HESSHydrology and Earth System SciencesHESSHydrol. Earth Syst. Sci.1607-7938Copernicus PublicationsGöttingen, Germany10.5194/hess-22-1299-2018Combining satellite data and appropriate objective functions for improved spatial pattern performance of a distributed hydrologic modelDemirelMehmet C.mecudem@yahoo.comhttps://orcid.org/0000-0003-4402-906XMaiJulianehttps://orcid.org/0000-0002-1132-2342MendigurenGorkahttps://orcid.org/0000-0001-5807-1299KochJulianhttps://orcid.org/0000-0002-7732-3436SamaniegoLuishttps://orcid.org/0000-0002-8449-4428StisenSimonsst@geus.dkhttps://orcid.org/0000-0001-6695-8412Geological Survey of Denmark and Greenland, Øster Voldgade 10, 1350 Copenhagen, DenmarkDepartment Computational Hydrosystems, UFZ – Helmholtz Centre for Environmental Research, Leipzig, GermanyDepartment of Geosciences and Natural Resource Management, University of Copenhagen, Copenhagen, DenmarkDepartment of Civil and Environmental Engineering, University of Waterloo, Waterloo, CanadaDepartment of Environmental Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, DenmarkDepartment of Civil Engineering, Istanbul Technical University, 34469 Maslak, Istanbul, TurkeyMehmet C. Demirel (mecudem@yahoo.com) and Simon Stisen (sst@geus.dk)20February20182221299131518September20179October201717January201818January2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://hess.copernicus.org/articles/22/1299/2018/hess-22-1299-2018.htmlThe full text article is available as a PDF file from https://hess.copernicus.org/articles/22/1299/2018/hess-22-1299-2018.pdf
Satellite-based earth observations offer great
opportunities to improve spatial model predictions by means of spatial-pattern-oriented model evaluations. In this study, observed spatial patterns
of actual evapotranspiration (AET) are utilised for spatial model
calibration tailored to target the pattern performance of the model. The
proposed calibration framework combines temporally aggregated observed
spatial patterns with a new spatial performance metric and a flexible
spatial parameterisation scheme. The mesoscale hydrologic model (mHM) is
used to simulate streamflow and AET and has been selected due to its soil
parameter distribution approach based on pedo-transfer functions and the
build in multi-scale parameter regionalisation. In addition two new spatial
parameter distribution options have been incorporated in the model in order
to increase the flexibility of root fraction coefficient and potential
evapotranspiration correction parameterisations, based on soil type and
vegetation density. These parameterisations are utilised as they are most
relevant for simulated AET patterns from the hydrologic model. Due to the
fundamental challenges encountered when evaluating spatial pattern
performance using standard metrics, we developed a simple but highly
discriminative spatial metric, i.e. one comprised of three easily interpretable
components measuring co-location, variation and distribution of the spatial data.
The study shows that with flexible spatial model parameterisation used in
combination with the appropriate objective functions, the simulated spatial
patterns of actual evapotranspiration become substantially more similar to
the satellite-based estimates. Overall 26 parameters are identified for
calibration through a sequential screening approach based on a combination
of streamflow and spatial pattern metrics. The robustness of the
calibrations is tested using an ensemble of nine calibrations based on
different seed numbers using the shuffled complex evolution optimiser. The
calibration results reveal a limited trade-off between streamflow dynamics
and spatial patterns illustrating the benefit of combining separate
observation types and objective functions. At the same time, the simulated
spatial patterns of AET significantly improved when an objective
function based on observed AET patterns and a novel spatial performance
metric compared to traditional streamflow-only calibration were included. Since the
overall water balance is usually a crucial goal in hydrologic modelling,
spatial-pattern-oriented optimisation should always be accompanied by
traditional discharge measurements. In such a multi-objective framework, the
current study promotes the use of a novel bias-insensitive spatial pattern
metric, which exploits the key information contained in the observed
patterns while allowing the water balance to be informed by discharge observations.
Introduction
Reliable estimations of spatially distributed actual evapotranspiration (AET)
are useful for various sustainable water resources management
practices such as irrigation planning, agricultural drought monitoring and
water demand forecasting in large cultivated areas (Wei et
al., 2017). Distributed hydrologic models can potentially provide this
insight since evapotranspiration (ET) is a major part of the water cycle. In spite of their
ability to simulate detailed spatial patterns of a range of hydrological
state variables and fluxes, distributed model evaluation remains focused on
temporal aspects of the aggregated streamflow variable
(Demirel et al., 2013; Schumann et al., 2013). We
are interested in including spatial AET patterns in the model calibration
using spatial parameterisations and complementary objective functions.
Different methods exist that utilise satellite-based land surface
temperature data to derive spatially detailed estimates of latent heat
fluxes from the land surface and canopy on a scale relevant for catchment
modelling (Kalma et al., 2008). Since AET cannot be
measured directly by satellite, surface energy balance models are developed
to estimate AET based on data from a range of spectral and thermal bands
(Guzinski et al., 2013; Norman et
al., 1995; Su, 2002). While these satellite-based estimates are usually
employed as a tool to understand and improve the model parameterisations
(Conradt et al., 2013; Hunink et al., 2017; Schuurmans et al., 2011), they can also be used to calibrate
models (Crow et al., 2003; Immerzeel and Droogers, 2008; Zhang et al., 2009). Therefore,
adding satellite-based observations to model calibration is not novel;
however, specifically evaluating spatial patterns in the calibration has
rarely been done (Stisen et al., 2011b).
Interesting examples exist where model calibration could benefit from the
spatial pattern information of actual evapotranspiration (Githui et
al., 2016; Li et al., 2009; Zhang et al., 2009) and satellite-based recharge
patterns (Hendricks Franssen et al., 2008). This paper
utilises monthly patterns of AET first to understand and organize ET-related
model spatial parameterisations and then to pursue a calibration. This is
because adding only temporal aspects of the spatial observations to the
objective function is not sufficient for achieving significant improvements
in simulated spatial patterns if model parameterisation is not flexible
enough to physically adjust to the observed pattern. Besides, the model
structure, parameterisations and calibration schemes have usually been
designed for streamflow optimisations (Vazquez et al.,
2011; Velázquez et al., 2010). In order to ensure compatibility between
the spatial pattern calibration target and model parameterisation, the
flexibility of the spatial model parameterisation needs to be reconsidered.
Recently, inadequate representation of spatial variability and hydrologic
connectivity of a well-known distributed model (VIC) has been reported by
Melsen et al. (2016). The mesoscale hydrologic
model (mHM) has the flexibility to alter the spatial patterns via
pedo-transfer function (PTF) parameters and by including a multi-scale
parameter regionalisation (MPR) scheme (Kumar et al., 2013; Samaniego et al.,
2010). Mizukami et al. (2017) incorporated this MPR approach
with VIC to estimate parameters for large domains based on geophysical data
for 531 basins. The multi-basin calibration results using MPR revealed
physically meaningful parameter fields without patchiness (discontinuities).
The study by Loosvelt et al. (2013) is one of few other examples that incorporate PTFs
for soil texture and moisture components of a hydrologic model.
All calibration strategies rely on the selection of performance metrics
indicating the goodness of fit of the model to be optimized. Choosing an
appropriate set of objective functions is crucial to build a robust
calibration strategy, since there will be trade-offs between different
objective functions or redundant information. In the hydrology literature,
there are a range of different temporal metrics for hydrograph matching while
metrics designed for spatial pattern matching are less common
(Koch et al., 2017; Rees, 2008). For distributed models,
spatial metrics usually evaluate cell-to-cell correlation and deviations
(e.g. Pearson's R and bias). The use of multi-component metrics as described
for discharge by Gupta et al. (2009) is, however, rare for
spatial pattern evaluation. An essential feature of our study is introducing
a new spatial efficiency (SPAEF) metric that contains three components,
i.e. correlation, variance and histogram intersection, providing reliable
bias-insensitive pattern information unlike other traditional metrics
focusing on only one aspect like correlation, mean squared error or bias.
Prior to model calibration, sensitivity analysis is usually conducted to
attribute response of the model outputs to the changes in model parameters
(Shin et al., 2013), which can enhance our
understanding of both temporal and spatial model behaviour
(Berezowski et al., 2015). In the context
of spatial model calibration, the sensitivity analysis should not only
identify the parameters that affect the water balance and hydrograph
dynamics but also the parameters that shape the spatial patterns of the
simulated states and fluxes. To achieve this, we have to design objective
functions that reflect the spatial pattern of the models and utilise these
in model parameter sensitivity analysis.
In light of the well-known equifinality problems in model calibration
(Beven and Freer, 2001) spatial pattern
evaluation can be useful for selecting the most appropriate parameter set
from a group of sets leading to both reasonable streamflow performance and
physically meaningful AET pattern. Immerzeel and Droogers (2008) showed how a semi-distributed
model of a basin in southern India could be constrained by using spatially
distributed observations with a monthly temporal resolution. Cornelissen et
al. (2016) highlighted the need to identify which model
parameters influence the simulated spatial pattern and showed that spatial
patterns of simulated evapotranspiration were most sensitive to the land-use
parameterisation, whereas precipitation was the most sensitive input data
with respect to temporal dynamics of the model. Rakovec et al. (2016)
used a total water storage (TWS) anomaly from the
Gravity Recovery and Climate Experiment (GRACE) satellites and
evapotranspiration estimates from FLUXNET data (https://fluxnet.ornl.gov/)
to improve model parameterisations for discharge simulations. They showed
that adding TWS anomalies to the calibration led to a reasonably good performance for
continental 83 European basins with different climatology.
The main objectives of this study are to incorporate spatial patterns of
satellite-based actual evapotranspiration data in the model calibration and
validation. In order to improve AET simulations, we use transfer functions
in the spatial model parameterisation that combine a priori maps of soil and
vegetation properties with few global calibration parameters in order to
enhance the spatial parameterisation flexibility and allow the parameter
field to adjust to an observed spatial patterns of AET from the catchment.
We also design a new multi-component metric specifically suited for
comparing spatial patterns of two continuous variables. Here, we prioritise
three main data properties, which are co-location, variation and
distribution. The calibration is conducted using three strategies for
objective function selection. First, streamflow metrics and spatial pattern
metrics are used in isolation during calibration and subsequently they are
combined in a more balanced model optimisation. In this way we can
investigate the trade-offs and robustness of the different approaches by
evaluating the performances regarding both streamflow and spatial patterns
during calibration and validation.
Study area and dataStudy area
The Skjern river basin is one of the most popular research basins in Denmark
as it is highly instrumented for hydrological monitoring, including eddy-flux
towers, a dense soil moisture network and other state-of-the-art monitoring
of hydrological variables (Jensen and Illangasekare, 2011).
The basin area is approximately 2500 km2, containing mostly sandy
soils (Fig. 1). The river is the largest in
Denmark by flow volume and located in the western part of the Jutland
peninsula, a region dominated by agriculture and forests together covering
∼ 80 % of the domain (Larsen et al.,
2016). The basin is mostly flat with a maximum altitude of 130 m and it
receives a mean annual precipitation of around 1000 mm
(Stisen et al., 2011a). The mean annual streamflow is
around 475 mm and monthly mean temperatures vary from 2 up to 17 ∘C
(Jensen and Illangasekare, 2011).
Skjern river basin location, soil type and land-use characteristics.
An average pattern of satellite-based actual evapotranspiration for June (average
of all years from 2001 until 2008) is presented to illustrate the interaction
between soil type and land use that generate the land surface flux patterns.
Overview of morphological and meteorological data used as input for mHM.
Acronyms: BIOS – BioScience Aarhus University, DMI – Danish Meteorological Institute,
GEUS – Geological Survey of Denmark and Greenland, MODIS – Moderate Resolution
Imaging Spectroradiometer, DGA – Danish Geodata Agency.
VariableDescriptionSpatialSourceresolutionQ (daily)StreamflowPointBIOSP (daily)Precipitation10 kmDMIETref (daily)Reference evapotranspiration20 kmGEUS and DMITavg (daily)Average air temperature20 kmGEUS and DMILAIFully distributed 12-monthly values based on 8-day1 kmMODIS and Mendiguren et al. (2017)time-varying leaf area index (LAI) datasetLand coverForest, agriculture and urban250 mGEUSDEM-related dataSlope, aspect, flow accumulation and direction250 mDGAGeology classTwo main geological formations250 mGEUSSoil classFully distributed soil texture data250 mGreve et al. (2007)Satellite-based data
The Moderate Resolution Imaging Spectroradiometer (MODIS) polar orbiting
platforms, Terra and Aqua, observe mid-latitude regions 4 times per day
at a spatial resolution of approximately 1 km × 1 km. The two-source energy
balance (TSEB) model proposed by Norman et al. (1995) based on the Priestley–Taylor approximation
(Priestley and Taylor, 1972) is used in this study to
calculate AET based on MODIS data under cloud-free conditions. The model
inputs are land surface temperature (LST), solar zenith angle (SZA), and albedo and height of canopy, all derived from MODIS observations
(Mendiguren et al., 2017). Additional
inputs such as climate variables of air temperature and incoming radiation
are obtained from ERA-Interim reanalysis data (Dee et
al., 2011). The main motivation of preparing a new AET dataset based on land
surface temperature is that most other available products are based mainly
on vegetation index data which may not be sufficient to assess the
complicated interplay among climate, soil and vegetation dynamics on the
AET patterns, especially during the growing season. For more details on our
newly produced AET data for Denmark, including equations, parameterisation,
calibration and validation, please refer to the recent study by Mendiguren
et al. (2017).
In this study, all remote-sensing-based AET data were averaged for each
month during the growing season across all years for the model calibration
period (2001–2008), resulting in six monthly mean maps from April to
September representing AET under cloud-free conditions. This ensures that in
spite of uncertainty in the individual instantaneous midday estimates of
AET, the monthly maps represent the general spatial pattern for each month
under cloud-free conditions. The individual daily AET patterns are evaluated
for temporal consistency by calculating the Pearson correlation between each
daily pattern and the monthly mean pattern for the given month. This
analysis showed that the overall average correlation between an individual
day and the monthly mean was 0.82. The satellite-based monthly AET maps are
validated against eddy-covariance measurements for three different land
cover types (forest, cropland and wetland) within the Skjern catchment and
display good agreement on the monthly timescale (Mendiguren et al., 2017). Despite
not being pure observations but rather estimates from an energy balance model based
on satellite observations, we will refer to these AET maps as reference
observations. Based on the sensitivity analysis in Mendiguren et al. (2017), which
showed that the TSEB is largely controlled by the satellite input of LST,
which can be considered an observation, it is assumed that the TSEB AET
estimates represent spatial patterns of AET that are suitable for pattern
evaluation of the hydrological model.
Hydrologic model
The mesoscale hydrologic model is a distributed model providing
various simulated spatial outputs, fluxes and states at different
spatio-temporal model resolutions (Samaniego et al., 2010, 2017).
The model includes pedo-transfer functions for soil parameterisation and
originally contains 53 global parameters that can be adjusted during
calibration. In this study, some parameters are fixed at a default value and
others have been added from the new spatial model parameterisations
resulting in a total of 48 global parameters for further analysis. The model
simulates major components of the hydrologic cycle, i.e. interception,
infiltration, snow accumulation and melting, evapotranspiration, groundwater
storage, seepage, and runoff generation. The readers are referred to the
study by Samaniego et al. (2010) for full model description,
assumptions, limitations and process formulations.
Table 1 provides a summary of the modelling data
used in this study. As shown in the table, meteorological data can be on a
different spatial scale than both morphological data and the model scale.
This flexibility arises from the fact that mHM incorporates a
multi-parameter regionalisation technique to swap between different scales
while calculating all fluxes and routing streamflow on a preferred model
scale. We run the model on 1 km × 1 km spatial scale and at daily time step. Some
processes like ET are calculated at an hourly time step then the final results
are aggregated to daily values. All morphological data are prepared on
250 m × 250 m scale. All three meteorological datasets, i.e. P, ETref and
Tavg, were originally at 10–20 km resolution. We re-sampled them to
1 km × 1 km using cubic interpolation. This interpolation method is used to avoid
patchiness in model simulations due to coarse grids on the native scale of
the metrological data. We use 12 monthly leaf area index (LAI) maps to represent the
climatology for both interception and PET correction for the entire period (2001–2014)
and the model warm-up period (1997–2000).
Spatial model parameterisation
In order to facilitate a meaningful spatial-pattern-oriented calibration of
a distributed model, we need to compromise between comprehensive (each cell
in the basin) and lumped (one cell – one basin) parameterisations, as the
first approach may require immense computer resources during calibration
and the latter approach usually results in a uniform pattern. For instance,
in a detailed calibration study by Corbari et al. (2013), each pixel in the catchment is
represented by a parameter whereas, in a coarse parameterisation, a uniform
parameter represents the entire catchment (Stisen et al.,
2017). In this study, we follow an intermediate level of parameterisation
comprised of several flexible spatial parameters and nonlinear equations,
allowing us to stretch the spatial contrast of simulated actual
evapotranspiration based on soil and vegetation properties. This level of
parameterisation is still physically meaningful as the parameters are tied
to the land surface characteristics of the basin via transfer functions.
Distributed root fraction coefficient
Root distribution with depth is generally perceived as being a function of
vegetation type (Jackson et al., 1996), and our
spatial parameterisation of root fraction distribution is initially separated
based on land covers of forest and agricultural crops. However, following
the site-specific soil and plant physical literature (Jensen et al., 2001; Madsen and Platou, 1983), we subdivide
the root fraction coefficient for agricultural crops as a function of field
capacity (FC). Here, spatial model parameterisation is implemented to the
root fraction calculation in the original mHM structure which follows the
asymptotic equation for vertical root distribution
(Eq. 1) proposed by Jackson et al. (1996).
Y=1-βcd,
where Y is the cumulative root fraction from soil surface to depth d (cm), and
βc is the root fraction coefficient. We substituted the root
fraction coefficient for agricultural crops (non-forest) with two new root
fraction parameters, i.e. one root fraction for maximum FC (clay) and one for
minimum FC (sand), which allow for full spatial distribution of root fraction
with varying FC. This relation between soil characteristics and effective
rooting depth is based on a site-specific database with more than 100 soil
and root profiles collected in Denmark (Table 19.4 in
Jensen et al., 2001) and the literature focusing on soil texture and
effective rooting depths in Denmark (Madsen, 1985, 1986; Madsen and Platou,
1983). The approach is not necessarily globally valid, but designed for the
specific region of western Denmark where very sandy soils (Fig. 1) are
cultivated for agricultural purposes even though the soil properties
influence root development. These parameters are used to form the root
fraction coefficient for soil with agriculture (βagriculture)
based on field-capacity-dependent root fraction in Eqs. (2) and (3).
FCnorm=FCi-FCminFCmax-FCmin,
where FCnorm is the normalised field capacity ranging from 0 to 1.
βagriculture=FCnorm⋅βmax+1-FCnorm⋅βmin,
where βagriculture is the new root fraction for soil with
agriculture comprised of root fraction for clay (βmax) and root
fraction for sand (βmin).
Dynamic ETref scaling function
As a second spatial parameterisation step, we incorporated remotely sensed
vegetation information, to downscale coarse climatological reference
evapotranspiration (ETref) to the model scale. This was done to
emphasise the effect of vegetation on the simulated spatial patterns of AET.
The original scaling factor in mHM is based on a lumped minimum correction
and an aspect-driven additional term. Using aspect ratio for ETref
correction makes sense in mountainous areas; however, this is found
to be irrelevant for the Skjern basin which is characterized by a low
topographical variation. The dynamic scaling function introduced here allows
the modeller to superimpose the imprint of LAI on the simulated AET patterns
via a downscaling of the ETref. The concept of a dynamic scaling
function (DSF) is similar to the concept of a crop coefficient used to convert
ETref to a potential evapotranspiration (ETpot) for a given
vegetation that differs from the reference crop. Our implementation follows
the equation for estimating the crop coefficient for natural vegetation
originally proposed by Allen et al. (1998). Similarly, Hunink
et al. (2017) compared different applications of crop
coefficients based on remotely sensed vegetation indices in hydrologic
modelling. They found that the effect of crop coefficient parameterisations
on the water balance is trivial and constant throughout the year; however,
it has a major effect on seasonal evapotranspiration and soil moisture
fluxes, showing the role of crop coefficients in spatial calibration. The
DSF, shown in Eq. (65), is simply a time–space
variable implementation of the crop coefficient for natural vegetation,
parameterized through a spatio-temporal LAI (no unit) component accounting for the
effects of characteristics that separate the actual vegetation from a
reference grass (well-watered 10 cm height and albedo of 0.23). These
characteristics include specific land cover, albedo and aerodynamic
resistance (Allen et al., 1998; Liu et al., 2017). This ensures a physically meaningful
downscaling from a coarse (here 20 km) ETref grid to the model
resolution (here 1 km).
ETpot=DFS⋅ETref,DSF=a+b1-e(-c⋅LAI),
where a in the model (ETref-a) is the intercept term representing
uniform scaling, b (ETref-b) represents the vegetation dependent
component, and c (ETref-c) describes the degree of
nonlinearity in the LAI dependency.
Methods
In this study, we applied a recently developed sequential screening method
(Cuntz et al., 2015) to select important parameters for
calibration. Since different parameters can be sensitive to different
hydrologic processes, we tested three different performance metrics to
evaluate process–parameter relationships. Two of these metrics are derived
from the hydrograph, i.e. Kling–Gupta efficiency (KGE, Gupta et al.,
2009) and KGE of only below-average streamflow (KGElow), whereas
the spatial efficiency metric focuses on the spatial pattern of actual evapotranspiration.
Objective functions
As an objective function for streamflow performance, we chose the
Kling–Gupta efficiency, shown in Eq. (6) (Kling and Gupta, 2009), and applied it
to both the entire time series and to the low-flow part of the hydrograph
(below mean discharge).
KGE=1-αQ-12+βQ-12+γQ-12,αQ=ρ(S,O)andβQ=σSσO,andγQ=μSμO,
where αQ is the Pearson correlation coefficient between observed
and simulated discharge time series, βQ is the relative
variability based on the fraction of standard deviation in simulated and in
observed values, and γQ is the bias term normalised by the standard
deviation in the observed data.
Since comparison of two spatial pattern maps is of obvious importance, a
bias-insensitive spatial performance metric is developed and used in this
study. In this context, we adopted the structure of the Kling–Gupta
efficiency while substituting the standard deviation term by a term based on
the coefficient of variation σO/σS and replacing the bias term with a histogram
comparison index to compare the intersection percentage of two histograms of
observed and simulated spatial maps. The histogram intersect is performed
after normalisation of the observed and simulated maps to a mean of 0 and
standard deviation of 1 (z score). This ensures that the histogram
comparison is unaffected by any bias or variance differences and solely
reflects the agreement in distribution of the variable in space. The main
utility of the histogram comparison is that it distinguishes between
different soil and vegetation groups reflected in the spatial pattern
results. This unique feature of being sensitive to clusters in the data
compliments the other two components in the equation, in particular the
correlation coefficient (α in Eq. 7) since
α is highly vulnerable to very distinct clusters of points aligned
on a diagonal axis. This can result in high correlation coefficient values
in spite of low correlation inside the individual clusters inevitably
misleading the model calibration. The separated clusters often occur in
environmental models where different land-use classes and soil classes
etc. can produce patchy spatial patterns. The new spatial efficiency metric
(optimal value equals to 1) is defined as follows:
SPAEF=1-(α-1)2+(β-1)2+(γ-1)2α=ρ(A,B)andβ=σAμA/σBμBandγ=∑j=1nminKj,Lj∑j=1nKj,
where α is the Pearson correlation coefficient between the observed AET
map (A) and simulated AET map (B) for a particular month, β is the
fraction of coefficient of variations representing spatial variability, and
γ is the percentage of histogram intersection (Swain and Ballard, 1991). The gamma (γ) is
calculated for a given histogram K of the observed AET map (A) and the
histogram L of the model simulated AET map (B), each one containing n
bins, i.e. herein 100 bins. The maps are standardised to a mean of 0 and a
standard deviation equal to 1 (z score) to avoid the effect of different
units. In this study, we compare AET from TSEB (in W m-2) based on
instantaneous satellite data with daily averaged AET (mm day-1) simulated by
the model and regard the satellite-based AET maps as the “observation”
even though they are more accurately AET “estimates” based on satellite
observations. Attempts to use numerous other spatial metrics including
Mapcurves, fractions skill score (FSS), Goodman and Kruskal's lambda, Theil's Uncertainty, empirical orthogonal functions (EOFs) and
Cramér's V (Cramér, 1946; Koch et al., 2015;
Rees, 2008) did not distinguish the general AET patterns or the
spatial efficiency metric. The strength of the spatial efficiency
metric is that each component contains different and non-overlapping
information. Moreover, the components are straightforward compared to the
aforementioned metrics. While the correlation term (α) expresses
only the spatial correlation of AET values, the coefficient of variation
term (β) expresses only the range or contrast in the image while the
histogram term (γ) only expresses the agreement on histogram shape
without considering either variation or correlation. Since all three terms
are bias-insensitive, the spatial efficiency only constrains the model
simulations with the pattern information in the satellite data while leaving
the water balance (bias) to be constrained by streamflow metrics.
Sequential screening of the model parameters
We applied the variance-based sequential screening (SS) method introduced by
Cuntz et al. (2015) to identify, with a low computational budget, the parameters
which are most informative regarding a certain model output M.
For this approach the parameters are sampled in trajectories as initially
described by Morris (1991) and improved by Campolongo et al. (2007). Each trajectory consists of (N+ 1)
parameter sets, assuming that N is the total number of model parameters. The
first parameter set in each trajectory is sampled randomly while all the
subsequent sets i (i> 1) differ to the prior set (i- 1) in exactly one parameter value.
Therefore, the whole trajectory is a path through the parameter space.
Trajectories allow us to sample the whole parameter space efficiently and
consider parameter interactions to certain extents. In the approach of Cuntz
et al. (2015), only a small number (M1) of such
trajectories are sampled to lower the computational burden. The resulting
(M1× (N+ 1)) model outputs are derived and the elementary
effects (EEs) are computed for each parameter. The EEs are then used to identify the
most informative parameters by deriving a threshold splitting the parameters
into a set Nu of uninformative and a set Ni of informative ones.
In the following, the first parameter set is again sampled randomly but then
only the uninformative parameters are perturbed meaning that the new
trajectory only consists of (Nu+ 1) parameter sets. The derivation of
model output and calculation of EEs is repeated. The major step is to
determine whether one of the previously uninformative parameters is now
above the threshold and if so it is added to the set of informative
parameters Ni. These steps are repeated until no further parameter is
added to the set Ni. At the end M2 trajectories are sampled to
confirm that the set of uninformative parameters Nu is stable and no
further parameter would be found to be informative.
Model calibration and validation
We calibrated the 1 km daily mHM for the Skjern basin in Denmark using the
well-known global search algorithm Shuffled Complex Evolution method from the University of
Arizona (SCE-UA) (Duan et al., 1992). The
SCE-UA algorithm is configured with two complexes running in parallel with
53 (2n+ 1) parameter sets in each complex and 27 (n+ 1) parameter sets per
sub-complex. Moreover, the maximum relative objective function change is set
to 1 % over five iterations as the model convergence criterion. This
criterion was usually reached after 3500 runs; in rare cases up to 8000 runs
were necessary. We evaluated the differences between monthly AET estimates
from the TSEB reference data and simulated AET from the hydrologic model for
the calibration period (2001–2008) and validation period (2009–2014).
Selected 26 parameters for calibration and their normalised sensitivity
indices sorted based on SPAEF column. Zero values are highlighted in italic.
The three bold values are the highest values of the three sensitivity indices.
ParameterDescriptionNormalised sensitivity KGEKGElowSPAEFETref-afIntercept – forest0.0220.1170.646ETref-cExponent coefficient0.0310.7320.490ETref-bBase coefficient0.4393.0130.317rotfrcofforeRoot fraction coefficient for forest areas0.0110.0130.162ETref-aIntercept – non-forest0.3083.2350.157ptfhigconstConstant in pedo-transfer function for soils with sand content higher than 66.5 %0.0630.2230.096rotfrcofclayRoot fraction coefficient for clay in agricultural cropland0.1010.2740.094ptfhigdbCoefficient for bulk density in pedo-transfer function for soils with sand content higher than 66.5 %0.0360.2570.070rotfrcofsandRoot fraction coefficient for sand in agricultural cropland0.1200.4390.061canintfactCanopy interception factor0.0040.0290.018orgmatforestOrganic matter content for forest0.1360.8930.014ptfhigclayCoefficient for clay content in pedo-transfer function0.0080.0330.011infshapefInfiltration shape factor0.1030.0990.006ptfkssandCoefficient for sand content in pedo-transfer function for hydraulic conductivity0.4152.7800.002ptfksconstConstant in pedo-transfer function for hydraulic conductivity of soils with sand content higher than 66.5 %0.2360.8420.001snotrestempSnow temperature threshold for rain and snow separation0.0340.2060.000ptfksclayCoefficient for clay content in pedo-transfer function for hydraulic conductivity0.0400.3130.000orgmatimperOrganic matter content for impervious zone0.0090.0200.000expslwintflwExponent slow interflow0.4123.4900.000slwintreceksSlow interception0.8721.2960.000intrecesslpInterflow recession slope0.6021.1050.000rechargcoefRecharge coefficient0.9350.6660.000geoparam1Parameter for geological formation 10.3280.1380.000geoparam2Parameter for geological formation 20.5580.2070.000strcelerityStreamflow celerity for routing0.3640.0620.000intstorcapfInterflow storage capacity factor0.1980.0100.000
The two streamflow stations are defined separately to follow the
improvements in each metric throughout the calibrations. After testing
different combinations of streamflow and spatial metrics, we chose two
streamflow metrics (KGE and KGElow) and one spatial efficiency
metric,
given by Eqs. (6) and (7), respectively. These objective functions are used
individually or combined in three model calibration cases based on (i) only
streamflow using equally weighted KGE and KGElow, (ii) only spatial
patterns of AET using spatial efficiency, (iii) both equally weighted
streamflow and spatial pattern matching using all three metrics. It should be
noted that the case 2 calibration is designed as a benchmark to explore how
good the pattern match can get when not considering streamflow performance,
even though the solution might not be interesting from a hydrological
perspective, since the bias insensitive spatial pattern metric does not
secure a reasonable water balance. To test the overall robustness of the
calibration framework we use an ensemble of nine calibrations for case 1 and
nine calibrations for case 3, each started from a different seed number. In
order to fairly weigh the objective functions, we retrieve the
residuals (ε) from the three objective functions based on a random
initial model run (Eqs. 8–10). We calculate the new weights which will
result in equal contribution to the total error (Φtotal),
i.e. 50 % from spatial metric and 50 % from the two streamflow metrics.
Ideally, if it exists the optimiser searches a parameter set resulting in
zero Φtotal otherwise the closest point to zero will be
considered as the optimum solution.
ΦQ=∑i=12εKGEi⋅ωKGEi2+∑i=12εKGElow,i⋅ωKGElow,i2,ΦSpatial=∑m=16εSPAEFm⋅ωSPAEFm2,Φtotal=ΦQ+ΦSpatial,
where ΦQ is the total Φ for streamflow of the two streamflow
gauges and ΦSpatial is the total Φ for spatial performances
of six summer months. For Q-only calibration, the weight for SPAEF (ωSPAEF)
becomes zero whereas for spatial-only calibration the weights for KGE and KGElow become zero.
ResultsSequential screening of the model parameters
Table 2 shows the sequential screening results
based on KGE, KGElow and SPAEF. Each objective function
reflects on different spatio-temporal dynamics of the catchment. While KGE
and KGElow evaluate high and low streamflow dynamics and biases, the
bias-insensitive SPAEF focuses on only spatial patterns of AET. From the
results it is clear that some of the highly sensitive parameters for
streamflow dynamics, especially interflow-related parameters,
groundwater-related geology parameters and single routing parameters, have
minor to zero influence on the spatial patterns of AET. The new ET
parameters, ETref-a (non-forest), -af (forest), -b and -c are
identified to be informative based on all objective functions. The root
fraction coefficient for forest (rotfrcoffore) appeared to be not very
important for streamflow metrics whereas it is crucial for SPAEF. Similarly,
the two newly introduced parameters, i.e. root fraction coefficient for sand
and clay (i.e. rotfrcofs and rotfrcofclay) soil, are informative based on all
three objective functions. Organic matter for forest (orgmatforest) is
especially important for low flows whereas organic matter for impervious
areas (orgmatimper) has zero influence on spatial patterns of AET. The
exponent slow interflow (expslwintflw) parameter is found to be most
informative for low flows while recharge coefficient (rechargcoef) is most
informative for streamflow and ETref-af is most informative for
calibrating spatial patterns of AET.
On average 475 model evaluations are required to split the total number of
48 parameters into informative and uninformative ones. However, the number
of iterations is dependent on objective function; therefore, 449 model runs
were required for KGE, 431 model runs for KGElow and 544 model runs for
SPAEF. This is in close agreement with the computational budget of 10N model
evaluations already reported by Cuntz et al. (2015). This also
makes the sequential screening method computationally very attractive
compared to other global search methods. However, the computational
advantage is at the cost of exploring a larger part of the parameter space,
and hence the sequential screening is mostly valuable for identifying
informative and non-informative parameters prior to calibration or further
assessment of the parameter behaviour. Overall, these results show that
there are 26 parameters above the threshold of 1 % of at least one case
(Table 2). In principal the parameters with zero
sensitivity (SPAEF column) can be fixed at some value during calibration,
which may lead to faster convergence, with a lower degree of freedom. However,
we include the same set of 26 parameters in all three calibration cases for consistency.
Model calibration and validation
The mHM model is calibrated using streamflow records (gauges A and B in
Fig. 1) from an 8-year period (2001–2008) and
validated for a recent period (2009–2014). A preceding 4-year period (1997–2000)
is used for model warm-up. We prepared remotely sensed monthly averaged AET
pattern maps calculated for these years considering only cloud-free days
from summer months. AET patterns of winter months are not considered since
it is mostly cloudy and ET is very low and uniform (energy limited) in winter.
Summary of the calibration results for three cases. Median and standard
deviation (SD) refer to the calibration ensemble ranked based on their total Φ.
The 26 selected parameters from SS are used in the following three
calibration strategies: (1) only streamflow-oriented (Q-only) calibration
using equally weighted KGE and KGElow, (2) only spatial-pattern-oriented
calibration using SPAEF, and (3) streamflow and spatial patterns of AET
together using all three objective functions with equal weights of 50 % on
spatial metric and 50 % for the two streamflow metrics (25 % each).
Table 3 provides the overall picture of the three
different calibration strategies where two of these strategies are based on
an ensemble of nine calibrations. Therefore, the basic descriptive
statistics are also given as robustness indicators. The results show that
the combined calibration (Q and Spatial) produces similar results to both
Q-only and Spatial-only calibrations focusing on streamflow and
spatial patterns of AET respectively. whereas the single-metric calibrations
gave very different results for the opposite objective functions, e.g. SPAEF
versus streamflow metrics. It is interesting that when comparing the calibration
ensemble with the median performance there is very limited trade-off between
the Q-only and the combined Q and Spatial calibrations, which have very
similar average KGE values. When looking specifically at the best-performing
ensemble member with lowest total Φ, there is a more pronounced
trade-off between the Q-only and Q and Spatial together calibrations, as the
streamflow performance is poorer when SPAEF is included in the group of
objective functions. The differences in the streamflow metrics indicate that
each objective function carries relevant but slightly conflicting
information. Moreover, the results show that the hydrologic model simulates
the best AET patterns in different months for different ensemble calibrations.
In other words, while one ensemble member has the best performance for
April, other calibrations may have the best performance for May and June.
This is a secondary trade-off which illustrates that the calibration might
benefit from temporal variability in the parameters controlling the spatial
parameterisation scheme. It should be noted that ranking of the calibrations
within the two ensembles is based on the overall Φ that is comprised
of all objective functions for the corresponding calibration. For that
reason, the best member of Q and Spatial calibration holds the lowest total Φ
comprised of the highest possible KGE, KGElow and SPAEF at the
same time but not necessarily the highest SPAEF alone. This resulted in a
slightly lower SPAEF mean of 0.395 for the best member compared to the
median member with a SPAEF mean of 0.396 (Table 3).
The results of the Q-only model calibration using only KGE and KGElow
reveal very poor simulated patterns of AET, with negative SPAEF for all
months. This is not surprising since this calibration is not constrained
regarding the spatial patterns, but also illustrates that discharge
observations alone contain no spatial pattern information of AET. In
contrast, the spatial-only calibration using only SPAEF shows a very poor
water balance, with negative KGE and a large bias. We are aware that
spatial-only calibration is not applicable or meaningful for hydrologic studies.
Scatter plots of total ΦSpatial versus total ΦQ
for all nine calibration ensemble members. First and second row sub-plots are the
same figures except for different extent, i.e. [10 10] and [1 5] to zoom into
the edge of the search space. Different radius of red circles is used to show
the optimum points for all nine ensemble members clearly.
Average hydrograph of all years in the calibration period (2001–2008)
to illustrate the ensemble of nine model calibrations with different seed numbers.
The model performance development through the calibrations (9 + 9) and
optimum points are shown using scatter plots in
Fig. 2, which displays all model runs with Φ values inside the specified plot ranges. The scatter plots illustrate
trade-offs between objective functions and consistency among calibration
ensemble members. The performance regarding spatial patterns (ΦSpatial)
displays a high degree of trade-off with all combined
calibrations achieving ΦSpatial values around 0.8 whereas the
Q-only calibrations achieve ΦSpatial values ranging from 2.8 to 4.4.
There are two main clusters in the Q-only calibrations: one around
0.11 ΦQ and the other around 0.25 ΦQ, whereas all nine Q and
spatial calibrations follow a similar level on the y axis (ΦSpatial).
It is surprising to see that SCE-UA did not always find the
same optimum solution with varying seed number, which is the case mainly for
the Q-only calibration. Perhaps more consistent optimum solutions for the
Q-only calibrations could have been achieved with tighter stopping rules and
the same initial parameter sets.
Similarly, the grey shades in Fig. 3 show the
ensemble range of simulated hydrographs for the Q-only and Q and Spatial
calibrations. From the hydrographs it is clear that the ensemble range for
station A is generally larger than that for station B, indicating larger uncertainty
for sub-basin A. Interestingly, Fig. 3 also
illustrates that the Q and Spatial calibration constrains the solution
better, not only in AET simulations, but also in streamflow simulations, as
indicated by the slightly narrower range in simulated streamflow for the Q
and Spatial calibrations. However, even though the range of hydrographs is
slightly narrower the simulations are also further from the observed measurements during summer months.
The corresponding simulated AET maps for the results presented in
Table 3 are shown in Fig. 4. This figure illustrates the monthly mean maps across all years of actual
evapotranspiration for the cloud-free days available for the remote sensing
estimates. Only the best-performing members from the two ensembles are
presented in this figure. The maps are normalised with their mean value to
use one representative colour bar in the legend. As indicated in Table 3, the resultant maps from Spatial-only
(third row in Fig. 4) and Q and Spatial calibrations (fourth row in Fig. 4) are obviously
more similar to the reference monthly maps (first row in Fig. 4) than the maps of Q-only calibration
(second row in Fig. 4). The results clearly show that the model can simulate
month-to-month variations in AET patterns reasonably well. The poor AET
performance in the Q-only maps is obvious in the second row of Fig. 4, where we see only a
uniform simulated AET pattern except for the forest areas revealing very
little information about variability in AET and the influence of soil and
vegetation. This is due to the fact that the KGE and KGElow objective
functions contain no information on the patterns of AET resulting in an
unconstrained optimisation regarding spatial pattern and variability.
Therefore, the optimiser randomly moves in the SPAEF solution space and
picks the best streamflow performance with no regard to AET patterns.
Although not perfect (average SPAEF = 0.46 and 0.40), the simulated
pattern match in the last two rows of Fig. 4 is
quite good compared to the remote-sensing-based estimate since the
simulation is able to represent the general pattern influenced by soil,
vegetation and land cover while maintaining a similar variance and smoothness.
Table 4 shows the same results as
Table 3 but for the validation period spanning from 2009 until 2014.
Obviously, the results are somewhat poorer than those for
the calibration period. A drop in performance for spatial-only and combined
metrics is mainly seen for KGElow and the total bias, whereas the SPAEF
for Spatial-only and Q and Spatial remains similar to the calibration periods
with average SPAEF around 0.4. Interestingly, there is no real trade-off for
streamflow metrics between Q-only and Q and Spatial calibrations for the
validation period, even for the best-performing ensemble member. Although a
better streamflow performance could be achieved by Q-only calibration during
calibration, this cannot be sustained during validation, indicating some
overfitting when using streamflow metric only. In contrast, the SPAEF
performance does not drop during validation for the combined Q and Spatial
optimisation, indicating less overfitting and a more robust model parameterisation.
Summary of the validation results for three cases. Median and standard
deviation (SD) refer to the validation ensemble ranked based on their total Φ.
Three different calibration strategies: streamflow-only (a), spatial-only (b), and streamflow and spatial together (c)
are compared with monthly TSEB estimates (d). Calibrations are evaluated
for monthly averages from April to September using cloud-free days. Note that
these maps are normalised with their mean to use one representative colour bar
and highlight the pattern information.
Discussion
In the initial phase of the study numerous flawed calibrations were carried
out in an attempt to produce simulated spatial patterns of AET similar to
the satellite-based reference patterns. However, the inability to produce
similar patterns was found to be caused by limitations in spatial model
parameterisation and spatial performance metric choice. Regarding the
spatial parameterisation, the initial model was based on a spatially uniform
parameterisation of root fraction coefficient and PET correction factor, two
parameters with major control on the simulated AET. Therefore, more flexible
yet physically meaningful parameterisations were implemented where full
spatial variability was enabled by combining 2–3 calibration parameters to
initial spatial distributions of soil type and LAI. Regarding the use of
appropriate spatial performance metrics, the initial attempts using standard
metrics of correlation coefficient, Mapcurves (Hargrove et al., 2006), coefficient of
variation, Goodman and Kruskal's lambda (Goodman and
Kruskal, 1954), agreement coefficient (Ji and Gallo, 2006),
Theil's uncertainty, EOF, and Cramér's V (Cramér, 1946; Koch et al., 2015; Rees,
2008) proved to be inadequate in a calibration framework, since undesired
visual patterns were achieved, e.g. with high correlation, but too-low
standard deviation or highly separate clusters. Therefore, we developed the
SPAEF metric which proved to be very efficient for calibrating the model to
a satisfying spatial pattern by combining correlation coefficient,
coefficient of variation ratio and histogram overlap in a robust metric that
guides the model calibration well. It is our experience and recommendation
that incorporating the spatial dimension in all aspects of the distributed
hydrological model development from model structure, parameterisation, metric
selection, sensitivity analysis and calibration is essential in order to
achieve significant improvement in the spatial pattern performance of a
model. We believe that traditional downstream discharge measurements contain
much more accurate and robust information on the overall water balance
compared to the non-continuous remotely sensed estimates, and therefore, the
model constraint on biases should only originate from these streamflow
observations. Conversely, it is well-known that aggregated streamflow
measurements contain no information on spatial patterns upstream of the
measurement (Stisen et al., 2011b).
Therefore, the combination of satellite-derived patterns and aggregated
streamflow measurements are an ideal way of constraining distributed
hydrological models. In fact, spatial patterns should always be considered
when evaluating distributed models. Even if detailed satellite estimates are
not available, expert judgments and land cover information should be used to
select the most appropriate parameter set (producing the most likely spatial
patterns) among equally likely solutions obtained through discharge-only
calibration. When a distributed model is applied, ideally it should not only produce satisfying discharge simulations, but at the same time
it should also produce realistic spatial patterns of states and fluxes such as AET and
soil moisture. White et al. (2017) also
highlighted the importance of getting the spatial patterns right in their
study since constraining the model against streamflow alone did not secure
robust land cover change scenario modelling.
The monthly spatial maps are built based on the AET patterns from
cloud-free days. Here, we ignore the temporal aspect and focus only on
the consistent spatial patterns for each month of the growing season. The
advantage of this approach is that only the main information content of the
satellite data, their spatial patterns, are utilised while the uncertainty
associated with the absolute values of the AET estimates are not influencing
the calibrations. In addition, the simulated monthly mean AET maps reflect
mainly the model parameterisation and to a lesser degree the day-to-day
variation in climate forcing. This is desirable since the aim of the model
calibration is to optimise the model parameterisation with a given climate
forcing dataset. The current calibration framework builds on the assumption
that the satellite-based estimate of AET patterns approximate an observed
pattern that is suitable for model optimisation. In general, the calibration
approach is deterministic by nature and does not consider error or
uncertainties in either observed discharge or AET patterns. Future work
could add this component to the approach. However, assessment of the
uncertainties in the observed spatial patterns are far from straightforward,
since the uncertainties of interest with the proposed approach are solely
related to the uncertainties related to the spatial patterns and not to
biases. Therefore, quantification of pattern uncertainties would require a
very dense network of actual evapotranspiration measurements.
The calibration results obtained in the current study, where three strategies
were tested with varying combinations of objective functions, showed that
with an appropriate metric design, limited trade-offs can be achieved when
combining streamflow and spatial pattern metrics in a joint calibration
framework. This is largely attributed to the nature of the metric, as the
spatial performance metric is bias-insensitive whereas the streamflow
metrics have very little sensitivity to spatial redistribution of AET
patterns as long as the spatial averages remain unchanged. Bias and
temporal variability of satellite-derived AET estimates could also be useful
for model optimisation; however, in this study, we deliberately limited the
information content of the satellite data to address the spatial patterns.
This was done because even though the satellite-based AET estimate is
validated against eddy-covariance stations (Mendiguren et al., 2017) they only
represent specific cloud-free days, limiting their value to assess the long
term water balance of the catchment. The calibration results using only
streamflow metrics revealed that this traditional calibration target cannot
guarantee satisfying spatial pattern performance even though the model
structure and parameterisation framework enables this without much
compromise,
as illustrated by the performance of the combined Q and Spatial calibrations
which resulted in very similar performance of both streamflow and spatial
patterns as the single objective calibrations individually.
The spatial model parameterisation applied in Skjern catchment can be site-specific due to the uniform land use (agricultural cropland) across soils
ranging from very coarse sandy soil to more loamy soils whereas the
calibration framework and SPAEF metric can be applied to any other river
basin in the world. Regarding the dynamic scaling function, developed for
incorporating remotely sensed LAI in ETref scaling, it should be noted
that the use of LAI to describe the deviation of each grid cell from the
assumed reference grass is a simplification. Albedo could also have been
included in the dynamic scaling function; however, one could argue that
albedo and LAI are somewhat correlated and including one of them is already
contributing the information about the other (Chen
et al., 2005; Liu et al., 2017; Stisen et al., 2008). Moreover, we limit
this study to temporally averaged spatial patterns of AET and deliberately
choose to ignore the day-to-day dynamics of AET. In this study, spatially
varying but temporally constant field-capacity-dependent root fraction is
utilised; however, it would be more elegant and physically more sound to
represent the seasonality in root-growth dynamics more realistically by
implementing a seasonally varying root fraction coefficient (beta) that is
similar to the concept of LAI-based PET correction using the DSF module.
Conclusions
Our study aimed at parameterising a distributed hydrologic model for
simulating distributed actual evapotranspiration patterns before an ensemble
calibration using satellite-based data. This order is crucial for
progressive hydrologic modelling with flexible model structure based on
open-source philosophy. All these steps should be suitable for the catchment
to give the model enough flexibility to adjust to pattern observations. The
calibration efforts will have a limited effect on spatial patterns if the
model parameterisation has not been investigated with pattern performance in
mind. Ideally, the models should offer different parameterisation schemes or
at least have room for development based on open-source philosophy so
that we can test different spatial parameterisations for a particular
calibration goal. Here, we implemented a field-capacity-dependent root
fraction coefficient determining the root profile over depth for different
soil and vegetation types. We introduced a dynamic scaling function which
imprints the leaf area index in the potential evapotranspiration. After
organising the spatial parameterisation of the model in a parsimonious
manner, we also reduced the number of parameters using sequential screening.
Only the informative parameters from the sequential screening are used in
the subsequent ensemble calibration exercise. We then assessed the effect of
different calibration strategies including monthly spatial patterns of
actual evapotranspiration in combination with traditional streamflow
observations. In the spatial calibration, the agreement between observed and
simulated spatial patterns is added as a part of the objective function used
for model optimisation. For that a multi-component bias-insensitive spatial
efficiency metric is used to evaluate the simulated AET maps. The
following conclusions can be drawn from our results:
Preparing the model parameterisation for spatial calibration is a key
element for achieving the calibration objectives. More specifically, the
model parameterisation needs to be designed to allow the spatial parameter
distribution to be optimized through calibration.
The newly proposed spatial efficiency metric (SPAEF) has proven to be robust
and easy to interpret due to its three distinct and complementary components
of correlation, variance and histogram matching.
Based on the multi-component calibration results, including spatial pattern
information in calibration significantly improves the spatial model
simulations while maintaining similar streamflow performance. For the
combined calibration, there is a limited trade-off between streamflow and
spatial patterns for the best-performing calibration ensemble compared to
the Q-only calibration. However, this trade-off disappears in the validation
test, indicating that a more robust parameter set is achieved during the
combined Q and Spatial calibration.
Overall, the hydrological modelling community can benefit from building
familiarity with several aspects of spatial model evaluation, including
spatial parameterisation and multi-component spatial performance metrics.
Pre-processing ET with crop coefficient type dynamic scaling function is
available in the mHM v5.7 and later versions (www.ufz.de/mhm/
and https://github.com/mhm-ufz/mhm). The Python and MATLAB scripts for
spatial efficiency (SPAEF) and a tutorial are available in the SPACE project
website (http://www.space.geus.dk/), GitHub (https://github.com/cuneyd/spaef/)
and via a Researchgate repository (Demirel et al., 2017).
The authors declare that they have no conflict of interest.
Acknowledgements
We would like to thank the three reviewers for their useful and constructive
feedback. We acknowledge the financial support for the SPACE project by the
Villum Foundation (http://villumfonden.dk/) through their Young
Investigator Programme (grant VKR023443). The TSEB code is retrieved from
https://github.com/hectornieto/pyTSEB. All MODIS data were retrieved from the
online Data Pool, courtesy of the NASA Land Processes Distributed Active
Archive Center (LP DAAC), USGS/Earth Resources Observation and Science (EROS)
Center, Sioux Falls, South Dakota, https://lpdaac.usgs.gov/data_access/data_pool.
Edited by: Florian Pappenberger
Reviewed by: Giacomo Bertoldi, Heye Bogena, and Renata Romanowicz
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