Using the Maryland Biological
Stream Survey Data
to
Test Spatial Statistical Models
N. Scott Urquhart
Joint work with
Erin P. Peterson, Andrew A. Merton,
David M. Theobald, and Jennifer A. Hoeting
All of Colorado State University, Fort Collins,
CO 80523-1877
MSS/MBSS # 1
FUNDING ACKNOWLEDGEMENT
The work reported here today was developed under the 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. The
views expressed here are solely those of presenter and STARMAP, the Program he
represents. EPA does not endorse any products or commercial services mentioned in this
presentation.
This research is funded by
U.S.EPA – Science To Achieve
Results (STAR) Program
Cooperative
# CR - 829095
Agreement
MSS/MBSS # 2
Maryland Bioglogical Stream Survey (MBSS) Sample Site Locations
0
Kilometers
30
Legend
MBSS sample sites
1:100,000 National Hydrography Dataset
Maryland
0
5,000
Meters
¯
MSS/MBSS # 3
OUR PATH TODAY
What are “Spatial Statistical Models”?
Measuring Distance in Space
The Maryland Biological Stream Survey

Outstanding data set to compare models
 A Few Results
 Work in Progress
MSS/MBSS # 4
GATHERING SOME INSIGHTS
Raise your hand if you
Had a statistics course – even in the
distant past
 Remember doing a t-test
 Did a simple linear regression (fitted a
line)
 Did a multiple regression
 Examined model failures
 Did analyses accommodating “correlated
errors”
 Have used spatial statistics, eg, kreiging

MSS/MBSS # 5
STATISTICS AND PREDICTION
 OBJECTIVE: Measure relevant
responses,
Like dissolved organic carbon (DOC), and
 Related variables at suitable sites, then
 Develop formula to predict DOC at

 Unvisited sites
 Why?

Clean Water Act (CWA) 303(d)
 requires states to identify “impacted” waters
and plan to eliminate impact
 What state has the $ to evaluate every
water? Predict, instead.
MSS/MBSS # 6
PREDICTIVE VARIABLES
 Predict DOC from measures such as








Area above the stream evaluation point
% Barren
% High Intensity Urban
% Woody Wetland (*)
% Conifer or Evergreen Forest Type (*)
% Mixed Forest Type (*)
% low intensity Urban (*)
To accommodate year diff’s:
 1996 & 1997 (*)
MSS/MBSS # 7
GIS TOOLS
 These variables require
Efficient delineation of watershed above
any point
 STARMAP has developed such software
 It is available
 Documented in a poster

MSS/MBSS # 8
PREDICTIVE MODELS
 Classical regression model would be:
Yi   0  1 X 1i   2 X 2 i 
  p X pi   i
where  i have a constant variance
and are UNCORRELATED.
 BUT “Everything is related to everything else,
but near things are more related than distant
things” Tobler (1970).

Thus the “uncorrelated” above is indefensible in
many cases
MSS/MBSS # 9
SO WHAT IS
SPATIAL STATISTICS?
 Spatial Statistics is a set of
techniques which
Allow correlated data
 Index the amount of correlation by
distance the points are apart
 Incorporate this correlation into
predictions

MSS/MBSS # 10
SO WHAT IS
SPATIAL STATISTICS II?
MSS/MBSS # 11
WHAT ARE “SPATIAL STATISTICAL
MODELS”?
MSS/MBSS # 12
MEASURING DISTANCE IN SPACE
MSS/MBSS # 13
The Maryland Biological Stream Survey
Outstanding data set to compare models
MSS/MBSS # 14
A FEW RESULTS
MSS/MBSS # 15
WORK IN PROGRESS
MSS/MBSS # 16
MSS/MBSS # 17
The Clean Water Act (CWA) of 1972 requires
• States, tribes, & territories to identify water quality (WQ) impaired stream segments
• Create a priority ranking of those segments
• Calculate the Total Maximum Daily Load (TMDL) for each impaired segment based upon
chemical and physical WQ standards
• A biannual inventory characterizing regional WQ
The Problem
• It is impossible to physically sample every stream within a large area
• Too many stream segments
• Limited personnel
• Cost associated with sampling
• Probability-based inferences used to generate regional estimates of WQ
• In miles by stream order
• Does not indicate where WQ impaired segments are located
• A rapid and cost-efficient method needed to locate potentially impaired stream segments
throughout large areas
Our Approach
• Develop a geostatistical model based on coarse-scale geographical information system
(GIS) data
• Make predictions for every stream segment throughout a large area
• Generate a regional estimate of stream condition
• Identify potentially WQ impaired stream segments
MSS/MBSS # 18
Dissolved Organic Carbon (DOC) Example
Fit a geostatistical model to DOC data and coarse-scale watershed characteristics
• Maryland Biological Stream Survey data 1996
• 7 interbasins & 343 DOC survey sites
• GIS data:
GIS data, scale, and sources.
Dataset
USGS National Hydrography Dataset (NHD)
USGS National Land Cover Dataset (NLCD)
National Elevation Dataset (NED)
Omernik's Level III Ecoregion
USGS Lithology
PRISM (Parameter-elevation Regressions on
Independent Slopes Model) temperature data
Scale
1:250,000
30 meter
30 meter
1:7,500,000
1:250,000
4 kilometer
Source
http://nhd.usgs.gov/
http://landcover.usgs.gov/natllandcover.asp
http://ned.usgs.gov/
http://www.epa.gov/wed/pages/ecoregions/level_iii.htm
USEPA Western Ecology Division, Corvallis, OR
http://www.ocs.orst.edu/prism/faq.phtml
MSS/MBSS # 19
Methods
Pre-process GIS data
• “Snap” survey sites to streams
• Calculate watershed attributes using the Functional Linkage of Watersheds and Streams
(FLoWS) tools (Theobald et al., 2005; Peterson et al., in review)
Calculate distance matrices for model selection
• R statistical software
• x,y coordinates for observed survey sites
Covariates selected using the Leaps and Bounds
regression algorithm.
Description
Covariate
% Water
WATER
% Emergent Wetlands
EMERGWET
% Woody wetlands
WOODYWET
%
Felsic
rock type in watershed
FELPERC
Mean minimum temperature (°C)
MINTEMP
(January to April)
Omernik's Level 3 Ecoregion 64
ER64
Omernik's Level 3 Ecoregion 65
ER65
Omernik's Level 3 Ecoregion 66
ER66
Omernik's Level 3 Ecoregion 67
ER67
Omernik's Level 3 Ecoregion 69
ER69
• Test all possible linear models using the 10 covariates
• 1024 models (210 = 1024)
• Distance measure: Straight-line distance (aka Euclidean)
• Autocorrelation function: Mariah
• Estimate autocorrelation parameters: nugget, sill, and range
MSS/MBSS # 20
Model Results
• Range of spatial autocorrelation: 21.09 kilometers
• Significant watershed attributes = WATER, EMERGWET, WOODYWET, FELPERC, and
MIN TEMP
Summary statistics for log10 DOC and model covariates.
Variable
Min
1st Qu.
Median
log10 DOC (mg/l)
-0.22
0.08
0.24
WATER (%)
0
0
0.16
EMERGWET (%)
0
0
0.13
WOODYWET (%)
0
0
0.27
FELPERC (%)
0
0
0.31
MINTEMP (°C)
-5.88
-3.06
-2.39
Mean
0.28
0.25
0.26
1.24
26.81
-2.49
3rd Qu.
0.43
0.28
0.35
1.15
55.26
-1.4
Max
1.20
4.64
4.85
22.01
100
0.03
σ2
0.25
0.44
0.44
3.28
36.14
1.47
Model fit
• Leave-one-out cross validation method and Universal kriging
• Overall MSPE = 0.93, R2 = 0.72
• One strongly influential site
• R2 without the influential site = 0.66
MSS/MBSS # 21
• East-West trend in model fit
• Conservative model fit: tends to underestimate DOC
• 35 MSPE values > 1.5
• These sites have similar covariate
values to nearby sites, but considerably
different DOC values than nearby sites
MSS/MBSS # 22
Model Predictions
Create prediction sites
• 1st, 2nd, and 3rd order non-tidal stream segments
• 3083 prediction sites = downstream node of each GIS stream segment
• Downstream node ensures that entire segment is located in same watershed
• More than one prediction location at stream confluences
• Covariates for prediction sites represent the conditions upstream from the segment,
not the stream confluence
Calculate distance matrices for model predictions
• Include observed and predicted survey sites
Generate predictions and prediction variances
• Assign values back to stream segments in GIS
• Universal kriging Algorithm
Prediction statistics
Summary Statistics for DOC predictions and prediction variances.
Variable
Min
1st Qu.
Median
Mean
Predictions
0.8
1.5
1.9
2.7
Prediction
Variances
0.049
0.095
0.122
0.171
3rd Qu.
3.0
Max
40.4
0.193
2.597
MSS/MBSS # 23
• 18 prediction values > 15.9 mg/l
• Also possessed 18 largest prediction variances
• Located in watersheds with large WATER, EMERGWET, or WOODYWET
values
• Large covariate values are not represented in the observed covariate data
• Represent 5973.03 kilometers of stream miles
Stream habitat characterization estimated as a percentage
of stream miles in DOC (mg/l) during 1996.
Thesholds
Miles
Kilometers
Percent
DOC < 5
3347.74
5387.67
90.2
5 ≤ DOC ≤ 8
248.67
400.19
6.7
DOC > 8
115.06
185.16
3.1
Total
3711.46
5973.03
100
MSS/MBSS # 24
Products
• Geostatistical model used to predict segment-scale WQ conditions at unobserved
locations
• Map of the study area that shows the likelihood of WQ impairment for each segment
• Can be tied to threshold values or WQ standards
• Technical and Regulatory Services Administration within the Maryland Department of
the Environment
• Modifying the USGS NHD to include:
• watershed impairments & stream-use designations by NHD segment
• Frank Siano, personal communication
• A methodology that illustrates how agencies can accomplish spatial analysis using GIS
data, MBSS data, and geostatistics
The Advantages
• Additional sampling is not necessary
• Compliments existing methodologies
• Derive a regional estimate of stream condition in two ways:
• Probability-based inferences about stream miles by stream order
• Sum prediction values in miles by stream order
• Identify potentially WQ impaired stream segments
• Methodology can be used for regulated constituents as well
• Nitrate, acid neutralizing capacity, pH, and conductivity can be accurately
predicted using geostatistical models (Peterson et al., in review2)
• Identify spatial patterns of WQ throughout a large area
• Identify areas where additional samples would provide the most information
• Model results can be displayed visually
• Allows professionals to communicate results with a wide variety of audiences
easily
MSS/MBSS
# 25
References
Hoeting J.A., Davis R.A., & Merton A.A., Thompson S.E. (in press) Model Selection for
Geostatistical Models. Ecological Applications. http://www.stat.colostate.edu
/%7Ejah/papers/index.html
Peterson E.E., Theobald D.M., & Ver Hoef J.M. (in review1) Support for geostatistical
modeling on stream networks: Developing valid covariance matrices based on hydrologic
distance and stream flow. Freshwater Biology.
Peterson E.E., Merton A.A., Theobald D.M., & Urquhart N.S. (in review2) Patterns of Spatial
Autocorrelation in Stream Water Chemistry. Environmental Monitoring.
Theobald D.M., Norman J., Peterson E.E., Ferraz S. (2005) Functional Linkage of
Watersheds and Streams (FLoWs) Network-based ArcGIS tools to analyze freshwater
ecosystems. Proceedings of the ESRI User Conference 2005. July 26, 2005, San Diego,
CA, USA.
Acknowledgements
The work reported here was developed under STAR Research Assistance Agreement CR829095 awarded by the U.S. Environmental Protection Agency to the Space Time Aquatic
Resource Modeling and Analysis Program (STARMAP) at Colorado State University. This
poster has not been formally reviewed by the EPA. The views expressed here are solely
those of the authors. The EPA does not endorse any products or commercial services
presented in this poster.
MSS/MBSS # 26