HESSHydrology and Earth System SciencesHESSHydrol. Earth Syst. Sci.1607-7938Copernicus PublicationsGöttingen, Germany10.5194/hess-20-1031-2016Sensitivity analysis of runoff modeling to statistical downscaling models in the western MediterraneanGrouilletBenjaminb.grouillet@gmail.comRuellandDenisdenis.ruelland@um2.frhttps://orcid.org/0000-0001-9026-1201Vaittinada AyarPradeebaneVracMathieuCNRS, Laboratoire HydroSciences, Place Eugene Bataillon, 34095 Montpellier, FranceLSCE, Laboratoire des Sciences du Climat et de l'Environnement, UMR CEA-CNRS-UVSQ 1572, CE Saclay l'Orme des Merisiers, 91191 Gif-sur-Yvette, FranceBenjamin Grouillet (b.grouillet@gmail.com), Denis Ruelland (denis.ruelland@um2.fr)8March2016203103110472July20151October20158January201623February2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://hess.copernicus.org/articles/20/1031/2016/hess-20-1031-2016.htmlThe full text article is available as a PDF file from https://hess.copernicus.org/articles/20/1031/2016/hess-20-1031-2016.pdf
This paper analyzes the sensitivity of a hydrological model to different
methods to statistically downscale climate precipitation and temperature over
four western Mediterranean basins illustrative of different
hydro-meteorological situations. The comparison was conducted over a common
20-year period (1986–2005) to capture different climatic conditions in the
basins. The daily GR4j conceptual model was used to simulate streamflow that
was eventually evaluated at a 10-day time step. Cross-validation showed that
this model is able to correctly reproduce runoff in both dry and wet years
when high-resolution observed climate forcings are used as inputs. These
simulations can thus be used as a benchmark to test the ability of different
statistically downscaled data sets to reproduce various aspects of the
hydrograph. Three different statistical downscaling models were tested: an
analog method (ANALOG), a stochastic weather generator (SWG) and the
cumulative distribution function–transform approach (CDFt). We used the
models to downscale precipitation and temperature data from NCEP/NCAR
reanalyses as well as outputs from two general circulation
models (GCMs) (CNRM-CM5 and IPSL-CM5A-MR) over the
reference period. We then analyzed the sensitivity of the hydrological model
to the various downscaled data via five hydrological indicators representing
the main features of the hydrograph. Our results confirm that using
high-resolution downscaled climate values leads to a major improvement in
runoff simulations in comparison to the use of low-resolution raw inputs from
reanalyses or climate models. The results also demonstrate that the ANALOG
and CDFt methods generally perform much better than SWG in reproducing mean
seasonal streamflow, interannual runoff volumes as well as low/high flow
distribution. More generally, our approach provides a guideline to help
choose the appropriate statistical downscaling models to be used in climate
change impact studies to minimize the range of uncertainty associated with
such downscaling methods.
Introduction
Climate change impact studies (CCIS) focusing on water resources have become
a hot topic in the last decade. However, such studies need reliable climate
simulations to drive hydrological models efficiently. General circulation
models (GCMs) have demonstrated significant skills in simulating climate
variables at continental and hemispherical scales but are inherently
incapable of representing the local sub-grid-scale features and dynamics
required for regional impact analyses. For most hydrologically relevant
variables (precipitation, temperature, wind speed, humidity, etc.), GCMs
currently do not provide reliable information at scales that are appropriate
for impact studies e.g.,. The mismatch between the
spatial resolution of the GCM outputs and that of the data required for
hydrological models is a major obstacle e.g.,. Some
post-processing is thus required to improve these large-scale models for
impact studies and downscaling methods have been developed to meet this
requirement.
Downscaling methods can be dynamical or statistical, both approaches being
driven by GCMs or reanalysis data. Dynamical downscaling methods correspond
to the so-called regional climate models (RCMs), aiming at generating
detailed regional and local information (from a few dozen km down to a
few km) from low-resolution simulations (generally with a horizontal
resolution ranging from 100 to 300 km) by simulating high-resolution
physical processes consistent with the required large-scale dynamics. Easier
and less costly to implement as compared to dynamical downscaling techniques,
statistical downscaling models (SDMs) are also used in anticipated hydrologic
impact studies under climate change scenarios for a review, see,
e.g.,. SDMs rely on determining statistical relationships
between large- and local-scale variables and do not try to solve the physical
equations that model atmospheric dynamics. Due to their statistical
formulation, they generally have a low computational cost and provide
simulations relatively rapidly. SDMs are based on a static relationship;
i.e., the mathematical formulation of the relation between predictands (i.e.,
the local-scale variable to be simulated) and predictors (i.e., the
large-scale information or data used as inputs in the SDMs) has to be valid
not only for the current climate on which the relationship is calibrated, but
also for future climates, for example. Most state-of-the-art SDMs belong to
one of the four following families : transfer functions,
weather typing, methods based on stochastic weather generators and model
output statistics (MOS) models, which generally work on cumulative
distribution functions (CDFs). Many studies demonstrated that caution is
required when interpreting the results of climate change impact studies based
on only one downscaling model e.g.,. It is thus recommended
to use more than one SDM to account for the uncertainty of the downscaling
e.g.,. However, uncertainty can be very high due to the
inability of some SDMs to realistically reproduce the local climate, and this
can be critical when the aim is to produce accurate inputs for hydrological
models at the basin scale in the context of CCIS. On the other hand, a
sensitivity analysis of hydrological modeling to different downscaling
methods can produce an indicator to assess the quality of downscaled climate
forcings via their ability to generate reasonable simulations of discharge
from hydrological modeling. This analysis can also help to quantify the
impact of the error in a runoff simulation that stems from SDMs.
Several works have already attempted to compare climate simulations,
downscaled or not, from a hydrological point of view. Although these studies
revealed significant differences between SDMs in hydrological responses
including seasonal variability of runoff e.g.,, interannual discharge dynamics
e.g.,, or the distribution of extreme events
e.g.,, they were not able to clearly conclude on how
to choose one method over another. Difficulties in selecting among different
SDMs may arise from the choice of relevant criteria. While some may be
appropriate from the statistical or climatological point of view, these
criteria may not adequately highlight the differences between the methods
with respect to the hydrological responses. As a result, the aforementioned
studies generally suggest an ensemble approach including several methods to
offer a range of downscaling uncertainty when studying climate change impact
on runoff. However, this uncertainty range can be reduced to a minimum if
inappropriate statistical downscaling methods are excluded from the ensemble
approach.
Our analysis of the literature revealed that no consensus has emerged on the
best downscaling techniques among the state-of-the-art SDMs in the context of
CCIS on runoff. This calls for an original protocol to assess the strengths
and weaknesses of the different SDMs in providing accurate hydrological
simulations according to different insights. Indeed, assessing water resource
availability for different uses requires accounting for different aspects of
the hydrograph including interannual runoff volumes, mean seasonal
streamflow, and low/high flow distribution. First, hydrologists need to
correctly reproduce the interannual water balance in order to evaluate
changes in the storage capacity of the hydrosystems, for instance. Second,
analysis of the interannual variability of flows makes it possible to test
the ability of the climate simulations to reproduce the occurrence of dry and
wet years, as well as the frequency and intensity of change. Third, surface
water resources can be evaluated through a seasonal analysis so as to focus
on intra-annual high and low flow events. While high flows are particularly
important, e.g., when the focus is on flood risk, low flows are generally
studied in connection with the water needed for agriculture and tourism, as
in these cases, there is generally an increase in water demand when flows are
low see, e.g.,. Consequently, assessing water
availability means focusing on low flows, which generally occur during peak
water demand.
Water resource issues are particularly important in the Mediterranean region,
which has been identified as a hot-spot of climate change .
The western Mediterranean basins are of particular interest since they are
characterized by complex and varying hydro-climatic conditions due to the
contrasted influences of the Atlantic Ocean and the Mediterranean Sea, and of
mountain ranges. These contrasted conditions offer an opportunity to account
for the uncertainty linked to the differences in spatial and temporal
patterns that may arise from one downscaling technique to another.
Study catchments (Herault, Segre, Irati and Loukkos) in the western
Mediterranean region with their topography and mean seasonal variability in
precipitation (P) and discharge (Q) for the period 1986–2005.
The aim of this study is to propose a method to analyze the sensitivity of
hydrological responses to different methods used to statistically downscale
climate values by means of criteria that are commonly used in CCIS to assess
the impact on water resources: volume of water flow, interannual and seasonal
variability of runoff, and distribution of extreme events, including high and
low flows. We compare statistical downscaling methods via a guideline aimed
at providing an overview of their capabilities to reproduce the main features
of the hydrograph in view of their use in CCIS.
The rest of this article is organized as follows. In Sect. 2 we describe the
basins in the western Mediterranean and a hydro-climatic analysis based on
the available data. In Sect. 3, we provide an overview of downscaling models
and of the steps involved in hydrological modeling. In Sect. 4, we summarize
the results for each hydrological indicator, and in Sect. 5 we discuss these
results and provide a short conclusion.
Study areas and hydro-climatic contextFour catchments in the western Mediterranean
Four catchments were chosen to account for the variety of hydro-climatic
conditions in the western Mediterranean region (Fig. 1): the Herault basin at
Laroque (910 km2, France), the Segre basin at Seo de Urgel
(1265 km2, Spain), the Irati basin at Liedena (1588 km2,
Spain) and the Loukkos basin at Makhazine (1808 km2, Morocco). These
basins were also chosen because they are located upstream from storage dams
and in areas in which withdrawals are negligible , so their
streamflow regime can be considered to be natural. For brevity's sake, the
basins are referred to as Herault, Segre, Irati and Loukkos.
The Herault basin, from 165 to 1565 ma.s.l., comprises two-thirds
karstified limestone favoring delayed and sometimes sudden restitution and
one-third of basement rocks with low groundwater reserves favoring surface
runoff. The mountainous basin of Segre, located upstream from the Ebro basin
in northern Spain from 670 to 2830 ma.s.l., is characterized by
basement rocks (granite and quartzite) and a rugged topography that favors
runoff. The Irati basin, from 407 to 2017 ma.s.l., is located
upstream from the Ebro basin. This mountainous catchment, composed mainly of
limestone and conglomerate, is characterized by a high upstream–downstream
topographic gradient favoring a rapid hydrological response. The Loukkos
basin, from 55 to 1668 ma.s.l., is characterized by sandstone and
marl successions favoring surface runoff.
Hydro-climatic data
Preliminary studies provided daily
hydro-climatic data (precipitation, temperature and streamflow) over a common
20-year period (1986–2005), thus making it possible to compare the basins.
Climate data for the Herault basin were extracted from the SAFRAN
8 × 8 km meteorological analysis system and
observed runoff was provided by the French ministry of ecology and
sustainable development from their Banque Hydro
database (MEDDE, 2010). As
mentioned by , SAFRAN is a gauge-based analysis system using
the optimal interpolation (OI) method described by . This
method has been found to outperform other objective techniques for
precipitation notably studied in France over the Cévennes area, a region
with very high spatial and temporal variability . Climate
data for the Segre and Irati basins were obtained by interpolating daily
precipitation and temperature measurements on an 8 × 8 km
grid with the inverse distance weighted (IDW) method . This
method is particularly efficient for gauge-based analyses of global daily
precipitation . The precipitation and temperature data were
extracted based on numerous stations available at the Ebro basin scale
, of which around 19 and 6 precipitation stations, and 10
and 3 temperature stations, concern the Irati and Segre catchments,
respectively. Elevation effects on temperature distribution were taken into
account using a digital elevation model and a lapse rate of
-6.65 ∘C / 1000 m estimated from the data. Daily
streamflow data were provided by the center of studies and experiments on
hydraulic systems (CEDEX, 2012). In the Loukkos basin, precipitation data
were interpolated on a 8 × 8 km grid based on 11 stations
using the IDW method. Since daily temperature data were only available from a
station located at the basin outlet, a universal lapse rate of
-6.5 ∘C / 1000 m was used for temperature
interpolation. Hydro-climatic data including daily streamflow were provided
by the Moroccan Département de Planification des Ressources en Eau
(DPRE). Due to the lack of additional data such as wind and humidity in the
Moroccan basin, a simple formula relying on solar radiation and temperature
was chosen to assess daily potential evapotranspiration (PE)
in each basin.
Selected predictors according to the SDM and the predictand. These
variables are the dew point at 2 m (D2), the temperature at 2 m (T2), the
sea level pressure (SLP), the relative humidity, the zonal and meridional
wind components, the geopotential height at the 850 hPa pressure level
(R850, U850, V850 and Z850) and the large-scale precipitation (PR). The
pre-processing (PC) of the predictors depends on the SDM.
SDMPredictandD2SLPT2U850V850Z850PRANAPRField of anomaliesField of anomaliesField of anomaliesField of anomaliesField of anomaliesField of anomalies-T-Field of anomaliesField of anomaliesField of anomaliesField of anomaliesField of anomalies-CDFtPR––––––RawT––Raw––––SWGPRFirst two PCsFirst two PCsFirst two PCsFirst two PCsFirst two PCsFirst two PCs–T–First two PCsFirst two PCsFirst two PCsFirst two PCsFirst two PCs–
The atmospheric variables used for the calibration of the SDMs as predictors
were selected from the National Centers for Environmental Prediction/National
Center for Atmospheric Research (NCEP/NCAR) daily reanalysis data
with a 2.5∘ spatial resolution, from 1 January 1976
to 31 December 2005. The variables covered the region [-15∘ E,
42.5∘ E] × [27.5∘ N, 50∘ N] encircling
the Mediterranean Sea as defined in and corresponding to 240
grid cells. For the temperature models, five predictors were used: the
temperature at 2 m (T2), the sea level pressure (SLP), as well as the
geopotential height and the zonal and meridional wind components at
850 hPa (respectively, Z850, U850 and V850). For precipitation
models, the same five predictors were used, and the dew point temperature at
2 m (D2) was added. The predictors and the pre-processing of those
predictors according to the SDM and the predictands are summarized in
Table 1. Calibration was performed over the usual four seasons in the
Northern Hemisphere. The calibrated SDMs were forced with three different
data sets: NCEP reanalysis data over the 1976–2005 calibration period and
with the IPSL-CM5A-MR from the French Institut Pierre Simon Laplace,
IPSL Climate Modelling Centre, and CNRM-CM5 from the
French National Centre for Meteorological Research, CNRM,
GCMs, regridded at a 2.5∘ spatial resolution, over the GCM historical
(or CTRL) period (i.e., 1986–2005). The regridding was done through a
bilinear interpolation in order to have the GCMs and NCEP data at the same
resolution. This is a requirement in order to use GCMs as predictors in the
different SDMs calibrated from NCEP at a 2.5∘ resolution. Over the
mid-latitudes, 2.5∘ correspond approximately to 250 km. The
Herault, Segre and Loukkos basins are included in a single GCM grid cell. The
Irati basin straddles two grid cells, split equally. Also, the basins are not
on the edge of the GCM grid and therefore are not subject to border effects
in interpolation.
The SDMs have been calibrated over a 30-year period (1976–2005) for the
Herault, Irati and Segre basins and a 20-year period (1986–2005) for the
Loukkos basin due to data availability before 1986. This choice results from
the need to use the maximum available time period for the SDM calibrations to
have them as robustly calibrated as possible. However, the GCM historical
period was defined over 1986–2005 in order to have a 20-year common period
for all the SDMs to be evaluated through their ability to provide reliable
hydrological simulations.
Hydro-climatic analysis
The four basins are characterized by a more or less pronounced Mediterranean
climate with low precipitation in summer and more abundant precipitation in
winter (see Fig. 1). Mean annual precipitation decreases from north to south,
from 1397 mm in the Herault basin to 935 mm in the Loukkos
basin. Mean annual precipitation in the Segre basin (813 mm) is low
compared to neighboring basins because of the rain shadow effect of the
mountains surrounding the basin, which often stops precipitation from the
Atlantic (west) as well as from the Mediterranean Sea (east). Summer is hot
and dry, especially in the Loukkos basin, which causes severe low flows
during this season. In contrast, winter is milder and wetter. In the Herault
and Irati basins, the precipitation peaks in spring and fall are produced by
precipitation events whose intensity can vary greatly over short periods. The
spring and fall streamflows are strongly influenced by these precipitation
events as well as by snowmelt in spring in the mountainous basins (mostly in
the Segre and Irati basins).
No significant trends in interannual variations in precipitation and
streamflow were observed in the four basins over the period 1986–2005.
Nevertheless, mean precipitation during the first 10 years of the study
period was 4 to 19 % higher than during the last 10 years, except in the
Segre basin (-3 %). Furthermore, the analysis of the precipitation
indices (Eq. 1) showed that the wet and dry years observed in the four basins
occurred at the same time in nearly half the years (grey lines in Fig. 2).
Mean annual temperature remained almost constant during the 1986–2005 period
and the temperature indices (Eq. 2) were the same in the four basins in
two-thirds of the years (Fig. 2).
IP=(Py-Py‾)/σPIT=(Ty-Ty‾)/σT,
where Py is the annual precipitation for the year y,
Py‾ is the mean of the annual precipitation, and
σP is the standard deviation of the annual precipitation.
Ty is the annual temperature for the year y,
Ty‾ is the mean of the annual temperature, and
σT is the standard deviation of the annual temperature.
Precipitation (IP=(Py-Py‾)/σP) and temperature (IT=(Ty-Ty‾)/σT) indices applied to the four basins
over the 1986–2005 period. The grey lines highlight years when the signs of
the indices are the same for the four basins. Py is the annual
precipitation for the year y, Py‾ is the mean of the
annual precipitation and σP is the standard deviation of the annual
precipitation. Ty is the annual temperature for the year y,
Ty‾ is the mean of the annual temperature and
σT is the standard deviation of the annual temperature.
Models and evaluation proceduresStatistical downscaling models
Based on the preliminary climatological study of , three
downscaling methods were retained according to their ability to reproduce
commonly used climatic patterns on the E-OBS grid scale
(0.44∘ or approximatively 50 km spatial resolution). These
SDMs were thus used to provide the climate data, i.e., precipitation and
temperature, used as inputs for the hydrological model at the basin scale.
For each variable, three models were calibrated and applied: analogs of
atmospheric circulation patterns (ANA), the cumulative distribution
function–transform approach (CDFt) and a stochastic weather generator (SWG).
The analog method and the stochastic weather generator are both calibrated
and run on a seasonal basis, using the usual four seasons of the Northern
Hemisphere, whereas the CDFt approach is run on a monthly basis. For ANALOG
and SWG, the calibration was performed on NCEP reanalysis. Conversely, for
CDFt, coming from the family of the bias correction (BC) techniques, the
calibration was performed directly on the GCM to downscale. Although CDFt is
derived from the quantile-mapping technique, none of the three SDMs is bias
corrected. Those three models (i.e., CDFt included) all have the
particularity of providing high-resolution precipitation and temperature
simulations (constrained by large-scale reanalysis or GCM data) and therefore
all belong to the family of the statistical downscaling methods. For all
three models, calibration was done over 1976–2005 (except for Loukkos, on
which data availability limited the calibration to 1986–2005). Their
assessment when applied to NCEP reanalysis and GCM data was performed
according to a common 20-year 1986–2005 evaluation period. Sections 3.1.1 to
3.1.3 describe the different models.
The analog model
The analog model used here is based on the approach of and
applied to the fields of anomalies over the Mediterranean region
[-15∘ E, 42.5∘ E] × [27.5∘ N,
50∘ N] as defined in Sect. 2.2. For any
given day to be downscaled in the validation period, it consists in
determining the day in the calibration period with the closest large-scale
atmospheric situation XANA. More precisely, for a given day, the
analog is taken from the 15 days before and after this date in the
calibration data set. Note that the days in the same year are excluded.
Therefore, this prevents the analog day from being too close (in time) to the
day to be downscaled. The closest large-scale atmospheric situation
XANA is determined by minimizing a distance metric (here the
Euclidian distance) between the large-scale situation (Xd) of the
day to be downscaled and the large-scale situation (Xc) of all
the days in the calibration period. More technically, this can be written as
XANA=argmin(dist(Xd,Xc)),
where argmin(f) is the function returning the minimum value of a function
f, here computed over all the Xc situations of the
calibration period. The daily large-scale atmospheric situations correspond
to the daily fields of anomalies of the predictors. Those anomalies were
calculated with respect to the seasonal cycle, as is classically done in
analog techniques; see, e.g., , and references therein.
Xd, the large-scale situation of the day to be
downscaled, corresponds to the fields of
anomalies of all the predictors of that day. Xc corresponds to
any large-scale situation (defined in the same way) in the calibration
period. Hereafter this model is referred to as ANA.
The CDFt model
The cumulative distribution function–transform (CDFt) method was originally
developed by to downscale wind velocity and was later
applied to temperature and precipitation in, for example, and
. The CDFt model is a quantile-mapping-based approach, which
consists in relating the local-scale cumulative distribution function (CDF)
of the variable of interest to the large-scale CDF (here from NCEP or GCMs)
of the same variable. Let FGc(x) and FOc(x)
define the CDFs of the variable of interest, respectively, from a GCM
(subscript G) and from a local-scale observation-based data set (subscript O)
over the calibration period (subscript c), and FGv(x) and
FOv(x) the CDFs over the validation period (subscript v).
First, CDFt estimates FOv(x) as
FOv(x)=FOcFGc-1(FGv),
with × in the range of the physical variable of interest. Then, a
quantile mapping between FGv and FOv is performed to
retrieve the physical variable of interest at the local scale. All the
technical details on Eq. (4) and subsequent quantile mapping can be found in
. Note that, for this method, only the variable of interest
(i.e., precipitation or temperature) at a large scale is used as a predictor.
In contrast to ANALOG and SWG, the CDFt approach comes from the family of the
bias correction (BC) techniques. In that sense, CDFt does not need NCEP
reanalyses for its calibration, but is directly calibrated to link GCM
simulations and high-resolution data (through their CDF). Note that CDFt is
used here as a downscaling technique and not a BC, since it is applied here
to downscale (i.e., to go from large scale to high resolution) temperature
and precipitation time series.
Schematic diagram of hydrological model GR4J. Adapted from
, and .
The stochastic weather generator model
The stochastic weather generator (SWG) model used in this study is based on
conditional probability distribution functions in a vector generalized linear
model (VGLM) framework, as in . This means that the
distribution family is fixed and the distribution parameters are estimated as
functions of the selected predictors.
Modeling precipitation is usually divided into two steps: first the
occurrence and second the intensity. The modeling of intensity has been
introduced in previous sections. The rain occurrence at a given location is
modeled as a binomial distribution B(1,p) using a logistic
regression LR, e.g.,. Let pi be the
probability of rainfall on day i conditional on an N-length
predictor (or covariate) vector Xi=(Xi1,…,XiN) as defined in
the previous section. The conditional probability of occurrence pi is
formulated through a LR as
logpi1-pi=p0+∑j=1NpjXi,j︷S=,pi=exp(S)1+exp(S),
where (p0,…,pN) is the vector
of coefficients to be estimated. The LR is only used for SWG. The analog and
CDFt models directly provide zeros or positive precipitation values.
Temperature is expected to follow a Gaussian distribution and rain intensity
a Gamma distribution. The mean μ and the standard deviation σ
of the Gaussian distributions and the shape α and the rate β
of the Gamma distributions are estimated as functions of the large-scale
predictors. The parameters σ, α and β at day
i are computed with a common formulation, illustrated here for the
α parameter:
logαi=α0+∑j=1NαjXi,j,
with (αj)j=0,…,N the regression coefficients to be
estimated, N the number of predictors, and Xi,j the jth
daily large-scale predictor for day i. Note that Eq. (7) models the
logarithm of the parameter of interest to ensure that the parameter obtained
(σ, α or α or β) is positive. The
parameter μ is formulated in the same way but without the positivity
(i.e., log) constraint:
μi=μ0+∑j=1NμjXi,j.
As in , the predictors used for this model are the two
first principal components (PCs) calculated from a principal component
analysis PCA, applied separately to each variable.
Hydrological simulationsHydrological model
The GR4j lumped conceptual model was chosen to simulate the
seasonal and interannual variations in runoff at a daily time step (see
Fig. 3). Many studies have demonstrated the ability of the model to perform
well under a wide range of hydro-climatic conditions
e.g., and notably in the Mediterranean
region e.g.,. This model relies on
precipitation (P) and potential evapotranspiration (PE) and is
based on a production function that determines the effective precipitation
(the fraction of the precipitation involved in runoff) that supplies the
production reservoir and on a routing function based on a unit hydrograph.
According to the available data (cf. Sect. 2.2), a simple formula relying on
solar radiation and temperature (cf. Eq. 9) was chosen to
assess daily potential evapotranspiration (PE).
PE=Reλρ×T+5100if(T+5)>0elsePE=0,
where Re is the extraterrestrial solar radiation
(MJm-2d-1) given by the Julian day and the latitude,
λ net latent heat flux (2.45 MJ kg-1), ρ water density
(kg m-3) and T the mean air temperature at a 2 m
height (∘C).
Four parameters are used in the GR4j basic version: the maximum capacity of
the soil moisture accounting store ×1, a groundwater exchange
coefficient ×2, the maximum capacity of routing storage ×3,
and a time base for unit hydrographs ×4. A three-parameter snow module
based on catchment-average areal temperature
was activated to account for the contribution of snow to runoff from the
catchments. Below a temperature threshold ×5, a fraction ×6 of
precipitation is considered to be snowfall; this fraction feeds the snow
reservoir. Above the threshold ×, a fraction ×7, weighted by
the difference between the daily temperature and the threshold ×5, is
taken from the snow reservoir to represent snowmelt runoff.
Optimization of hydrological simulations
The model parameters were calibrated and the simulation performances were
analyzed by comparing simulated and observed streamflow at a 10-day time step
(averaged from daily streamflow outputs) in a multi-objective framework. This
time step was retained because it constitutes an interesting compromise for
CCIS on water resources, between a daily time step useful for representing
small runoff effects and a monthly time step too coarse to capture
hydrological variability. The following objectives were considered: (i) the
overall agreement of the shape of the hydrograph via the Nash–Sutcliffe
efficiency (NSE) metric ; (ii) the agreement of the low flows
via a modified, log version of the NSE criterion; and (iii) the agreement
of the runoff volume via the cumulated volume error (VEC) and
the mean annual volume error (VEM).
NSE=1-∑t=1NQobst-Qsimt2/∑t=1NQobst-Qsim‾2,NSElog=1-∑t=1Nlog(Qobst+0.1)-log(Qsimt+0.1)2∑t=1Nlog(Qobst+0.1)-log(Qobs‾)2,VEC=∑y=1NyearsVobsy-∑y=1NyearsVsimy∑y=1NyearsVobsy,VEM=∑y=1NyearsVobsy-VsimyVobsy/Nyears,
where Qobst and Qsimt are, respectively, the observed and
simulated discharges for the time step t, N is the number of time steps for
which observations are available, Qobsy and Qsimy are the
observed and simulated volumes for year y, and Nyears is the number of
years in the simulation period.
The NSE criterion is as well-known form of the normalized least squares
objective function. Perfect agreement between the observed and simulated
values yields an efficiency of 1, whilst a negative efficiency represents a
lack of agreement worse than if the simulated values were replaced with the
observed mean values. The optimal value of the VEC and
VEM criteria is zero. The latter criterion express the relative
difference between observed and simulated values. This multi-objective
calibration problem was transformed into a single-objective optimization
problem by defining a scalar objective function Fobj that
aggregates the different objective functions:
Fobj=(1-NSE)+(1-NSElog)+VEC+VEM.
Calibration was performed in a 7-D parameter space by searching for the
minimum value of Fobj. To achieve this high-dimensional optimization
efficiently, the shuffle complex evolution (SCE) algorithm was used
.
Cross-calibration and validation of hydrological model
To test the performance of the hydrological model in contrasted conditions,
the calibration–validation periods were sub-divided using a differential
split-sample testing (DSST) scheme . Thus, two sub-periods of
10 years each divided according to the median annual precipitation for the
period were used either for calibration or for validation. These two
sub-periods define dry and wet year periods.
For the cross-calibration–validation process, three calibration–validation
periods (for the whole period, for dry years, and for wet years) were used to
test the performance of the hydrological model in contrasted conditions. A
2-year warm-up period was included at the beginning of each period to
attenuate the effect of the initialization of storage. In addition,
hydrological years starting in a typical low-flow period in the Mediterranean
region (from September to August) were used in the modeling process to
minimize the boundary limits of the model reservoir. The quality of the
simulations was then assessed by comparing the “optimal” parameter set for
each calibration period. For each basin, three simulations based on the three
sets of parameters were compared (see Fig. 4). The four criteria employed for
the multi-objective function (NSE, NSElog, VEC and
VEM) were used to assess the quality of the simulations.
Fobj is optimal at 0, and considered satisfactory below 1.
Cross-calibration/validation of the hydrological model.
(a) Seasonal representation (from September to August) of simulated
and observed runoff during the whole period (WHO, first row), dry years (DRY,
second row) and wet years (WET, third row) according to parameter sets
optimized, respectively, for the whole period (in grey), dry years (red) and
wet years (yellow). Fobj
(Fobj=(1-NSE)+(1-NSElog)+VEC+VEM) is computed on daily series. Fobj is optimal at
0, but is considered satisfactory below 1. (b) Normalized model
parameters obtained over the three calibration periods.
The hydrographs in Fig. 4a illustrate the ability of the model to correctly
simulate runoff in the basins, according to the parameter sets used for the
calibration periods “whole period”, “dry years” and “wet years”. All
Fobj values were below 1, underlining the quality of the
simulations. Whatever the calibration period (whole period, dry years or wet
years), the objective function Fobj did not vary more than 0.1
over the validation period (except for the Segre basin in the wet year
validation period). This shows the stability of the simulations when the
model is calibrated under contrasted hydro-climatic conditions. The lower
quality of the simulations for the Segre basin may be attributed to (i)
complex snowmelt processes that are not well represented by the hydrological
model; (ii) insufficient quality of data inputs due to the limited number of
precipitation and temperature gauges (e.g., only 2 precipitation gauges in a
total of 6 stations are included within the Segre basin, while 10 stations
are included within the Irati basin); and (iii) the very particular
hydro-climatic context characterized by a mountainous climatic barrier, which
limits Atlantic influence and reduces the quantity of solid and liquid
precipitation supplying the streamflow inside the basin. Although the
hydrological simulations were less efficient in this basin than in the
others, we found them sufficiently correct to provide an additional basin for
the inter-comparison of the SDMs through a regional analysis in different
hydro-climatic contexts.
Flowchart illustrating the method used to compare the three
downscaling methods through a hydrological sensitivity analysis.
Figure 4b shows that the parameter sets are quite stable whatever the
calibration period used for the basins. However, the model parameters were
normalized with respect to the lower and upper limits of the parameters
obtained. As a result, the more the bounds are widened, the less the
normalized parameters are able to account for the differences between the
calibration periods. Nonetheless, the relative stability of the normalized
parameters underlines the robustness of the model under contrasted climatic
conditions. However, in the Segre basin, differences in the GR4j native
parameters reflect the difficulty in correctly simulating runoff in this
basin including NSE values of around 0.7. Snow module parameters
(×5, ×6 and ×7) in the Herault and Loukkos basins
are less stable, but the contribution of snowfall in these basins is rather
small. Finally, the low drift of the parameters and the relatively
homogeneous simulations obtained whatever the calibration period led us to
retain the parameter set from the whole period to simulate streamflow under
the various climate data sets. To facilitate interpretation and to limit
biases in hydrological modeling, the simulated streamflow produced with the
best parameter set for the “whole period” calibration period was used as a
benchmark (instead of the observed data) for the comparison between the
climate data sets in the following steps.
Comparing downscaling methods from the point of view of water resources
Based on the preliminary calibration of the hydrological model, runoff
simulations forced by statistically downscaled climate simulations were
compared using hydrological indicators that reflect the main issues of impact
studies on water resources. Figure 5 illustrates the different steps of this
approach.
Cumulative volume error (VEC) between hydrological simulations
based on downscaled or raw climate data (ANA, CDFt, SWG, RAW) and the
reference (REF). Values are expressed in % of difference in the total
volume of water flowed during the period.
First, three low-resolution climate data sets (NCEP, CNRM and IPSL) were
downscaled using three different statistical methods (ANALOG, CDFt and SWG)
to produce new high-resolution hydro-climatic data sets (P and T). Daily PE
time series were calculated using the same formula as that
used to estimate PE from observed temperature.
After preliminary calibration over the whole reference period under
observation-based climate inputs, the hydrological model was then forced with
the nine sets of downscaled hydro-climatic data (high resolution) and the
three raw data sets (low resolution) to produce an ensemble of 12 runoff
simulations. These simulations were compared to a reference runoff simulation
(REF) corresponding to the model outputs over the whole reference period
calibrated with observation-based climate inputs. This comparison relies on
hydrological indicators that are relevant to the water resource challenges
according to four complementary aspects of the hydrograph: volume of the
water flow, interannual and seasonal variability of runoff, and streamflow
distribution. The water flow volume was assessed according to the cumulated
volume error (VEC; see Eq. 12). Interannual variability was
assessed according to a root mean square error applied to the sorted annual
flows. This criterion was then normalized by dividing the RMSE value by the
mean of annual observed discharge. Choosing a normalized root mean square
error criterion (NRMSE, Eq .15) applied to this distribution gets round the
non-synchronicity of the simulations. Note that applying the NRMSE criterion
to sorted flows may favor high flows. Seasonal variability was assessed using
a NSE criterion (Eq. 10) applied to the mean 10-day discharge series. The
last comparison criterion was based on the flow duration profile, divided
between high and low flows. High flows correspond to daily flows exceeding
the 95th percentile (> Q95); i.e., the 5 % highest daily flows or
flows exceeded 5 % of the time. Low flows correspond to daily flows not
exceeding the 80th percentile (< Q80); i.e., the 80 % lowest daily flows
or flows exceeded 20 % of the time. This value was deliberately chosen to
cover a wide range of flows to enable a meaningful distinction between
simulations while correctly representing low flows. Both high and low flows
were evaluated using a NSE criterion applied to the high and low flow time
series.
NRMSE=∑i=1NXobs,i-Xsim,i2/NXobs‾,
where Xobs is observed values and Xsim is simulated values at
time/place i. Xobs‾ is the mean of observed values.
Comparison of the downscaling methods according to the cumulative
volume error (VEC) used as a criterion to compare the downscaling
methods applied to NCEP, CNRM and IPSL climate inputs in the four basins. The
smaller the absolute value of the criterion, the better the simulation.
The 12 runoff simulations were compared via these five hydrological
indicators. Finally, the downscaling methods (from the runoff simulations
forced by the downscaled climate time series) were ranked using the same
indicators. The median of the related criterion (VEC,
NRMSEINT, NSESEAS, NSEHF or
NSELF) in the four study areas made it possible to rank the
downscaling methods according to their respective performances in a given
configuration: “climate data – indicator”. Next, the simulations were
combined by computing the median of the criteria values of the four basins,
and the three climate data sets to make it possible to rank them. Finally, an
additional criterion (Eq. 16) was used to aggregate the different
goodness-of-fit criteria to provide an overview of the performance of the
different downscaling models driven by distinct climate data sets. The lower
the aggregation criterion, the better the ranking.
IAGG=VEC+NRMSEINT+(1-NSESEAS)+(1-NSEHF)+(1-NSELF).
For the remainder of this paper, REF refers to the simulated runoff with the
parameters calibrated over the whole period based on the observed climate
data. RAW refers to the simulations with raw low-resolution climate data from
NCEP/NCAR reanalysis or GCM outputs over the reference period. ANA, CDFt and
SWG refer to the simulations based on climate data downscaled via the ANALOG,
CDFt and SWG methods, respectively.
Comparison of the sorted annual discharge simulated using REF data,
RAW (NCEP or GCM) data, and the three downscaling methods (applied to NCEP,
CNRM and IPSL) for each basin. The NRMSE values above each panel represent a
root mean square error applied to the sorted time series of annual discharge
normalized by dividing RMSE by the mean annual discharge of the reference
time series. The best values are in bold.
Comparison of seasonal variations in streamflow simulated using REF
data, RAW (NCEP or GCM) data, and the three downscaling methods (applied to
NCEP, CNRM and IPSL) for each basin. The NSE values for the mean 10-day
discharge between REF and the simulation concerned are given above each
panel. The best values are in bold.
Comparative analysis of hydrological responses to downscaled climate forcingsWater volumes
Water volumes were assessed through the cumulative volume error, i.e., the
error in the percentage of the cumulated volume of water flow over the whole
period (Table 2). ANALOG-based simulations generally reproduced water volumes
better than the other simulations. Nevertheless, differences appeared
depending on the input data used (NCEP, CNRM or IPSL) and on the basin
concerned (Fig. 6). Except in the Loukkos basin and for CNRM in the Herault
and Segre basins, RAW-based simulations were always improved by downscaling.
CDFt-based simulations were slightly better than ANALOG-based simulations in
reproducing cumulated volume of water with VEC absolute values
averaged between the four basins, with 12 % for CDFt and with 14 % for
ANALOG. In addition, the results of ANALOG-based simulations were more
constant without outlier criterion values. Criterion values can be considered
to be outliers when VEC is greater than 50 %, which may be seen
as an unacceptable error. In the Loukkos basin, simulations provided many
outliers with both SWG and CDFt. The CDFt method improved the results
according to the VEC criterion better than the other models.
SWG-based simulations ranked first for both criteria with NCEP as inputs, but
performed poorly with GCMs.
Interannual variability of streamflow
The ability to reproduce interannual runoff variability was assessed through
a root mean square error (NRMSEINT) criterion applied to the
sorted time series of annual discharge and normalized by dividing RMSE by the
mean annual discharge of the reference (see Fig. 7). In other words, for each
basin, the downscaling method and input data, and the annual discharge values
were sorted from the highest value to the lowest one to generate new
decreasing time series on which the NRMSE criterion was calculated with
respect to the sorted reference time series. The results show that the
interannual variability of runoff is correctly reproduced by the simulations
based on most of the downscaled climate data sets, particularly ANALOG- and
CDFt-based simulations in which NRMSE values rarely reached more than 30 %.
On the whole, RAW-based simulations were improved by downscaling, especially
when driven by NCEP and IPSL, except for SWG-based simulations driven by GCMs
(Fig. 7). Indeed, when driven by NCEP, the SWG method reproduced interannual
variability better than the other methods for three of the four basins, but
produced poor results with GCMs, in which case ANALOG- and CDFt-based
simulations generally performed better.
Seasonal variability of streamflow
Seasonal variability was assessed using a NSE criterion (Eq. 10) applied to the mean 10-day
discharge series. In most cases, the downscaling methods improved the
reproduction of the seasonal variability of streamflow compared to the
low-resolution raw data sets (see Fig. 8). This was particularly true of NCEP
reanalyses, for which downscaled inputs considerably improved the simulation
of the seasonal dynamics more realistically than with RAW-based simulations.
Although the ANALOG method did not systematically match the best NSE values,
on the whole, the method reproduced the seasonal variability better than
CDF-t and SWG. The CDFt method performed particularly well with GCMs as
inputs, but proved to be unsuitable with NCEP under the particular
hydro-climatic conditions that prevail in the Segre basin. Except with NCEP,
SWG-based simulations reproduced poorly the seasonal variability of runoff,
due notably to systematic overestimation of high-flow events.
Comparison of (a) the 5 % daily high flows and
(b) the 80 % daily low flows simulated with REF data, RAW (NCEP or
GCM) data, and the three downscaling methods (applied to NCEP, CNRM and IPSL)
for each basin. The NSE values calculated on the 5 % high and the 80 %
low flows are indicated on the right in each panel. NSE values higher than
0.5 for high flows and 0.8 for low flows are in bold.
Streamflow distribution: high and low flows
Streamflow distribution was divided between high flows, i.e., the 5 %
highest daily flows, and low flows, i.e., the 80 % lowest daily flows. Both
were evaluated using a NSE criterion applied to the high and low flow time
series. On the whole, the downscaling methods improved the reproduction of
the distribution of sorted high flows (Fig. 9a). However, it should be noted
that the downscaled simulations with CNRM data deteriorated raw data in the
Segre basin. Results showed that ANALOG generally reproduced the 5 %
highest flows best; the NSE values were quite stable and never below 0.47.
The CDFt-based simulation results were very close to those obtained with
ANALOG, with equivalent scores when NCEP or GCM data were used as inputs.
Nevertheless, it should be noted that ANA and CDFt reproduced less accurately
high flows in the Segre basin than in the other basins. This can be explained
by a lower efficiency of the hydrological model in this area as shown in
Sect. 3.2.3, thus leading to a reference simulated streamflow more uncertain
than in the other basins. The SWG method reproduced high flows well with NCEP
data as inputs, but not with GCM data.
Figure 9b shows the distribution of sorted low flows and the associated NSE
criterion. Moreover, applying a NSE criterion to the sorted low flows tended
to emphasize the differences between the simulations and thus made it easy to
distinguish simulations that reproduced low flows poorly. The downscaling
methods improved the representation of the 80 % lowest flows in all basins,
except for the SWG method with GCM data used as inputs. In general, the best
results were obtained from ANALOG-based simulations, with NSE values always
above 0.81. The CDFt-based simulations performed significantly better when
forced with GCMs than with NCEP. The SWG-based simulations were unable to
reproduce low flows when GCM data were used as inputs.
Efficiency of the different climatic data sets in reproducing
different aspects of the hydrographs from the four basins over the period
1986–2005: comparison of low-resolution data sets (RAW) and high-resolution
data sets downscaled using the ANALOG, CDFt or SWG methods forced by
NCEP/NCAR reanalyses and outputs from the CNRM and IPSL. The bars represent
the median of the indicator values of the four basins. The smaller the bar,
the better the result. Row “Median of NCEP-CNRM-IPSL” corresponds to the
median of the four basins for the three large-scale climate data sets (NCEP,
CNRM and IPSL). Column “Aggregation of indicators” sums the six
indicator values according to the following equation:
IAGG=|VEC|+NRMSEINT+(1-NSESEAS)+(1-NSEHF)+(1-NSELF).
Discussion and conclusions
The aim of this study was to test the ability of different statistical
downscaling climate models to provide accurate hydrological simulations for
use in climate change impact studies (CCIS) on water resources. To get round
the constraints represented by the inherent characteristics of each climate
model, we compared three statistical downscaling methods applied to three
low-resolution raw data sets: NCEP/NCAR reanalysis data and two GCM data
(CNRM and IPSL). The three downscaling methods were an analog method
(ANALOG), a stochastic weather generator (SWG) and the cumulative
distribution function–transform approach (CDFt). This allowed us to analyze
the sensitivity of runoff modeling at the catchment scale to 12 climatic
series (three raw low-resolution data sets and nine downscaled
high-resolution data sets). The sensitivity analysis was based on a
previously calibrated hydrological model validated with local hydro-climatic
observed data over a 20-year reference period. The model simulations served
as a benchmark for the comparison between the raw and downscaled data sets
from NCEP reanalysis and GCM outputs over the same period. The comparison
with the runoff simulations forced with raw and downscaled climate data sets
was based on hydrological indicators describing the main features of the
hydrograph: the ability to reproduce the cumulated volume of water flow,
interannual and seasonal variability of runoff, and the distribution of
streamflow events, including high and low flows. To account for uncertainty
related to the spatial variability of the downscaled climate simulations,
this approach was applied over four western Mediterranean basins of similar
size but that represent a wide range of hydro-meteorological situations.
The proposed sensitivity analysis enabled us to identify the strengths and
weaknesses of different statistical downscaling methods with respect to the
sensitivity of runoff simulations to low-resolution and high-resolution
downscaled climate data sets (see Fig. 10). Our study revealed the
performances that could be expected from downscaling techniques applied to
large-scale data sets to provide acceptable hydrological simulations. To
complement the usual calibration–validation exercises conducted by
climatologists for assessing the suitability of SDMs based on predictors and
to reanalyze grids see, e.g.,, we focused on a
validation protocol directly based on streamflow, thus allowing the combined
impacts of the downscaled precipitation and temperature inputs to be
considered through the hydrological response.
On the whole, the ANALOG-based simulations performed well in all the
situations tested, whatever the large-scale climate data set used as inputs
(NCEP or GCMs), notably in reproducing interannual and seasonal runoff and
low flows. ANALOG-based simulations were closely followed by CDFt-based
simulations, notably when GCM outputs were used, but with a lower variability
of scores than with ANALOG. On the contrary, the results clearly showed that
the SWG method should not be used “as is” in climate change impact studies
on water resources. Indeed, although the SWG-based simulations were
satisfactory when based on the NCEP large-scale climate data set, they
significantly underperformed when based on GCM outputs. Biases of the GCM
data with respect to the NCEP/NCAR reanalyses may explain the poor
performances of the SWG method. As SWG is calibrated with “perfect”
predictors from reanalyses, its application to biased GCM predictors led to
unsatisfactory SWG-based hydrological simulations. To make the SWG method
more applicable in climate change impact studies on runoff, one solution
could be to correct the GCM predictors with respect to reanalyses, as done
for example by before performing a dynamical downscaling.
Although the ANALOG method appeared to be the best SDM in this study, it may
suffer from certain limitations when used in a climate change context,
notably when downscaling GCM projections over the 21st century. One main
limitation is that ANALOG is not able to provide suitable simulations for the
extreme events if such events increase in intensity in the future see,
e.g.,. Indeed, by construction, as ANALOG works by resampling the
calibration set, it never supplies downscaled values beyond the range of the
calibration reference data set.
On the other hand, although CDFt-based simulations were less consistent than
ANALOG simulations, they were more sensitive to climate forcing and also more
sensitive to the chosen indicators. The CDFt method was particularly
appropriate when we focused on the cumulated volume, seasonal variability and
high flows. In addition, it should be noted that the CDFt method is the most
parsimonious technique since it generally needs only one variable as a
predictor. This could obviously be considered an advantage since the
complexity of CDFt is very low. However, this low level of complexity could
mean that some climate information needed to drive the CDFt more efficiently
will be missing. In that sense, one possible improvement could consist in
incorporating additional covariates in CDFt, as done by .
Nevertheless, the approach including those additional predictors means that
this conditional CDFt has to be calibrated on reanalyses or, at a minimum, on
the outputs of a climate model of which the day-to-day evolution of
large-scale weather states matches that of the real world. This could be a
limitation, since additional biases may appear with those constraints.
The next step will be exploring the potential impact of climate change on the
runoff in the basins studied here. To this end, an ensemble approach will be
proposed based on the construction of high-resolution climate scenarios using
different climate models, gas emission scenarios, and downscaling techniques.
In view of the acceptable hydrological simulations obtained with the ANALOG
and CDFt methods, it may be useful to develop high-resolution climate
forcings downscaled with these two methods in order to account for the
uncertainty of the downscaling, as recommended by some authors
e.g., for applications in climate change impact
studies. Our study also showed the benefits of evaluating the relevance of
SDMs in a given hydro-climatic context using a suitable validation protocol.
Indeed, selecting unsuitable downscaling methods, such as SWG with GCM
outputs, can expand the range of uncertainty linked to the range of SDMs.
Furthermore, our study showed that hydrological responses were sensitive to
the climate data sets used as inputs. Indeed, despite the significant
contribution of the downscaling methods, hydrological simulations are better
from reanalysis data than from GCM data. This demonstrates the limits of GCMs
in reproducing current climatic conditions and therefore the associated
hydrological responses. This point raises the question about the use of GCM,
and thus about the need to correct them afterwards for the evaluation of
future hydrological impact in CCIS. Finally, although it is commonly
acknowledged that the uncertainty resulting from climate modeling (GCMs, gas
emission scenarios and downscaling methods) is highest in a context of
climate change e.g.,, it should be noted
that the uncertainty stemming from hydrological modeling may also be high.
Several authors e.g.,
showed that the choice of the hydrological model (structural uncertainty) and
its parameterization (parameter uncertainty) could cause significant
variability in runoff simulations. Consequently, further analyses of the
applicability of the model parameters in a non-stationary context and with
different calibration criteria are needed before the model is used in future
climate conditions.
Similarly, the different sources of uncertainties and their propagation in
the hydrological projections need to be evaluated. To this end, a standard
ensemble approach based on various climatic, downscaling and hydrological
models may not be sufficient, since using many models without prior
validation of their efficiency can lead to very large uncertainty bounds due
to the poor quality of some models in the ensemble framework. Minimizing
uncertainty thus requires selecting models that perform reasonably well over
the reference period in the context of the current climate. Although this
cannot guarantee the quality of the models for future conditions, we believe
it is an essential step to provide more reliable and relevant hydrological
projections.
Acknowledgements
This work was part of the StaRMIP project (Statistical Regionalization Models
Inter-comparisons and hydrological impacts Project, grant agreement
ANR-12-JS06-0005-01), and the REMEMBER project (grant agreement
ANR-12-SENV-0001-01), both funded by the French National Research Agency
(ANR), as well as part of the GICC REMedHE project (2012–2015) funded by the
French Ministry of Ecology, Sustainable Development and Energy and the
ENVI-Med CLIHMag (Changement cLimatique et Impacts Hydrologiques au
Maghreb) project funded by the INSU-MISTRALS program. The authors are
grateful to Météo-France, the AEMET (Agencia Estatal de
Meteorología), the department of Water Research and Planning (DRPE) of
Morocco and the Hydraulic Basin Agency of Loukkos-Tetouan for having provided
the observed hydro-climatic data.Edited by: E. Zehe
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