Content uploaded by Martijn J. Booij
Author content
All content in this area was uploaded by Martijn J. Booij on Oct 19, 2017
Content may be subject to copyright.
Impact of climate change on river flooding assessed
with different spatial model resolutions
M.J. Booij*
Department of Water Engineering and Management, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Received 26 April 2002; revised 9 July 2004; accepted 30 July 2004
Abstract
The impact of climate change on flooding in the river Meuse is assessed on a daily basis using spatially and temporally
changed climate patterns and a hydrological model with three different spatial resolutions. This is achieved by selecting a
hydrological modelling framework and implementing appropriate model components, derived in an earlier study, into the
selected framework (HBV). Additionally, two other spatial resolutions for the hydrological model are used to evaluate the
sensitivity of the model results to spatial model resolution and to allow for a test of the model appropriateness procedure.
Generations of a stochastic precipitation model under current and changed climate conditions have been used to assess the
climate change impacts. The average and extreme discharge behaviour at the basin outlet is well reproduced by the three
versions of the hydrological model in the calibration and validation, the results become somewhat better with increasing model
resolution. The model results with synthetic precipitation under current climate conditions show a small overestimation of
average discharge behaviour and a considerable underestimation of extreme discharge behaviour. The underestimation of
extreme discharges is caused by the small-scale character of the observed precipitation input at the sub-basin scale. The general
trend with climate change is a small decrease of the average discharge and a small increase of discharge variability and extreme
discharges. The variability in extreme discharges for climate change conditions increases with respect to the simulations for
current climate conditions. This variability results both from the stochasticity of the precipitation process and the differences
between the climate models. The total uncertainty in river flooding with climate change (over 40%) is much larger than the
change with respect to current climate conditions (less than 10%). However, climate changes are systematic changes rather than
random changes and thus the large uncertainty range will be shifted to another level corresponding to the changed average
situation.
q2004 Elsevier B.V. All rights reserved.
Keywords: Climate changes; River flooding; Model resolution; Spatial scale; Appropriateness; HBV model; Meuse basin
1. Introduction
Global climate changes induced by increases in
greenhouse gas concentrations is likely to increase
temperatures, change precipitation patterns and
Journal of Hydrology 303 (2005) 176–198
www.elsevier.com/locate/jhydrol
0022-1694/$ - see front matter q2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.jhydrol.2004.07.013
* Fax: C31 53 489 5377.
E-mail address: m.j.booij@ctw.utwente.nl.
probably raise the frequency of extreme events (IPCC,
2001). These changes may have serious impacts on
society, e.g. on river deltas because of both sea level
rise and an increased occurrence of flooding events
(Jacobs et al., 2000). Flooding events may cause
enormous economical, social and environmental
damage and even loss of lives. This necessitates the
application of robust and accurate flood estimation
procedures to provide a strong basis for investments in
flood protection measures with climate change.
Flood estimation with climate change cannot be
done on a purely statistical basis, because extreme
value distributions may change in future. Therefore, a
more physically based approach should be used,
which incorporates meteorological and hydrological
information. This approach can be carried out with
analytical methods or with Monte Carlo simulation.
The first method uses simple, analytically solvable
equations, for example intensity–duration–frequency
(IDF) curves (e.g. Blo
¨schl and Sivapalan, 1997) in the
meteorological part and derived flood frequency
distributions in the hydrological part (e.g. Goel et
al., 2000). The second method involves the generation
of synthetic meteorological time series (e.g. Wilks,
1998) as input to a rainfall–runoff model (e.g. Lamb,
1999) to derive discharge series. An extreme value
distribution function can then be fitted to the peak
discharges as in the statistical approach. Diermanse
(2001) has identified two drawbacks when applying
analytical methods, i.e. the spatial heterogeneity of
inputs and processes is not incorporated, and the
interaction of different flood generating mechanisms
is not contained in these methods. One of the reasons
is that equations cannot be too complex, because they
should be solved analytically. The Monte Carlo
approach does not have this requirement and can be
used in climate change situations. Moreover, with the
latter approach an uncertainty assessment can be done
to evaluate the validity of the estimated floods with
climate change.
To use the physically based flood frequency
analysis, a selection of a meteorological model (i.e.
a precipitation model) and a river basin model should
be made. The choice of the meteorological model is
described extensively by Booij (2002a), where a
stochastic model was found to be appropriate for
generating precipitation with climate change for the
Meuse river basin (surface area about 20,000 km
2
)in
Western Europe. The results of this study and the
input of other climatological variables will be briefly
discussed here. The emphasis in this study is on the
selection of a river basin model.
A broad palette of models is available ranging from
simple, lumped black-box models to complex,
distributed models including lots of physics and
mathematics. These include empirical models, con-
ceptual models and physically based models. These
divisions are somewhat arbitrary and hybrid forms
exist in which different methods are combined.
The complexity of models does not only depend on
the model class to which they belong, but also on the
processes incorporated, the process formulations used
and the different space and time scales employed.
In general, models should be sufficiently detailed to
capture the dominant processes and natural varia-
bility, but not unnecessarily refined that computation
time is wasted or data availability is limited. It would
seem that an optimum model complexity associated
with minimum total uncertainty exists, with a balance
in uncertainties from input, model structure and
parameters. This raises the question what such an
appropriate model should look like given the specific
modelling objective and research area. More specifi-
cally, which physical processes and data should be
incorporated and which mathematical process formu-
lations should be used and at which spatial and
temporal scale, to obtain an appropriate model level.
Booij (2003) has developed a model appropriate-
ness procedure, in which subsequently dominant
processes, appropriate scales and associated appro-
priate process formulations are determined. The
emphasis has been put on the determination of the
appropriate spatial scales. The appropriate model
components derived in that study are implemented
here into an existing modelling framework to obtain
the appropriate model. Two other spatial resolutions
for the hydrological model are constructed to assess the
sensitivity of the results to spatial model resolution.
Previous studies (Middelkoop and Parmet, 1998;
Gellens and Roulin, 1998) have suggested that climate
change will result in an increase of flood frequencies
for the Meuse basin. However, they did not attempt to
simulate discharge behaviour on a daily basis using
spatially and temporally changed climate patterns.
The objective of this paper is to assess the impact
of climate change on flooding in the river Meuse on
M.J. Booij / Journal of Hydrology 303 (2005) 176–198 177
a daily basis using spatially and temporally changed
climate patterns and the three constructed hydrologi-
cal models. This objective is achieved by selecting a
hydrological modelling framework and implementing
the appropriate model components into this frame-
work (Section 2). The observed and modelled
climatological and hydrological data are briefly
described in Section 3. The estimation of the model
parameters and the model experiments are considered
in Section 4 and in Section 5 the results are presented
and discussed. Finally, the conclusions are drawn in
Section 6.
2. Selection and description of river basin model
The appropriate model components for the current
research objective have been derived by Booij
(2002a). The most important processes in the context
of climate change impacts on river flooding were
found to be precipitation, evapotranspiration, infiltra-
tion excess overland flow, saturation excess overland
flow, subsurface storm flow, subsurface flow and river
flow. The appropriate spatial model scale has been
assessed at about 10 km with a corresponding
temporal scale of 1 day (Booij, 2003). This appro-
priate model scale consists of several individual
variable scales, e.g. for land use (about 5 km) and
for extreme daily precipitation (about 20 km, see
Booij, 2002b). Surface flow can be appropriately
modelled with diffusion or kinematic wave-based
methods, whereas subsurface flow at a 10–60 km
scale can be simulated using simplified equations such
as Green–Ampt. Potential evapotranspiration should
be preferably calculated using the Penman–Monteith
equation or the Priestley–Taylor formulation if not all
the data are available.
This brief summary of the components of an
appropriate model already gives some directives
about which kind of model can be used for
implementation of these appropriate components.
Three main categories of hydrological models have
been considered in the introduction. Empirical models
are based on mathematical equations which do not
take into account the underlying physical processes
and therefore are not useful for implementation of the
appropriate model components. Physically based
models like SHE (Abbott et al., 1986) and IHDM
(Beven et al., 1987), on the other hand, incorporate
physical laws based on the conservation of mass,
momentum and energy. The governing equations
include a lot of parameters and must be solved
numerically. The high amount of parameters may
result in different parameter combinations giving
equally good output performances, which is usually
labelled as overparameterisation. The main solution is
to use more data, either through direct measurements
of parameters in the field or through measurement of
intern state variables like soil moisture contents.
Besides this overparameterisation effect, physically
based models generally incorporate too many pro-
cesses and too complex formulations at a too detailed
scale in the context of climate change and river
flooding as revealed by the appropriate components
found. Therefore, the so-called conceptual models
seem to be an attractive alternative, although they still
suffer from the overparameterisation problem.
Examples are given by Beven (1993) and Uhlenbrook
et al. (1999), who got very good model performances
for different parameter sets. Conceptual models are
usually able to capture the dominating hydrological
processes at the appropriate scale with accompanying
formulations. The conceptual models can therefore be
considered as a nice compromise between the need for
simplicity on the one hand and the need for a firm
physical basis on the other hand. A disadvantage may
be that it is generally impossible to derive the model
parameters directly from field measurements and
therefore calibration techniques must be used
(Refsgaard, 1996). Well-known conceptual models
are the Stanford watershed model (Crawford and
Linsley, 1966), the HBV model (Bergstro
¨m and
Forsman, 1973) and the Precipitation Runoff Model-
ling System—PRMS (Leavesley et al., 1983).
The next step is to choose one of the available
conceptual models for the implementation of the
appropriate model concepts. Therefore, conceptual
model intercomparisons may be used like the ones
performed by Franchini and Pacciani (1991) for seven
models and Ye et al. (1997) for three models.
However, these intercomparisons do not encompass
all important conceptual models and therefore the
model intercomparison of Passchier (1996) has been
used as primary directive for the choice of a model.
He selected 5 ‘event’ (single runoff event) models and
10 continuous hydrological models out of 31 models
M.J. Booij / Journal of Hydrology 303 (2005) 176–198178
for comparison on the basis of 7 criteria (e.g. state of
the art, application areas, level of complexity and
detail). His research objective was to select models for
rainfall–runoff modelling of the Rhine and Meuse
basin with emphasis on four specific aims, namely
land use impact modelling, climate change impact
modelling, real-time flood forecasting and physically
based flood frequency analysis. Besides these four
aims, 10 evaluation criteria (e.g. reliability, scientific
basis, scale, availability) have been used for all of the
31 models. Four continuous models [PRMS, SACRA-
MENTO (Burnash, 1995), HBV and SWMM (Huber,
1995)] and one event model (HEC-1; Feldman, 1995)
were evaluated as the best ones. These results and the
results for the four specific research aims were used to
select a few appropriate models for each of the four
research aims. The HEC-1 and HBV models were
found to be most appropriate for flood frequency
analysis, the HBV and SLURP (Kite, 1995) models
for assessment of climate change impacts on peak
discharges and the PRMS and SACRAMENTO
model for assessments of climate change impacts on
discharge regimes. It should be mentioned that HBV
only performed poorly on the criterion availability,
which means there are restrictions on its use and it is
not available online.
On the basis of this intercomparison, the HBV
model of the Swedish Meteorological and Hydro-
logical Institute has been chosen for implementation
of the appropriate model concepts and for sub-
sequently assessing the impact of climate change on
river flooding. The dominating processes precipi-
tation, evapotranspiration, subsurface flow and river
flow are represented in the model, several sub-basins
can be created to obtain the appropriate spatial scale
and simulations can be done with different time steps.
The processes infiltration excess overland flow,
saturation excess overland flow and subsurface
storm flow are represented by one fast flow com-
ponent, which was found to be sufficient for this
research objective. It may therefore be concluded that
the fast flow component can be considered as an
appropriate process instead of the separate fast flow
processes. The process formulations have approxi-
mately the same level of complexity as revealed being
appropriate from the literature analysis. For example,
surface flow is simulated by storage routing (overland
flow) and a modified version of Muskingum’s
equations (river flow) implying a kinematic or
diffusion wave type approach as recommended by
Booij (2002a). An additional advantage of the HBV
model is the large number of applications found
world-wide. It has been applied in more than 30
countries including many countries in Europe and its
applications cover basins in different climatological
and geographical regions, ranging in size from less
than 1 to more than 40,000 km
2
(Bergstro
¨m, 1995).
The HBV model is a conceptual model of river
basin hydrology which simulates river discharge
using precipitation, temperature and evapotranspira-
tion as input. The model consists of a precipitation
routine representing rainfall, snow accumulation and
snow melt, a soil moisture routine determining actual
evapotranspiration and overland and subsurface flow,
a fast flow routine representing storm flow, a slow
flow routine representing subsurface flow, a trans-
formation routine for flow delay and attenuation and a
routing routine for river flow. The model version used
is the HBV96 model (version 4.4). For a detailed
description of HBV96, the reader is referred to SMHI
(1999).
3. Observed and modelled data
3.1. Climatological data
One areally averaged temperature and one areally
averaged evapotranspiration series were used as input
into the river basin model. Observed station series
(12 for temperature and 8 for evapotranspiration)
were averaged for current climate conditions. Tem-
perature differences between current and changed
climate, simulated with the British HadCM3 general
circulation model (GCM), and a relation between
temperature change and evapotranspiration change
(Brandsma, 1995) were taken to obtain respectively
temperature and evapotranspiration series for changed
climate conditions. Precipitation for current and
changed climate conditions was modelled with a
random cascade precipitation model (see Booij,
2002a). The discrete random cascade model of Over
and Gupta (1996) has been used, because it is able to
represent non-rainy areas and it can appropriately be
adapted in rainfall–runoff modelling where a discrete
partitioning of sub-basins exists. This model
M.J. Booij / Journal of Hydrology 303 (2005) 176–198 179
comprises a temporal model for the complete region
and a spatial model for the disaggregation of this
precipitation to the appropriate scale (20 km). The
temporal model consists of a discrete first-order
four-state Markov chain determining precipitation
occurrence and a truncated two-parameter gamma
distribution describing precipitation amount. The
spatial disaggregation of the temporal precipitation
series is done using a discrete random cascade
approach with generators determined from a beta-
lognormal distribution.
The parameters of these models for current and
changed climate were determined from, respectively,
statistics of observed daily precipitation for the period
1970–1999 (39 stations) and modelled daily precipi-
tation from transient runs of three GCMs and two
RCMs (regional climate models). Only observed
precipitation series without missing data were used,
which means that half of the available number of 78
stations could not be used. The three GCMs are
CGCM1 (Boer et al., 2000), HadCM3 (Gordon et al.,
2000) and CSIRO9 (Gordon and O’Farrell, 1997) and
the two RCMs are HadRM2 (Jones et al., 1995) and
HIRHAM4 (Christensen et al., 1996). In these
models, current climate conditions are represented
by the period 1970–1999 and changed climate
conditions are represented by the period 2070–2099
with twice the current ‘equivalent’ CO
2
concentration
assuming an increase of 1% ‘equivalent’ CO
2
per
year. Part of the observed and modelled precipitation
statistics were downscaled to the appropriate spatial
scale for precipitation of 20 km. This scale is about
one-quarter of the spatial correlation length for
spatially varying precipitation fields associated with
the annual maximum of precipitation averaged over
the whole field (see Booij, 2002b). At the 20 km scale,
the bias permitted in the estimation of extreme
precipitation is about 10%. At this appropriate scale,
the precipitation model has generated precipitation as
input into the hydrological model. Two sets of five
simulations with the precipitation model were per-
formed. In the first set, all five climate models were
used to estimate average parameters for the precipi-
tation model and five different realisations of spatially
and temporally varying rainfall were generated. This
does not mean that variability and extreme values are
filtered out, but rather that a more stable and average
scenario, representing some well-known climate
models, is obtained. In the second set, each climate
model was used separately to estimate a parameter set
for the precipitation model and for each parameter set
(climate model) one realisation of spatially and
temporally varying rainfall was generated. In this
way, two sources of precipitation uncertainty can be
investigated, namely the natural stochasticity and
inter-model uncertainties. All relevant precipitation
statistics except wet day frequency for current and
changed climate were well simulated by the random
cascade model.
3.2. River basin data
Elevation, soil and land use data were used in the
set-up of the HBV-model. The digital elevation model
(DEM) data have a horizontal resolution of 1 km and
are provided by the US Geological Survey (1996).
The soil data have a horizontal resolution of about
2.5 km and originate from the European Soil Bureau
(King et al., 1994). These comprise soil texture and
soil parent material data. The land use data have a
horizontal scale of 0.25 km and are provided by the
European Environmental Agency (Bossard et al.,
2000). Daily discharge data at the basin outflow point
(Borgharen) and at four sub-basin outflow points were
employed in the simulations. More information about
the data used can be found in Booij (2003).
4. Modelling issues
4.1. Different spatial model resolutions: HBV-1,
HBV-15 and HBV-118
Different spatial model resolutions will be used to
see the effect of model resolution on the results. In this
way, a test of the appropriate model resolution can be
made. The appropriate model scale requires 225–250
sub-basins. The realisation of the schematisation for
the appropriate model is based on a digital elevation
model and finally resulted in 118 sub-basins (HBV-
118). This number of sub-basins is of the same order
of magnitude and assumed to be sufficient for
checking the appropriateness requirements. The
HBV-118 model is compared with a model consisting
of only 1 sub-basin (HBV-1) and a model with 15 sub-
basins (HBV-15) following a commonly used division
M.J. Booij / Journal of Hydrology 303 (2005) 176–198180
into the main sub-basins (RIZA, 2000). The three
different schematisations are given in Fig. 1.
4.2. Parameter estimation
In previous HBV studies, much experience in
parameter estimation has been gained and this can
be used here to derive the most important
parameters and to identify reasonable ranges of
parameter values. The studies used are summarised
in Table 1, where some important features of each
study are given. The parameter estimation consisted
of three steps:
1. determination of key parameters for calibration,
2. sensitivity analysis with key parameters to
obtain optimal parameter set for HBV-1 and
several sub-basins of HBV-15, and
3. ‘regionalisation’ of these parameters to derive
parameters for each sub-basin in HBV-15 and
HBV-118.
Fig. 1. Schematisations of the Meuse basin in (a) HBV-1 with points indicating discharge measuring stations, (b) HBV-15 and (c) HBV-118.
Table 1
HBV modelling studies
Reference Application area
(number of basins)
Number of
sub-basins
Surface area
(km
2
)
Calibration
period
Validation
period
Number of
simulations
Bergstro
¨m (1990) Sweden (1) 41 (0.3–35)!10
3
1981–1986 1987–1991
Diermanse (2001) Mosel, Germany (1) 1
a
27,030 Flood events w10
2
-SA
b
Harlin and Kung (1992) Sweden (2) 1 1370–4483 18–20 years w10
3
-MC
c
Krysanova et al. (1999) Elbe, Germany (1) 1–44 (1–81)!10
3
1981–1983 1984–1989
Lindstro
¨m et al. (1997) Sweden (7–10) 1 174–5975 10 years 10 years
Seibert (1999) Sweden (11) 1 7–950 1981–1990 w10
5
-MC
Uhlenbrook et al. (1999) Brugga, Ger. (1) 1 40 1975–1984 w10
5
-MC
Surface area indicates area of the sub-basins in the case of distributed HBV versions (number of sub-basins O1).
a
One parameter (FC) was ‘fully distributed’ into 27!10
3
different values (1 km
2
scale), precipitation gauge density and precipitation
averaging effect was assessed.
b
SA, sensitivity or similar analysis.
c
MC, Monte Carlo analysis.
M.J. Booij / Journal of Hydrology 303 (2005) 176–198 181
Steps 1 and 2 are briefly described below, step 3 is
described in the next section.
The most important and uncertain parameters
occur in the soil moisture and fast flow routine. The
main parameters in the soil moisture routine are FC
(maximum soil moisture storage in millimeter),
LP (fraction of FC above which potential evapotran-
spiration occurs and below which evapotranspiration
will be reduced) and BETA (determining the relative
contribution to runoff from a millimeter of precipi-
tation at a given soil moisture deficit). The main
parameters in the fast flow routine are a(measure of
non-linearity for fast flow; for aZ0, fast flow is the
outflow from a linear reservoir and for aO0, fast flow
becomes more and more non-linear), Q
H
(geometric
mean of mean discharge and mean annual maximum
discharge) and k
H
(recession coefficient at Q
H
).
Values and ranges of these parameters used in the
studies from Table 1 and two additional studies are
given in Table 2.
In the second step, multiple sensitivity analyses for
these parameters have been performed. Table 2 has
been used to determine the parameter ranges for
the multiple sensitivity analyses (SA) for HBV-1.
Additional univariate sensitivity analyses were done
for four sub-basins of HBV-15 (Lesse, Ourthe,
Amble
`ve and Vesdre) with overall parameter ranges
and values given in Table 2 as well.
The optimality of the model output (discharge) is
assessed in different ways, namely by applying the
Nash–Sutcliffe efficiency coefficient R
2
(Nash and
Sutcliffe, 1970), the relative volume error RVE and
the relative extreme value error REVE
R2Z1KPN
iZ1½QmðiÞKQoðiÞ2
PN
iZ1½QoðiÞK
Qo2(1)
RVE Z100 PN
iZ1½QmðiÞKQoðiÞ
PN
iZ1QoðiÞ(2)
REVEðTÞZ100 RVmðTÞKRVoðTÞ
RVoðTÞ(3)
where iis the time step, Nis the total number of time
steps, Qis the discharge and subscripts ‘o’ and ‘m’
means observed and modelled. RV(T) is the T-year
return value determined by fitting a Gumbel
Table 2
Parameter values and ranges from the studies in Table 1,Killingtveit and Sælthun (1995), SMHI (1999) and HBV-1, HBV-15 and HBV-118
Reference FC (mm) LP (–) BETA (–) a
a
(–) k
Ha
(day
K1
)Q
Ha,b
(mm day
K1
)
Bergstro
¨m (1990) 100–300 0.50–1.0 1.0–4.0
Diermanse (2001) 0–580 0.80 3.0
Harlin and Kung (1992) 50–274 0.73–1.0 1.0–5.9
Killingtveit and Sælthun (1995) 75–300 0.70–1.0 1.0–4.0
Krysanova et al. (1999) 220–391 0.70 2.0
Seibert (1999) 50–500 0.30–1.0 1.0–6.0
SMHI (1999)
c
200 0.9 2.0 1.0 0.17 3.0
Uhlenbrook et al. (1999) 100–550 0.30–1.0 1.0–5.0
HBV-1 (SA) 200–500 0.2–0.8 1.0–3.0 0.1–1.1 0.06–0.11
HBV-15 (SA) 100–400 0.2–0.8 1.0–3.0 0.8–1.1 0.08–0.15
HBV-1 (optimal values) 340 0.34 1.0 0.7 0.074 2.22
HBV-15 (optimal values)
Lesse 253 0.65 1.5 0.7 0.095 3.02
Ourthe 180 0.71 1.5 1.1 0.12 3.27
Amble
`ve 202 0.68 1.9 0.9 0.11 4.15
Vesdre 350 0.68 1.3 1.1 0.14 3.79
HBV-15 (regionalisation) 180–384 0.28–0.71 1.0–2.3 0.2–1.1 0.06–0.14 1.69–4.30
HBV-118 (regionalisation) 185–660 0.28–0.71 1.2–2.1 0.1–1.9 0.07–0.17 1.69–4.30
a
In the fast flow routine of HBV96 a,k
H
and Q
H
are used, while in older versions of HBV one or more recession coefficients k
i
were directly
used (without a). Therefore, comparisons between the fast flow routine parameters in the two versions cannot be made.
b
Q
H
can be directly determined from measured discharges and has not been calibrated.
c
Default values for HBV96.
M.J. Booij / Journal of Hydrology 303 (2005) 176–198182
distribution to annual maximum values and extra-
polating this distribution to T-year return values (20
and 100 years). Furthermore, visual inspections of the
observed and simulated hydrographs should always
accompany model experiments. Since the soil moist-
ure routine parameters particularly influence the
discharge volume, the criteria for the multiple
sensitivity analysis with FC, LP and BETA are RVE
and R
2
. On the other hand, the fast flow routine
parameters particularly affect the shape of the
hydrograph and extreme discharges and therefore R
2
and REVE are used as criteria in the bivariate
sensitivity analysis with aand k
H
.
4.3. Regionalisation
The HBV-15 and HBV-118 models cannot be
calibrated in the same way as the HBV-1 model,
because additional observed discharges for the
sensitivity analyses are only available for four sub-
basins. It is therefore necessary to determine the key
parameters of the other sub-basins in an alternative
way. The concept of ‘regionalisation’ is used for this
purpose. This involves the use of relationships
between key parameters and river basin character-
istics (e.g. land use, soil type) to assess the parameter
values for the remaining sub-basins. These relation-
ships can be established by employing the calibrated
parameters from the sensitivity analyses and the
corresponding basin characteristics or using relation-
ships from literature. Separate relationships for each
key variable or for example Hydrological Response
Units (HRUs) representing hydrologically similar
areas (e.g. Kite and Kouwen, 1992) can be used for
this purpose. The separate relationships for the five
key parameters in HBV-15 and the regionalisation for
HBV-118 are described below. The regionalisation
relationships are used to distribute the parameter
values for the sub-basins of HBV-15 around the mean
parameter values as obtained for HBV-1 and the
parameter values for the sub-basins of HBV-118
around the (eventually adjusted) mean parameter
values as obtained for HBV-15 and thus introducing
spatial variability of the parameters. The basin
characteristics used are assumed to indicate at least
the direction of variation of a particular parameter.
The soil moisture routine parameters FC and LP
are relatively scale independent (Bergstro
¨mand
Graham, 1998) and can be used at all covered scales
(w100–20,000 km
2
). This is in the same range as the
scales in Bergstro
¨m (1990). Parameter FC is the
maximum capacity of the soil to hold water and is
related to soil properties as the soil moisture content at
wilting point, the porosity and the soil depth. Here, the
FC from HBV-1 is distributed taking into account the
calibrated FC values from the four sub-basins in
HBV-15 and using the volumetric soil moisture
content at wilting point q
w
and the soil porosity f
(data on soil depths were not available)
FCwfKqw(4)
Parameter LP is the fraction of FC above which
potential evapotranspiration occurs. It is assumed to
be dependent on the volumetric soil moisture content
at wilting point q
w
and field capacity q
f
and on the soil
porosity fto account for the dependency of LP on FC
LPw
fKqw
qfKqw
(5)
Parameter BETA describes how the runoff coefficient
increases as the maximum soil moisture content FC is
approached. This parameter can be regarded more as
an index of heterogeneity than a measure of soil
properties (Bergstro
¨m and Graham, 1998). This is
because for low values runoff is gradually generated,
indicating heterogeneous conditions, whereas for high
values runoff is simultaneously generated, implying
homogeneous conditions. In general, this means for
large sub-basins with much heterogeneity smaller
values for BETA than for small sub-basins with
relatively little variability. Seibert (1999), on the other
hand, found an increase of BETA values with sub-
basin area A, although his relation was weak.
The former explanation (increasing BETA values
with decreasing area) will serve as a basis for a
BETA–area relationship, because it is physically
more plausible
BETAw1
A(6)
Parameter ais a measure of the non-linearity of the
fast flow process. Small sub-basins with steep hills
and low permeable soils will generally result in more
non-linearity in the fast flow mechanisms than large
sub-basins with flat terrains and high permeable soils.
The calibrated avalues were found to be most
M.J. Booij / Journal of Hydrology 303 (2005) 176–198 183
dependent on slope S
0
rather than on surface area or
soil type
awS0(7)
Parameter k
H
is a recession coefficient at high flow
rate Q
H
and can be approximated by estimating the
recession coefficient from an observed hydrograph at
flow rate Q
H
(SMHI, 1999). This parameter is
influenced by similar factors as aand calibrated k
H
values were found to be most dependent on slope S
0
as
well
kHwS0(8)
Results of the regionalisation are given in Fig. 2,
where regionalisation relations for the five HBV
parameters with calibrated and regionalised values are
given. The relations between the parameters and
their indicators are poor (k
H
and LP) to moderate
Fig. 2. Regionalisation relations for five HBV parameters (FC, LP, BETA, a(alpha) and k
H
) with calibrated and regionalised values for HBV-15
(see also Table 2).
M.J. Booij / Journal of Hydrology 303 (2005) 176–198184
(FC and BETA) and reasonable (a). It should be noted
that only four calibrated values for each parameter
(from four sub-basins) have been used to estimate the
regionalisation relations and thus the parameters of
the remaining eleven sub-basins. This introduces a lot
of uncertainty, which may be amplified by extrapol-
ation of the regionalisation relations outside their
calibrated ranges (in particular for LP and a).
Therefore, care should be taken in applying these
relations to other areas.
The regionalisation for seven variables (addition-
ally Q
H
and Q
perc
) in HBV-118 is described in detail
by Van der Wal (2001). He used only one indicator
based on the slope, the soil texture and the soil parent
material representing the reaction behaviour of the
sub-basin to distribute the seven key parameters
among the 118 sub-basins. For this purpose, the three
characteristics were each divided into three cat-
egories representing a fast, medium or slow reaction
behaviour. For example, areas with slopes larger than
3.6% are characterised as fast, between 1.4 and 3.6%
as medium and smaller than 1.4% as slow. The
resulting categorisation for each characteristic was
quantified using three values K1 (fast), 0 (medium)
and 1 (slow). Finally, the indicator for each sub-basin
was obtained by summing the values for each
characteristic and thus obtaining a range for this
indicator between K3 and 3. The indicator has been
used to vary the parameter values of the HBV-118
sub-basins around the (eventually adjusted) mean
parameter values as obtained for HBV-15 through a
similar calibration procedure as explained in Section
4.2. The resulting parameter ranges are given in
Table 2.
4.4. Model experiments
The impact of climate change on river flooding is
assessed with HBV-1, HBV-15 and HBV-118 in four
steps. These four steps are the calibration described
above, the validation, the simulation under current
climate conditions with synthetic precipitation and the
simulation under changed climate conditions with
synthetic precipitation. A description and summary of
the climatic input for the four steps are summarised in
Tables 3 and 4, respectively. Information about the
model experiments with HBV-1, HBV-15 and HBV-
118 is given in Table 5.
Table 3
Description of climatic input for model experiments
Precipitation Temperature Evapotranspiration
Calibration Stations (39) 1970–1984 Stations (12)1970–1984 Stations (8) 1970–1984
Validation Stations (39) 1985–1996 Stations (12) 1985–1996 Stations (8) 1985–1996
Current climate Random Cascade Model (76), 30 years, 5 realisations
a
Stations (12) 1967–1996 Stations (8) 1967–1996
Changed climate Random Cascade Model (76), 30 years, 10 realisations
b
StationsCchange (12)
1967–1996
StationsCchange (8)
1967–1996
a
Five realisations using the same precipitation model parameters for HBV-1 and HBV-15, one realisation for HBV-118.
b
Five realisations using the same precipitation model parameters (natural stochasticity) and five realisations using parameters derived from
each model separately (3 GCMs and 2 RCMs; inter-model uncertainty) for HBV-1 and HBV-15, one realisation for HBV-118.
Table 4
Summary of climatic input for model experiments
Precipitation (20 km scale) Temperature (areally averaged) Evapotranspiration (areally averaged)
Average (mm) Standard
deviation (mm)
Average (8C) Standard
deviation (8C)
Average (mm) Standard
deviation (mm)
Calibration 2.6 4.8 8.7 6.4 1.8 1.6
Validation 2.7 5.2 9.0 6.7 1.9 1.7
Current climate 2.7–2.9 4.9–5.1 8.8 6.5 1.8 1.6
Changed climate
Stochasticity 2.7–3.0 5.7–6.0 12.5 7.4 2.1 1.9
Inter-model
uncertainty
2.1–2.9 5.2–6.4
M.J. Booij / Journal of Hydrology 303 (2005) 176–198 185
The point precipitation series from stations are
interpolated using Thiessen polygons. These areally
averaged precipitation series are combined with the
HBV-1, HBV-15 and HBV-118 schematisations from
Fig. 1 to obtain areally averaged precipitation series
for 1, 15 and 118 sub-basins, respectively. The areally
averaged random cascade precipitation series are
combined with the HBV-1, HBV-15 and HBV-118
schematisations in the same way.
5. Climate change impact on river flooding
in the Meuse basin
5.1. Calibration
The optimal values for the soil moisture routine
parameters were obtained by requiring that RVE
should be less than 1% and R
2
should be as high as
possible. The optimum values are poorly defined and
are given in Table 2. A similar approach has been
conducted for the fast flow routine parameters by
requiring that REVE should be less than 10% and R
2
should be as high as possible. The resulting aand k
H
values are given in Table 2 as well. During these
sensitivity analyses, the values of the other (less
important) parameters were kept at pre-determined
values based on univariate sensitivity analyses and the
studies mentioned in Table 1. The calibrated par-
ameter values are generally within the ranges from
other studies. The value for the parameter LP is low,
which means that potential evapotranspiration occurs
already under relatively dry conditions. Although this
could yield an overestimation of the total evapotran-
spiration, observed and simulated water balances
compared favourably. The optimal values of the soil
moisture and fast flow routine parameters for the four
sub-basins (Lesse, Ourthe, Amble
`ve and Vesdre) are
summarised in Table 2 as well.
The optimal parameter values for HBV-1 and the
four sub-basins of HBV-15 together with q
w
,q
f
and f-
values based on soil texture (Rawls et al., 1993), S
0
values based on elevation data and Avalues are used
to quantify the regionalisation relationships from
Eqs. (4)–(8). Finally, these equations have been used
to determine the parameters values for the remaining
11 sub-basins (see Table 2).
Next, the results obtained with the chosen
parameter values for HBV-1, HBV-15 and HBV-118
can be compared. Therefore, Fig. 3 shows the daily
discharge at Borgharen for one arbitrary year (1984)
with a considerable peak for the observed and HBV-1,
HBV-15 and HBV-118 simulated situation. The
observed hydrograph is simulated realistically by all
three models, although the performance becomes
somewhat better with an increasing number of sub-
basins. Fig. 4 gives the extreme value distribution of
annual extremes for the observed and simulated
series. Most striking feature is the good simulation
by HBV-15 and HBV-118, but also by HBV-1. The
resulting criteria R
2
, RVE [by means of average] and
REVE [by means of RV(100)] together with the
standard deviation of daily discharges are summarised
in Table 6. This table mainly confirms the findings
from the visual inspection; the good simulation of
average discharge behaviour illustrated by high R
2
values and the proper simulation of extremes
(difference is negligible for HBV-15 and HBV-118).
5.2. Validation
In the validation, the parameter values are kept
the same as in the calibration, but the simulations
are repeated with other, independent input series
Table 5
Model experiments with HBV-1, HBV-15 and HBV-118
HBV-1 HBV-15 HBV-118
Calibration Discharge (1) 1970–1984 Discharge (5), regionalisation, 1970–1984 Discharge (5), regionalisation, 1970–1984
Validation Discharge (1) 1985–1996 Discharge (5) 1985–1996 Discharge (5) 1985–1996
Current climate Discharge (1), 30 years,
5 realisations
Discharge (5/15), 30 years,
5 realisations
Discharge (5/118), 30 years,
1 realisation
Changed climate Discharge (1), 30 years,
5 realisations
Discharge (5/15), 30 years,
10 realisations
Discharge (5/118), 30 years,
1 realisation
M.J. Booij / Journal of Hydrology 303 (2005) 176–198186
(see Tables 3 and 5). The results are shown in Figs. 5
and 6 and Table 6.Fig. 5 shows the daily discharge at
Borgharen for December 1993 through March 1995
with two considerable peaks for the observed and
HBV-15 and HBV-118 simulated situation. The
observed hydrograph is simulated realistically by the
two models, even better than in the calibration. Fig. 6
gives the extreme value distribution of annual
extremes for the observed and simulated series.
Again the extreme value distribution is well simulated
by all models. The resulting criteria R
2
, RVE and
REVE and the standard deviation of daily discharges
at Borgharen are summarised in Table 6. Addition-
ally, Table 7 gives R
2
,RVEandREVEfor
the calibration and validation for the four sub-basins.
The differences between average discharge behaviour
of the sub-basins modelled by HBV-15 and HBV-118
are small. Extreme discharges are generally better
simulated by HBV-118 in the calibration, where in the
validation HBV-15 is a bit better. This also shows that
the regionalisation method only slightly influences the
model performance, although this performance is
dependent on, e.g. the spatial resolution of precipi-
tation as well. More discharge measurements could
possibly show in future the advantages and/or
disadvantages of HBV-118 with respect to HBV-15
as well as the preference of one regionalisation
method over another.
Fig. 3. Observed and simulated discharge for 1984 for (a) HBV-1, (b) HBV-15 and (c) HBV-118.
M.J. Booij / Journal of Hydrology 303 (2005) 176–198 187
5.3. Synthetic current climate
The results of the random cascade model for the
current climate are used as input in HBV-1, HBV-15
and HBV-118 to simulate daily discharge series for
the current climate (see Table 5). Fig. 7 shows
the cumulative frequency distribution of daily dis-
charges for the observed series and five realisations
with HBV-1 and HBV-15 and one realisation with
HBV-118 for current climate. The only realisation
with HBV-118 is the maximum one in terms of HBV-
15 extreme discharges. Fig. 8 gives the extreme value
Fig. 4. Gumbel plot for annual maximum discharges for the period 1970–1984, observed and simulated with HBV-1, HBV-15 and HBV-118.
Regression lines for observed (solid), HBV-1 simulated (dotted), HBV-15 simulated (dashed) and HBV-118 simulated (dashed-dotted) are
also shown.
Table 6
Results from calibration, validation and simulations with precipitation model for current and changed climate
R
2
(–) Average Standard deviation RV(100)
Value
(m
3
s
K1
)
RVE
a
(%) Value
(m
3
s
K1
)
Diff.
a
(%) Value
(m
3
s
K1
)
REVE
a
(%)
Calibration Observed – 222 – 252 – 2929 –
HBV-1 0.85 222 0 251 0 2719 K7
HBV-15 0.87 231 C4 270 C7 2977 C2
HBV-118 0.88 224 C1 255 C1 2896 K1
Validation Observed – 235 – 300 – 3703 –
HBV-1 0.91 238 C1 307 C2 3817 C3
HBV-15 0.92 244 C4 324 C8 4008 C8
HBV-118 0.93 239 C2 303 C1 3772 C2
Synthetic
current climate
Observed – 229 – 275 – 3292 –
HBV-1 – 232–266 C1/C16 265–296 K4/C8 2553–3236 K22/K2
HBV-15 – 237–271 C3/C18 275–306 0/C11 2621–3226 K20/K2
HBV-118 – 244 C6 264 K4 2958 K10
Synthetic
changed
climate
HBV-1 – 204–264 K12/K1 253–334 K5/C13 2426–3565 K5/C10
HBV-15 – 207–266 K13/K2 260–344 K5/C12 2591–3661 K1/C13
HBV-118 – 258 C6 314 C19 3354 C13
Uncertainty HBV-15 – 208–244 K12/K10 270–299 K2/K2 2551–3530 K3/C9
a
Difference (diff.) in % with respect to the corresponding observed (calibration, validation, synthetic current climate) or simulated (synthetic
changed climate) value.
M.J. Booij / Journal of Hydrology 303 (2005) 176–198188
distribution of annual extremes for the observed and
simulated series. The five realisations are quantified in
Table 6 by means of the average and standard
deviation of daily discharges and the 100-year return
value RV(100).
The general trend from these figures and table is a
small overestimation of the average and standard
deviation (variability) of discharges and a consider-
able underestimation of extreme discharges in the
case of HBV-1 and HBV-15. HBV-118 slightly
Fig. 5. Observed and simulated discharge at Borgharen for December 1993–March 1995 for (a) HBV-15 and (b) HBV-118.
Fig. 6. Gumbel plot for annual maximum discharges for the period 1985–1996 as observed and simulated with HBV-1, HBV-15 and HBV-118.
Regression lines for observed (solid), HBV-1 simulated (dotted), HBV-15 simulated (dashed) and HBV-118 simulated (dashed-dotted) are
shown as well.
M.J. Booij / Journal of Hydrology 303 (2005) 176–198 189
Table 7
Results for tributaries from calibration and validation of HBV-15 and HBV-118
Calibration Validation
R
2
(–) Average
RVE
a
(%)
RV(100)
REVE
a
(%)
R
2
(–) Average
RVE
a
(%)
RV(100)
REVE
a
(%)
Lesse HBV-15 0.88 0 K10 0.89 C7K23
HBV-118 0.88 C1C2 0.91 C9K21
Ourthe HBV-15 0.80 C1K10 0.86 C4K3
HBV-118 0.87 C1K4 0.92 C4C4
Amble
`ve HBV-15 0.80 C1K12 0.87 C5K2
HBV-118 0.78 C3K2 0.84 C7C7
Vesdre HBV-15 0.80 0 K39 0.76 K4C1
HBV-118 0.77 C2K23 0.76 0 C18
a
Difference in % with respect to the corresponding observed value.
Fig. 7. Cumulative frequency distribution P(X!x) for daily discharges up to 1500 m
3
s
K1
for 30 years under current climate conditions for
(a) observed series and five precipitation realisations with HBV-1, (b) observed series and five precipitation realisations with HBV-15 and
(c) observed series and one precipitation realisation with HBV-118.
M.J. Booij / Journal of Hydrology 303 (2005) 176–198190
underestimates the discharge variability and under-
estimates extreme discharges with respect to HBV-15.
However, a general tendency for HBV-118 is hard to
identify, because only one precipitation realisation
has been used for HBV-118. The small overestimation
of average discharge behaviour can be explained by
the small overestimation of average precipitation
behaviour by the random cascade model (see Booij,
2002a; on average C8% for mean precipitation and
C4% for the standard deviation of daily precipi-
tation). However, the underestimation of extreme
discharges by HBV-1 and HBV-15 cannot be
explained by the statistics of the precipitation input.
The random cascade model rather overestimates than
underestimates extreme precipitation.
The main cause of this underestimation can be
found in the transformation of observed precipitation
at the point scale and simulated precipitation at the
20 km scale to areally averaged precipitation at the
basin (HBV-1, w150 km) or sub-basin scale (HBV-
15, w40 km and HBV-118, w13 km). This is
illustrated in Table 8 where the important statistics
from the precipitation model results at the HBV-15
and HBV-118 sub-basin scales for the observed
Fig. 8. Gumbel plot for annual maximum discharges for a 30-year period as observed (1970–1999) and simulated with five precipitation
realisations for HBV-1 and HBV-15 and one precipitation realisation for HBV-118 under current climate conditions. Only the minimum and
maximum of the five HBV-1 and HBV-15 realisations are shown. Regression lines for observed (solid), HBV-1 simulated (dotted), HBV-15
simulated (dashed) and HBV-118 simulated (grey dashed-dotted) are given as well.
Table 8
Daily precipitation statistics at the sub-basin scale for observed and random cascade modelled current climate
Sub-basin scale statistics HBV-15 HBV-118
Observed Modelled Diff. (%)
a
Observed Modelled Diff. (%)
a
Average (mm) 2.6 2.7 C4 2.6 2.7 C4
Standard deviation (mm) 4.8 4.6 K4 5.0 4.9 K2
Wet day frequency (–) 0.57 0.59 C3 0.53 0.51 K4
Temporal correlation cf. lag-1 (–) 0.31 0.29 K4 0.28 0.27 K4
20-year return value (mm) 53.6 51.7 K4 57.6 55.4 K4
100-year return value (mm) 66.3 63.7 K4 71.5 68.4 K4
5-day 100-year return value (mm) 136 109 K20 139 117 K16
8-day 100-year return value (mm) 173 139 K19 174 147 K15
10-day 100-year return value (mm) 193 158 K18 194 164 K15
a
Difference in % between modelled and observed statistic.
M.J. Booij / Journal of Hydrology 303 (2005) 176–198 191
and simulated situation (one realisation with
REVEzK20%) are summarised. In particular, the
5-day, 8-day and 10-day 100-year precipitation return
values are underestimated by the precipitation model
at the HBV-15 (by about 20%) and HBV-118 (by
about 15%) sub-basin scale, but also 1-day extreme
values and the standard deviation are underestimated
compared to the 20 km scale (where the precipitation
model mainly overestimates these statistics, see also
Booij, 2002a). This underestimation of generated
extreme precipitation at the sub-basin scale is in fact
an overestimation of observed extreme precipitation
at the sub-basin scale. Namely, the observed 5-day,
8-day and 10-day 100-year precipitation return values
in Table 8 are approximately the corresponding
observed point values.
The overestimation of the standard deviation
(variability) and extreme behaviour of observed
precipitation is explained by the fact that for a lot of
sub-basins, in particular for HBV-118, only one or
two stations are used as precipitation input into the
model. This results in observed input at the point scale
compared to simulated input at the (correct) 20 km
scale. Observed precipitation is considered as areally
averaged precipitation, but is actually point precipi-
tation. Consequently, observed precipitation shows
too much variability and extreme behaviour, which
will have implications for the parameter estimation
during calibration. Parameters are estimated under too
variable and extreme conditions, which may have
consequences for simulations under changed con-
ditions (e.g. land use and climate change). Unfortu-
nately, insufficient precipitation stations are available
to assess the areally averaged sub-basin scale
precipitation in a right way and therefore this
overestimation has occurred. The overestimation of
precipitation variability and extreme behaviour seems
to be common practice, because in most rainfall–
runoff modelling studies station precipitation is used
as input in stead of areally averaged precipitation at
the sub-basin scale.
The difference between HBV-15 and HBV-118 in
Table 8 (K20 and K15%) can be explained by the
fact that modelled precipitation is less averaged when
transformed to the HBV-118 scale than when
transformed to the HBV-15 scale. However, the
difference in discharge 100-year return values for
the HBV-15 and HBV-118 model using the same
(maximum) precipitation realisation (K2 and K10%,
respectively in Table 6) cannot be explained by these
differences in precipitation at the sub-basin scale. This
difference may be caused by differences in regiona-
lisation techniques and related differences in par-
ameter values (e.g. FC values in Table 2 cover a much
broader range in the case of HBV-118). In this way, it
gives some information about uncertainties due to
parameter estimation, but it does not give information
about uncertainties due to differences in processes
incorporated or process formulations. Nevertheless,
the calibration and validation results from HBV-15
and HBV-118 were comparable. Fig. 8 shows a large
difference (range) between the minimum and maxi-
mum of the modelled realisations (about 20%), which
illustrates the large impact of the stochasticity of the
precipitation process.
5.4. Synthetic changed climate
The climate change situation will be considered by
comparing the results obtained with input from the
precipitation model for current and changed climate
conditions. Fig. 9 shows the cumulative frequency
distribution of daily discharges for five realisations
with HBV-1 and HBV-15 and one realisation with
HBV-118 for the current and changed climate. Fig. 10
gives the 20-year and 100-year return values for the
current and changed climate. Quantitative figures are
shown in Table 6.
The general trend is a small decrease of the average
discharge and a small increase of the standard
deviation of the discharge (variability) and extreme
discharges with climate change. The decrease of the
average discharge has to do with the slight increase of
modelled average precipitation with climate change
(about 5%) combined with the considerable increase
of (potential) evapotranspiration (on average about
15%, see Table 4). The increase in discharge
variability and extreme discharges is the result of
the considerable increase of precipitation variability
and extreme precipitation (10–20%), but is less than
would be expected on the basis of the changes in
precipitation behaviour. There are even precipitation
realisations which have resulted in a small decrease of
the extreme value distribution for annual discharges
derived from both HBV-1 and HBV-15. As a
consequence of this, the range in extreme values has
M.J. Booij / Journal of Hydrology 303 (2005) 176–198192
increased with respect to the simulations for current
climate conditions. The HBV-118 model shows a
similar increase in 20-year and 100-year return values
with climate change as the corresponding realisations
for HBV-1 and HBV-15.
When using the HBV model for the assessment of
climate change impacts, it has been assumed that the
model is valid outside its calibration conditions. This
is partly checked in the validation step, where the
climatic input is more variable (see Table 4) resulting
in more variable and extreme discharge behaviour
(e.g. the 100-year return value in the validation period
is 25% larger than in the calibration period). However,
the HBV model versions showed even better results in
the validation step than in the calibration step.
Moreover, simulated extremes with climate change
are of the same order of magnitude as the extremes in
the calibration and validation periods. It is not
expected that rainfall–runoff processes in the HBV
model and corresponding parameters will change
considerably during these climate change conditions.
Obviously, other possible changes such as land use
changes or river restoration may require model and/or
parameter changes, but this will also be the case for
current climate conditions.
5.5. Uncertainties
The uncertainty in extreme discharges with climate
change is caused by various sources of uncertainty of
which the most important are: climatological input
(precipitation, evapotranspiration), model structure,
parameter values and extrapolation to large return
periods.
Fig. 9. Cumulative frequency distribution P(X!x) for daily discharges up to 1500 m
3
s
K1
under current and changed climate conditions for five
realisations of 30 years for (a) HBV-1 and (b) HBV-15 and one realisation of 30 years for (c) HBV-118.
M.J. Booij / Journal of Hydrology 303 (2005) 176–198 193
The uncertainty in the modelled standard deviation
of precipitation and extreme precipitation with
climate change was found to be large in Booij
(2002b), 30–50%. This uncertainty consisted of
climate model errors (differences between observed
and modelled climate), inter-model differences and an
estimation of climate forcing uncertainties. The effect
of inter-model differences on extreme river discharges
has been roughly assessed by using the results of each
individual climate model (CGCM1, HadCM3,
CSIRO9, HadRM2 and HIRHAM4) for climate
change conditions to assess a parameter set for the
random cascade precipitation model. These parameter
sets have been used to generate for each climate
model one realisation which served as input into the
HBV-15 model. The results are given in Fig. 11,
Fig. 10. Discharge 20-year (RV20) and 100-year (RV100) return values from a 30-year period as simulated with five precipitation realisations
for HBV-1 and HBV-15 and one precipitation realisation for HBV-118 under current and changed climate conditions. Only the minimum and
maximum of the five HBV-1 and HBV-15 realisations are shown.
Fig. 11. Gumbel plot for annual maximum discharges for a 30-year period as simulated with five precipitation realisations derived from the
average of the five climate models and five precipitation realisations derived from the five individual climate models under changed climate
conditions for HBV-15. Only the minimum and maximum of each of the five realisations are shown. Regression lines for the ‘realisations’
(dashed) and realisations from ‘individual climate models’ (dotted) are given as well.
M.J. Booij / Journal of Hydrology 303 (2005) 176–198194
where the minimum and maximum of the five
realisations of annual maximum discharges for a 30-
year period are given. The results of Fig. 10 for HBV-
15 under climate change conditions are shown as well
for comparison. These results can be regarded as
uncertainties in extreme discharges due to the
stochasticity of the precipitation process. It is found
in Fig. 11 that these uncertainties are even larger than
the uncertainties in extreme discharges due to inter-
model differences. The uncertainties due to individual
climate model errors are unimportant here, because
the climate model results have only been used to
derive relative changes in observed precipitation
statistics. It can be expected that the uncertainty in
extreme discharges due to climate forcing uncertain-
ties is at least as large as the two uncertainties in
Fig. 11.
The differences between the results of HBV-1,
HBV-15 and HBV-118 give some indication about
uncertainties in extreme discharges due to uncertain-
ties in model structure, although these differences are
mainly scale related. Small differences between
results of these different models have been found
(5–10%) and therefore this uncertainty source seems
to be relatively unimportant.
The effect of different key parameter values on the
results was investigated in the calibration phase of the
model, but mainly using HBV-1. In particular,
variations of the parameters determining the fast
runoff response (aand k
H
) can have significant
consequences for extreme discharges. For example,
a 50% change of aresults in approximately a 8%
change in the 100-year return value. However, this
reduction of uncertainty in parameters by the hydro-
logical model (50–8%) is much larger than the
reduction of uncertainty in precipitation statistics by
the hydrological model (e.g. 15–6%), i.e. the model
sensitivity to changes in parameters is much smaller
than the sensitivity to changes in precipitation. The
uncertainty in aand k
H
is estimated at 20% resulting
in a much smaller impact on the output uncertainty
than for example the impact of precipitation
uncertainty.
The uncertainty in extreme discharges due to
extrapolation can be roughly assessed by using
formulations, e.g. as proposed by Shaw (1983). The
uncertainty in the estimation of the 100-year return
value is 20% (one-sided) using a 90% confidence
interval and employing a 30-year series. The uncer-
tainty is 25% when using a 95% confidence interval.
This uncertainty can only be reduced by employing
longer time series as can be done for the observed
series (about 90 years, 12 and 15% uncertainty). This
cannot be performed with respect to the modelled
series for current and changed climate, because the
hydrological model needs to be calibrated with a
sufficient number of precipitation series of sufficient
length. In this respect, the 30-year series currently is
the maximum simulation length which can be used
without arriving at a too coarse spatial precipitation
scale. Other extreme value distributions (GEV,
Pearson type-III) may slightly reduce uncertainties
due to extrapolation.
Overall, the uncertainties in extreme discharges
due to precipitation errors and extrapolation errors
seem to be more important (more than 20 and about
20%, respectively) than uncertainties due to hydro-
logical model errors and parameter estimation errors.
These uncertainties should be quadratically summed,
because of the general random character of the
uncertainties resulting in an uncertainty of at least
30–40%.
6. Conclusions
An appropriate river basin model has been
constructed by implementing the appropriate model
components derived by Booij (2003) into the existing
modelling framework HBV. Additionally, two other
spatial resolutions for the hydrological model have
been set up to evaluate the sensitivity of the model
results to model resolution and to allow for a test of
the model appropriateness procedure. The supposedly
appropriate model has 118 sub-basins (HBV-118) and
the additional models have 1 and 15 sub-basin(s)
(HBV-1 and HBV-15). As far as possible, the three
models were calibrated and validated with equal data
series. Generations of a stochastic precipitation model
under current and changed climate conditions have
been used to assess the climate change impacts.
The average and extreme discharge behaviour at
the basin outlet (Borgharen) is well reproduced by the
three models in the calibration and validation, the
results become somewhat better with increas-
ing model resolution. The differences between
M.J. Booij / Journal of Hydrology 303 (2005) 176–198 195
the average discharge behaviour of the sub-basins
modelled by the two distributed models are small.
Extreme discharges are generally better simulated by
HBV-118 in the calibration, where in the validation
HBV-15 is somewhat better. The model results with
synthetic precipitation under current climate con-
ditions show a small overestimation of average
discharge behaviour and a considerable underestima-
tion of extreme discharge behaviour. The under-
estimation of extreme discharges cannot be explained
by the statistics of the synthetic precipitation input,
but is caused by the observed precipitation input at the
sub-basin scale. In most cases, this precipitation is not
an areally averaged quantity, but rather a point
quantity resulting in an overestimation of the standard
deviation (variability) and extreme behaviour of
observed precipitation at the sub-basin scale com-
pared to the generated precipitation. This seems to be
a very frequently occurring problem, which can be
dealt with by increasing the density of precipitation
stations in a river basin in an efficient manner.
The general trend with climate change is a small
decrease of the average discharge and a small increase
of the standard deviation of the discharge (variability)
and extreme discharges. The range in extreme
discharges for climate change conditions has
increased with respect to the simulations for current
climate conditions. This range results both from the
stochasticity of the precipitation process and the
differences between the climate models. Other
uncertainties include those related to the river basin
model structure, the parameter values and the
extrapolation to large return periods. Overall, it
appeared that the uncertainties in extreme discharges
due to precipitation errors and extrapolation errors are
more important than uncertainties due to hydrological
model errors and parameter estimation errors. The
total uncertainty is estimated at more than 40%. This
problem of uncertainty associated with model out-
comes is a phenomenon common to all scientific areas
where approximations of reality by means of models
are of interest. Numerous studies have assessed the
different uncertainties (e.g. Uhlenbrook et al., 1999;
Visser et al., 2000), but apparently no serious attempts
have been made to evaluate the whole uncertainty
cascade associated with the impact of climate change
on river flooding. Given the complexity of in
particular GCMs this seems to be very difficult if
not impossible to do, but at least some range of
possible outcomes should accompany a climate
impact study (e.g. Carter et al., 1999). Here, the
uncertainty in river flooding with climate change
(over 40%) is much larger than the change with
respect to current climate conditions (less than 10%).
However, climate changes are systematic changes
rather than random changes and thus the uncertainty
range will be shifted to another level corresponding to
the changed average situation. Therefore, a certain
confidence can be placed upon the direction of the
change, provided that no ‘surprises’ such as the
collapse of the thermohaline circulation in the North
Atlantic (Ganopolski et al., 1998) or the disintegration
of the West Antartic Ice Sheet (Oppenheimer, 1998)
will occur.
Acknowledgements
The daily station climatological data for Belgium
and for France have been provided by respectively
Luc Debontridder from the KMI (Belgian Royal
Meteorological Institute) and Christophe Dehouck
from Me
´te
´o France. The daily HadCM3GGa1 and
HadRM2 data have been kindly supplied by David
Viner of the Climate Impacts LINK Project (DETR
Contract EPG 1/1/68) on behalf of the Hadley Centre
and U.K. Meteorological Office. The daily CGCM1
data have been acquired from the Canadian Centre for
Climate Modelling and Analysis. The daily CSIRO9
data have been kindly provided by Janice Bathols of
CSIRO Atmospheric Research. Ole Bøssing Chris-
tensen of the Climate Research Division of the Danish
Climate Center prepared and helped a lot with the
daily HIRHAM4 data. Bob Jones of the European Soil
Bureau and Malene Bruun of the European Environ-
mental Agency kindly supplied the soil and land use
data, respectively. Eric Sprokkereef of RIZA gave the
essential Meuse basin data and Joop Gerretsen of
Rijkswaterstaat Limburg made the discharge data
available. Sten Bergstro
¨m of the Swedish Meteor-
ological and Hydrological Institute kindly provided
the HBV model. Koen van der Wal of the University
of Twente contributed a lot by taking care of the
HBV-118 simulations. The comments of Kees
Vreugdenhil of the University of Twente and three
M.J. Booij / Journal of Hydrology 303 (2005) 176–198196
anonymous reviewers helped to improve the manu-
script substantially.
References
Abbott, M.B., Bathurst, J.C., Cunge, J.A., O’Connell, P.E.,
Rasmussen, J.L., 1986. An introduction to the European
hydrological system—Syste
`me Hydrologique Europeen, SHE.
2. Structure of a physically-based, distributed modelling system.
J. Hydrol. 87, 61–77.
Bergstro
¨m, S., 1990. Parameter values for the HBV model in
Sweden (in Swedish). Technical Report no. 28, SMHI,
Norrko
¨ping.
Bergstro
¨m, S., 1995. The HBV model. In: Singh, V.P. (Ed.),
Computer Models of Watershed Hydrology. Water Resources
Publications, Highlands Ranch, pp. 443–476.
Bergstro
¨m, S., Forsman, A., 1973. Development of a conceptual
deterministic rainfall–runoff model. Nord. Hydrol. 4, 147–170.
Bergstro
¨m, S., Graham, L.P., 1998. On the scale problem in
hydrological modelling. J. Hydrol. 211, 253–265.
Beven, K., 1993. Prophecy, reality and uncertainty in distributed
hydrological modelling. Adv. Water Resour. 16, 41–52.
Beven, K.J., Calver, A., Morris, E.M., 1987. The Institute of
Hydrology distributed model. Technical Report 98, Institute of
Hydrology, Wallingford.
Blo
¨schl, G., Sivapalan, M., 1997. Process controls on regional flood
frequency: coefficient of variation and basin scale. Water
Resour. Res. 33, 2967–2980.
Boer, G.J., Flato, G.M., Ramsden, D., 2000. A transient climate
change simulation with greenhouse gas and aerosol forcing:
projected climate to the twenty-first century. Clim. Dynam. 16,
427–450.
Booij, M.J., 2002a. Appropriate modelling of climate change
impacts on river flooding. PhD thesis, University of Twente,
Enschede, ISBN: 90-365-1711-7.
Booij, M.J., 2002b. Extreme daily precipitation in Western Europe
with climate change at appropriate spatial scales. Int.
J. Climatol. 22, 69–85.
Booij, M.J., 2003. Determination and integration of appropriate
spatial scales for river basin modelling. Hydrol. Process. 17,
2581–2598.
Bossard, M., Steenmans, Ch., Feranec, J., Otahel, J., 2000. The
revised and supplemented Corine land cover nomenclature.
Technical Report 38, European Environment Agency,
Copenhagen.
Brandsma, Th., 1995. Hydrological impact of climate change: a
sensitivity study for the Netherlands. PhD thesis, Delft
University of Technology, Delft.
Burnash, R.J.C., 1995. The NWS river forecast system—catchment
modeling. In: Singh, V.P. (Ed.), Computer Models of Watershed
Hydrology. Water Resources Publications, Highlands Ranch,
pp. 311–366.
Carter, T.R., Hulme, M., Lal, M., 1999. Guidelines on the use of
scenario data for climate impact and adaptation assessment.
Version 1, Technical Report, IPCC-TGCIA, Norwich.
Christensen, J.H., Christensen, O.B., Lopez, P., Meijgaard, E., van
and Botzet, M., 1996. The HIRHAM4 regional atmospheric
climate model. Scientific Report 96-4, Danish Meteorological
Institute, Copenhagen.
Crawford, N.H., Linsley, R.K., 1966. Digital simulation in
hydrology—Stanford watershed model IV. Technical Report
39, Stanford University, Stanford.
Diermanse, F.L.M., 2001. Physically based modelling of rainfall–
runoff processes. PhD thesis, Delft University Press, Delft.
Feldman, A.D., 1995. HEC-1 flood hydrograph package. In:
Singh, V.P. (Ed.), Computer Models of Watershed Hydrol-
ogy. Water Resources Publications, Highlands Ranch,
pp. 119–150.
Franchini, M., Pacciani, M., 1991. Comparative analysis of several
conceptual rainfall–runoff models. J. Hydrol. 122, 161–219.
Ganopolski, A., Rahmstorf, S., Petoukhov, V., Claussen, M., 1998.
Simulation of modern and glacial climates with a coupled global
model of intermediate complexity. Nature 391, 351–356.
Gellens, D., Roulin, E., 1998. Streamflow response of Belgian
catchments to IPCC climate change scenarios. J. Hydrol. 210,
242–258.
Goel, N.K., Kurothe, R.S., Mathur, B.S., Vogel, R.M., 2000. A
derived flood frequency distribution for correlated rainfall
intensity and duration. J. Hydrol. 228, 56–67.
Gordon, H.B., O’Farrell, S.P., 1997. Transient climate change in the
CSIRO coupled model with dynamic sea ice. Mon. Weather
Rev. 125, 875–907.
Gordon, C., Cooper, C., Senior, C., Banks, H., Gregory, J.,
Johns, T., Mitchell, J., Wood, R., 2000. The simulation of
SST, sea ice extents and ocean heat transports in a version of the
Hadley Centre coupled model without flux adjustments. Clim.
Dynam. 16, 147–168.
Harlin, J., Kung, C.-S., 1992. Parameter uncertainty and simulation
of design floods in Sweden. J. Hydrol. 137, 209–230.
Huber, W.C., 1995. EPA storm water management model—
SWMM. In: Singh, V.P. (Ed.), Computer Models of Watershed
Hydrology. Water Resources Publications, Highlands Ranch,
pp. 783–808.
IPCC, 2001. Climate change 2001: the scientific basis. In:
Houghton, J.T., Ding, Y., Griggs, D.J., Noguer, M., van der
Linden, P.J., Dai, X., Maskell, K. (Eds.), Contribution of
Working Group I to the Third Assessment Report of the
Intergovernmental Panel on Climate Change. Cambridge
University Press, Cambridge.
Jacobs, P., Blom, G., Linden, G. van der, 2000. Climatological
changes in storm surges and river discharges: the impact on
flood protection and salt intrusion in the Rhine-Meuse delta.
Proceedings of the ECLAT-2 KNMI Workshop. Climatic
Research Unit, Norwich, pp. 35–48.
Jones, R.G., Murphy, J.M., Noguer, M., 1995. Simulation of climate
change over Europe using a nested regional-climate model. I.
Assessment of control climate, including sensitivity to location
of lateral boundaries. Q. J. R. Meteor. Soc. 121, 1413–1449.
Killingtveit, A., Sælthun, N.R., 1995. Hydropower development:
hydrology. Technical Report, Norwegian Institute of Technol-
ogy, Oslo.
M.J. Booij / Journal of Hydrology 303 (2005) 176–198 197
King, D., Daroussin, J., Tavernier, R., 1994. Development of a soil
geographical database from the soil map of the European
Communities. Catena 21, 37–56.
Kite, G.W., 1995. The SLURP model. In: Singh, V.P. (Ed.),
Computer Models of Watershed Hydrology. Water Resources
Publications, Highlands Ranch, pp. 521–562.
Kite, G.W., Kouwen, N., 1992. Watershed modeling using land
classifications. Water Resour. Res. 28, 3193–3200.
Krysanova, V., Bronstert, A., Mu
¨ller-Wohlfeil, D.-I., 1999.
Modelling river discharge for large drainage basins: from
lumped to distributed approach. Hydrol. Sci. J. 44,
313–331.
Lamb, R., 1999. Calibration of a conceptual rainfall–runoff model
for flood frequency estimation by continuous simulation. Water
Resour. Res. 35, 3103–3114.
Leavesley, G.H., Lichty, R.W., Troutman, B.M., Saindon, L.G.,
1983. Precipitation-runoff modeling system. User manual.
USGS water resources investigations report 83-4238, USGS,
Denver.
Lindstro
¨m, G., Johansson, B., Persson, M., Gardelin, M.,
Bergstro
¨m, S., 1997. Development and test of the distributed
HBV-96 hydrological model. J. Hydrol. 201, 272–288.
Middelkoop, H., Parmet, B., 1998. Assessment of the impact of
climate change on peak flows in the Netherlands—a matter of
scale. Proceedings of the Second International Conference on
Climate and Water, Helsinki University of Technology,
Helsinki, pp. 20–33.
Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through
conceptual models. Part I—a discussion of principles. J. Hydrol.
10, 282–290.
Oppenheimer, M., 1998. Global warming and the stability of the
West Antartic Ice Sheet. Nature 393, 325–332.
Over, T.M., Gupta, V.K., 1996. A space–time theory of mesoscale
rainfall using random cascades. J. Geophys. Res. 101, 26319–
26331.
Passchier, R.H., 1996. Evaluation hydrologic model packages.
Technical Report Q2044, WL/Delft Hydraulics, Delft (www.
wldelft.nl).
Rawls, W.J., Ahuja, L.R., Brakensiek, D.L., Shirmohammadi, A.,
1993. Infiltration and soil water movement. In: Maidment, D.R.
(Ed.), Handbook of Hydrology. McGraw-Hill, New York
(Chapter 5).
Refsgaard, J.C., 1996. Terminology, modelling protocol and
classification of hydrological models. In: Abbott, M.B.,
Refsgaard, J.C. (Eds.), Distributed Hydrological Modelling.
Kluwer, Dordrecht, pp. 17–39.
RIZA, 2000. Topographic data for the Meuse basin. Technical
Report, RIZA, Arnhem.
Seibert, J., 1999. Regionalisation of parameters for a conceptual
rainfall–runoff model. Agric. Forest Meteorol. 98, 279–293.
Shaw, E.M., 1983. Hydrology in Practice. Chapman & Hall,
London.
SMHI, 1999. Integrated Hydrological Modelling System (IHMS).
Manual version 4.3. SMHI, Norrko
¨ping.
Uhlenbrook, S., Seibert, J., Leibundgut, C., Rodhe, A., 1999.
Prediction uncertainty of conceptual rainfall–runoff models
caused by problems in identifying model parameters and
structure. Hydrol. Sci. J. 44, 779–797.
US Geological Survey, 1996. Global 30-arc second elevation data
set. Technical Report, USGS, Sioux Falls.
Van der Wal, K.U., 2001. Meuse model moulding. On the effect of
spatial resolution. MSc thesis, University of Twente, Enschede.
Visser, H., Folkert, R.J.M., Hoekstra, J., de Wolff, J.J., 2000.
Identifying key sources of uncertainty in climate change
projections. Clim. Change 45, 421–457.
Wilks, D.S., 1998. Multisite generalization of a daily stochastic
precipitation generation model. J. Hydrol. 210, 178–191.
Ye, W., Bates, B.C., Viney, N.R., Sivapalan, M., Jakeman, A.J.,
1997. Performance of conceptual rainfall–runoff models in low-
yielding ephemeral catchments. Water Resour. Res. 33,
153–166.
M.J. Booij / Journal of Hydrology 303 (2005) 176–198198
