Model intercomparison experiments are widely used to investigate and improve hydrological model performance. However, a study based only on runoff simulation is not sufficient to discriminate between different model structures. Hence, there is a need to improve hydrological models for specific streamflow signatures (e.g., low and high flow) and multi-variable predictions (e.g., soil moisture, snow and groundwater). This study assesses the impact of model structure on flow simulation and hydrological realism using three versions of a hydrological model called MORDOR: the historical lumped structure and a revisited formulation available in both lumped and semi-distributed structures. In particular, the main goal of this paper is to investigate the relative impact of model equations and spatial discretization on flow simulation, snowpack representation and evapotranspiration estimation. Comparison of the models is based on an extensive dataset composed of 50 catchments located in French mountainous regions. The evaluation framework is founded on a multi-criterion split-sample strategy. All models were calibrated using an automatic optimization method based on an efficient genetic algorithm. The evaluation framework is enriched by the assessment of snow and evapotranspiration modeling against in situ and satellite data. The results showed that the new model formulations perform significantly better than the initial one in terms of the various streamflow signatures, snow and evapotranspiration predictions. The semi-distributed approach provides better calibration–validation performance for the snow cover area, snow water equivalent and runoff simulation, especially for nival catchments.

Hydrological models are widely applied in water engineering for design and scenario impact investigations. Depending on the type of application, the catchment characteristics and data availability, different model conceptualizations and parameterizations are considered. In many cases, the choice of the model is the result of the modeler's experience. However, hydrologists have developed objective and rigorous frameworks to evaluate and improve hydrological models.

A common approach to discriminate different model structures is to conduct
model intercomparison experiments. Such experiments have been helpful for
exploring model simulation performance of lumped

In a similar way, this paper compares different model structures in terms of
both runoff simulation and hydrological realism. More specifically, we
investigate the relative importance of model equations and spatial
discretization on flow simulation, snowpack representation and
evapotranspiration estimation. This correspondence between model and
“reality”, often described as “working for the right reasons”

We apply this framework to the MORDOR hydrological model

Main components of MORDOR V0, V1 and SD models in terms of water balance, runoff production, snow model, routing scheme and spatialization. For each module and model, the number of free parameters is given.

The comparison of the three hydrological models is based on an extensive
dataset composed of data from 50 catchments. This dataset collects different
operational case studies from EDF activities. These catchments are located in
mountain regions, manly in the Alps (10 catchments), the Pyrenees (5
catchments) and the Massif Central (29 catchments). Four catchments are
located in the northeast of France (Ardennes and Jura and Vosges regions),
one in the northwest (Brittany region) and one in Corsica. Figure

Localization of the catchments studied.

For each catchment the following data were collected: (i) discharge, (ii) rainfall, (iii) temperature, (iv) potential and actual evapotranspiration, and (v) fractional snow cover (FSC) and local snow water equivalent (SWE).

The discharge data
are provided by EDF and French water management agencies. The average length
of records at all these stations combined is around 25 years, ranging from 9 years for Ouvèze at Bèdarrides (southern Alps) to 53 years for Sioule at
Fades (Massif Central). The whole discharge dataset consists of 1526 hydrologic years. The average runoff for the whole
dataset is around 800 mm yr

Evapotranspiration data used for validation come from the MOD16 satellite
global evapotranspiration product

The historical MORDOR model is a lumped conceptual rainfall–runoff model. Its structure is similar to that of many conceptual-type models with different interconnected storage. Is is a continuous model that can be used with a time step ranging from hourly to daily. The required input data are a representative estimate of areal precipitation and air temperature.

The main components of the model are as follows: (i) an evaporation function that determines the
potential evaporation as a function of the air temperature; (ii) a rainfall
excess and soil moisture accounting storage

In this configuration, the MORDOR V0 model has 22 free parameters (see Table

However, various reasons to improve the model have appeared recently: (i) an
increase in model performance in terms of floods and low-flow simulations may
broaden model applications; (ii) representation of snow processes must be
improved to allow for snow data assimilation, particularly for long-term snow
melt forecasts; (iii) representation of orographic meteorological variability
should be taken into account; and (iv) simplification of the model's
structure and parameterization may improve the efficiency of model
calibration and reduce parameter equifinality

The revised model formulation, hereafter called MORDOR V1, does not modify
the overall catchment conceptualization. In the following parts, we
distinguish changes in (i) the water balance formulation, (ii) the runoff
production, (iii) the snow model and (iv) the routing scheme. Special focus
on the MORDOR V1 components and fluxes is given in Appendix

The water balance formulation includes a simplified vegetation component,
with a maximum evaporation that is derived from the potential
evapotranspiration PET using a crop coefficient

The model identifies three flux components: (i) surface runoff, (ii) subsurface exfiltration and (iii) base flow. Surface runoff is generated by
excess water coming from

The snow model is derived from a classical degree-day scheme, with a few
important additional processes: (i) a cold content able to dynamically
control the melting phase; (ii) a liquid water content in the snowpack;
(iii) a ground-melt component; and (iv) a variable melting coefficient, depending
on the potential radiation assumed to model the changing albedo effect
throughout the melting season. The accumulation phase is controlled by the
discrimination of the liquid and solid fractions of the precipitations. From
the temperature, these fractions are derived from a classical parametric

The transfer function is applied to the sum of the runoff contributions. Its
formulation is based on the diffusive wave equation

The semi-distributed MORDOR model is an improvement of the MORDOR V1 model,
which includes a spatial discretization scheme. This discretization is based
on an elevation zone approach, which is known to be both parsimonious and
efficient for mountainous hydrology

Durance at La Clapière catchment:

The runoff signatures are viewed in such a way that streamflow data can be
broken up into several samples, each of them a manifestation of catchment
functioning

the time series of flow is obviously the first signature that has to be reproduced by the model (hereafter called

the long-term mean daily streamflow is used to focus on the capacity to reproduce seasonal variation of observations (hereafter called

the flow duration curve focuses on the capacity to reproduce streamflow variance and extremes (hereafter called FDC);

the flow recessions during low flow periods focus on streamflow recessions (hereafter called

the lag-1 streamflow variation is the last signature focusing on short-term variability (hereafter called d

To go further, model realism is also evaluated in regards to three other
hydrological variables: (i) the fractional snow cover, (ii) the snow
water equivalent and (iii) the actual evapotranspiration.
However, these data suffer from many limitations and uncertainties (see
Sect.

The model is calibrated using an efficient genetic algorithm inspired by

The multi-criterion composite objective function (OF) to be minimized
during calibration is expressed as follows:

To evaluate the model, we adopted the split-sample test advised by

Model performance is quantified using the classical Nash–Sutcliffe efficiency
(NSE). This criterion is commonly used for evaluation of hydrological
models and is therefore suitable to use as a benchmark for this study. In
addition, it allows for the consideration of different metrics for calibration and
posterior evaluation. NSE criteria are systematically calculated for all
the streamflow signatures

This section presents the results of the model comparison. We focus on improvements in terms of model performance and the representation of snow and evapotranspiration processes.

Performance of the three versions of the model on the validation
periods, for five streamflows signatures:

Mean NSE for each hydrological signature and for the three model
versions:

Fractional snow cover regime on eight mountainous catchments. Comparison of MOD10 FSC product with the three model versions. For each catchment, the considered period is given. NSE values are calculated on FSC regimes.

Observed and simulated snow water equivalent (SWE) time series on the Durance at La Clapière catchment. NSE values are calculated on SWE time series.

Observed and simulated snow water equivalent (SWE) regimes on the
Durance at La Clapière catchment, for three measurement stations:

Actual evapotranspiration regime on eight pluvial catchments. Comparison of MOD16 AET product with the three model versions. For each catchment, the considered period is given. NSE values are calculated on AET regimes.

Figure

To go further, we compare the mean NSE obtained for each hydrological
signature and for the three model versions. At the same time, we distinguish
pluvial and nival catchments, according to the classification of

One of the objectives of this study was to improve the model representation of snow processes. Hereafter, we investigate this question using two types of data. The first one is a catchment-scale average of the FSC provided by the MOD10 product, available over the 2000–2012 period. Due to uncertainties and missing data, we consider only the long-term mean daily FSC. The second one is the snow water equivalent on the local scale, derived from our NRC observation network.

Figure

Figure

The realism of the hydrologic representation is also investigated considering
the water balance, by comparing simulated ET fluxes and MOD16
satellite-derived data available over the 2000–2012 period. Due to
uncertainties and missing data, we consider only the long-term mean daily ET.
In addition, considering MOD16 limitations on mountainous areas, we focus on
eight low-altitude catchments where it may be considered as realistic. These
catchments have been selected from the pluvial sample (35 catchments),
considering data availability. Figure

Comparison with MOD16 data suggests that this new seasonality is more
realistic, as illustrated by NSE values (see legends of Fig.

In this study we validated improvements in an operational hydrological model, using a multi-catchment, multi-criterion and multi-variable framework. From the historical version of the model, two alternative structures were evaluated. Within the first, the physical equations were revisited to better represent the main hydrological components, such as evapotranspiration and snow, and to reduce model parameters. The second alternative structure integrates this new formulation in an elevation zone spatialization (semi-distributed scheme).

A first evaluation focused on runoff simulation with a multi-criterion split-sample test. Five criteria were identified to focus on various streamflow signatures. For each criterion, the two alternative models perform significantly better than the initial one. On pluvial catchments, improvements are mainly due to the new physical formulation. In contrast, orographic discretization provides the main gains on nival catchments. Finally, the new semi-distributed model shows significantly better performance for runoff simulation for all catchments and for all criteria.

The second evaluation was performed on two independent hydrological variables, not used for model training: snow and evapotranspiration. The objective was to reinforce our conclusions, by performing a discharge-independent validation. The results clearly demonstrate model improvement. This semi-distributed structure simulates snow processes quite realistically. The simulation of snow cover and snow water equivalent are significantly improved. The realism of the water balance is also improved in the new model formulation. When compared with satellite proxy, the evapotranspiration dynamic is shown to be substantially improved.

This paper has therefore shown that MORDOR SD provides a very efficient tool for wide-ranging hydrological applications to hydrological simulation in pluvial and nival catchments. The performance and versatility of this new model version are very significantly improved. At the same time, its structure has been simplified (especially concerning snow processes) with fewer free parameters. Currently, further experience with MORDOR SD is being gained as it is implemented in the EDF flood-forecasting chain and in hydrological studies. An assimilation scheme is also being implemented, which integrates both discharge and snow measurement. Future work will focus upon implementation of a fully distributed version of the MORDOR SD model over large-scale catchments and in ungauged contexts.

The data that support the findings of this study are available from the corresponding author.

This section details the MORDOR SD model structure. Figure

Overview of MORDOR SD model components and fluxes.

Schematic representation of MORDOR SD storage.

The MORDOR SD model is based on a succinct description of the catchment,
through the following characteristics: (i) sbv, the watershed area (km

The model has as input data, for each elevation zone

From the potential evapotranspiration PET

with

The aim of storage

For each elevation zone

MORDOR SD free parameters, units, range and description.

For each elevation zone

The storage

The storage

The storage

The deep storage

The model identifies three flux components: (i) surface runoff

Table

The MORDOR SD model is written in FORTRAN 90. The model runs at different temporal resolution. The duration of a simple model simulation (i.e., model run and evaluation criteria computation) is approximately 1 s and depends on the time step and on the length of time series. For instance a daily simulation over 50 years takes less than 1 s and an hourly simulation over 10 years takes approximately 2 s. Concerning the calibration process (approximately 40 000 model runs), the algorithm takes approximately 10 min for a daily time step over 50 years and approximately 45 min for an hourly time step over 10 years. The post-processing and graphical tools are developed in R language.

The authors declare that they have no conflict of interest.

The authors would to acknowledge the referees for their helpful comments. We are grateful to W. Troup for Figs. 1 and S1. Edited by: Matthias Bernhardt Reviewed by: Markus Hrachowitz and one anonymous referee