Geoscience Reference
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data. This study is a nice lead in to the next approach to the regionalisation problem, since it makes use
of the hydrograph characteristics at the gauged sites directly.
Given the limitations shown by the studies that attempt to regionalise model parameter values, recent
work on regionalisation has tried to work to estimate the hydrograph characteristics of an ungauged
catchment directly. This approach actually has a long history, but only in the specific circumstances,
mentioned earlier, when the site of interest is not too far upstream or downstream from a stream gauge.
Then, unless there are obvious differences between the sites, the recommended approach to regionalisation
is simply to scale the observed hydrograph by catchment area. For such sites, this is the approach to beat
(IH, 1999; Merz and Bl oschl, 2004). The nearest gauge, however, may not actually be the best gauge to
use (though see the work of Zhang and Chiew (2009) for an example where spatial proximity performed
slightly better than physical similarity as defined by catchment characteristic measures). Archfield and
Vogel (2010) suggest a method for deciding which nearby gauge might give the best results.
Amore sophisticated version of this technique has been recently provided by Parada and Liang (2010).
They treat the ungauged catchment discharge as a hidden variable to be estimated on the basis of uncertain
observations (in this case, the discharges from two nearby catchments and predicted discharges for
the study catchments using default parameter values in the VIC-3L model, see Box 2.2). The hidden
variable is expected to be related to the observations by some arbitrary nonlinear transform. They then
frame the problem as a recursive variational Bayesian Kalman Filter, using kernel functions to linearise
the estimation problem. The procedure leads to better predictions in terms of bias, correlation and root
mean square error than either the default model or the donor catchment discharges. Best results for low
flows are obtained by using the log
10
transformation of the observations. The method can also produce
estimates of the uncertainty in the predicted discharges, though the authors do not show this in their
hydrograph plots.
But the site of interest may not be close to a stream gauge, of course, so that it then becomes more
difficult to estimate the hydrograph characteristics. Yadav
et al.
(2007) suggest that rather than trying to
estimate model parameters for such sites, it might better to estimate hydrograph characteristics directly
and then use those characteristics to constrain the uncertainty in using a model to represent the study
catchment. The question then is what indices of hydrograph behaviour might most easily be extrapolated
and which might be most useful to constrain model uncertainty. Such indices are used quite widely in
hydroecological studies. Olden and Poff (2003) compiled 171 different indices from previous literature.
Shamir
et al.
(2004) show how selected indices can be useful in hydrological model calibration since
they can reflect different components of the hydrological response. Bardossy (2007) used some simple
indices of the discharge annual mean and variance to evaluate the predictions of model parameter sets
from donor catchments when applied to ungauged sites.
Yadav
et al.
(2007) took this further in using 39 different hydrological indices (relating to aspects
of high flow, average flows, low flows, rate of rise, event frequencies, timing and climate) on 30 UK
gauged catchments chosen to reflect a range of areas, annual rainfalls, baseflow index and flow duration
curves. They showed that there is redundancy of information between some characteristics which are
highly correlated. They then developed (independent) step-wise regression equations to relate chosen
hydrograph indices to the physical characteristics of the gauged catchments. Some 19 indices were then
estimated for test catchments treated as ungauged, together with their estimation uncertainty. This gave a
basis for evaluating runs of a rainfall-runoff model, in this case, the five-parameter HYMOD conceptual
model. Monte Carlo realisations of the parameters were generated and the characteristics of the model
outputs compared with the estimated hydrograph indices. High flow event frequency, runoff ratio and
the slope of the flow duration curve provided strong regionalisable constraints while producing reliable
predictions in the sense of bracketing the observed flows. Not all the regression equations, however, gave
good predictions of the equivalent hydrograph indices for the test catchments; if too many constraints
were used in testing the model realisations, all the models tried could be rejected. Zhang
et al.
(2008)
extended this work to use a directed search algorithm that would be more efficient at finding model
