Terrain Analysis Tools for Terrain Analysis Tools for Routing Flow and Calculating Routing Flow and Calculating Upslope Contributing AreasUpslope Contributing Areas

John P. WilsonJohn P. Wilson

Terrain Analysis for Water Resources Terrain Analysis for Water Resources Applications Symposium 2002Applications Symposium 2002

Today’s TopicsToday’s Topics

Guiding principlesGuiding principles Proposed flow routing algorithmsProposed flow routing algorithms Flow routing methods implemented in Flow routing methods implemented in

TAPES-GTAPES-G Sensitivity of computed topographic Sensitivity of computed topographic

attributes to choice of flow routing attributes to choice of flow routing methodmethod

Key decisions, problems, and Key decisions, problems, and challengeschallenges

Scales / Processes / Scales / Processes / RegimesRegimes

Global

Meso

Topo

Micro

Nano

Cloud cover and CO2 levels control primary energy inputs to climate and weather patterns

Prevailing weather systems control long-term mean conditions; elevation-driven lapse rates control monthly climate; and geological substrate exerts control on soil chemistry

Surface morphology controls catchment hydrology; slope, aspect, horizon, and topographic shading control surface insolation

Vegetation canopy controls light, heat, and water for understory plants; vegetation structure and plant physiognomy controls nutrient use

Soil microorganisms control nutrient recycling

Water Flow on HillslopesWater Flow on Hillslopes

Land Surface ShapeLand Surface Shape

Courtesy Graeme Aggett 2001

Terrain Shape …Terrain Shape …

Terrain shape / drainage structure Terrain shape / drainage structure important at toposcaleimportant at toposcale

Locally adaptive gridding procedures Locally adaptive gridding procedures work well with contour and stream line work well with contour and stream line datadata

Need filtering / interpolation methods Need filtering / interpolation methods that respect surface structure for that respect surface structure for remotely sensed elevation sourcesremotely sensed elevation sources

Choose resolution based on data sources Choose resolution based on data sources / quality and not the application at hand/ quality and not the application at hand

Flow Direction / Catchment Flow Direction / Catchment AreaArea

Flow direction shows Flow direction shows path of water flow …path of water flow …

Upslope contributing Upslope contributing area A is area of land area A is area of land upslope of a length of upslope of a length of contour lcontour l

Specific catchment Specific catchment area is A/larea is A/l

Proposed Flow Routing Proposed Flow Routing AlgorithmsAlgorithms

Vary depending on granularity with Vary depending on granularity with which aspect is computed and whether which aspect is computed and whether single or multiple flow paths are single or multiple flow paths are allowedallowed

Single flow direction algorithmsSingle flow direction algorithms D8 (O’Callaghan and Mark 1984)D8 (O’Callaghan and Mark 1984) Rho4 / Rho8 (Fairfield and Leymarie 1991)Rho4 / Rho8 (Fairfield and Leymarie 1991) Aspect-driven (Lea 1992)Aspect-driven (Lea 1992)

… … Flow Routing Algorithms (2)Flow Routing Algorithms (2)

Multiple flow direction algorithmsMultiple flow direction algorithms FD8 (Quinn et al. 1991)FD8 (Quinn et al. 1991) FMFD (Freeman 1991; Holmgren 1994)FMFD (Freeman 1991; Holmgren 1994) DEMON (Costa-Cabral and Burges 1994)DEMON (Costa-Cabral and Burges 1994) R.flow (Mitasova and Hofierka 1993; R.flow (Mitasova and Hofierka 1993;

Mitasova et al. 1995, 1996)Mitasova et al. 1995, 1996) D∞ (Tarboton 1997)D∞ (Tarboton 1997) Form-based method (Pilesjo et al. 1998)Form-based method (Pilesjo et al. 1998)

Courtesy Qiming Zhou and Xuejun Liu 2002

TAPES-G AlgorithmsTAPES-G Algorithms

Single-flow-direction D8 methodSingle-flow-direction D8 method Randomized single-flow-direction Randomized single-flow-direction

Rho8 methodRho8 method Multiple-flow-direction FD8 and Multiple-flow-direction FD8 and

FRho8 methodsFRho8 methods DEMON stream-tube methodDEMON stream-tube method

TAPES-G InputsTAPES-G Inputs

Square-grid DEMSquare-grid DEM Important decisions about extent Important decisions about extent

of study area and how to handle of study area and how to handle edge effects, spurious sinks or pits, edge effects, spurious sinks or pits, etc.etc.

Interested in hydrologic Interested in hydrologic connectivity of topographic surfaceconnectivity of topographic surface

TAPES-G OutputsTAPES-G OutputsAttributes Units Definition

1,2 X, Y Usually metres X and Y coordinates as determined from the DEM

3 Flow direction None Computed using D8 or Rho8 algorithm4 Z Usually metres Elevation as read from the DEM

5 Contributing area Square metres or number of cells

Area draining out of each cell

6 Flow width Multiple of cell width Width associated with flow leaving the cell7 Slope Percent Slope in the steepest downslope direction8 Aspect Degrees clockwise from north The direction of the steepest downslope slope9 Profile curvature Radians per 100 metres Curvature of the surface in the direction of

steepest descent10 Plan curvature Radians per 100 metres Curvature of contour drawn through the grid

point11 Tangent curvature Radians per 100 metres Plan curvature multiplied by sine of slope angle12 Elevation residual Usually metres Difference between original DEM and

depressionless DEM13 Flow path length Usually metres The longest flow path from the catchment

divide or edge of DEM to the cell14 d(As)/ ds None Rate of change of specific catchment area

along the flow path

Final Cottonwood Creek Final Cottonwood Creek DEMDEM

Aspect / Primary Flow Aspect / Primary Flow Direction?Direction?

Shows aspect Shows aspect computed using computed using finite difference finite difference methodmethod

Poor choice of Poor choice of scale bar?scale bar?

Primary Flow Direction Primary Flow Direction (FLOWD)(FLOWD)

Approximate surrogate for aspect since it Approximate surrogate for aspect since it identifies direction to the nearest identifies direction to the nearest neighbor with maximum gradientneighbor with maximum gradient

FLOWD = 2FLOWD = 2jj - 1 - 1

where where jj = arg max = arg max ii = 1,8 = 1,8

The approximate aspect corresponding to The approximate aspect corresponding to this flow direction is this flow direction is ΨΨD8D8 = 45 = 45jj

)(9

ih

zz i

D8 SFD AlgorithmD8 SFD Algorithm

Does well in valleysDoes well in valleys Produces many Produces many

parallel flow lines parallel flow lines and problems near and problems near catchment boundarycatchment boundary

Cannot model flow Cannot model flow divergence in ridge divergence in ridge areasareas

D8 SFD AlgorithmD8 SFD Algorithm

Diagram shows detail Diagram shows detail near catchment near catchment boundaryboundary

Dark cells not located Dark cells not located on boundary – due to on boundary – due to subtle change in subtle change in aspect as it swifts aspect as it swifts from south to from south to southeastsoutheast

Rho8 SFD AlgorithmRho8 SFD Algorithm

Breaks up parallel Breaks up parallel flow paths / flow paths / produces mean flow produces mean flow direction equal to direction equal to aspectaspect

More cells with no More cells with no upslope connectionsupslope connections

Produces unique Produces unique result each timeresult each time

FD8 MFD AlgorithmFD8 MFD Algorithm

Distributes flow on Distributes flow on hillslopes to each hillslopes to each downslope neighbor downslope neighbor on a slope-weighted on a slope-weighted basisbasis

Specify cross-Specify cross-grading threshold to grading threshold to disable this feature disable this feature in valleysin valleys

FD8 Flow Dispersion WeightsFD8 Flow Dispersion Weights

DEMON AlgorithmDEMON Algorithm

Flow generated at each source pixel Flow generated at each source pixel and routed down a stream tube and routed down a stream tube until edge of DEM or a pit is until edge of DEM or a pit is encounteredencountered

Stream tubes constructed from Stream tubes constructed from points of intersections of a line points of intersections of a line drawn in gradient direction and a drawn in gradient direction and a grid cell edgegrid cell edge

DEMON Stream-Tube DEMON Stream-Tube AlgorithmAlgorithm

Three variants Three variants used in TAPES-G – used in TAPES-G – related to …related to … Choice of DEMChoice of DEM Use of grid Use of grid

centroids in place centroids in place of verticesof vertices

Definition of aspectDefinition of aspect

Upslope Contributing AreaUpslope Contributing Area

Computed with Computed with contour-based contour-based stream tubes stream tubes in northern in northern part of part of catchment …catchment …

TAPES-C Element NetworkTAPES-C Element Network

Contour DEM ElementsContour DEM Elements Set of elements formed Set of elements formed

by contours and flow by contours and flow lineslines

Proceeding uphill, flow Proceeding uphill, flow lines are terminated (A) lines are terminated (A) and added (B, C) to and added (B, C) to maintain even spacingmaintain even spacing

Lines are constructed Lines are constructed using either a minimum using either a minimum distance (BD) or distance (BD) or orthogonal (CE) criterionorthogonal (CE) criterion

Specific Catchment AreaSpecific Catchment Area

Percentage of 30 m Cells With Values in Ranges IndicatedMedian <40 40-70 70-110 110-180 >180

D8 57.2 30.9 27.6 13.3 13.7 14.6Rho8 41.1 39.3 28.2 11.8 10.6 10.2FRho8 88.9 13.0 24.9 18.7 23.1 20.3DEMON 105.4 11.7 22.1 20.1 20.2 25.9

105 km105 km22 Squaw Creek catchment in Squaw Creek catchment in Gallatin National Forest, MontanaGallatin National Forest, Montana

Results derived from 30 m DEMS Results derived from 30 m DEMS for 3 USGS 1:24,000 scale map for 3 USGS 1:24,000 scale map quadranglesquadrangles

Specific Catchment Area MapsSpecific Catchment Area Maps

Secondary Topographic Secondary Topographic AttributesAttributes

Secondary Topographic Secondary Topographic AttributesAttributes

Sediment Transport Capacity Sediment Transport Capacity IndexIndex

Percentage of 30 m Cells With Values in Ranges IndicatedMean 0-10.0 10.1-20.0 20.1-30.0 30.1-40.0 >40

D8 19.4 33.7 32.5 17.3 8.0 8.4Rho8 16.1 43.6 32.4 13.2 5.3 5.6FRho8 20.3 28.1 31.2 21.6 11.3 7.9DEMON 21.9 25.9 30.4 21.8 11.6 10.4

Grid ComparisonsGrid Comparisons

Flow routing algorithm D8 Rho8 FRho8 DEMOND8 XRho8 56.5 XFRho8 55.7 50.9 XDEMON 54.0 49.3 70.6 X

Key Decisions and ChallengesKey Decisions and Challenges

Methods can be distinguished based Methods can be distinguished based on equation used to estimate aspect on equation used to estimate aspect and whether or not they permit flow and whether or not they permit flow to two or more downslope cellsto two or more downslope cells

Most of the results produced thus far Most of the results produced thus far relate to coarse resolution DEM relate to coarse resolution DEM productsproducts

Sensitivity analysis results are Sensitivity analysis results are difficult to extrapolate to new study difficult to extrapolate to new study sitessites

New Data SourcesNew Data Sources

Several presentations about SAR Several presentations about SAR and LIDAR technology data at this and LIDAR technology data at this conferenceconference

Must develop and/or find methods Must develop and/or find methods for filtering and interpolation that for filtering and interpolation that respect surface structure for these respect surface structure for these remotely sensed elevation sourcesremotely sensed elevation sources

Interpolation ResultsInterpolation ResultsTIN IDW

Thin plate spline TOPOGRID

Surf.tps (GRASS)

Courtesy Graeme Aggett 2001

Better Sensitivity Analyses? Better Sensitivity Analyses?

Topographic AttributesTopographic Attributes

ElevationElevation SlopeSlope Profile curvatureProfile curvature Plan curvaturePlan curvature Distance from ridge linesDistance from ridge lines Incident solar radiationIncident solar radiation Topographic wetness indexTopographic wetness index Sediment transport capacity indexSediment transport capacity index

Fuzzy ClassificationFuzzy Classification

Split study area into three equal partsSplit study area into three equal parts Took stratified random sample and Took stratified random sample and

extracted topographic attributesextracted topographic attributes Performed several fuzzy k-means Performed several fuzzy k-means

classificationsclassifications Calculated confusion index and F and H Calculated confusion index and F and H

parameters and generated fuzzy and parameters and generated fuzzy and crisp landform class mapscrisp landform class maps

Final Landform ClassesFinal Landform Classes

Valley bottomsValley bottoms Main drainage linesMain drainage lines Lower slopesLower slopes Steep, shaded north-facing slopesSteep, shaded north-facing slopes Narrow ridge linesNarrow ridge lines Steep, south-facing, drier upper Steep, south-facing, drier upper

slopes and broad ridgesslopes and broad ridges

Cluster Centers and Cluster Centers and RangesRanges

Input data C1 C2 C3 C4 C5 C6ELEV 2094 2175 2316 2522 2540 2599SLOPE 1.97 5.04 9.26 21.61 13.10 22.18PROFC 0.01 -1.03 0.00 -0.47 2.58 -0.44PLANC -0.15 1.00 -0.24 0.01 -1.34 0.13RDPRX 6.23 6.04 5.54 5.40 0.10 5.48SOLAR 9.44 9.22 9.18 6.79 8.72 10.42WET20 13.17 16.92 12.02 11.32 10.77 11.47SED20 3.30 6.64 5.13 6.24 4.77 6.34

Input data C1 C2 C3 C4 C5 C6ELEV 1840-2731 1781-2749 1807-2962 1929-3118 1972-3101 2029-3223SLOPE 0-8.5 0-22.4 2.2-27.2 8.9-34.3 1.8-32.4 8.1-41.3PROFC -1.1-1.0 -5.2-0.8 -3.0-1.4 -4.5-1.7 1.0-6.6 -4.1-1.1PLANC -1.5-1.3 -0.6-8.1 -5.2-2.3 -5.2-3.4 -5.0-2.1 -3.9-5.8RDPRX 4.6-8.3 4.6-8.1 4.6-7.2 4.6-7.1 0.0-4.6 4.6-7.1SOLAR 8.7-10.2 7.4-10.6 7.6-10.3 3.5-8.8 4.7-11.2 8.7-11.9WET20 11.0-17.4 13.0-22.2 9.8-14.4 9.6-14.5 9.6-12.2 9.5-14.4SED20 1.7-5.4 4.5-9.1 3.5-6.8 5.4-7.4 2.9-6.0 5.1-8.4

Summary Data for Six ClassesSummary Data for Six Classes

Topo-climatic class Area (km2) Area (%)1. Valley bottoms 930.31 26.182. Drainage channels 369.81 10.413. Lower slopes 1048.33 29.514. N-facing steep slopes 370.85 10.445. Ridges 260.27 7.336. S-facing steep slopes 519.33 14.62Lakes 53.53 1.51

Final Map?Final Map?

Closing CommentsClosing Comments

Several graduate students working on Several graduate students working on new data sources and fuzzy new data sources and fuzzy classification of landscapesclassification of landscapes One is looking at performance of five flow One is looking at performance of five flow

routing algorithms in different landform routing algorithms in different landform classes with 5 m SAR DEM for exampleclasses with 5 m SAR DEM for example

May be able to answer one or two May be able to answer one or two questions if there is time availablequestions if there is time available