PUB in practice: case studies - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 325

the recession of evaporation during the dry season (see
Section 10.4.5 ). The crux of the framework is that we take
into account that the available observations and related
catchment behaviour through the chosen signatures are
uncertain and that the user does not have a conventional
calibration data set at their disposal (i.e., a concomitant and
long series of input and output data observed at

Hard statistical information: It was assumed that the
spectral density function of river flows can be constrained
by the mean

μ Q , the standard deviation σ Q and lag-1

autocorrelation ρ 1 (Q) of the river flow process. Therefore,

μ Q , ρ 1 (Q) allowed us to define a three-element

target vector

σ Q and

to resemble a spectral density objective

the function.

Monthly water balance estimates based on a monthly
auxiliary rainfall runoff model, calibrated on the old
monthly averaged records of rainfall and runoff (see
Section 6.4.2 ): This is soft hydrological information
because the limits could not be objectively defined
following the framework outlined above. This auxiliary
model has been calibrated using available monthly
ground-station rainfall data from the Global Historical
Climate Network (GHCN) in the period 1956

required time step).
The parameter inference of the framework is based on
GLUE, using limits of acceptability (Beven, 2006 ) on the
signatures to separate behavioural from non-behavioural
models. A crucial issue tackled within the framework is
how the limits of acceptability are derived in an objective
way. Winsemius et al.( 2009 ) showed that this can be done
by estimating the uncertainty in the signatures. This is done
by retrieving samples of the signature from available data
on a year-by-year basis. The samples are then transformed
to a Gaussian distribution using the normal quantile
transform (Montanari and Brath, 2004 ) and the standard
deviation used to construct a 95% confidence interval. Any
sample that stays within the confidence interval of each
signature is accepted as behavioural. We define a signature
as

73. The
model then allowed for a reconstruction of the monthly
discharges at the basin outlet for the period 2002

-

-

6, the run
time period of the daily modified HBV model. The daily
time step model can then be constrained towards reprodu-
cing (in a statistical sense) the long-term discharges pro-
vided by the monthly auxiliary model. Further information
on the derivation of the limits can be found in Winsemius
et al.( 2009 ).
Recession of evaporation in the dry season: This is soft
information because only one dry season of evaporation
estimates was available. Several targets were defined
based on the evaporation being the total dry-season evap-
oration. Furthermore, the evaporation-sensitive parameters
were constrained spatially distributed in an independent
Monte Carlo experiment. This led to a number of prelim-
inary constraints on parameters S max and l p , which are
equivalent to the active soil moisture zone (i.e., where
roots are actively transpiring) and the fraction of soil
moisture, where transpiration becomes moisture limited.
This experiment is fully described by Winsemius et al.
( 2008 ).
The derived limits of acceptability of each target value
are given in Table 11.11 . A large number of Monte Carlo
runs were performed and analysed following the frame-
work described above. In each run, all the above-shown
targets were evaluated. Only models obeying all of these
targets were accepted.

when this objective approach to defining the
limits of acceptability can be followed and

' hard '

if this
objective approach cannot be followed. In this case,
stronger assumptions on the nature of error are required
or a subjective decision needs to be made on the limits.
The inference can be performed stepwise on each signa-
ture in turn. Analysis of the intermediate results provides
the modeller with insights into which part of the parameter
space and, consequently, which outputs are well con-
strained by means of the included information and what
constraints are still lacking. The user may then decide what
information has the potential to further condition the par-
ameters and, if deemed feasible, to collect this information.
After the collection of new information, the procedure may
be repeated to update the parameter distributions with new
targets. More information about the calibration framework
is given by Winsemius et al.( 2009 ).

' soft '

Results
Chosen signatures and limits of acceptability
In order to apply the calibration framework proposed here,
after analysing the available hydrological data, the following
objectives have been identified along with the related target
values to be used to drive the parameter estimation:
Slope of

Validation
It should be clear by now that the calibration of the rainfall −

runoff model, shown in the previous sections, is fully
indirect, meaning that no concomitant time series of mod-
elled and observed discharges could be generated to per-
form a classic direct calibration. The validation carried out
here is therefore fully independent of any performed cali-
bration and hence it is a validation in the true sense: not
only have the collected records been left out

the recession limb of the hydrograph (see

Section 10.4.5 ).
Hard hydrological information: spectral properties of
non-concomitant daily river flows (Montanari and Toth,
2007 ; see Section 10.4.5 ). in the