Triangulated Irregular Networks and Similarity in Landscape - PowerPoint PPT Presentation

Triangulated Irregular Networks and Similarity in Landscape Processes Enrique R. Vivoni, Valeri Y. Ivanov, Vanessa Teles, Rafael L. Bras and Dara Entekhabi Massachusetts Institute of Technology AGU Fall Meeting, Session H21F December 10, 2002

Landscape Representation How can we capture abundant high-resolution Earth remote sensing data in hydrologic and geomorphic models? Large-scale Modeling of Earth Science Systems Shuttle Radar Topography Mission (~25 m) and Landsat imagery (~30 m) in Costa Rica (Courtesy NASA SRTM)

Landscape Modeling How can we minimize the tradeoffs between model resolution, accuracy and computational expense in landscape modeling? USGS 30 m AUS 25 m Raster DEM Raster DEM aggregation 360 m DEM 1260 km 2 130 basins 808 km 2 aggregation 6,238 cells 1260 km 2 26 basins Raster Grid Modeling Sub-basin Modeling

Triangular Irregular Networks Multiple-resolution TINs provide a flexible data structure for distributed hydrogeomorphic modeling at large scales. Hydrographic Hydrologic TIN Model TIN Model Arkansas-Red River Baron Fork 808 km 2 54,438 nodes 500,000 km 2 (6% 30-m DEM) 19,805 nodes (4% 1-km DEM) Watershed TIN Modeling Regional TIN Modeling

Triangular Irregular Networks TINs are a piece-wise linear interpolation of x, y, z points to create triangular elements of varying size using the Delaunay criteria. Triangle Edge Voronoi cell Node Computational Data Structure

Triangular Irregular Networks Sequential methods for constructing TINs include additional constraining criteria based on the landscape process of interest. Traditional Approach Hydrographic TINs Hydrologic TINs Constrains TIN with Samples points according Samples points according streams and basin boundary to hydrologic criteria to slope criteria

Methodology Arc/Info GIS utilized to construct TINs from multiple data sources (DEMs, HRUs, landscape features) using 3 methods. TIN-Index Analysis Package (TIAP): http://hydrology.mit.edu/tRIBS

Methodology Hydrography DEM processing • Stream network • Contributing area • Channel surveys • Flow directions • Lakes • Channel extraction • Wetlands • Basin delineation • Basin boundaries • Projection Landscape forms Land-surface data • Floodplain • HRUs • Riparian zones • Vegetation classes • Alluvial fans • Soil units • Terraces • Geologic units • Sub-basins

Landscape Similarity How can we incorporate knowledge of landscape process organization a priori into a computational model? Landscape Indices Terrain Analysis • Concise methods for describing terrain processes. • Useful for distribution function modeling (e.g. TOPMODEL) of terrain processes, usually assuming steady-state. Wetness Index • Measured strictly from DEM providing a ( ) priori estimate of landscape behavior. λ = β ln a tan • Imply process similarity within classes of distribution function. Slope Hydrologic Criteria • Coupled to TIN mesh to provide objective, Criteria non-arbitrary, physically-based initialization for distributed models.

Landscape Similarity Terrain Distribution function Analysis • Value range • Contributing area • Bin number • Pixel slopes • Soil properties • Index equation Similarity Resolution TIN Model function • Process based • Proximity filter • Multiple-resolution • Functional type • Adaptive • Bounds • Embeds behavior • Step size

Landscape Similarity 60,000 nodes Proximity filter utilized to sample DEM according to landscape index value. 60,000 nodes • Multiple resolutions mimic landscape index. • High-resolution in regions of hydrologic significance (e.g., saturated areas, hollows). • Low-resolution in regions contributing less to hydrologic response (e.g. flat upslope areas).

Landscape Similarity Example applications: f ( a , β ) Wetness Index of Beven and Kirkby ( ) λ = β ln a tan • Saturation-excess runoff • Transport-limited sediment transport m n β     a sin = T     c  22 . 13   0 . 0896  • Shallow rainfall-triggered landsliding   ρ β  − β  T sin tan =   s Q 1     c ρ φ a tan     w Landslide Index of Montgomery and Dietrich Erosion Index of Moore and Wilson Owl Creek Watershed ln (T c )

Statistical Evaluations RMSE between TIN and DEM (meters) 14 CONUS basins using USGS 30-m DEMs and 25-m SRTM DEMs Data Reduction factor for TIN ( d = n t / n g ) • Abo Arroyo (NM): A=1000km 2 , σ =236 m • Flint River (GA): A=698km 2 , σ =20 m • Lost Creek (UT): A=576km 2 , σ =195 m • Illinois River (OK): A=1627km 2 , σ =41 m Hydrographic TIN Performance

Statistical Evaluations Statistical Comparison of TINs with Aggregated DEM: Basin Scale • Equal number of TIN nodes or DEM cells Primary and Secondary Terrain Descriptors • Different distribution of element sizes • Different sampling technique

Statistical Evaluations Statistical Comparison of TINs with Aggregated DEM: Continental Scale Mississippi River Basin (3,196,675 km 2 ) HYDRO 1K DEM data (1km resolution) Data reduction ( d = 0.03) • DEM aggregation consistently worse. • Hydrologic TIN captures terrain properties • Large-scale applications using wetness index

Model Evaluations TIN-based Real-time Integrated Channel-Hillslope Integrated Basin Simulator (tRIBS) Landscape Development (CHILD) • Multiple runoff mechanisms (saturation) • Overland sediment transport • Variable source area near channel/hollows • Landslide susceptibility • Dynamic water table and soil moisture • Land-surface evolution

Model Evaluations tRIBS Comparison over Baron Fork using Traditional and Hydrologic TINs to illustrate impact of resolving saturated areas according to wetness index. Basin Streamflow Hydrograph Basin Saturation Fraction

Model Evaluations Surface saturation frequency (%) due to coupled surface-subsurface runoff over 7 month simulation period using weather radar forcing. Surface Runoff Dynamics Runoff Percentage Traditional Hydrologic Infiltration-excess runoff 5.88 5.96 Saturation-excess runoff 27.00 18.94 Perched return flow 6.71 3.51 Groundwater exfiltration 60.41 71.58 Groundwater Dynamics Depth to water table Traditional Hydrologic Mean Depth (m) 4.19 3.38 Std Depth (m) 3.07 2.29

Model Evaluations CHILD Comparison over Owl Creek using Traditional and Erosion TINs to illustrate impact of resolving areas according to erosion index. Basin Sediment Erosion

Model Evaluations Sediment volume (m 3 ) erosion due to diffusion and fluvial processes over 14 year simulation period using rain gauge forcing. Traditional (topographic) TIN Erosion-index TIN

Final Remarks Conclusions (1) Multiple-resolution TINs provide a flexible data structure for distributed hydrogeomorphic Future Directions modeling at large scales . (a) Multiple-resolution, nested TINs for (2) A new method for modeling across differing scales. embedding process behavior (b) Exploring TIN aggregation effect on using a landscape index into a distributed model output. TIN mesh performs well and is theoretically attractive . (c) Generalizing hydrologic and geomorphic indices for multi-purpose modeling. (3) Statistical and distributed (d) Regional and continental-scale tests of model tests of the TIN terrain distributed model performance using products illustrate advantages of similarity TINs. capturing process behavior in landscape representation.

Supporting Documentation

Functional Relations Wetness Index Erosion Index Landslide Index between points Distance Index values

Similarity TINs Landslide Application in Tolt River (WA) Erosion Application in Owl Creek (TX) m n β     a sin = T     c  22 . 13   0 . 0896    β ρ  − β  T sin tan =   Q s 1     c ρ φ a tan     w

Groundwater Dynamics Traditional Hydrologic method method Mean = 4.19 m Mean = 3.38 m Std = 3.07 m Std = 2.29 m