PUB in practice: case studies - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 303

Table 11.7. Indices of performance obtained by cross-validating the regional approaches (ungauged basins) and through
a resampling experiment (scarcely gauged basins)

ε σ ε P 1 % P 2 % P 3 %

Cross-validation
Statistical − 0.104 0.175 29.4 9.8 60.8

Parametric 0.109 0.314 31.4 9.8 58.8

Graphical − 0.134 0.141 21.6 21.6 56.9

Resampling experiment
1 year 0.127 0.327 53.9 21.7 24.4

2 years 0.095 0.258 66.3 16.4 17.3

5 years 0.070 0.186 78.2 9.2 12.6

¯ is the mean relative residual over all sites and durations of interest and σ ε the standard deviation of the relative residuals; percentage of
cases for which NSE > 0.75 (P 1 , good to fair fit), 0.75 ≥ NSE > 0.50 (P 2 , fair to poor fit) and NSE 0.50 (P 3 , poor fit), where NSE
stands for Nash - Sutcliffe efficiency of predicted FDC over the durations of interest (i.e., D ∈ [0.3, 1.0]).

Results
The performance of the methods was tested in terms of
cross-validation of the regional approaches, i.e., the assess-
ment of the reliability of long-term FDCs predicted in
ungauged basins through regional models, and through a
resampling experiment, i.e., the reliability of long-term
FDCs estimated on the basis of short records of 1, 2 or 5
years length (i.e., scarcely gauged basins). The results are
presented in Table 11.7 and Figure 11.35 .
The cross-validation shows that for ungauged sites the
reliabilities of the three regional models are comparable to
one another, even though they have different theoretical
backgrounds and were implemented using different pro-
cedures. The error

method presented by Fennessey and Vogel, 1990 ); a quan-
tile regression method, named the

'
(adapted from the method presented by Franchini and
Suppo, 1996 ); and a non-parametric approach based upon
the utilisation of dimensionless FDCs (see e.g., Figure
11.32 ), named the

'

parametric approach

(adapted from
Smakhtin et al., 1997 ). See Section 7.3 for a brief descrip-
tion of these methods.
The performance of each approach in predicting the
long-term FDC for durations D

' graphical approach '

[0.3, 1.0] in ungauged
sites was assessed through a comprehensive cross-
validation procedure (i.e., leave-one-out, or jack-knife
resampling procedure) and expressed through statistical
indices and error

∈

duration curves (see Table 11.7 and left
panels in Figure 11.35 ).

- duration curves of Figure 11.35 (left

panels) are very similar, and also Table 11.7 (cross-
validation) reports similar indices of reliability. In particu-
lar, it can be seen from index P 3 in Table 11.7 that the jack-
knifed FDCs from all three models are poor fits to the
corresponding empirical curves in roughly 60% of the
cases.
When it comes to the prediction of long-term FDCs in
scarcely gauged sites

-

A series of resampling experiments was carried out to
assess the sensitivity of empirical FDCs to record length.
The main aim of these experiments was to quantify for
the same study area the reliability of estimates of the
long-term FDC based upon short records (scarcely
gauged catchments). The analysis considered 14 river
basins with at least 25 years of daily runoff (see Figure
11.32 ), and consisted of the following steps: (i) from the
n years of daily flows of the historical sample, the m

(estimation based on short

records), duration curves

reported in Figure 11.35 and the indices of Table 11.7
show that 5 years of observed runoff are generally suffi-
cient to obtain better estimates of the long-term FDCs
than those produced by the best performing regional
model. This result highlights the remarkable value asso-
ciated with observed runoff, even if they are exceptional.

the comparison of the error -

¼ n

- l + 1 consecutive sub-samples with record length equal

to l years are extracted; (ii) the empirical FDCs of each
sub-sample of record length l are constructed and com-
pared with the empirical FDC of the entire period of
record. The various comparisons of step (ii) are per-
formed for durations D [0.3, 1.0] and the results are

summarised for the study area in terms of the same
indices used for comparing the reliabilities of the three
regional approaches (see Table 11.7 and right panels in
Figure 11.35 ).

∈

Discussion
Concerning the cross-validation of the regional procedure,
the three approaches show similar levels of overall reliabil-
ity (slightly higher performance for statistical and