Prediction of annual runoff in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 95

Figure 5.24. Squared correlation
coefficient (r 2 ) of predicting annual
runoff (left) and inter-annual runoff
(right) in ungauged basins stratified
by regionalisation method. Each
symbol refers to a result from the
studies shown in Table A5.1 (annual
runoff) and Table A5.2 (inter-annual
runoff). Lines indicate studies that
compared different methods for the
same set of catchments. Boxes show
25%

Annual runoff Interannual variability

1.0

0.8

0.6

0.4

- 75% quantiles.

0.2

Regression Index Spatial

proximity

Process
based

Proxy
data

Regression Index

Regionalisation method

Regionalisation method

median r 2 of 0.65 and 0.57 respectively. The results of
the regression method have a much larger scatter. In gen-
eral, the performance is somewhat lower than the perform-
ance obtained for mean annual runoff since, clearly, inter-
annual variability is harder to predict.

These are all interpolation methods including geostatistical
approaches. Process-based models are only rarely applied
and are represented here by four results that used different
rainfall runoff models. Finally, eight results that estimate

annual runoff based on proxy data are available.
For annual runoff, spatial proximity methods show the
best performance with median r 2 values close to 0.89.
These results are mainly from north-eastern USA and
France where a considerable number of stream gauges
exist. The performance of regression methods tends to be
slightly lower. The studies come from a mix of continents.
Two studies in Europe compared spatial proximity with
regression and found significantly better performance of
spatial proximity. In regions where annual runoff varies
rather smoothly in space and where a reasonable number of
stream gauges exist, it is not surprising that spatial prox-
imity methods would perform well. It should also be noted
that some of the results for the regression methods are
based on volumetric runoff values (crosses in Figure
5.24 ) so, if only specific runoff is considered, the median
performance is actually lower.
Index methods (such as Budyko) also perform quite well,
in fact as well as or better than regression, considering that
some of the regression results are for volumetric runoff. The
performance of process-based methods (mainly runoff
models) tends to be lower, with a median r 2 of around 0.7.
Clearly, the performance strongly depends on the way the
models are calibrated to existing runoff data. For complete-
ness, methods that use tree ring (proxy) data were included
but, not surprisingly, suggest that the main focus of tree ring
chronology is to reconstruct past runoff variability rather
than to predict runoff in the present climate.
For the prediction of inter-annual runoff variability the
regression and index methods perform similarly, with a

-

How does data availability impact performance?
Figure 5.25 shows the predictive performance as a function
of the number of catchments analysed in each study. Most of
the studies used relatively large data sets, although this
probably reflects the fact that most studies evaluate the
accuracy of predictions in space. An exception is the pre-
diction of temporal variability by proxy methods (i.e., tree
rings), which is usually tested only on single catchments.
The results indicate that the performance does not seem
to depend on the size of the data set. Apparently, only data
from a small number of gauged catchments are needed in
order to predict mean annual runoff within the study area in
ungauged basins. There may be two effects related to scale.
The first is that the total heterogeneity tends to increase as
the size of a region increases, which would be expected to
lower the performance if the same method is used in the
entire region. The second is that, with increasing sample
size, the methods may be adjusted more reliably to the
existing runoff data. These two effects may counterbalance
each other as the size of the data set increases. The predic-
tion of inter-annual runoff variability, on the other hand, is
more specific and improves with the availability of larger
data sets.
More detailed insight into the dependency of perform-
ance on both method and number of catchments per study
is shown in Figure 5.26 . Index-based methods have been
evaluated mostly for data sets with more than 200 catch-
ments, while spatial proximity and regression methods