Hydrological simulations are facilitated by methods that use topographic indices ( Beven and Kirkby 1979; O'Loughlin 1981; Moore et al. 1991; Wolock 1993a). This approach, originally put forth independently by Beven and Kirkby (1979) and by O'Loughlin (1981), has become ever more powerful with the linkage of hydrological models with GIS and modern computer graphics techniques. Two widely used, topographically based models are TOPMODEL ( Beven and Kirkby 1979) and TOPOG ( Dawes and Short 1988). These models are not truly distributed in the sense of accounting for flows from point to point in a three-dimensional (or even two-dimensional) space. Rather, they account for variability in the hydrological response of different areas of a catchment by using an index to catchment wetness based on topography. Areas within the basin possessing the same value of the topographic index are assumed to behave the same hydrologically, regardless of their location on the landscape. Many efforts over the last four years have focused on alterations of the form of the topographic index and on improvements in the methodology for computing the indices.
The most common (and most simple) index used in catchment models is
ln(A
/tan 
), where ln(.) is the natural
logarithm, A
is the area drained per unit contour or
the specific area, and tan 
is the slope ( Moore et
al. 1991; Wolock 1993a). Regions of the landscape that drain
large upstream areas or that are very flat give rise to high values of
the index; thus areas with the highest values are most likely to
become saturated during a rain or snowmelt event and thus are most
likely to be areas that contribute surface runoff to the stream.
Within TOPMODEL, the topographic index is used to compute the depth to the water table, which in turn influences runoff generation. Troch et al. (1993) investigated the spatial distribution and temporal evolution of the water table depth using remotely sensed data from the Multisensor Airborne Campaign (MACHYDRO) 1990 in their study of two basins within the experimental catchment at Mahantango Creek in Pennsylvania. They showed that the assumption of a linear relationship between the depth to water table and the topographic index is reasonable.
The topographic index most often is computed from DTM's. The algorithm used to compute flow direction and the resolution or scale of grid data affects the computation of the index. The elevation data used in computing topographic indices are specified either on a regular grid or at irregularly spaced intervals along contours. In either event, terrain attributes depend on estimation of the directional derivatives of the surface specified by the grid-based or contour-based elevations.
The commonly used single flow path method assumes that the
contour length (used in computing the specific area, A
)
is given by the length or resolution of a grid cell. All area
accumulated upstream of a given grid cell drains to only one of
eight neighboring grid cells, that with the steepest angle of descent.
This method was developed initially by O'Callaghan and Mark (1984)
and has been termed the deterministic-8 node ( D8) algorithm.
Noting problems with traditional maximum descent ( D8) slope
methods, Fairfield and Leymaire (1991) presented new procedures
to determine flow-line direction that give more accurate representations
of slope and aspect. Fairfield and Leymaire (1991) showed that
their slope-weighted, stochastic version of the D8 algorithm
(termed Rho8: random-eight node) provided a more
realistic representation of flowpath networks. Alternatively,
a multiple-flow-path procedure allows accumulated upslope area for any
one grid cell to be distributed among cardinal and diagonal
downslope directions, where a fraction of the area can drain into
each neighbor weighted by the degree of slope. Comparing the
distribution of ln(
/tan 
) computed with the
single versus multiple flow path algorithms, Quinn et al.
(1991) showed that a multiple flow path algorithm provides a more
realistic representation of flows. Moore et al. (1993a)
further modified the D8 and Rho8 algorithms to incorporate
flow dispersion; these modified, multiple flowpath algorithms
are abbreviated FD8 and FRho8.
Moore (1993) compared five popular algorithms for estimating
A
: the traditional single flow path D8 version,
the two multiple flow path slope-weighted FD8 and FRho8
versions described above which use gridded terrain data, the DEMON
(Digital Elevation Model Networks; Costa-Cabral and Burges
1994) stream-tube approach for gridded data, and the conceptually
similar TAPES-C stream-tube approach for vector-based digital
elevation data. All methods were used to compute the specific area of
the Coweeta experimental catchment in North Carolina. The
comparison revealed that the method chosen affects the outcome, but
that differences in the computations of the various multiple flow
path methods are small. Moore (1993) recommended that any of
the four multiple flow path algorithms are suitable for computing
A
for topographically based models and all are
significant improvements over the traditional D8 method.
The resolution or scale of gridded terrain data also influences
the computation of topographic distribution functions. Quinn et
al. (1991) compared the distribution of ln(A
/tan
) computed with 12.5 m grid cells to that of coarser 50 m
grid cells. Using the coarser data, a greater percentage of high values
of the index was obtained relative to values for the finer data.
Similar results were obtained by Chairat and Delleur (1993) in
a comparison of the index computed using 30, 60, and 90 m resolution
grid cells for a small basin in Indiana.
Zhang and Montgomery (1994) computed the topographic index
(A
/tan 
) using DEM grid sizes of 2, 4, 10, 30, and
90 m. The indices derived at each level of resolution were used
to parameterize both TOPOG to investigate surface saturation zones
and TOPMODEL to compute hydrographs of two basins in the northwestern
U.S. The calculated values of the topographic index, and hence the
model results were quite sensitive to grid size. The results using
the finest grid sizes (2 and 4 m grid cells) were not very different
from those using the 10 m grid size; results for the 30 and 90 m
scales, however, were significantly different from those obtained with
the finer grids. Zhang and Montgomery (1994) observed that
runoff processes were controlled by physical features of the landscape
of about ten meters in length in the relatively steep basins that
they studied. In general, Zhang and Montgomery (1994) recommend
that landscape features of interest guide the choice of resolution of
DEMs used to calculate topographic indices for hydrological models,
and suggest that a 10 m grid size is appropriate for many
topographically based hydrological modelling efforts in relatively
steep terrain.
Wolock (1993b) studied how the distribution of
ln(A
/tan 
) changes with size of sub-basin,
investigating a hierarchy from very small basins (0.1 to
1 km
) to much larger basins (1 to 100 km
). The
distribution was very sensitive to increases in basin size in the range
of 0.1 to 1 km
. In the 1-100 km
scale range, however,
the moments of the distribution showed only small variability.
Although topography is a dominant factor in describing water flows
in soils in steeply sloping areas, other factors become relatively
more important in basins of low relief and with more gentle slopes.
Barling et al. (1994) present a quasi-dynamic wetness index
for simulations of soil moisture in these environments, relaxing the
steady state assumption of the ln(A
/tan 
) index.
Their approach accounts for the time it takes for water to redistribute
and recharge across a basin after a rainfall event, and yields
improved representation of soil moisture patterns over the steady
state wetness index for the cases for which they had
data.
The validity of the assumption in TOPMODEL that the water table
(i.e., the surface of the saturated zone, mimics surface topography
has also been the subject of study. Hinton et al. (1993) showed
that this assumption is not valid in a glacial till catchment of
the Canadian shield. Quinn et al. (1991) present a method
for adjusting ln(A
/tan 
) in instances where
this assumption is not valid by incorporating a reference level, which
can deviate from the slope of the surface, in areas where subsurface
flow pathways are thought to deviate from surface topography.
A number of studies have presented variations on the basic topographic wetness index, incorporating additional information affecting soil moisture distribution. Factors such as the spatial distribution of soil characteristics, vegetation, and meteorological conditions, in addition to topography, can affect the soil moisture content ( Moore et al. 1991). To calculate spatially distributed evaporation, Famiglietti et al. (1992) and Famiglietti and Wood (1994a,b) combined TOPMODEL with an energy balance model. Moore et al. (1993b) developed a modified version of the topographic index to account for the spatial distribution of radiation, which in turn affects evapotranspiration; they use an area weighing method that accounts for effects of soil properties, deep seepage, recharge, and evapotranspiration.
Wetness indices have proven to be very useful in calculating runoff hydrographs for upland catchments. Despite their current popularity, they should not be taken to provide a completely accurate picture of the distribution of soil wetness over a catchment. Attempts to correlate these indices with measures of soil wetness have met with limited success ( Jackson 1991; Barling et al. 1994).