Embedding Landscape Processes into Triangulated Irregular Networks for Distributed Hydrogeomorphic Modeling Enrique R. Vivoni, Valeri Y. Ivanov, Vanessa Teles, Rafael L. Bras and Dara Entekhabi Ralph M. Parsons Laboratory Massachusetts Institute of Technology EAE03 Session HS21 April 10, 2003
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 808 km 2 897,494 cells 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 modeling at large scales. They minimize tradeoffs between model resolution, accuracy and computational expense. 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
Hydrographic TINs 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
Hydrologic 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.
Hydrologic Similarity TINs 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
Hydrologic Similarity TINs Proximity filter utilized to sample DEM using index value. • Multiple resolutions mimic landscape index. • High-resolution in regions of hydrologic significance. • Low-resolution in regions contributing less to hydrologic response (e.g. flat upslope areas).
Other Similarity Measures 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 )
Similarity Resolution Functions Wetness Index Erosion Index Landslide Index between points Distance Index values Index-based Point Selection with Proximity Filter (1) Bounded by two landscape measures: Cell resolution (r) and hillslope length (L = 1 / 2D d ). (2) Proximity determined in relation to the similarity index histogram. Peak value used to indicate sharp change in proximity filter size. (3) Prior knowledge of histogram regions of importance (e.g. tail of TOPMODEL).
Statistical Evaluations: Terrain Variability 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: Terrain Attributes 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: Continental Scales 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
Distributed Modeling: Hydrology TIN-based Real-time Integrated Basin Simulator (tRIBS) • Coupled vadose and saturated zones with dynamic water table. • Moisture infiltration waves. • Soil moisture redistribution. • Topography-driven lateral fluxes in vadose and groundwater. • Radiation and energy balance. • Interception and evaporation. Surface-subsurface hydrologic • Hydrologic and hydraulic routing. processes over complex terrain. See: Ivanov, Vivoni, Bras and Entekhabi (2003)
Distributed Modeling: Geomorphology Channel-Hillslope Integrated Landscape Development (CHILD) • Landscape evolution and dynamic terrain morphology. • Channel-hillslope fluvial processes • Overland sediment transport and deposition. • Channel meandering. • Alluvial stratigraphy. • Floodplain and eolian deposition. Coupled flow and sediment transport • Landslide susceptibility processes over dynamic terrain See: Tucker, Lancaster, Gasparini and Bras (2001)
Model Evaluations: Runoff and Saturation Hydrographic TIN Hydrologic TIN 808 km 2 6.7% DEM cells 6.7% DEM cells • Variability due to terrain slopes. • Variability due to wetness index. • Coefficient of variation of triangle • Coefficient of variation of triangle area (CV A = 2.06). area (CV A = 0.88).
Model Evaluations: Runoff and Saturation tRIBS Comparison over Baron Fork (OK) using Hydrographic and Hydrologic TINs to illustrate impact of resolving saturated areas using wetness index. Basin Streamflow Hydrograph Basin Saturation Fraction
Model Evaluations: Runoff and Saturation Surface saturation frequency (%) due to coupled surface-subsurface runoff over simulation period using weather radar forcing. Surface Runoff Dynamics Runoff Percentage Hydrographic 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 Hydrographic Hydrologic Mean Depth (m) 4.19 3.38 Std Depth (m) 3.07 2.29 Spatial Distribution of Saturation Frequency
Model Evaluations: Sediment Yield CHILD Comparison over Owl Creek (TX) using Hydrographic and Erosion TINs to illustrate impact of resolving areas according to erosion index. Hydrographic TIN 6.8% DEM cells CV A = 1.17 100 km 2 6.8% DEM cells CV A = 1.17 Erosion TIN Basin Sediment Yield
Model Evaluations: Sediment Yield Sediment volume (m 3 ) erosion due to diffusion and fluvial processes over 14 year simulation period using rain gauge forcing. Hydrographic TIN Percent Basin Area with Erosion Volume Peak Erosion Hydrographic Erosion Volume (m 3 ) TIN TIN < 0 77.17 81.94 0 – 25 14.05 9.57 25 – 50 6.60 5.79 Erosion TIN 50 – 100 1.91 2.36 100 – 150 0.17 0.31 150 – 200 0.07 0.03 > 200 0.02 0.01 Spatial Distribution of Erosion Volume
Model Evaluations: Landslide Initiation CHILD Comparison over Tolt River (WA) using Hydrographic and Landslide TINs to illustrate impact of resolving areas according to landslide index. 250 km 2 Coupling Hydrologic and Slope Stability Model Factor of Safety: 6.1% DEM cells [ ] + θ φ − ρ ρ C C cos tan 1 R / Hydrographic TIN = + r s w w b FS ρ θ θ h g sin sin s b Relative Wetness: aR = R min , 1 w θ K h sin s s 6.1% DEM cells Function of Soil, Wetness and Terrain Slope Landslide TIN
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