Terrain Analysis using Grids David G. Tarboton dtarb@cc.usu.edu http://www.engineering.usu.edu/dtarb

Overview Complete Exercise 3 Spatial Analysis and Raster Calculations Runoff Generation Interpolation Geomorphology, Topographic Texture and Drainage Density Objective Selection of Channelization threshold TauDEM software

Reflections on Exercise 3 There is a lot of stuff going on when we execute the Arc Hydro terrain processing and watershed delineation tools. Lets think a little bit about what this means

Duality between Terrain and Drainage Network Flowing water erodes landscape and carries away sediment Topography defines drainage direction on the landscape Threshold drainage area to define a stream: 4.5 km2 (20,000 15m DEM cells)

Grid used to represent a continuous surface field x y f(x,y)

Direction of Steepest Descent 30 30 67 56 49 52 48 37 58 55 22 67 56 49 52 48 37 58 55 22 Slope:

Eight Direction Pour Point Model 32 16 8 64 4 128 1 2

Grid Network

Contributing Area Grid 1 1 1 1 1 1 1 1 1 1 4 3 1 1 4 3 3 1 1 3 1 1 1 12 1 1 1 1 2 12 1 1 1 2 16 1 1 2 1 16 3 6 1 3 6 25 2 1 2 25 TauDEM convention includes the area of the grid cell itself.

Contributing Area > 10 Cell Threshold Stream Definition 1 4 3 12 2 16 25 6 Contributing Area > 10 Cell Threshold

Stream Segmentation 1 3 2 4 5 6 5 5 ArcHydro Page 74

Catchment Definition Same Cell Value

Catchments For every stream segment, there is a corresponding catchment Catchments are a tessellation of the landscape through a set of physical rules

Raster Zones and Vector Polygons One to one connection DEM GridCode Raster Zones 3 4 5 Catchment GridID Vector Polygons

Drainage Lines and Drainage Points DrainageLines are drawn through the centers of cells on the stream links. DrainagePoints are located at the centers of the outlet cells of the catchments ArcHydro Page 75

Area goes to Line Connectivity For each catchment there is a unique drainage line GridID is same on both Catchment and Drainage Line

Adjoint Catchments Adjoint catchment: the remaining upstream area draining to a catchment outlet. ArcHydro Page 77

Raster Calculator Cell by cell evaluation of mathematical functions

Losses (Evaporation, Infiltration) Example Precipitation - Losses (Evaporation, Infiltration) = Runoff 5 6 7 6 - 3 3 2 4 = 2 3 5 2

Cell based discharge mapping flow accumulation of generated runoff Radar Precipitation grid Soil and land use grid Runoff grid from raster calculator operations implementing runoff generation formula’s Accumulation of runoff within watersheds

Runoff generation at a point depends on Rainfall intensity or amount Antecedent conditions Soils and vegetation Depth to water table (topography) Time scale of interest These vary spatially which suggests a spatial geographic approach to runoff estimation

Rainfall-Runoff Function for Texas http://www. crwr. utexas Po = 800mm/yr

Map-Based Surface Water Runoff Estimating the surface water yield by using a rainfall-runoff function Runoff, Q (mm/yr) Q P Runoff Coefficient C = Q/P Accumulated Runoff (cfs) Precipitation, P (mm/yr)

Modeling infiltration excess Empirical, e.g. SCS Curve Number method CN=100 90 80 70 60 50 40 30 20

Runoff generation processes Infiltration excess overland flow aka Horton overland flow P P f P qo f Partial area infiltration excess overland flow P P P qo f P Saturation excess overland flow P P qo qr qs

TOPMODEL Beven, K., R. Lamb, P. Quinn, R. Romanowicz and J. Freer, (1995), "TOPMODEL," Chapter 18 in Computer Models of Watershed Hydrology, Edited by V. P. Singh, Water Resources Publications, Highlands Ranch, Colorado, p.627-668. “TOPMODEL is not a hydrological modeling package. It is rather a set of conceptual tools that can be used to reproduce the hydrological behaviour of catchments in a distributed or semi-distributed way, in particular the dynamics of surface or subsurface contributing areas.”

Specific catchment area a is the upslope area per unit contour length [m2/m  m] Upslope contributing area a Stream line Contour line

Saturation in zones of convergent topography TOPMODEL and GIS Surface saturation and soil moisture deficits based on topography Slope Specific Catchment Area Topographic Convergence Partial contributing area concept Saturation from below (Dunne) runoff generation mechanism Saturation in zones of convergent topography

Slope Specific Catchment Area ln(a/S) or ln(a/tan) [tan=S] is a wetness index that determines the locations of saturation from below and soil moisture deficit.

TOPMODEL soil moisture deficit example Given Ko=10 m/hr f=5 m-1 Qb = 0.8 m3/s A (from GIS) ne = 0.2 Compute R=0.0002 m/h l=6.90 T=2 m2/hr Raster calculator -( [ln(sca/S)] - 6.90)/5+0.46 http://www.engineering.usu.edu/dtarb/rrp.html

Raster calculation – some subtleties Resampling or interpolation (and reprojection) of inputs to target extent, cell size, and projection within region defined by analysis mask + = Analysis mask Analysis cell size Analysis extent

Interpolation Apparent improvement in resolution may not be justified Estimate values between known values. A set of spatial analyst functions that predict values for a surface from a limited number of sample points creating a continuous raster. Apparent improvement in resolution may not be justified

Interpolation methods Nearest neighbor Inverse distance weight Bilinear interpolation Kriging (best linear unbiased estimator) Spline

Nearest Neighbor “Thiessen” Polygon Interpolation Spline Interpolation Nearest Neighbor “Thiessen” Polygon Interpolation

Hydrologic processes are different on hillslopes and in channels Hydrologic processes are different on hillslopes and in channels. It is important to recognize this and account for this in models. Drainage area can be concentrated or dispersed (specific catchment area) representing concentrated or dispersed flow.

Delineation of Channel Networks and Subwatersheds 500 cell theshold 1000 cell theshold

100 grid cell constant support area threshold stream delineation

200 grid cell constant support area based stream delineation

How to decide on support area threshold ? 3 12 Why is it important?

Examples of differently textured topography Badlands in Death Valley. from Easterbrook, 1993, p 140. Coos Bay, Oregon Coast Range. from W. E. Dietrich

Logged Pacific Redwood Forest near Humboldt, California

Canyon Creek, Trinity Alps, Northern California. Photo D K Hagans

Gently Sloping Convex Landscape From W. E. Dietrich

Mancos Shale badlands, Utah. From Howard, 1994.

Topographic Texture and Drainage Density Driftwood, PA Same scale, 20 m contour interval Sunland, CA

Lets look at some geomorphology. “landscape dissection into distinct valleys is limited by a threshold of channelization that sets a finite scale to the landscape.” (Montgomery and Dietrich, 1992, Science, vol. 255 p. 826.) Suggestion: One contributing area threshold does not fit all watersheds. Lets look at some geomorphology. Drainage Density Horton’s Laws Slope – Area scaling Stream Drops

Drainage Density Dd = L/A Hillslope length  1/2Dd B B Hillslope length = B A = 2B L Dd = L/A = 1/2B  B= 1/2Dd L

Drainage Density for Different Support Area Thresholds EPA Reach Files 100 grid cell threshold 1000 grid cell threshold

Drainage Density Versus Contributing Area Threshold

Hortons Laws: Strahler system for stream ordering 1 3 1 2 1 2 1 1 1 1 1 2 2 1 1 1 1 1 1

Bifurcation Ratio

Area Ratio

Length Ratio

Slope Ratio

Slope-Area scaling Data from Reynolds Creek 30 m DEM, 50 grid cell threshold, points, individual links, big dots, bins of size 100

Constant Stream Drops Law Broscoe, A. J., (1959), "Quantitative analysis of longitudinal stream profiles of small watersheds," Office of Naval Research, Project NR 389-042, Technical Report No. 18, Department of Geology, Columbia University, New York.

Stream Drop Elevation difference between ends of stream Note that a “Strahler stream” comprises a sequence of links (reaches or segments) of the same order Nodes Links Single Stream

Break in slope versus contributing area relationship Suggestion: Map channel networks from the DEM at the finest resolution consistent with observed channel network geomorphology ‘laws’. Look for statistically significant break in constant stream drop property Break in slope versus contributing area relationship Physical basis in the form instability theory of Smith and Bretherton (1972), see Tarboton et al. 1992

Statistical Analysis of Stream Drops

T-Test for Difference in Mean Values 72 130 T-test checks whether difference in means is large (> 2) when compared to the spread of the data around the mean values

Constant Support Area Threshold

200 grid cell constant support area based stream delineation

Local Curvature Computation (Peuker and Douglas, 1975, Comput Local Curvature Computation (Peuker and Douglas, 1975, Comput. Graphics Image Proc. 4:375) 43 48 48 51 51 56 41 47 47 54 54 58

Contributing area of upwards curved grid cells only

Upward Curved Contributing Area Threshold

Curvature based stream delineation

Channel network delineation, other options 4 5 6 3 7 2 1 8 Contributing Area 1 2 3 Grid Order 1 4 3 12 2 16 25 6

Grid network pruned to order 4 stream delineation

Slope area threshold (Montgomery and Dietrich, 1992).

The D Algorithm Tarboton, D. G., (1997), "A New Method for the Determination of Flow Directions and Contributing Areas in Grid Digital Elevation Models," Water Resources Research, 33(2): 309-319.) (http://www.engineering.usu.edu/cee/faculty/dtarb/dinf.pdf)

Contributing Area using D

Useful for example to track where sediment or contaminant moves

Useful for example to track where a contaminant may come from

Useful for a tracking contaminant or compound subject to decay or attenuation

Useful for a tracking a contaminant released or partitioned to flow at a fixed threshold concentration

Transport limited accumulation Useful for modeling erosion and sediment delivery, the spatial dependence of sediment delivery ratio and contaminant that adheres to sediment

Useful for destabilization sensitivity in landslide hazard assessment Reverse Accumulation Useful for destabilization sensitivity in landslide hazard assessment with Bob Pack

TauDEM in ArcGIS Visual Basic ESRI ArcGIS 8.x+9.x Toolbar Visual Basic GUI application Standalone command line applications C++ COM DLL interface Available from TauDEM C++ library Fortran (legacy) components http://www.engineering.usu.edu/dtarb/ Data Access libraries (grid, shape, image, dbf) ESRI gridio API (Spatial analyst) Data formats Vector shape files ASCII text grid Binary direct access grid ESRI binary grid

Are there any questions ? AREA 1 AREA 2 3 12