Digital Elevation Model based Hydrologic Modeling

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 http//snobear.colorado.edu/IntroHydro/geog_h
  ydro.html

3
Runoff generation processes
P
Infiltration excess overland flow aka Horton
overland flow
f
P
qo
P
f
Partial area infiltration excess overland flow
P
P
qo
P
f
P
Saturation excess overland flow
P
qo
P
qr
qs
4
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.627-668.
• 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
Specific catchment area a is the upslope area per
unit contour length m2/m ? m
Numerical Evaluation with the D? Algorithm
Topographic Definition
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) 309-319.)
(http//www.engineering.usu.edu/cee/faculty/dtarb/
dinf.pdf)
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
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.

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 gt 1.
• i.e.

15
Topmodel
Specific catchment area a m2/m ? m (per unit
coutour length)
z
16
Slope
Specific Catchment Area
Wetness Index ln(a/S) from Raster
Calculator. Average, l 6.91
17
Numerical Example

• Given
• Ko10 m/hr
• f5 m-1
• Qb 0.8 m3/s
• A (from GIS)
• ne 0.2

• Compute
• R0.0002 m/h
• l6.90
• T2 m2/hr

Raster calculator -( ln(sca/S) - 6.90)/50.46
18
Calculating Runoff from 25 mm Rainstorm

• Flat areas and z lt 0
• Area fraction (81 1246)/158938.3
• All rainfall ( 25 mm) is runoff
• 0 lt z ? rainfall/effective porosity 0.025/0.2
  0.125 m
• Area fraction 546/15893 3.4
• Runoff is P-z0.2
• (1 / Sat_during_rain ) (0.025 - (0.2 z))
• Mean runoff 0.0113 m 11.3 mm
• z gt 0.125 m
• Area fraction 14020/15893 88.2
• All rainfall infiltrates
• Area Average runoff
• 11.3 0.025 25 0.083 2.47 mm
• Volume 0.00247 15893 30 30 35410 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
outlet

102.4
72.4
30
72.4
42.4
0

23
(No Transcript)
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 ?