MSS/MBSS # 1

Joint work withJoint work withErin E. Peterson, Andrew A. Merton, Erin E. Peterson, Andrew A. Merton, David M. Theobald, and Jennifer A. David M. Theobald, and Jennifer A.

HoetingHoetingAll of Colorado State University, Fort All of Colorado State University, Fort

Collins, CO 80523-1877Collins, CO 80523-1877

Joint work withJoint work withErin E. Peterson, Andrew A. Merton, Erin E. Peterson, Andrew A. Merton, David M. Theobald, and Jennifer A. David M. Theobald, and Jennifer A.

HoetingHoetingAll of Colorado State University, Fort All of Colorado State University, Fort

Collins, CO 80523-1877Collins, CO 80523-1877

Using the Maryland Biological Using the Maryland Biological Stream Survey Data Stream Survey Data

to to Test Spatial Statistical ModelsTest Spatial Statistical Models

Using the Maryland Biological Using the Maryland Biological Stream Survey Data Stream Survey Data

to to Test Spatial Statistical ModelsTest Spatial Statistical Models

N. Scott UrquhartN. Scott Urquhart N. Scott UrquhartN. Scott Urquhart

MSS/MBSS # 2

This research is funded by

U.S.EPA – Science To AchieveResults (STAR) ProgramCooperativeAgreement

# CR - 829095

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.

FUNDING ACKNOWLEDGEMENT

MSS/MBSS # 3

Too many streamsToo many streams

Limited personnelLimited personnel

Cost of sampling is Cost of sampling is highhigh

Rapid assessment is Rapid assessment is difficultdifficult

Lawsuits filed by Lawsuits filed by environmental groups environmental groups demanding that the demanding that the requirements of the requirements of the CWA be metCWA be met

Too many streamsToo many streams

Limited personnelLimited personnel

Cost of sampling is Cost of sampling is highhigh

Rapid assessment is Rapid assessment is difficultdifficult

Lawsuits filed by Lawsuits filed by environmental groups environmental groups demanding that the demanding that the requirements of the requirements of the CWA be metCWA be met

The Problem

Electrofishing during EMAP sampling (Theobald, 2003)

MSS/MBSS # 4

Probability-Based Random Survey DesignsProbability-Based Random Survey DesignsProbability-Based Random Survey DesignsProbability-Based Random Survey Designs

Used to meet the requirements of CWA Used to meet the requirements of CWA Section 305(b)Section 305(b) Derive a regional estimate of stream condition Categorize and assign a weight based on

stream order

Provides a representative sample of streams 1st, 2nd, and 3rd order

Generate a statistical inference about theGenerate a statistical inference about the population of streams, within stream population of streams, within stream order, over a large area order, over a large area

DisadvantageDisadvantage Does not identify the spatial location of

impaired stream segments

Used to meet the requirements of CWA Used to meet the requirements of CWA Section 305(b)Section 305(b) Derive a regional estimate of stream condition Categorize and assign a weight based on

stream order

Provides a representative sample of streams 1st, 2nd, and 3rd order

Generate a statistical inference about theGenerate a statistical inference about the population of streams, within stream population of streams, within stream order, over a large area order, over a large area

DisadvantageDisadvantage Does not identify the spatial location of

impaired stream segments

MSS/MBSS # 5

PURPOSEPURPOSEPURPOSEPURPOSE

Develop a geostatistical Develop a geostatistical methodology based onmethodology based onCoarse-scale GIS

data &Field surveysTo predict

Water quality characteristics of

Stream segments found throughout a large geographic area (e.g., state)

Develop a geostatistical Develop a geostatistical methodology based onmethodology based onCoarse-scale GIS

data &Field surveysTo predict

Water quality characteristics of

Stream segments found throughout a large geographic area (e.g., state)

MSS/MBSS # 6

Maryland Biological Stream Survey (MBSS) Sample Site Locations

N

MSS/MBSS # 7

OUR PATH TODAYOUR PATH TODAYOUR PATH TODAYOUR PATH TODAY

What are “Spatial Statistical What are “Spatial Statistical Models”?Models”?

Measuring Distance in SpaceMeasuring Distance in Space The Maryland Biological Stream The Maryland Biological Stream

SurveySurvey Outstanding data set to compare

models Sketch Models CharacteristicsSketch Models Characteristics A Few ResultsA Few Results This Talk Reports Work in ProgressThis Talk Reports Work in Progress

What are “Spatial Statistical What are “Spatial Statistical Models”?Models”?

Measuring Distance in SpaceMeasuring Distance in Space The Maryland Biological Stream The Maryland Biological Stream

SurveySurvey Outstanding data set to compare

models Sketch Models CharacteristicsSketch Models Characteristics A Few ResultsA Few Results This Talk Reports Work in ProgressThis Talk Reports Work in Progress

MSS/MBSS # 8

GATHERING SOME INSIGHTSGATHERING SOME INSIGHTSGATHERING SOME INSIGHTSGATHERING SOME INSIGHTS

Raise your hand if you 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,

kriging

Raise your hand if you 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,

kriging

MSS/MBSS # 9

STATISTICS AND PREDICTIONSTATISTICS AND PREDICTIONSTATISTICS AND PREDICTIONSTATISTICS AND PREDICTION

OBJECTIVE: Measure relevantOBJECTIVE: Measure relevant responses, responses, Like dissolved organic carbon (DOC), and Related variables at suitable sites, then Develop formula to predict DOC at

Unvisited sites

Why? 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? Do survey, model=>predict, instead.

OBJECTIVE: Measure relevantOBJECTIVE: Measure relevant responses, responses, Like dissolved organic carbon (DOC), and Related variables at suitable sites, then Develop formula to predict DOC at

Unvisited sites

Why? 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? Do survey, model=>predict, instead.

MSS/MBSS # 10

PREDICTIVE VARIABLESPREDICTIVE VARIABLESPREDICTIVE VARIABLESPREDICTIVE VARIABLES

Predict DOC from measures such asPredict DOC from measures such as Area above the stream evaluation point % Barren % High Intensity Urban % Woody Wetland (* = included for

DOC) % Conifer or Evergreen Forest Type (*) % Mixed Forest Type (*) % low intensity Urban (*) To accommodate year diff’s:

1996 & 1997 (*)

Predict DOC from measures such asPredict DOC from measures such as Area above the stream evaluation point % Barren % High Intensity Urban % Woody Wetland (* = included for

DOC) % Conifer or Evergreen Forest Type (*) % Mixed Forest Type (*) % low intensity Urban (*) To accommodate year diff’s:

1996 & 1997 (*)

MSS/MBSS # 11

GIS TOOLSGIS TOOLSGIS TOOLSGIS TOOLS

These variables require These variables require Efficient delineation of watershed

above any point.

STARMAP has developed such software.

It is available. Documented in a poster here, and on

this web site: www.nrel.colostate.edu/projects/starmap/

These variables require These variables require Efficient delineation of watershed

above any point.

STARMAP has developed such software.

It is available. Documented in a poster here, and on

this web site: www.nrel.colostate.edu/projects/starmap/

MSS/MBSS # 12

PREDICTIVE MODELSPREDICTIVE MODELSPREDICTIVE MODELSPREDICTIVE MODELS

Classical regression model would be:Classical regression model would be:

BUT “Everything is related to everything BUT “Everything is related to everything else, but near things are more related else, but near things are more related than distant things” Tobler (1970).than distant things” Tobler (1970). Thus the “uncorrelated” above is

indefensible in many cases

Classical regression model would be:Classical regression model would be:

BUT “Everything is related to everything BUT “Everything is related to everything else, but near things are more related else, but near things are more related than distant things” Tobler (1970).than distant things” Tobler (1970). Thus the “uncorrelated” above is

indefensible in many cases

0 1 1 2 2

where have a constant variance

and are UNCORRELATED.

i i i p pi i

i

Y X X X

MSS/MBSS # 13

SO WHAT ISSO WHAT IS SPATIAL STATISTICS?SPATIAL STATISTICS?

SO WHAT ISSO WHAT IS SPATIAL STATISTICS?SPATIAL STATISTICS?

Spatial Statistics is a set ofSpatial Statistics is a set of statistical analysis techniques statistical analysis techniques whichwhich Allow correlated data, Index the amount of correlation by

distance the points are apart,

Incorporate this correlation into predictions.

Spatial Statistics is a set ofSpatial Statistics is a set of statistical analysis techniques statistical analysis techniques whichwhich Allow correlated data, Index the amount of correlation by

distance the points are apart,

Incorporate this correlation into predictions.

MSS/MBSS # 14

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

Distance Between Points (km)

Cor

rela

tion

DO

CSpatial Autocorrelation of Spatial Autocorrelation of Dissolved Organic CarbonDissolved Organic CarbonSpatial Autocorrelation of Spatial Autocorrelation of Dissolved Organic CarbonDissolved Organic Carbon

MSS/MBSS # 15

MEASURING DISTANCE IN SPACEMEASURING DISTANCE IN SPACEMEASURING DISTANCE IN SPACEMEASURING DISTANCE IN SPACE

Choices:Choices: In a straight line - “as the bird flies” Or network based – “As the fish swims”

Traditional spatial statistics uses theTraditional spatial statistics uses thefirst measure.first measure.

Our research has investigated theOur research has investigated thesecond:second:

Models Tested and compared using MBSS data

Choices:Choices: In a straight line - “as the bird flies” Or network based – “As the fish swims”

Traditional spatial statistics uses theTraditional spatial statistics uses thefirst measure.first measure.

Our research has investigated theOur research has investigated thesecond:second:

Models Tested and compared using MBSS data

MSS/MBSS # 16

GIS TOOLS USED = FLoWSGIS TOOLS USED = FLoWSAutomated tools needed to extract data about

hydrologic relationships between sample points did not exist!

1. Calculate watershed covariates for each stream segment

2. Calculate separation distances between sites

1 2

3

Straight-line

1 2

3

SymmetricHydrologic

1 2

3

AsymmetricHydrologic

3. Convert GIS data to a format compatible with statistics software

MSS/MBSS # 17

The Maryland Biological Stream SurveyThe Maryland Biological Stream Survey(MBSS)(MBSS)

The Maryland Biological Stream SurveyThe Maryland Biological Stream Survey(MBSS)(MBSS)

Outstanding data set to compare Outstanding data set to compare modelsmodels

Maryland Department of Natural Maryland Department of Natural ResourcesResources

1995, 1996, 1997Stratified probability-based randomStratified probability-based random

survey design survey design 955 sites in 17 interbasins Snapped sites to streams 74 sites were discarded

Could not locate survey segment

Outstanding data set to compare Outstanding data set to compare modelsmodels

Maryland Department of Natural Maryland Department of Natural ResourcesResources

1995, 1996, 1997Stratified probability-based randomStratified probability-based random

survey design survey design 955 sites in 17 interbasins Snapped sites to streams 74 sites were discarded

Could not locate survey segment

MSS/MBSS # 18

DATA USEDDATA USEDDATA USEDDATA USED

Some of our studies have used theSome of our studies have used the entire set of 881 (955-74) sites entire set of 881 (955-74) sites

Today’s report focuses on dataToday’s report focuses on data Collected in 1996

To reduce differences in DOC resulting from interannual variation, and

Reduce computational load Seven interbasins were visited

343 DOC samples were collected (312 usable)

Between March 1 and May 1, 1996.

Some of our studies have used theSome of our studies have used the entire set of 881 (955-74) sites entire set of 881 (955-74) sites

Today’s report focuses on dataToday’s report focuses on data Collected in 1996

To reduce differences in DOC resulting from interannual variation, and

Reduce computational load Seven interbasins were visited

343 DOC samples were collected (312 usable)

Between March 1 and May 1, 1996.

MSS/MBSS # 19

DISSOLVED ORGANIC CARBON DATA DISSOLVED ORGANIC CARBON DATA USED IN THIS ILLUSTRATIONUSED IN THIS ILLUSTRATION

DISSOLVED ORGANIC CARBON DATA DISSOLVED ORGANIC CARBON DATA USED IN THIS ILLUSTRATIONUSED IN THIS ILLUSTRATION

N

MSS/MBSS # 20

PREDICTORS PREDICTORS IMPORTANTIMPORTANTPREDICTORS PREDICTORS IMPORTANTIMPORTANTCovariate Description

Spatial 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

MSS/MBSS # 21

RESULTS

SLD models performed better than WAHD

Exception: Spherical model

Best models:• SLD Exponential, Mariah, and

Rational Quadratic models

• r2 for SLD model predictions

• Model predictions are almost identical

• Further analysis was restricted to Mariah

ExponentialRational

Quadratic MariahExponential 1 0.997 0.990Rational Quadratic 1 0.993Mariah 1

Autocovariance Model

Distance Measure MSPE r2

Exponential SLD 0.9394 0.7190WAHD 1.2337 0.6368

Spherical SLD 1.3391 0.6029WAHD 1.2187 0.6428

Mariah SLD 0.9311 0.7221WAHD 1.2326 0.6346

Hole Effect SLD 1.0136 0.6983Linear with Sill WAHD 1.2141 0.6388Rational Quadratic SLD 0.9447 0.7177

WAHD: weighted asymmetric hydrologic distanceSLD: straight-line distance

MSS/MBSS # 22

Results: Observed vs. predicted valuesResults: Observed vs. predicted valuesResults: Observed vs. predicted valuesResults: Observed vs. predicted values

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

• 312 sites • r2 = 0.72

• One influential site• r2 without that site = 0.66

MSS/MBSS # 23

WHERE DID WE PREDICT DOC?WHERE DID WE PREDICT DOC?WHERE DID WE PREDICT DOC?WHERE DID WE PREDICT DOC?

The seven interbasins surveyed in 1996The seven interbasins surveyed in 1996 Contained 3083 first, second, and third order non-tidal

stream segments. We created 3083 prediction locations by locating We created 3083 prediction locations by locating

thethe downstream node of each stream segment. downstream node of each stream segment. We used the downstream node to ensure that the entire

segment was located within the same watershed. This caused more than one prediction location to be

positioned at stream confluences. The covariates for the prediction locationsThe covariates for the prediction locations

represented the watershed conditions of the represented the watershed conditions of the individual segment rather than the confluence, individual segment rather than the confluence, Which would include all of the segments that flow into

that location.

The seven interbasins surveyed in 1996The seven interbasins surveyed in 1996 Contained 3083 first, second, and third order non-tidal

stream segments. We created 3083 prediction locations by locating We created 3083 prediction locations by locating

thethe downstream node of each stream segment. downstream node of each stream segment. We used the downstream node to ensure that the entire

segment was located within the same watershed. This caused more than one prediction location to be

positioned at stream confluences. The covariates for the prediction locationsThe covariates for the prediction locations

represented the watershed conditions of the represented the watershed conditions of the individual segment rather than the confluence, individual segment rather than the confluence, Which would include all of the segments that flow into

that location.

MSS/MBSS # 24

DOC Predictions – Expressed on a MapDOC Predictions – Expressed on a MapDOC Predictions – Expressed on a MapDOC Predictions – Expressed on a Map

MSS/MBSS # 25

Strong Model Fit

MSS/MBSS # 26

Dominated by coarse-scale landscape variables that are not constrained to watershed boundaries

ANC, PHLAB, NO3, and COND • Affected by landscape variables

- Geology type, agricultural & urban areas, atmospheric deposition of nitric and sulfuric acids

• Small nuggets < 7.5% of variability• Sample scale captured most variability in the data

DOC• Affected by allochthonous sources of organic matter

- Terrestrial plant material, soil, groundwater inputs, wetlands• Flow path is important: overland, sub-surface, groundwater• Large nugget

- Failure to represent the terrestrial flow path - Point sources of organic pollution - Fine-scale instream processes

Geostatistical Models with Strong Predictive Ability

MSS/MBSS # 27

Weak Model Fit

MSS/MBSS # 28

Geostatistical Models with Weak Predictive Ability

**Impossible to determine the source of the residual error**

SO4• Influenced by coarse scale processes

• Atmospheric inputs of sulfur, weathering of sulfate minerals• Results were inconclusive

• Similar to other studies (Herlihy et al., 1998)

What does this mean?• Finer scale processes dominate spatial patterns SO4?

• Well documented affects of atmospheric deposition of sulfuric acid • We proposed a poor model

• Impossible to detect strong patterns of spatial autocorrelation at any scale

TEMP & DO• Spatially and temporally variable over short distances

• Biological oxygen demand or water depth• Dominant ecological processes occur at a scale finer than the minimum

separation distance in the MBSS (50 m)

MSS/MBSS # 29

CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS

Spatial autocorrelation exists in streamSpatial autocorrelation exists in stream chemistry data at a relatively coarse chemistry data at a relatively coarse scale scale

Geostatistical models improve theGeostatistical models improve the accuracy of predictions accuracy of predictions

Patterns of spatial autocorrelationPatterns of spatial autocorrelation differ between chemical response differ between chemical response variables variables Influenced by ecological processes acting

at different spatial and temporal scales

Spatial autocorrelation exists in streamSpatial autocorrelation exists in stream chemistry data at a relatively coarse chemistry data at a relatively coarse scale scale

Geostatistical models improve theGeostatistical models improve the accuracy of predictions accuracy of predictions

Patterns of spatial autocorrelationPatterns of spatial autocorrelation differ between chemical response differ between chemical response variables variables Influenced by ecological processes acting

at different spatial and temporal scales

MSS/MBSS # 30

CONCLUSIONS - IICONCLUSIONS - IICONCLUSIONS - IICONCLUSIONS - II

Our results are scale specificOur results are scale specific Spatial patterns change with sample scale. Other patterns may emerge with shorter

minimum separation distances. Straight line measures of distance are OK.

Further research is needed at finerFurther research is needed at finer scales scales Watershed or reach scale

Questions are welcome – now or laterQuestions are welcome – now or later

Our results are scale specificOur results are scale specific Spatial patterns change with sample scale. Other patterns may emerge with shorter

minimum separation distances. Straight line measures of distance are OK.

Further research is needed at finerFurther research is needed at finer scales scales Watershed or reach scale

Questions are welcome – now or laterQuestions are welcome – now or later