ecologically representative distance measures for spatial modeling in stream networks
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Ecologically representative distance measures for spatial modeling in stream networks. Erin Peterson, David M. Theobald, and Jay Ver Hoef Natural Resource Ecology Laboratory Colorado State University Fort Collins, Colorado. Space-Time Aquatic Resources Modeling and Analysis Program. - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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Overview~IntroductionBackgroundObjectiveMethodologyProductsImprovements
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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ObjectiveTo develop the tools needed to programmatically extract and format the spatial data necessary for spatial interpolation along stream networks
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MethodologyFlow Dependent Example
Asymmetric hydrologic distance
Weight tributaries by flow volume
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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
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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
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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
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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
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RCA boundaries and NHD stream segments
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RCA ExampleUS ERF1.2 & 1 km DEM: 60,833 RCAs
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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
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Calculating Catchment Attributes From RCAs
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Catchment attribute = Local RCA attribute + Sum of upstream RCA attributes
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Calculating Catchment Attributes From RCAs
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Catchment attribute = Local RCA attribute + Sum of upstream RCA attributes
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Catchment attribute = % Local RCA attribute + Sum of upstream RCA attributes
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Catchment attribute = % Local RCA attribute + Sum of upstream RCA attributes
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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
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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
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Distance MatrixRecords downstream distance onlyContains information for: Downstream, upstream, and total distance
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Distance MatrixCBDDownstream distance A B = 2
A
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Distance MatrixCBDUpstream distance A B = Downstream distance B A = 3A
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Distance MatrixCBDTotal distance A B= Downstream A B + Downstream B A = 5
A
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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
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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
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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
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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
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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.