1. Hydrologic Properties of the Landscape
David G Tarboton
Utah State University

2. Outline Slope and Contributing Area The D Algorithm
TOPMODEL Wetness Index
Terrain Stability Mapping SINMAP ArcView Extension
Topographic texture and drainage density
TARDEM programs for watershed and channel network delineation

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

4. Contributing Area Grid Based Evaluation Topographic Definition
Upslope contributing area a
Stream line
Contour line
Grid Based Evaluation
Topographic Definition
Specific catchment area a is the upslope area per unit contour length [m2/m  m]

5. 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): ) (

6. Contributing Area using D

7. Topmodel - Assumptions
The soil profile at each point has a finite capacity to transport water laterally downslope.
e.g. or S Dw D

8. Topmodel - Assumptions
Specific catchment area a [m2/m  m]
(per unit coutour length)
The actual lateral discharge is proportional to specific catchment area.
R is
Proportionality constant
may be interpreted as “steady state” recharge rate, or “steady state” per unit area contribution to baseflow. S Dw D

9. Topmodel - Assumptions
Specific catchment area a [m2/m  m]
(per unit coutour length)
Relative wetness at a point and depth to water table is determined by comparing qact and qcap
Saturation when w > 1.
i.e. S Dw D

10. Topmodel z D Dw S Specific catchment area a [m2/m  m]
(per unit coutour length) S Dw D z

11. Slope
Specific Catchment Area
Wetness Index ln(a/S)
from Map Calculator.
Average, l = 6.91

12. Numerical Example K=10 m/hr T=2 m2/hr f=5 m-1 R=0.0002 m/hr l=6.91
Map calculator -( [ln(sca/S)] )/5+0.46

13. 6/12/2018
SINMAP - Terrain Stability Mapping Arcview Extension R T Pack, D G Tarboton, C.N. Goodwin
Illustrates GIS as a spatial modeling environment
Illustrates tight integration of model into GIS
Utilizes GRIDIO application programmers interface to access Grids from external programs
Utilizes customizability of ArcView to provide easy to use interface

14. Where is it Used
Forest and watershed management, forestry and forest engineering.
Determine volume of harvestable timber in annual allowable cut calculations.
Better plan timber development to minimize occurrence of landslides and resulting impacts.

15. Lardeau Creek, BC

16. Norrish Watershed, BC.

17. Norrish Watershed, BC.

19. Theoretical Basis
6/12/2018
The infinite plane slope stability model with wetness (pore pressure) obtained from a topographically based steady state hydrology model has been used to map terrain stability (e.g. Montgomery and Dietrich, 1994, WRR p1153)
Stream line
Contour line
Stream tube
Upslope contributing area a
1. Relative Wetness h q
2. Dimensionless Cohesion
Density Ratio
(assumed a constant of 0.5)

20. Area-Slope Plot FS > 1 w = 1 Stable, Saturated FS < 1 Unstable
Stable, Unsaturated

21. But Define Stability Index SI = Prob(FS > 1)
Soil parameters, C, f, T are uncertain and spatially variable.
Recharge parameter R is spatially and temporally variable.
range P
Define Stability Index
SI = Prob(FS > 1) C1 C2

22. Area-Slope plot with uncertainty
FS* > 1
SI = FS*
*(using most conservative end of each parameter range)
FS < 1
for all possible parameters
SI = 0
Most conservative parameter limits
Most destabilizing parameter limits
SI = Prob(FS >1)

23. SI derived analytically for each region
e.g. for region 2

24. Stability Class Definitions

25. SINMAP Inputs Topography (dictated by DEM) a - specific catchment area
θ - slope angle
Soil Parameters (given as a range)
C - dimensionless cohesion
tan Φ- tan of soil internal friction angle
R/T - soil hydraulic parameter

26. SINMAP Outputs 1. Specific Catchment Area Map 2. Stability Index Map
3. Soil Wetness Map
4. Calibration Plot
5. Statistical Tables

27. Stability Index Map

28. Slope-Area plot interactive calibration

29. SINMAP Implementation
Spatial Analyst includes a C programming API (Application Programming Interface) that allows you to read and write ESRI grid data sets directly.
Excerpt from gioapi.h
/ * GetWindowCell - Get a cell within the window for a layer,
* Client must interpret the type of the output 32 Bit Ptr
* to be the type of the layer being read from. *
* GetWindowCellFloat - Get a cell within the window for a layer as a 32 Bit Float
* GetWindowCellInt - Get a cell within the window for a layer as a 32 Bit Integer
* PutWindowCell - Put a cell within the window for a layer.
* Client must ensure that the type of the input 32 Bit Ptr
* is the type of the layer being read from.
* PutWindowCellFloat - Put a cell within the window for a layer as a 32 Bit Float
* PutWindowCellInt - Put a cell within the window for a layer as a 32 Bit Integer */
int GetWindowCell(int channel, int rescol, int resrow, CELLTYPE *cell);
int GetWindowCellFloat(int channel, int rescol, int resrow, float *cell);
int GetWindowCellInt(int channel, int rescol, int resrow, int *cell);
int PutWindowCellFloat(int channel, int col, int row, double fcell);
int PutWindowCellInt(int channel, int col, int row, int icell);
int PutWindowCell(int channel, int col, int row, CELLTYPE cell);

30. ' SINMAP.c.area
' BaseName is the full directory path name of the input DEM grid
BaseName = Self.Get(0)
'get the procedure from the dll library
area = DLLProc.Make(_avlsmDLL,"area",#DLLPROC_TYPE_INT16,
{#DLLPROC_TYPE_STR,#DLLPROC_TYPE_STR,#DLLPROC_TYPE_INT32,
#DLLPROC_TYPE_INT32})
if (area = NIL) then
av.Run("SINMAP.Error.OpFail",{2})
end
error = area.Call({BaseName+"ang",BaseName+"sca", 0, 0})
if (error > 0) then
av.Run("SINMAP.Error.OpFail",{"Grid and/or memory error reading/writing in area.c"})

31. Customizing the GUI

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

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

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

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

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

38. Channel network delineation options
6/12/2018
Channel network delineation options 4 5 6 3 7 2 1 8
Accumulation Area 1 4 3 12 2 16 25 6

39. Streams from 1:250,000 blue lines

40. 100 grid cell constant support area threshold stream delineation

41. 200 grid cell constant support area based stream delineation

42. Constant Support Area Threshold

43. Channel network delineation options
6/12/2018
Channel network delineation options 4 5 6 3 7 2 1 8
Accumulation Area 1 2 3
Grid Order 1 4 3 12 2 16 25 6

44. Grid network pruned to order 4 stream delineation

45. Curvature based stream delineation

46. Local Curvature Computation (Peuker and Douglas, 1975, Comput
Local Curvature Computation (Peuker and Douglas, 1975, Comput. Graphics Image Proc. 4:375)
6/12/2018 43 48 48 51 51 56 41 47 47 54 54 58

47. Contributing area of upwards curved grid cells only
6/12/2018

48. Upward Curved Contributing Area Threshold
6/12/2018

49. TARDEM Components Grid Processing Flood D8 Dinf Aread8 Areadinf
Gridnet
Grid to Hierarchical Vector Network
Netsetup
Hierarchical Vector to Arc Coverage
Arclinks
Arcstreams
Network and Subwatershed Analysis
Linkan
Streaman
Asfgrid
Subbasinsetup

50. Questions and Demo?
AREA 1
AREA 2 3 12