SEPA
United States
Environmental Protection
Agency
Policy, Planning,
And Evaluation
(PM-221)
EPA-230-05-89-059
June 1989
The Potential Effects
Of Global Climate Change
On The United States
Appendix I
Variability
Printed on Recycled Paper
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THE POTENTIAL EFFECTS OF GLOBAL CLIMATE CHANGE
ON THE UNITED STATES:
APPENDIX I - VARIABILITY
Editors: Joel B. Smith and Dennis A. Tirpak
OFFICE OF POLICY, PLANNING AND EVALUATION
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, DC 20460
MAY 1989
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TABLE OF CONTENTS
APPENDIX I: VARIABILITY
PREFACE iii
ANALYSIS OF CLIMATE VARIABILITY IN GENERAL CIRCULATION
MODELS: COMPARISON WITH OBSERVATIONS AND CHANGES IN
VARIABILITY IN 2xCO, EXPERIMENTS 1-1
L.O. Mearns, S.H. Schneider, S.L. Thompson, and L.R. McDaniel
CHANGE IN CLIMATE VARIABILITY IN THE 21st CENTURY 2-1
D. Rind, R. Goldberg, and R. Ruedy
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PREFACE
The ecological and economic implications of the greenhouse effect have been the subject of discussion within
the scientific community for the past three decades. In recent years, members of Congress have held hearings
on the greenhouse effect and have begun to examine its implications for public policy. This interest was
accentuated during a series of hearings held in June 1986 by the Subcommittee on Pollution of the Senate
Environment and Public Works Committee. Following the hearings, committee members sent a formal request
to the EPA Administrator, asking the Agency to undertake two studies on climate change due to the greenhouse
effect.
One of the studies we are requesting should examine the potential health and environmental
effects of climate change. This study should include, but not be limited to, the potential impacts
on agriculture, forests, wetlands, human health, rivers, lakes, and estuaries, as well as other
ecosystems and societal impacts. This study should be designed to include original analyses, to
identify and fill in where important research gaps exist, and to solicit the opinions of
knowledgeable people throughout the country through a process of public hearings and
meetings.
To meet this request, EPA produced the report entitled The Potential Effects of Global Climate Change on the
United States. For that report, EPA commissioned fifty-five studies by academic and government scientists on
the potential effects of global climate change. Each study was reviewed by at least two peer reviewers. The
Effects Report summarizes the results of all of those studies. The complete results of each study are contained
in Appendices A through J.
Appendix Subject
A Water Resources
B Sea Level Rise
C Agriculture
D Forests
E Aquatic Resources
F Air Quality
G Health
H Infrastructure
I Variability
J Policy
GOAL
The goal of the Effects Report was to try to give a sense of the possible direction of changes from a global
warming as well as a sense of the magnitude. Specifically, we examined the following issues:
o sensitivities of systems to changes in climate (since we cannot predict regional climate change, we
can only identify sensitivities to changes in climate factors)
o the range of effects under different warming scenarios
o regional differences among effects
o interactions among effects on a regional level
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o national effects
o uncertainties
o policy implications
o research needs
The four regions chosen for the studies were California, the Great Lakes, the Southeast, and the Great Plains.
Many studies focused on impacts in a single region, while others examined potential impacts on a national scale.
SCENARIOS USED FOR THE EFFECTS REPORT STUDIES
The Effects Report studies used several scenarios to examine the sensitivities of various systems to changes in
climate. The scenarios used are plausible sets of circumstances although none of them should be considered to
be predictions of regional climate change. The most common scenario used was the doubled CO2 scenario
(2XCO2), which examined the effects of climate under a doubling of atmospheric carbon dioxide concentrations.
This doubling is estimated to raise average global temperatures by 1.5 to 4.5°C by the latter half of the 21st
century. Transient scenarios, which estimate how climate may change over time in response to a steady increase
in greenhouse gases, were also used. In addition, analog scenarios of past warm periods, such as the 1930s, were
used.
The scenarios combined average monthly climate change estimates for regional grid boxes from General
Circulation Models (GCMs) with 1951-80 climate observations from sites in the respective grid boxes. GCMs
are dynamic models that simulate the physical processes of the atmosphere and oceans to estimate global climate
under different conditions, such as increasing concentrations of greenhouse gases (e.g., 2XCO2).
The scenarios and GCMs used in the studies have certain limitations. The scenarios used for the studies assume
that temporal and spatial variability do not change from current conditions. The first of two major limitations
related to the GCMs is their low spatial resolution. GCMs use rather large grid boxes where climate is averaged
for the whole grid box, while in fact climate may be quite variable within a grid box. The second limitation is
the simplified way that GCMs treat physical factors such as clouds, oceans, albedo, and land surface hydrology.
Because of these limitations, GCMs often disagree with each other on estimates of regional climate change (as
well as.the magnitude of global changes) and should not be considered to be predictions.
To obtain a range of scenarios, EPA asked the researchers to use output from the following GCMs:
o Goddard Institute for Space Studies (GISS)
o Geophysical Fluid Dynamics Laboratory (GFDL)
o Oregon State University (OSU)
Figure 1 shows the temperature change from current climate to a climate with a doubling of CO2 levels, as
modeled by the three GCMs. The figure includes the GCM estimates for the four regions. Precipitation
changes are shown in Figure 2. Note the disagreement in the GCM estimates concerning the direction of
change of regional and seasonal precipitation and the agreement concerning increasing temperatures.
Two transient scenarios from the GISS model were also used, and the average decadal temperature changes
are shown in Figure 3.
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FIGURE 1. TEMPERATURE SCENARIOS
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Goddard Institute for Space Studies
Geophysical Fluid Dynamics Laboratory
Oregon State University
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FIGURE 2. PRECIPITATION SCENARIOS
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Goddard InstKut* lor Spac* Studies
Geophysical Fluid Dynamics Laboratory
Oregon State University
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1980s 1990s 2000s 2010s 2020s 2030s 2040s 2050s
TRANSIENT SCENARIO A
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TRANSIENT SCENARIO B
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FIGURE 3.
GISS TRANSIENTS "A11 AND "B" AVERAGE
TEMPERATURE CHANGE FOR LOWER 48 STATES
GRID POINTS.
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EPA specified that researchers were to use three doubled CO, scenarios, two transient scenarios, and an analog
scenario in their studies. Many researchers, however, did not nave sufficient time or resources to use all of the
scenarios. EPA asked the researchers to run the scenarios in the following order, going as far through the list
as time and resources allowed:
1. GISS doubled CO2
2. GFDL doubled CO2
3. GISS transient A
4. OSU doubled CO2
5. Analog (1930 to 1939)
6. GISS transient B
ABOUT THESE APPENDICES
The studies contained in these appendices appear in the form that the researchers submitted them to EPA.
These reports do not necessarily reflect the official position of the U.S. Environmental Protection Agency.
Mention of trade names does not constitute an endorsement.
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ANALYSIS OF CLIMATE VARIABILITY IN GENERAL CIRCULATION MODELS:
COMPARISON WITH OBSERVATIONS AND CHANGES IN
VARIABILITY IN 2xCO2 EXPERIMENTS
by
L. O. Mearns
S. H. Schneider
S. L. Thompson
and
L. R. McDaniel
National Center for Atmospheric Research
Boulder, CO 80397-3000
Grant No. DW49932663-01-0
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CONTENTS
FINDINGS 1-1
CHAPTER 1: INTRODUCTION 1-2
PURPOSE OF THE STUDY 1-2
REVIEW OF PRIOR WORK 1-2
CHAPTER 2: METHODS 1-5
DESCRIPTION OF THREE NCAR CCM VERSIONS 1-5
STUDY AREA AND OBSERVATIONAL DATA 1-6
VARIABLES ANALYZED AND COMPUTATIONAL METHODS 1-6
CHAPTERS: COMPARISON OF OBSERVED VS. CHERVIN CONTROL RUN DATA 1-8
SOLAR RADIATION 1-14
PRECIPITATION 1-14
INTERANNUAL VARIABILITY STATISTICS OF TEMPERATURE AND
PRECIPITATION 1-18
CHAPTER 4: INTERCOMPARISONS OF THREE CCM VERSIONS AND OBSERVED DATA . 1-29
COMPARISONS OF MEAN CONDITIONS: TEMPERATURE AND PRECIPITATION .. 1-29
RELATIVE HUMIDITY 1-29
DAILY VARIABILITY OF TEMPERATURE 1-35
DAILY PRECIPITATION VARIABILITY 1-39
CHAPTER 5: PILOT STUDY OF CONTROL VS. CO2 PERTURBED RUNS 1-48
CHAPTER 6: SUMMARY AND CONCLUSIONS 1-54
APPENDIX 1: STATISTICAL TESTS OF DIFFERENCES IN VARIANCE OF SURFACE
TEMPERATURE 1-56
APPENDIX 2: STATISTICAL TESTS OF DIFFERENCES BETWEEN INTERQUARTILE
RANGES 1-57
REFERENCES 1-58
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FINDINGS1
This study concerns analysis of climatic variability in general circulation models first to determine how
faithfully the models reproduce measures of the present variability and then to examine how variability changes
in COU perturbed cases. The control run output of three different versions of the NCAR Community Climate
Model (CCM) is examined for selected regions of the United States including the Great Plains, the Southeast,
the Great Lakes region, and the upper West Coast. Mainly temperature and precipitation are analyzed, but some
preliminary analysis of relative humidity and solar radiation is also included. Interannual variability is analyzed
in one version (the Chervin version) for only the present day climate. Results indicate that this version
underestimates the interannual variability of temperature, but generally successfully reproduces the relative
variability of precipitation. Two versions of the CCM tend to overestimate daily temperature variability while
the third (Dickinson version) accurately reproduces it or slightly underestimates it. Reasons for these differences
are discussed. Daily precipitation variability is overestimated by two model versions (Chervin and Dickinson)
but fairly well reproduced by the Washington version. The CO2 perturbed run of one version (Washington)
produces mixed results for changes in daily temperature variability and tends to produce increased variability for
precipitation.
'The authors thank Rick Katz for providing statistical assistance and for comments on an earlier draft
of this paper. This research was partially supported by the ILS. Environmental Protection Agency under Grant
No. DW49932663-01-0.
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CHAPTER 1
INTRODUCTION
PURPOSE OF THE STUDY
In considering the impacts of climatic change on society it is recognized that impacts accrue not only from
the relatively slow trend in the mean of a climate variable, but also from the attending shifts in the frequency
of extreme events. This issue has already received some attention in the literature (e.g., Schwarz, 1977; Parry,
1978; Mearns et al., 1984) where the non-linear relationship between changes in the mean and extreme events
has been underlined.
Given the importance of extreme events to climate impact analysis, it is most appropriate to analyze
changes in statistical moments which affect changes in the frequencies of extreme events. All moments could
be important in this regard, but as a starting point (or minimally) the mean and variance of time series of climate
variables should be considered.
In this study we analyze the first and second moments of climate variable time series from selected
observational stations and those produced by general circulation model (GCM)l control and perturbed runs. Our
goal is first to determine how faithfully different GCMs reproduce these measures of the present variability and
then to present a pilot study illustrating a method of investigation of variability changes in CO2 perturbed cases.
We believe that this type of research should become an essential part of standard GCM diagnostic analyses. This
is because the variability performance of a GCM is relevant not only to the credibility of its control climate
statistics, but also because it serves as a diagnostic of the validity of model physics, since it is often internal
physical processes that give rise to climate variability. By comparing the relative performance (i.e., model vs.
observations) of various versions of the NCAR CCM (i.e., versions with different physical parameterizations or
formulations), we can both help to determine what formulations maybe needed for forecasting certain measures
of variability and how much credibility to assign to those forecasts.
REVIEW OF PRIOR WORK
Studies comparing variability statistics of GCM generated time series of climate variables relevant to
climate impacts to observed time series are not numerous in the atmospheric sciences literature, although studies
first appeared in the early 1980s (e.g., Manabe and Hahn, 1981; Chervin, 1981). Here we review five of the
more recent and relevant works which address comparison of variability. Very often these studies also involve
a study of the change in variability under doubled CO2 conditions.
Of particular interest to the focus of the present study is Chervin's (1986) investigation of interannual
variability and climate prediction, since we use the 20-year history tapes from Chervin's study as one of the GCM
data sets in our present study. He designed a special version of the NCAR CCMO(A) (CCM = Community
Climate Model) with seasonal variations of sea surface temperatures (SSTs). No other measures of SST
variability were included in order to eliminate external (i.e., SST) variability of interannual time series of climate
variables in the hope that discrepancies between modeled and observed variability would reflect the external
component of variability present in the observed data. The additional variability attributed to external (SST)
boundary conditions is considered the "potential predictability" of the climate. The model was modified such that
external boundary conditions remained the same each date of each year of the 20-year model run. This entailed
the prescription of monthly sea surface temperatures and sea ice distributions. The variability of mean sea level
pressure and 700-mb geopotential height were analyzed in the Northern Hemisphere, with particular focus on
the United States. Comparisons were made using the F-test. Results indicated that there were no significant
differences between modeled and observed variabilities of mean sea level pressure over the United States and
only limited areas of differences in the variability of 700-mb geopotential height It should be noted, however,
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that Chervin's assignment of potential predictability regions depends on the assumption that processes responsible
for the internal variation of the atmosphere are correctly simulated by the model.
Bates and Meehl (1986) also used the CCM to investigate changes in the frequency of blocking events
on a global scale under doubled CO, conditions. Their version of the CCMO(A) included a seasonal cycle,
computed hydrology, and a simple mixed layer ocean. The dynamical equations were solved, as by Chervin
(1986), with a 15-wave resolution with model physics computed on a 4.5° latitude and a 7.5° longitude grid size.
The statistics of the 500 mb height field are examined as well as blocking events defined as persistent positive
height anomalies. Blocking events are strongly related to persistent surface temperature anomalies, such as
heat waves in the summer. Hence, changes in the frequencies of blocking events have significant implications
for changes in the frequencies of extreme temperature events. In comparing 10 years of modeled data with
observed data, they found that the model does a "reasonable" job of simulating 500-mb height standard
deviations, particularly in winter in both hemispheres. The model, however, produces too few extreme blocking
events. Under doubled CO- conditions, standard deviations of 500-mb height and blocking activity were found
to decrease in all seasons.
Two studies have recently been conducted on local or regional scales using the U.K. Meteorological Office
5-layer GCM. The treatment of radiation and land surface processes has been modified, including a full diurnal
cycle. The model has a quasi-uniform grid of 330 km resolution (i.e., the number of latitudinal grid boxes
decreases with increasing latitude). Reed (1986) analyzed observed vs. model control run results for one grid
point in Eastern England, and addressed the problem of creating the appropriate correspondence between the
model grid square and the spatial average of several observation points. He analyzed the mean and variance
of surface air temperature for a 3-year integration of model runs. Compared to observations, the model tended
to produce too cool temperatures and too high variability as measured by the standard deviation. For
precipitation the model produced too many rain days but underpredicted extreme rain events of greater than
20 mm/day.
More recently Wilson and Mitchell (1987) examined the modeled distribution of extreme daily climate
events over Western Europe using the same model. Comparisons were made of minimum surface temperatures
and precipitation. Again the model produced temperatures that were too cold, and hence, extreme minimum
temperatures were overestimated. This problem was most pronounced in grid boxes away from the coasts. The
model also produces too much precipitation in Western Europe, but does not successfully reproduce observed
highest daily totals. The number of rain days is also overestimated. They go on to examine changes under
quadrupled CO2 conditions and find that variability of temperature generally decreases, which, given the general
warming, means that there is a marked reduction in the occurrence of freezing temperatures. The authors
compare the changes in ultra-annual temperature variability using the more rigorous procedures of Katz (1984)
as well as using the more conventional F-test. Both tests indicate a significant decrease in winter temperature
variability. The authors emphasize the need to examine variables of importance to climate impact analysis and
also the importance of using a model that faithfully reproduces the present day climate in terms of means and
extremes.
Hansen et al. (1988) used the GISS model II general circulation model to simulate the global climate
effects of time-dependent variations of atmospheric trace gases and aerosols. Several different scenarios of trace
gas increase from 1958 to the present were used. A 100-year control run was also produced. From this run it
was determined that globally the model only slightly underestimates the observed interannual temperature
variability. However, the model's variability tends to be larger than observed over land. Among the calculations
made with output from the transient (i.e., progressive climate change from scenarios of increasing CO2) run were
changes in the frequencies of extreme temperature events. This was accomplished by adding the change in
temperature with climate warming predicted by the model to observed local daily temperatures. Hence the
authors assumed no change in variability in making these calculations. Results indicate that predicted changes
in the frequency of extremes beyond the 1990s at such locations as New York, Washington, and Memphis,
become quite large and would have serious impacts.
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The studies reviewed above indicate some important shortcomings of GCMs with regard to their ability
to faithfully reproduce observed variability statistics. Clearly more research is needed to further determine the
sensitivity of the models to changes in the physics, resolution, etc., with regard to the determination of variability.
Moreover, only one of these studies is explicitly concerned with variables of importance to climate impact
analysis. We propose here to respond to Wilson and Mitchell's comments (as well as those of Mearns et al.,
1984) regarding the importance of studying the higher moments of climate variable statistics, and of carefully
verifying the models' ability to reproduce observed variability on regional scales, as the necessary prerequisites
to rigorously analyzing possible changes in these statistics under doubled CO2 conditions.
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MATERIAL eetowes re-
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METHODS
DESCRIPTION OF THREE NCAR CCM VERSIONS
Given that all GCMs differ in their ability to accurately reproduce the many measures of observed climate,
it is useful to compare the simulation skill of different model versions against the present climate in order to
document the possible ranges of errors and to evaluate more fully the effects of model structure differences.
This study uses the output from control runs of three different versions of the NCAR Community Climate
Model (CCM). However, the version of Chervin (1986) is the primary one used for comparison of observed and
model control output (i.e., model runs to simulate the actual present day climate), since it has the longest time
integration (20 years) and thus carries less sampling error than shorter runs. Model versions of Chervin (1986),
Washington (Washington and Meehl, 1984) and Dickinson (Dickinson et al., 1986) are described below.
The "Chervin" version of the CCMO(A) model used is documented in Chervin (1986). The CCMO is a
spectral general circulation model originally developed by Bourke and collaborators (Bourke, 1974; Bourke et
al., 1977), which has been modified by the incorporation of radiation and cloud parameterization schemes. The
model has a resolution for physical processes of approximately 4.5° in latitude and 7.5° in longitude, and there
are nine levels in the vertical. The major modification of the model made by Chervin was the inclusion of an
annual solar cycle featuring identical, seasonally varying forcing each year. Identical forcing each year was
accomplished by prescribing for each month ocean surface temperatures and sea ice distributions. The soil
moisture in CCMO(A) is fixed at 25% of field capacity (which supplies evapotranspiration at only 25% of
potential), and cloudiness is predicted interactively as a function of internally generated moisture fields. Hence
we compare here, the present day control climate runs of models incorporating physics different from those of
the CCMO(A) version of Chervin (1986) investigated in Chapter III.
Two other versions of the CCM are used; what we will call the "Washington" version of CCMO(A)
(Washington and Meehl, 1984), which includes an interactive thermodynamic ocean and surface bucket hydrology,
and the "Dickinson" version (Dickinson et al., 1986), a modification of CCM1(B) containing a diurnal cycle and
the Biosphere-Atmosphere Transfer Scheme (BATS).
The Washington model closely resembles the Chervin version of CCMO(A), except for the treatment of
the hydrologic cycle and the mixed layer ocean. The Washington CCM is coupled to a simple fixed depth (50
m) thermodynamic ocean model which accounts for seasonal heat storage in the upper layer of the ocean. Thus
sea surface temperatures are predicted, not prescribed as in the Chervin version. The ocean model, however,
does not account for vertical or horizontal heat transport by the ocean. A simple interactive bucket hydrology
parameterization is implemented, wherein model-derived precipitation and evaporation rates are used to simulate
changes in runoff, soil moisture and snow cover. The albedo scheme for land is identical to that used by Chervin.
The Dickinson model is the most advanced in terms of modeling surface-atmosphere interactions. As a
version of CCM1 (Williamson et al., 1987), there are also fundamental differences in the vertical subgrid scale
heat transport parameterization and the radiative scheme of Dickinson's model and those of Washington and
Chervin. In the CCM1, there are substantial changes in the radiative scheme. The solar albedo parameterization
is improved, absorption by H2O and O2 of solar radiation is improved, and the CO, and ozone absorptance
models are changed. Condensation occurs at 100% relative humidity rather than at 80% relative humidity as
in CCMO. In addition, the BATS model of surface-atmosphere interactions is included (Dickinson, 1986). This
model calculates the transfers of momentum, heat, and moisture between the earth's surface and atmospheric
layers. It also determines wind, moisture, and temperature in the atmosphere, within vegetative canopies, and
at the level of surface observations. It includes a very detailed surface hydrologic scheme which accounts for
vegetation type and amount, water use by the vegetation, etc. Dickinson's version also includes a diurnal
radiation cycle, which requires accounting for soil heat capacity. The ocean-atmosphere interaction is handled
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as in Chervin's version, with fixed seasonally varying sea surface temperatures. Both Washington and Dickinson
runs available so far consist of 3-year integrations, which implies much greater sampling uncertainty than for
Chervin's 20-year run.
STUDY AREA AND OBSERVATIONAL DATA
The primary study area encompasses the area covered by three grid boxes located in the Great Plains (GP)
region of the United States (see Figure 1). Three grid boxes are used instead of one so that the sensitivity of
the spatial aggregation of the model, in terms of relative accuracy compared to observed data, could be examined.
Because the only variability in the sea surface temperatures (SSTs) of two of the three versions of the CCM
are seasonal changes, this reduces the total natural variability of atmospheric climate. These particular grid boxes
(I, II and m on Figure 1) were selected because they are located well inland and in fairly homogeneous terrain
east of the "Rocky Mountains" in the model. Therefore, we anticipated this location to be less affected by
oceanic influences or regional topography than most other UJS. locations; the grid boxes also correspond to the
major wheat growing areas of the United States.
Three other grid boxes are also included in the analysis to represent other regions of the United States:
one in the southeastern US. (SE), one in the Great Lakes region (GL), and one on the northern west coast
(WC). These are also indicated on Figure 1.
Real data corresponding to each grid box were generated from the average of six observation stations for
time series of temperature and precipitation (NCAR, daily surface observations DS. 510). Solar radiation and
relative humidity real data were taken from one SOLMET observation station (data available from the National
Climate Data Center, Asheville) located in or near each grid box, except for the SE grid where two Solmet
stations were used. Figure 1 shows the location of all observation stations and grid boxes.
VARIABLES ANALYZED AND COMPUTATIONAL METHODS
Four variables deemed particularly relevant to climate impact analysis were chosen for this analysis: daily
mean surface air temperature, daily total 'precipitation, mean daily surface relative humidity, and daily mean
absorbed solar radiation at the surface. The model time series consisted of 20 years of data generated from the
Chervin GCM experiment, three years from the Washington experiment and three years from the Dickinson
experiment. For the Chervin and Washington models daily mean temperature is calculated as the average of
two 12-hour samples. For the Dickinson model, both maximum and minimum daily temperatures are available
from model output, and these are averaged to produce daily average values.
The 20-year observational data set for temperature and precipitation included the years 1949-68. Observed
mean daily temperatures were calculated as the average of daily maximum and minimum temperatures. The
observational data set for solar radiation and relative humidity covered 18 years (1958-1976), except at the WC
grid where only 10 years of observational data were available. Only absorbed, not incident surface radiation is
available from the models'output, so observed incident solar radiation was converted to absorbed by multiplying
by 1.0 - a, where a is the appropriate surface albedo value prescribed for land surfaces in the Chervin model
Only solar radiation results from the Chervin model are discussed in this paper. Observed relative humidity was
calculated from surface dew point and air temperature data using polynomial algorithms to determine actual and
saturation vapor pressure (Lowe, 1976).
For the Great Plains region, the analysis of time series is conducted on two different spatial scales: analysis
of each grid box individually, and analysis of the spatial mean derived from the average across the three grid
boxes (the latter referred to as "grand spatial means"). Analysis of the other three regions is conducted only on
the individual grid level.
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•Temperature and
Precipitation Stations
o Relative Humidity and
Radiation Stations
Figure 1. Model grid cells and station locations.
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CHAPTERS
COMPARISON OF OBSERVED VS. CHERVIN CONTROL RUN DATA
Figure 2 displays the time series of daily average temperature for modeled (Chervin) and observed data for
the four regions under investigation. The value plotted for each day for the modeled data consists of the
average on that day (cosists of the average of two 12-hour samples on the history tapes) over 20 years. For the
GP region an average is taken over the three grids. Observed data consist of the same except that six observation
stations make up the equivalent of each grid box. The daily observed temperature at each observation station
is calculated as the average of the recorded maximum and minimum daily temperatures.
It is evident from Figure 2 that, overall, the model simulates the annual cycle for the four regions fairly
well. There are regional differences, however. In the GP region the model annual range is slightly smaller than
that of the observed time series (Figure 2a), whereas in the GL region (Figure 2b) the model annual range is
greater. The least successful simulation is that for the SE grid (Figure 2c), where winter minima are too high
by about 7°C. Note that in the GP region, the model falls slightly short of attaining the appropriate maximum
temperatures in summer.
The most successful simulation is found at the WC grid (Figure 2d). This result is somewhat problematic,
since, of the four grids, WC has the greatest topographic variation, which is only crudely represented in the
CCM. It may be the case that the six particular observation stations chosen to represent the area luckily cancel
out the effect of topographic irregularity in the data. Perhaps more likely, the specified observed, and seasonally
varying sea surface temperatures (SSTs) impose a major oceanic effect on the climate of this ocean bordering
grid point.
Figure 3 displays histograms for modeled vs. observed temperature data for four key months for the GP
region (all three grids). The histograms are formed by including each day's observation at each grid point for
each year as a data point. Hence for January, the histogram contains 1860 observation points for the modeled
data (60x31). The histograms for January and April show generally good agreement between the modeled and
observed data. The distributions are very similar (approximately normal), although the modeled data tend to
be slightly too warm and have too wide a spread. In July the narrowing of distributions (both observed and
modeled) becomes evident. This seasonal change in daily variance is well simulated by the model, a gratifying
result. The transition month of October again shows good agreement between modeled and observed data as
the distributions widen again. Agreement in November and December (not shown) is also good, although the
modeled data again become slightly too warm, and the model distributions are also a little too wide.
Additional analyses were performed by comparing histograms from each of the three grids of the GP region
(histograms not shown). Preliminary results suggest that for January through March Grid I model data compare
well with observed data, but discrepancies are found at Grids n and III (model data are too warm). In
November and December at Grids I and II, the model histograms have long left tails (i.e., too many cold
extremes are produced). At Grid HI, too wide a distribution and too many warm events are evident. This is
all to say that the spatial aggregation over three grids mitigates discrepancies between model and observed
results and that the nature of departures from the observed distributions are not consistent among the three
grids malting up the spatial average.
Figures 4 and 5 present selected temperature histograms (for 4 months) for the GL and SE grids
respectively. At the GL grid, the model distributions are flatter and wider than those for observed data in the
winter and fall months, which indicates that both warm and cool extremes are over-represented by the model.
'However, in the spring and summer, the distributions (observed vs. model) are quite similar. At the SE grid the
observed and model distributions are similar in most months, except for winter months, when the model
distribution departs from that of the observed. Yet the model distribution widths are not dissimilar from those
of the observed in winter months. The good agreement of modeled and observed temperatures at the WC grid
is seen in Figure 6. Note the lower variability (indicated by narrower histograms) at this location in modeled
1-8
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GP123
GTLAKES
(L.
35
30
25
20
15
10
5
0
-5
-10
-15
-20
OBSERVED DATA
— MODELED DATA
60 120 180 740 300 360
SOEAST
35
30
25
20
15
10
5
0
-5
-10
-15
20
OBSERV£D DATA
MODEL DATA
60
c.
180 240
DAYS
300
3GO
35
30
25
20
15
10
5
0
-5
-10
-15
-20
35
30
25
20
15
°C JO
5
0
-5
-10
-15
-20
a.
OBSERVED DATA
MODEL DATA
ttfT
L
nji riTM'ti 111111 ii riTrriMMJ trm 111 ii n i
OBSERVED DATA
MODEL DATA
60
120
180 240
DAYS
Figure 2. Average temperature for a 20-year average year, Chervin model vs. observed for the four regions.
60 120 180 240 300 360
WCOAST
300 360
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75
60
45
30
15
The Percentoge of Events for the Intervals
± 2.5C" from the given Temp.
Three US Grids Stacked 20 Years per Grid
| OBSERVED
@ CHERVIN
JANUARY
_fel
-30 -20 -10
10 20 30 40
75
60
45
30
15
The Percentage of Events for the Intervals
± 2.5C" from the given Temp.
Three US Grids Stocked 20 Years per Grid
| OBSERVED
0 CHERVIN
APRIL
-30 -20 -10
10 20 30 40
75
60
45
30
15
| OBSERVED
0 CHERVIN
JULY
-30 -20 -10
0
CC)
10 20 30 40
(*)
75
60
45
30
15
| OBSERVED
@ CHERVIN
OCTOBER
Q __. - — - -p" ""-'
-30 -20 -10 0 10 20 30 40
(•C)
Figure 3. Histograms of daily temperature (°C) (20 years) for the three GP grids, four selected months.
1-10
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100 r
80
60
The Percentage of Events for the Intervals
± 2.5C° from the given Temp.
For the GTLAKES Grid, 20 years of data
20
OBSERVED
CHERVIN
JANUARY
-30 -20 -10
100 r
80
60
40
20
| OBSERVED
g CHERVIN
JULY
30 40
-30 -20
10 0
(•c)
10 20 30 40
100 r
80
60
40
20
The Percentage of Events for the Intervals
± 2.5C" from the given Temp.
For the GTLAKES Grid, 20 years of data
100
80
60
40
20
| OBSERVED
H CHERVIN
APRIL
-30 -20 -10 0 10
CO
. ' I OBSERVED
@ CHERVIN
OCTOBER
20 30 40
-30 -20 -10 0 10 20 30 40
CC)
Figure 4. Histograms of daUy temperature (°C) (20 years) for the GL grid, 4 selected months.
1-11
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100
80
60
40
20
The Percentage of Events for the Intervals
± 2.5C" from the given Temp.
For the SOEAST Grid. 20 years of data
| OBSERVED
0 CHERVIN
JANUARY
-30 -20 -10 0 10 20 30 40
(X)
100
80
60
40
20
@ CHERVIN
JULY
1 1 1 1 1 1
I
I
5
\
\
'^
'
-30 -20 -10 0 10
CO
20 30 40
(X)
100
80
60
40
20
The Percentage of Events for the Intervals
± 2.5C° from the given Temp.
For the SOEAST Grid. 20 years of data
|OBSERVED
CHERVIN
APRIL
100
80
60
40
-30 -20 -10 0 10 20 30 40
CO
| OBSERVED
0 CHERVIN
OCTOBER
•30 -20 -10 0 10 20 30 40
CO
Figure 5. Histograms of daily temperature (°C) (20 years) for the SE grid, 4 selected months.
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100 r
80
60
40
20
The Percentage of Events for 1he Intervals
± 2.5C° from the given Temp.
For fhe WCOAST Grid, 20 years of data
| OBSERVED
g CHERVIN
JANUARY
-30 -20 -10
0
(•C)
10 20 30 40
(X)
100 r
80
60
40
20
The Percentage of Events for the Intervals
± 2.SC* from the given Temp.
For the, WCOAST Grid, 20 years of data
| OBSERVED
B CHERVIN
APRIL
-30 -20 -10 0
CC)
10 20 30 40
(*)
100
80
60
40
20
100 r
| OBSERVED
0 CHERVIN
JULY
-30 -20 -10 0
CO
10 20 30 40
(X)
80
60
40
20
1 •OBSERVED
B CHERVIN
OCTOBER
-30 -20 -10 0 10 20 30 40
CO
Figure 6. Histograms of daily temperature CC) (20 years) for the WC grid, 4 selected months.
1-13
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and observed values compared to those at the other three locations. This reflects the lower variability expected
of a West Coast location resulting from the moderating oceanic influence and prevailing westerly wind. The
seasonal decrease in variability from winter to summer is again well simulated. However, the model slightly
overestimates the variability in the spring and fall as indicated by the wider model histograms for April and
October.
Possible explanations about the discrepancies (e.g., why this version of the model is too warm in winter and
too cold in summer in the GP region grids) will be offered later on.
SOLAR RADIATION
Solar radiation is relevant both for crop impact assessments and as a diagnostic of model-predicted
cloudiness. The daily average time series for absorbed solar radiation (model and observed) for the four regions
are presented in Figure 7. In the GP region the annual cycle is fairly well simulated but there are significant
departures of the modeled values from observed for March-May (day 60-day ISO) and September-November.
In both periods model values are too high. Similarly, at the GL grid, the model values are too high during most
months except for late summer. The poorest comparison is seen at the SE grid, where the model consistently
overestimates absorbed solar radiation in all months, which is consistent with the excessively warm temperatures
seen on Figure 2c. At the WC grid, the summer maximum is well simulated but winter minimum values are
too high so that the annual cycle of solar radiation is underestimated.
The selected monthly histograms for the GP region reflect overestimation of the amount of surface solar
radiation (Figure 8). In examining these histograms it should be recalled that comparison with observed values
for solar radiation and relative humidity are more problematic than for temperature and precipitation, since only
one observation station is used to represent each grid. Hence, the comparisons here should be made with some
caution. In general for the GP region, the modeled solar radiation values in each month, in addition to being
too high, have a narrower distribution than the observed values, and hence daily variability is underestimated.
The overall distribution shapes (model vs. observations) are rather dissimilar for most months, the greatest
discrepancy in distribution being seen in January although sampling considerations limit the confidence in
quantitative inferences). The narrowing range of values from summer to winter seen in the observations is well
reproduced by the model.
Of particular interest are conditions in spring (e.g., April on Figure 8) when modeled solar radiation is
frequently too high compared with observations. This suggests that cloudiness is too low. A possible explanation
for this arises from the fixed soil moisture in the model. In reality in spring the soil moisture content is usually
high, whereas the model soil moisture content is fixed at 25% of field capacity. This too low soil moisture will
limit evaporation and hence could result in an underestimation of cloud amount, which leads to an overestimation
of surface absorbed solar radiation. Moreover, possible overestimation of evaporation in summer (when soil
moisture can be less than 25% saturated) could also lower surface temperature by local cooling hi the form of
latent heat Of course more fundamental problems with large scale cloud parameterization schemes undoubtedly
also'contribute to the errors. Further analysis will be necessary to confirm these speculations.
At the other three grids (histograms not shown) (aside from the overall direction of error, too high or too
low) there are no striking contrasts hi the distributions, which suggests that the seasonal cycle of dairy variance
of solar radiation is qualitatively well represented by the model at these locations, even though there are
significant discrepancies in mean values.
PRECIPITATION
The most perplexing direct comparison of Chervin model and observed values occurs with precipitation.
The time series of average daily total precipitation for the four regions, displayed in Figure 9, clearly indicate
a substantial discrepancy between model and observations. Daily model absolute values at the U.S. grid points
1-14
-------
GP123
GTLAKES
_w
"5
500
400
300
200
100
500
400
300
200
100
OBSERVED
CHERV1N
OBSERVED
CHERVIN
60 120 180 240 300 360
SOCAST
w
-t—
"5
500
400
300
200
100
OBSERVED
CHERVIN
60 120 180 240 300 360
WCOAST
500
400
300
200
100
OBSERVED DATA .
MODEL DATA
60 120 180 240 300 360
DAYS
60 120 180 240 300 360
DAYS
Figure 7. Average daily absorbed solar radiation (18-year average), Chervin model vs. observed for the four
regions.
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100
The Percenloge of Events for the Intervals
± 25 Watts/m> from the labeled value
GP123 Grids, 18 Years of Data, with ADJ
JANUARY
• OBSERVED
123 CHERVIN
100
80
60
40
20
0L
25 75 125 175 225 275 325 375 425 475
(WaUs/m>)
JULY
• OBSERVED
^ CHERVIN
' •—l
25 75 125 175 225 275 325 375 425 475
(Watls/nv)
100
SO
(*)
60
40
20
The Percentage of Events for the Intervals
± 25 Watls/m> from the labeled value
GP123 Grids, 18 Years of Data, wilh ADJ
APRIL
OBSERVED
CHERVIN
100
80
60
40
20
25 75 125 175 225 275 325 375 425 475
(Watts/mO
OCTOBER
• OBSERVED
EH CHERVIN
25 75 125 175 225 275 325 375 425 475
(Watts/mO
Figure 8. Histograms of daily absorbed surface solar radiation for the three GP grids, four selected
months.
1-16
-------
mm
30
25
20
15
10
5
mm
15
10
GP123
OBSERVED
CHERVIN
60 120 180 240 300 360
SOEAST
OBSERVED
CHERVIN
360
GTLAKES
30
25
20
15
10
OBSERVED
CHERVIN
WCOAST
mm
30
25
20
15
10
5
0
OBSERVED
CHERVIN
60 120 180 240 300 360
60 120 180 240
DAYS
300
360
Figure 9. Average total daily precipitation for a 20-year average, Chervin model vs. observed, for the four
regions.
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\
are often three times greater than observed values, even though modeled global average precipitation amount
is close to the observed value of 5 mm/day. At the GP (average) grid the discrepancies seem to be worst in late
summer ~ the time we have speculated that excess evaporation from fixed soil hydrology would be most
serious. The annual cycle of precipitation is much better represented in that high precipitation values dominate
in the summer in both the observed and simulated series. The observed series for the GL and SE grids exhibit
no clear seasonal cycle, although there is a slight cycle similar to that of the GP region at the GL grid in the
model time series. At the WC grid the observed seasonal cycle of high winter and low summer precipitation
is well matched by a parallel (although greater in amount) simulated series.
Figures 10-13 present probability functions for total precipitation aggregated on a seasonal basis for the four
regions. The graphs also include table inserts displaying the relative percentages of rain days and percentage of
days with precipitation rates exceeding 20 mm/day. A rain day is defined as a day which receives greater than
0.1 mm of precipitation. At GP and SE the simulations consistently result in an over estimation of raindays,
although the discrepancy is most severe in the fall (Figures lOd and 12d) and is relatively minor in the spring.
At the GL grid, however, the model slightly underestimates raindays in the winter and fairly accurately
represents raindays for the other seasons. These anomalous results could be due to a number of factors,
including too much soil moisture in the fall in the Great Plains, or model structural factors such as the absence
in the model of mesoscale features such as the Great Lakes or spectral truncation errors in the water vapor field
In regard to the GL grid, added moisture and precipitation events which result from atmospheric interaction
with the Jakes, cannot be modeled. Perhaps, the good results for three of the four seasons at GL are due to
the cancelling of one type of model bias (too much local precipitation) with another (absence of lake influence).
At the WC grid (Figure 13), although percentage of raindays is overestimated, the relative percentages across
the four seasons are well reproduced. •
The probability functions are truncated just below 20 mm/day on the figures, but the percentage of
occurrences of extreme values (greater than 20 mm) is given by the table on the figure. In all seasons in all four
regions the model produces large numbers of precipitation events exceeding 20 mm/day, (e.g., from 15% in
the summer to 4% in winter at the GP region; observed percentages for the GP region range from 0.8 in summer
to 0.0 in the winter).
The best agreement for overall shapes of the density functions occurs for the GP region, where the best
matches are found in spring and-summer. -At the GL grid precipitation events up to five mm/day are
underestimated in most seasons. At the SE grid the model curves do not fall off as quickly as do the observed
curves, particularly in spring and fall. In most seasons at most locations, the model generates too few low
precipitation events (the first interval, 0.1-1.0 mm). This is particularly true for winter at the GL grid (Figure
lla). However, at the WC grid in summer, the model overpredicts all precipitation amounts including the lowest
amount category, as it does at the SE grid in all seasons but summer. Of course, this is consistent with the
overall tendency to simulate too much absolute precipitation at these grid points.
We believe it is important to track down the reasons why the precipitation amounts are so high in the model
in these four regions. Perhaps the'pretipitation parameterization criterion of 80% relative humidity in the model
for precipitation is too low so that there is too much precipitation. Also, the fixed soil hydrology could well be
responsible for overestimating evaporation and relative humidity, especially in late summer. This needs to be
tested by analyzing other grid points, other variables and other versions of the CCM with different physical
parameterizations. It may also be necessary to test other GCMs (especially those without spectral advection
of water vapor) or CCM versions where water vapor is treated by non-spectral formulations since we suspect
that spectral truncation of a heterogeneous field like water vapor could result in anomalously extreme
precipitation events.
INTERANNUAL VARIABILITY STATISTICS OF TEMPERATURE AND PRECIPITATION
Tables 1-5 present statistics on interannual variability for temperature and precipitation for the four
regions of analysis. Table 1 presents these for annual mean temperature and annual total precipitation for the
1-18
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The % of Events Greater Than .1mm The % of Events Greater Than .1mm
Bob Chen/in History Tapes Bob Chervin History Tapes
Three US Grids 20 Years Per Grid (STACKED) Three US Grids 20 Years Per Grid (STACKED)
Parameter
X of Rein Deyi
Maximum Volu« (mm)
X CT 20mm
OBSERVED
CHERVIN
PeremcUr OBSERVED CHERVIN
X of Rain Ooyi , , SB 71
Maximum Volu« (mm) 32.64 128.94
X CT 20mm 0.3 10.1
30
25
20
15
10
5
0
WINTER
OBSERVED
CHE"RVIN
5 10 15 20
mm / Day
30
25
20
15
10
5
0
SPRING
OBSERVED
CHERVIN
5 10 15
mm / Day
20
Parameter
X al Rein Day* ,
Uaxlmum Value (mm)
X CT 20mm
OBSERVED CHERVIN
37.55 167.5*
0.8 15.1
Porom.Ur OBSERVED CHERVIN
X of Rain Day* 40 67
Uaxlmum Valui (mm) 45.13 151.47
X GT 20mm 0.5 8.4
30
25
20
15
10
5
0
SUMMER
OBSERVED
CHERVIN
5 10 15 20
mm / Day
FALL
OBSERVED
CHERVIN
5 10 15
mm / Day
20
Figure 10. Probability functions of precipitation for the three GP grids, Chervin vs. observed for four seasons.
1-19
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The % of Events Greater Than .1mm
Bob Chervin History Tapes
GTLAKES US Grid, 20 Years of data
OBSERVED
Parameter
X of Rain Day* ,
Maximum Value (mm)
X CT 20mm
CHERVTN
30.44 86.40
0.2 11.4
The % of Events Greater Than .1mm
Bob Chervin History Tapes
GTLAKES US Grid, 20 Years of data
OBSERVED
Parameter
X of Rain Day*
Maximum Value (mm)
X CT 20mm
CHERVIN
'4*
40
35
30
25
20
15
10
5
0
WINTER
OBSERVED
CHERVIN
5 10 15 20
mm / Day
40
35
30
25
20
T5
10
5
0
SPRING
• OBSERVED
- CHERVIN
5 10 15 20
rnm / Day
Fn±r*., , ""H"
Maximum Value (mm) 41.99
X CT 20mm 0.3
Parameter
X of Rain Dan , v
Maximum Value (mm)
X CT 20mm
OBSERVED
CHERVIN
oo
40
35
30
25
20
15
10
5
0
SUMMER
- OBSERVED
- CHERVIN
5 10 15 20
mm / Day
40
35
30
25
20
15
10
5
0
FALL
OBSERVED
CHfRVIN
5 10 15 20
mm / Day
Figure 11. Probability functions of precipitation GL grid, Chervin vs. observed for four seasons.
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The % of Events Greater Than .1mm
Bob Chervin History Tapes
SOEAST US Grid, 20 Years of data
Poram.t.r OBSERVED CHERVIN
J5 of Rain Days S3 88
Maximum Value (mm) 41.36 133.02
Z 6T 20mm 3.0 10.0
The % of Events Greater Than .1mm
Bob Chervin History Tapes
SOEAST US Grid, 20 Years of data
Poram«l»r
X of Rain Oar* . .
Maximum V
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Mearns
The % of Events Greater Than .1mm
Bob Chervin History Tapes
WCOAST US Grid, 20 Years of data
Pcrom«l«r
X of Rain Days
Mcximum Volu* (mm)
X CT 20mm
OBSERVED CHERVIN
66 78
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Table 1. Great Plains (GP) Grids Average and Individual Grids -- Mean and
Variance Statistics For Annual Mean Temperature and Annual Total
Precipitation
Observations
Simulation
A.
T
P
B.
Grid
T
P
Grid
T
P
Grid
T
P
T -
P -
SD -
CV -
Mean
SD CV
Mean
SD CV
GRAND SPATIAL MEANS
8.89
558.9
0.72
80.6 14.4
8
2452
.93
.0
0.39*
283.0 11.6
INDIVIDUAL GRIDS
I
5.43
373.0
II
8.46
577.9
III
12.78
725.7
1.05
56.74 15.2
0.70
90.40 15.6
0.71
160.90 22.2
3
2619
9
2040
13
2690
.43
.1
.99
.2
.36
.8
mean temperature (°C)
total precipitation (mm)
standard deviation (°C)
coefficient of variation (%) . (Calculate<
0.55*
343.1 13.1
0.41*
399.1 19.5
0.42*
447.8 16.6
i only for precipitation).
temperature variances of model and observed data are significantly (0.05
level) different on the F-test.
1-23
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Table 2. Great Plains (GP)
Average Grids and Individual Grids -- Mean and
Variance Statistics for Seasonal Mean Temperature and Seasonal Total
Precipitation
Observations
Mean SD CV
A. GRAND SPATIAL MEANS
1. Winter (D.J.F)
T -5.14 1.64
P 59.7 16.. 2 27
2. Summer (J,J,A)
T 22.2 0.89
P 227.1 39.0 17
B. INDIVIDUAL GRIDS
1. Winter (D.J.F)
Grid I
T -9.5 2.8
P 42.2 10.2 24
Grid II
T -6.2 1.6
P 55.8 20.1 35
Grid III
T 0.35 1.1
P 81.3 29.4 36
2. Summer (J,J,A)
Grid I
T 19.4 1.0
P 161.8 42.7 26
Grid II
T 22.3 1.0
P 243.0 37.0 15
Grid III
T 24.9 1.2
P 276.9 79.6 28
T - mean temperature (°C)
P - total precipitation (mm)
SD - standard deviation (°C)
CV - coefficient of variation
* — temoerature variances of 1
Simulation
Mean SD CV
-4.2 1.2
.3 354.9 76.5 21.5
20.7 0.42*
.2 930.3 176.7 19.0
-10.7 1.5*
.0 267.3 88.5 33.1
-3.7 1.2
.8 255.4 74.7 29.3
1.7 1.3
.2 541.8 156.9 28.9
16.3 0.47*
.5 737.4 261.5 23.0
22.1 0.55
.2 775.0 184.4 23.8
23.8 0.14*
.7 877.7 318.5 36.3
(%) . (Calculated only for precipitation) .
model and observed data are sienificantlv (0.05
level) different on the F-tes*.
1-24
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Table 3. Great Lakes (GL) Grid -- Mean and Interannual Variance Statistics
For Annual and Seasonal Mean Temperature and Total Precipitation
Observations
Mean £D CV
ANNUAL
T 9.0 0.59
P 887.4 101.1 11.4
SEASONAL
Winter (D,J,F)
T -3.1 1.6
P 187.2 46.1 24.6
Summer (J,J,A)
T 20.5 0.88
P 254.9 32.6 12.8
Simulation
Mean SD £V
9.3 0.63
3345.4 336.7 10.1
-6.6 2.2
640.0 127.0 19.8
22.8 0.71
1105.4 269.7 24.4
T - mean temperature (°C)
P - total precipitation (mm)
SD - standard deviation (°C)
CV - coefficient of variation (%). (Calculated only for precipitation).
Table 4. Southeast (SE) Grid -- Mean and Interannual Variance Statistics For
Annual and Seasonal Mean Temperature and Total Precipitation
Observations
Mean SD CV
ANNUAL
T 16.6 0.58
P 1137.2 136.3 12.0
SEASONAL
Winter (D.J.F)
T 7.4 1.8
P 293.2 59.2 20.2
Summer (J,J,A)
T 25.5 0.73
P 317.0 54.2 17.1
T - mean temperature (°C)
P - total precipitation (mm)
SD - standard -deviation (°C)
CV - coefficient of variation (%) .
* — temoerature variances of mode'
Simulation
Mean SD CV
20.0 0.37
3085.5 305.7 9.9
14.1 1.0*
739.8 130.1 17.6
25.9 0.38*
786.4 203.9 25.9
(Calculated only for precipitation) .
L and observed data are si^nifieantlv fO.05
level) different on the F-test.
1-25
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Table 5. West Coast (WC) Grid -- Mean and Interannual Variance Statistics For
Annual and Seasonal Mean Temperature and Total Precipitation
Observations
Mean Sfi CV
ANNUAL
T 10.1 0.49
P 553.2 93.43 16.9
SEASONAL
Winter (D.J.F)
T 2.6 1.6
P 254.1 76.7 30.2
^ifipgr (J,J,A)
T 18.1 0.81
P 39.4 20.5 52.1
T - mean temperature (°C)
P - total precipitation (mm)
SD - standard deviation (°C)
CV - coefficient of variation (%) .
* — temoerature variances of model
Simulation
Mean jJfi CV_
10.1 0.46
1792.8 296.1 16.5
2.42 0.8*
723.8 199.6 27.6
17.7 0.17*
192.6 45.7 23.7
(Calculated only for precipitation) .
and observed data are sienificantlv (0.05
level) different on the F-test.
1-26
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GP region averaged for the three grids (referred to as grand spatial means on the table) and for the
threeindividual grids. Table 2 presents the same but for winter and summer seasonal values rather than annual
values. Tables 3, 4, and 5 present annual and seasonal values for the GL, SE, and WC grids, respectively. The
GP region is discussed first, where the effect of spatial aggregation is analyzed.
It can be seen from Table 1 that the grand spatial mean annual average modeled and observed temperatures
are very close in value, but that the variability (indicated by the standard deviations) of the modeled data is lower
than that of the observed data (significantly lower at the 0.05 level on the basis of the F-test for equality of
variances). Modeled results for precipitation clearly show the tremendous over estimation of total amounts (off
by up to a factor of five), but the relative variability (indicated by the coefficient of variation) is similar to that
of the observed data. This may be fortunate if it means that a simulation error in the absolute amount of
precipitation would not imply an error in model sensitivity to climatic forcing.
This remains to be investigated.
Values for the individual three grids show results qualitatively similar to those for the grand spatial means.
Mean temperatures are within one or two degrees C of observed values, and standard deviations within 0_5°C
of the observed. However, the direction of model error is not the same at all three grids. At Grid I the model
is cooler than the observations. Moreover, the errors of the individual grids are larger than those of the three
grid aggregation. Again, the modeled variability is significantly less than that of the observed data. The statistics
of precipitation for each grid reflect the direction of error inconsistency seen in the temperature statistics, i.e.,
two grids underestimate precipitation variability. while the third overestimates it.
Looking at seasonal values for the grand spatial means of temperature and precipitation (Table 2), it can
be seen that seasonal temperatures for winter and summer are well simulated, although the model is slightly too
cool in the summer. Decreases in variability from winter to summer are well simulated for both temperature
and precipitation. Again, this may be a good sign for forecasting climatic changes even if means are somewhat
in error.
The seasonal statistics for each grid square of the GP region are of course less similar (modeled and
observed) than for the averaged grid values, but the values are still quite close. The direction of error, however,
is not the same at each grid square. In winter, for example, the simulated temperature is slightly too cold at
grid I but slightly too warm at grids II and III. Again the model variability of temperature, indicated by the
standard deviations, is slightly lower than that of the observed temperatures, at all three grids for both summer
and winter.
Although we deliberately chose an eastern slope midcontinental region without much sub-grid scale spatial
heterogeneity as the primary area of analysis to minimize the anchoring effect of oceanic temperatures or
mesoscale effects of topography, it is still likely that model variability may be slightly lower because Chervin's
(1986) control run was designed to exclude variability of oceanic surface temperatures.
At the GL grid (Table 3) the annual model temperature is quite accurate compared to observed as is the
temperature variability (no significant difference according to the F-test at the 0.05 level). The relative variability
of precipitation (indicated by the coefficient of variation) is also very accurate. In winter, although the model
mean temperature is too low, the variability of temperature is relatively similar to that of the observed data The
variability of precipitation is also quite similar. In summer the model is slightly too warm, but the variability of
temperature is again well reproduced. The variability of precipitation, however, is overestimated by the model.
Note that the seasonal compensating errors in mean temperature account for the model's (ostensible) accuracy
in reproducing the annual mean temperature.
At the SE grid (Table 4) the model overestimates the mean annual temperature by 3.4°C, whereas the
variability is relatively well simulated (not significantly different at the 0.05 level). Precipitation, as has
consistently been the case, is overestimated, but the variability of precipitation is reasonably well reproduced,
the coefficient of variation being 12.0% for observed data and 9.9% for the model. The seasonal statistics
indicate that the error in the annual mean temperature value of the model is a result of the very high error in
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reproducing the winter mean temperature (Table 4). The temperature variance is fairly well simulated, but is
less than that of the observations. The simulation of the variability of winter precipitation is again relatively
accurate. In summer, the model variability of temperature is again less than the observed, whereas the variability
of precipitation of the model is higher than observed.
At the WC grid (Table 5) the model accurately reproduces the mean and standard deviation of temperature
and the variability of precipitation on an annual basis. However, temperature variability is underestimated in
both winter and summer. We speculate that the low model variability in winter could be due to the fixed SSTs
but that the low variability in summer is due to the fixed soil moisture. The relative variability of precipitation
is greatly underestimated in summer. Perhaps the model underestimation of the coefficient of variation of
precipitation at this west coast grid is associated with the absence of interannual SST anomalies in the model.
In summary, the Chervin model either successfully reproduces the interannual variability of temperature
(as at the GL grid) or underestimates it (at the GP grids, SE grid, and WC grid). The seasonal decrease in
variability of temperature from summer to winter is well reproduced at all grids. Regarding precipitation, the
relative variability (as measured by the coefficient of variation) is in general well simulated, although there is
an occasional overestimation by the model. Aggregating over the three grid boxes in the GP region produces
in general better comparisons with observations than for the individual grids, and directions of error of the
three GP grids are not consistent.
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CHAPTER 4
INTERCOMPARISONS OF THREE CCM VERSIONS AND OBSERVED DATA
COMPARISONS OF MEAN CONDITIONS: TEMPERATURE AND PRECIPITATION
Table 6 presents comparisons of annual and seasonal mean conditions (temperature and precipitation)
simulated by the three models and observations for the four grids. Statistics of interannual variability cannot
be analyzed because there are too few years of simulated data (Washington and Dickinson runs). The Chervin
model is consistently the most accurate in predicting mean annual temperatures. In terms of mean annual
precipitation totals, however, it is consistently the least accurate. The Washington model is in general the least
accurate in terms of temperature, but is the most accurate in terms of total precipitation at GP III and GL. It
is perhaps not surprising that a model that predicts sea surface temperature with a mixed layer ocean would
not simulate temperatures as well as the other models which have prescribed observed SSTs. The Dickinson
model best simulates total annual precipitation at the WC and SE grids. The Washington model also is the least
accurate in winter and summer temperatures at GP III and GL. In terms of seasonal distribution of precipitation
(i.e., percentage of annual total occurring in winter and summer) none of the models fare very well. However,
the high winter, low summer precipitation cycle of the WC grid is generally captured by all models. The
Washington model fails (relative to observed as well as to the other models) to reproduce the winter low-
summer high precipitation regime of GP HI and GL.
On the basis of mean annual and seasonal comparisons, no one model is clearly superior to the other two
regarding the accurate reproduction of all these measures of the climate at these locations. Reasons for these
contrasts will be explored in future research efforts.
RELATIVE HUMIDITY
Relative humidity comparisons are made among the three models because we anticipated significant
differences among the models, since their surface hydrology packages are so different and this would certainly
affect the modeling of surface relative humidity. We first present a detailed analysis of the Chervin version
relative humidity including a display of histograms, and then compare these results with those of Washington
and Dickinson.
The Chervin modeled average daily time series of relative humidity for the four regions compare poorly with
the observed values, which are presented in Figure 14. In the GP and GL regions the modeled series form the
mirror image of the observed series. At GP the observed series reaches its maximum values (approx. 70%) in
winter when the modeled series experiences its minimum (approx. 50%). There is a greater range of values
(summer vs. winter) in the simulated data, particularly at the GL grid. At the more humid SE grid, where the
seasonal cycle of relative humidity is muted, discrepancies are less serious. The model values show very little
variability. The strongest seasonal cycle in the observed data is found at the WC location, where values range
from about 85% in winter to 40% in summer. The model curve is virtually flat at 70% again pointing out the
models inability to simulate the seasonal cycle. Again, given the errors that fixed soil moisture could introduce,
perhaps the discrepancy should be anticipated.
The poor results at GP are further highlighted in the selected monthly histograms (Figure 15). The
distributions of the modeled data are greatly shifted relative to observed data in most months. The observed
distributions are roughly normal for all months, whereas the distributions formed from the modeled data depart
significantly from the normal distribution for most months (April-October). In addition, some model
distributions such as that of July, are much narrower than those formed from observed data, and thus exhibit a
narrower range and less variability. At the GL grid (Figure 16,4 selected months), the model distributions also
differ from the observed, but reduced variability in the model data is only seriously in evidence in the summer
months (e.g., July as shown in Figure 16). At the SE grid, the reduced variability of model data is again seen
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Table 6 . Four Grids - Multicomparisons of COM Model Version and Observed Mean
Temperature and Total Precipitation Statistics
CCM Model
SOUTHEAST (SE)
Annual
Mean Temperature (°C)
Total Precipitation (nun)
Winter
Mean Temperature (°C)
Total Precipitation (mm)
Summer
Mean Temperature (°C)
Total Precipitation (mm)
GREAT PLAINS (GP III)
Annual
Mean Temperature (°C)
Total Precipitation (mm)
Winter
Mean Temperature (°C)
Total Precipitation (mm)
Summer
Mean Temperature (eC)
Total Precipitation (mm)
GREAT LAKES (GL)
Annual
Mean Temperature (°C)
Total Precipitation (mm)
Winter
Mean Temperature (°C)
Total Precipitation (mm)
Summer
Mean Temperature (°C)
Total Precipitation (mm)
WEST COAST (WC)
Annual
Mean Temperature (°C)
Total Precipitation (mm)
Observed
16.6
1137.2
7.4
1137.2
25.5
317.0
12.8
725.7
0.4
81.3
24.9
276.9
9.0
887.4
-3.1
187.2
20.5
254.9
10.1
553.2
Chervin
20.0
3085.5
14.1
3085.5
25.9
786.4
13.4
2690.8
1.7
541.8
23.8
877.7
9.3
3345.4
-6.6
640.0
22.8
1105.4
10.1
1792.8
Wash
20.1
589.1
14.8
589.1
24.2
75.7
17.6
931.3
3.5
291.7
29.3
194.4
16.2
849.1
-1.2
250.5
31.7
156.4
13.7
707.4
Dick
21.5
1401.8
16.0
1401.8
26.6
346.9
15.3
1287.5
2.9
270.3
26.1
498.4
12.6
1902.4
-2.7
319.8
26.6
616.6
14.3
652.1
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Table 6 (continued).
CCM Model
Observed Chervin Wash Dick
Winter
Mean Temperature (*C) 2.6 2.4 5.3 4.2
Total Precipitation (mm) 254.1 723.8 340.6 207.6
Summer
Mean Temperature (°C)
Total Precipitation (mm)
18.1
39.4
17.7
192.6
24.4
15.7
26.4
24.7
T - temperature
Chervin - Chervin CCM version
Wash - Washington CCM version
Dick - Dickinson CCM version
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GP123
GTLAKES
100
80
60
40
20
100
80
60
40
20
OBSERVED
CHERVIN
60 120 180 240 300 360
SOEAST
OBSERVED
CHERVIN
100
80 -
60 -
40 I-
20 -
OBSERVED
CHERVIN
60 120 180 240 300 360
WCOAST
100
80
60 -
40
20 -
OBSERVED
CHERVIN
60 120 180 240 300 360 60 120 180 240 300 360
DAYS DAYS
Figure 14. Daily average relative humidity for an 18-year average, Chervin vs. observed for four seasons.
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100
80
60
40
The Percentage of Events for the Intervals
± 2.5 % Relative Humidity from the labeled value
GP123 Grid. 18 Years of Data
100
80
(*)
60
40
20
OL
JANUARY
• OBSERVED
13 CHERVIN
30 35 40 45 50 55 60 65 70 75 80 85 90 95
(% Relative Humidify)
JULY
• OBSERVED
ii CHERVIN
30 35 40 45 50 55 60 65 70 75 80 85 90 95
(% flelofive Humidify)
100
80
60
40
20
The Percentoge of Events for the Intervals
± 2.5 % Relative Humidity from the labeled value
GP123 Grid. 18 Years of Data
QL
100
80
60
40
20
0L
APRIL
| OBSERVED
^ CHERVIN
30 35 40 45 50 55 60 65 70 75 80 85 90 95
(% Relative Humidity)
OCTOBER
• OBSERVED
El CHERVIN
30 37 44 52 59 66 73 81 88 95
(% Relative Humidify)
Figure 15. Histograms of relative humidity (18 years) for the three GP grids, four selected months, Chervin
model vs. observed.
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The Percentage of Events for the Intervals
± 2.5 % Relative Humidity from the labeled value
GTLAKES Grid, 18 Year of Data, with ADJ
100 r
80
60
40
20
JANUARY
• OBSERVED
d CHERVIN
ILL
100
80
60
40
20
20 35 40 45 50 55 60 65 70 75 80 85 90 95
(% Relative Humidity)
JULY
• OBSERVED
® CHERVIN
30 35 40 45 50 55 60 65 70 75 80 85 90 95
(% Relative Humidity)
100
80
60
40
20
The Percentage of Events for the Intervals
± 2.5 % Relative Humidity from the labeled value
GTLAKES Grid, 18 Year of Data, with ADJ
APRIL
• OBSERVED
0 CHERVIN
....LL.LL
100
80
60
40
20
30 35 40 45 50 55 60 65 70 75 80 85 90 95
(% Relative Humidity)
OCTOBER
• OBSERVED
0 CHERVIN
30 37 44 52 59 66 73 81 88 95
(% Relative Humidity)
Figure 16. Histograms of relative humidity (18 years) for the GL grid, 4 selected months, Chervin model vs.
observed.
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in all months (Figure 17). It is difficult to even speculate on why the SE relative humidity should be both too
large and not variable enough relative to the observed humidity. Perhaps the proximity to the Atlantic Ocean,
coupled with horizontal diffusion is responsible. The absence of a diurnal cycle in CCMO could be another
factor.
These results may reinforce the speculation offered earlier, i.e., that fixed soil moisture is a major cause
of the discrepancies. In the GP and GL regions, winter/spring season soil moisture and relative humidity are
usually high, and warm season, especially late summer values, are usually low. The fixed soil moisture at 25%
of field capacity would thus cause too little evaporation, too low relative humidity, (perhaps) too few clouds and
too warm temperatures in the winter/spring and exactly the opposite in late summer. Such diagnostics are
consistent in pointing to the fixed hydrology as a potential cause of the late winter/late summer discrepancies
evident in the model for the GP and GL regions.
We present here a brief comparison of average daily relative humidity of the Washington and Dickinson
versions and contrast them with the Chervin version results. Both the Washington and Dickinson results are
more accurate (compared to observations) than those of the Chervin version. The Washington version (Figure
18) reproduces fairly well the seasonal cycle of relative humidity at the SE and WC grids. However serious
discrepancies are still found at the other two grids. Late summer minima are produced by the model at both
locations which have no correspondence in the observations. The Dickinson model is the most accurate of the
three models (Figure 19). The overall shapes of the relative humidity curves are successfully reproduced at each
grid. However, the Dickinson version also produces too much daily variability which is seen as "noise" on the
plots. The relative success of the Dickinson and Washington version is first of all a result of the interactive
surface hydrology used in both models (although the parameterizations are not the same). Furthermore, the over
all success of the Dickinson model is most likely due again to the superior treatment of surface interactions and
the inclusion of a diurnal cycle. The cause of the much higher variability of relative humidity for Dickinson's
model is not immediately obvious, but is partially related to the smaller sample size (three years) compared to
the Chervin output. The effect of vegetation on the hydrologic cycle, which is included in the Dickinson model
could also contribute to the high day-to-day variability. These conclusions, however, must be accepted with
caution, since the observed relative humidity is generally based on one station observation, and, in the case of
the GL grid, on one that is not even located within the grid area (see Figure 1).
DAILY VARIABILITY OF TEMPERATURE
The daily variance of temperature is first discussed qualitatively by comparing temperature histograms (3
models and observed) for January and July at the SE and GL grids (Figures 18 and 19). The Dickinson model
results exhibit the lowest variability, indicated by its comparatively narrow distributions. Washington and Chervin
model results are fairly comparable, showing relatively greater variability compared to both Dickinson and
observed data A possible explanation for the lowered daily temperature variability of the Dickinson model
concerns the more physically and biologically comprehensive surface energy balance used, which includes
consideration of soil heat capacity, an issue briefly mentioned above in the description of the Dickinson model.
Quantitative analysis of daily temperature variance is more complex than analysis of interannual variance
because of the need to consider the effect of autocorrelation in the time series. Autocorrelation refers to the
condition that the temperatures in the series are not independent one from another but tend to be correlated
over time. Katz (1984,1988) has developed a statistical method by which valid statistical comparisons of daily
variance may be performed. This method controls for the effect of autocorrelation by removing the
autocorrelation influence and creating a new time series of effectively uncorrelated daily temperatures. The
variance of this new series (known as the innovation variance) is then statistically analyzed via Z scores which
compare the two innovation variances by taking the difference of their natural logarithms. (Natural logarithms
are used to improve the normal approximation for moderate sample sizes). Removal of the autocorrelation effect
requires the representation of the time series as some order autoregressive process. The appropriate order is
selected via the Bayesian Information Criterion (BIC) (Schwarz, 1978). The mathematical details of the statistical
method are presented in the appendix (1).
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The Percentoge of Events for the Intervals The Percentage of Events for the Intervals
± 2.5 7» Relative Humidity from the labeled value * 2.5 % Relative Humidity from the labeled value
SOEAST Grid, 18 Year of Data, SC & TN averaged, with ADJ SOEAST Grid, 18 Year of Data, SC & TN averaged, with ADJ
100,
100
80
(*)
60
40
20
100
80
60
40
20
JANUARY
• OBSERVED
E3 CHERVIN
30 35 40 45 50 55 60 65 70 75 80 85 90 95
(% Relative Humidity)
JULY
• OBSERVED
@ CHERVIN
30 35 40 45 50 55 60 65 70 75 80 85 90 95
(% Relative Humidify)
(7.)
80
60
40
20
(7.)
MOO
80
60
40
20
APRIL
• OBSERVED
0 CHERVIN
..illl
30 35 40 45 50 55 60 65 70 75 80 85 90 95
(% Relative Humidity)
OCTOBER
• OBSERVED
0 CHERVIN
* ' * ' I t I I I • I « I I I . • . I
30 37 44 52 59 66 73 81 88 95
(% Relative Humidity)
Figure 17. Histograms of relative humidity (18 years) for the SE grid, 4 selected months, Chervin model vs.
observed.
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GP123
GTLAKES
100
80 -
60 '
40 -
20 -
OBSERVED
— WASHINGTON
100
80
60
40
20
60 120 180 240 . 300 560
SOEAST
OBSERVED
WASHINGTON
60 120 180 240 300 360
DAYS
100
80
60
40
20
OBSERVED
WASHINGTON
100
80
60
40
20
60 120 180 240 300 360
WCOAST
ffT ^
OBSERVED
WASHINGTON
60 120 180 240 300 360
DAYS
Figure 18. Daily average relative humidity for an 18-year average, Washington model vs. observed.
n
-------
GP123
100
80
60
40
20
GTLAKES
OBSERVED
DICKINSON
100
80
60
40
20
60 120 180 240 300 360
SOEAST
OBSERVED
DICKINSON
100
80
60
40
20
OBSERVED
DICKINSON
100
80
60
40
20
60 120 180 240 300 360
WCOAST
OBSERVED
DICKINSON
60 120 180 240 300 360 60 120 180 240
DAYS DAYS
Figure 19. Daily average relative humidity for an 18-year average, Dickinson model vs. observed.
300 360
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Daily temperature variances were tested for January and July at the GP UJ, SE, GL, and WC grids. Table
7 presents relevant results for all three CCM versions and observed data. We discuss the results for Chervin's
version first so as to contrast the daily variance results with the interannual variance results presented in Chapter
III.
At the GP III grid, the model daily variance for January is significantly higher (at the O.OS level) than that
of the observed data, whereas the July model variance is not significantly different from the observed. Note also
that different autoregressive model orders are selected according to the BIC criterion, which reflects different
autocorrelation structures. The first order autocorrelation coefficient (which indicates the relative dependence
of one day's temperature upon the previous day's) for the model series in January is significantly lower than the
observed, which is consistent with the innovation variance results. At the SE grid, the daily variability of the
model time series (as measured by the innovation variance) is greater than the observed series in both January
and July, as is the case at the WC grid. The greatest discrepancy occurs at the the GL grid in January where
the model innovation variance is seven times greater than the observed. This extreme overestimation may again
relate to the lack of moderating effects of the Great Lakes in the modeled temperatures. In contrast, the model
very successfully reproduces the autocorrelation function, the sample variance and hence the innovation variance
at the GL grid in July.
Note that as with the interannual variability, the reduction in daily variance from winter to summer is well
simulated at all locations.
These results on daily temperature variability contrast with the interannual variability results where model
variability tended to be lower than observed at these grids in winter and in summer. The direction of the daily
variance error (i.e., too high) may be related to the absence of soil heat capacity in the surface energy budget
calculations or absence of a diurnal cycle and attendant night tune temperature inversions. Further analysis (for
more months and at more grids) will be necessary to completely evaluate the nature of daily temperature
variance in the Chervin version of the CCM. So far it must be concluded that the model overestimates daily
temperature variance.
The results for Washington and Dickinson are not as dearcut as those for the Chervin model, because there
are only three simulated years available, but some overall tendencies can be identified. The Dickinson model
is often more successful than both the Washington and Chervin models in accurately reproducing daily variability,
based on the tests of equality of the innovation variances. The innovation variances of the Dickinson model
temperatures do not significantly differ from those of the observed data in five of the eight cases. The variance
is too low in two cases and too high in only one case. The Washington model successfully reproduces the
variance in only three of the eight cases and is too large in the other five cases, and the Chervin model variance
is too large in six of the eight cases. Hence, it can be said that the Dickinson model has the lowest temperature
variance, followed by the Washington and Chervin models. It should be noted that the Dickinson model is not
the most successful at reproducing the monthly temperature means although it is the most successful in
reproducing the daily variances. It is perhaps not surprising that the Dickinson model is most successful in
reproducing the daily variance if we are correct in our speculation as to why the Chervin model (as well as the
Washington model) tends to overpredict variance, that is that the neglect of surface heat capacity allows rapid
temperature variations with cloudiness, etc. Also, these models (especially Chervin's) use simple surface
hydrology.
DAILY PRECIPITATION VARIABILITY
The daily variability of precipitation is difficult to analyze due to the positively skewed nature of the
distribution. Comparisons of standard deviations can be very misleading. Moreover, comparisons must be made
on both frequency of occurrence and intensity. One of the most useful means of comparing distributions of daily
precipitation is through the box plot display (Tukey, 1977). In this display, the box height indicates the
interquartile range, a horizontal line through the box indicates the median, and the box whiskers (extreme ends)
indicate the maximum and minimum of the distribution. Other quantiles can also be indicated, such as the 90th
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Table 7. Dally Temperature Variance Statistics (°C) Chervin, Washington,
Dickinson Versions of the CC Control Runs Versus Observed
and
GREAT PLAINS (GP
January
Observations
Chervin
Washington
Dickinson
July
Observations
Chervin
Washington
Dickinson
SOUTHEAST (SE)
January
Observations
Chervin
Washington
Dickinson
July
Observations
Chervin
Washington
Dickinson
GREAT LAKES
January
Observations
Chervin-
Washington
Dickinson
July
Observations
Chervin
Washington
Dickinson
Order
III)
3
2
4
2
3
2
2
2
3
3
2
4
3
3
2
2
4
4
3
1
3
3
2
3
Mean
ro
-1.2
0.0
0.7
0.3
26.0
24.3
28.1
25.6
7.0
13.3
13.7
15.7
26.1
26.2
24.1
26.9
-4.0
-8.9
-3.8
-5.3
21.6
24.0
31.5
27.9
Lag 1
Coeff.
0.73
0.52
0.70
0.46
0.79
0.73
0.89
0.81
0.76
0.56
0.71
0.55
0.76
0.63
0.71
0.60
0.74
0.54
0.61
0.53
0.72
0.72
0.84
0.69
Sample
Variance
38.2
78.2
41.2
21.9
8.4
7.8
15.7
9.4
29.3
35.1
23.2
12.7
2.4
2.9
3.2
1.1
30.4
126.3
44.9
37.8
7.2
8.0
16.2
3.6
Innovation
Variance
15.6
51.5*
20.0
15.9
2.9
3.1
2.2
2.6
10.8
21.4*
9.5
7.3*
0.8
1.7*
1.5*
0.6
12.4
84.8*
27.7*
27.6*
3.0
3.3
4.3*
1.5*
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Table 7. (continued)
Order
WEST COAST (WC)
January
Observations
Chervin
Washington
Dickinson
3
3
2
1
Mean
1.2
1.7
4.5
3.3
Lag 1
Coeff.
0.85
0.66
0.76
0.67
Sample
Variance
17.0
24.8
17.9
9.3
Innovation
Variance
4.4
13.4*
7.6*
5.3
July
Observations
Chervin
Washington
Dickinson
2
3
3
3
19.6
18.2
25.2
28.1
0.77
0.80
0.82
0.86
4.7
12.4
16.9
12.3
1.8
3.5*
3.8*
2.3
Order - selected order of autoregressive process
Lag 1 Coeff - 1st order autocorrlation coefficient
* - model innovation variance significantly different from observed (0.05 level)
at WC, percentile. Figures 20a-d present box plots of the distribution of daily precipitation aggregated on a
seasonal basis for the three model versions and observations for the four grids. The distributions are formed
from the subset of rain day data (i.e., precipitation amounts less than 0.1 mm are not included). Rainfall
frequency (i.e., percentage of raindays for each season) is indicated by the numbers to the left near the upper
quartile of each box plot.
The results for Chervin's version have been already basically presented in the probability functions (Figures
10-13). Additionally, it is clear from the box plots that this model version greatly overestimates variability as
measured by the interquartile range, maximum values, and skewness. These results are somewhat uninteresting
since they largely follow from the fact that all precipitation amounts are overestimated to begin with.
Comparisons of the Dickinson version, Washington version, and observed distributions are on the whole more
interesting.
The Dickinson version also tends to produce greater variability compared to the observations. In general
the model interquartile ranges are much greater than those of the observations, even when the medians are quite
similar (as at GP III, Figure 20a). Maximum values are also usually greater, and the distributions are more
skewed. This last condition means that a greater portion of the data are small precipitation events. In general
the distributions differ most in the distance from the median to the upper quartile, i.e., the upper half of the data
is too dispersed (variable). This is not always the case, however. In fall at GP3, the distributions are very similar
regarding these measures, and the Dickinson model even has a lower maximum than the observations. In winter
the Dickinson model is clearly less variable than the observations, except that the distribution is more skewed.
The Washington model, in general, is the most successful in reproducing the daily variability of precipitation
of the observations. This model version produces the lowest errors in simulating the maximum values (e.g.,
winter at GL). The interquartile ranges are not as overestimated as in the case of the Chervin and Dickinson
models, but some are slightly too large. There also is a tendency for the Washington model to produce more
positively skewed distributions (e.g., summer at GL; spring at WC). There are cases where the daily variability
is somewhat less than the observations, such as the fall at GL and WC.) At the SE grid (Figure 20c) all
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40
45
40
97 128 167 151
30
30
E
20
20
10
0L .
j«»
egg
Winter Spring Summer Foil
Observed
10
0L ,_
Winter Spring Summer Toll
Chervln
40
30
20
10
62
li-
ft
Ql L
Winter Spring Summer Foil
Washington Control
40
30
20
10
42 61 47
n
OL L
f*
Winter Spring Summer Fell
Dickinson
Figure 20a. Box plots of daily precipitation, GP IH grid, four seasons; observed, Chervin, Dickinson, and
; Washington models. Numbers on left side of .each box plot are % raindays.
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40r
42
40
86 137 132 126
30
30
20
E
E
20
10 •
0L _
1
7f
a
Winter Spring Summer Toll
Observed
10
JT 1
Winter Spring Summer Fall
Chervin
E
40
30
20
10
58
Winter Spring Summer Fall
Washington Control
40
30
20
10
67 102 90
Winter Spring Summer Foil
Dickinson
Figure 20b. Box plots of daily precipitation, GL grid, four seasons; observed, Chervin, Dickinson, and
Washington models. Numbers on left side of each box plot are % raindays.
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40
30
o
•o
E
20
10
0L L
41 51
Ff
W
70
Winter Spring Summer Fall
Observed '
40
30
20
10
133 151 234 195
«
13
TT
Winler Spring Summer Fall
Chervin
49 42 67 118
*u
30
|
* 20
E
E
10
n
•
•
.
•i
-
_
E
3 E
40
30
i T
n
3 E
20
10
3
B
•
i
•
a
•»
^*
^^^•H
^^~
t
•»*
'
r*
3
ft t
t*-
•0
QP
Winter Spring Summer Fell
Woshinglen Cenirel
Winter Spring Summer Fall
Dickinson
Figure 20c. Box plots of daily precipitation, SE grid, four seasons; observed, Chervin, Dickinson, and
Washington models. Numbers on left side of each box plot are % raindays.
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o
•o
40
30
20
10
44
45
Wintir Spring Summer Foil
Observed
40
30
20
10
93 69 45 90
II
Winler Spring Summer Fell
Chervin
40
30
20
10
0L L.
Wlnler Spring Summer Foil
_ Woshinglon Control
40
30
20
10
0L ,_
Winler Spring Summer Foil
Dickinson
Figure 20d. Box plots of daily precipitation, WC grid, four seasons; observed, Chervin, Dickinson, and
Washington models. Numbers on left side of each box plot are % raindays.
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Table 8. Daily Precipitation Distribution Interquartile Ranges (mm): Observed,
Dickinson, Washington, and 2xC02.
Winter Spring Summer Fall
GREAT PLAINS (GP III)
Observed 2.3 4.6 5.4 5.4
Dickinson 6.9* 7.3* 9.6 5.8
Washington 4.6* 4.1 4.3 5.5
2xC02 5.1 4.2 6.5* 7.0*
GREAT LAKES (GL)
Observed 2.6 3.9 4.6 4.1
Dickinson 5.9* 8.6* 8.2* 8.0*
Washington 3.6** 5.4** 5.0 3.8
2xC02 5.5* 3.9 4.5 5.2
SOUTHEAST (SE)
Observed 8.0 6.7 5.5 6.1
Dickinson 6.9 3.6* 6.0 6.1
Washington 3.7* 2.8* 2.2* 3.0*
2xC02 3.1 3.1 1.9 3.5
WEST COAST (WC)
Observed
Dickinson
Washington
2xC02
4.7
4.0
4.8
5.1
2.7
5.0*
4.0*
3.1
1.7
4.5*
1.6
2.8*
3.9
5.7*
3.0
4.4
Significantly different from observed value at the 0.05 level, for
Washington and Dickinson cases; significantly different from Washington
(control) for 2xC02 case.
** - Significantly different from observed at the 0.1 level.
measures of variability indicate that the Washington model underestimates variability. However, since the model
generally underestimates all precipitation amounts at this location, it would be difficult to say that the variability,
separate from the errors in the mean, is actually underpredicted.
A quantitative comparison of interquartile ranges of observed, Dickinson, Washington, and 2xCO2 dairy
precipitation distributions are presented in Table 8. The 2xCO2 values in the table will be discussed in the next
section. Significant differences between model values and observed values, on the basis of the interquartile range
statistical test (see appendix 2), are indicated on the table by asterisks. On the basis of this test, the Washington
model accurately reproduces the observed interquartile range in 10 of the 16 cases, overpredicts in 2 of the 16
and underpredicts in 4. However, it should be remembered that the underpredfction of total precipitation for
all seasons at the SE grid results in the low variability in all four of these cases. If one considers the relative
variability (in this instance the interquartile range relative to the median), then the Washington model variability
at the SE grid is very similar to that of the observations in all seasons. The Dickinson model underpredicts or
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accurately predicts the interquartile range at the SE grid (all seasons), the WC grid in winter, and the GP m
grid in the fall. All other cases are overpredictions.
The results for the SE grid for all models form an interesting pattern. In terms of the observations,
comparing the four grid regions, highest amounts and greatest variability are found at this location; the models
consistently come closest to observations at the SE grid, and do not overpredict precipitation as much as they
typically do at the other grids. Perhaps this relative "underprediction" arises from the difficulty a 15-wave model
has in reproducing intense precipitation events associated with hurricanes or small scale coastal cyclones.
In terms of estimation of precipitation frequency, the Washington model consistently underestimates the
percentage of raindays in summer at all locations, and underestimates raindays in all seasons at GL. Aside for
GL, winter raindays are overestimated at the other grids. Other seasons and locations show no overall
tendencies.
There is less of a pattern of rainfall frequency errors in the Dickinson model. The only tendency is that
of underestimation of raindays in summer (all locations except GL). Otherwise, there is a mix of over and under
predictions at different locations and different seasons. Rainfall frequencies are relatively accurate in one third
of the cases.
It is very difficult to even speculate on the causes of these results for precipitation. For example, we already
mentioned the problem of grid or subgrid scale storms. Additionally, Dickinson's model contains a diurnal cycle
which could well alter the frequency of convective and large scale precipitation events, particularly in the
afternoon when humid synoptic conditions prevail. Unfortunately, such diagnostic information is not available
on the model history tapes we have used.
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CHAPTERS
PILOT STUDY OF CONTROL VS. CO2 PERTURBED RUNS
We include here a preliminary analysis of changes in temperature and precipitation under a scenario of
doubled CO,, using the output from Washington's control and doubled CO2 runs for the four grids, each case
consisting ofthree year runs. Of the three CCM versions discussed here, the Washington model is the only one
for which doubled CO2 experiments have been performed. Again, interannual variability could not be analyzed
because the 3-year time series are too short. However, examination of daily variance of temperature and
precipitation is presented.
Table 9 displays seasonal and annual mean values for temperature and precipitation for the control and
doubled CO2 cases. As is typical for GCMs, there is an annual temperature increase of between 2 and 3°C. The
increase is distributed rather evenly in all four seasons at WC and SE, whereas winters experience larger
increases at the two inland grids (GP III and GL). On an annual basis precipitation increases between 22 and
26% at three grids, but experiences a slight (2%) decrease at the SE grid. There are also potentially important
changes in the seasonal distribution of precipitation. At the GL and SE grids, a smaller percentage of the annual
total occurs during the summer in the CO2 perturbed case (e.g., from 13% to 6% at SE). Increased percentages
are obtained in the fall and spring. The WC area may benefit from redistribution since a slight increase in
percentage occurs there in summer. Seasonal redistributions of precipitation are important to consider from
a climate impacts point of view, particularly for agriculture.
Figure 21 presents histograms of temperature for 4 months for the control and perturbed cases at the SE
grid. What is most striking in this figure is the similarity in the distributions between the two cases. Aside from
the shift in the mean, there are no other visually obvious changes, except for a slight decrease in range for the
2xCO2 case in October. This condition is underlined by the statistics comparing daily temperature variance of
the control and perturbed runs for four months (Table 10) for the four locations. There are only two cases out
of the 16 where the innovation variances of the perturbed climate temperatures are significantly (at the 0.05
level) different from the control: in October at the SE grid where the innovation variance decreases (reflected
in Figure 21) and in October at the GP HI grid where the innovation variance increases in the perturbed case.
In the latter case an interesting condition exists where the sample variance decreases while the innovation
variance increases. In fact in 5 of the 16 cases, the direction of change of innovation and sample variances is in
opposite directions. This indicates the importance of the effect of autocorrelation on the sample variance and
its effect on physically meaningful measures of variability, such as the frequency of extreme events. It should also
be noted that noise in the data may also be partially responsible for the contrary directions. In the case of
October at GP III, the first order autocorrelation coefficient decreases significantly, whereas the means of the
two series are virtually the same.
It should be kept in mind that the lack of significant differences in innovation variances may be related to
the relatively small sample size of the Washington runs (only three years of data), which limits the power of
the statistical tests (i.e., the likelihood of accepting the null hypothesis when in fact it is false). These results may
in fact be reflecting the lack of power. Longer time integrations of runs will be necessary to resolve this issue.
Without regard to significance levels, it can be said that the innovation variances decrease in half the cases
and increase in half, whereas in 10 out of 16 cases the sample variances increase. From this information and
that in the preceding paragraph, it is obvious that no clear conclusions can be drawn. No general statement
can be made regarding the direction of change of daily temperature variability under CO2 wanned climate
conditions for three years of data from the Washington model at the locations investigated.
These results contrast with those of Wilson and Mitchell (1987), who used the same statistical tests on the
innovation variances presented here. They concluded that daily temperature innovation variances significantly
decreased in winter at two grid box locations in Europe. Decreases in spring were also recorded but were not
statistically significant. However, it should be noted that here we are comparing the results of two structurally
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Table 9. Control vs. Doubled C02 Mean Temperature and Total Precipitation
Statistics (Washington CCM)
Annual Winter Spring Summer Fall
SOUTHEAST (SE)
Temperature (°C)
Control 20.1 14.8 18.5 24.2 22.7
2xC02 22.1 17.1 20.2 26.6 24.7
Precipitation (mm)
Control 589.1 295.3 85.3 75.7 132.7
2xC02 575.9 211.5 120.9 35.0 208.4
GREAT PLAINS (GP III)
Temperature (°C)
Control 17.6 3.5 18.3 29.3 18.9
2xC02 20.0 7.4 19.6 32.1 20.8
Precipitation (mm)
Control 931.3 291.7 203.2 194.4 242.0
2xC02 1179.5 357.6 243.9 232.2 345.8
GREAT LAKES (GL)
Temperature (°C)
Control 16.2 -1.2 16.2 31.7 17.6
2xC02 19.4 3.7 17.2 34.9 21.6
Control 849.1 250.5 267.1 156.5 175.0
2xC02 1032.5 391.0 305.0 109.2 227.3
WEST COAST (WC)
Temperature (°C)
Control
2xC02
Precipitation
Control
2xC02
13
16
(mm)
707
867
.7
.3
.4
.5
5.
7.
340.
359.
3
4
6
2
9.
12.
248.
250.
8
5
2
1
24
27
15
37
.4
.3
.7
.1
15
17
102
220
.0
.7
.9
.5
different GCMs (NCAR spectral CCM vs. U.K. Met Office grid point model) at different locations (US. vs.
Europe) and across different time intervals (a season vs. one month). That these results do not agree is thus
unrevealing. Moreover, it cannot be assumed that variability of climate variables would change in the same
direction in different regions.
In conclusion, all that can be legitimately stated is that our preliminary analyses of the Washington model
results it do not support the finding that daily temperature variability tends to decrease with climate wanning.
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Table 10. Daily Temperature Variance Statistics (°C2) Washington Control vs. 2xC02
Control
JAN
2xC02
Control
APR
2xC02
Control
JUL
2xC02
Control
OCT
2xCO2
SE
Sample Innov
23.2 9.5
20.5 8.4
8.3 5.1
15.1 5.0
3.2 1.5
3.3 1.2
9.1 2.8
4.0 1.6*
GP3
Sample Innov
41.2 20.4
33.8 20.6
22.3 6.8
24.1 9.2
15.7 2.2
19.6 3.6
39.2 6.8
34.8 14.6*
GL
Sample Innov
44.9 27.7
54.8 34.6
41.0 16.8
26.3 12.8
16.2 4.3
17.1 4.7
45.3 16.2
26.2 15.3
we
Sample Innov
17.8 7.6
19.2 10.2
9.6 4.6
9.4 3.6
16.9 3.8
20.2 2.7
17.4 7.2
26.8 10.1
Sample = sample variance/ Innov - innovation variance.
JAN - January, APR = April/ JUL «= July/ OCT - October.
* = 2xC02 innov. variance is significantly different
from control variance at 0.05 level.
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100
80
60
20
The Percentage of Events for the Intervals
± 2.5C° from the given Temp.
For the SOEAST Grid, 3 years of data
| WASHINGTON
@ C02X2
JANUARY
•30 -20 -10 0 10 20
(•C)
30 40
100 r
SO
60
40
20
The Percentage of Events for the Intervals
± 2.5C" from the given Temp.
For the SOEAST Grid, 3 years of data
| WASHINGTON
0C02X2
APRIL
-30 -20 -10 0 10 20 30 40
100
80
60
40
20
•
| WASHINGTON
i C02X2
JULY
_L
1
\
j
tf
\t
\
1 i
j
\ i
! |
: |
i . i
(7.)
-30 -20 -10 0 10 20 30 40
100
80
60
40
20
0
• WASHINGTON
@ C02X2
OCTOBER
J_
-30 -20 -10
10 20 30 40
Figure 21. Histograms of daily temperature (°C), Washington control and
months.
SE grid, 4 selected
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There is, however, a problem in drawing credible conclusions regarding change in daily temperature
variance under climate change conditions, when the models do not reproduce actual variability very well, i.e.,
the model variability is usually quite significantly larger than observed variability. Any relationship between the
direction of error of control run vs. observations and possible "errors" in predicting variability under climate
change remains to be explored.
As described in Chapter 4, it is difficult to summarily compare daily variability of precipitation since
variability can be operationally defined in so many ways, such as by the standard deviation, maximum values,
changes in occurrence frequency, transitional probabilities, and other distribution characteristics, such as the
interquartile range. First, changes in rainfall frequency, and high extremes are presented. Then again we
present box plots of seasonal distributions of precipitation for the control and doubled CO2 runs of the
Washington version (Figure 22). Comparisons are made of the degree of skewness, maximum values, and
interquartile range. Quantitative comparison of interquartile ranges is provided in Table 8.
At GP m percentage raindays increases in summer and spring and maximum values increase in all seasons
but summer. At the GL grid percentage raindays, the maximum value, and percentage greater than 20 mm/day
all decrease in summer, whereas these three quantities increase in the winter and spring. At the SE grid
percentage of rain days decreases in the summer but increases in the spring and fall. Contrasts at the WC grid
are not very striking, except that there is a slight increase in rain days and maximum values in all seasons but
winter.
At the GP HI grid (Figure 22a) under doubled CO2 conditions maxima are clearly higher in three seasons
and virtually the same in the other (summer). In winter, summer, and fall the interquartile ranges are greater
in the doubled CO, case, but slightly less in the spring. From Table 8, the interquartile range increases are
significant (at the (X05 level) in the summer and fall. Ninetieth percentiles are greater in winter, spring, and
especially fall. On the basis of these measures, daily variability clearly increases in three seasons, and increases
at least on the basis of higher maximum values in the other (spring). Variability increases most clearly in fall,
At GL variability results are more mixed. Maxima are greater in all seasons except summer but
interquartile ranges are significantly greater only in winter. The doubled CO2 distributions are clearly more
skewed only in spring. Fall and winter are clearly more variable whereas the measures indicate mixed results
for summer and spring.
At the SE grid, both summer and winter are less variable based on these measures although in summer
the data are more skewed (higher proportion of low rainfall events). In fall and spring all measures indicate
greater variability. Interquartile ranges are greater, but not significantly so (Table 8).
At the WC grid, winter, summer, and fall are more variable based on these measures, but fall most dearly.
In spring, although there is a higher maximum, all other measures point to reduced variability.
In summary then, there are indications of greater daily variability of precipitation in the 2xCO2 runs in most
seasons at most locations (fall everywhere). Only in three of the total 16 seasons is daily precipitation
unambiguously less variable (summer and winter at GL and spring at WC). There is also a greater frequency
of precipitation under doubled CO2 conditions in 10 of the 16 season-locations.
In summary, the changes in daily temperature variability under the doubled CO, conditions are not very
striking at these particular grids. There is clearer indication of greater variability of precipitation, but ambiguities
remain. We need much longer time series to provide adequate sampling for analysis of both daily and
interannual variability.
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46 46 62 59
47
56 40 58
4U
30
o
"O
\ 20
E
E
10
•
•
-
•
*- ,
I
4U
30
20
10
i 0
.
-
•
'
a
c
, • J
l[
t
1
c
I
1
Winter Spring Summer Fall
Washington (Control and 2XCO2) at GPS
Winter Spring Summer Fall
Washington (Control and 2XC02) at GL
42
47
*tu
30
1
' 20
E
E
10
0
•
•
•
: I
-
,
E
i
S
4-U
30
20
10
" , 0
.
I
.
ii
1
E
Winter Spring Summer Fall
Washington (Control and 2XCO2) at SOEAST
Winter Spring Summer Fall
Washington (Control and 2XCO2) at WC
Figure 22. Box plots of daily precipitation, (a) GP ffl and GL grids (b) SE and WC grids, control (blank boxes)
and 2xCO2 (patterned boxes). Solid dot = 90th percentile; arrow with number = off scale meximum
value.
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CHAPTER 6
SUMMARY AND CONCLUSIONS
This study has presented analyses of comparisons of interannual and daily variability in GCM generated
time series of climate variables and observed climate time series in four regions of the United States. Variables
included temperature, precipitation, relative humidity, and absorbed solar radiation. An examination of the effect
of spatial aggregation of grid boxes on model errors in these variables is included for the Great Plains region.
In a more limited study involving temperature and precipitation (as well as some brief comments on relative
humidity) at the four locations, several control runs of different versions of the NCAR GCM are compared.
Finally, a preliminary investigation of changes in temperature and precipitation, both mean and variance, under
a climate change scenario is presented. Results may be summarized as follows.
Interannual variability of temperature is generally underestimated or properly predicted by the 20-year
simulation using the Chervin version of the CCM in all four regions. Interannual variability of precipitation as
measured by the coefficient of variation is generally in reasonable agreement with observed data, although it
is occasionally overestimated. This may be an encouraging result for the credibility of predicting climatic changes
given the large inaccuracy of the control run precipitation results in terms of absolute amounts. As expected
from sampling considerations, spatial aggregation of grids tends to improve results. When individual grids are
examined, directions of errors among the grids are often inconsistent (especially for precipitation variability).
From our preliminary results for temperature, it appears that the Chervin model overestimates daily temperature
variance. Solar radiation daily variance comparisons are not particularly interesting. However, there are
important and inconsistent regional contrasts in the direction of mean errors for solar radiation.
Comparisons of different CCM versions with observed data for mainly temperature and precipitation
produced more interesting results. There is considerable difference in how well the models reproduce mean
total precipitation for the four locations, ranging from the very good results of Dickinson's and Washington's
models (at different grids), to the overestimation of Chervin's model at all four locations. The Dickinson model
produced lower daily variability of temperature than the other two models or even occasionally than the
observations and was most successful in reproducing present daily variability. In the Chervin model surface
relative humidity is poorly simulated at all grids, and the daily variability is greatly underestimated. The
Dickinson model most successfully reproduced the annual cycle of relative humidity at all four grids, but also
displayed higher variability of relative humidity than the Chervin or Washington version. The reasons for these
discrepancies have yet to be explored in depth, but, as we speculated, are likely related to different
degrees of realism in the land surface parameterizations.
Regarding daily precipitation variability, Chervin's model greatly overpredicted the absolute variability, but
this is strongly tied to the much higher total precipitation amounts predicted by the model. Dickinson's model
does a better job of accurately reproducing daily precipitation variability, but there is still a tendency for
overprediction. Washington's model is by far the most accurate in reproducing observed variability. There are
also underpredictions, but these are generally related to Washington's underprediction of total precipitation
amount at the SE grid.
The preliminary investigation of the change in daily temperature variability under doubled CO, conditions
produced both increases and decreases in variance, but most of these changes were statistically insignificant at
all four locations for the three years of simulation available. Precipitation change results varied according to
location, e.g., from decreases in summer at the southeast (SE) and Great Lakes (GL) location to increases in
percentage of raindays in the summer in the Great Plains (GP HI). Daily precipitation variability increased more
often than not on the basis of distribution characteristics such as skewness and the interquartile range. Extreme
high precipitation events increased in all locations. Measures of the dispersion of the distributions (e.g.,
interquartile range) indicated greater variability of daily precipitation under doubled CO2 conditions. It is clear
that more analysis involving a greater number of grids and longer time series will be necessary to fully investigate
various measures of variability changes with changed climate.
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We plan to continue our statistical examination of variability in models of different structure in order to
help interpret existing CO, versus control cases. We also hope to perform CO2-perturbed experiments with
improved versions of the CCM such as those now being developed by Dickinson (described above) and S.L.
Thompson (which includes an interactive thermodynamic ocean and surface hydrology). While estimating the
effect of trace gas increases on various variability measures is our ultimate goal, many intermediate steps are
needed to explain the variability performance of various structurally different versions of the CCM, and their
comparison with observations.
It is obvious from our results so far that further improvements in GCMs are needed in order to accurately
reproduce regional mean climate and related climate variability. Among these would be higher horizontal
resolution so as to capture regional influences on climate, such as the Great Lakes; improved moisture transport,
condensation, and rainout parameterizations which would take into account potential effects on precipitation
variability (i.e., improving on spectral advection); improvements in interactive surface hydrology (e.g., BATS)
which appears to improve reproduction of surface relative humidity; inclusion of soil heat capacity which improves
the reproduction of of daily temperature variability. Other improvements not directly suggested by our results
include the coupling of complete ocean-atmosphere models which would improve the reproduction of interannual
variability, and the modeling of sub-gridscale phenomenon such as thunderstorms and hurricanes which would
contribute to better modeling of precipitation variability. The above list is far from exhaustive, but includes main
areas of improvement which would ameliorate the models' ability to reproduce climate variability on various
timescales. Only when this is accomplished can we place much faith in GCM forecasts of variability changes with
a perturbed climate.
Despite the strong reservations we have placed on the qualitative and quantitative inferences in this study
because of limited amounts of simulation data, we have given the detailed analyses anyway. It is our hope that
future studies (ours and those of other GCM investigators) will include analyses of variability similar to those
presented here as a routine part of GCM diagnostics.
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APPENDIX 1
STATISTICAL TESTS OF DIFFERENCES IN VARIANCE OF SURFACE TEMPERATURE
The test statistic used to determine differences in variance of surface temperature is taken from Katz
(1988). The procedures described below address two important problems encountered when trying to test
variances of atmospheric time series: autocorrelation of the time series and departures from the assumption
of normality. In regard to the first problem, tests are not performed on the variance of the original time series,
but rather on the innovation variance, which may be considered the variance remaining after the effect of
autocorrelation has been removed. The innovation variance is formed by fitting an AR(p) process (autoregressive
process of order p) to the time series. The residuals (or innovations) from this process constitute the innovation
variance:
P
Je=l
where a^ is the tth residual, X^ is the fth element of the time series of length n, X is the time average of the series,
and $1., k =l2,...p, are estimates of the autoregression coefficients. An unbiased estimator of the innovation
variance is then:
•Z-iT^Zlg*. (A2)
and all symbols are as previously defined. The residual time series is referred to as the "prewhitened data"
The test statistic for determining if two innovation variances (1) and (2) are equal (Le., the null hypothesis)
is asymptotically normally distributed,
"" " —*" * (A3)
where s is the standard error of hi S^2, and is given by
-,1/2
(A4)
where 72 K the sample kurtosis. The statistic (A3) is in terms of the logarithms to improve the Gaussian
approximation for moderate sample size. Moreover, because this statistic has an adjustment for the sample
kurtosis, procedures based on (A3) are robust against the innovations (Le., the residuals) departing from the
normal distribution.
The testing procedure begins with autoregressive model identification, Le., the correct order is selected
using some criterion such as the Bayesian Information Criterion (BIC) (Katz, 1982; Schwarz, 1978), which we
used. Using (Al) the prewhitened time series are obtained, and the innovation variances are estimated using
(A2). The test of significance (A3) is then applied to the two innovation variances, and significance levels
determined Here we used a significance level of 0.05 to establish significant difference between two variances.
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APPENDIX 2
STATISTICAL TESTS OF DIFFERENCES BETWEEN INTERQUARTILE RANGES
Given two sets of ordered data of daily precipitation, with interquartile ranges IQR(l) and IQR(2), the test
statistic for determining if the interquartile ranges are equal (i.e., the null hypothesis) is asymptotically normally
distributed,
IQR(2) -
+ «»[/gjz(i)l}'/» ' (AS)
where s*(IQK) is the variance of the interquartile range IQR, i.e., the variance of the difference between the
upper and lower quartiles (UQ and LQ). This can be expressed as
»*(VQ - LQ) = s*(UQ) + s*(LQ) - 2cov(UQ, LQ) , (A6)
where cov(UQLQ) is the covariance of the upper and lower quartiles.
In general, the variance of the pth sample quantile, X, where r = approx.np, (n = sample size) is given
by:
**(Xr) =
where F(£ ) is the distribution function, £ is the pth population quantile (i.e., F(£ ) = p), and / = f, the
density of the population (Kendall and Stuart, 1967). An estimate of 1 is given by:
Sm'r = (Xr+m ~ Xr~m) ' (A8)
where n is the sample size and m is some distance from r (Hall and Sheather, 1988). Then substituting for -fi\ •* in
(A7) we have J^f}
where s2 is the estimated variance. Hence, in the case of the variance of the interquartile range, setting UQ-
LQ equal to X-X^ and substituting (A9) in (A6), we finally have
(A10)
For the interquartile range, p1 = 1/4, p2 = 3/4 and we use m = n/8, which is consistent with the approach of
McGill et al. (1978) for determining confidence intervals for medians. A significance level of 0.05 is used to
determine significant difference between interquartile ranges.
1-57
-------
Mearns
REFERENCES
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circulation model coupled to a simple mixed layer ocean model. Monthly Weather Review 114:687-701.
Bourke, W. 1974. A multi-level spectral model. I. Formulation and hemispheric integrations. Monthly Weather
Review 102:687-701.
Bourke, W., B. McAvaney, K. Puri, and R. Thurling. 1977. Global modeling of atmospheric flow by spectral
methods. Methods in Computational Physics 17:267-324.
Chervin, R.M. 1986. Interannual variability and seasonal predictability. Journal of the Atmospheric Sciences
43:233-251.
Chervin, R.M. 1981. On the comparison of observed GCM simulated climate ensembles. Journal of the
Atmospheric Sciences 38:885-901.
Dickinson, R.E., A. Henderson-Sellers, P J. Kennedy, and M.F. Wilson. 1986. Biosphere-Atmosphere Transfer
Scheme (BATS) for the NCAR Community Climate Model. NCAR Technical Note 275. Boulder, CO: National
Center for Atmospheric Research.
Hall, P., and S J. Sheather. 1988. On the distribution of a studentized quantile. J. Royal Statistical Society (B)
50:381-391.
Hansen, J., I. Fling, A. Lads, S. Lebedeff, D. Rind, R. Ruedy, G. Russell, and P. Stone. 1988. Global climate
changes as forecast by the Goddard Institute for Space Studies three-dimensional model. Journal of Geophysical
Research 93(D8):9341-9364.
Katz, R.W. 1982. Statistical evaluation of climate experiments with general circulation models: A parametric
time series modeling approach. Journal of Atmospheric Science 39:1446-1455.
Katz, R.W. 1984. Procedures for Determining the Statistical Significance of Changes in Variability Simulated
by an Atmospheric General Circulation Model Climate Research Institute Report No. 48. Corvallis, OR:
Oregon State University.
Katz, R.W. 1988. Statistical procedures for making inferences about changes in climate variability. Journal of
Climate 1:1057-1068.
Kendall, M.G., and A. Stuart. 1967. The Advanced Theory of Statistics. 2nd edition. Volume 1: Distribution
theory. New York, NY: Hafner Publishing Co.
Lowe, P.R. 1976. An approximating polynomial for the computation of saturation vapor pressure. Journal of
Applied Meteorology 16:100-103.
Manabe, S., and D.G. Hahn. 1981. Simulation of atmospheric variability. Monthly Weather Review
109:2260-2286.
McGffl, R., J.W. Tukey, and WA. Larsen. 1978. Variations of box plots. American Statistician 32:12-16.
Mearns, L.O., R.W. Katz, and S.H. Schneider. 1984. Extreme high-temperature events: Changes in their
probabilities with changes hi mean temperature. Journal of Climate and Applied Meteorology 23:1601-1613.
Parry, M.L. 1978. Climatic Change, Agriculture and Settlement Folkstone, UJfc Dawson.
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Mearns
Reed, D.N. 1986. Simulation of time series of temperature and precipitation over eastern England by an
atmospheric general circulation model. Journal of Climatology 6:233-257.
Schwarz, G. 1978. Estimating the dimension of a model. Annals of Statistics 6:461-464.
Schwarz, H.E. 1977. Climatic change and water supply: How sensitive is the Northeast? In: Climate, Climate
Change and Water Supply. Washington, DC: National Academy of Sciences, pp. 111-120.
Tukey, J.W. 1977. Exploratory Data Analysis. Reading, MA: Addison-Wesley.
Washington, W.M., and GA. Meehl. 1984. Seasonal cycle experiment on the climate sensitivity due to a
doubling of CO, with an atmospheric general circulation model coupled to a simple mixed-layer ocean model.
Journal of Geophysical Research 89(D6):9475-9503.
Wilson, CA., and J.F.B. Mitchell. 1987. Simulated climate and CCyinduced climate change over Western
Europe. Climate Change 10:11-42.
Williamson, D.L., J.T. Kiehl, V. Ramanathan, R.E. Dickinson, and J.T. Hack. 1987. Description of NCAR
Community Climate Model (CCM1). NCAR Technical Note 28S. Boulder, CO: National Center for
Atmospheric Research.
1-59
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CHANGE IN CLIMATE VARIABILITY IN THE 21st CENTURY
D. Rind
Goddard Space Flight Center
Institute for Space Studies
2880 Broadway
New York, NY 10025
and
R. Goldberg
Institute for Global Habitabffity
Columbia University
New York, NY 10027
R. Ruedy
Sigma Data Service Corporation
2880 Broadway
New York, NY 10025
Interagency Agreement No. DW80932629-01-1
-------
CONTENTS
ACKNOWLEDGMENTS Si
FINDINGS 2-1
CHAPTER 1: INTRODUCTION 2-2
CHAPTER 2: MODEL AND CLIMATE CHANGE EXPERIMENTS 2-3
CHAPTERS: MEAN VALUES 2-4
CHAPTER 4: YEAR-TO-YEAR VARIABILITY 2-10
CHAPTERS: DAILY VARIABILITY 2-15
CHAPTER 6: VARIABILITY OF THE DIURNAL CYCLE 2-28
CHAPTER 7: DISCUSSION 2-30
CHAPTER 8: CONCLUSIONS 2-33
REFERENCES 2-34
-------
ACKNOWLEDGMENTS
We thank Frank Abramopoulos, who helped with statistical tests, and William Weinstein who helped with
computing. We also thank Linda Mearns and Stephen Schneider for their interest and encouragement in the
course of this work, and Thomas Karl for useful comments in review. This research was supported by the
United States Environmental Protection Agency, while climate modeling at GISS is supported by the NASA
Climate Program Office.
iii
-------
Rind
FINDINGS1
As climate changes owing to the increase of greenhouse gases, there is the potential for climate variability
to change as well. The change in variability of temperature and precipitation in a transient climate simulation,
where trace gases are allowed to increase gradually, and in the doubled CO2 climate is investigated using the
GISS general circulation model. The current climate control run is compared with observations and with the
climate change simulations for variability on three time-scales: interannual variability, daily variability, and the
amplitude of the diurnal cycle. The results show that the modeled variability is often larger than observed,
especially in late summer, possibly owing to the crude ground hydrology. In the warmer climates, temperature
variability and the diurnal cycle amplitude usually decrease, in conjunction with a decrease in the latitudinal
temperature gradient and the increased greenhouse inhibition of radiative cooling. Precipitation variability
generally changes with the same sign as the mean precipitation itself, usually increasing in the warmer climate.
Changes at a particular grid box are often not significant, with the prevailing tendency determined from a
broader sampling. Little change is seen in daily persistence. The results are relevant to the continuing
assessments of climate change impacts on society, though their use should be tempered by appreciation of the
model deficiencies for the current climate.
'Although the information in this report has been funded wholly or partly by the U.S. Environmental
Protection Agency under Interagency Agreement No. DE80932629-01-1, it does not necessarily reflect the
Agency's views, and no official endorsement should be inferred from it.
2-1
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Rind
CHAPTER 1
INTRODUCTION
The increasing concentration of greenhouse gases in the atmosphere has led to the likelihood of
substantial climatic warming in the coming decades. The climate perturbation is usually expressed in terms of
the change of the mean value of specific parameters, such as temperature or precipitation. However, in many
instances, a change in climate variability would have as great an influence as a change in the mean. This is
especially true for biologically oriented processes, such as tree growth or agriculture, where killing frosts or
anomalous heat waves can destroy the crop regardless of the "mean temperature" for the month or year.
Solomon and West (1985) emphasized the lack of suitable projections of changes in climate variability as a
limiting factor in evaluating the response of forests to the projected climate change. As implied by this opinion,
were variability to change as climate warms, it would likely alter the impact of the greenhouse warming on
society.
The United States Environmental Protection Agency (EPA) is currently studying the potential effects of
climate change on various aspects of society, including agriculture, forestry, and water resources (EPA, 1988),
The EPA study uses climate change results for the monthly mean temperature and precipitation as calculated
by several different general circulation models (GCMs). However, the study assumes variability will not change
from its present magnitude. This was done out of necessity, since no systematic study of possible alterations in
variability had been undertaken. The variability change produced by the GCMs was not used directly, since there
had also been no study of how realistic their variability was for the current climate simulation. Thus interannual
and daily variations were taken from observed data for a 30-year time period, and the models' monthly mean
climate change values were simply appended to them. It was recognized that this conservative approach might
well underestimate the influence of the projected climate changes, in the sense that many of society's processes
are inherently arranged with the current variability in mind. In an attempt to determine whether the GCMs
could be used for an estimate of the change in variability, and what change would have resulted, the following
study was undertaken.
The GISS GCM was one of the models providing data for the climate change assessments. Results used
were from both the GISS doubled CO2 run with its current climate control, and a transient climate change
experiment in which trace gases are increased gradually. To assess how well this model can simulate the
observed variability we compare model and observed interannual and dairy variations of temperature and
precipitation for the four geographic areas of concern in the EPA analysis: southeast United States, the Great
Lakes region, the Southern Great Plains, and the West Coast. We also compare how the variability for these
time scales is altered in the climate change simulations. We then repeat these comparisons for the diurnal cycle
variation of temperature. The results of this study provide a first estimate of how variability changes with climate
change.
2-2
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Rind
CHAPTER 2
MODEL AND CLIMATE CHANGE EXPERIMENTS
The model used is the GISS GCM (Hansen et aL, 1983) run at the 8° x 10° resolution. The model
numerically solves the conservation equations for mass, momentum, energy, and moisture. It includes
parameterizations for rain and snow generation, cloud cover, short wave and long wave radiation, surface fluxes,
etc., and uses two ground layers for surface hydrologjc calculations. For climate change experiments, the ocean
temperatures are allowed to adjust but ocean heat transports, required to produce current sea surface
temperatures, are specified as unchanged. Uncertainties in climate models' cloud cover, ground hydrology, and
ocean parameterizations induce uncertainties in model responses to climate change forcing.
The model has been run for both doubled CO2 experiments (Hansen et aL, 1984X and the transient
climate change, in which trace gases are allowed to accumulate gradually, and the climate change is calculated
for the next 100 years. This transient experiment has been reported in several different forums (Hansen et aL,
1987,1988), and the results reported here correspond to a trace gas growth scenario in which current trends are
continued into the future unchanged. Both climate change experiments will be used in this analysis, depending
on the availability of model output for the various time-scales of variability.
2-3
-------
Rind
CHAPTERS
MEAN VALUES
Temperature and precipitation results will be reported for the four areas of the United States which are
the focus of the EPA climate-change effects study. The four grid box regions for the 8° x 10° resolution model
are shown in Figure 1, along with the cities that are used for comparison purposes (Table 1). We present in
Table 2(a,b) a comparison of the model and observed temperature and precipitation for the 4 months, with
observations obtained by averaging values for the nine cities within or in the proximity of each of the grid boxes.
The reason for chosing nine cities will be discussed in Chapter 4. The model results are averages over 10 model
years (10 independent samples) for the control run, doubled CO2 study, and transient experiments decades.
We evaluate the statistical significance of the differences between the model and observations, and the
model and climate change experiments, by using the first moment test variate (Chervin, 1981), which equals the
difference in mean values divided by the square root of the sum of the squares of the standard deviations.
Standard deviations for observations, current climate, and doubled CO2 climate are given in Table 3. We use
the hypothesis that there is no difference between the means, and reject it at the a priori selected significance
level of 5%, for a two-sided critical region. Cases in which the hypothesis is rejected, and thus values can be
determined to be significantly different, are indicated by an asterisk in Table II. Note that even if we cannot
prove a significant difference, it does not necessarily indicate that the model is reproducing the current
temperatures or precipitation. It may be that we simply do not have enough data to disprove the assumption.
Thus in the cases where the differences are not significant, we must simply say we cannot reject the hypothesis
(rather than accepting it).
Model monthly mean temperatures (Table 2a) are significantly different from the observed during summer
and fall. In these seasons the model is consistently cooler, due most likely to the ground hydrology scheme which
keeps too much moisture in the ground hi summer (Hansen et al., 1983). As the winter temperatures are more
accurately reproduced, the model tends to underestimate the seasonal temperature cycle by 15-20%.
Model monthly mean precipitation values (Table 2b) are generally realistic for the southeast and Great
Lakes grid boxes, while they tend to overestimate the rainfall for the west coast and southern Great Plains.
These discrepancies will affect the precipitation distributions discussed below.
Thus as indicated in Table 2, in about half the cases the model produces significantly different mean
temperature and precipitation values when compared with observations. This properly raises doubts about the
validity of model-produced changes in these fields, as well as changes in variability. We return to this question
in the discussion section; here we simply note that the model discrepancies must be borne in mind when
evaluating the results.
The current climate control run utilized the atmospheric composition of 1958. Also shown hi Table 2 are
the model-predicted changes for the decades of the 2010s, 2030s, 2056-2065, and the equilibrium doubled CO2
results. The annual average global mean warming for the 2010s was about 1°C relative to the control run, for
the 2030s about 2°C, and for 2056-2065 about 4.2°C. Close to one-half of the temperature changes in the 2010s
are significant, while temperature changes in later decades and for the doubled CO2 climate are usually so.
The doubled CO2 results are averages for years 26-35 from the experiment, when the atmosphere was
42°C warmer and temperature was no longer changing. In that respect it can be compared with the values for
2056-2065, in which the wanning was reached in a transient mode. Cases in which the two temperatures are
significantly different are indicated by a plus sign hi Table 2; several of the cases fall into this category, with the
equilibrium doubled CO2 changes being smaller than that for the decade around 2060. In the cases which lack
significant differences, there is no consistent sign of the difference. For the purposes of the following discussion
we will look upon the experimental results for the 2060 time period as being similar to those for equilibrium
doubled CO2.
2-4
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Rind
47.0
Figure 1. Location of grid boxes for model results, and cities from which observed data has been used for
comparison. The cities corresponding to the numbers are listed hi Table 1.
2-5
-------
Rind
Table 1. Stations Used to Obtain Grid Box Averages
SOUTHERN GREAT PLAINS
<31-39°N, 95-105°U)
1. DENVER
2. 600DLAND
3. UICHITA
4. ALBUQUERQUE
5. AMARILLO
UEST COAST
(39-47"N, 115-125'U)
6. TULSA
7. EL PASO
8. MIDLAND
9. UACO
1. YAKIHA
2. LEUISTON
3. EUGENE
4. REDMOND
5. BOISE
6. MEDFORD
7. RED BLUFF
8. RENO
9. ELY
SOUTHEAST
(31-39°N, 75-85°U>
1. INDIANAPOLIS
2. WASHINGTON
3. NASHVILLE
4. CHARLOTTE
5. NORFOLK
GREAT LAKES
<39-47°N. 75-85°U>
6. MONTGOMERY
7. SAVANAH
8. WILMINGTON
9. COLUMBUS
1. SLTE ST. MARIE
2. FLINT
3. BUFFALO
4. SYRACUSE
5. FT. UAYNE
6. CLEVELAND
7. U1LLIAMSPORT
8. COLUMBUS
9. PITTSBURG
2-6
-------
Rind
Table 2a. Monthly Average Mean Temperatures (°C)
MONTH
LOCATION
DBS CURRENT
TEMP
JANUARY
APRIL
JULY
OCTOBER
S.G. PLAINS
SOUTHEAST
UEST COAST
6RT. LAKES
S.6. PLAINS
SOUTHEAST
UEST COAST
6RT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
2
2
-0
-4
14
14
8
8
26
25
21
21
15
15
10
10
.32
.79
.08
.79
.30
.46
.59*
.41
.80*
.60*
.40*
.69*
.55*
.49
.84*
.88*
TEMP
-0
4
-1
-2
14
14
6
7
20
22
16
18
12
15
8
6
.07
.40
.23
.72
.08
.36
.85
.52
.50
.86
.84
.61
.83
.28
.21
.41
2010s 2030s
a T
1.
2.
1.
0.
0.
2.
1.
1.
1.
1.
0.
2.
1.
1.
1.
2.
87
10
38
06
44
31*
82*
45
19*
68*
60
06*
52
51
72
15*
6 T
3.
1.
3.
1.
4.
5.
2.
3.
1.
2.
3.
2.
1.
3.
3.
2.
-2060
07*
71
71*
84
06*
07*
43*
08*
84*
44*
55*
89*
76
01*
42*
81*
6 T
5.39*
4.74*
4.17*
5.16*
5.32*
5.79*
5.58*
3.52*
4.84*
4.57*
4.14*
3.75*
6.24*
4.80*
4.96*
5.89*
2xC02
A T
5.0*
4.0*
6.0*
6.0*
5.0*
4.0*+
6.0*
5.0*+
4.0*
3.0*
3.0*
4.0*
7.0*
5.0*
5.0*
4.0*+
Table 2b. Monthly Average Precipitation (mm d"1)
MONTH
JANUARY
APRIL
JULY
OCTOBER
LOCATION
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.6. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
DBS CURRENT
PREC
0.46*
2.83
2.18*
2.04*
1.31
2.93
0.94*
2.73
1.99*
4.07
0.25*
2.82
1.22
2.14
0.91
2.16
PREC
2.08
2.85
4.03
2.98
1.93
2.27
2.40
2.08
4.31
4.51
1.54
2.44
0.57
1.87
1.40
1.62
2010s 2030s -2060
d P
-0.07
-0.29
-0.19
-0.79
1.44
0.77
-0.16
-0.15
-0.43
-0.21
0.41
0.01
0.03
1.57
0.59
0.04
A P
0.00
-0.96
0.08
-0.81
1.36
-0.50
-0.02
-0.34
-0.23
0.25
0.09
0.70
0.57
-0.39
-0.55
0.04
A P
1.12*
-0.41
0.13
-0.43
1.39
0.25
-1.19
0.14
-0.33
0.06
0.73
-0.16
0.27
0.19
0.39
0.32
2xC02
a P
-0.76+
0.27
0.93
0.07
-0.47
0.54
0.04+
0.25
1.05
1.60
0.14
0.61
0.02
-0.06
0.57
-0.25
2-7
-------
Rind
Table 3a Interannual Standard Deviations of Temperature (°)
GRID BOX
S.G. PLAINS
SOUTHEAST
LEST COAST
GREAT LAKE
JAN FEB
DBS 2.0 2.0
CONT 3.1 2.7
2C02 2.1 1.9
STD 0.7 0.7
OBS 2.3 2.3
CONT 3.0 2.3
2C02 2.1 1.9
STD 0.3 0.6
OBS 2.1 1.7
CONT 2.2 2.4
2C02 1.7 2.1
STD 0.7 0.6
OBS 2.4 2.5
CONT 3.0 1.8
2C02 1.5* 1.8
STD 0.6 0.7
MAR
1.9
2.2
1.7
0.5
2.1
2.2
1.7
0.5
1.2
1.7
2.2
0.4
2.0
1.7
1.8
0.6
APR
1.4*
2.5
1.2*
0.5
1.2*
2.4
1.2*
0.4
1.4
1.6
1.2
0.4
1.4
2.3
1.3
0.4
MAY
1.2
1.3
0.7*
0.3
1.4
1.9
0.7*
0.3
1.3
1.2
1.5
0.4
1.7
2.0
1.6
0.4
JUN
1.2
1.1
1.0
0.3
1.0
0.9
1.0
0.2
1.3
1.3
1.3
0.6
1.1
1.5
1.0
0.3
JUL
1.1
0.9
1.1
0.4
0.7*
1.3
1.1
0.3
0.9
1.5
1.6
0.5
1.0
1.3
1.1
0.5
AUG
0.9
1.3
0.9
0.5
0.8*
3.1
0.9*
0.7
1.3*
4.2
3.5
0.7
1.1
1.7
1.6
0.7
SEP
1.3
1.5
2.0
0.5
1.1
1.2
2.0
0.5
1.5*
3.0
2.6
0.6
1.3
1.8
1.4
0.4
OCT
1.4
2.1
1.9
0.4
1.4
2.0
1.9
0.5
1.1*
2.5
2.7
0.5
1.7
1.8
1.8
0.3
NOV
1.5
2.4
1.5
0.8
1.3
1.4
1.5
0.7
1.3
2.1
2.4
0.5
1.5
1.4
1.9
0.5
DEC
1.5
2.5
2.3
0.6
1.9
2.9
2.3
0.4
1.5
1.3
2.3
0.4
2.2
2.2
2.5
0.5
Table 3b. Interannual Standard Deviations of Precipitation (mm d"1)
GRID BOX
S.G. PLAINS
SOUTHEAST
UEST COAST
GREAT LAKE
OBS
CONT
2C02
STD
OBS
CONT
2C02
STD
OBS
CONT
2C02
STD
OBS
CONT
2C02
STD
JAN
0.3*
1.0
0.9
0.4
0.7*
1.5
1.9
0.3
0.8*
1.6
0.9*
0.3
0.7
1.0
1.1
0.2
FEB
0.3*
1.2
1.5
0.3
0.9
1.5
1.7
0.2
0.7
1.2
1.6
0.6
0.7
0.5
0.8
0.2
MAR
0.6*
1.7
1.4
0.3
0.8*
1.5
2.0
0.5
0.5
0.6
1.5*
0.2
0.7
1.2
1.3
0.3
APR
0.6*
1.5
1.9
0.6
0.8
1.2
2.0
0.4
0.5*
1.5
1.2
0.2
0.7
0.8
1.5*
0.3
MAY
0.7*
1.4
1.4 '
0.4
0.7*
1.9
1.9
0.5
0.5*
1.3
1.5
0.2
0.8
1.3
1.4
0.2
JUN
0.7
1.0
2.0*
0.3
0.8
1.2
1.5
0.4
0.4*
1.2
1.9
0.3
1.0
1.4
1.0
0.4
JUL AUG SEP
0.8 0.6 0.9*
1.2 1.0 0.4
1.9 1.3 1.0*
0.3 0.2 0.2
0.9* 0.8* 1.2
1.9 2.0 1.6
1.9 2.0 2.0
0.3 0.3 0.6
0.1* 0.3* 0.3
0.9 0.6 0.3
0.6 0.8 0.2
0.1 0.2 0.1
0.6* 0.8* 0.8
1.2 1.5 1.0
1.5 1.1 0.7
0.3 0.1 0.4
OCT
0.8
0.6
1.5*
0.3
0.9
1.4
1.9
0.4
0.6
0.9
1.4
0.2
1.0
0.8
1.7*
0.2
NOV
0.5*
1.2
0.8
0.2
0.8*
1.7
1.9
0.3
0.9*
1.7
2.0
0.5
0.7*
1.3
1.0
0.3
DEC
0.4*
0.8
0.7
0.2
0.8
1.4
1.6
0.4
1.1
1.5
1.9
0.3
0.7
1.2
0.9
0.2
2-8
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Rind
The precipitation changes (Table 2b) are not significant, although the doubled CO? or equivalent 2060
changes usually indicate increased rainfall: 23 of the 32 cases shown for these time periods have increased
precipitation. From standard binomial probability testing for increase versus decrease, this or higher percentages
of increase would occur less than 1% of the time simply by chance. As discussed in more detail (Rind, 1988a)
the 10-year average changes are generally on the order of one (interannual) standard deviation regardless of
the size of area averaging. Such differences would require integrations for many years to establish their
significance. We will see this tendency repeated throughout the study: individual results often show little
significant change, although a majority of the results show the same sign of the change. Note also that as the
doubled CO, and 2060 precipitation differences are not significantly different, we again treat the two simulations
as being similar.
Given this character of the modeled climate change, we now investigate the model's variability compared
to the observed, and indicate how variability changes as the climate warms. The time-scales of variability are
investigated hi inverse order, starting with the longest accessible scale of year-to-year variability, then daily, and
finally the diurnal cycle amplitude.
2-9
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Rind
CHAPTER 4
YEAR-TO-YEAR VARIABILITY
How does the modeled year-to-year variability compare with observed variability? We compare the model
variability from a 100-year control run for the present climate (Hansen et al., 1988) with the interannual
variability obtained from the stations shown in Figure I/Table 1 for the 1951-1980 time period The results of
this comparison are given in Table 3a for the relevant areas. To determine significant differences, we evaluate
the second-moment test variate, equal to the square root of the F statistic, from the ratio of model to observed
standard deviations (Chervin, 1981). Following Chervin, we determine the significance at the a priori selected
10% significance level using the hypothesis of equal variances. Significant differences are again indicated by an
asterisk. For comparison we also show the standard deviation of the 10-year standard deviation, determined by
breaking the 100-year run up into 10 equal intervals. Note again the test allows us only to determine whether
significant differences exist between the model and observations, and not to prove that the model is actually
reproducing the current climate values.
Overall the modeled and observed temperature variability are in good agreement, statistically different
at the 10% level in only 7 of the 48 cases. However, the model in summer generally overestimates the variability,
even if the magnitude of the difference is not significant. The modeled surface air temperatures in summer are
sensitive to the ground hydrology parameterization, which is very crude in this and most other climate models.
It would appear to allow for greater variability in soil moisture and surface air temperature than occurs in the
real world, an effect which is exaggerated by August when the ground can become completely dry in the model
owing to continual evapotranspiration (the parameterized vegetation does not completely shut off moisture loss
before the ground dries out entirely).
The comparison between model and observed interannual variability of rainfall is shown in Table 3b. In
almost half the cases the values are significantly different, with the model variability generally larger than
observed; this is especially true in the areas and seasons where mean precipitation amounts were overestimated
(e.g., West Coast in summer, Southern Great Plains in winter, Table 2b). With excessive precipitation there is
more scope for variability. However, even in other regions, the modeled values are generally too high. The
model produces one value for rainfall each time step over the entire grid box; thus either it rains or it does not
In the observations, it can rain at one station and not another, and the result is to smooth the grid box average
value and reduce variability. When we reduced the number of stations used for assessing the observed variability
from nine to five, precipitation variability increased by some 33%, while temperature variability was relatively
unchanged. This indicates the uncertainty that must be attached to the "observed" interannual precipitation
variability for a grid box as a whole. Again, the deviation of the modeled variability from observed will likely
affect the confidence that can be placed in the climate change assessments.
What should we expect for changes in the interannual standard deviation of temperature and precipitation
as climate warms? If there are physical reasons for expecting changes, then we can establish an a priori
expectation of sign change. We begin with temperature, and discuss precipitation later in this chapter.
Climate models have been unanimous in predicting that high latitudes should warm more than lower
latitudes (e.g., Schlesinger and Mitchell, 1987). High latitudes have greater static stability, so that low level
warming is trapped near the surface, rather than being converted to higher altitudes as occurs in the tropics.
Furthermore, snow and sea ice melting at higher latitudes reduces the surface albedo, allowing more solar
radiation to be absorbed, and leading to greater heat ventilation from the oceans during winter.
Because of this latitudinal variation in temperature change, the temperature differential between low and
high latitudes is expected to decrease, a result which again holds true in the different climate models (e.g., Rind,
1987). Were the latitudinal temperature differences to be completely eliminated (as is apparently the case for
Venus), temperature variability on all time scales would tend toward zero; the variability currently results from
the advection of cold and warm pools of air into a region, pools which accumulate at high and low latitudes
2-10
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Rind
respectively. All that would be left to provide for advective temperature changes would be land/ocean or other
longitudinal temperature contrasts. As the equilibrium doubled CO2 climate reduces the latitudinal temperature
contrasts, this should lead to reduced temperature variability in the future.
In addition, the synoptic scale systems of high and low pressure which are responsible for adverting
different air masses into a region gain their energy from the latitudinal temperature gradient via the baroclinic
process. As this temperature gradient decreases, so should the energy of these systems, as has been seen in
doubled CO, climate studies (Rind, 1987). Again, this should result in reduced temperature variability.
With these expectations in mind, numerous studies have been made, looking for a trend in variability as
climate has warmed over the past century (e.g., Angell and Korshover, 1978; Barnett, 1978; Ratcliffe et al., 1978;
van Loon and Williams, 1978; Diaz and Quayle, 1980). None of these studies has found such a trend, although
the warming over this time period, on the order of 0.6°C (Hansen and Lebedeff, 1987), has not been particularly
large when compared with the projected future wanning. Does the model show decreased variability as the
climate warms?
In Table 3a, we show the monthly standard deviation of temperature for the last 10 years of both the
current climate control run and the doubled CO2 run on the 8° x 10° resolution. The significance of the changes
at the 10% level are determined as discussed previously. In only six of the cases are the differences significant,
although there is a general tendency for the expected reduced variability from January through April in the
doubled COA[AD2 climate (13 of the 15 months which show changes from the four grid boxes have reductions,
and all six of the significant changes show reduced variability).
To determine whether the tendency for reduced variability during winter would be evident in a broader
sample, a comparison was made for 13 grid boxes over the United States for the months of January through
April. In 70% of the approximately 50 cases the control run standard deviations were lower than those for the
doubled CO2 run. However, the grid boxes are not necessarily independent; Hansen and Lebedeff (1987)
computed the correlation coefficient of annual mean temperature changes for pairs of randomly selected stations
having at least 50 years of records. They found that for mid-latitudes, the correlation dropped off to 0.5 at
approximately 1200-km separation, and to 0.1 at 3000-km separation. While those authors used the 1200-km
distance as representative of independent data points, to absolutely guarantee that we are dealing with
geographically independent regions, we look at grid boxes more than 3000 km apart (i.e., every fourth grid box).
Grid boxes 4000 km apart were chosen at random in the Northern Hemisphere extratropics (20-70°N)
during whiter, when the high latitude amplification of the temperature change is greatest (Hansen et at, 1984).
In 60% of the 150 cases, the standard deviations decreased. Evaluating this result, standard binomial distribution
theory shows that such a change, or even greater percentage reductions, would have occurred by chance less than
1% of the time. We show in Figure 2 the change of the standard deviation during January. As evident in the
figure, and the fact that only 60% of the cases show a decrease, as well as the sampling for the United States,
the reduction does not occur at all grid boxes in all winter months. However, there can be no doubt about the
reality of the effect on the largest spatial scales; for the extratropics during winter, the latitudinal average surface
air temperature standard deviation decreases in the doubled CO2 climate more than 80% of the time. And in
the months for which the climate change shows a decrease in the latitudinal temperature gradient (September
through May), the interannual variability for the Northern Hemisphere as a whole decreases in every month in
the warmer climate.
How should precipitation variability change as climate warms? An indication can be gained by comparing
the model's variability relative to the observed with the model's mean values relative to observed. As noted
above, where the model severely overestimates precipitation for the mean, it also does so for its variation, as
greater magnitude differences between years are possible when rainfall values are greater. As climate warms,
there is increased evaporation from the oceans, and an increase in the hydrologic cycle, with global rainfall higher
by about 11% (Rind, 1988a,b). With all else tile same, this should lead to increased variability, and the annual
2-11
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Rind
global average variability does increase in the doubled CO2 climate by some 3%. Diaz and Quayle (1980) failed
to find any significant differences in precipitation variability between warm and cold decades, although the
temperature changes were much smaller than is being considered here for doubled CO2.
The standard deviation of monthly average precipitation in the climate change experiments is given in
Table 3b. The results maintain the character we have seen throughout; on an individual basis, very few of the
changes are significantly different (7 of the 48 cases). Overall, however, the expected tendency emerges, as 31
out of the 44 total months in which a change is recorded have increased variability in the doubled CO2 climate.
The tendency was particularly striking in the Southeast, in which the variability in the warmer climate did not
decrease for any month of the year, including autumn, when the actual mean precipitation values decreased by
0.6 mm day1 (Rind, 1988a).
To look at a broader sample, we need to know the spatial scale for independent precipitation
measurements. Rind and Lebedeff (1984) investigated the correlation coefficient between the precipitation
trends for stations in the United States, and found that at a distance of 500 km the correlation had already
dropped to 0.4. Diaz and Quayle (1980) have clearly shown that the changes in precipitation and precipitation
standard deviation between different decades have smaller spatial scales than the corresponding temperature
changes. Thus in this case we use 1000 km as the length scale for independent measurements. Referring to the
22 grid boxes over the United States and continguous North America for the 12 months, 65% received
precipitation increases in the doubled CO2 climate (Rind, 1988a). Examination for variability changes indicated
that out of the 264 cases, 62% showed increased variability, which would occur by chance (along with even higher
percentages) less than 0.1% of the time. When the study is repeated using grid boxes 2000 km apart, increased
variability still occurred with a probability which would have occurred by chance less than 1% of the time. On
even larger spatial scales, the hemispheric and global standard deviations increased each month. The change in
standard deviation is shown in Figure 3 for July. Again note that although general increases occur, there are
some regions with decreased variability. When this figure is compared with the GISS model change in
summertime precipitation in the doubled CO, climate (as shown in Schlesinger and Mitchell, 1987) it is evident
that the largest changes in interannual variability occur in regions where there are large changes in the mean
precipitation itself, and both the mean and variance changes have the same sign. Thus the near equality of
percentage of locations which show increases hi mean precipitation over the United States, and those which have
increased variability, is not fortuitous.
When the change in variability is of the same sign as the change in the mean, it indicates that the change
in relative variability is minimized, which may be important in some applications. To examine this issue more
closely, the sign of the change of the mean was compared to the sign of the change in interannual variability for
the grid boxes and months described above. In 50% of the cases, grid boxes over the United States and adjacent
North America had increases in both quantities, while in 23% of the cases there were decreases in both. Thus
in 73% of the cases the sign of the change in variability was the same as the sign of the change in the mean. Of
the other 27%, 16% had increased mean precipitation but decreased variability.
To summarize the results of this section, at individual stations changes in the interannual standard
deviation of temperature and precipitation were generally not significant. However, when a larger geographical
region is considered, the number of independent grid boxes which show a decrease in interannual temperature
variability and an increase hi interannual precipitation variability in the doubled CO2 climate is significant, with
the changes noted 60-70% of the time. As emphasized by this value, as well as the results shown in Table 3 and
Figures 2 and 3, the sign of these changes simply represent tendencies, not uniform results.
2-12
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Rind
STD. DEV. OF SURF AIR TEtlP (°C)
JANUARY
2C02-CON
Figure 2. Latitude:longitude presentation of the change in the interannual standard deviation of surface air
temperature in January, doubled CO2 climate minus control. The tic marks indicate latitudes of
0°, ±30", and ±60°, and longitudes of Of and ±90°.
2-13
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Rind
A STD. DEV. OF PREC. dim d'1)
JULY
2C02-CON
Figure 3. As in Figure 2 for the change in the interannual standard deviation of precipitation in July, doubled
CO2 climate minus control.
2-14
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Rind
CHAPTERS
DAILY VARIABILITY
In this section our interest is in comparing daily variations in temperature and precipitation, for
observations versus the modeled current climate, and for the climate change experiments. For temperature, the
daily mean value is compared with the monthly average value and the departure noted; the results are then
tabulated for the length of the record, 30 years in observations, 10 years for the different model runs. The
distribution of these departures can then be compared. While this technique is straightforward for the model
values, in which a single temperature represents the entire grid box, the situation is not as clear for the
observations.
How many stations are needed to produce a representative result for the area equivalent to the model
grid box? In Figure 4, we compare the distribution of daily temperature departures from the monthly mean for
30 years of April data (1930-1960) when using 3, 5, and 7 stations respectively, for the Southern Great Plains in
April. In each case the stations were widely distributed throughout the grid box. While some changes can be
noted, the results are rather similar regardless of the number of stations used.
Comparisons were also made between the distributions of observed and modeled precipitation for the
same grid boxes and months. Due to the importance of true drought episodes, the frequency of occurrence of
absolutely no precipitation was recorded separately from very light precipitation. The distribution of precipitation
as a function of number of stations is shown in Figure 5. Here the results are very different. As the station
number is increased, the frequency of days with absolutely no rainfall decreases, and the frequency with light
rainfall increases. This is not unexpected, since light rainfall occurs with significant spatial variability, and the
more stations utilized, the better the chance of recording it. However, it does indicate that the comparison of
observed and modeled rainfall distributions will depend on the number of stations utilized.
When the number of stations used was increased to nine, the resulting distribution in the test cases did
not differ significantly from the distribution obtained with seven (with significance determined in the manner
described below), for either temperature (compare Figure 4 with Figure 7, top left) or precipitation. The use
of nine stations in each grid box thus appeared to be adequate for these purposes, although the more uniform
the station distribution, the better the grid box representation. The stations are indicated in Figure 1; as is
evident we also occasionally chose to use stations which were just outside the grid box, in order to secure a more
area-wide representation of the results.
In comparing distributions of this sort, considerable problems are encountered when attempting to
evaluate the significance of differences between them. Daily temperature values are unlikely to be independent,
as some degree of persistence is prevalent for several days. The daily variance can be defined in terms of
autocorrelation coefficients and an uncorrelated contribution. Katz (1984) provided a procedure for investigating
the significance of the changes hi the uncorrelated contribution. Wilson and Mitchell (1987) employed his
technique, and found a significant decrease in the uncorrelated daily variance during winter.
However, our interest is not in the uncorrelated component, it is in the actual daily variation. As climate
warms, and the latitudinal temperature gradient decreases, there is the potential for decreases in the mean zonal
wind flow, leading to slower movement of synoptic scale systems. This might produce a change in persistence,
which would contribute to the change in daily variations and would be an important component to recognize.
The problem in including the correlated changes is that it reduces the number of independent data points being
used, a factor which must be considered in the statistical evaluation.
Thus we adopted the following approach. We first calculated the autocorrelation function for the
temperature and precipitation data sets for both observations and the different models experiments. An example
of the observed and modeled temperature autocorrelation functions for the southeast grid box for April is shown
2-15
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Rind
50
APRIL OBSERVED DAILY TErvEfuimz DISTRIBUTION
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(TOP - AVERAGE TEM>> C C)
Figure 4. Distribution of observed daily temperature departures from monthly means for the Southern Great
Plains grid box for 30 years of April data (1930-1960) using three stations (top), five stations
(middleX and seven stations (bottom).
2-16
-------
APRIL OBSERVED PfECIPITATION 01STRIBU1IOK
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70
APRIL OB5ERVEC PRECIPITATIOK DISTRIBUTION
-------
Rind
in Figure 6. The area under the curve represents the persistence in the data set, in days. This value was
calculated for each autocorrelation function, and is the value used to reduce the number of independent
observations in the statistical tests described below.
The results of this analysis are presented in Table 4. Comparing the model with observations, there is
a tendency for the model to have greater persistence, especially during the warm season, and more so for
precipitation than temperature. The coarse grid used in this model might be expected to retard the movement
of synoptic scale systems, increasing the time of persistence; and the simplified ground hydrology could set up
stronger positive feedbacks to precipitation changes than exist in the real world. Note also the smaller
persistence associated with precipitation; the persistence value of close to one day obtained for these regions for
the observations is in agreement with the general independence of precipitation on the preceding day found by
Chin and Miller (1980).
What happens as climate changes? As indicated above, the a priori assumption is that if wanning and
reduced latitudinal temperature gradient slows the zonal mean winds, synoptic scale systems might move more
slowly and increase persistence in the future. In fact, while the latitudinal temperature gradient at the surface
does decrease, the latitudinal temperature gradient aloft increases, as convection transports heat to the tropical
upper troposphere. Thus in the GISS doubled CO2 experiments the zonal kinetic energy actually increases
slightly (Rind, 1987); thus it is not clear what to expect, and referral to the average persistence times shown in
Table 4 indicates no obvious trend for either temperature or precipitation. As noted by Rind (1987), the change
in zonal kinetic energy depends strongly on the .degree of high latitude temperature change amplification
produced in the model, and so may well be model dependent. This implies that changes in persistence may be
so as well.
To compare distributions of data, several statistical methods are available. One can bin the data, as in
Figures 4 and 5, and use the chi-squared test to evaluate whether the null hypothesis, that the two distributions
arise from the same population, can be judged unlikely. The greater the difference in number for each grouping,
the more likely the null hypothesis can be rejected. Alternatively, one can generate the distribution function of
the continuous data set, and use the Kolmogorov-Smirnov (KS) test to evaluate differences (e.g., Knuth, 1969).
In this study, we employ both techniques on the daily temperature and precipitation distributions. When we
compare the results from the two techniques in the evaluations of significance at the 5% level (i.e., significant
versus non-significant X the results were in agreement 84% of the time, with the same value for both temperature
and precipitation. This lends confidence to the evaluation of significance; however, it must be mentioned that
there are uncertainties in the calculation of the absolute value for the chi-squared test, such as the Yates*
approximate correction for using discrete distributions of frequencies (Panofsky and Brier, 1968), and
uncertainties associated with significance levels for large data sets with the KS test (Knuth, 1969). It is important
to recognize that the characterization of significance is perhaps not as important as the nature of the similarities
or differences.
To use the chi-squared statistic when the data set is not completely independent, the chi-squared value
must be reduced by the fraction of the data which is correlated (Knuth, 1969). For example, in evaluating
whether the distributions in Figure 4 are significantly different, the chi-squared value must be divided by 3, the
value of persistence shown in Table 4 for temperature observations in the southeast grid box in April When
applied to this example, omitting categories in which the numbers are less than five (as noted by Panofsky and
Brier, 1968), the result indicates that the three distributions are not significantly different, even at the 10% level
When correcting for lack of independence in the KS test, the number of observations (30 months x 30
days/month = 900) is reduced accordingly.
Comparisons were made between 30 years of observations (1951-1980) and 10 years of the control run
for the transient experiment for the four grid boxes during the months of January, April, July, and October.
(Here the fact that the degree of dependence in the distributions being compared differs (Table 4) implies that
a weighted average correction must be applied.) The results show that the model and observed daily
temperature variations about the monthly mean are rarely significantly different, occurring only once in the
2-18
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Rind
OBSERVED
---- nODEL
/CISS
7.0
Figure 6. Autocorrelogram of observed and modeled daily temperature* for southeast grid box in April.
2-19
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Rind
Table 4a. Daily Persistence of Temperature (days)
MONTH
JANUARY
APRIL
JULY
OCTOBER
LOCATION
S. 6. PLAINS
SOUTHEAST
UEST COAST
6RT. LAKES
S. 6. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
OBS
2.
2.
2.
2.
2.
3.
2.
3.
2.
2.
2.
2.
3.
3.
3.
2.
CURRENT
72
17
94
32
51
04
38
06
36
44
91
10
32
00
01
42
2
2
2
2
4
4
2
2
3
3
3
2
3
4
2
3
.26
.35
.46
.25
.22
.26
.58
.89
.98
.63
.85
.82
.50
.04
.54
.60
2010s 2030s -2060
2.
2.
2.
2.
2.
3.
3.
2.
2.
3.
3.
4.
2.
3.
3.
2.
10
76
26
28
99
63
10
99
57
83
91
07
82
49
26
82
1
2
2
2
2
2
3
2
4
3
4
2
3
3
2
3
.90
.25
.67
.21
.92
.93
.20
.62
.36
.71
.28
.97
.95
.79
.97
.64
2
2
2
2
3
3
2
2
3
3
4
3
3
3
3
3
.20
.69
.27
.47
.08
.31
.87
.45
.42
.10
.65
.85
.86
.19
.14
.79
Table 4b. Daily Persistence of Precipitation (days)
MONTH
JANUARY
APRIL
JULY
OCTOBER
LOCATION
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
OBS CURRENT
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
.24
.17
.76
.14
.24
.23
.30
.21
.33
.16
.21
.10
.47
.27
.66
.30
1
1
1
1
1
2
2
2
2
2
1
2
1
2
2
1
.78
.80
.95
.64
.82
.32
.17
.15
.14
.64
.63
.32
.86
.39
.48
.73
2010s 2030s -2060
1
1
2
1
2
2
2
1
2
2
2
2
1
2
1
2
.76
.96
.14
.70
.88
.62
.38
.99
.09
.14
.74
.20
.96
.22
.95
.13
1
1
1
1
2
2
2
1
1
2
2
2
I
2
1
2
.48
.80
.77
.51
.81
.51
.36
.66
.88
.78
.38
.58
.71
.21
.92
.08
2
1
1
1
2
2
1
1
1
1
2
2
3
2
2
2
.34
.68
.94
.78
.05
.17
.93
.88
.99
.66
.11
.49
.28
.31
.81
.28
2-20
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Rind
at the 5% level. Shown in Figure 7 are distributions from observations (top) and model (bottom) for the
Southern Great Plains (left) and the Great Lakes (right). Although the distributions are not significantly
different, it is clear that the model produces days with greater temperature extremes than is observed. (Note
that since we are using 30 years of observations and only 10 years of model results, the likelihood of finding
extreme values is larger in the observations, contrary to the actual results.) This tendency occurs continually and
implies that there are feedback processes in the real atmosphere that limit surface temperature deviations over
a grid-box sized area which do not operate with the same magnitude in the model. The difference is not a
function of the number of stations used for the observations: the results of Figure 4, for the same month and
location, show that even with three stations the extreme temperatures are not recorded.
To determine how the daily temperature variability changes with climate, distributions were produced for
the four grid boxes and months from the transient experiment results for the years 2010-2019, 2030-2039, and
2056-2065. As noted above, the first two time periods experienced global mean warming of about 1° and 2°C
respectively, relative to the control run with the 1958 atmospheric composition, and during the last time period
the global warming of 4-2°C was equivalent to the doubled CO2 equilibrium warming with the GISS model
Comparison with the control showed that the model distributions did not in general differ from that for today,
and there was no obvious progression as climate warmed. The results showed considerable individuality, both
from month to month and as a function of location. The distributions for the southeast grid box for April are
given in Figure 8; while changes occur, they are neither systematic nor significant.
Although the distributions may not generally differ significantly overall, a change in the occurrence of
extreme temperature values could be important. The standard deviation of the values about the monthly mean
give greater weight to extreme values, and so these have been calculated for the same cases. The results for
observations, the current climate control run, and the climate change experiments are given in Table 5a The
asterisk indicates significance at the 10% level, calculated, as before, using the second-moment test variate
(Chervin, 1981), correcting the number of independent data points from the persistence values shown in Table
4a As expected, model values are greater than observed, due to the model's greater extremes.
The interannual variations showed that standard deviations generally decreased, but the changes at
individual locations were usually not significant. The decrease was anticipated due to the reduction in latitudinal
temperature gradient and eddy energy. The same processes could be expected to reduce daily temperature
variations. The changes shown in Table 5a are of the same nature; they generally show decreases, but only
occasionally are the changes significant. For the winter/early spring months of January and April decreases
occur in 18 of the 24 cases. Were the locations geographically independent, this percentage of decrease would
be significant at the 3% level, using binomial probabilities. As the southeast and Great Lakes grid boxes are
contiguous, it would be necessary to consider a wider sample to make a firmer assessment.
Precipitation distributions were also tested. Comparison between the model and observations is affected
by the fact that the monthly average precipitation may be very different from the observed for the grid box as
a whole (Table 2b); similar differences in monthly average temperature were not a factor in the temperature
comparison since the daily departures from each monthly mean temperature were being recorded. The
precipitation difference could not be removed in a unique fashion: if the grid box had twice as much rainfall as
observed, should each rainfall occurrence be reduced in intensity by a factor of two, or should the frequency of
rainfall be changed? Rather than arbitrarily altering model values, we decided to evaluate the distributions as
they were.
As can be seen in Table 2b, for the southeast and Great Lakes grid boxes, the model simulates the
observed precipitation reasonably well. For the west coast and southern Great Plains grid boxes the model
produces too much rain. Thus it could be expected that these latter two areas would have significantly different
rainfall distributions, from the model, and such is the case - in three of the four seasons the model and observed
precipitation distributions differed at better than the 5% level in those regions. In contrast, the Great Lakes grid
box showed significant differences only once. Overall, model and observed values differed slightly more than
one-half of the time.
2-21
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Figure 7. Observed (top) and model (bottom) dafly temperature departure from the monthly mean for the
Southern Great Plains in April (left), and the Great Lakes in April (right).
-------
APRIL GISS CONTROL MM TEWERATUC DISTRIBUTION
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Figure 8. Distribution of daily temperature departure from the jnenthfy mean for the southeast grid box in
Apr! for the current climate (lop leftX the 2010s
-------
Rind
Table Sa. Daily Temperature Standard Deviations (°C)
MONTH
LOCATION
OBS CURRENT
S.D.
JANUARY
APRIL
JULY
OCTOBER
S.G. PLAINS
SOUTHEAST
(JEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
4
4
3
4
3
3
2
4
1
1
2
2
3
3
3
4
.81*
.53*
.63*
.97
.72*
.71*
.59*
.65*
.74*
.50*
.40*
.38*
.79*
.59*
.15*
.09*
S.
8
6
5
5
5
5
4
6
2
2
3
3
5
5
6
5
D.
.15
.90
.86
.79
.77
.50
.29
.15
.56
.34
.56
.02
.16
.21
.51
.46
2010s 2030s -2060
a s
0
-0
-0
0
-0
-0
0
-0
0
0
0
-0
1
-0
-0
-0
.0.
.61
.14
.61
.44
.57
.65
.77*
.51
.54
.14
.03
.48
.16*
.54
.55
.37
a s
-1
-1
0
-0
-0
-1
0
-0
-0
-o
0
-0
0
-0
-0
0
.0.
.19*
.14*
.05
.33
.27
.61*
.60
.26
.19
.22
.54
.84*
.97
.25
.30
.91
A S
-0
-0
-0
-0
-0
-1
0
-1
0
-0
0
-0
1
-0
-0
-0
.D.
.83*
.23
.16
.44
.80
.24
• 33
.39*
.18
.24
.28
.14
.35*
.73
.80
.06
Table Sb. Daily Precipitation Standard Deviations (mm d"1)
MONTH
LOCATION
OBS CURRENT
S.D.
JANUARY
APRIL
JULY
OCTOBER
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
S.G. PLAINS
SOUTHEAST
UEST COAST
GRT. LAKES
1.
4.
3.
2.
2.
4.
1.
3.
2.
4.
0.
3.
2.
3.
1.
3.
08*
35
23*
23*
51*
35*
41*
85*
79
13*
57*
68*
75*
77
86*
58*
S.
2
4
4
4
3
3
2
3
3
3
1
2
1
3
2
2
D.
.80
.62
.55
.06
.26
.85
.76
.29
.08
.31
.53
.48
.79
.88
.69
.26
2010s 2030s ~2060
J S
0
-1
-0
-1
0
0
0
-0
-0
0
0
-0
0
0
1
0
.D.
.05
.20*
.18
.07*
.94*
.95*
.07
.43
.10
.28
.44*
.06
.52*
.72*
.20*
.52*
J S
0
-1
0
-0
1
-0
1
-0
-0
0
0
0
0
-0
-0
0
.D.
.05
.35*
.34
.94*
.99*
.15
.02*
.31
.09
.29
.24*
.72*
.34*
.15
.63*
.76*
J S
1
-0
0
-0
1
0
-0
0
0
0
0
0
0
-0
1
0
.D.
.68*
.85*
.13
.50*
.17*
.81*
.12
.44
.36
.11
.71*
.35
.00
.28
.34*
.95*
2-24
-------
Rind
In the majority of cases, the model produced less days of light rain than did the observations. This is
illustrated by the distributions for the southeast grid box in October (Figure 9, left). Note that it occurs even
though the modeled mean monthly rainfall is only slightly less than observed (Table 2b). As shown in Figure
5, it is just this no rain/light rain distinction that is particularly dependent on the number of stations included
in the observations. In the Great Lakes region, extreme rainfall values occur somewhat more frequently in
observations in summer and autumn, as exemplified by the difference between the otherwise very similar
distributions in July (Figure 9, right). Extreme values occur more frequently in the model in winter in all four
regions. The difference in extreme events is evident in the standard deviations for the model and observations
(Table 5b).
To determine the change in distribution as climate warms, similar analyses were made for the decades
of the 2010s, 2030s, and 2056-2065. The distributions were significantly different about one-fourth of the time,
with no general progression over the decades. Shown in Figure 10 are the distributions for the west coast in
April, which has a steady increase in the days with no rain as the climate warms and dries.
Extreme events tended to vary, but an overall tendency does emerge. The assumption made for the
interannual standard deviations was that the magnitude of variability would increase if precipitation did. As
shown in Table 5b, the standard deviations in the climate change experiments were significantly different from
the control more than one-half of the time with no general progression over the decades. (Note, however, that
the use of the capital F distribution to evaluate significance in this case is not strictly valid, because the daily
precipitation distribution does not have a bell-shaped appearance.) A comparison of Tables 2b and 5b indicates
that the significant changes in variability coincided in sign with the change in mean precipitation.
In summary, the daily variability of precipitation tended to change with the same sign as the precipitation
change itself, e.g., increasing when mean precipitation values did. Precipitation distributions changed significantly
about one-fourth of the time, again influenced by mean value changes. Temperature variability on this time,
scale tended to decrease, but this cannot be proven statistically with the sample at hand, while temperature
distributions showed no obvious change. Nor was there any obvious change in persistence as climate warmed.
2-25
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PRECIPITATION (MM / DAY)
OCTOBER GISS CONTROL HUN PRECIPITATION DISTRIBUTION
CHID BOX - 31.3 - 39.1 N . 75.0 - 65.0 U
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PRECIPITATION
/ DAY)
PRECIPITATION (Ml / OAYt
Figure 9. Observed (top) and model (bottom) daUy precipitation intensities for the southeast in October (left)
and the Great Lakes in July (right).
-------
APRIL GISS CONTROL RUN PRECIPITATION DISTRIBUTION
OIIO SB - U.I - 47.0 N . 113.0 - l«.0 U
APRIL GISS 2030 PRECIPITATION DISTRIBUTION
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PRECIPITATION (ttl / DAY)
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PRECIPITATION (NI / DAY)
Figure 10. Daily precipitation intensities for the west coast grid box in April for the current climate (top left),
and 2010s (bottom left), the 2030s (top rightX and 2056-2065 (bottom right).
-------
Rind
CHAPTER 6
VARIABILITY OF THE DIURNAL CYCLE
The GISS general circulation model includes a diurnal cycle, and for certain applications, especially those
involving vegetation, variations in the amplitude of the diurnal temperature cycle as climate changed would be
an important result. The expectation is that the amplitude should decrease, since additional CO2 (and water
vapor in the wanner climate) would act as greenhouse material in limiting radiative cooling at night, while
leaving solar radiational heating during the day unaffected. Karl et al. (1984, 1986, 1987) have reported a
decrease in the diurnal temperature range, especially during summer.
We first compare the model's diurnal cycle with the observed. Shown in Table 6 is a comparison of the
model's annual average diurnal temperature range with observations (U.S. Air Force, 1979) calculated using the
cities in Figure I/Table 1 in each grid box (in some cases we had to use data which was available only for
neighboring stations). In both cases the daily temperature maximum was compared with the daily temperature
minimum to determine the diurnal range. The model values average very close to the observed, with a ratio of
dose to one (model/observed = 1.01 ± 27), although there is a tendency for model values to be higher in late
summer, when the model ground dries out. The phasing also is appropriate, with temperature peaking during
the mid-afternoon.
The change in the diurnal cycle amplitude for each month in the doubled CO2 climate is shown hi Table
6. The prevailing tendency is for the diurnal cycle amplitude to decrease in summer; out of the 12 records for
the 3 months of June-August, decreases were recorded in 10 cases. The magnitudes of the decreases ranged
from less than 1% to as much as 27%. There is no doubt about the reality of this effect; for the United States
as a whole, during these 3 months 87% of the grid boxes showed decreases in the diurnal cycle amplitude.
Given that the summer, when light winds occur, would be the season most likely to have its temperatures
dominated by radiative effects, this result would appear to be in accordance with expectation. However,
examination of the results indicates that other factors are operating as well. In the winter, spring, and fall
seasons, the modeled doubled CO2 climate features cloud cover decreases at night, which may offset radiative
decreases due to different trace gas concentrations. In these seasons both increases and decreases in the diurnal
cycle amplitude occur, with daytime temperature increases often exceeding those at night. In summer in the
model there is little cloud cover change at night, which presumably allows the trace gas radiative effect to
become apparent, and the warming is generally greater at night (thus reducing the diurnal temperature
amplitude). This example illustrates how simple expectations can be altered by other aspects of the climate
system.
2-28
-------
Rind
Table 6. Diurnal Temperature Range (°C)
GRID BOX JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
S.G.PLAINS DBS 12.1 12.3 13.2 13.0 12.9 13.1 12.6 12.8 12.7 13.2 12.8 12.0
CONT 10.5 11.2 12.5 15.4 10.4 10.1 9.7 11.2 21.8 19.2 13.6 10.9
2C02 10.2 12.3 13.5 16.0 10.2 9.9 10.6 10.9 17.5 19.6 14.0 11.3
SOUTHEAST DBS 9.2 10.0 10.5 11.4 12.4 10.5 10.0 10.1 10.3 11.0 10.6 9-6
CONT 9.1 10.1 11.1 13.6 9.1 8.7 9.3 10.9 13.6 13.2 11.0 9.3
2C02 9.3 9.5 12.4 12.8 8.5 7.9 7.3 8.0 13.6 13.3 10.5 9.7
UEST COAST OBS 9.0 10.0 11.3 12.3 13.1 13.5 14.6 13.8 14.3 12.6 10.4 8.7
CONT 6.6 6.9 8.7 12.1 10.0 10.7 13.1 17.1 19.0 14.8 10.1 7.1
2C02 6.5 7.5 8.6 13.2 9.5 10.1 11.5 17.0 20.3 14.4 9.0 8.2
GREAT LAKE OBS 8.3 8.9 9.5 10.9 11.6 11.6 11.4 11.2 11.2 10.8 8.3 7.6
CONT 7.4 7.3 8.4 11.4 8.9 9.7 10.5 12.7 14.3 10.1 7.7 6-7
2C02 7.0 7.2 9.4 12.7 9.1 9.4 10.2 12.8 15.0 11.9 8.9 7.2
2-29
-------
Rind
CHAPTER?
DISCUSSION
The results show that the year-to-year temperature variability and extremes in the daily temperature
variability tended to decrease in the warmer climate during the winter and early spring. The precipitation
variability on both time scales tended to increase, to the extent that the mean precipitation itself increased. The
diurnal cycle amplitude tended to decrease in summer. In this section we discuss how likely these results are
to be true, and briefly comment on their potential consequences.
The primary question that must be addressed is whether the model deficiencies for the current climate
invalidate the results for future changes. This question is relevant when assessing the validity of predicted
changes in the mean values as well as changes in variability. The comparison of modeled and observed
temperatures and precipitation for the four grid boxes and four seasons has indicated the following deficiencies:
1) the model is too cool during summer and fall; 2) the model produces too much rain along the west coast and
in the southern Great Plains; 3) the model generally overestimates temperature variability in summer, on both
the interannual and daily time scales; 4) the model overestimates the interannual precipitation variability, and
has too few days of light rain, as opposed to no rain, each month; and 5) the model persistence is too large,
especially during summer and for precipitation. While these errors are not always large or significant, they are
often of greater magnitude than the modeled climate change results. Can we believe the results under these
circumstances?
A comparison was made of results from n the 4° x 5° version of the GISS climate model (when using
doubled atmospheric CO, and the sea surface temperature changes produced in the equilibrium 8° x 10°
experiment, as discussed in Rind, 1987; 1988a,b), with those from the 8s x 10°. The finer resolution model
control run produces less rain for the western United States (e.g., 1.4 mm d~1 in summer, compared with 2.6 mm
d~1 in the coarse grid, Rind, 1988a) and smaller interannual variability (0.1 mm d*1 for the summer as a whole,
compared with 0.5 mm d~ with the coarser grid, Rind, 1988b), both of which are more realistic characteristics.
In the doubled CO2 simulations, there are smaller changes in the finer grid run for this region (Rind, 1988b),
indicating that the climate change experiment mimics some of the characteristics of the control run. As the
changes in precipitation variability are closely tied to the changes in mean precipitation, we might expect that
the finer grid model would have reduced variability changes in that region. We could not use this model for the
variability study, as it did not generate its own sea surface temperatures directly (nor were they allowed to vary
from year to year), but the results do imply that model deficiencies can be expected to contaminate climate
change estimates, both for mean changes and changes in variability.
What then can be gained from studies made with admittedly imperfect models? The current models can
be used to explore potential physical interactions which they may be able to elucidate, albeit in an imperfect
manner. As an example, the models have been used to estimate the global wanning due to a doubling of
atmospheric carbon dioxide. The magnitudes of warming produced may be inaccurate because of the strong
positive feedback that is provided by the cloud cover response in the models, since cloud cover parameterizations
are currently very crude. Nevertheless, the models have shown the potential strength of this physical process,
and have highlighted the necessity to model clouds more accurately. By running model experiments we hope to
learn what mechanisms are of first-order importance in climate change. This task requires models which allow
for the multiplicity of interactions possible in the complicated, highly nonlinear physical system.
In the studies here, we are concerned with whether variability changes will occur along with the projected
climate change. The physical processes that are being examined are 1) does the high latitude temperature
change amplification produce significant reductions in interannual and daily temperature variability, 2) does the
increased global rainfall produce increased precipitation variability; and 3) does the increased greenhouse
capacity of the atmosphere reduce the diurnal temperature range. The results in toto verity these physical
assumptions but with important caveats as to their generalizability. They thus give us a crude estimate as to the
importance of the physical processes, and emphasize what must be done to improve our understanding. For
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example, to get better estimates of precipitation variability, we must produce better representations of the mean
value. While this could have been stated a priori, this study, which clearly indicates the relationship of changes
in precipitation variability to the mean changes, helps to quantify the issue.
The reduction in the latitudinal temperature gradient during winter is approximately 10% in the GISS
doubled CO2 model, and the eddy energy decrease is about 5%. The model results indicate that these
differences translate into average reductions in temperature variability of the order of 10% (Tables 3 and 5).
The reliability of that conclusion is tempered by the tendency of this model to overestimate the variability for
the current climate. Especially important in this regard is the need for a more realistic hydrology scheme which
could limit late summer water loss and prevent unrealistic temperature changes. An additional uncertainty arises
because of the lack of agreement among models as to what the reduction in the latitudinal temperature gradient
will really be. The doubled CO2 climate simulation done at the Geophysical Fluid Dynamics Laboratory
produces a reduction in this temperature gradient that is two times as large. The results from this study imply
that the decrease in temperature variability in their model might well exceed the values determined here. The
use of several different models further serves to clarify areas requiring further research.
The diurnal cycle change is predominantly a radiative effect, and as noted, would be expected to be most
apparent when winds are light, in summer. The model does reproduce this result However, it also indicates
the importance of competing effects, such as altered cloud cover, in occasionally reversing the sign of the change.
While we cannot necessarily believe the individual results in this regard, owing to uncertainty in cloud and
convection schemes, they do highlight the ability of models to provide interactions from other elements of the
climate system which can cause the result to deviate from expectations. As models are developed which produce
better representations of the current climate, and contain more sophisticated parameterizations for these
processes, we should be able to increase our confidence in such projections.
Changes in variablity may well be affected by processes that have been omitted in the standard climate
change experiments. For example, significant interannual variability is associated with changes in ocean
dynamics, such as the El Nino phenomenon. While the GISS model allows sea surface temperatures to change,
it does not allow ocean dynamics to change. Were El Nino events to occur with an altered frequency, this would
undoubtedly influence interannual variability, at least in specific regions. Ultimately, all variability studies, as well
as model projections for mean climate changes, will have to be done with coupled ocean/atmosphere models.
The model does not include hurricanes, which occur on spatial scales (-100 km) too small to be resolved
Emanuel (1987) estimated that the CO, wanning of the tropical oceans could increase hurricane intensity by
40-50%, an effect which would add to the future hydrologic variability.
If the results obtained here prove to be valid, what effects are likely as the result of the changes in
variability? Decreased temperature variability would appear to be a positive factor in societal planning, limiting
the variance around the mean with which we would have to deal. However the variability changes studied here
will be superimposed upon a changing mean climate. The impact of changes in the interannual, daily, and
diurnal cycle temperature variability on society will have to be compared with the potentially rapid rate of change
of the mean temperature itself. All these factors will be folded in together in the climate that we experience,
so even with reduced interannual temperature variability, the large decadal-scale warming might dominate the
perception of temperature instability.
An increased variability of precipitation associated with an increase in mean precipitation might leave the
relative variability unchanged. Nevertheless, society would likely alter its expectations of the mean conditions,
and so increases in variability would still be likely to have a pronounced effect. Droughts, defined as lack of
water availability relative to expectation or demand, might be expected to increase, as would floods. In
conjunction with, the likelihood of increased hurricance intensity, this would stress both ecosystems and
civilization's structures. At the time of this writing (the late summer of 1988), we have had a graphic
demonstration of such a world: the destructive power of hurricane Gilbert, the devastating floods of Bangladesh,
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forest fires sweeping the western United States, and the impact of drought in the central Great Plains and the
southeast, affecting everything from 30% of the nation's crops to the cooling water and hydroelectric capacity
of power plants. Potential changes in precipitation variability need to be factored into the decision-making
process.
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CHAPTERS
CONCLUSIONS
In this study we have looked at how variability on three time-scales, the inter-annual, daily, and diurnal
cycle, may change in the future based on model projections. We concentrate on the areas of the southeast
United States, the southern Great Plains, the west coast, and the Great Lakes. Extensive comparisons are made
of observations and the model simulations of the current climate.
The primary results of this study are:
1) The interannual temperature and precipitation variability does not change significantly on the grid box level,
but on a broader area, the sign of the change is significant, with temperature variability decreasing and
precipitation variability increasing (as mean precipitation increases).
2) The daily variability in temperature is not significantly different, although there is a tendency for decreases.
Precipitation variability on this time scale changes in the same manner as the mean precipitation.
3) The amplitude of the diurnal temperature range decreases in summer.
These results must be viewed in the context of the comparison between observations and the model's
current climate, which shows the model is often too cool and wet, and somewhat too variable. The lack of
significance of the changes in variability on the grid box level may well be related to an insufficient length of time
of simulation, as the only variable whose variability changed significantly on this scale (daily precipitation) had
the largest independent data set to work with. Alternatively, procedures should be developed to take advantage
of the predominance of changes of a specific sign, which characterize these results. Finally, the impact of
changes in variability on these time scales must be viewed in the context of the projected rapid change of the
mean values themselves, to understand their potential consequences for society.
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