Ecologically representative distance measures for spatial modeling in stream networks Erin Peterson, David M. Theobald, and Jay Ver HoefNatural Resource Ecology LaboratoryColorado State UniversityFort Collins, Colorado

The work reported here was developed under STAR Research Assistance Agreements 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

Overview~IntroductionBackgroundObjectiveMethodologyProductsImprovements

Spatial Models and Terrestrial SystemsWildlifeReich et al., 2000; Pleydell et al., 2004; Carroll, 1998

VegetationChong et al., 2001; Hudak et al, 2002; Merganic et al., 2004

FireRobichaud and Miller, 2003; Flores-Garnica and Omi, 2003

AgricultureDobermann and Ping, 2004; Jurado-Exposito et al, 2003; Van Bergeijk et al., 2001

SnowErxleben et al., 2002; Josberger and Mognard, 2002; Bales et al. 2001

Spatial Models and Aquatic SystemsLakes and EstuariesLittle et al., 1997; Rathbun, 1998; Altunkaynak et al., 2003

Stream NetworksSpatial dependenceDent and Grimm, 1999 Nutrient availabilityTorgensen et al., In Press Cutthroat troutHydrologic distanceGardner et al., 2003 temperatureEuclidean, symmetrical hydrologic, and symmetrical hydrologic weighted by stream order

PredictionYuan, 2004 Euclidean distanceKellum, 2003 Acid neutralizing capacity

Distance measures for stream dataStream data: chemical, physical, biological

Functional distances: Must represent the biological or ecological nature of the variable of interest

Euclidean distance: Is it an appropriate measure of distance?Influential continuous landscape variables: geology or agriculture

Symmetrical hydrologic distanceHydrologic connectivity: Fish movement

Asymmetrical hydrologic distanceLongitudinal transport of material: Benthic macroinvertebrates or water chemistry

Applying Spatial Statistical Models to Stream NetworksDistances and relationships are represented differently depending on the distance measureDistance measures for spatial modeling in stream networksMust represent the biological or ecological nature of the dependent variable

Applying Spatial Statistical Models to Stream NetworksDistances and relationships are represented differently depending on the distance measureDistance measures for spatial modeling in stream networksMust represent the biological or ecological nature of the dependent variable

Applying Spatial Statistical Models to Stream NetworksDistances and relationships are represented differently depending on the distance measureDistance measures for spatial modeling in stream networksMust represent the biological or ecological nature of the dependent variable

Applying Spatial Statistical Models to Stream NetworksDistances and relationships are represented differently depending on the distance measureDistance measures for spatial modeling in stream networksMust represent the biological or ecological nature of the dependent variable

Applying Spatial Statistical Models to Stream NetworksDistances and relationships are represented differently depending on the distance measure

Challenge: Spatial autocovariance models developed for Euclidean distance may not be valid for stream distances

Distance measures for spatial modeling in stream networksMust represent the biological or ecological nature of the dependent variable

New Spatial Statistical Models for Stream NetworksDeveloped by Jay Ver Hoef, Alaska Department of Fish and Game (Ver Hoef et al., Submitted)

Spatial statistical models for stream networksMoving average modelsIncorporate flow and use hydrologic distanceRepresents discontinuity at confluencesImportant for pollution monitoring

Measuring Hydrologic DistanceOn the groundHip chain or tape measure

Manually using a mapTopographic maps or air photosScale master, string, straight edge

Geographical information system (GIS)Gardner et al., 2003 ArcView scriptRathbun, 1998 Estuaries: Digitizing shoreline, partition estuary and streams into convex polygons, and finding shortest path through polygonsTorgensen et al., In Press Coastal cutthroat trout in OregonArcInfo AML

ObjectiveTo develop the tools needed to programmatically extract and format the spatial data necessary for spatial interpolation along stream networks

MethodologyFlow Dependent Example

Asymmetric hydrologic distance

Weight tributaries by flow volume

Calculate reach contributing areas (RCAs) for each stream segment

Accumulating RCAs: Calculate digitally derived explanatory variables and spatial weights

Calculate hydrologic distance

Calculate proportional influencesGIS Tools

Automated = more efficient for large datasetsMAHA National Hydrography dataset (NHD) = 186,290 stream segmentsSample points Hydrologic distance between every sample point and every other connected pointWritten in Visual Basic for Applications (VBA) using ArcObjects and ArcGIS version 8.3

Use easily accessible input data with national coverage NHD Digital elevation model (DEM)

Free data!Makes regional analysis more cost effective

Tool Requirements

Create reach contributing areas (RCAs)Methods and VBA program developed by David M. Theobald and John Norman

Input Data: NHD waterbodies and reaches, DEM, & flowdirection grid

Grows contributing areas away from each stream segment using WATERSHED commandStops at a depression in DEM

Bumps RCA boundary at each iterationPrevents boundary delineation at slight depression in DEM

Output: Overland hydrologic contributing area for each NHD segment

Framework of RCAsNon-overlapping, contiguous tessellation of RCAs

RCAs are networked up & downstream based on stream network topology

Conceptually similar to HUCsRepresents hydrologic connectivityFiner set of analytical units

1 to 1 relationshipReaches are linked to catchmentsFor each RCA, attributes such as:AreaTopographyLand use, soils, geology, vegetation, etc.

Efficient method for calculating catchment attributes Flexible: can be used for multiple datasets

RCA boundaries and NHD stream segments

RCA ExampleUS ERF1.2 & 1 km DEM: 60,833 RCAs

Accumulating RCAs:Calculating digitally derived explanatory variablesInput Data: Geometric network Retains topological relationshipsCreated using NHD data & sample sightsRCA attributes contained as segment weightsSet flow direction

Accumulate RCA attributes downstreamIForwardStar and INetTopology provide access to logical network

Catchment attribute = Local RCA attribute + Sum of upstream RCA attributesFlexibilityCan be used for multiple datasetsMany sample points fall midway on a segment Interpolate % distance along arc and calculate % catchment attribute

Final Output: Cumulative catchment attributes stored in edge attribute tableExplanatory variables in spatial models

Calculating Catchment Attributes From RCAs

Catchment attribute = Local RCA attribute + Sum of upstream RCA attributes

Calculating Catchment Attributes From RCAs

Catchment attribute = Local RCA attribute + Sum of upstream RCA attributes

Catchment attribute = % Local RCA attribute + Sum of upstream RCA attributes

Catchment attribute = % Local RCA attribute + Sum of upstream RCA attributes

MethodologyGIS Tools:

Calculate reach contributing areas (RCAs) for each stream segment

Accumulating RCAs: Calculate digitally derived explanatory variables and spatial weights

Calculate hydrologic distance

Calculate proportional influences

Input Data: NHD and sample sites

Methods:Set flow direction NHD segments digitized against flowGeometric network tracing functionsFind Path

Output: FlexibleContains upstream, downstream, and total hydrologic distance between sample sitesUser defines functional distance measureAll information provided in 1 distance matrixFormat: NxN distance matrix used in spatial interpolationComma delimited text fileCompatible with statistics software

Programmatically calculate hydrologic distances and relationships

Distance MatrixRecords downstream distance onlyContains information for: Downstream, upstream, and total distance

Distance MatrixCBDDownstream distance A B = 2

A

Distance MatrixCBDUpstream distance A B = Downstream distance B A = 3A

Distance MatrixCBDTotal distance A B= Downstream A B + Downstream B A = 5

A

AC = 0.3251 * 0.8018 * 1.0BC = 0.6749 * 0.8018 * 1.0Proportional InfluenceProportional influence of one point on another = Product of edge proportional Influences in downstream pathOutput: NxN weighted incidence matrix

Proportional influence: influence of each neighboring sample site on a downstream sample site

Weighted by catchment area: Surrogate for flow

Calculate influence of each upstream segment on segment directly downstream

Find Path function in ArcGIS

ProductsData Required for Spatial Modeling

Observed valuesSample points

Explanatory variablesCatchment attributes: Area, landuse type, topography

NxN distance matrixHydrologic distance from every sample point to every other sample pointRepresents flow relationships

NxN weighted distance matrixNeighbors weighted by catchment areaSurrogate for flow

ArcGIS Version 9

GeoNetworkNot ESRIs Geometric NetworkReplaces the IForwardStar ObjectFaster and more efficient

Python scripts allow faster development & better user documentation

Building the Functional Linkage of Watersheds and Streams (FLOWS) toolboxImprovements

Future ResearchCollaborations between ecology, GIS, and statisticsFunctional distances

Can new functional distance measures be applied using existing statistical methods?

Develop new statistical methodsAllow spatial models to more accurately represent processes in aquatic systems

Questions?

One of the reasons so few studies have attempted to predict in stream networks is: Special Issue of Environmental and Ecological Statistics Does this need more detail?' This purpose of this program is to calculate the direction (upstream vs. downstream) and hydrologic' distance between sample sites. Only the downstream distance is recorded in the distance table, but the' upstream and total hydrologic distances are also stored in the table. For instance, the downstream' hydrologic distance from site A to site B is recorded in the table. The upstream hydrologic distance from' site A to site B is equal the downstream hydrologic distance from site B to site A. The total hydrologic' distance between sites A and B is equal to the downstream hydrologic distance from site A to Site B + the' downstream hydrologic distance from site B to site A. The downstream distances are stored in a dbf file,' which is converted to an NxN matrix of downstream distances and output as a comma delimited text file.' This purpose of this program is to calculate the direction (upstream vs. downstream) and hydrologic' distance between sample sites. Only the downstream distance is recorded in the distance table, but the' upstream and total hydrologic distances are also stored in the table. For instance, the downstream' hydrologic distance from site A to site B is recorded in the table. The upstream hydrologic distance from' site A to site B is equal the downstream hydrologic distance from site B to site A. The total hydrologic' distance between sites A and B is equal to the downstream hydrologic distance from site A to Site B + the' downstream hydrologic distance from site B to site A. The downstream distances are stored in a dbf file,' which is converted to an NxN matrix of downstream distances and output as a comma delimited text file.' This purpose of this program is to calculate the direction (upstream vs. downstream) and hydrologic' distance between sample sites. Only the downstream distance is recorded in the distance table, but the' upstream and total hydrologic distances are also stored in the table. For instance, the downstream' hydrologic distance from site A to site B is recorded in the table. The upstream hydrologic distance from' site A to site B is equal the downstream hydrologic distance from site B to site A. The total hydrologic' distance between sites A and B is equal to the downstream hydrologic distance from site A to Site B + the' downstream hydrologic distance from site B to site A. The downstream distances are stored in a dbf file,' which is converted to an NxN matrix of downstream distances and output as a comma delimited text file.' This purpose of this program is to calculate the direction (upstream vs. downstream) and hydrologic' distance between sample sites. Only the downstream distance is recorded in the distance table, but the' upstream and total hydrologic distances are also stored in the table. For instance, the downstream' hydrologic distance from site A to site B is recorded in the table. The upstream hydrologic distance from' site A to site B is equal the downstream hydrologic distance from site B to site A. The total hydrologic' distance between sites A and B is equal to the downstream hydrologic distance from site A to Site B + the' downstream hydrologic distance from site B to site A. The downstream distances are stored in a dbf file,' which is converted to an NxN matrix of downstream distances and output as a comma delimited text file.