1. Digital Elevation Model based Hydrologic Modeling
Outline
Physical runoff generation processes
Modeling infiltration excess
Modeling saturation excess (TOPMODEL)
Semi-distributed hydrologic modeling with TOPNET

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. Runoff generation processes contd.
Subsurface stormflow P P P qs
Perched subsurface stormflow P
Horizon 1
Horizon 2 P qs P

5. Seasonal variation in saturated area

6. Dominant processes of hillslope response to rainfall (Dunne 1978)
Thin soils; gentle concave footslopes; wide valley bottoms; soils of high to low permeability
Direct precipitation and return flow dominate hydrograph; subsurface stormflow less important
Horton overland flow dominates hydrograph; contributions from subsurface stormflow are less important
Variable source concept
Subsurface stormflow dominates hydrograph volumetrically; peaks produced by return flow and direct precipitation
Topography and soils
Steep, straight hillslopes; deep,very permeable soils; narrow valley bottoms
Arid to sub-humid climate; thin vegetation or disturbed by humans
Humid climate; dense vegetation
Climate, vegetation and land use

7. 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

8. Modeling infiltration excess
Rigorous – Richards equation w
r=w-f z f t1 t2 t3 
Generally requires numerical solution

9. Modeling infiltration excess
Conceptual, e.g. Green and Ampt, Horton, Philip w
r=w-f z
fc(t) or fc(F)
if w > fc then
f=fc, r=w-f
else
f=w, r=0 f fc 
t or F

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

11. SCS Curve Number, CN
Relates storm rainfall and runoff (0<CN<100)
Computed as a function of soil and land use using a lookup table
All soils of the US grouped into four Hydrologic Soil Groups (A, B, C, D) where A is freely draining sand and D is poorly draining clay
Hydrologic Soil Group is a component property in Statsgo

12. SCS Curve Number Grid

13. Cell based discharge mapping using weight grid in flow accumulation
Radar Precipitation grid
Soil and land use grid
Runoff grid from raster calculator operations implementing runoff generation formula’s
Flow accumulation using runoff grid as weights from hydrology toolbar

14. 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.”

15. 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

16. Saturation in zones of convergent topography

17. 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): ) (

18. 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

19. 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 lateral transmissivity [m2/h]
S local storage deficit [m]
z local water table depth [m]
m a parameter [m]
f a scaling parameter [m-1]

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

21. 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

22. 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

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

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

25. Numerical Example Given Compute Ko=10 m/hr R=0.0002 m/h f=5 m-1 l=6.91
Qb = 0.8 m3/s
A (from GIS)
Compute
R= m/h
l=6.91
T=2 m2/hr
Raster calculator -( [ln(sca/S)] )/5+0.46

26. 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 = 0.025/0.25 = 0.1 m
Area fraction 410/15893 = 2.5%
Runoff is P-z*0.25
(1 / [Calculation3 ]) * ( (0.25 * [depthtosat]))
Mean runoff m =11.7 mm
z > 0.1 m
Area fraction 14156/15893 = 89.1 %
All rainfall infiltrates
Average runoff
11.7 * * = 2.37 mm
Volume = * * 30 * 30 = m3