Embedding Landscape Processes into Triangulated Irregular Networks - - PowerPoint PPT Presentation

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

Shuttle Radar Topography Mission (~25 m) and Landsat imagery (~30 m) in Costa Rica

(Courtesy NASA SRTM)

How can we capture abundant high-resolution Earth remote sensing data in hydrologic and geomorphic models?

Large-scale Modeling of Earth Science Systems

Landscape Modeling

How can we minimize the tradeoffs between model resolution, accuracy and computational expense in landscape modeling?

Sub-basin Modeling USGS 30 m Raster DEM 360 m DEM 1260 km2 130 basins Raster Grid Modeling 808 km2 6,238 cells

aggregation

AUS 25 m Raster DEM 1260 km2 26 basins

aggregation

808 km2 897,494 cells

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.

Watershed TIN Modeling Hydrographic TIN Model 808 km2 54,438 nodes (6% 30-m DEM) Regional TIN Modeling Hydrologic TIN Model 500,000 km2 19,805 nodes (4% 1-km DEM) Baron Fork Arkansas-Red River

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.

Computational Data Structure Voronoi cell Node Edge Triangle

Triangular Irregular Networks

Traditional Approach Hydrographic TINs Hydrologic TINs

Sequential methods for constructing TINs include additional constraining criteria based on the landscape process of interest.

Samples points according to slope criteria Constrains TIN with streams and basin boundary Samples points according to hydrologic criteria

Hydrographic TINs

• Contributing area
• Flow directions
• Channel extraction
• Basin delineation
• Projection

DEM processing Landscape forms

• Floodplain
• Riparian zones
• Alluvial fans
• Terraces

Land-surface data

• HRUs
• Vegetation classes
• Soil units
• Geologic units
• Sub-basins

Hydrography

• Stream network
• Channel surveys
• Lakes
• Wetlands
• Basin boundaries

Landscape Indices

• Concise methods for describing terrain

processes.

• Useful for distribution function modeling

(e.g. TOPMODEL) of terrain processes, usually assuming steady-state.

• Measured strictly from DEM providing a

priori estimate of landscape behavior.

• Imply process similarity within classes of

distribution function.

• Coupled to TIN mesh to provide objective,

non-arbitrary, physically-based initialization for distributed models.

Hydrologic Similarity

How can we incorporate knowledge of landscape process

• rganization a priori into a computational model?

( )

β λ tan ln a =

Slope Criteria Terrain Analysis Wetness Index Hydrologic Criteria

Hydrologic Similarity TINs

• Contributing area
• Pixel slopes
• Soil properties
• Index equation

Terrain Analysis Similarity TIN Model

• Process based
• Multiple-resolution
• Adaptive
• Embeds behavior

Resolution function

• Proximity filter
• Functional type
• Bounds
• Step size

Distribution function

• Value range
• Bin number

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

Wetness Index of Beven and Kirkby Landslide Index of Montgomery and Dietrich Erosion Index of Moore and Wilson Example applications: f(a, β)

• Saturation-excess runoff
• Transport-limited sediment transport
• Shallow rainfall-triggered landsliding

Owl Creek Watershed

ln (Tc)

              − = φ β ρ ρ β tan tan 1 sin

w s c

a T Q

n m c

a T             = 0896 . sin 13 . 22 β

( )

β λ tan ln a =

Similarity Resolution Functions

Wetness Index Erosion Index Landslide Index Distance between points Index values (1) Bounded by two landscape measures: Cell resolution (r) and hillslope length (L = 1 / 2Dd). (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). Index-based Point Selection with Proximity Filter

Statistical Evaluations: Terrain Variability

14 CONUS basins using USGS 30-m DEMs and 25-m SRTM DEMs

• Abo Arroyo (NM): A=1000km2, σ=236 m
• Flint River (GA): A=698km2, σ=20 m
• Lost Creek (UT): A=576km2, σ=195 m
• Illinois River (OK): A=1627km2, σ=41 m

Hydrographic TIN Performance RMSE between TIN and DEM (meters) Data Reduction factor for TIN (d = nt/ ng)

Statistical Evaluations: Terrain Attributes

Statistical Comparison of TINs with Aggregated DEM: Basin Scale

• Equal number of TIN nodes or DEM cells
• Different distribution of element sizes
• Different sampling technique

Primary and Secondary Terrain Descriptors

Statistical Evaluations: Continental Scales

Statistical Comparison of TINs with Aggregated DEM: Continental Scale Mississippi River Basin (3,196,675 km2) 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.
• Hydrologic and hydraulic routing.

Surface-subsurface hydrologic processes over complex terrain.

See: Ivanov, Vivoni, Bras and Entekhabi (2003)

Channel-Hillslope Integrated Landscape Development (CHILD)

Distributed Modeling: Geomorphology

Coupled flow and sediment transport processes over dynamic terrain

See: Tucker, Lancaster, Gasparini and Bras (2001)

• Landscape evolution and dynamic

terrain morphology.

• Channel-hillslope fluvial processes
• Overland sediment transport and

deposition.

• Channel meandering.
• Alluvial stratigraphy.
• Floodplain and eolian deposition.
• Landslide susceptibility

Model Evaluations: Runoff and Saturation

Hydrographic TIN Hydrologic TIN

• Variability due to terrain slopes.
• Coefficient of variation of triangle

area (CVA = 2.06).

• Variability due to wetness index.
• Coefficient of variation of triangle

area (CVA = 0.88).

6.7% DEM cells 6.7% DEM cells

808 km2

Model Evaluations: Runoff and Saturation

Basin Streamflow Hydrograph Basin Saturation Fraction tRIBS Comparison over Baron Fork (OK) using Hydrographic and Hydrologic TINs to illustrate impact of resolving saturated areas using wetness index.

Model Evaluations: Runoff and Saturation

71.58 60.41

Groundwater exfiltration

3.51 6.71

Perched return flow

18.94 27.00

Saturation-excess runoff

5.96 5.88

Infiltration-excess runoff

Hydrologic Hydrographic Runoff Percentage 2.29 3.07

Std Depth (m)

3.38 4.19

Mean Depth (m)

Hydrologic Hydrographic Depth to water table

Surface Runoff Dynamics Groundwater Dynamics Surface saturation frequency (%) due to coupled surface-subsurface runoff

• ver simulation period using weather radar forcing.

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. Basin Sediment Yield

6.8% DEM cells 6.8% DEM cells CVA = 1.17 CVA = 1.17

Hydrographic TIN Erosion TIN 100 km2

Model Evaluations: Sediment Yield

Sediment volume (m3) erosion due to diffusion and fluvial processes over 14 year simulation period using rain gauge forcing. Hydrographic TIN Erosion TIN

2.36 1.91 50 – 100 0.31 0.17 100 – 150 5.79 6.60 25 – 50 0.01 0.02 > 200 0.03 0.07 150 – 200 9.57 14.05 0 – 25 81.94 77.17 < 0 Erosion TIN Hydrographic TIN Peak Erosion Volume (m3)

Percent Basin Area with Erosion Volume Spatial Distribution of Erosion Volume

Model Evaluations: Landslide Initiation

6.1% DEM cells 6.1% DEM cells

Hydrographic TIN Landslide TIN CHILD Comparison over Tolt River (WA) using Hydrographic and Landslide TINs to illustrate impact of resolving areas according to landslide index. Coupling Hydrologic and Slope Stability Model

[ ]

θ ρ ρ φ θ θ ρ sin / 1 tan cos sin

b w w b s s r

R g h C C FS − + + =

        = 1 , sin min θ

s s w

h K aR R

Factor of Safety: Relative Wetness: Function of Soil, Wetness and Terrain Slope

250 km2

Model Evaluations: Landslide Initiation

Stability of land mass due to saturation evaluated as a function of rainfall threshold over the landslide-based triangulated terrain.

25.96 25.37 2.5 31.59 30.18 5 17.74 17.95 1 36.74 34.16 25 35.18 33.36 10 12.72 13.52 0.5 5.94 7.19 Landslide TIN Hydrographic TIN Rainfall Threshold (mm/hr)

Percent Unstable Area in Basin under Steady Rainfall Rate Spatial Distribution of Factor of Safety Hydrographic TIN Landslide TIN

Final Remarks

(1) Multiple-resolution TINs provide a flexible data structure for distributed hydrogeomorphic modeling at large scales. (2) A new method for embedding process behavior using a landscape index into a TIN mesh performs well and is theoretically attractive. (3) Statistical and distributed model tests of the TIN terrain products illustrate advantages of capturing process behavior in landscape representation.

(a) Multiple-resolution, nested TINs for modeling across differing scales. (b)Exploring TIN aggregation effect on distributed model output. (c) Generalizing hydrologic and geomorphic indices for multi-purpose modeling. (d) Regional and continental-scale tests of distributed model performance using similarity TINs.

Conclusions Future Directions

TIN terrain resolution varied through the use of an elevation error tolerance (zr) for a variety of basins of different topographic characteristics. Original 30 - DEM ng = 897,949 nodes nt = 38,365 nodes nt = 175,730 nodes d = 0.2 d = 0.04 Elevation Accuracy (m) d = nt/ng TIN Aggregation Curve TINs

Model Evaluations: Scaling and Aggregation

tRIBS Hydrologic Model accuracy and performance evaluated as a function of the terrain aggregation for the Peacheater Creek basin (64 km2) for 1997-98.

Model Evaluations: Scaling and Aggregation

d = 0.94 d = 0.42 d = 0.05 Basin Streamflow Hydrograph TIN Aggregation Curve

Rainfall partitioning in coupled surface-subsurface model influenced by terrain

• aggregation. Higher resolution leads to greater groundwater discharge.

Model Evaluations: Scaling and Aggregation

d = nt / ng

Groundwater discharge Infiltration-excess Perched return flow Saturation-excess

Runoff Mechanism Scaling