&EPA
United States
Environmental Protection
Agency
Atmospheric Research and
Exposure Assessment Laboratory
Research Triangle Park NC 27711
Research and Development
Uncertainty in North
American Wet
Deposition lsoplet.li
Maps:
Effect of Site
Selection and Valid
Sample Criteria
EPA/600/4-90/005
August 1990
-------
-------
EPA/600/4-90/005
August 1990
UNCERTAINTY IN NORTH AMERICAN
WET DEPOSITION ISOPLETH MAPS:
EFFECT OF SITE SELECTION AND VALID
SAMPLE CRITERIA
J. C. Simpson
A. R. 01 sen
Prepared for ''•
the U.S. Environmental Protection Agency
under a Related Services Agreement with
the U.S. Department of Energy
Contract DE-AC06-76RLO 1830
Pacific Northwest Laboratory
Richland, Washington 99352
-------
NOTICE
This document has been reviewed in accordance with
U.S. Environmental Protection Agency policy and ,
approved for publication. Mention of trade names
or commercial products does not.constitute endorse-
ment or recommendation jfor use. ' %- . ;. :
11
-------
ABSTRACT
This report considers several issues related to the preparation of
isopleth maps for the display of spatial patterns of wet deposition.
The valid sample criteria and data completeness rating used in the data
summarization process are described. The data interpolation technique.
kriging, is presented and it's derivation in terms of generalized least
squares regression is given. Four different annual summaries for pH.
sulfate concentration, and sulfate deposition in 1986 are prepared using
either the Unified Deposition Database Committee (UDDC) definition of
valid sample criteria or a relaxed valid sample criteria and the UDDC
data completeness rating or a relaxed data completeness! rating. The
kriged estimates for the different annual summaries and^ the differences
between these estimates are contoured. The effects of relaxing the
valid sample criteria and data completeness rating are discussed.
Conclusions are drawn about network operation, network design and the
uncertainty of contour maps. It is recommended that in! the case where
the objective is contour maps to show regional patterns:. the emphasis in
most regions needs to be on the number of valid samples per site and the
regional representativeness of the sites.
i i i
-------
CONTENTS ;
ABSTRACT ...... j... i i 1
1.0 INTRODUCTION ...... 1.1
2.0 DESCRIPTION OF WET DEPOSITION DATA SETS ......... 2.1
2.1 WET DEPOSITION DATA SOURCES ...... 2.1
2.2 DATA SUMMARIZATION PROCESS , ••• 2-3
2.'3 SITE SELECTION PROCESS 2.6
2.4 DEFINITION OF ALTERNATIVE DATA SETS,USED IN STUDY ....... 2.10
3.0 KRIGING 3.1
3.1 KRIGING ASSUMPTIONS ...;... 3.1
3.2 SEMI-VARIOGRAM ESTIMATION , ... 3.2
3.3 KRIGING ESTIMATOR >> • •' 3.5
3.4 GENERALIZED LEAST SQUARES (GLS) REGRESSION 3.6
3.5 DERIVATION OF THE GLS ESTIMATOR ,... 3.7
3.6 WITHIN-SITE VARIATION i. • • • 3.10
3.7 ADVANTAGES OF GLS APPROACH ; . 3.11
4.0 VARIOGRAM ESTIMATES » • • • 4.1
5.0 RESULTS \ 5.1
5.1 CONTOUR MAPS OF THE ESTIMATES. .............. 5.1
5.2 CONTOUR MAPS OF THE DIFFERENCES 5.9
6.0 CONCLUSIONS '• •' • • 6.1
7.0 REFERENCES , 7.1
APPENDIX A - COMPARISON OF 1985 PH CONTOUR MAPS .' A.I
IV
-------
TABLES
2.1 Definition of Data Completeness Measures i, 2.9
2.2 Data Completeness Level Criteria for Annual Summaries... 2.10
2.3 The Number of Sites for Each of the Four Sets of pH and
Sulfate Summaries , 2.13
2.4 The Number of Sites Where pH Values Changed by the UDDC
Versus Relaxed Valid Sample Criteria and the Magnitudes
of Those Changes ; 2.13
2.5 The Number of Sites Where Sulfate Values Changed by the
UDDC Versus Relaxed Valid Sample Criteria and the
Magnitudes of Those Changes 2,14
2.6 The Sixteen Sites with the Largest Changes in Their pH
and /or Sulfate Concentrations as a Result of Using the
Relaxed Versus UDDC Valid Sample Criteria 2.15
2.7 The Samples Within the 16 Sites (Shown in Table 2.6) Which
Did Not Meet the UDDC Valid Sample Criteria 2.17
FIGURES •
2.1 Location of Sites in the Relaxed Valid Sample Criteria
and Completeness Rating Subset i 2.11
3.1 Semi-Van" ogram Models Where the Sill and Range are One for
All the Models Except the Power Models Where "b" is Set to
One and the Semi-Variogram is Truncated at One at Distance
of One 3.4
4.1 Semi-Variogram for each of the Subsets of pH, Sulfate
Concentration and Sulfate Distributions 4.3
5.1 Contours of pH Estimates Using the UDDC Valid Sample
Criteria/UDDC Data Completeness Rating Subset.. 5.2
5.2 Contours of Sulfate Concentrations (mb/1) Estimates Using
the UDDC Valid Sample Criteria/UDDC Data Completeness Rating
Subset 5.3
5.3 Contours of Sulfate Depositions (g/sq m) Estimates; Using
the UDDC Valid Sample Criteria/UDDC Data Completeness Rating .
Subset .., 5.4
5.4 Contours of pH Estimates of the Four Subsets Using the
UDDC or Relaxed Valid Sample Criteria (UVSC or RVSG)
and the UDDC or Relaxed Data Completeness Rating
(UDCR or RDCR) 55
-------
5.5
5.6
5.7
5.8
5.9
Contours of Sulfate Concentration (mg/1) Estimates
of the Four Subsets Using the UDDC or Relaxed Valid
Sample Criteria (UVSC or RVSC) and the UDDC or
Relaxed Data Completeness Rating (UDCR or RDCR) 5.7
Contours of Sulfate Deposition (g/sq m) Estimates ;
of the Four Subsets Using the UDDC or Relaxed Valid ' !
Sample Criteria (UVSC or RVSC) and the UDDC or Relaxed \
Data Completeness Rating (UDCR or RDCR) ...;.; 5.8
Comparison of Sulfate Concentration and Deposition
Estimates With and Without Parson. West Virginia
Site Present .
5.10
Differences in pH Estimates for Selected Pairs of Subsets 5.11
Differences in Sulfate Concentration Estimates for
Selected Pairs of Subsets .5.12
5.10 Differences in Sulfate Deposition for Selected Pairs of Subsets 5.13
5.11 Extent and Magnitude of Effect the Parson, West Virginia ;
Site has on the Sulface Concentration and Deposition ;..... 5.18
VI
.
-------
1.0 INTRODUCTION
Junge (1963) operated the first precipitation chemistry network in
the United States and reported the data by using isopleth maps of ion
concentrations. Since then a number of regional and national isopleth
maps of precipitation chemistry data have been published: Semonin
(1981). Cowling (1982). Calvert et al. (1983). Hunger and iiisenreich .
(1983). Barrie and Hales (1984). Ellis et al. (1983). arid Husar (1988).
The researchers determined the location of the contours on these maps
either by subjectively using expert opinion to hand draw them or simple
weighting schemes such as inverse distance squared. ,
More recently several researchers have used the geostatistical
technique termed kriging to estimate the spatial surface and then
display the surface using isopleth maps. Eynon and Switzer (1983) and
Finkelstein (1984) published isopleth maps based on two alternative
kriging approaches.. Since then a number of authors have used kriging in
the production of maps: Seilkop and Finkelstein (1987), Barchet (1987).
Wampler and Olsen (1987). Guertin et,al. (1988). Haas et al. (1988). and
Venkatram (1988). Bilonick (1985) and Le and Petkau (1988) applied
spatial time series models to precipitation chemistry data in North
America.
The National Atmospheric Deposition Program (NADP) and the Acid
Deposition System (ADS) regularly publish United States and North
American isopleth maps of annual precipitation chemistry. NADP
coordinates the NADP/NTN network and uses the network data to produce
annual maps starting with 1983 data. NADP (1987) is an'example of their
publications. The ADS combines the NADP/NTN network data with data from
several other North American precipitation chemistry monitoring networks
to produce annual isopleth maps for North America. See Olsen and Watson
(1984). Olsen and Slavich (1985). Olsen and Slavich (1986), Sweeney and
Olsen (1987). Sweeney and Olsen (1988). and Olsen (1988). NADP uses a
constrained distance-squared weighting function to estimate the surface
while ADS uses kriging to estimate the surface. A more detailed
1,1
-------
explanation comparing the approaches is given in an informal report by
01 sen (1988). which is reproduced as Appendix A. ,
In 1988. researchers concerned with wet .deposition data organized
two spatial analysis workshops. The first,workshop on regional janalysis
of wet deposition for effects research,was held June 7-8. 1988 in
Corvallis. Oregon. Vong et al. (1989) summarize the workshop
discussion. The workshop focussed on issues connected with estimating
wet deposition an non-monitored sites and did not explicitly consider
presentation of regional wet deposition surfaces as isopleth maps. One
conclusion of the workshop is that .kriging is currently a preferred
technique for interpolation to non-monitored sites. The second workshop
focussed explicitly on presentation as isopleth maps and was held
October xx. 1988 in Champaign. Illinois. The workshop organizers:
prepared standard data sets for North America and invited six different
organizations to use the standard data sets to produce isopleth maps.
Methods used by the organizations included hand drawn by an expert,
inverse distance squared. Cressman's objective weighting, other • ..
objective analysis schemes," and several kriging alternatives. No
workshop report is available at this time. Our conclusions frorii the
workshop are that regardless of the interpolation technique the .broad
overall regional features of the surface are very similar across .
'techniques but local features do differ when different techniques are
used. ...,•:,.".;•
The production of an isopleth map involves: 1) selection of sites
to be used in surface estimation, 2); calculation, of .an annual summary ,
value at a monitored site. 3) selection of a surface estimation I
technique, 4) selection on how to display the estimated surface; and 5)
production of a final document quality display. Decisions made :for each
of these can affect the final display and how it is perceived. 'When the
surface is displayed using isopleth maps, alternative choices can result
in different maps. Even if agreement on these issues could be reached,
the wet deposition data has measurement .error associated with the
sampling and laboratory analysis process. Hence an isopleth mapj has
uncertainty associated with the location of its isopleth lines due to
1.2
-------
measurement error and to the uncertainty associated with possible.
i
alternative production decisions. <
Isopleth maps are a common method of summarizing and displaying
the spatial pattern for wet deposition over North America. The process
includes determining annual summaries at wet deposition monitoring
"sites1, selecting sites with representative data, estimating "a spatial
surface by interpolating the selected sites to a regular grid, and then
displaying the surface using an isopleth map. It is generally.
recognized that the location of the isopleth lines can be affected by
the procedures used at each stage of the process. In fact, isopleth
maps for the same annual time period and ion species constructed by
different organizations have been constructed, for example, the pH map
for 1985 given in the NAPAP Interim Assessment report (Barchet 1987) and
the pH map for 1985 in the NADP/NTN Annual Data Summary! report (NADP
1987). The maps do differ and the question arises as to why. (Olsen
1988). A natural follow-up question is can an agreement be reached on
what the "correct" process is to go from sample data collected at sites.
to the "correct" isopleth map. i
An isopleth map is a display of an estimated surface. Data at
monitored sites used in the surface estimation process are only
estimates of wet deposition at the monitored site. Hence, the location
of the isopleth lines would still have uncertainty associated with them
even if organizations would agree to use the same data, same sites and
same surface estimation methodology. The uncertainty of the data at the
site and the uncertainty associated with estimating wet deposition at
non-monitoring locations as part of the surface estimation methodology
both contribute to the uncertainty in the location of the isopleth
lines. A natural question is how to determine (estimate) the
uncertainty on the location of the isopleth lines. i
This report investigates the impact on estimated surfaces due to
the use of alternative procedures for estimating wet deposition at
individual monitoring sites and for selecting representative monitoring
sites. The impact of alternative surface estimation methodologies is
not explicitly investigated.
1.3
-------
-------
2,0 DESCRIPTION OF WET DEPOSITION DATA SETS
The purposes of this section are: 1) to describe wet deposition
monitoring data sources, data summarization processes, and site
selection processes that have been used by organizations who produce
isopleth maps for wet deposition ion species and 2) define alternative
data sets used in this report. No attempt is made to include all?
procedures that have been used. The discussion is focusised on the
processes used to define the alternative data sets used:later in the
report.
2.1 WET DEPOSITION DATA SOURCES
Various, federal, state, and local governmental agencies and
private industry organizations support networks of sites for the
collection and chemical analysis of precipitation samples, i.e.. for wet
deposition monitoring. Determining which networks of sites to include
is a primary decision in a study of wet deposition spatial patterns.
Issues typically considered in the selection process are: 1) objectives
and spatial coverage of the network. 2) quality assurance associated
with the data. 3) compatibility of network monitoring, laboratory, and
data validation protocols. 4) availability of data, and 5) special
requirements/restrictions by spatial pattern study organization. • The
first three issues are associated with the representativeness and
compatibility of the data. The latter two issues are typically
operational issues rather than representativeness issues. The selection
of different networks to be included in spatial pattern studies for the
same year can potentially be a major source of differences between
isopleth maps prepared by two organizations. Interpretation or
comparison of isopleth maps requires an understanding and assessment of
the network selection criteria used. i
I
,!
The wet deposition data used for this study are from six regional
or national networks that contribute data to the Acid Deposition System
(ADS) (Watson and Ol.sen 1984). The networks are the Multi -State
Atmospheric Pollution and Power Production Study initiated precipitation
chemistry network (MAP3S/PCN), the National Atmospheric Deposition
2.1
-------
Program/National Trends Network (NADP/NTN). the Utility Acid
Precipitation Study Program (UAPSP), the Canadian Acid Precipitation
Monitoring Network (CAPMoN). the Acidic Precipitation in Ontario -Study
daily (APIOS-D) .and cumulative (APIOS-C) networks. Sweeney and'. 01 sen
(1988) give additional descriptions of the networks. Criteria jused in.
selecting these networks are: 1) the network provides regional or •
national coverage at regionally representative sites. 2) each network
has an implemented quality assurance program.,3) the network chemical
analysis laboratories participate in an,inter-laboratory comparison
program, and 4) the data are readily available in a common format from
ADS. I
The decision to use these networks does impact the spatial pattern
displayed by an isopleth map. Site'selection protocols for the; networks
restricts location of sites within urban areas and minimizes impact of
local point source emissions. Although not an'explicit site selection
protocol, almost all sites are located away from mountainous regions. '
Consequently, isopleth maps based on the networks may not reflect
variations In the spatial surface related to local point sources
effects, urban influences, or elevation effects. Any spatial pattern
derived will at best reflect the broad regional or national structure of
wet deposition. The impact of this decision on isopleth maps will not"
be explicitly studied in the report. i
The networks used in the study.each has a chemicaV analysis
laboratory that performs sample analyses and a data, management function
that checks the reasonableness of .the s,ample analysis results using
information available from the analysis and from the sample field notes.
That is. each network receives data from a laboratory which has:been
subjected to internal laboratory checks and.to sampling protocol checks.
The checks result in supporting comments and data flags being attached
to the samples. The ADS data base incorporates all of the comments,
codes and flags. A quality assurance program is used by each of the
networks to insure that their protocols are implemented and their
laboratories are in.control. In addition, 'all of the laboratories
participate.in inter!aboratory comparison studies.
2.2
-------
2.2 DATA SUMMARIZATION PROCESS
Calculation of an annual summary from sample data collected at a
site requires criteria for assessing whether a sample data value is
valid or invalid for the purposes of the study. These criteria are
called valid sample criteria. Even with careful attention, some samples
collected must be declared invalid because of the violation of some
aspect of a network's protocol that affects the sample's
representativeness of. the precipitation chemistry. In some cases, such
as severe contamination by debris, the sample is clearly not
representative of the precipitation chemistry. In other cases, such as
bulk sampling or non-protocol sample period, whether the sample is
representative of the precipitation chemistry during the period is not
as clear. Currently, a sample's representativeness and a criteria for a
valid sample have not been generally developed and accepted. Valid
sample criteria that do exist are based on the best professional
judgements of wet deposition monitoring researchers. ' ' .
To study the impact of different valid sample criteria, hence
indirectly sample representativeness, two alternative valid sample
criteria have been defined for the study. One alternative uses the
valid sample criteria developed by the Unified Deposition Database
Committee (UDDC) (01 sen et al 1987). The other alternative relaxes the
UDDC valid sample criteria by removing two UDDC valid sample criteria.
This alternative is termed the relaxed valid sample Criteria.
,i
The UDDC valid sample criteria have been designed to incorporate
each network's comments, codes and flags into the decision process of
determining whether an individual wet deposition sample result is to be
included or excluded from a summary. The discussion on screening for
valid samples is stated in terms of the ADS data base common record
format (Watson and Olsen. 1984) with some reference to network specific
Codes as necessary for clarification. I
j-
All networks include note codes which are informational in nature.
Some codes denote reasons why sample results are not available or
reported. Other codes describe conditions present in the field, and
2.3 •
-------
during sample transit and sample receipt. Unless explicitly stated
elsewhere, these note codes are not used in determining whether a sample
is valid. The basic premise is that each network has screened I
individual sample results for possible contamination. If a sample
result passes the network's screening, it is assumed that possible
sample contamination indicated by field or lab comments did not
materially affect the sample ion species concentrations.
A set of valid sample criteria has been designed for each network.
Each sample associated with a sampling period is screened to determine
whether the sample meets specific criteria. The screening criteria use
the informational comments and codes provided by each network. The
criteria are: |
All sampling periods for which it is known that no ;
precipitation occurred are considered valid sample
periods. This applies mainly to weekly, monthly and 28-
day sampling protocols. For event and daily sampling
protocols the absence of a sample record for a day
implies that no precipitation occurred. -;
The wet deposition sample must be a wet-only sample. All
samples identified as bulk, partially bulk or undefined.
are invalid.
• Wet deposition samples that have insufficient
precipitation to complete a chemical analysis for a.
specific ion species are invalid for that specific ion j
species. Event/daily samples are most likely to have
this occur. .
An individual ion species concentration accompanied by a
comment code designating the measurement to be "suspect"
or "invalid" is declared an invalid sample. Deletion of
the ion species concentration by the network for the same
reason has the same result. '••
2.4
-------
The actual sampling period for a wet deposition sample
must be close to the network's protocol sampling period.
Specifically, the following conditions lead to an invalid
sample: . r ..
For NADP/NTN. actual sample period less than
6 days or greater than 8 days. This includes
all NADP/NTN samples coded "LD" with measured
precipitation. ;
For APIOS-C, actual sample period less than
21 days or greater than 35 days.
For UAPSP, actual sample period greater than 1
day.
The restriction to wet-only samples used for the'UDDC valid sample
criteria may be too stringent and their exclusion may result in a bias.
For the networks used in the study, the sample chemistry is checked for
internal consistency and for consistency with historical data from the
site. Hence severe contamination due to an exposed bucket will cause
other data flags to be set. Large differences between;wet-only and bulk
sample chemistry may not be common in networks designed with wet-only
sampling protocols. Typically, the sampler fails at some time during
the sampling .period, violating the protocol. Exclusion of bulk samples
can cause a bias in annual precipitation weighted mean'concentrations,
especially if an ion species has a seasonal pattern at!a site. It may
be more appropriate to include a bulk sample as the best estimate of
concentration rather than exclude the sample.and in effect use the
annual precipitation weighted mean concentration as the estimate for the
sample. No detailed study has been completed to study this question.
The UDDC valid sample criteria also restricts the actual sample
period length of a sample to be within a few days of the network's
protocol sampling period. For example. NADP/NTN samples must be 6. 7,
or 8 days in length. The reason for the restriction is to maintain
consistency within the data. Again however, no objective study has been
2.5 i
-------
completed to show the effect of departure from a daily, weekly, or four^
weekly sampling period. The criteria may be overly restrictive and
introduce a bias as stated above for bulk samples. '•
2.3 SITE SELECTION PRnr.FSS . . ',
Calculation of an annual summary based on valid data at a si'te
does not imply that the annual summary represents the chemistry of
precipitation that occurred at the site during the year. This may be
due to the sampling not being completed continuously at the site/ to
incomplete collection of individual precipitation events (low collection
efficiency), to chemical changes occurring in the sample during or after
sample collection, or to precipitation associated with invalid samples
having concentrations different, than that associated with valid samples
(e.g.. seasonal effects).
The study defines and uses two alternative site selection criteria
for assessing the completeness, i.e..representativeness, of the apnual
summary. One is the UDDC data completeness criteria which incorporates
both an annual and a quarterly criteria. The other, called the relaxed
data completeness criteria, is a relaxed UDDC criteria which eliminates
the UDDC quarterly criteria and weakens the UDDC annual criteria.
The Unified Deposition Database Committee defined five
quantitative data completeness measures and assigned annual and ;
quarterly thresholds to each of the five measures in constructing 'their
UDDC data completeness criteria. The following questions concerning
data completeness and temporal representativeness motivated the
measures: for what portion of the summary period is the occurrence and
amount of precipitation known; what portion of the precipitation volume
collected is associated with valid deposition samples: what percent of
the time and what percent of the samples collected are associated With
valid samples: and what fs the ratio of the wet deposition sample volume
to the precipitation measured by a standard gage?
Data completeness measures are based on the assumption that the
entire season or year consists of sample periods that account for,every
2.6
-------
day of the summary period. It is normal for a site to 'have incomplete
information for some precipitation events during a summary period, to
deviate from established collection protocols due to circumstances
outside the operator's control, or to collect samples that are
subsequently eliminated during -the network's data screening process.
Therefore, it is necessary to establish criteria for determining when
sufficient valid wet deposition data are present to calculate a
meaningful seasonal or annual summary for a site. Data completeness
measures are designed to quantify the amount of information upon which a
data summary is based and enable criteria to be established that
indicate the quality of the summary. Five data completeness measures
are proposed: percent precipitation coverage length, percent total
precipitation, percent valid sample length, percent of samples with
measured precipitation that are valid and percent collection efficiency.
A sixth measure, percent sea salt correction is applied to sulfate
summaries for sites within 100 km of a coast. Definitions for the data
completeness measures are given in Table 2.1.
i
The data completeness measures are the basis for assigning a data
completeness level (1 to 4) to each seasonal and annual summary. The
criteria for the data completeness levels are given in Table 2.2. A
summary with data completeness level 1 has the best information, or the
highest level of data completeness. The least confidence is given to a
summary with data completeness level 3. Level 4 summaries fail level 3
criteria. They are viewed as not providing a representative summary for
the period. In order for a data summary to be assigned a specific
level, all criteria listed for the level must be met. The most
favorable level attained is assigned to the summary. A summary,that
does not meet one or more of the criteria for level 3 is assigned as
level 4. ;
f
The collection efficiency data completeness level criteria for a
seasonal summary is relaxed somewhat for Canadian winter summaries
compared to other seasons due to the generally poorer collector
performance for snow sampling. If the criteria for other seasons is
applied to winter months when a large percentage of the precipitation in
2.7 !
-------
Canada Is in the form of. snow, then only a few locations meet even the
level 3 criterion. It is believed that a lower percentage could; be ..--•
accepted for winter because the problems are primarily due to undercatch
of snow. An under-collected snow sample may reasonably represent the
concentration but not the deposition.
The data completeness level for an annual summary is based on
annual criteria as well as criteria for the four quarters. January-
March. April-June. July-September, and October-December, which comprise
the year. The addition of quarterly criteria to the annual criteria is
to insure that adequate data from each quarter is present in the annual
summary. Because the emphasis is on insuring adequate data for an
annual- summary, some quarterly criteria are relaxed from the seasonal
criteria (see Table 2.2).
!
The relaxed data completeness criteria applies only the annua-1
%PCL (£90£) and %TP (>602) data completeness measures. ; ATI quarterly
criteria are dropped. Sites meeting the relaxed data'completeness ;
criteria but not the UDDC criteria, almost exclusively fail the
quarterly criteria. The quarterly criteria are intended to insure that
all quarters of the year are represented in an annual summary. However.
the criteria may be overly restrictive. The relaxed criteria result in
almost all sites that monitored continuously during a year being
included in the study. ' ,
2.8
-------
TABLE 2.1. Definition of Data Completeness Measures
Data.
Completeness
Measure
%PCL
35VSL
%VSMP
SCOLEFF
SSEASALT
Definition
Percent precipitation coverage length is the percent of the
summary period for which information on whether or not
precipitation occurred is available. If precipitation is
known to have occurred during a particular sampling period
but no measurement of the amount is available, then no
knowledge of precipitation is assumed. This measure can be
less than 100% because the site started (stopped) operation
after (before) the beginning (end) of the summary period or
because equipment or operator problems! caused the site to be
shut down for a portion of the summary period.
Percent total precipitation is the percent of the total
precipitation depth measured that is associated with valid
samples collected during the summary period.
Percent valid sample length is the percent of the days durin
the summary period for which valid samples are obtained.
Note that sample periods with no precipitation are considers
valid samples. !
i
Percent valid samples with measured precipitation is the
percent of all wet deposition samples during the summary
period that are valid samples.
Percent collection efficiency is the ratio of the wet
deposition sample volume (converted to a depth) to the total
precipitation depth as measured by a collocated rain gauge.
Only valid samples with both a collocated standard rain gaug
and sample volume measurement available are used.
Percent sea salt correction is the percent of the average
sulfate concentration that .is estimated to be due to sea
salt, using sodium or magnesium as tracers of sea salt.
2.9
-------
TABLE 2.2. Data Completeness Level Criteria for Annual Summaries
Annual Data Completeness Level
£95%
£75%
£80%
£70%
£80%(70%)*
£80%(50%)*
£80%
£90%
£60%
£70%
£60%
£60%(40%)*
£60%(40%)*
£60%
£90%
£50%
£60%
£50%
£50%(30%)*
£50%(30%)*
£50%
Data Completeness Measure
%PCL
Annual and
each quarter
%TP, SVSL. %VSMP
Annual and
each quarter
%COLEFF
Annual and
for winter and
spring, summer, autumn
%SEASALT
* The bracketed value applies to Canadian sites.
2.4 DEFINITION OF ALTERNATIVE DATA SETS USED IN STUDY
The UDDC valid sample criteria (UVSC) versus relaxed valid sample
criteria (RVSC) and the UDDC data completeness rating (UDCR) versus
relaxed data completeness rating (RDCR) create four subsets of sites
(UVSC/UDCR. UVSC/RDCR. RVSC/UDCR and RVSC/RDCR) for both the pH'and
sulfate observations. The locations of the sites in the RVSC/RDCR
subset are shown in Figure 2.1. The estimation technique used in this
study (kriging) requires that, the phenomenon be stationary in the region
being investigated. For pH and wet deposition of sulfate, this
stationarity requirement is not met when considering the entire United
States and southern Canada as one region (Vong et. al. 1989). Therefore
this study is restricted to southern Canada and eastern United States
(less the southern most states). As seen in Figure 2.1, the pH I
observations are at the same sites as the sulfate observations with the
exception of the six sites without pH observations. The number :of sites
in each of the subsets are shown in Table 2.3. Of the 194 sites, in the
/ "* i
region shown in Figure 2.1, that have pH and sulfate summaries in 1986,
185 sites (95.4%) have annual pH summaries and 191 sites (98.5%) have
annual sulfate summaries which meet the minimal requirements
(RVSC/RDRC). When the most stringent requfrements (UVSC/UDCR) are used,
only 113 sites (58.2%) have annual pH summaries and 125 sites (64.4%)
2.10
-------
0 300
Kilometers
2 Collocated Sites
* Sites with nopH
Region used for semi-
variogram estimation
— Region containing grid nodes
FIGURE 2.1. Location of Sites in the Relaxed Valid Sample Criteria
and Relaxed Data Completeness Rating Subset
2.1]
-------
have annual sulfate summaries which meet these requirements. The
difference between the UDCR and RDCR is solely in the number of sites in
the subsets. The primary difference between the UVSC and RVSC subsets
is that at approximately one third of the sites the summaries change in
value. Additionally, the RVSC subsets have a few more sites, since more
samples are included in the annual summary causing the data completeness
rating to improve.
The number of sites whose observations changed and the magnitude
of those changes are shown in Tables 2.4 and 2.5. for pH and sulfate
respectively. As seen in Tables 2.4 and 2.5. the majority of the
changes-in the observations are relatively small. The 16 sites.'within
the region where estimates are calculated (see Figure 2.1), with!the
largest changes in their observations are shown in Table 2.6. A? seen
in this table, most of the large changes in pH and sulfate are at the
same sites. !
Table 2.7 shows the samples from the 16 sites shown in Table 2.6
which did not meet the UDDC valid sample criteria. There are two causes
for these samples to be rejected, either the collector is open during
the collection period when it is not raining (bulk) or the sample
collection period violates the networks protocol by being either too
long or too short. The precipitation weighted average of pH and 'sulfate
concentration are given for most of the samples, as data validation
procedures of the networks did not indicate anything unusual about the
chemistry of these samples. As seen in Table 2.7. three of the sites
each have samples with extremely high sulfate concentration (greater
that 50 mg/1). Although there is little precipitation' associated with
these samples, even when precipitation weighted averages are calculated.
these samples have a significant effect on the average. These unusual
samples also have extremely small collection efficiencies (percent of
.predicted sample volume, from the rain gauge, that is contained in the
actual sample). For a number of other sites, the samples that did not
meet the UDDC valid sample criteria all occur contiguously in time (the
NADP samples represent one week while for the APIOS-G network one1 sample
2.12 :
-------
represents a four week period). For sites that have a seasonal trend,
the loss of a month or more of data can significantly raise or lower the
annual average. ]
A fifth subset of observations for the sulfate observations is
investigated. This set consisted of the UVSC/UDCR subset with the
extreme value at Parsons. West Virginia (ADS ID 075a) removed. This
subset is used to demonstrate the range and magnitude of the effect that
one unusual site can have.
TABLE 2.3.
S04
The Number of Sites for Each of the Four Sets of pH
and Sulfate Summaries
RDCR
UDCR
RDCR
UDCR
uvsc
184
113
UVSC
190
125
RVSC
185
122
RVSC
191
133
TABLE 2.4. The Number of Sites Where pH Values Changed by
the UDDC Versus Relaxed Valid Sample Criteria
and the Magnitudes of Those Changes
(RVSC - UVSC)
(-0.127,-0.100)
(-0.100.-0.050)
C-0.050,-0.025)
(-0.025.-0.005)
(-0.005. 0.000)
no change
( 0.000, 0.005)
( 0.005. 0.025)
( 0.025. 0.050)
( 0.050. 0.096)
UDCR
1
3
1
11
10
80
9
5
2
0
RDCR
2
3
3
13
13
114
14
7
5
2
2.13
-------
TABLE 2.5. The Number of Sites Where Sulfate Values
Changed by the U.DDC Versus Relaxed Valid
Sample Criteria and the Magnitudes of Those
Changes
(Rvsc-uvsn
(-0.27. -0.25)
(-0.25. -0.15)
(-0.15. -0.05)
( -.05. -0.00)
no change
( 0.00. 0.05)
( 0.05. 0,15)
(0.15. 0.25)
(0.25. 0.50)
( 0.50. 0.52)
SO/i Deoosltlon (
(-0.33. -0.25)
(-0.25. -0.15)
(-0.15. -0.05)
(-0.05. -0.00)
no change
( 0.00. 0.05)
( 0.05. 0.15)
(0.15. 0.25)
( 0.25, 0.50)
( 0.50. 0.53).
UDCR
0
0
2
14
89
11
9
4
3
1
is/in2)
UDCR
0
0
2
14
89
11
8
3
5
1
.BJ&fi
1
2
3
19
120
16
11
6
4
1
1
2
2
20
120
16
10
4
7
1
2.14
-------
to
M-
4-> O
X
O)
o;
o w
^. <»
0= C_>
Q.
O)
•si 3 ^
j= g o 91
1— (/I I—
OOOOOOOOOO-r-OOOOO
•^^^••^••^^••^•^•'a-^1'*^''*. ^l'^''1*'
eoeocMrtootoeocNjCNjeooio^coeooo
•^:-ooois-o>oooo>coo)O)O>
o>.
03
0>
4v«
2
9L
.1
S
'5.
: o
2 oj-Q.15
11 1111 | §
£-«8ffl2>2 |
c_j .— _ ?y *^ *^^ /i\ /A
S99e999e9eesEsya s««^o«I 5
eeee99eeees9eeee ilglBsIf>
c C"Q —i oj
O O O O
..
<<
^
c/3®3 e\iwr>-P5r^«o3f^ooo4ooT-ocoow o>
-------
•a
cu
=9
C
o
o
i-l'v, CM-| oococMioooooorocn-r-OTi-flooioco j—
55 I co° c\i c\i CM' t-^ i-^ c\i c«i c\i co' o' ^ c\i c\i eo' o j£»
O -H
Q. iS
UJ —
a
l_ 3j co'cMCMCM^T-icM«eJe\ic> '-
< " "~ T- to o p.
uj '"
CM §
o .2
og coi-iocMCMi-^cooinmcoiocococo ^ -2 .•§
fc OOOoOOOoOOOOOOC3o .£ CO JjJ — 'o
^ ,++,+ + +, + + + + + + +, -^v.^
CO O (jj *"*"
QJ ••*>•••—***w*^*i**^i—w-^-wj-^--^"u*T"^w <2)C .92 2" Si i
cdd t^°. °it>:00. T<°. "T'?03. ":^i°'* c fi 3> E 5! i
UJ CM CNJ CO CM T— r— CM CO CM CO •>— ^— CMCMCOi— OC3)CDQ-™CO c/1
V= .E "Q. f= OT -O ™ CD
coj1 Sc3EpS:aS'Q.
c cr> is. '" *™ Q ^ > Q E
*^1 ^hi *^7^! * " * _• •••••••• "^ ^v jrt T^ V^ x^ i^lS *n
^ji CM Y** CM CM ^H* ^^ OJ CO CM CM ^~ T^ ^^ ^M CM ^** •'•• ^^ ^^ ri TLJ ,js
^5^5o<"-^*i'®>i
3 "5.Q S ® "5.-*-
u CCQ— CDd5'-"pO
,_ col9 co-trTreoco«-«i-T-i-cMT-r>.cM'*co e°8^*"*'*"'£ScD
o — *LS*2O>O)COJ3
-Q p CO CO (jj Q) CZ C C^ "^ C
§« OCO^^'co'cocDiaa
Z°3^j CM-rJ-^Mm-e-m^^-CM'^ts.rvi^.m ^^ U.>Z
cc
o
o
a.
Is
Q. £
BS
1
a.
155
%&#
CO
_CD
Q.
(O
CO
CO 2
< co
1
2.10
-------
TABLE
ADS
SITE ID
032a
0.43b
047a
073a
077a
163a
168a
!87a
I88a
I92a
208a
241a
250a
276a
420a
495a
2,7
. The Samples
Within
the 16 :
Did Not Meet the UDDC Vali
% TOTAL
M
JLJ
1
6
1
3
1
2
1
1
2
4
2
1
2
2
1
1
1
2
2
2
1
1
6
1
1
1
1
CAUSE
period
period
bulk
bulk
bulk
period
bulk
bulk
bulk
bulk
bulk
bulk
period
bulk
bulk
period
period
period
bulk
bulk
bulk
bulk.
bulk
bulk
period
period
period
PRECIP
25.6
11.2
3.5
4.3
4.4
12.0
0.8
0.3
0.9
5.5
3.0
0.1
7.5
18.7
13.5
2.7
9.9
6.1
5.8
2.2
2.5
8.2
12.4
0.5
2.2
2.2
7.8
Sites (Sh
d Sample
SULFATE
PRECIP oH CONG tooZIl
20.6
9.0
3.0
3.6
5.3
12.4
1.0
0.4
1.0
5.2
2.8
0.1
8.0
18.9
13.9
4.7
16.9
7.3
5.6
2.1
2.2
7.2
10.8
0.4
3.6
3.5
12.7
4.600
4.334
4.190
4.506
3.770
4.662
6.44
3.75
4.726
4.158
4.182
3.860
4.666
4.751
4.120
5.020
4.570
4.053
4.542
4.044
6.96
4.23
4.556
2.680
4.640
7.120
6.210
1 .450
3.040
7.790
2.152
9.560
1.102
1.250
74.050
51.995
2.441
4.734
1.478
2.826
4.100
0.800
1.700
4.744
1^540
11.321
5.824
2.750
3.906
69.320
1.100
1.300
own in Table 2.
Criteria
6) Which
COMMENTS
no sample volume
July
July
5.8% collection efficiency
1 1 .2% and 24.8% collection
efficiency
February and March
i
i
35.1% collection
i
March and April
March i and April
I
efficiency
February and March
2.9% collection
i
November
December, 2.0%
efficiency
collection
2.17
-------
-------
3.0 KRIGIN6
To investigate the effects of using the four different subsets of
the observations, the observations are interpolated unto a regular grid
using a variation of kriging. Kriging has often been the tool used to
make predictions of a spatial phenomenon (e.g. sulfate deposition) at
unobserved sites (e.g. a grid node). Kriging's popularity is based on
the fact that the estimates it produces are 'sensible' and it also
produces a variance that is often used in setting confidence intervals
about the estimates.
3.1 KRTfiING ASSUMPTIONS • '
Let Z(>0 be a realization of a spatial phenomenon. For example,
Z(A) can be the sulfate deposition at a site and A is the location of
the site in two dimensional space (A- (x.y)). 'Simple1 Kriging assumes
that the increments (difference between the sulfate deposition at two
sites). CZ(A') - ZU)3. are stationary in the weak sense. That is.
and
E[Z(x') - ZOO] - 0
VAR[Z(x,') - Z(x)] = 2y(h)
(1)
(2)
where
h - distance between x. and x.1
y(h) - semi-variogram . :
Equation (1) states that the expected difference between the two
sites is zero or that the expected sulfate depositions are constant over
the region of interest. Equation (2) states that the increment has a
variance and this variance is a function (called the semi-variogram)
only of the distance between the two sites.
When there is a systematic change (drift or trend) in the spatial
phenomenon, then
3.1 ]
-------
ECZ(X)] -
where mfe) is usually modeled as a low order polynomial.
equation (3),
(3)
Now, usiing
E[Z(x') - ZOO]
') - m(x) .
(4)
and
VAR[ZC0 - ZOO] = 2y(h) - [mfc1) -
1 (5)
Thus, the increments no longer have a constant expected value and
the variance of the increments is a function of both the semi -variogram
and the drift. Now the variance of the increments cannot be modeled by
the semi-variogram alone. The problem at this point is that to be able
to estimate the drift, the semi-variogram needs to be known, and:to be
able to estimate the semi-variogram. the drift needs to be known.;
Unfortunately, neither are known.
In practice, often the drift is ignored. There are two common
justifications given for ignoring the drift. First, the actual
estimates derived from kriging only uses a subset of the sites near the
point being estimated, thus if the drift is 'small' in the
'neighborhood' of the point being estimated then the drift's effect on
the estimates will be negligible. The second justification is that
'what's drift to one person is correlation to the next."
3.2 SEMI-VARIQGRAM ESTIMATION :
As seen in equation (2), under the assumption that the increments
are stationary in the weak sense, the variance of the increments ;are
modeled by the semi-variogram. The semi-variogram model must be >of a
form so that the variance is non-negative. ;
Five of the more common semi-variogram models which give non-
negative values are: I
3.2
-------
1. Power Model
y(h) = b|hp for 0 < p < 2 i
i
(when p-1, the semi-van'ogram is simply a linear ;model)
2. Spherical Model
1 Ihl3'
2 r3 .
Y(h) - C
3. Cubic Model
for |h| < r
for |h| > r
35 mil 7 Jill 3
I. H ' I I n -i- * I — •* ' ' «. ""
LJilll
4 r? J
y(h)
4. Exponential Model
5. Gaussian Model
In the 'above equations, r equals the range of the semi -van" ogram
and C equals the sill. The range can be thought of as
influence'. If the distance between two sites is less
for |h| < r
for |h| > r
the 'zone of
than the range,
then the value of one site influences the value of the other site. If
the distance between two sites is greater than the range, then the sites
are independent. The sill is the bound on the semi-variogram and
provides an estimate of the overall variability. The power model does
not have a range or a sill. The exponential and gaussian models never
reach their sill. Figure 3.1 gives a comparison of these semi-variogram
models where the sill and range are one for all the models except the
3.3
-------
power models where b is set to one and the semi-van"ogram is truncated
at one at distance one. As seen in Figure 3.1. a wide range of semi-
variograms can be modeled using these five models. j
1.0H
3
CO
0.5
0.0-
Cubic
Exponential -„
Power, p=1/2
Spherical
Gaussian
Power, p=3/2
0.0
FIGURE 3.1.
0.5 1.0
Distance (h)
1.5
Semi-Van'ogram Models Where the Sill and Range
are One For All the Models Except the Power Models
Where "b" is Set to One and the Semi -Van"ogram is
Truncated at One at Distance of One
When h is zero. g(0) must also be equal to zero. However, if the
semi-van"ogram does not tend to zero for measurements taken at
arbitrarily close points, then there is a discontinuity of the semi-
variogram at the origin. This discontinuity is called the nugget
effect. If there is a nugget effect, the variogram model is adjusted to
take it into account. For example, if the model is linear with a nugget
of size CQ (the intercept) then
for |h| > 0
for |h| = 0
= b|h| + C0
y(h) = 0
3.4
-------
The semi -van' ogram is estimated- by
N(h)
?
h) "
(6)
where '
Z(Xj + h) - Z(}(j) = difference between a pair of observations
which are a distance h apart
N(h) = number of pairs of points actually taken
into the sum.
In practice h is a range of distances. ;
3.3 KRTRING ESTIMATOR . |
The Kriging estimator is <
j
n !
where ;
YQ = the Kriging estimator at grid node XQ
X. = kriging weights i
Z(x,j) = the observed sulfate deposition at site xi
ri - the number of sites used in the estimator.
i
The number of sites used in the estimator, n, is only a small
fraction of the total number of sites (generally between 8 and 16).
Only 'close1 observations are used to reduce the size;of the matrices
that need to be manipulated. As long as the semi -variogram -model has a
small nugget as compared to the sill, then the weights decrease rapidly
with distance from
negligible weight.
and thus observations that are 'far' from A have
3.5
-------
The 'simple' Kriging variance is
n
= 2
n n
Zy
£-t A:A:
where
iXj) = semi-van"ogram. g(h) where h is the
distance between x. and x- .
"i -M
If the semi-variogram has a sill and there is no drift, the;
Kriging variance may be stated in terms of variances and covariances.
n n
n
X
o-
where
= covariance between
and
a2 = variance of Yg. (sill).
3.4 GENERALIZED LEAST SQUARES (GLS) REGRESSION
(7)
Least squares regression assumes that the errors in the
observations are independent. That is. the deviations from a trend
surface fit using least squares regression and the actual observations
are independent. If it assumed that these errors are not independent,
then generalized least squares regression can be used to estimate;the
trend surface. For example, in kriging the dependence in the errors is
assumed to be a function only of the distance between the observations.
Because these errors are related, they also form a 'surface' that fits
on top of the trend, surface. Therefore, it makes sense to also estimate
the error 'surface1 and then add it to the trend surface.
3.6
-------
3.5 nFRTVATIQN OF THE GLS ESTIMATOR
The GLS model is
Y =
where
YJ
x =
(YrY2,.
°1 X1
1 xrt
.,Yn)
• fm(2L,)
1 xn yn . . . fm(x.) -
a low-order polynomial of
fin,)
(i.e. distributed with mean zero and
covariance matrix c^V, the form of the
distribution (e.g. Gaussian) need not be
specified until required for computing
confidence intervals, etc.)
the sill of the semi -van' ogram.
Then
3.7
-------
a2(X'V1X)-1 .
Now, the value of the realization at the unobserved location >u is
where
Then.
so
Thus.
COV[£,e]
(
where
v
3.8
-------
Then.
Now.
where^ is the vector of kriging weights
VAR[^0] = VAR[^'Y] = 1'VAR[YJ2, =
2a2Y0'V-1X(X'V-1X)-1(X<:)1 -
VAR[Y0]
and
COV[ YQ , YQ ] = COV[ 1'Y , YQ ] = ^'COV[ Y , Y
1 4-a2(X'-\£'V-1X){XIV-1X)-1X'V-1V
00
0
So,
VAR[ Y0 - YQ ] = VAR[ YQ ] + VAR[ YQ ] - 2COV|[ YQ ,
3.9
-------
thus.
'-1
'-1-1
' - V0'V-X>(X'V-X)-(X01
This is the kriging variance. '•
3.6 WITHIN-SITE VARIATION
The nugget- effect in kriging is often attributed to the within-
site variation. The practical result of using the nugget effect in
kriging is to force the surface through the observations. That is. the
kriging estimate at a site which has an observation is that observation.
Thus the surface has 'spikes' wherever there are observations. These
'spikes' have no surface area associated with them, they are a jump .
discontinuity at the site of the observation. Additionally, the sites
with duplicate observations must be preprocessed (usually the mean
observation is calculated), since only one observation per site can be
used.
In the GLS estimation .procedure, the within-site variation is
accounted for by an additional parameter in the model.
where
31 and £ are uncorrelated.
These two sources of error can be combined so that
where
y. ~ ,(0,a2V + aI)
3.10
-------
Then in the derivations shown in Section S.S.^Vis replaced by
+ a2| Note that Y is not changed. j
This formulation assumes that the within-site variation is the
same for all sites. However, if the information is available, each site
could have it's own within-site variation and ajl is simply replaced
with a diagonal matrix, with the diagonal elements being the within-site
i
variation at each site. !
I
i
By using this within-site variation formulation. ! the only time the
estimate will differ from the kriging estimate using the nugget is at
the observation. Now the estimate is no longer the same as the
observation. Additionally, sites with duplicate observations do not
need to be preprocessed. The algorithm in essence uses their mean.
estimate at a site
That is. the
the data. In the
ion, this
to wet deposition
no inherent
If there is no within-site variation, then the
where there is an observation will be that observation
model assumes that there is no variation (or error) in
original application of kriging to ore reverse estimati
assumption may be valid. However, in applying kriging
summaries, the assumption that the data at a site has
variability or error does not appear to be valid.
3.7 ADVANTAGES DF RLS APPROACH
When the variance-covariance matrix is specified using a function
that is dependent on distance, the GLS approach is kriging. However,
the GLS approach has the flexibility to both investigate the phenomenon
of interest and to add additional information to the model.
Often one semi-variogram does not fit the entire region of
interest. Currently, to get around this problem, the region is divided
into several smaller regions. The boundaries of the sub-regions are
usually artificial and ad-hoc procedures must be used! to blend the
results for the separate sub-regions together. By doing a 'moving' GLS,
where only a relatively small number of observations near the point of
interest are used in the estimation process, the changes in the 'sill'
3,11
-------
of the semi-variogram can be investigated over the region of interest.
Additionally, by using a 'moving1 approach, the problem with the
boundaries of the arbitrarily chosen regions no longer exist, !
The 6LS approach allows other information to be added to jbhe
model. For example, there are some pollutants that are highly '
correlated with population density (e.g. automobile exhausts). ,
Additionally, information about population density across the United
States can be obtained or well estimated with census information. By
adding this population information to the model, observations in urban
areas will not cause overestimation in nearby rural areas and
observations in rural areas will not cause underestimation in nearby
urban areas.
3.12
-------
4.0 VARIQGRAM ESTIMATES
From previous studies it is known that one semi-yariogram does not
fit the entire region shown in Figure 2.1. The shape of the semi-
variograms for pH and sulfate precipitation concentration and deposition
are primarily due to the 'depression', for pH. and 'hump', for sulfate.
in the surface that is centered around northeastern West Virginia.
These surfaces maintain about the same slopes within the smaller region
shown in Figure 2.1. Outside this region the slopes change markedly
(increases with pH and decreases with sulfate) and thus the semi -
\
variogram model also changes.
•i
Because our concern in this paper is about the effects of changing
criteria for data, we will only look at the region where one variogram
reasonably works. Because the exact boundary for this region is not
known, the semi-variograms are calculated using only the sites within
the smallest region. However, the grid is expanded to the larger region
and any site shown in Figure 2.1 is potentially used i;n the estimate.
Figure 4.1 shows the raw semi-variograms and the estimated models
for pH, sulfate concentration and sulfate deposition. As seen in this
figure the semi-variograms do not change very much between the four
different subsets. Therefore, one semi-variogram model can be used for
all four subsets. The 'nugget' that is observed at the origin of these
semi-variograms is used as the estimates of the within-site variation.
Additionally, since we use the GLS method the semi-variogram model is
converted to it's covariance equivalent (see equation ;7). The pH has a
linear model with a sill of 0.03 (pH units)2, a.range of 1280 kilometers
and a within-site variance of 0.002 (pH units)2. The range of the
linear model is artificially set beyond the actual range used since the
covariance model needs a range. The sulfate concentration has an
exponential model with a sill of 0.44, (mg/1)2 a range of 1150
kilometers and a within-site variance of 0.02 (mg/1)2. The sulfate
deposition has an exponential model with a sill of 0.70 (g/m2)2. a range
of 960 kilometers and a within-site variance of 0.03 (g/m2)2. The
4.1
-------
exponential model actually never reaches the sill, the ra.nge given above
is the distance where the model is 95 percent of the sill. l
4.2
-------
(E
OC
o
o
oc
0.040
0.036
0.032 '
0.028
0.024
0.020 •
0.016 '
0.012
0.008
0.004
0.000
0.60
0.55
O.SO
0.45
g 0.40
| 0.35
1 0.30
§ 0,25
E "0.20
«» 0.15
0.10
0.05
0.00
1.1:
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
ui
v>
RVSC/RDCR
RVSC/UDCR
UVSC/RDCR
UVSC/UDCR
1—i—i—i. i- ' i—•—r—«—\—'—i ' i ^~ ^T r
0 129 256 385 513 641 769 897 1026 1154 1282
KILOMETERS
Sulfate Concentration
— T - r— i - T— 1 - r— | - 1 - 1 - 1 - 1 r— HI r
128 256 385 513 610 769 897 1026 1154 1282
KILOMETERS
Semi-variogram Model
Sulfate peposltlon
FIGURE 4.1
,—i—|—r—|—i—i—«—i—«—i i i « n"1 i ' r
128 256 385 513 641 769 897 1026 1154 1282
KILOHETERS \
Semi-variogram for each of the Subsets of pH. Sulfate
Concentration and Sulfate Distributions
4.3
-------
-------
5.0 RESULTS
The GLS variation of kriging, described in section 3, is used to
estimate the pH, sulfate concentration, and sulfate deposition for each
of the subsets at grid nodes of a regular square grid. This procedure
uses the eight closest sites to the grid node in the estimate. The grid
nodes are 32 kilometers apart and the area of the grid, shown in
Figure 2.1. consists of 3669 nodes. This grid is then contoured using
bilinear interpolation in SAS (procedure gcontour).
The contour maps of the pH and sulfate concentration and
deposition show, in broad terms, the effects of using different subsets
of the observations. Additionally, contour maps of the differences
between several of the different subsets at each grid node are prepared.
These maps show the 'local1 effects, both extent and magnitude, of using
different subsets of observations.
5.1 CONTOUR MAPS OF THE ESTIMATES j
Figures 5.1. 5.2. and 5.3 show the contoured estimates of pH.
sulfate concentration and deposition, respectively, using the UVSC/UDCR
subsets of observations. These maps are shown for two reasons. First.
they are the maps that use the observations that meet the current, and
most stringent, sample validity and data completeness criteria. Thus.
the effects of using different subsets of observations are judged
relative to these maps. Secondly, these maps are large enough to
include details, such as the contour levels, that become lost as the
i'.
maps are reduced in size for comparisons. As seen in Figures 5.1 and
5.2. the pH and sulfate concentrations have relatively smooth contour
maps. However, as seen in Figure 5.3, sulfate deposition's contour map
has several mounds and depressions. The sulfate deposition is the
multiple of the sulfate concentration and total precipitation. The
mounds and depressions in the sulfate deposition contour map are due to
precipitation gradients that are not parallel to the concentration
gradients or to local precipitation that is unusually high or low
compared to neighboring sites.
5.1 ;
-------
FIGURE 5.1. Contours of pH Estimates Using the UDDC Valid Sample Criteria/
UDDC Data Completeness Rating Subset1
-------
FIGURE 5.2. Contours of Sulfate Concentrations (mg/1) Estimates Using the
UDDC Valid Sample Criteria/UDDC Data Completeness Rating
Subset. . j
b.3
-------
FIGURE 5.3.
Contours of Sulfate Depositions (g/sq m) Estimates Using the
UDDC Valid Sample Criteria/UDDC Data Completeness Rating •
Subset , :
5.4
-------
Figures 5.4, 5.5. and 5.6 show the contoured estimates of pH,
sulfate concentration and deposition, respectively, using all four
subsets of observations. In these figures, the number of sites used
increases from left to right (UDCR versus RDCR) and the value of the
observations change from top to bottom (UVSC versus RVSC).
The pH estimates (see Figure 5.4) increase in Ontario and Quebec
when the number of sites used increase, from UDCR to RDCR. This region
has few sites, so the addition of a few more sites has a profound effect
on the contours. The additional sites also produced increases in pH in
northeastern New York, northern Virginia, southern West Virginia.
eastern Tennessee, northern Alabama, northern Mississippi and Arkansas
decreases in North Carolina, eastern Wisconsin, and southwestern
Indiana. Along the border of Pennsylvania and New York the value of the
observation at one site (ADS ID 047a: NADP; Jasper. New York) has a
profound effect when the UVSC is used versus the RVSC. This site is not
in the UVSC/UDCR subset. ;
The sulfate concentration estimates (see Figure 5,,5) change i.n
Ontario and Quebec when the number of sites used increase, from UDCR to
RDCR. As with pH this region has few sites, so the addition of a few
more sites has a profound effect on the contours. However, for sulfate
concentration there is a decrease to the north and an increase in the
south. The increase in sites have a profound effect ion the largest
contour. 3.5 mg/1. When the UDCR is used, this contour is confined to
northern West Virginia, southeastern Ohio and southwestern Pennsylvania.
However with the additional sites
-------
FIGURE 5.4.
Contours of pH Estimates of the Four Subsets Using the UDDC or
Relaxed Valid Sample Criteria (UVSC or RVSC) and the UDDC or
Relaxed Data Completeness Rating (UDCR or RDCR). The Values of
the Contour Lines are Given in Figure 5.1.
5.6
-------
FIGURE 5.5. Contours of Sulfate Concentration (mg/1) Estimates of the Four
Subsets Using the UDOC or Relaxed Valid Sample Criteria (UVSC
or RVSC) and the UDDC or Relaxed Data Completeness Rating
(UDCR or RDCR). The Values of the Contour Lines are Given in
Figure 5.2. '
5.7
-------
0 300
Kilometers
UVSC/UDCR
UVJ5C/RDCR
RVSC/UDCR
FIGURE 5.6. Contours of Sulfate Deposition (g/sq m) Estimates of the Four
Subsets Using the UDDC or Relaxed Valid Sample Criteria (UVSC
or RVSC) and the UDDC or Relaxed Data Completeness Rating
(UDCR or RDCR). The Values of the Contour Lines are Given in
Figure 5.3.
5.8
-------
The sulfate deposition estimates (see Figure 5.6) increase in
southern Ontario, southern Wisconsin and northern Ohio when the number
of sites used increase, from UDCR to RDCR. The_3.0,g/m2 contour moved ,,
approximately 300 kilometers west. The presence of two sites on the
southwestern border of Indiana bordering on Illinois
-------
0 300
Kilometers
Concentration
with
Parsons, wv
Concentration
without
Parsons, WV
Deposition
with
Parsons, wv
Deposition
without
Parsons, wv
FIGURE 5.7. Comparison of Sulfate Concentration and Deposition Estimates
With and Without Parsons. West Virginia Site Present. The; Rest
of the Sites Belong to UVSC/UDCR Subset. See Figures 5.2 and 5.3
for the Values of the Contour Lines.'
5.10
-------
RVSC/RDCR
minus
UVSC/UOCR
UVSC/RDCR
minus
UVSC/UDCR
r
RVSC/UDCR
minus
UVSC/UDCR
RVSC/RDCR
minus
UVSC/RDCR
Figure 5.8. Differences in pH estimates for selected pairs of subsets. The
dark lines indicate an increase in the estimate and the light lines
indicate a decrease in the estimate. The ou.ter contour is 0.025,
the middle contour is 0.05 and the interior Contour is 0.10.
5.11
-------
0 300
Kilometers
RVSC/RDCR
• minus
UVSC/UDCR
r
UVSC/RDCR
minus
UVSC/UDCR
r
RVSC/UDCR
minus
UVSC/UDCR
RVSC/RDCR
nrrinus
UVSC/RDCR
FIGURE 5.9. Differences in Sulfate Concentration Estimates for Selected Pairs
of Subsets. The Dark Lines Indicate an Increase in the Estimate
and the Light Lines Indicate a Decrease in the Estimate, the Outer
Contour is 0.25 mg/1 and the Interior Contour is 0.5 mg/1.
5.12
-------
0 300
Kilometers
RVSC/RDCR
minus .
UVSC/UDCR
UVSC/RDCR
minus
UVSC/UDCR
RVSC/UDCR
minus
UVSC/UDCR
RVSC/RDCR
minus
UVSC/RDCR
FIGURE 5.10.
Differences in Sulfate Deposition for Selected Pairs of Subsets
The Dark Lines Indicate an Increase in the Estimate and the
Light Lines Indicate a Decrease in the Estimate. The Outer
Contour is 0.25 g/sq m and the Interi-or Contour is 0.5 g/sq m.
5.13
-------
subsets. The primary difference in these groups is the change in the
site values, however there are a few additional sites. The lower right
map is the difference between the UVSC/RDCR and the RVSC/RDCR subsets.
The differences in these groups are the changes in the values of the
observations with only one additional site on the Vermont-New York
border. For each of these maps, the dark contours indicate an increase
in estimates from the the UDDC to the relaxed definition(s) while the
lighter contours indicate a decrease in the estimates. For pH the outer
contour indicates a difference of 0.025. the second contour is for a
difference of 0.05 and the third contour is for a difference of 0.1.
For sulfate only two contour levels are used. The outer contour is 0.25
mg/1 for the concentration and 0.25 g/m2 for the deposition, while the
p
inner contour is 0.50 mg/1 for the concentration and 0.50 g/nr for the
deposition. The additional sites that are used in each comparison are
indicated with dark squares while the site locations that are the same
(although the value of the observation may have changed) are indicated
with white squares. In the maps showing the differences between strict-
all and relaxed-all. only one additional site is used and it is
indicated with an X. ,
The effects of changing the subsets for pH, shown in Figure 5.8.
extend over a large area in many different regions. As seen in this
figure, the additional sites are the primary cause of these differences
(the maps of RVSC/RDCR minus UVSC/UDCR and UVSC/RDCR minus UVSC/UDCR are
quite similar). The few additional sites in Ontario and Quebec cause an
area whose length is greater than 1000 kilometers to be increased by
more than 0.1 pH units. The additional sites in Arkansas, northern
Mississippi and northern Alabama also increases the pH estimates
throughout this region as much as 0.1 units. The additional sites;in
southern Ontario reduced the pH in this region, although much of this
region is over Lake Huron. Several additional sites effected 'local'
regions of over one hundred kilometers in diameter, with several of the
regions have considerable area with estimates that changed by more that
0.05 units. Only the five sites with the largest changes in their pH
observations (see Table 2.6, sites 047a (Jasper, New York). 208a (Lac Le
5.14
-------
Croix. Ontario), 241a (Gaylord. Michigan), 420a (Vincennes, Indiana).
and 495'a (Mooseonee, Ontario)) have a noticeable effect (see RVSC/RDCR.
minus UVSC/RDCR). Of these sites. 495a (Mooseonee. Ontario) which is"
the northern most site shown in Ontario has the largest effect. The
size of this effect is due to the sparsity of data in the region. As
seen in Table 2.7. the changes in the values for sites 420a (Vincennes.
Indiana) and 495a (Mooseonee, Ontario) are primarily due to one sample
with extremely unusual pHs. These samples have extremely poor
collection efficiencies (2.9% and 2.0%, respectively,, of the sample
volume predicted from the rain gauge is actually present in the
collector). Site 047a (Jasper. New York) is very unusual, on one map it
causes an increase, on another map it causes a decrease and on the other
two maps it has no effect. This site has only one sample that is added
(see Table 2.7), however, it is also the only sample in June that is
analyzed, thus when the sample is removed, all of June is essentially
removed. Without this sample, the pH value is large compared to it's
neighboring sites. When the sample is added, the pH decreased and the
site is no longer large compared to it's neighboring sites.
The effects of changing the subsets for sulfate concentration.
shown in Figure 5.9. are greatest in southern Ontario. As seen in this
figure, the additional sites are the primary cause of these differences.
Most of the new sites are in southern Ontario and have higher
concentrations than their neighboring sites. These sites have poor UDDC
data completeness ratings and are only included when the data
i
completeness rating in relaxed. Their poor ratings are primarily
because of their low collection efficiencies. The three sites with the
largest changes in the sulfate concentrations (see Table 2.4. sites 047a
(Jasper, New York), 163a (Caribou, Maine) and 420a (Vincennes, Indiana))
have a noticeable effect. The extent of the effects are related to the
density of neighboring sites, with the size increasing as the density
decreases. The extent of the effect due to site 163a (Caribou. Maine).
is effected by site 436a (Presque Isle. Maine) that is just southwest of
it. When the UODC valid sample criteria is used to select the samples.
these two sites are similar (1.32 mg/1 at 163a verses 1.55 mg/1 at
436a). thus there is no effect on the UVSC/RDCR minus UVSC/UDCR map.
5.15 !
-------
When the relaxed valid sample criteria is used to select the samples.
both site's observations increase (1.84 mg/1 at 163a verses 1.70 mg'/l. at
436a), thus the extent of the effect shown on the has a RVSC/RDCR minus
UVSC/RDCR map has a diameter of a little over 100 kilometers (the .
averages of these two sites change from 1.44 mg/1 to 1.77 mg/1).
However on the RVSC/UDCR minus UVSC/UDCR map the diameter of the area
effected has increased to over 200 kilometers because the values change
from 1.32 mg/1 (163a only) to 1.77 mg/1. The increase in the sulfate
concentration at site 163a is due to two samples with unusually high
sulfate concentration (52 mg/1 precipitation weighted average) with very
low collection efficiencies (11.2* and 24.8%). Sites 420a along the the
Indiana-Illinois border (Vincennes. Indiana) and 154a along the Indiana-
Kentucky border (Rockport. Indiana) also effect each other. Under the
strict criteria for selecting samples their sulfate concentrations are
2.62 mg/1 and 2.65 mg/1. respectively. However only site 154a has an
effect when UVSC/RDCR and UVSC/UDCR are compared because of the lower
observations to the south of 154a. However when the valid sample
criteria is relaxed, site 420a increases to 3.08 mg/1 and causes an
effect with a diameter of close to 200 kilometers without the present of
154a and about 100 kilometers when 154a is present. The large increase
at site 420a is primarily due to one sample with a concentration of 69
mg/1 and a collection efficiency of only 2.9%. Finally, as with pH. the
effects of site 047a (jasper. New York) change with the different maps
and the reasons are the same as before.
The effects of changing the subsets for sulfate deposition, shown
in Figure 5.10. are also greatest in southern Ontario. As seen in this
figure, the additional sites are again the primary cause of these
differences. Unlike the sulfate concentration, not all the effects, in
southern Ontario, are an increase in the estimates. While the sulfate
concentration (see Figure 5.9) at some sites are high compared to the
neighboring sites, their sulfate deposition is low when compared to the
'same neighboring sites. This anomaly is a result of the very low :
precipitation at these sites. The effects of sites 154a and 420a in
southwestern Indiana are larger than those shown for the sulfate
concentration primarily because of the high precipitation at site 154a.
5.16
-------
These sites together account for an increase of 0.5 ig/m in sulfate
deposition over an area with a diameter of over 200 kilometers. As with
pH and sulfate concentration, site 047a remains a very unusual site.
Although the sulfate concentration increases to a level that is similar
to it's neighboring sites, when the valid sample criteria is relaxed,
this site has a low precipitation, amount as compared to its neighbors.
Thus, although the sulfate deposition increase when 'the valid sample
criteria is relaxed, this new value is still low compared to it's
neighboring sites.
The extent and magnitude of effect that the -Pajrsons, West Virginia
site has on the 'local' sulfate concentration and deposition estimates
are shown in Figure 5.11. The extent of this effect, is over a region
with a diameter of approximately 400 kilometers. This region is limited
by the use of only the eight closest sites in the estimation process.
The magnitude of the effect increases to over 0.5 mg/1 for the
concentration and 1.5 g/m2 for the deposition. The region of those
magnitude's of effect or approximately 100 kilometers. The magnitude of
the effect-of the sulfate deposition's much greater than that for the
sulfate concentration because of the high precipitation at this site.
547
-------
0 300
Kilometers
Concentration
Deposition
FIGURE 5.11.
Extent and Magnitude of Effect the Parsons. West Virginia Site
has on the Sulfate Concentration and Deposition. The Concentration
Contours are 0.5. 0.25. 0.10 and 0.001 mg/1 and the' Deposition
Contours are 1.5. 1.0. 0.5 a.25 and 0.001 g/sq m.
5.10
-------
6.0 CONCLUSIONS
Application of UDDC valid sample criteria requires that the UDDC
rating be used to ensure representativeness throughout all seasons.
This is a conservative position for inclusion of data for maps. As seen
with site 047a and other sites shown in Table 2.7. when the UDDC valid
sample criteria is used, blocks of data over a period of greater than a
month may be lost. When a site has seasonal trends, the loss of that
much data can adversely effect the annual estimates.
Relaxed valid sample criteria may or may not lead to
representative annual summaries for the year. Sites must be evaluated
with respect to other nearby sites or years. Seasonal criteria may not
guarantee representativeness. That is. using the UDDC data completeness
rating requirement does not protect you. As seen in Table 2.7, at a
number of sites, the relaxed valid sample criteria let a number of
extremely unusual samples to be included in the annual estimates.
However, all these samples have very small collection efficiencies.
Possibly, the collection efficiency needs to be examined on a sample by
sample basis, instead of seasonally and annually. j
Representativeness of a site for its surrounding area is very
important with a sparse network. Does the sulfate concentration and
deposition at the Parsons. West Virginia site represent the area within
200 kilometers of it? ;
Although the relaxed data completeness rating allows the number of
sites used to increase by over 50%. except for a few sites, these
additional sites did not change the spatial patterns of wet deposition
on a region scale. Most of the changes due to the additional sites are
on a local scale where these differences are smaller than the scale used
in regional isopleth maps. The few additional sites which do have a
profound effect are located in areas where there is a sparsity of .site's
(e.g. northern Ontario) or whose summaries are changed markedly due to
either the addition of an extremely unusual sample or, the addition of a
large contiguous number of samples. Thus, for contour maps whose
6.1 ;
-------
objective is to show regional pattern, the key issue is not the number
of sites but the location of the site and the validity of the samples
from the site.
There are two sources of uncertainty in the contour maps that need
to be addressed. First, the within-site variation in the annual
summaries. Because there are so few collocated sites, the within-site
variation is poorly estimated and thus any variance estimate from
kriging is also poorly estimated. Second, the variation from year to
year in the annual summaries at a site have not been considered. For
example, at Parsons. West Virginia the annual sulfate depositions (g/m2)
are 4.4 (1979). 4.4 (1980). 4.6 (1981). 4.0 (1982). 3.1 (1983). 3.4
(1984), 4.8 (1985). 5.3 (1986) and 3.0 (1987). It should be noted that
in 1985 and 1986. 19% and 9%. respectively, of the precipitation has no
chemistry results for sulfate. This occurs primarily in months when the
sulfate concentration is low at this site (late fall). Additionally, in
1987 the annual precipitation was only 73% of the average annual ;
precipitation for'the previous eight years.
For network operations, the implication of this study is that
sites must give valid data for the entire year. The loss of a large
number of contiguous samples renders the site useless for the purpose of
annual summaries. The relationship between small sample collection
efficiency and the representativeness of the sample's chemistry needs to
be reevaluated.
For network design, the implication of this study is that the
total number of sites is less important than the representativeness of
the site. When considering a region the size of the eastern United
States, where the sheer magnitude of the region forces sites to be
hundreds of kilometers apart, the summaries from one site can profoundly
impact a large region. If that site is not representative of the region
between sites, then it will bias the results.
6.2
-------
7.0 RFFFRFNCES
Barrie L A. and J. M. Hales. 1984. "The Spatial Distributions of
Precipitation Acidity and Major Ion Wet Deposition in North America
during 1980." Tell us 36B. pp. 333-355.
Bilonick R A 1985. "The Time-Space Distribution of Sulfate
Deposition in the Northeastern United States." Almpju FnvKon. 19.
11. pp. 1829-45.
Calvert. J.. J. N. Galloway. J. M. Hales. G M H1dy-^-.
A Lazrus, J. Miller. V. Mohnen. and M. F. Uman. 1983. Acid
Deposition. Atmospheric Processes in Eastern North America. National
Academy Press. Washington. D.C.
Cowling E B 1982. "Acid Precipitation in Historical Perspective."
Fnviron. Sc1 . Tech. 16. 2. pp. 110A-123A. ,
Eynon. B. P.. and P. Switzer. 1983. "The Variability of Rainfall
Acidity." r.anariian J. Statistics 11. 1. PP. 11-24.
Finkelstein. P. 1984. "The Spatial Analysis of Acid Precipitation
Data." .1.' Climate and Applied Met. 23. pp. 52-62.
f
Guertin, K.. J. -P. Villeneuve. S. Deschenes. and G.'Jaques. 1988.
"The Choice of Working Variables in Geostatistical Estimation of Acid
Precipitation." AtTT™- Environ. 22. 12. pp. 2787-2801.
Haas. T. C.. J. C. Moore. P. L. Chapman, and J. H. Gibson. 1988. "Acid
Deposition: The Structure Analysis and Kriging of a Process with
First and Second Order Non-Stationarity," submitted for publication.
Dept. of Statistics and Natural Res. Ecology Lab., Colo. State Univ..
Ft. Collins. Co. !
Junge C. E. 1963. Air Chemistry and Radioactivity!. International
Geophysics Series. Vol. 4. Academic Pres. New York. pp. 311-346.
le D N. and J. Petkau. 1988. "The Variability of Rainfall Acidity
"Revisited." r.anadian j. Statistics 16. 1. pp. 151-38.
Munger J W.. S. J. Eisenreich. 1983. "Continental -Scale Variations
in Precipitation Chemistry." Environ. Sci . Tech. II. 1. pp. 32A-42A.
NADP 1984. "NADP/NTN Annual Data Summary. Precipitation Chemistry in
the United States." National Atmospheric Deposition Program
Coordinator's Office. Natural Resource Ecology Lab. Colorado State
Univ.. Fort Collins, Co. September 1987. ;
j
01 sen A R. 1988. "1986 Wet Deposition Temporal and Spatial Patterns
in North America." U.S. Environmental Protection Agency. Research
Triangle Park. North Carolina.
7.1
-------
Olsen, A. R., and A. L. Slavich. 1986. "Acid Precipitation in North
America: 1984 Annual-Data Summary from ADS Data Base."
EPA-600/4-86-033. USEPA. RTF1. NC.
Olsen. A. R.. and A. L. Slavich. 1985. "Acid Precipitation in North
America: 1983 Annual Data Summary from ADS Data Base."
EPA-600/4-85-061. USEPA. RTF. NC.
Olsen. A. R.. and C. R. Watson. 1984. "Acid Precipitation in North
America: 1980. 1981. and 1982 Annual Data Summaries Based on ADS
Data Base." EPA-600/7-84-097. USEPA. RTP. NC.
Seilkop, S. K.. and Finkelstein, 1987.
and Trends in Eastern North America.
Met. 2fi. pp. 980-994.
"Acid Precipitation Patterns
1980-84." J. Climate and Applied
Semonin. R. 6. 1981. "Seasonal Precipitation Concentrations and :
Depositions for North America from the CANSAP/NADP Network." in
Nineteenth Progress Report to U.S. DOE. Pollutant Characterization
and Safety Div.. Contract DE-AC02-76EV01199.
Sweeney, J. K. and A. R. Olsen. 1987. "Acid Precipitation in North
America: 1986 Annual and Seasonal Data Summaries from Acid
Deposition System Data Base." Report EPA/600/4-88. EMSL ORD USEPA.
Research Triangle Park. N. C.. November 1987.
Venkatram. A. 1988. "On
Acid Precipitation Data
the Use of
" Atrnos. Environ
Kriging in the Spatial Analysis of
22., 9. pp. 1963-76.
Vong. R.. S. Cline. 6. Reams,
Haas, J. Moore. R. Husar.
1989. "Regional analysis
Report EPA/600/3-89/030.
J, Bernert. D. Charles. J. Gibson. T.
A. R. Olsen. J. C. Simpson, and S. Seilkop.
of Wet Deposition for Effects Research."
Wampler, S. J. and A. R. Olsen. 1987. "Spatial Estimation of Annual
Wet Acid Deposition Using Supplemental Precipitation Data." Preprint:
Tenth Conf. on Probability and Statistics (held in Edmonton. Canada).
American Meteorological Society. Boston. Mass.
7.2
-------
APPENDIX A !
COMPARISON OF 1985 pH CONTOUR MAPS
Anthony R. 01 sen
Pacific Northwest Laboratory
June 22, 1988
This paper gives a comparison of the 1985 pH maps that; appear in the
NAPAP Interim Assessment (NAPAP 1987) and in the NADP 1985 Annual Data Summary
report (NADP 1987).
Figure 1 reproduces the NADP report map and Figure 2 reproduces the NAPAP
report contour map, prepared by Pacific Northwest Laboratory (PNL). The first
feature of the maps that differs is the use of different: contour levels.
This makes any comparison difficult. Judgement of whether the maps agree
depends on who makes the judgement and what is the intended purpose of the
maps. An appropriate purpose for the map appears to be a semi-quantitative
display of the spatial pattern of pH during 1985. With this as the purpose,
the two maps appear to agree.
The production of contour maps is a problem of surface estimation and
display. All solutions will not agree exactly in the location of contour
lines but strong qualitative agreement'should be expected. I have taken a
closer look at the production process for the maps. First, I reviewed the
production processes used by NADP and PNL to determine the steps used. Second,
I requested that PNL and NADP prepare several alternative maps to investigate
possible reasons for quantitative differences in the maps.
PRODUCTION PROCESSES
The production of a contour map includes the following:
Calculation of an annual pH value at a site,
Selection of sites to be used in surface estimation,
Selection of a surface estimate technique,
Display of the estimated surface,
Production of final document quality contour map.
NADP and PNL use the same calculation procedure to obtain an annual pH value
for a site. The pH values for sites that NADP and PNL both used in preparing
-------
-------
APPENDIX A
COMPARISON OF 1985 DH CONTOUR MAPS
-------
the maps agree in all cases. Both use pH to the nearest hundredth in the
production process. Note that pH values that appear on the maps are rounded
to the nearest tenth. Because of the rounding, contour lines may include or
exclude sites that appear to be on the "wrong" side.
The NADP and PNL maps do use different sites for the surface estimation.
NADP uses only NADP/NTN network sites. NADP used 123 NADP/NTN sites and PNL
used 183 sites from multiple networks. PNL uses sites from the MADP/NTN,
UAPSP, MAP3S, CAPMoN, and APIOS networks. Fewer NADP sites (20) are used by
PNL than by NADP. This is due to using different criteria for inclusion of a
site. The major difference is that PNL includes a quarterly criteria as well
as an annual criteria. The underlying data completeness measures are
calculated the same, the difference is in which measures are applied and what
cutoff criteria is used. Based on our current knowledge on the relationship
between the criteria and the "representativeness" of the annual summary, I do
not believe that a case can be made for preferring either the NADP or:the PNL
criteria. Both are reasonable choices.
NADP and PNL use entirely different surface estimation algorithms. The
initial step in both algorithms is to estimate the surface on a regular grid.
The regular grid is then used to determine the location of the contour lines.
NADP uses a grid on a transverse mercator projection at an unknown but
reasonable grid density. PNL uses an 80 km grid on a Lambert conic projection
that is near-distance preserving. NADP uses the SURFACE II graphics system
(Sampson 1984). The gridding routine uses a constrained distance-squared
weighting function applied to the eight nearest site locations (a maximum
search radius is imposed). PNL uses the kriging algorithms in BLUEPACK
software (Delfiner 1979). Kriging also is distance-weighted but the distance
weights are derived from the variation observed in the site data. The pH
weights are from a spherical semi-variogram. Eight sites are used with a
restriction that each octant from the grid node contributes a site, if
available within a maximum search radius.
-------
Smooth contour lines are interpolated from the regular grid. NADP uses
the "CONT" function in Surface II, which uses a piecewise Bessel interpolation
within a grid cell. PNL uses the DISSPLA graphics contouring function with a
cubic spline interpolation, termed "spline under tension." I review the maps
that are computer generated for consistency with the monitoring site data.
This review typically includes removing contours in the West, deleting
extensions of contours over the ocean, and subjectively smoothing contours,
especially in data sparse regions, to remove non-data supported features.
ALTERNATIVE MAP COMPARISON
Since NADP and PNL used different sets of sites and different surface
estimation and contouring algorithms, four alternative maps are produced for
the four possible combinations. As a point of departure, Figures 1 and 2 are
the original maps as they appeared in the NAPAP interim assessment and the
NADP 1985 Annual Data Summary. The sites included in the NADP data set (123
sites) and the PNL data set (183 sites) are shown in Figures 3 and 4,
respectively. |
For the comparison, PNL produced two maps (Figures 5 and 6) using our
standard surface estimation and contouring procedure. Contour levels were
changed to be the same as the NADP original map. The same kriging semi-
variogram is used for both maps (same as used in NAPAP map). The maps provide
an assessment of differences that arise from using different subsets of sites.
My assessment is that the maps agree very well east of the Mississippi River
within the United States. The 4.7 and 4.9 contours have bends in the south
that are not supported by site data. These would be subjectively smoothed to
remove "artificial" features. The 5.1 contour extends into the West where
contouring is questionable. The 4.5 contour differs in Canada and Maine due
to the PNL data set including Canadian sites. The 4.3 contour differs in
northern New York. Other differences in the contours are small. In Figure
7, an expanded view of eastern North America for the original PNL NAPAP map
is given for comparison. !
-------
NADP used the NADP contouring algorithm to produce a map based on the NADP
data set sites (Figure 8) and the PNL data set sites (Figure 9). The maps
agree very well east of the Mississippi within the United States. The
differences between them are similar to those present between the two PNL
maps. The areas, west of Mississippi and Canada, where the density of sites
differs between the two data sets show the greatest differences.
The NADP map (Figure 8) and the PNL map (Figure 5) using the 123 sites
in the NADP data set are remarkably similar. The north, northeast and
southwest portion of the NADP 4.3 contour extends farther than the PNL contour.
The southern portion of the 4.7 NADP contour extends into Texas while the PNL
•contour does not. Larger differences occur for the 5.1 contour in the west,
reflecting sparse data support in this region. The NADP map (Figure 9) and the
PNL map (Figure 6) using the 183 sites in the PNL data set show differences
remarkably similar to the previous comparison.
SUMMARY
My assessment of the comparison of the different data sets and the
different "contouring" algorithms used by NADP and PNL is that they produce
remarkably similar maps. Agreement is best where the density of sites is
greatest and poorest where the density is lowest. Inclusion of Canadian sites
does aid 1n completing contours in the northeast. This is to be expected.
When the algorithms are compared on the same data set, the differences are no
greater than differences observed when using same algorithm with different
data sets. The computer drawn NADP maps appear to be smoother than the
computer drawn PNL maps. This is related to the density of grids used and
the selection of a smoothing parameter.
-------
REFERENCES j
Delfiner, P., J.P. Delhomme, J.P. Chiles, D. Renard, and F Irigoin. 1979.
BLUEPACK 3-D. Centre De Geostatistique et De Morphologies, Fontainebleau,
France.
National Acid Deposition Program. 1987. NADP/NTN Annual Data Summary.
Precipitation Chemistry in the United States. 1985. Natural Resource
Ecology Laboratory, Colorado State University, Fort Collins, CO.
National Acid Precipitation Assessment Program. 1987. Interim Assessment;
The Causes and Effects of Acidic Deposition. Vol. Ill Atmospheric Process,
U.S. Government Printing Office, Washington, DC.
Sampson, Robert J. 1984. SURFACE II GRAPHICS SYSTEM. Kansas Geological
Survey, Lawrence, Kansas.
-------
-------
5-1
FIGURE 1. NADP Original 1985 Annual Data Summary pH Map
-------
1985 Annual •
Precipitation-Weighted pH
FIGURE 2. PNL Original NAPAP Interim Assessment
Document 1985 pH Map
-------
FIGURE 3. Sites Used in NADP pH Data Set
-------
1985 Annual
pH
PNL June 1988
FIGURE 4. Sites Used in PNL pH Data Set
-------
FIGURE 5. PNL Kriging Map Using NADP Data Set Sites
-------
FIGURE 6. PNL Kriging Map Using PNL Data Set Sites
-------
FIGURE 7. PNL Computer Drawn Map for Original NAPAP
Interim Assessment pH Map
-------
FIGURE 8. NADP Map Using NADP Data Set Sites
-------
FIGURE 9. NADP Map Using PNL Data Set Sites
•&U.& GOVERNMENT IttlNTING OFFICE: H*0 • 74S-BV2MM
-------
-------
-------
c
§ 0 °
~ O -^
3 O CD
• < O
® ro
•""* <
l|
(D W
? -i
2 o
3 "O
-* o
o 3
? o
Jen
o. g
go
3 3
S 3
3° ni
c
foT
o-
0
-
0
,
-------
|