1. Digital Elevation Model based Hydrologic Modeling
Outline
Topography and Physical runoff generation processes (TOPMODEL)
Raster calculation of wetness index
Raster calculation of TOPMODEL runoff
Extendability of ArcGIS using Visual Basic Programming

2. Physical Processes involved in Runoff Generation
From

3. 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

4. Map of saturated areas showing expansion during a single rainstorm
Map of saturated areas showing expansion during a single rainstorm. The solid black shows the saturated area at the beginning of the rain; the lightly shaded area is saturated by the end of the storm and is the area over which the water table had risen to the ground surface. [from Dunne and Leopold, 1978]
Seasonal variation in pre-storm saturated area [from Dunne and Leopold, 1978]

5. 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

6. 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.”

7. 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

8. Saturation in zones of convergent topography

9. Numerical Evaluation with the D Algorithm
Specific catchment area a is the upslope area per unit contour length [m2/m  m]
Numerical Evaluation with the D Algorithm
Topographic Definition
Upslope contributing area a
Stream line
Contour line
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): ) (

10. Hydrological processes within a catchment are complex, involving:
Macropores
Heterogeneity
Fingering flow
Local pockets of saturation
The general tendency of water to flow downhill is however subject to macroscale conceptualization

11. TOPMODEL assumptions
The dynamics of the saturated zone can be approximated by successive steady state representations.
The hydraulic gradient of the saturated zone can be approximated by the local surface topographic slope, tan.
The distribution of downslope transmissivity with depth is an exponential function of storage deficit or depth to the water table
To is lateral transmissivity [m2/h]
S is local storage deficit [m]
z is local water table depth [m] (=S/ne)
ne is effective porosity
m is a storage-discharge sensitivity parameter [m]
f =ne/m is an alternative storage-discharge sensitivity parameter [m-1]

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

13. Topmodel - Assumptions
Specific catchment area a [m2/m  m]
(per unit contour 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

14. 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

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

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

17. Numerical Example Given Compute Ko=10 m/hr R=0.0002 m/h 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

18. Calculating Runoff from 25 mm Rainstorm
Flat area’s and z <= 0
Area fraction ( )/15893=8.3%
All rainfall ( 25 mm) is runoff
0 < z  rainfall/effective porosity = 0.025/0.2 = m
Area fraction 546/15893 = 3.4%
Runoff is P-z*0.2
(1 / [Sat_during_rain ]) * ( (0.2 * [z]))
Mean runoff m =11.3 mm
z > m
Area fraction 14020/15893 = 88.2 %
All rainfall infiltrates
Area Average runoff
11.3 * * = 2.47 mm
Volume = * * 30 * 30 = m3

19. Why Programming

20. GIS estimation of hydrologic response function
Amount of runoff generated
Travel time to outlet
Distance from each grid cell to outlet along flow path (write program to do this)
Distance from each point on contributing area
overlay grid to outlet distances with contributing area.

21. Steps for distance to outlet program
Read the outlet coordinates
Read the DEM flow direction grid. This is a set of integer values 1 to 8 indicating flow direction
Initialize a distance to outlet grid with a no data value
Convert outlet to row and column references
Start from the outlet point. Set the distance to 0.
Examine each neighboring grid cell and if it drains to the current cell set its distance to the outlet as the distance from it to the current cell plus the distance from the current cell to the outlet.

22. Programming the calculation of distance to the outlet5 1 8 7 6 3 2 4 5 6 7
Direction encoding 1 2 3
Distances to outlet
72.4
102.4 30
42.4
72.4

24. Visual Basic Programming in ArcMAP
References
ESRI, (1999), ArcObjects Developers Guide: ArcInfo 8, ESRI Press, Redlands, California.
Zeiler, M., (2001), Exploring ArcObjects. Vol 1. Applications and Cartography. Vol 2. Geographic Data Management, ESRI, Redlands, CA.

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