Introduction
Consistent, long-term data of meteorological and hydrological variables at a
high spatial resolution are needed for many applications, including
(i) impact assessment studies, such as for drought, flood, or climate change
analysis ,
and (ii) studies that need spatially and temporally continuous,
observation-based datasets, e.g., for downscaling or disaggregating climate
model outputs or for establishing Ensemble Streamflow Prediction
and reverse Ensemble Streamflow Prediction approaches .
Continuous observations of hydrologic fluxes and states are economically and
logistically not feasible on regional to national scales
. In situ soil moisture observations, for example, are
scarcely available. These point-scale observations are representative for a
small control volume of a few cubic centimeters. Evapotranspiration measurements at eddy
covariance stations have footprints of tens to hundreds of meters but they
are available at less than 1000 stations worldwide ().
Alternatives include remote sensing or reanalysis products such as NCEP-CFSR
or ERA-INTERIM . Hydrologic products derived
from remote sensing are broadly available, but they do not consider the
conservation of mass, i.e., the closure of the water balance. Moreover, these
products are not spatially and temporally continuous due to reliance on
cloud-free conditions . Reanalysis products, in
contrast, provide continuous data but they have coarse spatial resolutions of
at most 1/4∘ , which is not suitable for regional-scale applications.
Hydrologic models driven by ground-based meteorological observations are the
prime alternative to derive spatially and temporally consistent water fluxes and
states at large spatial domains. For example, ; and provided model-based datasets on a national
scale. These data are based on the Variable Infiltration Capacity (VIC) model
and have, at most, a spatial resolution of 1/16∘
and cover the contiguous United States, Mexico, China, and parts of Canada.
; and provide data on the
same domain with a focus on meteorological data. A set of four models was
used in the NLDAS project to assess the water balance components over the
contiguous United States . Studies by
; and focus on the global domain. The
spatial resolution of these global datasets is at most 1/2∘, and
many of these studies focus on meteorological forcings rather than hydrologic
variables.
The resolution of the abovementioned model-derived datasets are coarse
according to , who stated a need for higher-resolution data
and models for purpose of, e.g., flood and drought forecasting. Moreover,
stated that water resources or river basin managers will
favor highly resolved data at resolutions of 1–5 km.
The application of observational-derived model products, however, also has
some limitations. First, due to a limited amount of observed variables
modeling approaches, such as the estimation of potential evapotranspiration
(Ep), have to be adopted to the available data. As a result,
temperature-based Ep methods may be preferred to more physically
based approaches (e.g., radiation based). Second, the interpolation of point
observations induces uncertainties depending on the applied interpolation
method. Further, small-scale, convective precipitation events may not be
caught by gauging networks and lead to an underestimation in precipitation.
Furthermore, hydrological models are subject to different sources of
uncertainty, i.e., input, model structural, and parametric uncertainty
. All of the aforementioned uncertainties propagate to the
model results and can superpose each other . The overall
uncertainty of hydrological models is therefore summarized as predictive
uncertainty. Uncertainties are often not considered when deriving hydrological
or hydro-meteorological datasets e.g.,. As a result, predictive uncertainties are often not addressed
but may have substantial implications on subsequent studies, as shown by
. Herein, we will focus on the predictive uncertainties
caused by equifinal parameter sets.
The specification of model parameters, which are valid beyond catchment
boundaries poses another challenge in the application of hydrologic models over
large domains. Large-scale hydrologic model studies apply either parameters
originating from a single catchment , filter behavioral
parameters from predefined sets , extrapolate or
regionalize parameters or hydrological variables from observed to unknown
locations , or use an uncalibrated
model . A methodology considering the
calibration in individual basins for creating a set of regionalized
parameters,
which are later on filtered for behavioral solutions in all considered
basins,
could be an alternative approach. Such an approach combines all of the aforementioned strategies.
The aim of this study is to derive a model based, consistent set of
national-scale hydrological data for Germany within the period 1951–2010. We
address the need for highly resolved data by conducting observation-driven
hydrological simulations at a spatial resolution of 4 km × 4 km
(1/25∘). Daily fields of evapotranspiration, soil moisture,
groundwater recharge, and grid-cell-generated runoff as well as
precipitation, temperatures, and potential evapotranspiration are made freely
available. To our knowledge, such a consistent and long-term dataset for
Germany has not been freely available until now. The dataset accounts for
predictive uncertainties by considering a set of equifinal parameters. An
parameter estimation approach for deriving a set of 100 parameters on the
national scale is developed. We further aim to assess and evaluate the
spatiotemporal distribution of the simulated hydrological states and fluxes
as well as their uncertainties using multiple validation variables at
different scales. Finally, the parametric uncertainties are analyzed
regarding their explanatory variables for the simulated fluxes and their
propagation between different model compartments.
Study domain and datasets
The study is conducted on the territory of Germany, which covers an area of
approximately 357 000 km2 (Fig. ). The region, located
in central Europe, is mainly characterized by a humid climate but nonetheless
has north-to-south and east-to-west climatic gradients. The topography varies
from low-altitude, flat areas in the north (North German Plain) over
mid-altitude mountains in central Germany (Central Uplands) to the high-altitude
Alpine foothills and the Alps in the south. Whereas the northwestern
part of Germany is still under maritime influence, the eastern part has a
more continental climate that is characterized by colder winters and less
precipitation.
Study area showing the seven basins used for estimation of the
ensemble parameter sets for Germany. The different colors are making the
basins better distinguishable. The points E1–E7 denote eddy
covariance stations, which are used for the evaluation of evapotranspiration
and soil moisture.
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The assessment of water fluxes and states is restricted to the national
borders of Germany because meteorological data and land-surface
characteristics are available in this domain. Thus, only basins entirely
covered by German territory are used to derive parameters for the
hydrological model. These seven major basins are depicted in
Fig. . These basins represent the topographic and
hydro-climatic gradient within Germany (see Table ). They
range in size from 6000 to 48 000 km2 and are characterized by mean
elevations ranging from 60 m a.s.l. (Ems basin) to 560 m a.s.l. (Danube
basin). All basins have a comparable degree of urbanization ranging between 6
and 10 %. A remarkably low amount of forest is observed in the Ems basin,
where agriculture and pasture are the dominant land use.
Due to different climatic regimes the average streamflow of the seven basins
ranges from 161 to 469 mm a-1. The low-lying Ems reaches a remarkably
high discharge due to maritime influence, whereas the Saale River is
characterized by the lowest streamflow. The runoff coefficient of the Saale
differs significantly from the other basins, which originates from the high
degree of anthropogenic influence within this basin; 3 of the 10 largest dams
in Germany are located there (Bleiloch – 215 million m3, the Hohenwarte
– 182 million m3, and the Rappbode reservoir – 109 million m3).
Furthermore, open-pit mining has a large influence on the water budget of
this basin.
Basin properties and water balance characteristics of the seven major German
river basins. The geographical location of the basins is depicted in
Fig. . Abbreviations: avg – average, SD – standard
deviation, min – minimum, max – maximum, P – precipitation, Q – streamflow, Ea –
evapotranspiration (P-Q), Ep –
potential evapotranspiration.
Major
Basin
Elevation
Land cover
Water balance
Dryness
Runoff
basins
area [km2]
[m]
[%]
[mm a-1]
index [–]
coeff. [–]
avg
SD
min
max
forest
sealed
mixed
P
Q
Ea
Ep/P
Q/P
Mulde
6200
386
201
75
1212
26
10
64
798
344
454
0.88
0.43
Ems
8400
60
36
10
383
13
8
79
802
312
490
0.89
0.39
Neckar
12 700
445
153
124
1015
35
10
55
914
356
558
0.85
0.39
Main
23 700
356
113
93
1044
39
6
55
793
247
546
0.97
0.31
Saale
24 800
287
162
56
1139
23
8
69
645
161
484
1.13
0.25
Weser
37 700
223
165
8
1116
34
7
59
781
276
505
0.91
0.35
Danube
47 500
558
170
302
2329
32
6
62
948
469
479
0.80
0.49
Land surface properties
The land-surface characteristics required by the hydrologic model include a
50 m digital elevation model (DEM) acquired from the Federal Agency for
Cartography and Geodesy , a digitized soil map at a scale of
1 : 1 000 000 , and a hydrogeological map at a scale of
1 : 200 000 . The soil map contains information on soil
textural properties, such as the sand and clay contents of different soil
horizons. The soils are classified into 72 soil types and have an average
depth of 1.8 m. The hydrogeological map comprises 23 classes and gives
information about saturated hydraulic conductivities and karstic areas. Based
on the DEM, additional information, such as the slope, aspect, flow
direction,
and flow accumulation, are inferred. Land cover information is derived from
CORINE land cover scenes of the years 1990, 2000, and 2006 . The
period prior to 1990 is assumed to be static and is represented by the scene
of 1990. All datasets are remapped to a common spatial resolution of
100 m × 100 m using a nearest neighbor approach.
The location and shape of the major basins (Fig. ) are
derived via an automated delineation, which is based on gauging station and
terrain information (flow accumulation and flow direction). Streamflow data
are provided by the and the . The results of the
delineation are approved via comparison with the CCM River and Catchment
Database . In addition to the seven major basins (as
described above), the model is set up in 222 additional, smaller basins to
cross-validate the model performance.
Meteorological forcings
The hydrologic model is forced with daily fields of precipitation and
minimum, maximum, and average temperature. They are derived from local
observations operated by the national weather service . The
station network comprises, on average, 3800 rain gauges and 570 climate
stations per year (period: 1951–2010), which have an average minimum
distance of 6 and 14 km between neighboring stations, respectively.
These local observations are interpolated on a regular grid of
4 km × 4 km using external drift Kriging. The terrain elevation
(DEM) is used as the external drift, and the Kriging weights are based on a
theoretical variogram. The variogram is estimated for all of Germany by
fitting to an empirical variogram (see Appendix ). To avoid
discontinuities in the interpolated meteorological forcings and consecutively
in the hydrologic simulation, an estimation of multiple variograms for
different climatic zones or distinct morphological regions has been rejected.
The spatial resolution of 4 km × 4 km is seen as appropriate,
considering the aforementioned station network density of precipitation
observations. The quality of the interpolation is assessed by the Jackknife
method (leave-one-out strategy), which leads to a mean relative bias of
0.64 % for all precipitation stations (see Appendix ).
Subsequently, daily fields of potential evapotranspiration are estimated with
the Hargreaves–Samani method , using interpolated
temperatures (average, minimum, and maximum).
The interpolation of the precipitation is evaluated with gridded
precipitation data (REGNIE) provided by the German Meteorological Service
(). The REGNIE data are based on the same
observations and have a spatial resolution of 1 km. They are derived by
applying a multiple linear regression approach, which accounts for daily
atmospheric conditions and terrain properties, such as elevation, slope, and
aspect . After remapping the REGNIE data to the
aforementioned 4 km × 4 km grid by bilinear interpolation, a
satisfactory correspondence between the interpolation and the REGNIE
precipitation data is found (see ). The spatially
averaged bias of the daily fields is 0 with a standard deviation of
0.11 mm d-1 within the period 1951–2010.
Methodology
The mesoscale Hydrological Model mHM
mHM (www.ufz.de/mhm) is a distributed hydrologic model that accounts
for the following main processes: snow accumulation and melting,
evapotranspiration, canopy interception, soil water infiltration and storage,
percolation, and runoff generation. These processes are conceptualized as
water fluxes between internal model states similar to existing models, such
as HBV or VIC . Snow accumulation and
melting processes are based on the improved degree-day method, which accounts
for increased snow melting during intense rainfall events
. A three-layer discretization is used to account for the
processes that represent the root-zone soil moisture dynamics. The two upper
layers end in 0.05 and 0.25 m, and the
lowest layer is spatially variable in depth depending on the soil map. On
average, the lowest layer is 1.8 m deep in Germany. The evapotranspiration
from soil layers is estimated as a fraction of the potential
evapotranspiration depending on the soil moisture stress and the fraction of
vegetation roots present in each layer. The runoff generation in mHM is
formalized as the sum of the direct runoff, slow and fast interflow, and
baseflow components. The runoff generated at every grid cell is routed to the
outlet using the Muskingum–Cunge algorithm. For a detailed model description,
interested readers may refer to and .
To date the model has been successfully applied to various river basins
across Europe (including Germany), the USA , and worldwide .
A feature that is unique to mHM is its technique for estimating effective
model parameters: Multiscale Parameter Regionalization;
). Its basic concept is to estimate parameters (e.g., soil
porosity) based on physiographic properties (e.g., sand and clay content) and
transfer functions (e.g., pedotransfer functions). These transfer functions
depend on transfer or global parameters (e.g., factors of the
pedotransfer functions) that are time invariant and location independent. For
the domain of Germany, 68 global parameters were purpose to an automated
calibration (described in Sect. ). An overview of the
global parameters and the resulting effective model parameters can be found
in the Supplement.
This regionalization of model parameters is conducted at the high-resolution
land surface property input, e.g., 100 m × 100 m. In a second step
these parameters are subsequently upscaled to the user-specified resolution of
the hydrologic simulations, e.g., 4 km × 4 km, by applying
parameter-specific upscaling rules . This procedure
yields in effective parameter values (e.g., soil porosity), which are used for the
simulation of hydrological processes (e.g., soil water retention). Thus, the
effective parameters account for the sub-grid variabilities of land surface
properties, such as terrain or soil information.
Derivation of representative parameter sets
One of the goals of this study is to derive consistent model parameters to
perform nationwide simulations of water fluxes and states. A two-step
parameter selection procedure was used for this purpose. In the first step,
we estimate 100 sets of global parameters via calibration in each of the
seven inner German river basins (Fig. ) independently.
In the next step, we transfer these calibrated parameter sets to the
remaining basins. The parameter sets exceeding a Nash–Sutcliffe model
efficiency of 0.65 (NSE ≥ 0.65) in all seven basins during the
evaluation period (1965–1999) are retained. This parameter selection
procedure ensures that the resulting ensemble parameter sets do not exhibit
spatial discontinuities at basin boundaries.
The calibration is performed using the dynamically dimensioned search (DDS)
algorithm (). The objective function for calibration
consists of an equally weighted power-law function for the NSE
of the streamflow and the logarithm of the streamflow to
consider high and low flows within the objective function. A compromise
programming technique using a power law with an
exponent p=6 is used to estimate the multi-objective function (Φ).
This technique ensures equal improvement of the different measures ϕi
during a multi-objective calibration. The overall objective function Φ
is given as
Φ=∑i=12wipϕip1pwith∑wi=1
with
ϕ1=NSE(Q)=1-∑t=1T(Qt^-Qt)2∑t=1T(Qt-Q‾)2,ϕ2=NSE(lnQ)=1-∑t=1T(lnQt^-lnQt)2∑t=1T(lnQt-lnQ‾)2,
where wi is the weight (w1=w2=0.5) for a particular measure ϕi,
Qt^ and Qt denote the modeled and observed streamflow at a time
step t, respectively. Q‾ is the mean of the observed streamflow over
all time steps T.
A period of 5 years from 2000 to 2004 is chosen for model calibration. This
time period reflects various hydrologic conditions ranging from a high-impact
flood event in central Europe in August 2002 to a significant drought event
in 2003. The remaining 35 years of available data (1965–1999) are used for
model evaluation. All simulations are conducted with a 5-year spin-up period
to abrogate the influence of initial conditions.
In total, 100 independent calibration runs are performed for each of the seven
basins (Fig. ). Using 2000 model iterations per calibration
run led to a large number of model evaluations per basin (200 000). Finally,
100 of the 700 parameters sets are retained to derive nationwide ensemble
simulations of water fluxes and states at a daily resolution.
Validation data
In addition to streamflow in the seven major German river basins, the model
performance is evaluated against streamflow in 222 additional basins and
complementary datasets including evapotranspiration, soil moisture, and
groundwater recharge. The cross-validation of ensemble parameter sets in basins
that have not been used for parameter inference should prove the ability of the
model to satisfactorily estimate streamflow in various regions of Germany with
differing hydrologic characteristics.
The basins for cross-validation are distributed all over Germany and range in
size from 100 to 8500 km2. A detailed characterization of these basins
is given in Table S3 in the Supplement. A subset of these basins contains
sub-basins of seven major basins. The simulation time period is adopted for
the available streamflow observations but is at least 10 years. The mean
simulation time period of all 222 basins is 42 years. The streamflow
estimation in these basins is evaluated using the ensemble median NSE, and
its uncertainty is characterized by the range between the 5th and 95th
percentiles of NSEs of the ensemble simulation.
Local evapotranspiration observations are available at seven eddy covariance
towers located in Germany (Fig. ,
www.europe-fluxdata.eu). Carbon and water fluxes, as well as all
components of the energy balance, latent heat (or evapotranspiration
Ea), sensible heat H, ground heat flux G, and net radiation
Rn, are measured at the towers. The energy balance is, however,
often not closed at the towers so that the
observed fluxes usually underestimate the real values, which needs to be
corrected before comparison with a model conserving the water balance. We
apply a correction to the observed fluxes similar to .
The corrected evapotranspiration values at the eddy sites are compared with
the corresponding model estimates based on the root mean squared error (RMSE),
the Pearson correlation coefficient (ρ), and the bias.
Additionally, soil moisture observations, undertaken at eddy covariance
stations, are used to evaluate modeled soil moisture. Soil moisture is
measured using Time-Domain Reflectometer (TDR) or Frequency-Domain Reflectometer (FDR) sensors, which have a control volume of a few
cubic centimeters. This is much smaller than the model resolution of
100 m × 100 m. A direct comparison between observed and simulated
soil moisture may therefore be misleading due to differences in spatial
representativeness and sampling depth. Here we aim to analyze the temporal
dynamics of soil moisture by normalizing the respective soil moisture time
series . The anomalies are calculated as
z(t)=SM(t)-μσ,
where μ is the mean and σ is the standard deviation of the entire
soil moisture (SM) time series at a daily resolution. It is not possible to use
deseasonalized values (normalization with monthly values) because the time
periods of the available observations are too short (≈6 years). The
modeled soil moisture is defined herein as the fraction of porosity, i.e.,
the soil water content divided by porosity.
The mHM simulation for comparing the observations at the location of the eddy
covariance stations is conducted with deactivated lateral processes on a
single grid cell. The model resolution (100 m × 100 m) is adapted
to the size of the footprint of the energy flux measurements, which is
typically several tens to hundreds of meters. Rather than downscaling the
model results, the hydrologic processes are modeled at the resolution of the
observations. The transferability of mHM across scales is presented in
and .
The model is evaluated with spatially distributed data, i.e.,
evapotranspiration and groundwater recharge, additionally to the evaluation
of the model at the point or local scale. A remote-sensing-based dataset is
used for evaluating the monthly modeled evapotranspiration between 2001 and
2010. For this purpose we used the gridded evapotranspiration
(Ea) dataset based on the Moderate Resolution Imaging
Spectroradiometer (MODIS), which was acquired from the Numerical Terradynamic
Simulation Group at the University of Montana . The
spatial resolution is approximately 5 km × 5 km (0.05∘),
which is close to the model resolution of 4 km × 4 km. The
evapotranspiration estimates are based on the Penman–Monteith energy balance
equation using global daily temperature, actual vapor deficit, incoming solar
radiation as well as remotely sensed leaf area index, fraction of
photosynthetic active radiation, albedo, and land cover characteristics. The
meteorological variables are based on the reanalysis product from the Global
Modeling and Assimilation Office, whereas vegetation products are derived
from MODIS. Interested readers may refer to
for a detailed description of the MODIS Ea product.
As a second spatial dataset, we utilize a long-term estimate of annual
recharge over Germany (1961–1990). Due to the lack of observations, the
estimated recharge from the Hydrologic Atlas of Germany is taken
here as a reference. This recharge estimate is obtained using a multiple
regression model accounting for long-term-estimated generated runoff, depth
of the groundwater table, and regionalized baseflow indices
. The regionalized baseflow indices are estimated with a
linear regression based on the ratio between direct runoff and total runoff as
well as terrain properties, such as slope and land cover among others. Due to
the various assumptions and mathematical fittings behind this recharge
estimate, it is taken as an indication for model evaluation rather than an
evidence. The gridded recharge estimate is available at a
1 km × 1 km spatial resolution, which is remapped to a
4 km × 4 km resolution using bilinear interpolation to be
comparable to the model estimates.
Uncertainty of ensemble model simulations
The uncertainty of the modeled evapotranspiration, groundwater recharge,
grid-cell-generated runoff, and soil moisture is assessed by two different
criteria. First, the spatially distributed uncertainties are presented as
maps showing the coefficient of variation cv, which is defined as
cv=σμ,
in which μ is the mean and σ the standard deviation of the
ensemble simulations. A large cv describes a large variation in
the modeled flux or state normalized with μ. μ and σ are
derived from the 100 ensemble realizations of the hydrologic model mHM on
every grid cell. The variances within the ensemble simulation are caused by
predictive uncertainties. These uncertainties stem from the parametric
uncertainty itself and from the transfer of parameters to locations that have
not been used for model calibration. In the following, the variations of the
ensemble simulations are denoted as uncertainty.
Model performance expressed as Nash–Sutcliffe efficiency (NSE) at
daily (a, b) and monthly (c, d) resolutions for the calibration
period 2000–2004 (a, c) and validation period 1965–1999
(b, d). The white box plots show the results of the on-site
calibration, whereas the gray box plots are simulations using the 100
ensemble parameter sets for Germany. Please note that the y axis starts at
NSE = 0.5.
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Second, to assess the temporal variation of the uncertainty throughout a
year, the range and normalized range of the respective flux or state are
considered. The range is defined as the difference between the 5th (p5)
and 95th (p95) percentiles of the ensemble simulation, whereas the
normalized range is defined as
r=p95-p5p50,
where p50(x) denotes the median value of the ensemble simulation (50th
percentile). The 5th and 95th percentiles are chosen to exclude potential
outliers from the analysis.
Results and discussion
The model simulations are evaluated against multiple variables available at
different spatial and temporal resolutions. These include daily and monthly
time series of streamflow measured at the basin outlets, soil moisture, and
evapotranspiration at seven eddy covariance sites, monthly fields of
satellite retrieved evapotranspiration, and a long-term, annual recharge map.
mHM simulations are carried out at an hourly timescale at two spatial
resolutions, i.e., 100 m × 100 m at the eddy covariance stations
and 4 km × 4 km at the basin level and for the nationwide ensemble
simulations. Finally, an analysis of the model runs for the nationwide water
fluxes and states, including grid-cell-generated runoff (QG),
evapotranspiration (Ea), groundwater recharge (R), and
soil moisture (SM), is presented. The focus here is to provide a comprehensive
overview of regional-scale water fluxes and states over Germany and analyze
the uncertainty in modeled variables due to an ensemble of model parameters.
The uncertainties are investigated with respect to their temporal and spatial
distributions and their triggering sources. Finally, the interaction of
uncertainties through the different model states and fluxes is analyzed.
Streamflow evaluation in major German river basins
In this section we present the evaluation of mHM simulated streamflow with
observations in terms of NSEs at daily and monthly timescale for a validation
(1965–1999) and a calibration (2000–2004) period. Additionally, we show the
hydrographs resulting from the ensemble parameter sets in comparison with
observed streamflow.
The daily streamflow dynamics in the major German basins is satisfactorily
captured by the model revealing a mean NSE of 0.89 and 0.84 using the on-site
calibrated parameters in the calibration and validation periods, respectively
(white boxes in Fig. a and b). The model performance is lower
during the validation period in comparison to the calibration period. Such a
deterioration of model performance, which is common to other hydrological
model applications, is caused by differences in hydro-meteorological regimes
between the calibration and validation periods
and constraining (overfitting) of the parameters to compensate for errors in
the model structure . Using the on-site calibrated parameter
sets, the model exhibited improved performance for monthly streamflow
simulations with an average median NSE of 0.97 and 0.92 during the
calibration and validation period, respectively (white boxes in
Fig.c and d).
Observed and modeled monthly streamflow for the seven basins,
which were used for parameter inference. The figure shows 1 decade
(1990–1999) of the evaluation period. The solid dark gray line depicts the
median model results and the light gray band depicts the range between the
5th and 95th percentile of the 100 ensemble simulations.
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The ensemble parameter sets, which are depicted as the gray boxes in
Fig. , also reveal appropriate model performance. The median
NSE corresponding to the ensemble parameter sets is 0.80 for daily streamflow
in the validation period averaged across the seven basins. The median NSE of
the ensemble parameters drops by approximately 6 % compared to that of
the on-site estimated parameters. This loss is reasonable considering that
the ensemble parameter sets are a compromise solution, which should perform
well across all seven basins (see Sect. ). The performance
loss can be attributed to changes in the specific basin climatic and
land-surface conditions including terrain, soil, and vegetation properties.
Changes in the predictive uncertainty corresponding to on-site and ensemble
parameter sets are assessed using the range of model performance. The spread
of NSEs for the monthly streamflow is considerably narrower compared to the
daily flows (Fig. ). The high temporal variability of the daily
streamflow is smoothed when averaged over a longer (monthly) timescale
leading to an overall better correspondence between observed and simulated
flows.
The ranges of NSEs corresponding to the 100 on-site and ensemble parameter
sets are comparable across the investigated basins with exception of the Main
and Danube basins. In these two basins the ensemble parameter sets provided a
relatively larger range of NSEs. The relatively higher spread in the NSE in
those basins is likely to stem from the fact that different basins are
sensitive to different parameters. For example, the Ems basin, located in the
maritime-influenced north, is not as sensitive to snow parameters as the
alpine-influenced Danube basin. Consequently, parameters that originate from
the Ems basin potentially deteriorate ensemble predictions in the Danube
basin. A simultaneous calibration of
multiple, distinct basins would be beneficial for deriving hydrological
fluxes and states at national or continental scales.
Examples of the modeled streamflow time series are given in
Fig. . In general, the model is able to adequately capture
the discharge dynamics across the investigated basins. A relatively lower
model skill in capturing the discharge dynamics in the Saale basin can
be attributed to heavy human interactions. The highly regulated streamflow in
the headwaters of the Saale (see Sect. ) is difficult to
capture and thus leads to lower performance because mHM includes no reservoir
operation. The main discharge mechanisms of Saale are considered to be
adequately captured because the median NSEs are exceeding 0.85 and 0.7 at the
monthly and daily resolutions for the ensemble parameter sets, respectively
(Fig. ).
Interestingly, this basin shows equal or higher performance for the
ensemble parameter sets compared to the on-site parameter sets in the evaluation
period. A similar behavior can be observed for the Weser basin. We conclude
that streamflow simulations in some basins improve by gaining knowledge from
remote locations.
Budyko plot and performance maps for 100 ensemble parameter sets at
222 basins spread over Germany. The upper row depicts evaluations based on
daily values (a, b, c), whereas the lower row depicts monthly
streamflow evaluations (d, e, f). In the first column the basins
are presented as Budyko plots (a, d), which are color-coded based
on the ensemble median NSE for daily (a) and
monthly (d)
streamflow values. The gray band envelops different estimations of the Budyko
curve . A separation to
energy- (Ep/P<1) and water-limited basins (Ep/P>1) can be made
based on the x axis. The center column depicts the location of the 222
basins shown in the Bydyko plots using the same color code (b, e).
The right column shows the range of the 5th and
95th ensemble percentiles for the NSE on daily (c) and
monthly (f) basis. (a), (b), (d), and (e) share the left color bar, and
(c) and (f) share the right color bar. The simulation period is adopted
according to the available streamflow observations but is at least 10 years
(average = 42 years).
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The Mulde basin has a tendency to underestimate peak flows
(Fig. ). This could be attributed to the precipitation
product. The headwaters of the Mulde basin are located in the Ore mountains
at the border between Germany and the Czech Republic (Fig. ).
In addition to a sparse network of rain gauges in these mountainous area, a
lack of information on meteorological variables from the neighboring country
(i.e., the Czech Republic) leads to an underestimation of precipitation in
the interpolation process, especially for orographic-driven events. The model
performance for the Mulde is comparably superior to those found by other
studies, such as or .
The results presented in this section show that the method for determining
ensemble parameter sets (Sect. ) leads to satisfactory
estimations of streamflow in the basins used for parameter inference.
Overall, the model performance shown herein compares well to those of other
studies, such as ; and . A further investigation of the
applicability of the ensemble parameter sets on additional, smaller basins is
shown in the following section.
Streamflow evaluation at non-calibrated basins
Following , the model performance is evaluated across 222
basins diverging in size and geographical location. The streamflow data of
these proxy locations have not been used during the model calibration. This
cross-validation test focuses on evaluating the model performance against
streamflow simulations along a diverse range of climatic and land-surface
conditions. The evaluations shown in Fig. indicate a
satisfactory agreement between simulations and observations. The daily
streamflow simulations (Fig. a, b) reveal a median NSE value
of at least 0.5 across the investigated basins based on the ensemble
parameter sets. The overall average NSE value is 0.68. As expected, the model
exhibits better skill in capturing monthly streamflow dynamics, with an
ensemble median NSE averaged across all basins of approximately 0.81
(Fig. d, e). Furthermore, the ensemble median NSE exceeded a
value of 0.75 in more than 20 % of the basins for the daily flows and
80 % for the monthly flows. The spatial variability of the median NSE
across the investigated basins is low with a standard deviation of
approximately 0.09 for both daily and monthly flows.
To illustrate different climatic regimes of the 222 basins, we make use of
the dryness index Ep/P . Various studies describe the
relationship between the dryness and evaporative index Ea/P
and span an
uncertainty band around Budyko's curve. The model performance of the 222
basins is plotted in panels (a) and (d) of Fig. using these
indexes. It separates the basins into energy- (Ep/P<1) and water-limited
conditions (Ep/P>1). The simulated evapotranspiration Ea is used to
derive the Budyko plot to identify potential errors in the water balance
closure (Fig. a, d). All basins under investigation lie
perfectly within the uncertainty ranges of the reported theoretical curves.
Please note that energy-limited basins are closer to the lower uncertainty
line of the reported curves, whereas water-limited basins tend to the upper
curve. In consequence basins with energy limitation tend to underrepresent
the original Budyko curve and develop to overrepresentation for water-limited
locations. In conclusion, the water balances of those basins are well closed,
with a mean closure error of 1 % for the median simulation. The
performance is comparable for basins in different climatic regimes. Such
behavior is not obvious as studies such as and
found a significant dependency on the climatic regime.
However, a tendency to perform better in large basins is observed. A similar
conclusion was drawn by .
Observed (Ea,obs) versus ensemble median modeled
evapotranspiration (Ea,mod) on daily basis at the seven eddy
covariance stations (Fig. , Table ).
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We further analyzed the relationship between model performance and
physiographic attributes (e.g., terrain or land cover characteristics). These
analyses did not show any significant relationship (see
Fig. ). The absence of pairwise relationships between model
performance and climatic or land-surface characteristics confirms the
validity of the derived ensemble parameters for the national scale. In
contrast, and observed significant
dependencies between model performance and basin characteristics, such as
aridity or basin area.
The uncertainty for the individual basins caused by the ensemble parameter
sets is expressed as the range between the 5th and 95th percentiles of
the NSE (Fig. c, f). Substantial performance differences occur
in 70 % (45 %) of the basins exceeding a range of 0.1 NSE for the
daily (monthly) flow simulations. A geographical dependency of the
uncertainty cannot be found as no spatial clustering is observed. Whereas
daily flows show almost no relation between median NSEs and the uncertainty
range, i.e., worse performing basins reveal high uncertainties,
the monthly NSEs show less
uncertainty if the corresponding model performance is high.
The evaluation of the ensemble parameter sets presented in this section supports
the hypothesis that the ensemble parameter sets are valid on the national
scale. Studies such as ; and
validate their models based on streamflow over a large
sample of basins and observed similar or lower NSEs. In the following section,
evapotranspiration, soil moisture, and groundwater recharge estimates are
evaluated.
Exemplary time series of observed and modeled monthly
evapotranspiration and daily soil moisture anomalies at four eddy covariance
stations (Fig. , Table ). The four
stations are chosen because they represent the two major mHM land cover
classes (forest and mixed) and have 3 consecutive years of data without
significant data gaps. Further the four station are spread over the three
regions where eddy covariance observations are available. The solid dark
gray line depicts the median model results and the light gray band depicts
the range between the 5th and 95th percentile of the
100 ensemble simulations.
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Evapotranspiration and soil moisture evaluation at eddy covariance
stations
The ensemble model simulations are further evaluated with the
evapotranspiration (Ea) and SM observed at seven
eddy covariance stations (Fig. ) to assess the model's
ability to represent other fluxes and states next to streamflow. The ensemble
median of the daily sum of evapotranspiration is plotted against the
corresponding observations in Fig. , and the resulting error
metrics are summarized in Table .
The scatter plots shown in Fig. indicate no systematic
over- or underestimation of the observed evapotranspiration. The highest
deviation in terms of RMSE is observed during summer, when the highest fluxes
occur, and the lowest during winter, in which the contribution of
Ea is lowest among all seasons. The average bias estimated across
all stations during spring is 0.34 mm d-1, whereas it is 0.08, 0.04,
and 0.04 mm d-1 for winter, summer, and autumn, respectively. The
slight overestimation of the modeled Ea during spring is likely
caused by the lack of a dynamic vegetation growth module in mHM. Thus, the
onset of the vegetation period may not be captured adequately by the model.
With respect to the vegetation class, the stations E1 and E6 covered by crops
have the largest errors, with Ea RMSEs of 19.4 and
15.4 mm month-1 for monthly evapotranspiration, respectively
(Table ). These errors arise because of the high impact of
human interactions on croplands, e.g., due to seeding, harvesting, or
irrigation, compared to other vegetation classes. Additionally, the land
cover class cropland is not explicitly represented within the model; rather,
it is generalized within a mixed land cover class, representing all land
cover types different from sealed and forest. Varying goodness of fit for
different land covers and seasons for evapotranspiration at eddy flux towers
were found for the four land surface models used in NLDAS and
thus are not uniquely observed for mHM.
In general, errors of local evapotranspiration estimates can be attributed to
limitations of the Hargreaves–Samani approach for estimating the potential
evapotranspiration. This approach may be inappropriate for local weather
conditions. Because this method approximates the net radiation based on the
minimum and maximum daily temperatures, local phenomena such as short-term
cloudiness, e.g., due to convective precipitation cells, are not accounted
for. This effect is especially high in summer, which causes the lowest
correlations between observations and simulations during this period.
Unfortunately, only temperature-based methods are supported by the available
input data. Please notice that the observational error caused by the energy
balance closure gap is, on average, 33 % for the herein considered
stations before applying the abovementioned mathematical corrections.
In terms of temporal dynamics, the model is able to capture the observed
evapotranspiration quite well across the different eddy covariance sites, as
exemplarily shown in the upper panel of Fig. . The model
is able to adequately represent the observed monthly dynamics with an average
correlation of approximately 0.93 (Table ). The correlation
between the observed and the simulated daily evapotranspiration is at least
0.77, with the exception of the cropland site E1.
The lower panel of Fig. shows the performance of mHM in
representing the daily soil moisture anomalies, which are generally in good
correspondence with observations. The temporal dynamics of observed soil
moisture anomalies during the wetting and drying phases are well captured by
the model. The resulting correlation shown in Table at
different eddy stations ranges between 0.53 and 0.93. These correlations were
similar to those of other studies, such as . The lowest
values are observed at cropland sites, which is due to the abovementioned
human interaction and land cover class representativeness. The amplitude of
the observed soil moisture anomalies is adequately captured by the model.
Still, some peaks are not reproduced satisfactorily, which could be due to
the non-representativeness of the 100 m × 100 m model grid cell
for TDR/FDR soil moisture measurements. Thus, the simulated soil moisture is
smoother compared to the observation because it represents the effective soil
moisture of the entire grid cell.
Evaluation of evapotranspiration Ea and soil moisture
SM at seven eddy covariance stations. The evaluation is based on daily
and monthly values for the available observation period. The
location of the eddy stations is depicted in
Fig. . Abbreviations: RMSE – root mean squared error,
ρ – Pearson correlation coefficient, Ea –
evapotranspiration, SM – soil moisture.
ID
Station name
Period
Land cover
Monthly Ea
Daily Ea
Daily SM
[mm mon-1]
[–]
[mm d-1]
[–]
[–]
RMSE
Bias
ρ
RMSE
Bias
ρ
ρ
E1
Gebesee
2003–2008
cropland
19.14
0.61
0.85
1.01
0.02
0.67
0.62
E2
Hainich
2000–2007
DBF1
11.72
6.99
0.95
0.62
0.23
0.87
0.68
E3
Mehrstedt
2003–2006
grassland
12.44
5.78
0.94
0.74
0.18
0.79
0.80
E4
Wetzstein
2004–2008
ENF2
9.86
1.58
0.96
0.73
0.05
0.84
0.80
E5
Grillenburg
2004–2008
grassland
13.93
-4.19
0.94
0.89
-0.14
0.8
0.93
E6
Klingenberg
2004–2008
cropland
15.39
9.38
0.93
0.86
0.31
0.77
0.53
E7
Tharandt
1997–2008
ENF2
13.39
7.71
0.96
0.72
0.26
0.83
0.82
1 Deciduous broadleaf forest. 2 Evergreen needleleaf
forest.
Comparison of monthly estimates of evapotranspiration from mHM and
MODIS in the period 2001–2010. The ensemble is represented by the ensemble
mean of 100 evapotranspiration estimates. The comparison is based on three
metrics: (a) relative bias, (b) Pearson correlation coefficient, and (c) root
mean squared error (RMSE). The respective units are given in brackets.
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Evaluation with spatially distributed data
In this section, we present results of the model skill in representing
gridded fluxes over the entire German domain. The first comparison is
conducted for the assessment of reproducing the monthly fields of modeled
Ea against the remotely sensed MODIS product. The results are
summarized in Fig. in terms of three key metrics:
relative bias, correlation, and RMSE. The analysis is conducted using the
ensemble mean of Ea from the 100 model simulations. The modeled
Ea is able to adequately capture the spatiotemporal features of
the MODIS derived product with the majority of grid cells (74 %) having a
relative absolute bias of less than 10 %. Notable differences among these
two evapotranspiration datasets are appearing in lowland areas along the
Danube River basin in southern Germany, where the modeled Ea
exhibited a dry bias compared to MODIS. An opposite trend of positive bias in
modeled Ea is observed for grid cells lying along the coastal
region in northern Germany. The temporal correspondence between both
evapotranspiration datasets is also remarkably high with an average Pearson
correlation coefficient of 0.96 (standard deviation 0.02). Notably, both
evaporation datasets exhibit pronounced seasonal variability leading to a
high temporal correspondence between them.
The second assessment evaluates the modeled groundwater recharge with
long-term annual values from the Hydrologic Atlas of Germany (HAD)
. mHM's long-term recharge estimate implicitly represents the
baseflow component of the total runoff based on the assumption that the
underground basin is closed and that there are no external losses (e.g.,
irrigation or pumping). Consequently, this analysis serves as a proxy for
assessing the model skill for partitioning the total runoff into interflow
and baseflow. The comparison of the spatial pattern of the recharge shows
good accordance between the two maps with a correlation coefficient of
approximately 0.8 (Fig. ). The spatial pattern of the
recharge follows the known climatology of Germany with high recharge rates
being observed in areas with high precipitation amounts (e.g., Alps –
region 11 in Fig. ).
Comparison of mean annual groundwater recharge (R) modeled with
(a) mHM and from (b) the Hydrologic Atlas of Germany . Panel (c) shows the difference (a–b) between the two datasets. The units are [mm a-1] for all panels.
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There are some significant differences between the modeled and HAD
groundwater recharge, particularly at cells characterized by urbanization
(i.e., Munich, Hamburg, Berlin, and the metropolises of Ruhrgebiet in the
northwest). The model tends to underestimate the HAD recharges, with
differences as high as approximately 200 mm a-1. Notably, the herein
used version of mHM treats sealed areas as almost impermeable, which is
unrealistic. This issue has been resolved in recent mHM versions (5.0 and
higher). In general, the HAD estimate of recharge is, on average,
31 mm a-1 higher compared to the ensemble mean simulation. This
mismatch arises from the differences in potential evapotranspiration
(Ep), which were used for both estimates. The Ep
estimates used for the HAD are lower than those used for mHM
simulations and result in higher water amounts remaining in the underground.
Besides these mismatches, the spatial pattern of the modeled groundwater
recharge compares well with the HAD estimates (Fig. ).
Spatial patterns of ensemble means and uncertainties
The estimated evapotranspiration (Ea) and grid-cell-generated
runoff (QG), as well as their uncertainty, which is expressed as
the coefficient of variation of the ensemble simulations, are presented in
Fig. . In addition to these simulation results,
Fig. shows the mean annual precipitation, dryness index, and
land surface properties, i.e., porosity and dominating land cover type. Thus,
Fig. is used to analyze the spatial patterns of uncertainty
and their main causes.
Water balance variables, their coefficients of variation, and land-surface characteristics for Germany. (a) Mean annual precipitation P,
(b) ensemble mean annual evapotranspiration Ea, (c) grid-cell-generated
runoff QG, (d) dryness index Ep/P, (e) sum of porosities (saturated soil
water content) of all model layers, (f) coefficient of variation of the
ensemble of annual evapotranspiration and (g) generated runoff, (h) dominating
land cover class on a 4 km × 4 km grid. The mean values and
coefficients of variation are based on the period 1951–2010.
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The high precipitation amounts above 1000 mm a-1 in panel (a)
correspond to mountainous areas in Germany. The driest region is located in
the northeastern part of Germany. This is, on the one hand, due to its
distance to the sea (continental climate) and, on the other hand, due to the
Central Uplands in the western and central part of Germany. These mountains,
especially the Harz mountains (central Germany), capture most of the
precipitation events brought from the west. The low amounts of precipitation
in the east lead to lower amounts of evapotranspiration
(Fig. b) and grid-cell-generated runoff
(Fig. c) in this region compared to the rest of Germany.
Thus, the northeastern part of Germany is characterized by high dryness
indexes of 1.2 and above. The uppermost dryness indexes up to 1.4 are located
in the lee of the Harz mountains. The average dryness index in Germany is
0.98. Another region characterized by high dryness indexes is the Upper Rhine
Valley, which is known to have a locally warmer climate compared to its
neighboring regions. Mountainous regions are characterized by stronger energy
limitation due to high precipitation amounts, which results in dryness
indexes lower than 0.65.
The spatial distribution of the uncertainty, i.e., the coefficients of
variation (see Sect. ), of the grid-cell-generated runoff
(Fig. g) is mainly governed by the dryness index
(Fig. d). The Spearman rank correlation between both
variables is 0.92. The uncertainty patterns of evapotranspiration
(Fig. f) have a closer relation to soil textural properties,
i.e., porosity (Figure e), with a Spearman rank coefficient of
0.58 as compared to the dryness index (rank correlation = 0.28). Locations of
high uncertainty in Ea, e.g., northern Germany, correspond to
regions of high porosities. Within this region, soils are dominated by sand
and are highly conductive, which results in low water holding capacities. The
modeled evapotranspiration is highly dependent on the soil parameterization
because soil water is the main source of evaporative water. In contrast, the
uncertainty patterns of grid-cell-generated runoff, e.g., (QG) in
the northeastern part of Germany and the Upper Rhine Valley, correspond to
high values in the dryness index in those regions.
In conclusion, the spatial distribution of the uncertainty in
evapotranspiration is influenced by the parameterization of the soil, whereas
the runoff uncertainty pattern is dominated by the dryness index. The
patterns appearing in the evapotranspiration and grid-cell-generated runoff
at the location of big cities (orange areas in panel (h) of
Fig. ) are caused by the abovementioned old representation
of sealed areas for mHM versions prior to 5.0.
Spatiotemporal distribution of uncertainties
This section focuses on the spatiotemporal differences of uncertainties
caused by the 100 ensemble parameter sets. Figure shows the
climatological dynamics and the normalized ranges (see
Sect. ) of the respective variables, i.e.,
evapotranspiration (Ea), SM, groundwater recharge (R), and
grid-cell-generated runoff (QG). The rows refer to different
environmental zones in Germany , which are depicted in the
upper right corner of Fig. . For comprehensibility only a
selection of five environmental zones is depicted therein, representing the
region of high dryness indexes in the north (zone 2), central Germany
including Central Uplands (zones 4 and 9), the foothills of the Alps
(zone 10), and the Alps (zone 11).
Spatiotemporal patterns of uncertainty for five different
environmental zones in Germany. The locations of the different zones are
depicted on the map on the upper right. The presented hydrologic variables
are evapotranspiration (Ea), soil moisture (SM), recharge (R), and
grid-cell-generated runoff (QG). The uncertainty ranges and the ensemble median
refer to the left ordinate (black and gray), whereas the normalized
uncertainty range refers to the right ordinate (blue). The reference period
for the climatological values is 1951–2010.
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The magnitude of the evapotranspiration uncertainty, i.e., the uncertainty
range, is lowest among the four variables. Evapotranspiration is estimated by
scaling the potential evapotranspiration with the water availability in
several reservoirs, i.e., the interception storage, the surface ponds in
sealed areas, and the soil moisture. Notably, most of the areas in Germany
are characterized by humid and continental climate where the Ea
is constrained by available energy. The evapotranspiration is thus mainly
driven by the potential evapotranspiration. A relatively large uncertainty in
soil moisture does not directly propagate to evapotranspiration uncertainty.
The highest uncertainties are observed for the groundwater recharge. This
model's internal variable is neither closely related to the model input as
Ea nor indirectly constrained by calibration as the generated
runoff. In consequence, its
uncertainty is highest among the four variables.
The evapotranspiration uncertainty shows almost no dynamics during the course
of the year. In contrast, the uncertainty in recharge and runoff
changes significantly
during the course of the year. Whereas the dynamics of the groundwater
recharge and its uncertainty are positively correlated, the correlation for
soil moisture and its uncertainty is negative. Thus, the recharge uncertainty
is the lowest for low recharge values, which occur in summer when the
subsurface reservoirs are comparably dry. The low amplitude of the soil
moisture uncertainty is reasoned in the high persistence of soil moisture.
Regions of high porosity and low dryness indexes in northern Germany have
more distinct dynamics compared to southern locations. The uncertainty of the
generated runoff is a composite of the dynamics of soil moisture and recharge
and thus shows the distribution of water among the model's internal
reservoirs.
Summary and conclusion
In this study, we present the derivation and evaluation of a high-resolution
(4 km × 4 km) dataset of hydrologic and meteorological fluxes and
states for Germany covering the period 1951–2010, which is freely available.
The dataset incorporates 100 spatially consistent ensemble simulations, which
are analyzed regarding their uncertainty caused by the parameter estimation.
The parameter sets of the ensemble simulations are determined by a two-step
parameter selection method. The model is calibrated in seven basins, and the
parameter sets are filtered based on the cross-validation results in all of
the basins. Thus, the uncertainty is composed of the uncertainty in parameter
estimation and the uncertainty stemming from transferring these parameters to
remote locations. The ensemble simulations are evaluated with streamflow,
evapotranspiration and soil moisture observations, and recharge data.
A comparable study by focuses on the provision of a 100
member ensemble dataset, which is focusing on meteorological variables for major
parts of North America. Similar to the study presented herein they evaluate the
data in a large sample of basins, i.e., 671. We, however, conclude that 100
realizations is an appropriate sample size for an uncertainty assessment study.
The evaluation regarding streamflow at 222 additional basins revealed a
median NSE of 0.68. Thus, the 100 ensemble parameter sets are considered to
be representative for Germany. The evaluation with evapotranspiration from
eddy covariance stations showed deficiencies in mHM. Especially in spring,
deviations of the modeled and observed Ea indicate room for
improving the representation of vegetation dynamics within mHM. The sites
covered by cropland showed the largest deviations from evapotranspiration
observations because croplands are highly human-influenced (seeding, harvest,
or eventually irrigation), which makes it difficult to model their dynamics
at the local scale. Additionally, cropland is generalized in a mixed land
cover class in mHM. Soil moisture estimations at the same locations have been
in good agreement with the observed dynamics.
The second part of the study focuses on the uncertainty of the simulated
hydrological fluxes and states due to uncertainties in parameter estimation.
It is shown that uncertainty varies in time, location, and magnitude between
hydrological variables. Among all of the variables, the uncertainty was the
lowest for evapotranspiration and the highest for groundwater recharge. The spatial distribution of runoff uncertainty is
closely related to the spatial distribution of the dryness index. In
contrast, the uncertainty patterns of evapotranspiration estimates are mostly
connected to soil properties. In general, the highest uncertainties occur in
the northeastern part of Germany, which is characterized by low precipitation
amounts and high soil porosities. The temporal variation of uncertainties is
almost constant for evapotranspiration, medium for grid-cell-generated runoff
and soil moisture, and high for groundwater recharge and depends on
geographical location.
Based on these results we suggest incorporating additional data, e.g., in situ
soil moisture or satellite observations, into the calibration procedure to better
constrain the model's internal states. The results of this study emphasize the
importance of the considering parametric uncertainty for
historical analysis, nowcasting, and forecasting in hydrology.