1. Terrain Analysis using Grids
David G. Tarboton

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

6. Direction of Steepest Descent30 30 67 56 49 52 48 37 58 55 22 67 56 49 52 48 37 58 55 22
Slope:

7. Eight Direction Pour Point Model32 16 8 64 4
128 1 2

8. Grid Network

9. Contributing Area Grid1 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.

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

11. Stream Segmentation 1 3 2 4 5 6 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. Raster Zones and Vector Polygons
One to one connection
DEM GridCode
Raster Zones 3 4 5
Catchment GridID
Vector Polygons

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. Losses (Evaporation, Infiltration)
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 Texas http://www. crwr. utexas
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 90 80 70 60 50 40 30 20

25. 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

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

28. 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

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
Given
Ko=10 m/hr
f=5 m-1
Qb = 0.8 m3/s
A (from GIS)
ne = 0.2
Compute
R= m/h
l=6.90
T=2 m2/hr
Raster calculator -( [ln(sca/S)] )/5+0.46

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 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

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

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

35. 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.

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. How to decide on support area threshold ?3 12
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. Topographic Texture and Drainage Density
Driftwood, PA
Same scale, 20 m contour interval
Sunland, CA

46. 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

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 ordering1 3 1 2 1 2 1 1 1 1 1 2 2 1 1 1 1 1 1

51. Bifurcation Ratio

52. Area Ratio

53. Length Ratio

54. Slope Ratio

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

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

57. 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

58. 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

59. Statistical Analysis of Stream Drops

60. T-Test for Difference in Mean Values72
130
T-test checks whether difference in means is large (> 2)
when compared to the spread of the data around the mean values

61. Constant Support Area Threshold

62. 200 grid cell constant support area based stream delineation

63. 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

64. Contributing area of upwards curved grid cells only

65. Upward Curved Contributing Area Threshold

66. Curvature based stream delineation

67. Channel network delineation, other options4 5 6 3 7 2 1 8
Contributing Area 1 2 3
Grid Order 1 4 3 12 2 16 25 6

68. Grid network pruned to order 4 stream delineation

69. Slope area threshold (Montgomery and Dietrich, 1992).

70. 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): ) (

71. Contributing Area using D

73. Useful for example to track where sediment or contaminant moves

74. Useful for example to track where a contaminant may come from

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

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

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

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

79. 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
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

80. Are there any questions ?
AREA 1
AREA 2 3 12