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A Topographically-Controlled Soil Saturation Model Using GISProject completed by Robert Treat, Fall 2007
The Topographic Index
The topographic index (or wetness index) is a semi-quantitative value that seeks to take into account
topographic effects such as slope and upslope contributing area on the directionality and accumulation of
surface runoff, and is formally stated as:
Topographic Index (TI) = ln(a / tanβ)
Where a = A/c = upslope contributing area/unit contour length perpendicular to flow, and β = local slope.
The higher the TI for an area, the more likely it is to become saturated during a precipitation event and
generate overland flow.
Application of the TI using a DEM in ArcGIS involves calculation of slope,
upslope contributing area, and flow accumulation. Calculating these values
with a raster dataset was done using a set of hydrological tools contained
within the ArcGIS spatial analyst, which use a slope raster to calculate
The first tool was the flow direction function, which assigns a value to each
cell based on 2n
, where n ranges from 0 to 7 in a clockwise direction (0 being
east, 2 being south, 4 being west, etc). This is illustrated visually in Figure 4
below. Each value represents the direction of overland flow for that cell by
assuming the entire cell drains to its steepest down-slope neighbor,
calculated as Δelevation/center-to-center cell distance.
With flow direction, sinks can be identified. A sink is a cell which does not flow
into any other, in other words a cell where all 8 adjacent cells flow into it.
Sinks can be natural, as in the case of lakes or ponds, or may represent error
in data due to resolution. ArcGIS also contains a hydrological tool designed to
identify sinks and remove them. Fortunately, the DEM used was interpolated
in a hydrologically correct manner, ensuring all sinks are natural occurrences.
Finally, a third ArcGIS tool uses flow direction pathways to calculate the
accumulation of cells in each cell by a series of summations.
Three sinks were classified using the flow direction function, which can be seen on Figure 5 below. These were
identified as natural features using ortho photos at half-foot resolution, obtained from the MEGIS website. Three
of the lakes in the bottom photo were not present at the time of DEM creation, and are therefore not seen in the
continued TI analysis.
Using the flow direction raster, a layer representing the accumulation of cells was created which takes the
appearance of a stream network, as any overland flow would be topographically driven to these locations as
expected. This can be seen below in Figure 6.
One prediction of this model is that the flat area in the southeast corner of the map, where the TI values
indicate a high propensity for accumulation over a broad, flat area, should be relatively wet near surface.
This is, in fact, the case as three ‘lakes’ not seen on the quadrangle map have been created as gravel
pits were excavated below the near-surface water table and later became flooded (Figure 8 above).
Another feature of this model is the ability to predict rather detailed stream channel paths. One example
of this is near the area of Small Hill, outlined by the blue square in Figure 7, and seen below close-up.
Figure 9 on the left shows how predicted runoff paths follow along v-shaped contours, and Figure 10 on
the right shows how predicted runoff paths flow through areas of low elevation, which are stream
channels, and can be traced backwards towards their source areas.
When water is precipitated in a catchment, there are four methods by which it can eventually be
discharged into a stream channel (Hornberger, 1998). Of these four methods, overland flow is perhaps
the most readily observed in our daily lives. This can be seen whenever one goes for a walk after a
major precipitation event and steps on seemingly dry ground, only to find it is saturated with water and
cannot support weight, or when normally dry areas become temporary stream channels, often leading
to extreme erosion.
Overland flow primarily occurs when precipitation cannot infiltrate the ground, due to either an
impermeable surface (such as bedrock or pavement), or where the soil has become saturated.
Modeling how overland flow will behave in a catchment is particularly important when trying to predict
the effects humans will have on the hydrological cycle through land-based activities such as
development, and provides critical information when planning for flood routing controls.
One method of predicting the likelihood of overland flow is by developing a soil saturation model that
acts to predict which areas are likely to become saturated during a precipitation event. One component
of commonly-used soil saturation models is known as the topographic index, or wetness index, which
accounts for the effects of topographic control on the flow of water over the land surface. Influences
such as geology and soil type are not included in this model.
Area of Study
The area modeled in this project is that of the Gorham, Maine quadrangle, the extent of which can
be seen below in Figure 1. The digital elevation model (DEM) for the same area is also pictured
below in Figure 2 overlaying the 1:24000 scale topographic map. All three maps were obtained
from the Maine Office of GIS website (http://apollo.ogis.state.me.us/http://apollo.ogis.state.me.us/). This area was chosen simply
out of personal interest.
Figure 1 Map of the Gorham quadrangle Figure 2 Digital elevation model for Gorham
quadrangle overlaying 1:24000 scale topo map.
Figure 4 Flow chart illustrating algorithms for calculating flow
direction from elevation differences, and accumulation of cells
along flow paths.
When thought of in terms of the above data layers, the TI then becomes:
TI = ln(a / tanβ) = ln([flow accumulation]*10 / tan [slope])
Where a = number of upslope contributing cells*100m/10m. It should be noted that unit contour length
perpendicular to flow is not always 10m, as diagonal flow would require a 14m length. Unfortunately, there is no
realistic way to differentiate this when working with such a large number of cells, providing a degree of error.
Figure 5 Layer produced using flow direction
function, with identified sinks shown in color.
Aerial photos to right show sinks to be natural
Figure 6 Flow accumulation layer, which
resembles a river network. This makes sense,
as most overland flow would eventually be
driven to stream channels by topography.
Application of the previous formula to the raster layers produces Figure 7 below, where the white
spaces are dataless values created by very flat areas such as ponds and flat land, where overland flow
would also accumulate. As one might expect, the TI values come to resemble a rather intricate drainage
system. Blue values indicate potential sites for rivers or streams (even intermittent ones), while red
values can be seen to represent areas of high slopes along hills or banks.
Though modeling overland flow using a topographic-based approach does provide a reasonable
approximation to reality, it should be noted that topography is not the only factor controlling overland
flow. Geology and soil type play important roles in ground permeability, which directly influences
hydrological flow patterns.
For instance, the gravel pits mentioned earlier lie in an outwash plain, and although the topographic
index predicts a high degree of overland flow in the area due to the flat slope, the underlying material is
very permeable, which may limit the actual amount of surface accumulation. Similarly, impermeable
surfaces created due to urban development may increase the amount of overland flow generated in
Cell schematics from ArcGIS help fileCell schematics from ArcGIS help file
Hornberger, et. al. 1998.Hornberger, et. al. 1998. Elements of Physical HydrologyElements of Physical Hydrology. Baltimore: John Hopkins University Press.. Baltimore: John Hopkins University Press.
MEGIS Resources (http://megis.maine.gov/catalog/MEGIS Resources (http://megis.maine.gov/catalog/)
Topographic map: U.S. Geological Survey (USGS), Maine Office of Geographic Information Systems(MEGIS) (comp.)(ed.) 1999/12/31Topographic map: U.S. Geological Survey (USGS), Maine Office of Geographic Information Systems(MEGIS) (comp.)(ed.) 1999/12/31
Aerial photos: Bradstreet Consultants, Inc. (www.bradstreet.com), Maine Office of Geographic Information Systems (comp.)Aerial photos: Bradstreet Consultants, Inc. (www.bradstreet.com), Maine Office of Geographic Information Systems (comp.) 2004/02/16
Gorham DEM: U.S. Geological Survey (USGS), Maine Office of Geographic Information Systems (MEGIS) (ed.)Gorham DEM: U.S. Geological Survey (USGS), Maine Office of Geographic Information Systems (MEGIS) (ed.) 2004/07
Figure 3 Slope raster, from which
hydrological patterns were calculated
Figure 7 Map showing calculated topographic index values
Figure 8 Aerial photo shows high water
table, indicated by flooded gravel pits
Figure 9 Predicted flow paths follow along
v-shaped contours and stream paths.
Figure 10 White represents low elevation
areas where stream channels are present.
Predicted flow paths can be seen to follow, as
well as be traced upstream.