Geoscience Reference
In-Depth Information
of (
a/
tan
β
) was carried out for the downslope edge of each element. Although an approximation, this
method was felt to be justified by its relative efficiency and because field observations of flow paths could
be used in defining the slope elements to be analysed. In particular, the effects of field drains and roads in
controlling effective upslope contributing areas could be taken into account. Such human modifications
of the natural hydrological flow pathways are often important to the hydrological response but are not
normally included in the digital terrain maps (DTMs) of catchment areas commonly used in topographic
analysis today.
However, given a DTM, more computerised methods are now available. Quinn
et al.
(1995) demon-
strate the use of digital terrain analysis (DTA) programs, based on raster elevation data, in application
to catchment modelling studies based on TOPMODEL. There are subjective choices to be made in any
digital terrain analysis. Techniques of determining flow pathways from raster, contour and triangular
irregular network DTMs are discussed in Section 3.7. Different DTA techniques result in different flow-
path definitions and therefore different calculations of “upslope contributing area” for each point in the
catchment. The resolution of the DTM data will also have an effect. The DTM must have a fine enough
resolution to reflect the effect of topography on surface and subsurface flow pathways adequately. Coarse
resolution DTM data may, for example, fail to represent some convergent slope features. However, too
fine a resolution may introduce perturbations to flow directions and slope angles that may not be reflected
in subsurface flow pathways which, in any case, will not always follow the directions suggested by the
surface topography (see, for example, the work of Freer
et al.
(1997), who suggest that bedrock topog-
raphy may be a more important control in some catchments). The appropriate resolution will depend on
the scale of the hillslope features, but 50 m or better data is normally suggested. Anything much larger
and, in most catchments, it will not be possible to represent the form of the hillslopes in the calculated
distribution of the (
a/
tan
β
) index.
Experience suggests that the scale of the DTM used and the way in which river grid squares are treated
in the DTA do affect the derived topographic index distribution, in particular inducing a shift in the
mean value of (
a/
tan
β
). There is a consequent effect on the calibrated values of parameters (especially
the transmissivity parameter) in particular applications. This is one very explicit example of how the
form of a model definition may interact with the parameter values required to reproduce the hydrology
of a catchment. In this case, two different topographic analyses of a catchment may require different
effective transmissivity values for hydrograph simulation. However, in one study, Saulnier
et al.
(1997b)
have suggested that excluding river grid squares from the distribution results in calibrated transmissivity
parameter values that are much more stable with respect to changing DTM resolution. An alternative
adjustment has been suggested in developing a block version of TOPMODEL for use at very large scales
(BTOPMC) in which the
a
developed from topographic analysis within a block can be adjusted by a
function
f
(
a
) within the range 0-1 (Ao
et al.
, 2006; Takeuchi
et al.
, 2008). BTOPMC is now being
used to support a global flood alert system (GFAS) for large scale catchments in sparsely gauged areas,
driven by satellite-derived rainfall estimates at the UNESCO International Centre of Excellence for Water
Hazard and Risk Management (ICHARM) in Japan.
The simplicity of the TOPMODEL structure has allowed this problem to be studied in some detail
but similar considerations of an interaction between grid scale and model parameters must apply to even
the most physically based, fully distributed models (Beven, 1989; Refsgaard, 1997; Kuo
et al.
, 1999). In
the last decade, there has been an interesting analysis of this grid-scale dependence of the topographic
index by Nawa Pradhan
et al.
(2006, 2008). They point out that both the effective contributing area and
the steepest gradients in a raster grid are dependent on the size of the grid elements and propose ways
of adjusting both, when topographic data are available at one scale and the target resolution is at a finer
scale. The adjustment of the
a
value is simply to divide by the ratio of the grid lengths (coarse/target).
The adjustment for slope is based on assuming that the fractal properties of topography imply scaling
similarity, at least for a range of scales (this tends to break down at very fine scales). They make use of a
relationship suggested by Zhang
et al.
(1999) to estimate a local fractal dimension
D
from the standard
