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\begin{document}

\title{Towards more credible models in catchment hydrology to enhance
hydrological process understanding: Preface}



\author[1]{Jens Christian Refsgaard}%
\author[2]{Juliane Mai}%
\author[3]{Markus Hrachowitz}%
\author[4]{Sharad K. Jain}%
\author[1]{Simon Stisen}%
\affil[1]{De Nationale Geologiske Undersogelser for Danmark og Gronland}%
\affil[2]{University of Waterloo Department of Civil and Environmental Engineering}%
\affil[3]{Technische Universiteit Delft Afdeling Watermanagement}%
\affil[4]{Indian Institute of Technology Roorkee Department of Civil Engineering}%


\vspace{-1em}



  
  \date{May 29, 2024}


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\selectlanguage{english}
\begin{abstract}
Catchment modelling has undergone tremendous developments during the
past decades. In the 1970s, the focus was on simulation of catchment
runoff with process descriptions and data inputs being lumped to the
catchment scale. Later developments included spatially distributed
models allowing data inputs and hydrological processes to be simulated
at model grid scale, i.e. much finer than catchment scale. These models
were able to explicitly simulate various processes such as soil
moisture, evapotranspiration, groundwater and surface runoff. With the
advancements in remote sensing technology and availability of
high-resolution data, increased attention has in recent years been given
to enhancing the capability of catchment models to reproduce spatial
patterns and in this way improve our understanding of hydrological
processes and the physical realism of catchment models. This development
process has involved a wide spectrum of different aspects in the
modelling process, reaching from an improved understanding of
uncertainties in data, model parameters and model structures to new
protocols for good modelling practices in water management. Recognizing
the important role of biodiversity and social aspects, hydrologists are
now extending the scope of their models to capture the interactions
between water, biota and human social systems.%
\end{abstract}%



\sloppy


\textbf{Towards more credible models in catchment hydrology to enhance
hydrological process understanding: Preface}

Jens Christian Refsgaard\textsuperscript{1}

Juliane Mai\textsuperscript{2,3,4}

Markus Hrachowitz\textsuperscript{5}

Sharad K. Jain\textsuperscript{6}

Simon Stisen\textsuperscript{1}

\textsuperscript{1} Department og Hydrology, Geological Survey of
Denmark and Greenland (GEUS), Copenhagen, Denmark

\textsuperscript{2} Civil and Environmental Engineering, University of
Waterloo, Waterloo, ON, Canada

\textsuperscript{3} Computational Hydrosystems, Helmholtz Centre for
Environmental Research--UFZ, Leipzig, Germany

\textsuperscript{4} Center for Scalable Data Analytics and Artificial
Intelligence--ScaDS.AI, Leipzig, Germany

\textsuperscript{5} Department of Water Management, Faculty of Civil
Engineering and Geosciences, Delft University of Technology, The
Netherlands

\textsuperscript{6} Department of Civil Engineering, Indian Institute of
Technology, Roorkee, India

\section*{Introduction}

{\label{introduction}}

Catchment modelling has undergone tremendous developments during the
past decades. In the 1970s, the focus was on simulation of catchment
runoff with process descriptions and data inputs being lumped to the
catchment scale. Later developments included spatially distributed
models allowing data inputs and hydrological processes to be simulated
at model grid scale, i.e. much finer than catchment scale. These models
were able to explicitly simulate various processes such as soil
moisture, evapotranspiration, groundwater and surface runoff. With the
advancements in remote sensing technology and availability of
high-resolution data, increased attention has in recent years been given
to enhancing the capability of catchment models to reproduce spatial
patterns and in this way improve our understanding of hydrological
processes and the physical realism of catchment models. This development
process has involved a wide spectrum of different aspects in the
modelling process, reaching from an improved understanding of
uncertainties in data, model parameters and model structures to new
protocols for good modelling practices in water management. Recognizing
the important role of biodiversity and social aspects, hydrologists are
now extending the scope of their models to capture the interactions
between water, biota and human social systems.

This Special Issue (SI) of Hydrological Processes is the result of an
open call for abstracts announced in October 2020. The SI comprises a
collection of 14 papers authored and co-authored by 77 scientists from
37 research institutions in 16 countries. Based on the key focus for
each of the papers we have grouped them into five thematic topics: (i)
review papers; (ii) papers developing and testing new process
descriptions; (iii) papers focusing on how model calibration can improve
process descriptions; (iv) papers exploring how the use of multiple
model structures can improve model performance and process descriptions;
and (v) papers focusing on modelling uncertainties. The grouping of the
papers into the five topics should be considered as indicative only,
because all papers address more than one of the five themes. The key
findings in the papers of this Special Issue are summarized in the
following five topic sections.

\section*{Review papers}

{\label{review-papers}}

Refsgaard et al. (2022) review developments in hydrological modelling of
catchment response over the past 60 years. Several important
advancements have driven these developments. Scientists now have much
better understanding of hydrological processes, leading to their
improved representation in models. Another advancement is improved
availability of data -- more variables, at higher frequency, and
observed at more places. Multi-band remote sensing data at higher
spatial and temporal resolutions and algorithms to compute data of
missing variables at the required scales by using the satellite data
have added to the richness of databases. Scientists also have access to
increasing computational power, enabling them to use larger volumes of
data and an ensemble of models. However, it has also been realized that
such developments have not necessarily resulted in better modelling
approaches. In addition, Refsgaard et al. (2022) illustrate the
importance of spatial resolution and improved data resolutions in a case
study, where a model setup was run at 100 m and 500 m resolutions. While
the two models perform equally well for simulation of catchment
discharge, the underlying processes such as streamflow partitioning
differ significantly.

The paper by Wheater et al. (2022) reviews recent developments and
discusses scientific and technical challenges of large-scale cold region
hydrological modelling with a focus on the Canadian community
hydrological land surface scheme MESH (Mod\selectlanguage{ngerman}élisation Environmental
Communautaire -- Surface and Hydrology). Cold regions are crucial for a
large part of the global population and face major and rapid changes due
to global warming. At the same time the hydrology is particularly
complex, because it includes cold region processes such as permafrost,
frozen soil, snow and glaciers, where hydrological processes often are
controlled by phase change energetics. Modelling of large river basins
in cold regions are often subject to relatively sparse data coverage and
application of remote sensing data has recently shown important
benefits. A key conclusion is that cold region hydrology is particularly
sensitive to temperature changes and that even small biases in forcing
data from global climate models pose large challenges. Wheater et al.
(2022) furthermore conclude that the understanding and description of
hydrological processes related to permafrost and frozen soil as well as
certain glacier processes poses significant challenges and scopes for
improvement.

\section*{New process descriptions}

{\label{new-process-descriptions}}

The study by Bronstert et al. (2023) focuses on description of
infiltration excess (Hortonian surface runoff) in catchment models. In
particular, they investigate the importance of micro- and macropores in
the infiltration process. The study is based on good datasets from well
instrumented infiltration/infiltration-excess experiments and
observations at three spatial scales: point, field and catchment (115
km\textsuperscript{2}). Two modelling hypotheses were then tested
against these field data, namely an approach without macropores, which
is traditionally used in catchment models, and an approach based on
double-porosity soil enabling a combined modelling of high infiltration
rates in macropores and dampened soil moisture distribution after
termination of infiltration. The results from tests at point and field
scale suggest that both modelling approaches are capable of reproducing
soil moisture dynamics, but that the inclusion of macropores results in
more realistic soil hydraulic parameters. The results from catchment
scale show that the macropore based approach is more robust in
reproducing flood hydrographs for different rainfall intensities and
generally outperforms the modelling approach without macropores.
Altogether Bronstert et al. (2023) conclude that macropores are of high
relevance for infiltration and soil moisture dynamics during periods of
high intensity rainfall and therefore should be considered in catchment
modelling focusing on simulation of flood events.

While it is well known that stream discharge in vegetated catchments
during dry periods can exhibit natural fluctuations of up to 10\% daily,
the capability of catchment models to reproduce such behavior and
explain the underlying processes has so far rarely been tested. Le
Cecilia et al. (2022) use the CATHY physically-based integrated
surface-subsurface hydrological model to study the complex processes
generating diel streamflow fluctuations in a 2.67
km\textsuperscript{2}agricultural catchment in Switzerland. After
demonstrating that the model is capable of satisfactorily simulating the
diel streamflow fluctuations, including the timing of short-living
streamflow peaks attributed to irrigation, the model was subsequently
used to test alternative hypotheses for which processes may contribute
to these fluctuations. The results show that evapotranspiration is the
dominant process generating diel fluctuations, while changes in
saturated hydraulic conductivity due to diel soil temperature
fluctuations caused an amplitude of the diel streamflow signal 10 times
smaller than evapotranspiration.

The study by Riazzi et al. (2022) uses a travel time tracking method to
simulate stream electrical conductivity (EC) using high frequency
(hourly) monitoring data from the 369 km\textsuperscript{2} Duck River
catchment in Tasmania, Australia. Two modelling approaches are tested.
The first approach assumes that evapotranspiration is the only process
driving the changes in EC, while the second assumes that the water
salinity in catchment storages is a function of water age in these
storages. The results show that the two hypotheses are equally
successful in simulating EC concentrations and tracking its event and
seasonal dynamics, and hence it is not possible to differentiate which
of the two underlying hypothesis are better supported by the available
observational data. Given that EC data from operational observation
networks is much more widely available than other tracer data, Riazzi et
al. (2022) conclude that using EC data to calibrate travel time models
is a promising approach.

In contrary to other papers studying individual hydrological processes
or the impact of process descriptions on discharge or solute fluxes at
the catchment output, Gaur et al. (2022) evaluate how well a spatially
distributed hydrological model is able to reproduce observed spatial
patterns within the catchment. They use the MIKE SHE with 5 km x 5 km
resolution to simulate the hydrological response of the 19,276
km\textsuperscript{2} Subarnarekha catchment in Eastern India. The study
compares model simulations with remote sensing derived patterns for
evapotranspiration and soil moisture. The comparison is made using three
spatial performance metrics, i.e. joint empirical orthogonal functions
(EOF), fractional skill scores (FSS) and spatial efficiency (SPAEF). The
results demonstrate the potential and value of hydrological model
calibration to observed spatial patterns across time.

\section*{Model calibration and improved process
understanding}

{\label{model-calibration-and-improved-process-understanding}}

Beven et al. (2022) present a novel invalidation approach to calibrate
an ensemble of Dynamic Topmodel parameter sets in a study examining the
potential for hillslope storage bunds to mitigate the effects of
downstream flooding in the 209 km\textsuperscript{2} River Kent
catchment in UK. The model invalidation approach is based on a GLUE-like
methodology, where the acceptability thresholds in a first
goodness-of-fit step is defined to reflect the uncertainty associated
with input and discharge data. 118 realizations out of 100,000 survived
evaluations of hydrograph peaks in three years with major floods. While
most model calibrations are confined to such goodness-of-fit measures of
how well models perform in discharge simulations, Beven et al. (2022)
introduced an additional evaluation step, where only the simulations
with at least 10\% of the area producing overland flow during the
largest storm were accepted. This fitness-for-purpose measure reduced
the acceptable realizations to 67. Altogether, the 67 surviving
realizations are not necessarily those that give the highest
Nash-Sutcliffe efficiency values, but those that are considered most
suitable for assessing the impact of certain flood mitigation measures
in the catchment.

De Lavenne et al. (2022) use the HYPE model for 111 catchments spread
across the USA to evaluate the effect of calibration against both
discharge and sediment data instead of only discharge data and to
evaluate five hypotheses for overland flow process descriptions. The
results confirm previous findings that inclusion of a second data set
(in this case sediment) in a multi-objective calibration approach
generally lead to significantly improved simulations for sediment
concentrations with only a slightly reduced performance for discharge.
The five overland flow modelling hypotheses consist of the existing
formulation using three parameters and four new formulations using one
or two parameters. The results show that the performance for discharge
simulations is not improved by the new hypotheses, while the
performances for sediment concentrations are improved. In addition,
equifinality is reduced by the new hypothesis due to a lower number of
model parameters.

La Folette et al. (2022) study streamflow simulation in the 16.9
km\textsuperscript{2} Elder Creek catchment in Northern California,
where the geology is characterized by fractured bedrock overlain by a,
typically thin (0.5 m), soil layer. This is the first study where
unsaturated weathered bedrock water storage is explicitly incorporated
in a catchment model and used as a calibration target. They calibrate a
lumped rainfall-runoff model against three observations targets: i) only
streamflow data; ii) only rock moisture data; and iii) both streamflow
and rock moisture data. The calibration is performed by evaluating
10,000 parameter sets using the concept of pareto optimality. The
results show that the model calibrated against both streamflow and rock
moisture data is capable of accurately simulating the dynamics in rock
moisture and streamflow, while a calibration against streamflow data
alone may result in relatively poor simulation of rock moisture dynamics
and a calibration against rock moisture alone may result in relatively
poor simulation of streamflow dynamics. Furthermore, the results show
that the calibrated parameter values appear more physically realistic
when calibrating against both streamflow and rock moisture data. The
study concludes that incorporation of rock moisture data can lead to a
more robust model, that without sacrificing the accuracy of streamflow
simulations can provide increased accuracy of some model results and
decreased parameter uncertainty.

\section*{Exploring multiple model
structures}

{\label{exploring-multiple-model-structures}}

Astagneau et al. (2022) hypothesize that the response of a catchment to
high-intensity rainfall events is highly heterogeneous due to complex
interactions among the hydrological processes at short temporal and
spatial scales. The aim of their study is to improve the simulation of
summer floods by using a lumped conceptual rainfall--runoff model. They
modify the GR5H model and test three hypotheses: i) large rainfall
intensities increase the volume of effective rainfall, ii) large
rainfall intensities induce a faster routing of effective rainfall to
the catchment outlet, and iii) a combination of these two hypotheses. A
large database consisting of 10,652 flood events in 229 French
catchments are used. The results show that when the storages and fluxes
of a lumped conceptual model dynamically depend on rainfall intensities,
the errors in flood volume are less (at least in simulations at hourly
time step). It is noted that these conclusions specifically hold good
for a particular model structure and further testing with other models
and the data from other regions would be required to establish the wider
applicability. Since intense rainfall events do not last long, the
intensity-dependent functions are triggered for very small number of
time steps. To address the calibration issues arising due to the above
hypotheses, Astagneau et al. (2023) suggest regionalizing the parameters
of the intensity-dependent function.

Saavedra et al. (2022) investigates if hydrological consistency in
contrasting climate periods can be improved by sampling the model space
with a simple pareto framework and if such a model selection procedure
can reduce uncertainties in precipitation elasticities and temperature
sensitivities. They use the Framework for Understanding Structural Error
(FUSE) to produce 78 different hydrological model structures from four
different conceptual parent models. To test the ability of models to
predict impacts of climate change, they perform differential
split-sample tests of the models by calibrating on dry periods and
evaluating on wet periods and vice versa. The models are tested on three
catchments in Peru with areas ranging from 3545 km\textsuperscript{2} to
9586 km\textsuperscript{2}. The results show that it is possible to
identify some model structures that robustly simulate catchment-scale
hydrology under different climate conditions, and that these are not
necessarily the structures that perform the best for traditional
efficiency metrics. The results also show that the model selection
procedure resulted in a significant reduction in the spread in
precipitation elasticities and temperature sensitivities.

Sinha et al. (2022) perform an intercomparison test of the GR4J lumped
conceptual model against the spatially distributed mHM model using data
from 50 catchments in UK. The models are calibrated by optimizing the
Nash-Sutcliffe efficiency. Subsequently, the model performances in
validation periods are evaluated by four performance metrics as well as
five hydrological signatures characterizing the ability of the models to
reproduce different components of the flow. The results support previous
findings that a lumped conceptual models can perform equally well, and
in some cases slightly better, than a more complex model, when the
modelling objective is limited to discharge simulation.

\section*{Modelling uncertainties}

{\label{modelling-uncertainties}}

Feigl et al. (2022) present a novel method of analyzing errors of
process-based models attributing the model errors at each time step to
specific input variables and model settings. This approach is helping to
understand where model processes might need improvement, model input
data might be of low quality or where model processes might be missing.
The presented approach is a novel combination of (a) Machine Learning
(using a data-driven model to learn predicting model errors), (b)
Shapley Additive exPlanations and Principal Component Analysis
(attributing errors to model inputs and variables), and (c) clustering
(deriving groups of time steps that show similar error generation
characteristics). The methodology is applied to the water temperature
model HFLUX for a 3.45 km\textsuperscript{2} Canadian catchment. The
results show that errors can be clustered in three groups related to
specific processes indicating where model adjustments can lead to
improved performance.

Moraga et al. (2022) present a new framework to quantify and partition
the uncertainty in hydrological projections originating from climate
models and natural climate variability. The approach is tested in the
478 km\textsuperscript{2} Kleine Emme and the 1730
km\textsuperscript{2}Thur mountainous catchments in Switzerland. The
study uses one emission scenario and nine climate models. The outputs of
the climate models are stochastically downscaled using a two-dimensional
weather generator producing a 90-member ensemble covering the period
2010-2089, and the hydrology is simulated using the spatially
distributed TOPKAPI-ETH model. The results show that uncertainty of the
annual streamflow projections is dominated by stochastic uncertainty due
to large natural variability of precipitation. The same applies to
extreme high flows. In contrary, snowmelt and liquid precipitation
exhibit robust climate signals illustrating that streamflow uncertainty
during warm seasons and at high altitudes are dominated by climate model
uncertainty.

\section*{Conclusions}

{\label{conclusions}}

The 14 papers in the Special Issue present novel developments and
perspectives in catchment hydrological modelling enhancing our
understanding of hydrological processes and contributing to solving
real-life problems. The wide spectrum of approaches described in the
papers illustrates that improved understanding of hydrological processes
is not limited to better process equations but also can be achieved
through model evaluation including one or more of the following
approaches: tests on multiple catchments with varying hydrological
regimes, calibration using multiple data types, analyses of alternative
model structures and uncertainty analyses.

\section*{REFERENCES}

{\label{references}}

Astagneau, P. C., Bourgin, F., Andréassian, V., Perrin, C. (2022).
Catchment response to intense rainfall: Evaluating modelling hypotheses.
Hydrological Processes,
2022;36:e14676.\emph{https://doi.org/10.1002/hyp.14676}

Beven, K., Page, T., Hankin, B., Smith, P., Kretzsmar, A., Mindham, D.,
Chappell, N. (2022). Deciding on fitness-for-purpose-of models and of
natural flood management. Hydrological Processes,
2022;36:e14752.\emph{https://doi.org/10.1002/hyp.14752}

Bronstert, A., Niehoff, D., Schiffler, G. R. (2023). Modelling
infiltration and infiltration excess: The importance of fast and local
processes. Hydrological Processes,
2023;37:e14875.\emph{https://doi.org/10.1002/hyp.14875}

De Lavenne, A., Lindström, G., Strömqvist, J., Pers, C., Bartosova, A.,
Arheimer, B. (2022). Evaluation of overland flow modelling hypothesis
with a multi-objective calibration using discharge and sediment data.
Hydrological Processes,
2022;36:e14767.\emph{https://doi.org/10.1002/hyp.14767}

Feigl, M., Roesky, B., Herrnegger, M., Schulz, K., Hayashi, M. (2022).
Learning from mistakes -- Assessing the performance of uncertainty in
process-based models. Hydrological Processes,
2022;36:e14515.\emph{https://doi.org/10.1002/hyp.14515}

Gaur, S., Singh, B., Bandyopadhyay, A., Stisen, S., Singh, R. (2022).
Spatial pattern-based performance evaluation and uncertainty analysis of
a distributed hydrological model. Hydrological Processes,
2022;36:e14586.\emph{https://doi.org/10.1002/hyp.14586}

La Cecilia, D., Camporese, M. (2022). Resolving streamflow diel
fluctuations in a small agricultural catchment with an integrated
surface-subsurface hydrological model. Hydrological Processes,
2022;36:e14768.\emph{https://doi.org/10.1002/hyp.14768}

La Folette, P. T., Hahm, W. J., Rempe, D. M., Dietrich, W. E., Brauer,
C. C., Weerts, A. H., Dralle, D. N. (2022). Multicriteria analysis on
rock moisture and streamflow in a rainfall-runoff model improves
accuracy of model results. Hydrological Processes,
2022;36:e14536.\emph{https://doi.org/10.1002/hyp.14536}

Moraga, J. S., Peleg, N., Molnar, P., Fatichi, S., Burlando, P. (2022).
Uncertainty in high-resolution hydrological projections: Partitioning
the influence of climate models and natural climate variability.
Hydrological Processes,
2022;36:e14695.\emph{https://doi.org/10.1002/hyp.14695}

Refsgaard, J. C., Stisen, S., Koch, J. (2022). Hydrological process
knowledge in catchment modelling -- Lessons and perspectives from 60
years development. Hydrological Processes,
2022;36:e14463.\emph{https://doi.org/10.1002/hyp.14463}

Riazzi, Z., Western, A. W., Bende-Michl, U. (2022). Modelling electrical
conductivity variation using a travel time distribution approach in the
Duck River catchment, Australia. Hydrological Processes,
2022;36:e14721.\emph{https://doi.org/10.1002/hyp.14721}

Sinha, S., Hammond, A., Smith, H. (2022). A comprehensive
intercomparison study between a lumped and a fully distributed
hydrological model across a set of 50 catchments in the United Kingdom.
Hydrological Processes,
2022;36:e14544.\emph{https://doi.org/10.1002/hyp.14544}

Saavedra, D., Mendoza, P. A., Addor, N., Llauca, H., Vargas, X. (2022).
A multi-objective approach to select hydrological models and constrain
structural uncertainties for climate impact assessments. Hydrological
Processes, 2022;36:e14446.\emph{https://doi.org/10.1002/hyp.14446}

Wheater, H. S., Pomeroy, J. W., Pietroniro, A., Davison, B., Elshamy,
M., Yassin, F., Rokaya, P., Fayad, A., Tesemma, Z., Princz, D., Loukili,
Y., DeBeer, C. M., Ireson, A. M., Razavi., S., Lindenschmidt, K.-E.,
Elshorbagy, A., MacDonald, M., Abdelhamed, M., Haghnegahdar, A.,
Bahrami, A. (2022). Advances in modelling large river basins in cold
regions with Modélisation Environmentale Communautaire -- Surface and
Hydrology (MESH), the Canadian hydrological land surface scheme.
Hydrological Processes,
2022;36:e14557.\emph{https://doi.org/10.1002/hyp.14557}

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