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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

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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.EPAScience To Achieve Results (STAR) Program Cooperative Agreement # CR-829095 This research is funded by U.S.EPAScience To Achieve Results (STAR) Program Cooperative Agreement # CR-829095

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Collaborators Dr. David M. Theobald Natural Resource Ecology Lab Department of Recreation & Tourism Colorado State University, USA Dr. N. Scott Urquhart Department of Statistics Colorado State University, USA Dr. Jay M. Ver Hoef National Marine Mammal Laboratory, Seattle, USA Andrew A. Merton Department of Statistics Colorado State University, USA

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Overview

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Water Quality Monitoring Goals Create a regional water quality assessment Ecosystem Health Monitoring Program Identify water quality impaired stream segments

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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

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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)

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SCALE: Grain Substrate Biotic Condition Overhanging Vegetation Segment River Network Network Connectivity Tributary Size Differences Network Geometry Stream Network Connectivity Flow Direction Network Configuration Drainage Density Confluence Density Cross Sectional Area Channel Slope, Bed Materials Large Woody Debris Biotic Condition, Substrate Type, Overlapping Vegetation Detritus, Macrophytes Microhabitat Segment Contributing Area Riparian Vegetation Type & Condition Floodplain / Valley Floor Width Localized Disturbances Land Use/ Land Cover Landscape Climate Atmospheric deposition Geology Topography Soil Type Microhabitat Shading Detritus Inputs Riparian Zone Nested Watersheds Land Use Topography Vegetation Type Basin Shape/Size COARSE FINE Reach Aquatic Terrestrial

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Fit an autocovariance function to data Describes relationship between observations based on separation distance Geostatistical Modeling Separation Distance Semivariance Sill Nugget Range 1000 0 0 10 Distances and relationships are represented differently depending on the distance measure

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Distance Measures & Spatial Relationships A B C Straight-line Distance (SLD) Geostatistical models typically based on SLD

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A B C Symmetric Hydrologic Distance (SHD) Hydrologic connectivity: Fish movement Distance Measures & Spatial Relationships

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A B C Asymmetric Hydrologic Distance Longitudinal transport of material Distance Measures & Spatial Relationships

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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

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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.

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Patterns of Spatial Autocorrelation in Stream Water Chemistry

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Evaluate 8 chemical response variables 1.pH measured in the lab (PHLAB) 2.Conductivity (COND) measured in the lab μmho/cm 3.Dissolved oxygen (DO) mg/l 4.Dissolved organic carbon (DOC) mg/l 5.Nitrate-nitrogen (NO3) mg/l 6.Sulfate (SO4) mg/l 7.Acid neutralizing capacity (ANC) μeq/l 8.Temperature (TEMP) °C Determine which distance measure is most appropriate SLD SHD WAHD More than one? Find the range of spatial autocorrelation Objectives

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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

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Baltimore Annapolis Washington D.C. Chesapeake Bay Maryland, USA Study Area

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Spatial Distribution of MBSS Data N

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GIS Tools Automated 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 WAHD 4.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 12 3 SHDAHD

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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 =

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Proportional influence (PI): influence of each neighboring survey site on a downstream survey site Weighted by catchment area: Surrogate for flow volume A B C D E F G H survey sites stream 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

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Proportional influence (PI): influence of each neighboring survey site on a downstream survey site Weighted by catchment area: Surrogate for flow volume A B C D E 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

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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

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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: Geostatistical Modeling Methods

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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: Maximizing the log-likelihood with respect to B and sigma2 yields: 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

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Covariance matrix for SLD and SHD models Fit exponential autocorrelation function where C 1 is the covariance based on the distance between two sites, h, given the autocorrelation parameter estimates: nugget ( ), sill ( ), and range ( ). Geostatistical Modeling Methods Covariance matrix for WAHD model Fit exponential autocorrelation function (C 1 ) Hadamard (element-wise) product of C 1 & square root of spatial weights matrix forced into symmetry ( )

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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: r 2 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) 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

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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).

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SLD SHD WAHD 180.79301.76 Range of spatial autocorrelation differs: Shortest for SLD TEMP = shortest range values DO = largest range values Results Mean Range Values SLD = 28.2 km SHD = 88.03 km WAHD = 57.8 km

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MSPE 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

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Strong: ANC, COND, DOC, NO3, PHLAB Weak: DO, TEMP, SO4 GLM SLD SHD WAHD r2r2 Results r2r2 Predictive ability of models:

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Discussion Sites 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 SHDWAHD SLD

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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

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Discussion Probability-based random survey design (-) affected WAHD Maximize spatial independence of sites Does not represent spatial relationships in networks Validation sites randomly selected Frequency Number of Neighboring Sites 244 sites did not have neighbors Sample Size = 881 Number of sites with 1 neighbor: 393 Mean number of neighbors per site: 2.81

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Discussion 4500 0 Difference (O – E) Number of Neighboring Sites 0 1234567 8 91011121314171516 WAHD GLM Not when neighbors had: Similar watershed conditions Significantly different chemical response values WAHD models explained more variability as neighboring sites increased

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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 4500 0 Number of Neighboring Sites 0 1234567 8 91011121314171516 WAHD GLM Difference (O – E)

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Predictive Ability of Geostatistical Models r2r2 PH Coarse Fine Scale of influential ecological processes ANC NO3 COND DOC SO4 DO 0 0.5 1.0 TEMP

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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

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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

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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

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N 1996 MBSS DOC Data 020 Kilometers

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Potential covariates Methods

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Potential covariates after initial model selection (10) Methods

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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

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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: r 2 for the observed vs. predicted values

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Results SLD models performed better than WAHD Exception: Spherical model Best models: SLD Exponential, Mariah, and Rational Quadratic models r 2 for SLD model predictions Almost identical Further analysis restricted to SLD Mariah model Exponential Spherical Mariah Hole EffectLinear with Sill Rational Quadratic Autocorrelation Function MSPE

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Results Covariates for SLD Mariah model: WATER, EMERGWET, WOODYWET, FELPERC, & MINTEMP Positive relationship with DOC: WATER, EMERGWET, WOODYWET, MINTEMP Negative relationship with DOC FELPERC

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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 Model coefficients represent change in log10 DOC per unit of X

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r 2 Observed vs. Predicted Values n = 312 sites r 2 = 0.72 1 influential site r 2 without site = 0.66

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Squared Prediction Error (SPE) Model Fit

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SLD models more accurate than WAHD models Landscape-scale covariates were not restricted to watershed boundaries –Geology type –Temperature –Wetlands & water Discussion

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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

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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

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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

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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

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Generate Model Predictions Prediction sites Study area –1 st, 2 nd, and 3 rd 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

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DOC Predictions (mg/l)

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Weak Model Fit

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Strong Model Fit

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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

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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 accuracy Western 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

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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

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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

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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

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Questions?

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