Terrain Analysis using Grids

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

2. 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

3. 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

4. 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)

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

6. 67 56 49 52 48 37 58 55 22 Direction of Steepest Descent 30 30 67 56 49 52 48 37 58 55 22 Slope:

7. 32 64 128 16 1 8 4 2 Eight Direction Pour Point Model

8. Grid Network

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

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

11. 1 1 2 1 2 3 5 3 3 5 4 4 4 4 4 6 6 6 Stream Segmentation 5 5 ArcHydro Page 74

12. Catchment Definition Same Cell Value

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

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

15. 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

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

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

18. Raster Calculator Cell by cell evaluation of mathematical functions

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

20. 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

21. 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

22. Rainfall-Runoff Function for Texashttp://www.crwr.utexas.edu/gis/gishyd98/library/wbtexas/sect5.htm Po = 800mm/yr

23. 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)

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

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

26. 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.”

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

28. TOPMODEL and GIS Saturation in zones of convergent topography • 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

29. 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.

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

31. 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

32. Interpolation 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

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

34. Spline Interpolation Nearest Neighbor “Thiessen” Polygon Interpolation

35. 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.

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

37. 100 grid cell constant support area threshold stream delineation

38. 200 grid cell constant support area based stream delineation

39. AREA 2 3 AREA 1 12 How to decide on support area threshold ? Why is it important?

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

41. Logged Pacific Redwood Forest near Humboldt, California

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

43. Gently Sloping Convex Landscape From W. E. Dietrich

44. Mancos Shale badlands, Utah. From Howard, 1994.

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

46. “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.) Lets look at some geomorphology. • Drainage Density • Horton’s Laws • Slope – Area scaling • Stream Drops Suggestion:One contributing area threshold does not fit all watersheds.

47. 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

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

49. Drainage Density Versus Contributing Area Threshold

50. 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