
184.22
16.79
28.13
34.99
11.47
13.44
14.87
17.00
20.06
22.24
23.96
26.11
28.27
31.09
34.63
39.51
42.78
45.28
52.95
26.11
27.32
8.79
-3.18
-1.12
-0.13
1.20
3.70
6.67
10.18
14.96
20.22
25.87
34.40
53.28
83.28
112.85
149.12
14.96
23.28
29.41
43. Contribution to Sea Level by 1990-2100 (cm)
Cumulative Greenhouse Contribution
Normalized Contribution
0.10
0.50
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
99.50
99.90
Median
Mean
StdDev
-5.930
-2.960
-1.280
2.040
5.480
11.860
20.730
26.420
31.560
36.310
41.400
47.610
54.990
66.160
76.730
88.880
102.880
116.020
157.190
36.310
38.542
22.219
-62.900
-38.780
-25.100
-11.520
-4.760
2.220
11.380
17.710
23.070
27.770
32.650
38.120
45.310
55.730
66.590
77.830
90.750
104.990
147.680
27.770
28.735
23.019
171
-------
Appendix 1-B
44. Contribution to Sea Level by 2200 (cm)
Cumulative Greenhouse Contribution Normalized Contribution
0.10 -12.460 -69.670
0.50 -4.730 -64.390
1.00 -0.590 -41.480
2.50 4.600 -17.190
5.00 12.470 -3.960
10.00 28.050 11.640
20.00 49.950 32.480
30.00 65.050 48.160
40.00 77.540 61.800
50.00 91.040 74.680
60.00 106.700 88.850
70.00 125.730 106.920
80.00 152.910 133.240
90.00 200.230 178.500
95.00 253.610 232.700
97.50 307.870 284.120
99.00 385.290 374.610
99.50 500.670 468.630
99.90 650.440 781.240
Median 91.040 74.680
Mean 107.871 89.142
StdDev 83.857 83.309
45. Annual Greenhouse Contribution to Sea Level by Climate Reviewer in the year 2100 (mm/yr)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley All
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
-0.82
-0.61
-0.41
-0.12
0.23
0.54
0.78
1.00
1.24
1.52
1.97
2.62
3.18
3.88
4.72
1.00
1.16
1.14
1.47
1.87
2.26
2.78
3.57
4.23
4.93
5.67
6.40
7.37
8.48
10.25
12.45
14.90
17.82
5.67
6.27
3.42
1.40
1.77
2.24
2.87
3.77
4.49
5.32
6.16
6.99
7.99
9.51
12.13
15.06
17.46
21.06
6.16
6.98
4.20
1.30
1.75
2.01
2.55
3.21
3.80
4.50
5.03
5.77
6.73
7.75
9.28
11.26
13.36
16.80
5.03
5.71
3.36
1.49
1.91
2.31
2.73
3.38
3.86
4.43
4.97
5.64
6.33
7.28
8.66
9.83
11.25
13.88
4.97
5.43
2.49
1.43
1.80
2.23
2.89
3.71
4.50
5.08
5.86
6.71
7.95
9.40
11.50
13.46
16.10
20.82
5.86
6.80
4.33
0.93
1.51
1.93
2.43
3.24
3.90
4.63
5.42
6.29
7.40
8.79
11.29
14.39
16.77
22.63
5.42
6.36
4.56
1.69
2.01
2.35
2.74
3.44
3.87
4.27
4.57
4.99
5.51
6.12
6.92
7.62
8.38
9.18
4.57
4.77
1.60
-0.27
0.22
0.75
1.54
2.67
3.50
4.17
4.84
5.60
6.49
7.70
9.70
11.83
14.29
17.82
4.84
5.43
3.79
172
-------
Emissions Scenario E
C. RESULTS FROM SENSITIVITY ANALYSIS USING IPCC SCENARIO E
46. Global Warming by Climate Reviewer, 1990-2100 (°C)
Cumulative Balling Bretherton Hoffert MacCracken Manabe
Rind Schneider Wigley All
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
-0.42
-0.27
-0.18
-0.05
0.10
0.25
0.37
0.50
0.61
0.74
0.91
1.12
1.32
1.47
1.60
0.50
0.52
0.45
0.97
1.12
1.31
1.55
1.91
2.20
2.56
2.89
3.21
3.56
4.03
4.85
5.66
6.22
6.87
2.89
3.05
1.30
0.97
1.14
1.30
1.56
1.91
2.19
2.45
2.69
3.00
3.33
3.80
4.45
5.23
5.87
6.74
2.69
2.91
1.21
0.92
1.09
1.28
1.49
1.88
2.20
2.46
2.75
3.00
3.39
3.86
4.64
5.35
5.99
6.70
2.75
2.94
1.26
0.94
1.06
1.27
1.53
1.85
2.14
2.43
2.72
3.03
3.36
3.78
4.42
4.95
5.40
6.15
2.72
2.86
1.15
0.79
1.04
1.26
1.51
1.92
2.26
2.55
2.83
3.17
3.56
4.11
4.88
5.60
6.16
6.84
2.83
3.05
1.34
0.73
1.06
1.27
1.59
1.98
2.29
2.62
2.95
3.31
3.80
4.37
5.46
6.30
6.88
8.87
2.95
3.30
1.81
1.38
1.56
1.77
1.95
2.28
2.52
2.74
2.96
3.18
3.46
3.76
4.27
4.72
5.18
5.57
2.96
3.05
0.91
-0.09
0.10
0.37
0.82
1.53
1.96
2.31
2.63
2.96
3.31
3.79
4.54
5.26
5.97
6.72
2.63
2.71
1.49
47. Global Warming by Climate Reviewer, 1990-2200 (°C)
Cumulative Balling Bretherton Hoffert MacCracken Manabe
Rind Schneider Wigley
All
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
-0.53
-0.34
-0.22
-0.01
0.20
0.39
0.62
0.83
1.05
1.29
1.54
1.91
2.17
2.46
2.69
0.83
0.89
0.75
1.66
1.96
2.31
2.84
3.47
4.05
4.66
5.33
6.03
6.86
7.72
9.54
10.97
12.38
14.15
5.33
5.80
2.70
1.72
2.01
2.33
2.78
3.34
3.90
4.35
4.98
5.64
6.42
7.49
9.09
10.24
11.79
13.91
4.98
5.53
2.60
1.63
2.04
2.32
2.76
3.44
3.94
4.57
5.19
5.87
6.69
7.76
9.39
11.03
12.27
14.23
5.19
5.71
2.71
1.64
1.89
2.30
2.75
3.43
3.99
4.59
5.18
5.95
6.70
7.76
9.49
11.11
12.30
13.65
5.18
5.74
2.75
1.53
1.94
2.26
2.68
3.43
4.05
4.66
5.24
5.80
6.59
7.51
9.24
10.46
11.88
12.96
5.24
5.63
2.57
1.44
1.94
2.32
2.85
3.49
4.21
4.86
5.42
6.19
7.19
8.38
10.25
12.12
13.72
16.07
5.42
6.11
3.09
2.67
2.95
3.27
3.64
4.25
4.67
5.10
5.54
5.97
6.52
7.17
8.24
9.06
9.78
10.82
5.54
5.76
1.78
-0.09
0.20
0.62
1.44
2.78
3.55
4.23
4.86
5.54
6.36
7.36
8.97
10.42
11.95
13.72
4.86
5.15
2.95
173
-------
Appendix 1-C
48. Greenhouse Contribution to Sea Level by Climate Reviewer, 1990-2100 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
49. Greenhouse Contribution to Sea Level by Climate Reviewer, 1990-2200 (cm)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider
Wigley
All
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
-5.61
-3.90
-2.21
-0.25
2.38
4.38
6.20
8.06
10.32
12.67
15.78
20.57
24.61
28.21
33.60
8.06
9.39
8.65
13.25
16.58
19.86
23.64
30.38
35.30
39.69
44.90
50.60
56.87
65.19
76.82
88.73
100.48
118.40
44.90
48.53
21.67
12.51
15.81
19.83
23.66
30.03
34.66
39.68
45.64
51.19
57.74
65.39
78.89
90.99
104.95
118.65
45.64
49.13
23.49
11.84
15.47
19.39
22.90
27.64
32.66
37.60
41.42
46.39
52.60
59.77
69.74
79.54
93.03
108.52
41.42
44.87
20.23
14.09
17.34
19.00
22.84
28.72
33.52
37.88
41.92
46.93
52.92
59.10
68.36
76.50
86.73
102.30
41.92
44.65
18.59
11.70
15.70
19.35
23.71
29.98
35.15
40.6?
46.01
51.78
58.19
68.40
80.34
91.37
101.20
121.74
46.01
49.63
23.39
11.74
14.63
18.21
22.00
28.40
33.26
38.30
43.68
49.53
56.67
66.11
79.95
92.81
106.35
124.41
43.68
48.50
25.87
16.05
19.54
22.44
26.47
30.79
34.86
37.93
41.27
44.62
49.10
54.04
61.99
67.66
72.01
78.81
41.27
42.75
13.72
-0.99
2.37
6.15
13.31
23.30
29.58
35.00
40.05
45.46
51.95
59.77
71.41
82.48
95.10
109.88
40.05
42.18
23.79
All
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
-8.67
-5.42
-2.04
1.21
5.94
10.91
15.57
20.32
26.37
31.93
38.98
51.61
65.06
78.43
102.08
20.32
24.41
22.41
32.40
43.35
49.40
62.22
78.00
93.67
109.41
126.84
143.81
167.55
196.57
242.18
295.55
348.57
453.22
126.84
144.68
87.60
22.59
39.77
47.84
66.81
88.11
109.70
131.68
154.71
178.64
205.08
249.08
317.11
370.09
430.31
529.82
154.71
174.50
109.00
32.01
40.30
47.17
57.86
74.35
88.27
100.94
115.58
132.00
152.17
175.32
215.59
27032
333.60
405.23
115.58
132.10
81.14
34.06
41.70
48.17
57.23
72.37
83.54
95.61
108.78
122.79
138.85
158.74
197.21
232.10
263.60
338.84
108.78
120.76
64.22
29.78
39.55
48.55
66.15
85.58
100.64
118.23
141.36
161.97
195.87
228.89
287.00
354.23
421.85
561.67
141.36
165.47
114.42
27.06
36.64
46.06
57.89
75.13
91.23
110.25
126.84
148.44
174.85
216.48
284.68
342.70
424.52
578.21
126.84
155.27
112.69
40.49
46.63
53.50
61.43
72.32
82.16
89.17
96.95
104.73
113.90
126.52
145.29
159.70
177.99
193.48
96.95
100.73
32.74
-0.60
5.34
14.87
32.79
59.56
77.44
92.54
108.37
126.52
149.02
181.83
237.34
297.46
357.57
447.37
108.37
127.24
96.00
174
-------
Emissions Scenario E
50. Annual Greenhouse Contribution to Sea Level by Climate Reviewer in the year 2100 (nun/yr)
Cumulative Balling Bretherton Hoffert MacCracken Manabe Rind Schneider Wigley
All
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
-0.74
-0.57
-0.36
-0.03
0.33
0.69
1.01
1.28
1.55
1.87
2.41
3.14
3.73
4.38
5.24
1.28
1.43
1.29
2.12
2.55
3.05
3.70
4.59
5.46
6.29
7.13
8.00
9.23
10.44
12.53
14.95
17.67
20.53
7.13
7.83
3.95
2.11
2.50
3.05
3.90
4.98
5.90
6.87
7.85
8.93
10.25
12.17
15.20
18.54
21.61
24.97
7.85
8.87
5.04
1.91
2.39
2.86
3.40
4.28
5.07
5.75
6.44
7.39
8.34
9.64
11.30
13.42
15.61
19.40
6.44
7.18
3.80
2.14
2.63
3.06
3.60
4.45
5.05
5.71
6.35
7.10
7.97
9.05
10.66
12.18
13.60
16.21
6.35
6.85
2.92
1.95
2.38
2.96
3.80
4.82
5.75
6.52
7.44
8.44
9.82
11.59
14.12
16.26
19.15
24.59
7.44
8.42
4.91
1.37
2.08
2.59
3.28
4.24
5.09
5.94
6.95
7.96
9.30
10.81
13.97
17.07
20.28
26.65
6.95
7.95
6.34
2.46
2.89
3.29
3.81
4.56
5.16
5.57
5.95
6.44
7.05
7.70
8.61
9.53
10.30
11.10
5.95
6.15
1.87
-0.20
0.30
0.97
2.01
3.55
4.57
5.41
6.20
7.11
8.17
9.59
11.95
14.46
17.27
21.18
6.20
6.84
4.64
175
-------
Appendix 1-D
D. RESULTS FROM SENSITIVITY ANALYSIS USING ALTERNATIVE
EMISSIONS POLICIES AND/OR FIXING PARTICULAR PARAMETERS
(using Schneider values for Climate coefficients)
51. Forcing, 1990-2100 (W/m2)
Cumulative
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
Fixed Emiss.
2025
2.51
2.71
2.91
3.12
3.40
3.57
3.78
3.98
4.17
4.37
4.59
4.86
5.13
5.43
5.87
3.98
3.99
0.69
Fixed Emiss.
2050
2.25
2.55
2.83
3.09
3.47
3.77
4.02
4.37
4.69
4.96
5.30
5.77
6.09
6.56
7.06
4.37
4.40
1.03
Fixed Emiss.
2100
1.82
2.25
2.67
3.05
3.56
3.99
4.36
4.91
5.41
5.87
6.37
7.16
7.71
8.29
8.91
4.91
5.00
1.58
52. Global Warming, 1990-2100 (°C)
Cumulative
Fixed Emiss. Fixed Emiss. AT2x=2.6 AT2x=4.0 Fix Emiss.2025
2025 2050 and AT2x=4.0
Fix Emiss.2050 Fixed Emiss.
and AT2x=4.0 2100
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
0.26
0.50
0.70
0.89
1.21
1.45
1.71
1.97
2.25
2.62
3.15
3.96
4.87
5.39
6.79
1.97
2.28
1.62
0.25
0.49
0.71
0.94
1.28
1.55
1.83
2.12
2.43
2.89
3.45
4.35
5.32
5.99
7.27
2.12
2.47
1.75
0.85
1.06
1.24
1.47
1.75
1.97
2.20
2.39
2.59
2.81
3.10
3.56
3.90
4.34
4.92
2.39
2.46
0.85
0.89
1.34
1.66
2.05
2.46
2.77
3.04
3.33
3.59
3.93
4.37
5.13
5.63
6.63
9.21
3.33 •
3.52
1.66
0.70
1.37
1.64
1.93
2.25
2.48
2.66
2.86
3.07
3.27
3.61
4.11
4.81
5.74
7.12
2.86
3.01
1.25
0.65
1.38
1.69
2.01
2.35
2.60
2.85
3.07
3.30
3.57
3.90
4.53
5.15
6.21
7.83
3.07
3.23
1.38
0.32
0.50
0.72
0.99
1.37
1.68
1.96
2.31
2.70
3.16
3.82
4.78
5.74
6.54
7.62
2.31
2.66
1.63
176
-------
Alternative Policies
53. Global Wanning, 1990-2200 (°C)
Cumulative
%
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
Fixed Emiss.
2025
0.50
0.86
1.09
1.43
1.87
2.24
2.64
3.09
3.51
4.19
5.25
6.49
7.88
8.88
10.95
3.09
3.60
2.22
Fixed Emiss.
2050
0.50
0.88
1.10
1.49
1.99
2.40
2.81
3.33
3.87
4.64
5.80
7.21
8.84
10.00
12.04
3.33
3.95
2.50
AT2x=2.6
0.82
1.39
1.74
2.12
2.70
3.15
3.60
4.00
4.44
4.88
5.42
6.20
6.88
7.41
8.18
4.00
4.10
1.59
AT2x=4.0
1.22
1.71
2.53
3.07
3.98
4.65
5.25
5.85
6.45
7.07
7.90
9.06
10.03
10.80
11.66
5.85
5.96
2.30
Fix Emiss.2025
and AT2x=4.0
1.96
2.41
2.82
3.17
3.67
4.01
4.32
4.59
4.88
5.17
5.62
6.18
6.72
7.20
7.75
4.59
4.65
1.29
Fix Emiss.2050 Fixed Emiss.
andAT2x=4.0 2100
1.81
2.37
2.79
3.24
3.83
4.26
4.64
5.02
5.35
5.76
6.24
7.09
7.66
8.09
8.93
5.02
5.09
1.58
0.45
0.77
1.01
1.43
2.10
2.64
3.22
3.86
4.75
5.67
6.88
9.27
11.32
13.06
15.53
3.86
4.73
3.28
54. Greenland Contribution to Sea Level, 1990-2200 (cm)
Cumulative Fixed Emiss. Fixed Emiss.
% 2025 2050
AT2x=2.6 AT2x=4.0
Fix Emiss.2025 Fix Emiss.2050 Fixed Polar Fixed Shelf
andAT2x=4.0 andAT2x=4.0 Amplification Melt
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
-3.10
-0.51
0.46
1.72
3.80
5.98
8.28
11.48
15.17
20.12
29.79
50.23
72.89
99.18
152.78
11.48
20.33
26.91
-4.88
-0.89
0.40
1.85
4.03
6.39
9.08
12.45
16.94
22.30
32.52
57.75
85.35
110.41
163.42
12.45
21.98
30.17
-2.97
-0.54
0.92
2.58
5.47
8.34
11.44
14.73
19.20
24.43
33.97
50.79
73.77
103.23
156.88
14.73
23.68
23.85
-11.36
-2.18
0.72
3.52
8.28
12.95
17.79
23.29
30.05
40.55
58.62
85.49
1 14.99
155.30
204.99
23.29
35.94
35.63
-3.90
-0.94
1.07
3.42
7.46
11.11
14.83
18.38
24.12
31.35
42.73
63.09
89.34
118.29
177.22
18.38
28.35
29.12
-5.24
-1.01
1.14
3.54
7.97
11.78
15.80
19.70
25.91
34.11
47.73
72.90
98.13
133.75
192.69
19.70
31.08
31.94
-1.25
1.02
2.38
3.71
6.08
8.51
11.37
15.06
19.17
25.00
34.40
53.05
78.69
100.98
128.44
15.06
22.87
23.48
-7.20
-1.23
0.46
1.87
4.31
6.88
10.17
14.45
19.90
26.24
38.80
68.68
105.33
135.70
184.60
14.45
26.79
35.98
177
-------
Appendix 1-D
55. Antarctic Contribution to Sea Level, 1990-2200 (cm)
Cumulative Fixed Emiss. Fixed Emiss.
% 2025 2050
AT2x=2.6
AT2x=4.0 Fix Emiss.2025 Fix Emiss.2050 Fixed Polar Fixed Shelf
andAT2x=4.0 andAT2x=4.0 Amplification Melt
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
-85.66
-54.92
-32.45
-18.27
-8.36
-2.70
1.12
8.03
16.75
24.56
39.21
67.56
112.47
160.00
312.73
8.03
21.22
63.53
-85.32
-54.86
-32.37
-18.34
-8.16
-2.52
1.47
8.36
17.29
25.37
40.82
71.70
117.74
165.92
320.75
8.36
22.86
67.88
-86.36
-52.54
-32.19
-18.21
-7.76
-2.22
2.47
9.72
17.64
26.46
40.41
70.39
113.00
153.85
250.21
9.72
22.39
64.75
-86.42
-52.60
-32.03
-17.09
-6.25
-0.79
7.03
15.91
25.18
34.96
58.15
108.79
161.15
259.87
432.36
15.91
36.45
91.53
-86.40
-50.69
-30.49
-16.44
-7.08
-1.04
5.08
14.16
22.33
32.07
51.99
96.15
145.50
237.64
360.28
14.16
31.41
82.45
-86.41
-50.56
-31.11
-16.41
-6.84
-0.89
5.97
15.00
23.22
34.03
54.48
101.33
152.59
245.56
367.75
15.00
33.44
86.13
-86.32
-55.00
-32.50
-19.47
-9.27
-3.27
0.42
7.19
15.58
24.16
36.67
64.42
99.90
158.73
241.42
7.19
18.49
56.11
-89.06
-59.40
-34.17
-17.64
-7.10
-2.06
2.49
8.85
17.17
25.15
35.10
49.46
68.14
85.80
114.74
8.85
12.77
34.36
56. Greenhouse Contribution to Sea Level, 1990-2100 (cm)
Cumulative Fixed Emiss. Fixed Emiss. AT2x=2.6
% 2025 2050
AT2x=4.0 Fix Emiss.2025 Fix Emiss.2050 Fixed Polar Fixed Shelf
andAT2x=4.0 andAT2x=4.0 Amplification Melt
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
6.19
8.96
11.93
15.68
20.94
25.20
29.69
34.23
39.69
46.23
55.17
69.05
80.92
94.33
114.67
34.23
39.38
24.21
6.10
9.16
12.28
16.40
21.84
26.34
30.85
36.20
41.83
48.30
57.86
72.90
84.02
98.25
116.39
36.20
41.17
24.71
11.44
15.86
18.91
22.99
27.28
30.84
34.42
37.87
41.09
44.19
48.98
56.28
65.69
73.29
91.37
37.87
39.47
15.93
17.43
22.74
26.65
32.84
38.56
43.12
47.92
52.52
56.26
60.83
66.45
77.82
87.91
101.69
127.37
52.52
55.05
27.79
17.39
22.05
25.99
30.89
36.02
40.51
43.95
47.57
51.02
55.42
61.36
71.36
81.01
94.64
119.32
47.57
50.35
21.21
17.70
22.26
26.65
31.84
37.39
41.92
45.98
50.28
53.72
58.13
63.96
74.57
84.75
98.78
122.55
50.28
52.98
26.47
6.75
9.28
12.45
16.56
22.16
26.28
31.09
36.20
42.50
48.24
57.86
71.34
82.18
95.94
115.84
36.20
40.99
23.43
7.50
9.61
12.63
16.03
22.09
27.10
31.73
36.93
41.61
48.64
57.79
71.95
84.53
96.44
111.48
36.93
41.23
23.54
178
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Alternative Policies
57. Greenhouse Contribution to Sea Level, 1990-2200 (cm)
Cumulative Fixed Emiss. Fixed Emiss.
% 2025 2050
AT2x=2.6 AT2x=4.0 Fix Emiss.2025 Fix Emiss.2050 Fixed Polar Fixed Shelf
andAT2x=4.0 and AT2x=4.0 Amplification Melt
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
12.31
19.10
25.28
33.92
45.81
55.34
68.60
79.10
94.39
1 14.66
144.06
194.98
242.92
301.47
458.03
79.10
101.92
87.91
11.27
18.63
25.66
34.20
48.02
57.88
71.79
85.13
100.48
126.41
156.05
212.99
252.97
318.53
470.70
85.13
109.67
96.10
21.61
30.43
38.43
46.84
60.26
72.55
83.82
96.57
108.57
123.00
142.65
184.40
235.53
296.95
381.07
96.57
111.58
80.14
29.59
48.64
57.84
69.26
88.23
105.75
122.52
140.37
158.21
178.84
210.27
268.68
341.12
412.93
563.71
140.37
162.15
115.73
38.24
48.66
55.94
68.40
81.84
92.43
102.17
113.93
125.92
142.41
167.13
216.99
278.49
332.70
453.67
113.93
134.52
96.09
36.79
50.59
57.26
70.97
84.97
98.10
110.58
124.05
137.23
153.63
179.21
233.43
291.52
372.00
499.95
124.05
144.51
104.72
10.35
16.41
23.99
33.74
47.30
60.68
73.37
91.42
109.17
134.13
169.31
230.99
274.72
339.43
405.36
91.42
114.58
90.19
8.76
19.61
26.63
34.45
48.28
62.87
76.96
92.67
109.67
131.95
167.54
218.39
265.20
309.72
384.61
92.67
111.77
84.50
58. Year by which Climate Contribution to Sea Level Exceeds 50 cm
Cumulative Fixed Emiss. Fixed Emiss. AT2x=2.6
% 2025 2050
AT2x=4.0 Fix Emiss.2025 Fix Emiss.2050 Fixed Polar Fixed Shelf
andAT2x=4.0 andAT2x=4.0 Amplification Melt
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
2048
2059
2068
2077
2092
2108
2121
2139
2157
2184
>2200
>2200
>2200
>2200
>2200
2139
2048
2059
2067
2076
2089
2103
2116
2131
2148
2177
>2200
>2200
>2200
>2200
>2200
2131
2066
2077
2084
2092
2102
2109
2116
2123
2134
2149
2171
>2200
>2200
>2200
>2200
2123
2052
2061
2067
2074
2081
2087
2092
2097
2103
2113
2124
2146
2177
>2200
>2200
2097
2052
2061
2068
2075
2084
2092
2098
2105
2112
2121
2133
2155
2179
>2200
>2200
2105
2052
2061
2068
2074
2082
2089
2095
2100
2107
2116
2128
2149
2174
2198
>2200
2100
2049
2061
2069
2078
2090
2103
2113
2128
2146
2171
>2200
>2200
>2200
>2200
>2200
2128
2050
2060
2069
2078
2090
2102
2114
2127
2143
2168
>2200
>2200
>2200
>2200
>2200
2127
179
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Appendix 1-D
59. Annual Greenhouse Contribution to Sea Level in the year 2100 (mm/yr)
Cumulative
1.00
2.50
5.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
95.00
97.50
99.00
Median
Mean
StdDev
Fixed Emiss. Fixed Emiss. AT2x=2.6
2025 2050
AT2x=4.0 Fix Emiss.2025 Fix Emiss.2050 Fixed Polar Fixed Shelf
andAT2x=4.0 andAT2x=4.0 Amplification Melt
0.25
0.58
0.93
1.29
1.90
2.48
3.07
3.76
4.48
5.42
6.58
8.90
11.30
14.05
18.86
3.76
4.64
4.20
0.09
0.55
0.99
1.42
2.04
2.72
3.39
4.17
4.99
5.98
7.37
10.05
12.56
15.92
21.45
4.17
5.13
4.45
0.19
0.98
1.45
2.02
2.93
3.65
4.24
4.90
5.58
6.40
7.35
8.99
10.81
13.36
17.79
4.90
5.42
3.89
0.57
1.39
2.18
3.05
4.28
5.14
6.10
7.13
7.95
9.16
10.57
13.03
16.74
19.30
25.80
7.13
8.03
7.67
0.13
1.34
2.04
2.79
3.67
4.21
4.75
5.30
5.98
6.62
7.84
9.88
12.68
15.68
20.25
5.30
6.13
4.90
0.42
1.21
2.06
2.90
3.92
4.58
5.24
5.90
6.61
7.47
8.80
10.88
13.94
17.16
22.94
5.90
6.78
7.46
0.15
0.38
0.76
1.48
2.25
3.01
3.75
4.59
5.60
6.97
8.58
11.27
13.58
16.18
20.41
4.59
5.62
4.65
0.19
0.55
0.99
1.50
2.29
3.07
3.88
4.72
5.69
6.89
8.44
11.45
13.93
16.60
19.86
4.72
5.69
4.89
180
-------
APPENDIX 2
1. Historic Contribution (1890-1990) from Various Sources According to IPCC (1990) (cm)
(unreported result)
Low
Best Estimate
High
Thermal Expansion
Small Glaciers
Greenland
Antarctica
Total
4.47
1.35
0.26
-5.20
6.57
5.43
1.17
-0.52
12.65
9.64
13.85
2.69
0
26.18
Note: These results were not published in IPCC 1990. They were calculated using the Wigley & Raper (1992) version of
the gas cycle and ocean models.
181
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APPENDIX 3
MISCELLANEOUS INFORMATION CONCERNING ANTARCTIC
ICE SHEET RESEARCH
1200
1100
1000
900
800
700
'C/T 600
.9 500
!j| 400
^ 300
!§ 200
100
2
1 —
0
Antarctic Ice Sheet
Research
Global Change
Research
1984 1985 1986 1987 1988 1989 1990
1991
1992
Year
Figure A3-1. Failure of Ice Sheet Research Budgets to Benefit from Increased Global Change Research.
SOURCE: National Science Foundation; Annual Reports of the United States Global Climate Research Program Office and the
predecessor National Climate Program Office.
182
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December 2, 1991
Dr. John Houghton, Chairman
IPCC Working Group I
Meteorological Office
London Road
Bracknell
United Kingdom
Dear Dr. Houghton:
We congratulate you on the contributions you have been making to the assessment of
environmental implications of increasing greenhouse gases. Because we understand that
you are considering possible revisions of the analysis, we would like to offer a number of
comments on the chapter on sea level rise.
In 1985 the seven of us authored a National Academy of Sciences Report entitled
"Glaciers, Ice Sheets, and Sea Level: Effect of a CO2-Induced Climatic Change" which
provided perhaps the first comprehensive report on the possible contributions of
land-based ice to future changes of sea level. From that experience, we are very
sympathetic with the difficulties you face in attempting to develop low, medium and high
scenarios of sea level rise. Given the lack of sufficient observations and validated models
that describe how glaciers respond to changing climate, one must inevitably make
assumptions based on far less evidence than one would like.
We are pleased that in a number of ways, the IPCC report went beyond our 1985 report.
However, we are concerned by the conclusion that even in the worst-case scenario there
will be no positive Antarctic contribution to sea level change.
Our 1985 report included three glacial modeling efforts, two of which projected the
contribution from Antarctica to be less than 10 cm in the next century. The third study, by
Robert Thomas of NASA, however, suggested that the contribution from Antarctica was
likely to be 24 cm with a high scenario of about 80 cm and a worst case scenario of
220 cm. Considering all three modeling studies and the likelihood of increased snowfall
over Antarctica, we concluded that the contribution of Antarctica to global sea level
change by 2100 was likely to be between -10 and +100 cm, with values in the range 0
to 30 cm considered most likely. By contrast, the IPCC report appears to project an
Antarctic contribution of -10 to 0 cm by the year 2100 (calculated using the equations
on p. 276 and the temperature graph on page 190).
Our concern is that we do not believe there is any new evidence which justifies the implicit
IPCC conclusion that we can project the Antarctic contribution to sea level change much
more accurately now than we could in 1985. Specifically:
183
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(1) There seems to be no new evidence indicating that the Thomas study is necessarily
wrong. Certainly it relies on unproven assumptions, such as extrapolating data from a
single ice stream to the rest of the continental margin. But so the IPCC report could be
criticized; for example, although it takes great care in parameterizing large scale
meteorology and simulating frozen-bed ice dynamics, it does not realistically simulate the
wet-bed, sliding ice dynamics that dominate West Antarctica and parts of East Antarctica.
Moreover, IPCC equations imply that global cooling of a few degrees would cause glaciers
to retreat, in contradiction to empirical evidence. Also, note that Jenkins (1991) recently
estimated that a warming of even 0.6°C beneath the Ronne ice shelf could accelerate the
basal melt rate from a current value of 0.5 meters per year to 2.5 meters per year; by
contrast, Thomas' scenarios with 24-80 cm sea level rise were based on the assumption
that the increase in basal melt rates would be only one meter per year.
(2) Several new results support the hypothesis that the West Antarctic ice sheet has
a history of repeated rapid discharges. First, sea level records with increased temporal
resolution (e.g., at Barbados) suggest repeated periods of rapid sea level rise, for which
the only plausible mechanism would seem to be discharge of grounded ice. Second, the
sedimentary record in the seas around West Antarctica reveals repeated advances and
retreats of the ice sheet during the last 20,000 years. Third, diatoms collected under the
ice sheet 700 km from the present margin indicate that site was an open marine
environment at some time in the past 600,000 years, possibly during the previous
interglacial period; most of the West Antarctic ice sheet must have disappeared for marine
conditions to exist so far into the ice sheet interior. These results need to be considered
along with recent observations of large rapid changes in the flow of parts of the West
Antarctic ice sheet.
(3) No credible global climate model/ice sheet simulations have been carried out for
transient changes next century. Indeed, in view of possible nonlinearities of some ice sheet
processes with increasing global temperature, we do not believe we can reliably state the
sign of Antarctic contributions to sea level change for the full range of climate change
scenarios considered by IPCC.
In summary, although we do not have difficulty with a position that the Antarctic
contribution to sea level change in the next century is likely to be small, possibly negative,
we believe that there is still a large degree of uncertainty. We hope that this viewpoint can
be represented in the revised IPCC analysis.
Sincerely,
Mark F. Meier
David G. Aubrey James E. Hansen
Charles R. Bentley W Richard Peltier
Wallace S. Broecker Richard C. J. Somerville
184
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REFERENCING CONVENTIONS AND ACKNOWLEDGEMENTS
Referencing Conventions
Acknowledgements
This study does not attempt to provide a com-
prehensive review of the literature concerning the
processes that contribute to sea level. Chapters 1, 7,
8, and 9 only reference studies that were necessary
to support a particular assertion made in the text. In
Chapters 2 through 6, almost all of the studies refer-
enced were either sources of models that we used,
or analysis upon which we based particular assump-
tions. Thus, many important studies on
climatic, oceanic, and glacial processes are omitted
from this study solely because we did not use them
in conducting our analysis. The failure to provide a
reference for a specific insight or assumption does
not imply that this study is the first to publish the
particular idea.
Referenced studies are introduced using sever-
al different signals, depending on the extent to which
a study supports a particular proposition. When the
proposition in the text is clearly stated in the study
cited, no signal is used; we simply cite the study.
When the proposition is not directly stated in the
study, but is logically implied by what the study does
state, we introduce the study using the signal see.
When the proposition in the text is analogous to, but
different from, a proposition in the study cited, we
introduce the report using the signal cf. When the
proposition in the text is contradicted by a study, we
use the signal but see. When the proposition in the
text is undermined but not contradicted by a study
that reaches an opposite result on an analogous
issue, we introduce the study with but cf. When two
studies reach different results, and the reason for the
difference illustrates an assertion made in the text,
we introduce the two studies with the signals:
"compare with
-------
(University of Waikato, New Zealand) also examined
that initial draft and encouraged us to draw the dis-
tinction between a probability distribution that
includes uncertainty regarding future emission rates,
and a distribution that is conditional upon a particular
emissions policy.1 Richard Tol (Institute for
Environmental Studies, Amsterdam, The Netherlands)
reviewed the draft report, and suggested procedures
for incorporating random fluctuations in tempera-
tures. Richard Park (Abt Associates, Bethesda,
Maryland) and Vincent Pito (Maryland Department of
Natural Resources) reviewed the final report, shortly
before typesetting.
Several other people directly assisted this
effort. King Wayne Chan (Graphic Visions
Associates, Gaithersburg, Maryland) prepared all
the figures illustrating cumulative probability distri-
butions. Melodic Jackson (Technical Resources
International, Rockville, Maryland) copy edited
parts of the manuscript; Carlos Gonzales, Drayton
Hawkins, Jr. and David Cissel (TRI) reworked most
of the original figures for publication purposes.
Richard Wetherald (Geophysical Fluid Dynamics
Laboratory, Princeton, New Jersey) helped to formu-
late GFDL's assessment of the confidence that
should be attributed to the climate sensitivity range
of 1.5-4.5°C.2 Jim Fastook (University of Maine)
and Doug MacAyeal (University of Chicago) assist-
ed by providing models and data that we would have
liked to use, but which were unfortunately too com-
plex to be incorporated into our analysis.
We are also indebted to several people who
indirectly contributed to this effort. Patrick
Michaels (University of Virginia) provided early
encouragement for our use of the delphic approach
as a procedure for including the views of both
Chapter 7, "The Implications of Alternative Emission Rates".
Chapter 3A, "Expert Judgement, Climate Sensitivity".
"mainstream" climatologists and the so-called
"greenhouse skeptics." Steve Elgar (Washington
State University) and Richard Peltier (University of
Toronto) provided us with substantial insights con-
cerning the scientific community's difficulty in pro-
viding information oriented toward decision mak-
ing, as well as the tendency to view clearly-specified
probability distributions as being more subjective
than undocumented specifications of high and low
parameter values. John Topping (Climate Institute,
Washington, D.C.) was a continuing source of ideas
for possible uses of the information produced by this
report. William Cline (Institute for International
Economics) encouraged us to consider probabilities
and long time horizons.
In addition to the people who participated in
this study, we wish to acknowedge the contribution
of Technical Resources International, Incorporated
(Rockville, Md.). Based on a preliminary version of
this report drafted by EPA staff, TRI obtained or pro-
grammed all models used in.this report, carried out
the computations, produced all figures other than the
cumulative probability distributions, and copy-edit-
ed the final report.
Finally, we are grateful to William Nordhaus
(Yale University) and Gary Yohe (Wesleyan
University) for undertaking a Monte Carlo analysis
in 1983 concerning emission rates of carbon diox-
ide. We also thank John S. Hoffman, whose early
efforts to project sea level rise included 50 scenarios
based largely on expert opinion, and as such, were a
precursor for the analysis published herein. Without
the help of these people, as well as the continuing
support of EPA's Climate Change Division, this
report would not have been possible.
186
4U.S GOVERNMENT PRINTING OFFICE: 1995- 399 - 369 / 40169
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