Prediction of runoff hydrographs in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 253

Regression between calibrated model parameters and
catchment characteristics
An alternative approach is to relate the calibrated model
parameters individually to catchment characteristics in the
gauged catchments through empirical relationships, and
use these to estimate the model parameters in the ungauged
basin. Regression models have been tested in different
studies. For example, Kokkonen et al.( 2003 ) found the
drying parameter of the IHACRES model to be negatively
related to mean overland flow distance (r

0.85

0.80

Calibration

Proximity

0.75

Similarity

0.70 Regression

0.76) and the
time constant governing the rate of recession in the slow
store to be related to topographic slope (r

¼ −

0.66) in the
Coweeta catchment, North Carolina. Merz and Blöschl
( 2004 ) found the very fast storage coefficient to be nega-
tively correlated with elevation and slope, implying that
direct surface runoff may be particularly flashy in the high
altitude catchments in Austria. The R² of the relationship,
however, never exceeded 0.37. Seibert ( 1999 ) related the
model parameters of the HBV model (Bergström, 1976 )to
attributes of 11 Swedish catchments within the NOPEX
area. The relationships between forest percentage and
snow parameters could be interpreted on hydrological
grounds but other relationships could not. The rank correl-
ation coefficient between a non-linearity parameter of run-
off generation and catchment area was r²

¼ 0.65

Median

0.60

1 3 10 30 100 300

Stream gauge density (stations per 100 000 km 2 )

Figure 10.25. Effect of stream gauge density of possible donor
catchments on the Nash Sutcliffe performance of predicting runoff in

ungauged basins by a conceptual runoff model based on spatial
proximity and similarity approaches in France. From Oudin et al.
( 2008 ).

-

One would expect that the performance of the spatial
proximity-based method depends on the density of stream
gauging stations since it builds on the spatial smoothness
of the controls. Oudin et al.( 2008 ) assessed the effect of
the stream gauge density by progressively decreasing the
density of possible donor catchments used for each
ungauged catchment. The analysis was performed for a
total of 913 catchments in France. Figure 10.25 presents
their results in terms of the median model efficiencies in
their region as a function of stream gauge density. This
shows that with 5 to 20 gauges per 100 000 km², the
performance of both proximity and similarity methods is
around 0.67 and increases for higher stream gauge dens-
ities. The regression approach (see below) gives a perform-
ance of 0.67 irrespective of the number of gauges. This
means that even with a moderate number of stream gauges,
the proximity and similarity methods outperform the
regression. The two stream gauge network examples in
Chapter 3 ( Figure 3.4 ) represent stream gauge densities
of about 50 gauges (Ethiopia) and 500 gauges (Austria)
per 100 000 km², assuming that half the stream gauges can
actually be used for transferring parameters to ungauged
basins (while the other half may either be regionally non-
representative or have data problems). Applying the prox-
imity curve in Figure 10.25 to these two cases gives
performances of 0.70 and 0.75 for Ethiopia and Austria,
respectively. Of course, the actual performances in these
two countries will be different as the hydrological variabil-
ity and the data quality will be different.

0.87, but most
other parameters exhibited few significant correlations
with catchment attributes. Young ( 2006 ) suggested that
regressions may be useful for runoff models with a small
number of parameters (less than five). For a study in the
UK they were able to relate the mean storage capacity and
the quick flow routing time constant from a runoff model
to the fractional extents of HOST soil classes.
Another example of the regression approach is presented
in Figure 10.26 , taken from the work of Carrillo et al.
( 2011 ), who applied the semi-distributed hsB model
developed by Troch et al.( 2003 ) to 12 catchments across
a climate gradient east of the Rocky Mountains, USA.
They performed regressions on all readily available catch-
ment characteristics to different model parameters, in an
attempt to reveal useful regionalisation patterns. Only a
small number of significant relationships were obtained in
this way, as shown in Figure 10.26 . Although most param-
eters were not related to catchment characteristics, some
relationships were found for six non-snow dominated
catchments. The few significant regressions that were
obtained all have some association with vegetation cover,
indicating the role of vegetation in the co-evolution of
catchment characteristics with climate, perhaps through
biotic manipulation of soils.
Ideally, the relationship between model parameters and
catchment characteristics should be hydrologically justifi-
able to give confidence for extrapolation to ungauged
basins. However, as suggested in some of the studies

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