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Erin Peterson
Environmental Risk Technologies
CSIRO Mathematical & Information Sciences
St Lucia, Queensland
Predicting Water Quality Impaired Stream Segments using
Landscape-scale Data and a Regional Geostatistical Model
The work reported here was developed under STAR Research Assistance Agreement CR-829095 awarded by the U.S.
Environmental Protection Agency (EPA) to Colorado State University. This presentation has not been formally reviewed by
EPA. EPA does not endorse any products or commercial services mentioned in this presentation.
Space-Time Aquatic Resources Modeling and Analysis Program
This research is funded by
U.S.EPA凡Science To AchieveResults (STAR) ProgramCooperativeAgreement # CR -829095
This research is funded by
U.S.EPAScience To AchieveResults (STAR) ProgramCooperativeAgreement # CR -829095
Collaborators
Dr. David M. TheobaldNatural Resource Ecology LabDepartment of Recreation & TourismColorado State University, USA
Dr. N. Scott UrquhartDepartment of StatisticsColorado State University, USA
Dr. Jay M. Ver HoefNational Marine Mammal Laboratory, Seattle, USA
Andrew A. MertonDepartment of StatisticsColorado State University, USA
Introduction~
Background~
Patterns of spatial autocorrelation in stream
water chemistry~
Predicting water quality impaired stream segments using landscape-scale data and a regional geostatistical
model: A case study in Maryland, USA
Overview
Water Quality Monitoring Goals
• Create a regional water quality assessment• Ecosystem Health Monitoring Program
• Identify water quality impaired stream segments
Probability-based Random Survey Designs
Advantages• Statistical inference about population of streams over
large area• Reported in stream kilometers
Disadvantages
• Does not take watershed influence into account• Does not identify spatial location of impaired stream
segments
Purpose
Develop a geostatistical methodology based on coarse-scale GIS data and field surveys that can be used to predict water
quality characteristics about stream segments found throughout a large geographic area (e.g., state)
SCALE: Grain
Substrate
Biotic Condition
OverhangingVegetation
Segment
River Network
Network Connectivity
Tributary Size DifferencesNetwork Geometry
Stream Network
ConnectivityFlow Direction Network Configuration
Drainage DensityConfluence Density
Cross Sectional AreaChannel Slope, Bed MaterialsLarge Woody Debris
Biotic Condition, Substrate Type, Overlapping VegetationDetritus, Macrophytes
Microhabitat
Segment Contributing Area
Riparian Vegetation Type & ConditionFloodplain / Valley Floor Width
Localized DisturbancesLand Use/ Land Cover
Landscape
ClimateAtmospheric depositionGeology
TopographySoil Type
Microhabitat
ShadingDetritus Inputs
Riparian Zone
Nested Watersheds
Land UseTopography
Vegetation TypeBasin Shape/Size
COARSE
FINE
Reach
AquaticTerrestrial
Fit an autocovariance function to data• Describes relationship between observations based on
separation distance
Geostatistical Modeling
Separation Distance
Sem
ivar
ian
ce
Sill
Nugget Range
10000
0
10
Distances and relationships are represented differently depending on the distance measure
Distance Measures & Spatial Relationships
A
B
C
Straight-line Distance (SLD)Geostatistical models typically based on SLD
A
B
C
Symmetric Hydrologic Distance (SHD)Hydrologic connectivity: Fish movement
Distance Measures & Spatial Relationships
A
B
C
Asymmetric Hydrologic DistanceLongitudinal transport of material
Distance Measures & Spatial Relationships
A
B
C
Challenge: • Spatial autocovariance models developed for SLD may
not be valid for hydrologic distances– Covariance matrix is not positive definite
Distance Measures & Spatial Relationships
Asymmetric Autocovariance Models for Stream Networks
• Weighted asymmetric hydrologic distance (WAHD)
• Developed by Jay Ver Hoef
• Moving average models
• Incorporate flow volume, flow direction, and use hydrologic distance
• Positive definite covariance matrices
Flow
Ver Hoef, J.M., Peterson, E.E., and Theobald, D.M., Spatial Statistical Models that Use Flow and Stream Distance, Environmental and Ecological Statistics. In Press.
Evaluate 8 chemical response variables1. pH measured in the lab (PHLAB)2. Conductivity (COND) measured in the lab μmho/cm3. Dissolved oxygen (DO) mg/l4. Dissolved organic carbon (DOC) mg/l5. Nitrate-nitrogen (NO3) mg/l6. Sulfate (SO4) mg/l7. Acid neutralizing capacity (ANC) μeq/l8. Temperature (TEMP) °C
Determine which distance measure is most appropriate• SLD• SHD• WAHD• More than one?
Find the range of spatial autocorrelation
Objectives
Dataset
Maryland Biological Stream Survey (MBSS) Data
• Maryland Department of Natural Resources– Maryland, USA – 1995, 1996, 1997
• Stratified probability-based random survey design
• 881 sites in 17 interbasins
GIS ToolsAutomated tools needed to extract data about hydrologic relationships
between survey sites did not exist!
Wrote Visual Basic for Applications (VBA) programs to:
1. Calculate watershed covariates for each stream segment• Functional Linkage of Watersheds and Streams (FLoWS)
2. Calculate separation distances between sites• SLD, SHD, Asymmetric hydrologic distance (AHD)
3. Calculate the spatial weights for the WAHD4. Convert GIS data to a format compatible with statistics software
FLoWS tools will be available on the STARMAP website:http://nrel.colostate.edu/projects/starmap
1 2
3
1 2
3
SLD
1 2
3
SHD AHD
Spatial Weights for WAHD
Proportional influence (PI): influence of each neighboring survey site on a downstream survey site• Weighted by catchment area: Surrogate for flow volume
1. Calculate the PI of each upstream segment on segment directly downstream
2. Calculate the PI of one survey site on another site• Flow-connected sites• Multiply the segment PIs
BA
C
Watershed Segment B
Watershed Segment A
Segment PI of A
Watershed Area A
Watershed Area B=
Proportional influence (PI): influence of each neighboring survey site on a downstream survey site• Weighted by catchment area: Surrogate for flow volume
A
BC
DE
F
G
H
survey sitesstream segment
Spatial Weights for WAHD
1. Calculate the PI of each upstream segment on segment directly downstream
2. Calculate the PI of one survey site on another site• Flow-connected sites• Multiply the segment PIs
Proportional influence (PI): influence of each neighboring survey site on a downstream survey site• Weighted by catchment area: Surrogate for flow volume
A
BC
DE
F
G
H
Site PI = B * D * F * G
Spatial Weights for WAHD
1. Calculate the PI of each upstream segment on segment directly downstream
2. Calculate the PI of one survey site on another site• Flow-connected sites• Multiply the segment PIs
Data for Geostatistical Modeling
1. Distance matrices• SLD, SHD, AHD
2. Spatial weights matrix• Contains flow dependent weights
for WAHD
3. Watershed covariates • Lumped watershed covariates
– Mean elevation, % Urban
4. Observations• MBSS survey sites
Validation Set• Unique for each chemical response variable
Initial Covariate Selection• 5 covariates
Model Development• Restricted model space to all possible linear models• 4 model sets:
Response Significant CovariatesANC (μeq/l) PASTUR, LOWURB, WOODYWET, YR96, YR97COND (μmho/cm) HIGHURB, LOWURB, COALMINE, YR96, NORTHINGDOC (mg/l) WOODYWET, CONIFER, MIXEDFOR, LOWURB, NORTHINGDO (mg/l) DECIDFOR, HIGHURB, WOODYWET, YR96, YR97NO3 (mg/l) PASTUR, PROBCROP, ROWCROP, LOWURB, WATERpH Lab PROBCROP, DECIDFOR, WOODYWET, ACREAGE, CONIFERSO4 (mg/l) LOWURB, COALMINE, NORTHING, ER67, ER69TEMP (°C) PROBCROP, LOWURB, WATER, YR96, YR97
Geostatistical Modeling Methods
Geostatistical model parameter estimation• Maximize the profile log-likelihood function
Geostatistical Modeling Methods
Log-likelihood function of the parameters ( ) given the observed data Z is:2, ,
)()'(2
1log
2
1)2log(
2);,,( 1
222
XZXZ
nZ
Maximizing the log-likelihood with respect to B and sigma2 yields:
2log
2
1)ˆlog(
2)2log(
2),ˆ,ˆ;( 22 nnnZprofile
ZXXX 111 ')'(ˆ 1
2ˆ ˆ( ) ' ( )
ˆZ X Z X
n
and
Both maximum likelihood estimators can be written as functions of alone
Derive the profile log-likelihood function by substituting the MLEs ( ) back into the log-likelihood function
2ˆ ˆ,
Covariance matrix for SLD and SHD models• Fit exponential autocorrelation function
1 1 21 2
1 if 0( ; , )
(1 )exp( / ) if 0
hC h
h h
where C1 is the covariance based on the distance between two sites, h, given the autocorrelation parameter estimates: nugget ( ), sill ( ), and range ( ).0 1 2
Geostatistical Modeling Methods
1 0
1
0 locations are not flow connected,
( , | ) (0) if location 1 = location 2,
( ) otherwise.D
i j
j B j
C s s C
w C h
Covariance matrix for WAHD model• Fit exponential autocorrelation function (C1)• Hadamard (element-wise) product of C1 & square root of spatial
weights matrix forced into symmetry ( )Dj B jw
Geostatistical Modeling Methods
Model selection between model types• 100 Predictions: Universal kriging algorithm • Mean square prediction error (MSPE)• Cannot use AICC to compare models based on different distance
measures
Model comparison: r2 for observed vs. predicted values
Model selection within model set• GLM: Akaike Information Corrected Criterion (AICC)• Geostatistical models: Spatial AICC (Hoeting et al., in press)
2
12),,;(2 2
kpn
kpnZAICC profile
where n is the number of observations, p-1 is the number of covariates, and k is the number of autocorrelation parameters.
http://www.stat.colostate.edu/~jah/papers/spavarsel.pdf
Results
Summary statistics for distance measures• Spatial neighborhood differs• Affects number of neighboring sites• Affects median, mean, and maximum separation distance
* Asymmetric hydrologic distance is not weighted here
Summary statistics for distance measures in kilometers using DO (n=826).
Distance Measure N Pairs Min Median Mean Max
Straight Line Distance 340725 0.05 101.02 118.16 385.53
Symmetric Hydrologic Distance 62625 0.05 156.29 187.10 611.74
Pure Asymmetric * Hydrologic Distance 1117 0.05 4.49 5.83 27.44
SLD
SHD
WAHD
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
ANC COND DOC DO NO3 PHLAB SO4 TEMP
Ran
ge
(km
)
180.79 301.76
Range of spatial autocorrelation differs:• Shortest for SLD• TEMP = shortest range values• DO = largest range values
Results
Mean Range ValuesSLD = 28.2 kmSHD = 88.03 kmWAHD = 57.8 km
ANC
0.00
50000.00
100000.00
150000.00
200000.00
250000.00
300000.00
350000.00
GLM SL SH WAH
COND
0.00
5000.00
10000.00
15000.00
20000.00
25000.00
30000.00
35000.00
40000.00
GLM SL SH WAH
DOC
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
GLM SL SH WAH
DO
0.00
0.50
1.00
1.50
2.00
2.50
GLM SL SH WAH
NO3
0.00
0.20
0.40
0.60
0.80
1.00
1.20
GLM SL SH WAH
SO4
0.00
50.00
100.00
150.00
200.00
250.00
300.00
350.00
400.00
GLM SL SH WAH
TEMP
6.50
7.00
7.50
8.00
8.50
9.00
GLM SL SH WAH
PHLAB
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
GLM SL SH WAH
MS
PE
GLM
SLD
SHD
WAHD
Distance Measures: • GLM always has less predictive ability• More than one distance measure usually performed well
• SLD, SHD, WAHD: PHLAB & DOC• SLD and SHD : ANC, DO, NO3• WAHD & SHD: COND, TEMP
• SLD distance: SO4
Results
Strong: ANC, COND, DOC, NO3, PHLAB Weak: DO, TEMP, SO4
GLM
SLD
SHD
WAHD
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
ANC COND DOC DO NO3 PHLAB SO4 TEMP
R2r2
Results
r2 Predictive ability of models:
Discussion
• Site’s relative influence on other sites• Dictates form and size of spatial neighborhood
Important because…• Impacts accuracy of the geostatistical model predictions
Distance measure influences how spatial relationships are represented in a stream network
SHD WAHDSLD
SLD
SHD
• Geostatistical models describe more variability than GLM
Patterns of spatial autocorrelation found at relatively coarse scale
• > 1 distance measure performed well• SLD never substantially inferior• Do not represent movement through network
Different range of spatial autocorrelation?• Larger SHD and WAHD range values • Separation distance larger when restricted to
network
SLD, SHD, and WAHD represent spatial autocorrelation in continuous coarse-scale variables
Discussion
Probability-based random survey design (-) affected WAHD• Maximize spatial independence of sites
• Does not represent spatial relationships in networks
• Validation sites randomly selected
0 2
244
149133
109
66
38 32
12 7
3519 15 13 6 1 0
0
275
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Fre
quen
cy
Number of Neighboring Sites
244 sites did not have neighbors Sample Size = 881Number of sites with ≤1 neighbor: 393Mean number of neighbors per site: 2.81
Discussion
0
45004500
0
Diff
ere
nce
(O
– E
)
Number of Neighboring Sites
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1715 16
WAHD GLM
Not when neighbors had:• Similar watershed conditions• Significantly different chemical response values
WAHD models explained more variability as neighboring sites increased
GLM predictions improved as number of neighbors increased
• Clusters of sites in space have similar watershed conditions– Statistical regression pulled towards the cluster
• GLM contained hidden spatial information– Explained additional variability in data with > neighbors
Discussion
0
45004500
0
Number of Neighboring Sites
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1715 16
WAHD GLM
Diff
ere
nce
(O
– E
)
Predictive Ability of Geostatistical Models
r2
PH
Coarse
Fine
Sca
le o
f in
flue
ntia
l e
colo
gic
al p
roce
sse
s ANC
NO3
COND
DOC
SO4
DO
0 0.5 1.0
TEMP
Conclusions
1) Spatial autocorrelation exists in stream chemistry data at a relatively coarse scale
2) Geostatistical models improve the accuracy of water chemistry predictions
3) Patterns of spatial autocorrelation differ between chemical response variables• Ecological processes acting at different spatial scales
4) SLD is the most suitable distance measure at regional scale at this time• Unsuitable survey designs• SHD: GIS processing time is prohibitive
Conclusions
5) Results are scale specific• Spatial patterns change with survey scale• Other patterns may emerge at shorter separation distances
6) Further research is needed at finer scales• Watershed or small stream network
7) New survey designs for stream networks• Capture both coarse and fine scale variation• Ensure that hydrologic neighborhoods are represented
Predicting Water Quality Impaired Stream Segments using
Landscape-scale Data and a Regional Geostatistical Model: A Case Study In
Maryland
Objective
Demonstrate how a geostatistical methodology can be used to compliment regional water quality monitoring efforts
1) Predict regional water quality conditions
2) Identify the spatial location of potentially impaired stream segments
N
1996 MBSS DOC Data
0 20
Kilometers
n Min 1st Qu. Median Mean 3rd Qu. Max σ2312 0.6 1.2 1.7 1.9 2.7 15.9 1.8
Potential covariates
Covariate DescriptionSpatial Resolution
AREA Catchment area (ha) 30 meterURBAN % Urban 30 meterBARREN % Barren 30 meterWATER % Open Water 30 meterCONIFER % Conifer or evergreen forest type 30 meterDECIDFOR % Deciduous forest type 30 meterMIXEDFOR % Mixed forest type 30 meterEMERGWET % Emergent Herbacious Wetlands 30 meterWOODYWET % Woody or shrubby wetlands 30 meterCOALMINE % Coalmine 30 meterEASTING Easting - Albers Equal Area Conic 1 footNORTHING Northing - Albers Equal Area Conic 1 footER63-ER69 Omernik's Level III Ecoregion 1:7,500,000MEANELEV Mean elevation in the watershed 30 meterSLOPE Mean slope in the watershed 30 meterARGPERC % Argillaceous rock type in watershed 1:250,000CARPERC % Carbonic rock type in watershed 1:250,000FELPERC % Felsic rock type in watershed 1:250,000MAFPERC % Mafic rock type in watershed 1:250,000SILPERC % Siliceous rock type in watershed 1:250,000
MEANKMean soil erodability factor in watershed (adjusted for rock fragments) 1 kilometer
MAXTEMP Mean annual maximum temperature (°C) 4 kilometerMINTEMP Mean minimum temperature for January - April (°C) 4 kilometerPRECIP Mean precipitation for January - April (mm) 4 kilometerANPRECIP Mean annual precipitation 4 kilometer
Methods
Potential covariates after initial model selection (10)
Covariate DescriptionSpatial Resolution
AREA Catchment area (ha) 30 meterURBAN % Urban 30 meterBARREN % Barren 30 meterWATER % Open Water 30 meterCONIFER % Conifer or evergreen forest type 30 meterDECIDFOR % Deciduous forest type 30 meterMIXEDFOR % Mixed forest type 30 meterEMERGWET % Emergent Herbacious Wetlands 30 meterWOODYWET % Woody or shrubby wetlands 30 meterCOALMINE % Coalmine 30 meterEASTING Easting - Albers Equal Area Conic 1 footNORTHING Northing - Albers Equal Area Conic 1 footER63-ER69 Omernik's Level III Ecoregion 1:7,500,000MEANELEV Mean elevation in the watershed 30 meterSLOPE Mean slope in the watershed 30 meterARGPERC % Argillaceous rock type in watershed 1:250,000CARPERC % Carbonic rock type in watershed 1:250,000FELPERC % Felsic rock type in watershed 1:250,000MAFPERC % Mafic rock type in watershed 1:250,000SILPERC % Siliceous rock type in watershed 1:250,000
MEANKMean soil erodability factor in watershed (adjusted for rock fragments) 1 kilometer
MAXTEMP Mean annual maximum temperature (°C) 4 kilometerMINTEMP Mean minimum temperature for January - April (°C) 4 kilometerPRECIP Mean precipitation for January - April (mm) 4 kilometerANPRECIP Mean annual precipitation 4 kilometer
Methods
Fit geostatistical models• Two distance measures: SLD and
WAHD
Restricted model space to all possible linear models
• 1024 models per set • 9 model sets
Parameter Estimation• Maximized profile log-likelihood
function
Methods
Autocorrelation Function SLD WAHD
Exponential
Spherical
Mariah
Hole Effect
Linear with Sill
Rational Quadratic
Methods
• Spatial AICC (Hoeting et al., in press)
Model selection within distance measure & autocorrelation function
Model selection between distance measure & autocorrelation function• Cross-validation method using Universal kriging algorithm
– 312 predictions• MSPE
Model comparison: r2 for the observed vs. predicted values
Results
SLD models performed better than WAHD
Exception: Spherical model
Best models:• SLD Exponential, Mariah,
and Rational Quadratic models
r2 for SLD model predictions• Almost identical• Further analysis restricted
to SLD Mariah model
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 2 3 4 5 6
SLD
WAHD
Exp
on
enti
al
Sp
her
ical
Mar
iah
Ho
le E
ffec
t
Lin
ear
wit
h S
ill
Rat
ion
al
Qu
adra
tic
Autocorrelation Function
MS
PE
ExponentialRational
Quadratic MariahExponential 1 0.997 0.990Rational Quadratic 1 0.993Mariah 1
Results
Covariates for SLD Mariah model:WATER, EMERGWET, WOODYWET, FELPERC, & MINTEMP
Positive relationship with DOC:• WATER, EMERGWET, WOODYWET, MINTEMP
Negative relationship with DOC• FELPERC
Nugget Sill Range Intercept WATER EMERGWET WOODYWET FELPERC MINTEMP
0.15 0.28 7.02 0.28 0.05 0.04 0.02 -0.0005 0.07
Cross-validation interval: 95% of regression coefficients produced by leave-one-out cross validation procedure
Narrow intervals• Few extreme regression coefficient values
– Not produced by common sites– Covariate values for the site are represented in observed data– Not clustered in space
Cross-validation intervals for Mariah model regression coefficients
Statistic WATER (%) EMERGWET (%) WOODYWET (%) FELPERC (%) MINT (°C)Minimum 0.0469 0.0306 0.0156 -0.0006 0.0616Maximum 0.0537 0.0425 0.0187 -0.0004 0.071Mean 0.0501 0.0344 0.0176 -0.0005 0.0655Standard Dev 0.0007 0.0009 0.0002 0.00005 0.000795% Lower Limit 0.0485 0.0322 0.017 -0.0006 0.064395% Upper Limit 0.0522 0.0366 0.0179 -0.0005 0.0669
Model coefficients represent change in log10 DOC per unit of X
R2 = 0.7221
0
18
0 5 10 15Observed DOC mg/l
Pre
dic
ted
DO
C m
g/l r2 = 0.7221R2 = 0.7221
0
18
0 5 10 15Observed DOC mg/l
Pre
dic
ted
DO
C m
g/l r2 = 0.7221
r2 Observed vs. Predicted Values
n = 312 sitesr2 = 0.72
1 influential siter2 without site = 0.66
• SLD models more accurate than WAHD models
• Landscape-scale covariates were not restricted to watershed boundaries
– Geology type– Temperature– Wetlands & water
Discussion
Regression Coefficients
Narrow cross-validation intervals • Spatial location of the sites not as important as watershed
characteristics
Extreme regression coefficient values• Not produced by common sites• Not clustered in space
Local-scale factor may have affected stream DOC • Point source of organic waste
Discussion
North and east of Chesapeake Bay - large SPE values• Naturally acidic blackwater streams with elevated DOC
• Not well represented in observed dataset – 2 blackwater sites
• Geostatistical model unable to account for natural variability– Large square prediction errors
– Large prediction variances
Spatial Patterns in Model Fit
SPE values
West of Chesapeake Bay - low SPE values• Due to statistical and spatial distribution of observed data
– Regression equation fit to the mean in the data – Most observed sites = low DOC values
• Less variation in western and central Maryland – Neighboring sites tend to be similar
• Separation distances shorter in the west – Short separation distances = stronger covariances
Spatial Patterns in Model Fit
SPE values
What caused abrupt differences?• Point sources of organic pollution
– Not represented in the model
• Non-point sources of pollution– Lumped watershed attributes are non-spatial – Differences due to spatial location of landuse are not
represented– Challenging to represent ecological processes using coarse-
scale lumped attributes– i.e. Flow path of water
Model Performance
Unable to account for abrupt differences in DOC values between neighboring sites with similar watershed conditions
Generate Model Predictions
Prediction sites• Study area
– 1st, 2nd, and 3rd order non-tidal streams– 3083 segments = 5973 stream km
• ID downstream node of each segment– Create prediction site
• More than one site at each confluence
Generate predictions and prediction variances• SLD Mariah model• Universal kriging algorithm• Assigned predictions and prediction variances back to
stream segments in GIS
Water Quality Attainment by Stream Kilometers
Threshold values for DOC• Set by Maryland Department of Natural Resources• High DOC values may indicate biological or ecological stress
Theshold DOC (mg/l)Stream
Kilometers PercentLow < 5.0 5387.67 90.2Medium 5.0 - 8.0 400.19 6.7High > 8.0 185.16 3.1
Implications for Water Quality Monitoring
• Can be used to provide an estimate of regional stream DOC values• Cannot identify point sources of organic pollution
1) One geostatistical model can be used to predict DOC in stream segments throughout a large area
2) Tradeoff between cost-efficiency and model accuracyWestern Maryland
• Can be described using a single geostatistical model
Eastern and northeastern Maryland • Accept poor model fit• Collect additional survey data• Develop a separate geostatistical model for eastern Maryland
Implications for Water Quality Monitoring
3) Apply this methodology to other regulated indices
• e.g. conductivity and pH• Categorize predictions into potentially impaired or unimpaired status• Report on attainment in stream miles/kilometers
Conclusions
1) Geostatistical models generated more accurate DOC predictions than previous non-spatial models based on coarse-scale landscape data
2) SLD is more appropriate than WAHD for regional geostatistical modeling of DOC at this time• Probability-based random survey designs• Maryland, USA
3) Adds value to existing water quality monitoring efforts• Used to evaluate/report regional water quality conditions• Additional field sampling is not necessary• Generate inferences about regional stream condition • ID spatial location of potentially impaired stream segments
4) Model predictions and prediction variances• Additional field efforts concentrated in
– Areas with large amounts of uncertainty – Areas with a greater potential for water quality
impairment
5) Model results displayed visually• Communicate results to a variety of audiences
Conclusions