Terrain Analysis Tools for Routing Flow and Calculating Upslope Contributing Areas John P. Wilson Terrain Analysis for Water Resources Applications Symposium 2002

Today’s Topics Guiding principles Guiding principles Proposed flow routing algorithms Proposed flow routing algorithms Flow routing methods implemented in TAPES-G Flow routing methods implemented in TAPES-G Sensitivity of computed topographic attributes to choice of flow routing method Sensitivity of computed topographic attributes to choice of flow routing method Key decisions, problems, and challenges Key decisions, problems, and challenges

Scales / Processes / Regimes 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 Hillslopes

Land Surface Shape Courtesy Graeme Aggett 2001

Terrain Shape … Terrain shape / drainage structure important at toposcale Terrain shape / drainage structure important at toposcale Locally adaptive gridding procedures work well with contour and stream line data Locally adaptive gridding procedures work well with contour and stream line data Need filtering / interpolation methods that respect surface structure for remotely sensed elevation sources Need filtering / interpolation methods that respect surface structure for remotely sensed elevation sources Choose resolution based on data sources / quality and not the application at hand Choose resolution based on data sources / quality and not the application at hand

Flow Direction / Catchment Area Flow direction shows path of water flow … Flow direction shows path of water flow … Upslope contributing area A is area of land upslope of a length of contour l Upslope contributing area A is area of land upslope of a length of contour l Specific catchment area is A/l Specific catchment area is A/l

Proposed Flow Routing Algorithms Vary depending on granularity with which aspect is computed and whether single or multiple flow paths are allowed Vary depending on granularity with which aspect is computed and whether single or multiple flow paths are allowed Single flow direction algorithms Single 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) Multiple flow direction algorithms Multiple 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; Mitasova et al. 1995, 1996) R.flow (Mitasova and Hofierka 1993; 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 Algorithms Single-flow-direction D8 method Single-flow-direction D8 method Randomized single-flow-direction Rho8 method Randomized single-flow-direction Rho8 method Multiple-flow-direction FD8 and FRho8 methods Multiple-flow-direction FD8 and FRho8 methods DEMON stream-tube method DEMON stream-tube method

TAPES-G Inputs Square-grid DEM Square-grid DEM Important decisions about extent of study area and how to handle edge effects, spurious sinks or pits, etc. Important decisions about extent of study area and how to handle edge effects, spurious sinks or pits, etc. Interested in hydrologic connectivity of topographic surface Interested in hydrologic connectivity of topographic surface

TAPES-G Outputs

Final Cottonwood Creek DEM

Aspect / Primary Flow Direction? Shows aspect computed using finite difference method Shows aspect computed using finite difference method Poor choice of scale bar? Poor choice of scale bar?

Primary Flow Direction (FLOWD) Approximate surrogate for aspect since it identifies direction to the nearest neighbor with maximum gradient Approximate surrogate for aspect since it identifies direction to the nearest neighbor with maximum gradient FLOWD = 2 j - 1 where j = arg max i = 1,8 i = 1,8 The approximate aspect corresponding to this flow direction is Ψ D8 = 45j The approximate aspect corresponding to this flow direction is Ψ D8 = 45j

D8 SFD Algorithm Does well in valleys Does well in valleys Produces many parallel flow lines and problems near catchment boundary Produces many parallel flow lines and problems near catchment boundary Cannot model flow divergence in ridge areas Cannot model flow divergence in ridge areas

D8 SFD Algorithm Diagram shows detail near catchment boundary Diagram shows detail near catchment boundary Dark cells not located on boundary – due to subtle change in aspect as it swifts from south to southeast Dark cells not located on boundary – due to subtle change in aspect as it swifts from south to southeast

Rho8 SFD Algorithm Breaks up parallel flow paths / produces mean flow direction equal to aspect Breaks up parallel flow paths / produces mean flow direction equal to aspect More cells with no upslope connections More cells with no upslope connections Produces unique result each time Produces unique result each time

FD8 MFD Algorithm Distributes flow on hillslopes to each downslope neighbor on a slope-weighted basis Distributes flow on hillslopes to each downslope neighbor on a slope-weighted basis Specify cross-grading threshold to disable this feature in valleys Specify cross-grading threshold to disable this feature in valleys

FD8 Flow Dispersion Weights

DEMON Algorithm Flow generated at each source pixel and routed down a stream tube until edge of DEM or a pit is encountered Flow generated at each source pixel and routed down a stream tube until edge of DEM or a pit is encountered Stream tubes constructed from points of intersections of a line drawn in gradient direction and a grid cell edge Stream tubes constructed from points of intersections of a line drawn in gradient direction and a grid cell edge

DEMON Stream-Tube Algorithm Three variants used in TAPES-G – related to … Three variants used in TAPES-G – related to … Choice of DEM Choice of DEM Use of grid centroids in place of vertices Use of grid centroids in place of vertices Definition of aspect Definition of aspect

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

TAPES-C Element Network

Contour DEM Elements Set of elements formed by contours and flow lines Set of elements formed by contours and flow lines Proceeding uphill, flow lines are terminated (A) and added (B, C) to maintain even spacing Proceeding uphill, flow lines are terminated (A) and added (B, C) to maintain even spacing Lines are constructed using either a minimum distance (BD) or orthogonal (CE) criterion Lines are constructed using either a minimum distance (BD) or orthogonal (CE) criterion

Specific Catchment Area 105 km 2 Squaw Creek catchment in Gallatin National Forest, Montana 105 km 2 Squaw Creek catchment in Gallatin National Forest, Montana Results derived from 30 m DEMS for 3 USGS 1:24,000 scale map quadrangles Results derived from 30 m DEMS for 3 USGS 1:24,000 scale map quadrangles

Specific Catchment Area Maps

Secondary Topographic Attributes

Sediment Transport Capacity Index

Grid Comparisons

Key Decisions and Challenges Methods can be distinguished based on equation used to estimate aspect and whether or not they permit flow to two or more downslope cells Methods can be distinguished based on equation used to estimate aspect and whether or not they permit flow to two or more downslope cells Most of the results produced thus far relate to coarse resolution DEM products Most of the results produced thus far relate to coarse resolution DEM products Sensitivity analysis results are difficult to extrapolate to new study sites Sensitivity analysis results are difficult to extrapolate to new study sites

New Data Sources Several presentations about SAR and LIDAR technology data at this conference Several presentations about SAR and LIDAR technology data at this conference Must develop and/or find methods for filtering and interpolation that respect surface structure for these remotely sensed elevation sources Must develop and/or find methods for filtering and interpolation that respect surface structure for these remotely sensed elevation sources

Interpolation Results TINIDW Thin plate splineTOPOGRID Surf.tps (GRASS) Courtesy Graeme Aggett 2001

Better Sensitivity Analyses?

Topographic Attributes Elevation Elevation Slope Slope Profile curvature Profile curvature Plan curvature Plan curvature Distance from ridge lines Distance from ridge lines Incident solar radiation Incident solar radiation Topographic wetness index Topographic wetness index Sediment transport capacity index Sediment transport capacity index

Fuzzy Classification Split study area into three equal parts Split study area into three equal parts Took stratified random sample and Took stratified random sample and extracted topographic attributes Performed several fuzzy k-means classifications Performed several fuzzy k-means classifications Calculated confusion index and F and H parameters and generated fuzzy and crisp landform class maps Calculated confusion index and F and H parameters and generated fuzzy and crisp landform class maps

Final Landform Classes Valley bottoms Valley bottoms Main drainage lines Main drainage lines Lower slopes Lower slopes Steep, shaded north-facing slopes Steep, shaded north-facing slopes Narrow ridge lines Narrow ridge lines Steep, south-facing, drier upper slopes and broad ridges Steep, south-facing, drier upper slopes and broad ridges

Cluster Centers and Ranges

Summary Data for Six Classes

Final Map?

Closing Comments Several graduate students working on new data sources and fuzzy classification of landscapes Several graduate students working on new data sources and fuzzy classification of landscapes One is looking at performance of five flow routing algorithms in different landform classes with 5 m SAR DEM for example One is looking at performance of five flow routing algorithms in different landform classes with 5 m SAR DEM for example May be able to answer one or two questions if there is time available May be able to answer one or two questions if there is time available