1. Grid-Based Modeling with Digital Elevation Models
David G Tarboton
Utah State University
(several slides from David Maidment)

2. Outline Grid data structures Surface flow models
Channel network and watershed delineation
Reading:
Modeling our world Chapter 9.
Arc Hydro Model Chapter 4 on Drainage Systems.

3. Numerical representation of a spatial surface
Grid
TIN
Contour and flowline

4. A grid defines geographic space as a matrix of identically-sized square cells. Each cell holds a numeric value that measures a geographic attribute (like elevation) for that unit of space.

5. The grid data structure
Grid size is defined by extent, spacing and no data value information
Number of rows, number of column
Cell sizes (X and Y)
Top, left , bottom and right coordinates
Grid values
Real (floating decimal point)
Integer (may have associated attribute table)

6. Definition of a Grid Cell size Number of rows NODATA cell (X,Y)
Number of Columns

7. Line as a Sequence of Cells

8. Polygon as a Zone of Cells

9. Cell Networks

10. Grid Zones

11. Floating Point Grids
Continuous data surfaces using floating point or decimal numbers

12. Value attribute table for categorical (integer) grid data
Attributes of grid zones

13. Spatial Surfaces used in Hydrology
Elevation Surface — the ground surface elevation at each point

14. Topographic Slope Defined or represented by one of the following
Surface derivative z
Vector with x and y components
Vector with magnitude (slope) and direction (aspect)

15. Drainage area (also called contributing area or flow accumulation)
Concentrated at a point
Dispersed - specific catchment area

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

17. Wetness index a/S or ln(a/tan)
a/S evaluated at each point in the terrain
Of importance in topographically based modeling of runoff generation by saturation from below with TOPMODEL

18. Surface Flow Models The Eight direction pour point model
The D vector surface flow model

19. A Case Study of Hog Pen Creek
Hog Pen Ck
4 km
4 km

20. Watershed Delineation by Hand Digitizing
Drainage direction
20 ft contour
100 ft contour
Stream Center Line
Watershed divide
Outlet

21. 30 Meter Mesh Standard for 1:24,000 Scale Maps and the National Elevation Dataset

22. Digital Elevation Model (DEM) Elevations
Contours
720
700
680
740

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

24. Eight Direction Pour Point Model32 16 8 64 4
128 1 2
ESRI Direction encoding

25. Eight Direction Pour Point Model D84 5 6 3 7 2 1 8
Band/GRASS/TARDEM Direction encoding

26. Grid Network

27. Contributing Area Grid1 4 3 12 2 16 25 6 1 4 3 12 2 16 6 25
Drainage area threshold > 5 Cells

28. Filling in the Pits
DEM creation results in artificial pits in the landscape
A pit is a set of one or more cells which has no downstream cells around it
Unless these pits are filled they become sinks and isolate portions of the watershed
Pit filling is first thing done with a DEM

30. Watershed Draining to This Outlet

31. Watershed and Drainage Paths Delineated from 30m DEM
Automated method is more consistent than hand delineation

32. Stream Segments in a Cell Network1 3 2 4 5 6 5 5

33. Subwatersheds for Stream Segments
Same Cell Value

34. Topographic Slope ? Topographic Definition Drop/Distance
Limitation imposed by 8 grid directions.

35. The D Vector Surface Flow Model
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): ) (

36. Contributing Area using D

37. DEM based delineation of channel networks and subwatersheds
Hydrologic processes are different on hillslopes and in channels. It is important to recognize this and delineate model elements that account for this.
Concentrated versus dispersed flow.
Objective delineation of channel networks using digital elevation models.
500 cell theshold
1000 cell theshold

38. 100 grid cell constant support area threshold stream delineation

39. 200 grid cell constant support area based stream delineation

40. How to decide on drainage area threshold ?3 12

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

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. Contrasting Interpretations
“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.)
“any definition of a finite channel network is arbitrary, and entirely scale dependent.” (Band, 1993, in “Channel Network Hydrology”, edited by Beven and Kirkby, p15.)

47. Lets look at some geomorphology.
Suggestion: One contributing area threshold does not fit all watersheds.
Lets look at some geomorphology.
Horton’s Laws
Stream Drops

48. Hortons Laws: Strahler system for stream ordering1 3
most upstream is order 1
when two streams of a order i join, a stream of order i+1 is created
when a stream of order i joins a stream of order i+1, stream order is unaltered 1 2 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 1

49. Bifurcation Ratio

50. Length Ratio

51. Area Ratio

52. Slope Ratio

53. Constant Stream Drops

54. 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

55. 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

56. Statistical Analysis of Stream Drops Threshold drainage area of 20 upwards curved grid cells to create a stream

57. 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

58. Statistical Analysis of Stream Drops
Threshold = 10
Dd = 2.5
t = -3.5
Threshold = 15
Dd = 2.1
t = -2.08
Threshold = 20
Dd = 1.9
t = -1.03
Stream drop test for Mawheraiti River. For each upward curved support area threshold the stream drop for each stream is plotted against Strahler stream order. The large circles indicate mean stream drop for each order The weighted support area threshold, drainage density (in km-1) and t statistic for the difference in means between lowest order and all higher order streams is given.

59. 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

60. Contributing area of upwards curved grid cells only

61. Upward Curved Contributing Area Threshold

62. Constant Support Area Threshold

63. Curvature based stream delineation with threshold by constant drop analysis

64. 200 grid cell constant support area based stream delineation

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

66. Grid network pruned to order 4 stream delineation

67. Summary Concepts
Grid data structures represent surfaces as an array of cells
The elevation surface represented by a grid digital elevation model is used to derive surfaces representing other hydrologic variables of interest such as
Slope
Drainage area
Wetness index
Watersheds and channel networks

68. Summary Concepts (2)
The eight direction pour point model approximates the surface flow using eight discrete grid directions.
The D vector surface flow model approximates the surface flow as a flow vector from each grid cell apportioned between down slope grid cells.

69. Summary Concepts (3) Channel networks obey Hortons laws.
Use consistency with Hortons laws to adapt support area threshold and drainage density to the natural texture of the topography.
Use curvature based methods to allow channel network drainage density to be spatially variable to adapt to variable topographic texture.