PUB in practice: case studies - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 312

Figure 11.42. Plot of standardised
residuals vs. predicted values for the
mean flood model (PRT, fixed region
and ROI, NSW).

BGLS-FIXED REGION BGLS-ROI

3

2

1

0

-1

-2

-3

0.5 1.5 2.5 3.5

Fitted mean from BGLS

4.5 5.5 6.5

Figure 11.43. QQ-plot of the
standardised residuals vs. z score for
the skew model (PRT, fixed region,
ROI, NSW).

Skew

3
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
-3

y = 0.9874x - 0.0021
R 2 = 0.993

-3 -2 -1 0 1 2 3

y = 1.0141x + 0.0041
R 2 = 0.9941

BGLS-FIXED REGION

BGLS-ROI

Standardised residual

interval (ARI), I tc,Y is the design rainfall intensity for
duration equal to time of concentration (t c ) and Y year
ARI, rain is mean annual rainfall (mm), S1085 is the main
stream slope of the central 75% of its length, and forest is
the fraction of the basin area forested. Here t c is obtained
from t c ¼

assess model adequacy using a leave-one-out cross-valid-
ation approach.
To assess the underlying model assumptions (i.e., the
normality and homoscedasticity of residuals), diagnostic
plots of the standardised residuals vs. predicted values were
examined. The predicted values were obtained from leave-
one-out cross-validation. Figure 11.42 shows the plot for the
fixed region and ROI models to predict the first parameter of
the LP3 distribution, the mean flood. Under the assumption
of normality one would expect about 95%of the standardised
residual values to fall between ±2. For the LP3 mean flood
this is largely the case. Moreover, the residuals appear to be
homoscedastic with respect to the fitted LP3 mean flood.
Similar results were obtained for the LP3 skew, LP3 standard
deviation and flood quantile models.

area 0 : 38 , where t c is in hours and area is in
km 2 . The parameters mean, stdev and skew correspond to
the mean, standard deviation and skew of ln(Q) where Q is
the annual maximum flood discharge.
The overall performance of the Bayesian GLS regres-
sion method was evaluated using leave-one-out cross-
validation. The site of interest was left out in building the
model, so it was in effect being treated as an ungauged site.
This was repeated for all the sites considered in the study.
The relative root mean square error (RRMSE) was used to

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