Prediction of annual runoff in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 97

861 catchments located in 82 countries around the world.
No data for the inter-annual runoff variability were avail-
able, so the Level 2 assessment presents only results for
mean annual runoff. In order to identify differences in
global and local scale analysis an additional assessment
for 220 catchments in Austria was also performed (Vig-
lione et al., 2013b ). Based on the data availability and
global coverage, three approaches were applied: two stat-
istical approaches, global and regional regression, and a
Budyko index model. The normalised error (NE) and the
absolute normalised error (ANE) were used as perform-
ance indicators (Table 2.2). The NE highlights biases in the
methods, while the ANE is a measure of the overall per-
formance. For comparison with the other runoff signatures
in Chapter 12 , the r² of annual runoff were calculated for
all methods of both the global and the Austrian data. The
25% and 75% quantiles of these r² are 0.52 and 0.81,
respectively.
Performance measures are presented in the following
figures as a function of the aridity index, mean annual air
temperature, mean elevation and catchment area. Note that
the ANE is an error measure, so it has been plotted down-
wards on the vertical axis to make it comparable with the
performance measures, i.e., higher up in the plot is better.

underestimate mean annual runoff. It should be noted that
the Budyko relationship was not calibrated but the regres-
sion coefficients were. The dependence of ANE on air
temperature shows a similar, but less pronounced pattern.
This means the difficult climates to predict are the arid
catchments and not necessarily the catchments with a
warm climate.
A clear relationship does not seem to exist between
ANE and catchment area. For regression models, the
variability of ANE performance between catchments of
the same size is larger than for the Budyko model. This
variability is the largest for catchments larger than 1000
km 2 . The Budyko model seems to be a robust method.
Even though there is a tendency for underestimating run-
off, the results are more consistent for a given catchment
size.

Which method performs best?
Figure 5.29 summarises the performance for different
regionalisation approaches, stratified by the aridity index.
The top, middle and bottom panels show the performance
for all catchments, and catchments with an aridity index
below and above 1, respectively. Overall the Budyko
model performs better than the two regression approaches.
Regional regressions perform better than global regression.
While the performance in humid catchments is quite simi-
lar for all three approaches, in arid regions the performance
of the Budyko approach is much better than that of regres-
sions. The built-in principle of water versus energy com-
petition included in the Budyko model appears to provide
an inherent advantage for mean annual runoff prediction
compared to purely statistical approaches, particularly in
arid regions. It should also be noted that in arid regions the
regional regressions perform significantly better than
global regressions, while this is not the case in humid
regions.

To what extent does runoff prediction performance depend
on climate and catchment characteristics?
Before analysing the NE and ANE of the three chosen
approaches, a regression analysis of mean annual runoff
with area, mean annual precipitation and mean annual
temperature (T A ) was performed in order to understand
which predictors are important for mean annual runoff
under different climatic conditions. The r 2 -value, calcu-
lated based on specific runoff, did not exceed 0.5 for any
of the regressions. This indicates that the size of catch-
ments and global climate variability control only part of
mean annual runoff patterns. While all three predictors
were significant for estimating mean annual runoff in
humid, cold and arid conditions, the analysis showed that
for tropical climates T A does not play any role.
The ANE error measure of mean annual runoff with
respect to the four climate and catchment characteristics
is presented in Figure 5.27 . The results clearly indicate that
the performance of all models decreases with increasing
aridity (top panel). For global regression and regional
regression the median ANE is around 0.2 for humid catch-
ments and 1 or larger for arid catchments. For the Budyko
approach, the errors in the arid catchments are smaller than
for the other methods. Apparently the structure of the
Budyko is more suited to predicting mean annual runoff
in arid catchments than regressions. The regression models
tend to overestimate mean annual runoff in arid catchments
( Figure

Global scale results vs. local scale results
The results of the Level 2 assessments compared the
performance of statistical and index methods on a global
scale. The performance of methods for mean annual
runoff prediction in a particular region depends on the
hydrological variability, as well as data availability. As
an example, Figure 5.30 compares different approaches
for mean annual runoff prediction in 220 catchments in
Austria (Viglione et al., 2013b ), which is generally
humid with the aridity index ranging from 0.2 to 1.4.
The following methods were used: the global regression
model fitted to the global data set of Peel et al.( 2010 )
using catchment area, mean annual precipitation and air
temperature as catchment characteristics; the Budyko
approach; a regional regression model fitted to the Aus-
trian data (using the same catchment characteristics as 5.28 ), while Budyko generally tends to