A method of multiple working hypotheses was applied to a range of catchments in the Mediterranean area to analyse different types of possible flow dynamics in soils during flash flood events. The distributed, process-oriented model, MARINE, was used to test several representations of subsurface flows, including flows at depth in fractured bedrock and flows through preferential pathways in macropores. Results showed the contrasting performances of the submitted models, revealing different hydrological behaviours among the catchment set. The benchmark study offered a characterisation of the catchments' reactivity through the description of the hydrograph formation. The quantification of the different flow processes (surface and intra-soil flows) was consistent with the scarce in situ observations, but it remains uncertain as a result of an equifinality issue. The spatial description of the simulated flows over the catchments, made available by the model, enabled the identification of counterbalancing effects between internal flow processes, including the compensation for the water transit time in the hillslopes and in the drainage network. New insights are finally proposed in the form of setting up strategic monitoring and calibration constraints.
Flash floods are “sudden floods with high peak discharges, produced by
severe thunderstorms that are generally of limited areal extent”
(IAHS-UNESCO-WMO, 1974;
The large specific discharges and intensities of precipitation lead to the
flash floods being classified as extreme. Nevertheless, those events are not
scarce nor unusual, since on average, there were no fewer than five flash
floods a year in the Mediterranean Arc between 1958 and 1994
A major area of interest for flash floods is, therefore, better risk assessment, which enables them to be forecasted and the relevant populations to be pre-warned. Greater knowledge and understanding is required to better identify the determining factors that result in flash floods. In particular, in order to implement a regional forecasting system, the properties of the catchments and the climatic forcing and linkages between them that lead to flash flood events need to be characterised.
Due to the challenges involved in forecasting flash floods, there has been
considerable research done on the subject over the last 10 years. Examples
include the HYDRATE (Hydrometeorological data resources and technologies for effective flash flood forecasting, 2006–2010;
In the northwestern Mediterranean context – especially concerned with specific
autumnal convective meteorological events – the European cited research
particularly demonstrates the importance of cumulative rainfall
The geochemical monitoring of eight intense precipitation events over a
3.9 km
Finally the geological properties themselves appear to be markers of the
storage capacities available over the timescales involved in flash floods
(that are of the order of a day). From simple flow balances of flash flood
events
The knowledge gained about the development of the flow processes (for
example, the tracing of events carried out during the FLOODSCALE project;
Moreover, hydrological models viewed as ”tentative hypotheses about catchment
dynamics” are interesting tools for
testing hypotheses about hydrological functioning using a systematic
methodology. A considerable amount of recently published works has involved
comparative studies, using numerical models to develop or validate the
hypotheses about the type of hydrological functioning that is most likely to
reproduce hydrological responses accurately
The multiple working hypotheses framework is usually applied using a flexible
conceptual and lumped model framework, such as FUSE (Framework for
Understanding Structural Errors, Clark et al., 2008) or SUPERFLEX (Flexible
framework for hydrological modeling, Fenicia et al., 2011). However,
The objective is to test a number of proposed hydrological mechanisms that occur during flash flood events in a set of contrasting catchments in the French Mediterranean area. While the proportion of flows passing through the soil appears to be significant, questions arise about how they form:
Are they subsurface flows that take place in a restricted area of the root layer as a result of
preferential path activation? Or are they lateral flows taking place at greater depth, comparable to those seen in some aquifers? Does the geological bedrock or an altered substratum play a role limited to that of mere
storage reservoir, or is it actively involved in flood flows formation? Which are the flow processes proportions, according to the events and the catchments?
Locations
of the catchments studied, with a topographic visualisation at a resolution
of 25 m (Source – IGN;
The geology of the
Ardèche catchment
The aim of this article is to attempt to answer these questions using a
multi-model approach that tests different types of hydrological dynamics. The
study was based on MARINE (Modélisation de l'Anticipation du Ruissellement et des
Inondations pour des évéNements Extrêmes), a
physically based, distributed hydrological model
We studied the behaviour of four catchments and eight nested catchments in
the French Mediterranean Arc (Fig.
Physiographic properties and hydrological statistics of the 12
catchments. Here, ID is the coding name of the catchments used at
Fig.
The main physiographical and hydrological properties of the catchments are
presented in Table
The Ardèche and the Gard catchments have been subject to intensive
monitoring and studies (see later references,
The hydrometric data were derived from the network of operational
measurements (HydroFrance databank,
Flood events with peak discharges that had exceeded the 2 year return period
for daily discharge (
The MARINE model structure, parameters and variables. The
Green–Ampt infiltration equation contains the following parameters:
infiltration rate
Precipitation measurements were taken from Météo France's ARAMIS (Application Radar à la Météorologie Infra-Synoptique) radar network
As the MARINE model is event-based, it must be initialised to take into
account the previous moisture state of the catchment, which is linked to the
history of the hydrological cycle. This was done using spatial model outputs
from Météo-France's SIM (Safran-Isba-Modcou, Habets et al., 2008) operational chain, including a meteorological analysis
system (SAFRAN;
Properties of the flash flood events as an average on the event set
(
The MARINE model is a distributed mechanistic hydrological model especially developed for flash flood simulations. It models the main physical processes in flash floods: infiltration, overland flow and lateral flows in soil and channel routing. Conversely, it does not incorporate low-rate flow processes such as evapotranspiration or base flow.
MARINE is structured into three main modules that are run for each catchment
grid cell (see Fig.
The MARINE model works with distributed input data such as (i) a digital elevation model (DEM) of the catchment to shape the flow pathway and distinguish hillslope cells from drainage network cells according to a drained area threshold, (ii) soil survey data to initialise the hydraulic and storage properties of the soil, which are used as parameters in the infiltration and lateral flow models, and (iii) vegetation and land-use data to configure the surface roughness parameters used in the overland flow model.
The MARINE model requires parameters to be calibrated in order to be able to
reproduce hydrological behaviours accurately. Based on sensitivity analyses
of the model
We proposed several modifications to Module 2 – the subsurface downhill flow submodel – covering the three hypotheses of hydrological functioning:
The deep water flow model (DWF) assumed deep infiltration and the formation
of an aquifer flow in highly altered rocks. In hydrological terms the
pedology–geology boundary was transparent. The soil column could be modelled
as a single entity of depth The subsurface flow model (SSF) assumed that the formation of subsurface
lateral flows was due to the activation of preferential paths, like the in
situ observations of The subsurface and deep water flow model (SSF-DWF) assumed that the presence
of subsurface flow was due not only to local saturation of the top of the soil column, but also to the
development of a flow at depth, as a result of significant volumes of water
introduced by infiltration and a very altered substratum whose apparent
hydraulic conductivity was already relatively high. This hypothesis of the
process led to a modelling approach analogous to the SSF model
(Fig.
The soil water content prior to simulation was similarly initialised for
each model in order to ensure that, for a fixed depth of altered rock, the
same volume of water was allocated for all models. The SIM humidity indices
(Sect.
DWF model of flow generation by infiltration at depth and support of a
deep aquifer
SSF and SSF-DWF models of flow generation by the saturation of the
upper part of soil column and activation of preferential paths (
The three hydrological models studied, DWF, SSF and SSF-DWF, were calibrated
for each catchment by weighting 5000 randomly drawn samples from the
parameter space for each model (the Monte Carlo method). The weighting was
done using the DEC (Discharge Envelope Catching) score (Eq.
Given the lack of information, these uncertainties
The modelling uncertainties
Results of the models were first assessed and benchmarked using performance
scores (Sect. The period of rising flood waters is between the moment when the observed flow
rate exceeds the mean inter-annual discharge of the catchment and the date
of the first flood peak. The stage of high discharges includes the points for which the observed flow
was greater than 0.25 times the maximum flow during the event. The stage of flood recession begins after a period of
The DEC score has provided a standard assessment of the modelling errors,
enabling a reasonable weighting of the simulations. However, for a sake of
easy understanding, the percentage of acceptable points of the simulated
median time series, Qmed_INT [%]
Conversely, Qmed_INT was not relevant for the evaluation of the capacity to
reproduce recessions, because the calculation of this score during the
recession interval strongly depends on performance at high discharges.
Instead, we used the
The evaluation was completed through the description of the modelling errors
(Sect.
Those confidence intervals were standardised according to the DEC modelling
error definition (Eq.
where
The latter definition allows for an informative translation of the prior and
posterior confidence intervals
Qmed_INT scores, with mean Qmed_INT scores obtained for the calibration
.
Figure
Uniform results are observed on the Gard catchment at Corbès and Anduze
(no. 2a and no. 2b) and on the Salz catchment (no. 4); the SSF and SSF-DWF
models demonstrated clearly superior performances for all stage-specific
assessments of those catchments. For the Gard catchment at Mialet (no. 2c),
the detailed assessment (Fig.
On the Ardèche catchments (no. 1a, no. 1b, no. 1c and no. 1d), the
overall performances reflect the simulation of the high discharges and of the
flood recessions. There, the DWF model gives the best results for simulating
those hydrographs' stages. Conversely, it deals slightly less well with the
simulation of the rising flood waters. As shown in Sect.
Assessment of the models by catchment in the different stages of
the hydrographs.
On the Hérault, the detailed evaluation enabled us to distinguish the
performance of the different models. On the one hand, for the two larger
catchments (no. 1a and no. 1b), the DWF model performed slightly better for
rising flood waters simulations, while the SSF model gave more clearly better
simulations of the flood recessions. On the other hand, the SSF-DWF model
generated the best simulations of the rising flood waters and of the high
flows on the upstream catchments of La Terrisse (no. 3c) and Valleraugue
(no. 3d), while the DWF model simulated a better flood recession. These
contrasting results explained why there is not a specific model that stands out on this
catchment. In addition, it suggests a marked influence of the physiographic
properties on the development of flow processes, because they are correlated
with the differences in the geological and topographical properties of the
Hérault (no. 3; see Fig.
Summary of the models' benchmark. A colour is attributed for each score and each catchment when one model gives a clearly superior performance, or two colours are attributed for each score and each catchment when two models give clearly superior performances: the score of a model is defined as clearly superior when the lower bound of its confidence interval is higher than the median values obtained with the other models. The superiority of a model might be half attributed if the criteria is only respected for the calibration processes. Colour attribution: orange for the DWF model, blue for the SSF model, green for the SSF-DWF model and grey when the superiority of one's model is undetermined.
Figure
A first group of catchments is where the SSF and SSF-DWF models uniformly perform either similar or better than the DWF models. This
is the case for the Gard (no. A second group of catchments is where the DWF model gives the best results
according to all the scores, except for the rising flood waters assessment. This is the case for the
downstream Ardèche catchments (no. 1a, no. 1b and no. 1c). A third group is where the models' results are not really discernible. For
those catchments, the DWF model appears to simulate the rising
flood and the high discharge slightly better, while the recession is better represented by
the SSF model. This is the case for the downstream Hérault catchments
(no. 3a and no. 3b). A last group is where the SSF-DWF model generates the rising
flood and the high discharge slightly better, while the recession is better represented by
the DWF model. The head watersheds of the Hérault (no. 3c and no. 3d) and of the Ardèche (no. 1d) catchments are in this group.
For the sake of conciseness, only the simulation over one catchment is
presented. Figure
Calibration of the three models for the Ardèche catchment at
Ucel (no. 1b). The results of the simulation of five flood hydrographs
and the inherent modelling errors (Eq.
Representing the soil column with either one compartment (the DWF model) or
two compartments (SSF or SSF-DWF models) leads to a distinct a priori
confidence interval of modelling errors (grey). The DWF model constrains the
simulated flows at the beginning of the event, before the onset of
precipitation, because the width of the confidence interval of the modelling
errors is low at that point. More specifically, it tends to underestimate the
initialisation discharges, because the variation interval of the errors over
this period is predominantly negative. This may explain this model's relative
difficulty in reproducing the onset of floods, since the calibration of the
parameters did not allow the acceptability zone in this part of the
hydrograph to be reached. A resulting interpretation applicable to the
catchment sets is that good results in modelling the rising flood waters with
the DWF model mean that the observed rising flow is relatively slow and
could be reached in spite of the restrictive modelling structure (for
example,
no. 3
Likewise, it can be noted that the one-compartment structure (i.e. the DWF
model) allows for flexibility in the modelling of high discharges and flood
recessions, because the confidence interval of the modelling errors is quite
large over these periods in the hydrograph. However, it also led to the
underestimation of high discharges and flood recessions. In fact, the prior
modelling error interval (in grey) has a negative bias with respect to
the acceptability zone. The calibration finally allows the simulations to be
selected at the intersection of the acceptability zones and the a priori
confidence in modelling errors. This generally corresponds to the calibration
of a low-depth altered rock,
Conversely, the two-compartment structure (the SSF and SSF-DWF models) offers
flexibility in modelling the beginning of events, flood warnings and high
discharges, but the ability to model flood recessions is more constrained.
SSF and SSF-DWF models simulate fast flood recessions in comparison to the DWF
model, suggesting that good results in modelling the flood recession with the
SSF model that might be interpreted as a fast return to normal or low discharge are
observed on the related catchments (as example, no.
In the SSF and SSF-DWF models, the addition of a flux calibration parameter
in the subsoil horizons not surprisingly leads to wider variations in the a
priori modelling errors. A surprising finding, however, is that the
calibration of the lateral conductivity of the deep layer,
The proportional volumes of the water making up the hydrographs, which arise
from the three main simulated paths (on the surface, through the top or
through the deep layer of the soil), were calculated. Figure
The runoff contribution simulated by the DWF model even further discredits
that model for representing the hydrological behaviour of the Gard (no. 2)
and Salz (no. 4) catchments. Really high proportion of runoff contribution
over the entire hydrograph were simulated, ranging from 40 % to 98 %. In
contrast, the few experimental measurements made on the Gard
Proportion of surface runoff in the flows at the outlet. Left: The proportion over the whole hydrograph. Right: the proportion at high discharges (observed flow greater than 0.25 times the maximum flow during the event).
Realistic models and parameter sets for the Hérault catchment at
Saint-Laurent-le-Minier (no. 3b).
The assessment of the flow contributions through the most suitable model's
simulations for each catchment revealed in Sect.
On the downstream catchments of the Hérault (no. 3a, no. 3b), the variation intervals of the surface flows estimated by the three models overlap. It may explain why the three models can achieve good reproductions of the hydrological signal; the calibration step makes it possible from that integrated point of view to obtain an analogous distribution of the flow processes.
Notwithstanding the uncertainty related to the choice of the model when any model has been identified most suitable through the performances, the largest uncertainties are related to the parameterisation of the models, a consequence of the equifinality of the solutions when calibrating a hydrological model against the sole criterion of the reproduction of the hydrological signal. While in terms of plausibility, several sets of parameters may be equivalent, even for the same model, these sets of parameters are likely to lead to a different hydrological functioning.
Comparison of the results of four equally plausible simulations for
the Hérault at Saint-Laurent-le-Minier (Table 3).
Spatialised outputs for a given moment during the event of
18 October 2009 for the Hérault at Saint-Laurent-le-Minier (during the development of the flood, where
Spatialised and integrated changes in moisture levels and flow velocities
generated within the catchments have been considered in order to give new
details on the different impacts of the models' structure, but also to
explain the resulting uncertainty when assessing the flow processes'
distribution. Next, the results of four simulations are described and are
equally considered to be plausible according to the DEC criterion obtained
from the DWF and SSF models (two simulations per model, see Table 3). The Hérault catchment at
Saint-Laurent-le-Minier (no. 3b) has been considered because of the
equivalence of the models in representing that catchment.
Figure
In terms of hydrographs, which is quite logical given the similar likelihood scores,
the simulations differed very little. The notable difference in the
generation of hydrographs is the contribution of the different simulated
flow paths. The proportions of water passing through the soil column (via sub-
or surface-soil horizons) were highly variable, with an average of 39 % for
the DWF2 model, 53 % for the SSF2 model, 61 % for the DWF1 model and 68 %
for the SSF1 model (Table
The choice of a model's structure (DWF and SSF) implied differences in soil
moisture spatial distribution and dynamics, which in turn impacted the timing
of the flow processes. In the DWF structure, the soil moisture distribution
is sensitive to the soil depth spatial distribution as a result of the
decrease in the simulated intra-soil flows as a function of water table
height (cf. Sect.
As a result of the contrasting soil moisture dynamic, the flow velocities
simulated in the soil showed consecutive differences. At the start of
flooding, the SSF structure resulted in an early increase in flow velocities
due to a higher and more homogeneous saturation level of the upper soil layer
(Fig.
The dynamics in the drainage network were impacted by the choice of
the structure as well. The runoff velocities' average reflected the earlier inlet of
the subsurface flow processes through the fast saturation of the upper
compartment with the SSF model (Fig.
The choice of parameters mainly implied different ranges of values for the
velocities simulated in the soil, on the surface of the hillslope and in the
drainage network. The calibration of the
Several orders of magnitude were actually allowed while respecting the
calibration objective, because the transit times of the different water
pathways compensate each other. As foreshadowed by those four configurations,
the selection of plausible parameter sets for any model in any catchment
shows (i) a positive correlation between the parameters
The benchmark of the models' performance on the catchment set leads to
reveal four subsets, suggesting four distinct hydrological behaviours. According to
the modelling assumptions (Sect. The SSF and SSF-DWF models showed better overall performance (with no
particular pattern) in the first subset, the Gard (no. 2) and Salz
(no. 4) catchments. This suggests, on the one hand, rapid catchment
reactivity with fast rising flood waters as well as a fast flood recession, and
on the other hand, the formation of the flows in the soil through local saturation
tied to the climate forcing. Although the models exhibited similar
performances, the contrasting physiographic characteristics of these
catchments suggest that there are different explanations for this better fit
of the SSF-DWF model. On the Gard, the very high intensities of the
observed events (Table The considerable hydrological responses in terms of volume on the
Ardèche second subset appear to be linked to hydrological activity at
depth, including that which takes place during intense floods, as suggested by the
better fit of the DWF model. Here, in particular, the model gave a better
representation of the relatively slow and uniform hydrological recessions
from one event to the next, reflecting an aquifer-type flow whose discharge
properties are only governed by the properties of the catchment bedrock only. This
interpretation is enforced by the field studies achieved at the time in a
granite experimental sub-catchment localised in the downstream part of the
Gard (Sect. The third subset consists of the downstream part of the Hérault
(no. 3a and no. 3b). The models' performances contrasted with the
Hérault catchment heads (no. 3c and no. 3d), suggesting hydrological behaviours related to the contrasting geological properties. An
interpretation of hydrological functioning is nevertheless not possible,
given the similar overall results offered by the models and that no
distinctions can be drawn according to other criteria. The last subset consists of the catchment heads (no. 1d, no. 3c, and
no. 3d). We observed superior performances from the DWF and SSF-DWF
models, with a particular improvement in the forecasting of rising flood
waters when using the SSF-DWF model. This suggests the presence of several
types of flow in the soil with strong support from flows at depth, which
corroborates the high mean inter-annual discharges associated with these
catchments, and additionally the presence of rapidly formed flows, providing
a good simulation of the rising flood waters. The fact that the model
SSF-DWF, which precisely alleged to represent the simultaneous setting up of
shallow and deep subsurface flows, did not completely outperform the two
other models is interesting. From our point of view, it points out the limit
of their artificial implementation, using a threshold infiltration from the
top layer to the deep one. In reality, the simultaneous setup of the two
fluxes more likely refers to the spatial heterogeneity of the soil
properties, especially in the head watersheds
within a catchment cell
(2.5 km
The submitted multi-hypothesis test classically faced the equifinality issue related to the parameter uncertainty and highlighted the uncertainty related to the model's structure. The comparative and detailed description of the simulation revealed the model's structure controls, thus giving almost direct guidelines to overcome the equifinality issue.
One of the objectives of the study, the assessment of the flow contributions
to the hydrographs, is not completely reached, mainly because of the
parameter uncertainty (Sect.
The equifinality of the models in several catchments mostly points out the
limit of the assessment of hydrological model through the sole use of the
hydrological discharge time series at the outlet. Leading up to a
multi-criteria calibration, the detailed comparative description outlined the
discrepancies of the simulations and thus provided guidelines for integrating
judicious information to differentiate the models' adequacy. The
distinguished saturation spatial patterns generated by the DWF and SSF
structures suggest the relevancy of the soil moisture distribution assessment
along hillslopes and soil heterogeneities, as the first structure implied a
soil moisture dynamic related to local soil properties, while the latter
implied a soil moisture pattern related to the distance to the drainage
network. In addition, the description of the a priori modelling errors
(Sect.
The objective of the study was to improve our understanding of flash flooding in the French Mediterranean Arc. In particular, attention was paid to the dynamics of soil saturation in catchments during these events and their possible relationship with the physiographic diversity encountered. The method used consisted of the consideration of hydrological models as a diagnostic tool to test hypotheses about the functioning of catchments.
Based on the structure of the MARINE model, a hydrological model with a physical and distributed basis, three types of dynamic of soil saturation were postulated and tested. In the first case (the DWF model), we assumed an aquifer dynamic with an infiltration at depth and the generation of a strong base support according to the volume of infiltrated water. In the second case (the SSF model), it was the activation of preferential paths at the soil–altered-rock interface that generated the majority of the flows passing through the soil, with the lower part of the soil column serving only as a storage reservoir. In the third case (the SSF-DWF model), there was flow generation via both the activation of preferential pathways, initially by the saturation of the top of the soil column, and a significant increase in the base flux via the subsequent infiltration of water present at deeper levels.
The same calibration strategy was used for the three models on a set of 12 catchments, which are representative of the diverse characteristics of the Mediterranean Arc. Whether a model offers a good fit was evaluated on the basis of scores representing overall or partial model performance in terms of simulating the hydrographs, the proportions of the processes simulated, and the timing and form of flood recession.
The specific use of a multi-hypothesis framework supports a clear comparison of the hydrological behaviours, which has in turn provided the main basis of the insights of this study. From the application and validation of the three hydrological models, the 12 catchments of the study could be classified into four categories, including (i) the Gard and Salz catchments, for which the SSF model is better suited to reproducing the hydrological signal, highlighting the importance of local and surface soil dynamics in the generation of flows especially at the beginning of a flood, (ii) the Ardèche catchments, for which the DWF model most accurately reproduces the observed flows, which indicates more regular and integrated hydrological functioning at the catchment level, with the flows generated being directly related to the moisture history and rainfall volumes, (iii) the Hérault catchments at Valleraugue and La Terrisse and the Ardèche catchment at Meyras, which have steep-sloped catchment heads where the SSF-DWF model stands out, suggesting both sustained and significant hydrological activity at depth during flash floods and surface activity in the establishment of early flows at the beginning of events, and (iv) the Hérault catchments at Laroque and Saint-Laurent-le-Minier, for which no model shows any significant difference.
The modelling results help to draw consistent assumptions of hydrological behaviours, which corroborate, when available, the knowledge and observations on the overall hydrological functioning of the catchments or the experimental estimations of flow processes. The results suggest that the behaviour of catchments under extreme forcing is a continuation of the hydrological functioning normally encountered.
The assessment of the flow processes in the catchments remains uncertain, owing to the equifinality issue. The analysis of the internal processes enabled the explanation of the compensation effects between the simulated flow pathways and the resulting uncertainty of the calibrated parameter sets on the sole basis of the discharge time series. In addition, other detailed descriptions of the simulations, such as the spatial dynamic of the soil moisture distribution or the modelling errors, highlighted the actual impacts of the model's assumptions on the simulations. The revealed discrepancies between models, namely the range of values of the flow velocities, the spatial pattern of the soil moisture, the early rising limb timing and the recession rate of the hydrographs, finally defined pertinent milestones for improving the assessment of the model's adequacy.
Hydrometric data come from the network of operational
measurements (HydroFrance databank,
AD developed Module 2 of the MARINE code. AD performed model simulations and prepared the paper. All authors discussed the results and contributed to the text.
The authors declare that they have no conflict of interest.
This work was partly funded by the Eurorégion Pyrénées-Méditerranée (PGRI-EPM project) and the French Central Service for Flood Forecasting (SCHAPI). Edited by: Markus Hrachowitz Reviewed by: two anonymous referees