Karst development influences the hydrological response of catchments. However, such an impact is poorly documented and even less quantified, especially over short scales of space and time. The aim of this article is thus to define karst influence on the different hydrological processes driving runoff generation, including interbasin groundwater flow (IGF) for elementary catchments at the storm-event timescale. IGFs are estimated at the scale of the river reach, by comparing inlet and outlet flows as well as the effective rainfall from the topographic elementary catchment. Three types of storm-event descriptors (characterizing water balance, hydrograph shape and lateral exchanges) were calculated for the 20 most important storm events of 108 stations in three French regions (Cévennes Mountains, Jura Mountains and Normandy), representative of different karst settings. These descriptors were compared and analysed according to catchment geology (karst, non-karst or mixed) and seasonality in order to explore the specific impact of karst areas on water balance, hydrograph shape, lateral exchanges and hydrogeological basin area. A statistical approach showed that, despite the variations with study areas, karst promotes (i) higher water infiltration from rivers during storm events, (ii) increased characteristic flood times and peak-flow attenuation, and (iii) lateral outflow. These influences are interpreted as mainly due to IGF loss that can be significant at the storm-event scale, representing around 50 % of discharge and 20 % of rainfall in the intermediate catchment. The spatial variability of such effects is also linked to contrasting lithology and karst occurrence. Our work thus provides a generic framework for assessing karst impact on the hydrological response of catchments to storm events; moreover, it can analyse flood-event characteristics in various hydro-climatic settings and can help with testing the influence of other physiographic parameters on runoff generation.
Understanding runoff generation requires a good knowledge of the different processes involved in catchment response to rainfall events, i.e. how precipitation is converted into underground, subsurface or surface flow. These processes are affected by several factors, such as the thickness and nature of soil, land use, hydrological conditions, or geology. While most of these can be documented or measured, it may be difficult to define the role of geology in a comprehensive way, especially when underground drainage networks are involved, as in karst areas. Karstification, the result of carbonate-rock dissolution, promotes infiltration and groundwater flow through enlarged fissures and voids (Bakalowicz, 2005), locally dramatically reducing drainage density on the surface and thus affecting the hydrological response of a catchment. These groundwater flows can be considered interbasin groundwater flows (IGF) if they do not return to surface within the considered catchment. IGF amplitude and sign can be linked to the area of the hydrogeological basin, which can be different from the area of the topographic one.
Karst impacts on flood processes are mostly documented through case studies. As an example, Zanon et al. (2010) showed that during a flash flood in 2007 in Slovenia, a karst area reduced flooding, which was more important in a non-karst neighbouring zone, receiving less precipitation. Likewise, Delrieu et al. (2005) observed, for an exceptional storm event in 2002, lower runoff coefficient values for the karstic catchment compared to the hard-rock catchment in the eastern zone of the Cévennes Mountains. De Waele et al. (2010) and Charlier et al. (2015, 2019) determined that, depending on the location on the river profile, karst areas could result in streamflow losses or gains due to the high spatial variability of the hydrogeological karst features. Other frequently described processes are groundwater rising, leading to reduced infiltration and important surface runoff (López-Chicano et al., 2002; Bonacci et al., 2006), and backflooding or sinkhole flooding due to conduit constriction (Maréchal et al., 2008; Bailly-Comte et al., 2009).
The diversity of observed processes during storm events in karst catchments does not allow for drawing a straightforward analysis on the control of karst in flood runoff generation. For the purpose of understanding the mechanisms involved in this control, there is a need for regionalized studies, covering a large-scale analysis of karst impact over short time periods when the catchment reacts after storm events. It is reasonable to think that karst can alternately increase or decrease storm impacts, depending on its capacity to infiltrate precipitation or to release stored water, i.e. depending on the direction of IGF it promotes. Despite the early conceptualization of IGF (Eakin, 1966), its major role in karst hydrological processes is tackled by very few studies (Le Moine et al., 2007; Lebecherel et al., 2013). Some authors tried to improve model capacities to reproduce karst-based IGF, such as Nguyen et al. (2020) with SWAT, Le Moine et al. (2008) with GR4J or Scanlon et al. (2003) comparing a distributed and a lumped model. Nevertheless, those studies that are dedicated to the improvement of model performance are not devoted to describe and understand all flood components in karst catchments.
On the one hand, most studies including karst system descriptors are based on a purely hydrogeological point of view and are very integrative, as they tend to characterize the karst aquifer as a whole, by analysing daily spring discharge. Gárfias-Soliz et al. (2009) found that system memory, response time and mean input–output delay are relevant indicators for karstification, in addition to a necessary consideration of the structural complexity and heterogeneity of the lithology. Hartmann et al. (2013), using 10 system signatures, performed a model parameter sensitivity analysis to investigate their links with hydrological processes on five European and Middle Eastern karst sites. Basha et al. (2020) proposed six recession curve equations for the classification of karst aquifers, depending on their flow characteristics. On the other hand, some studies accounting for a spatialization of catchments focus on low-flow issues and surface-water–groundwater interaction (e.g. Covino et al., 2011; Mallard et al., 2014). Moreover, most regionalization studies tend to spatialize annual indices (Sivapalan et al., 2011) or model parameters (Parajka et al., 2005; Oudin et al., 2008), and they usually exclude catchments with identified IGF (Merz and Blöschl, 2004) or karst areas (e.g. Laaha and Blöschl, 2006).
Regional spatial analyses need to be based on reliable data at the highest resolution available. For this purpose, the scale of the elementary catchment – i.e. subdivision of a basin following available gauging stations – appears to be the best resolution for long-term monitoring. Elementary catchment can be either the drained area of a headwater catchment controlled by a gauging station or the drained area between two gauging stations (intermediate catchment). When considering surface and groundwater components, the delineation method of elementary catchments is questionable (topographic versus hydrogeological boundaries). Despite the importance of groundwater processes in karst areas, topographic catchment delineation remains a more robust reference for several methodological reasons. First, IGF can be defined as groundwater flow crossing topographic divides, as this concept emerged with the evidence of certain groundwater systems extending beyond the limits of valleys (Eakin, 1966). A perfectly delineated groundwater basin would then show IGF equal to zero. For this reason, studies related to IGF often use the topographic catchment spatial reference (Genereux et al., 2005; Schaller and Fan, 2009; Bouaziz et al., 2018; Nguyen et al., 2020; see also a synthesis in Fan, 2019). Second, although groundwater contributes to flood flow in karst catchments, the surface runoff component should not be completely discarded. Exclusive consideration of hydrogeological catchments could thus lead to wrong surface contribution assessment depending on their surface drainage network. Third, as some groundwater flows are aligned with the main surface drainage axis, hydrogeological catchments would encompass the whole river, making it impossible to study the spatial variability of parameters along the river, at the elementary catchment scale. Finally, topographic delineation is reliable and easily reproducible, while groundwater delineation is characterized by a strong uncertainty and variability in karst areas.
This article aims at providing a new methodology to characterize the spatial variability of karst influence on hydrological processes affecting runoff generation, including IGF, at the storm-event timescale. IGFs are estimated at the scale of the river reach, by comparing inlet and outlet flows as well as the effective rainfall from the topographic elementary catchment. The present study complements the previous work by Le Mesnil et al. (2020), which described the role of karst areas using annual water-budget indicators at the elementary catchment scale. Here, descriptors are calculated for major storm events at 108 stations in three areas in France (Cévennes Mountains, Jura Mountains and Normandy) with different karst settings. The descriptors are of three types: water balance, hydrograph shape and lateral exchange. Water-balance descriptors are obtained from discharge and precipitation depths, analysing the respective importance of the different flows during storm events. They help with understanding how catchments transform precipitation into surface and underground flow. Such descriptors are of great interest to assess the spatial variability of catchment hydrological response (Sivapalan et al., 2011). Hydrograph-shape descriptors are derived from catchment hydrographs recorded at inlet and outlet stations during storm events. They describe hydrological processes (Raghunath, 2006) and, when analysed on successive stations, help with characterizing flood-wave routing. Lateral-exchange descriptors are based on lateral hydrographs, simulated with the diffusive wave equation (DWE; Moussa, 1996) applied between two gauging stations (for intermediate catchments only). They provide information on lateral inflow and outflow at the elementary catchment scale. Lateral flow is mainly the result of IGF, effective rainfall, variations in aquifer storage and overbank phenomena. A particular analysis is performed on IGF, which are expressed in depth as well as in theoretical catchment area variation, and seasonal influence is discussed.
The three types of descriptors are compared and analysed according to the catchment geology type (classified as “karst”, “non-karst” or “mixed”), in order to explore its impact on runoff generation processes. The paper thus provides a framework for assessing the impact of a given physiographic parameter on the hydrological response of catchments to storm events.
We calculated 15 descriptors (five for each of the three types) of catchment
response to storm events and assessed their variability as a function of
karst occurrence. To this end, we grouped elementary catchments into three
different geology types, based on relative areas of their main geological
formations. Catchments underlain by only karstified rock are in the karst
group (K), whereas catchments containing only non-karstified rock are in the
non-karst group (NK). Any catchment with a combination of both karstified
(
Descriptors are complementary but not necessarily independent from each
other. They are of three types and were chosen to provide relevant
information on different processes:
Water-balance descriptors show the respective importance of the different
flows occurring during storm events and allow for understanding how catchments
transform rainfall into surface and underground flow. Such descriptors are
volumes (expressed as depth [mm]) or volume ratios. They can be calculated
at headwater-catchment or intermediate-catchment outlets, with the latter
involving subtracting inlet flow from outlet flow. This was applied to the
108 elementary catchments. Hydrograph-shape descriptors describe the dynamics of storm events and
flood-wave routing. They combine peak-flow variation, characteristic times
and flood-wave celerity. Characteristic times can be obtained from any
measured hydrograph, whereas peak-flow variation and celerity are evaluated
between inlet and outlet hydrographs (for intermediate catchments only),
considering catchments with only one inlet station and some intermediate
catchments having several inlets when covering the confluence of streams.
This was applied to all 108 elementary catchments for characteristic times
and to the 36 intermediate catchments with only one inlet regarding peak-flow
variation and celerity. Lateral-exchange descriptors provide information on the dynamics of lateral
inflow and outflow affecting an elementary catchment reach, as well as on
the respective contributions of channel diffusivity and lateral exchanges to
peak-flow variations. This analysis is based on lateral hydrographs,
simulated with the DWE, that are applied to intermediate catchments with one inlet.
Lateral exchanges may be a combination of effective rainfall (P
The 15 descriptors were calculated on elementary catchments for 20 selected strongest storm events. For the sake of representativeness, this selection was based on both rainfall and streamflow records. From the available data time series spanning several decades (see Sect. 3.1 for more details), the 10 strongest precipitation and 10 strongest streamflow events were extracted. Care was taken not to select the same events via the two extraction methods.
Streamflow is measured at several gauging stations along a given river,
defining elementary catchments. For the most upstream station of a river,
the elementary catchment corresponds to the ordinary topographic catchment.
Otherwise, the elementary catchment is an intermediate one, covering the
portion of the basin drained between two gauging stations (Fig. 1). In the
case of intermediate catchments, streamflow is calculated following Eq. (1)
as the difference between outlet flow (
Main hydrological flow types at the elementary catchment and
storm-event scales, with corresponding measured and simulated hydrographs.
Flow definitions are given in Eqs. (1) to (5). The corresponding volumes,
integrated for the storm event, are noted
For each storm event, volumes of the different flows in an elementary
catchment are calculated (Fig. 1). Total discharge volume, noted V
For each storm event, five more descriptors were calculated, characterizing
hydrograph morphology and storm-event dynamics. Characteristic times are of great interest in storm hydrology and constitute a widely used framework,
allowing convenient catchment and event comparisons (Bell and Om Kar, 1969).
Here, we use three of them. The time constant of the rising limb
In the case of intermediate catchments, the peak-flow variation (
For catchments with one inlet station, a lateral-flow hydrograph is
simulated, using the solution of the inverse problem of the DWE assuming
that the lateral flow is uniformly distributed along the channel (Moussa,
1996; see Appendix B). The DWE has two free parameters: the
celerity
Storm hydrograph with characteristic times and discharge values.
Theoretical examples of simulated lateral hydrographs
From the simulated lateral hydrograph, five descriptors were calculated.
First, the peak-flow-variation descriptor
As simulated lateral hydrographs are based on the difference between
discharge volumes at the inlet and outlet of catchments, they also integrate
precipitation on the elementary catchment during storm events. In order to
focus on groundwater exchanges and suppress the influence of effective
rainfall (
The remaining lateral-exchange term combines IGF and potential aquifer
storage variation ( IGF
Once all descriptors have been calculated, a statistical analysis is performed for comparative purposes. For each descriptor, the obtained values are grouped in different samples, by (i) geology type (K, M, NK) and (ii) study area (C, J, N) for karst catchments only (K geology type). This allows for characterizing the impact of karst areas on the hydrological response and provides additional information on regional specifics of this impact.
The results are presented as boxplots to discuss how the distribution of
the descriptors varies for all samples. Then, statistical tests assess the
significance of the results. Twin-sample
Temporal data used in this paper are the following:
Hourly streamflow data from the French public streamflow database “Banque
Hydro” ( Hourly rainfall data are from Comephore (Tabary, 2007)
covering 1997 to 2005 and Antilope (Champeaux et al., 2011) from 2006 to
2018. Both data sets are measurement reanalyses edited by the French public
meteorological service Météo-France ( Daily potential evapotranspiration depths are from “Safran” (Système d'Analyse Fournissant des Renseignements Atmosphériques à la Neige; Vidal et
al., 2010), edited by the French meteorological service (Météo-France). They are used for estimating effective rainfall (Appendix C).
Hourly rainfall data are available from 1997 onward, and hourly streamflow
data periods vary depending on the catchments. Table 1 shows periods of
availability of both data sets for 11 hydrographic catchments in three areas
of France, covering a total area of almost 25 000 km
Studied catchments and associated available data.
Spatial data used in this paper are the following:
Boundaries of topographic catchments, from the French National Watershed
Database (Base Nationale des Bassins Versants, BNBV). It was edited by the French Central Service for
Hydrometeorology and Support on Flood Forecasting (Service Central d'Hydrométéorologie et d'Appui à la Prévision des Inondations, SCHAPI) and the French
Research Institute for Agriculture, Food, and the Environment
(Institut National de Recherche en Agriculture, Alimentation et Environnement, INRAE). BDLISA database ( Map of available soil-water capacity from INRAE (Le Bas, 2018), used for
estimating effective rainfall (Appendix C).
The previously described methodology was applied to three areas in France,
including 11 hydrographic basins and representing a total area of 25 000 km
In the Cévennes Mountains (Fig. 4b), six hydrographic basins were
studied, including 51 gauging stations. They are mostly so-called binary
karst basins, with head catchments on hard rock receiving around
1500 mm yr
The Jura Mountains region corresponds to the Doubs river basin, a few kilometres upstream from its confluence with the Saône river, which includes 39 gauging stations. Outcrops mostly consist of extensively karstified Jurassic limestone and marl, except in the extreme northern and western parts of the region. Precipitation follows a strong elevation gradient, with annual values ranging from 1700 mm on upstream catchments at heights of 1400 m (a.s.l) to 1200 mm at the outlet at an elevation of around 200 m (a.s.l).
In Normandy, four hydrographic basins covered 18 gauging stations. The two eastern basins are tributaries of the Seine, with the other two being coastal basins. The climate is maritime, and annual rainfall ranges from 700 to 1000 mm. Rivers in the eastern part of the area drain chalky limestone with karst covered by clay. The midwestern zone is underlain by Jurassic limestone, corresponding to the western border of the Paris Basin.
The surface area of elementary catchments depends upon the location of gauging stations. They have similar ranges for each geology type and study areas (Fig. 5a), and the potential bias induced by scale effect is limited. Figure 5b shows the strong variability of reach mean slope with geology type. This can be explained by the morphology of karst plateaus that are prone to intense erosion, forming canyons with low slopes controlled by the base level. Moreover, higher-elevation ground is mostly underlain by hard-rock (i.e. non-karst) terrains. Contrasting slopes should thus not be seen as a bias but as the result of an intrinsic characteristic of limestone areas, coinciding with karst occurrence. Reach mean slope on karst catchments has similar values for the three study areas, with a maximum variation in median slope of 5 ‰ from Normandy to the Cévennes.
Elementary catchment area
Figure 5c and d present the distribution of precipitation and discharge depth for the 20 strongest storm events (see Sect. 2.1) in the 108 elementary catchments, grouped by geology type (K: karst, M: mixed, NK: non-karst) and by study area (C: Cévennes, J: Jura, N: Normandy) for K catchments. A major contrast in precipitation depth is highlighted, with a median value of 100 mm per event for the Cévennes catchments, which is higher than the maximum recorded value for the Normandy catchments (80 mm). Jura Mountains catchments have an intermediate position, with a median rainfall-event depth of around 50 mm. A similar variation is observed for geology types, with median-event rainfall depth increasing from 45 mm on K catchments to 105 mm on NK catchments. This is partly due to the Cévennes upstream catchments of non-karst hard rock receiving intense rainfall. Nevertheless, this has no major influence on the descriptor values since they are normalized by rainfall. The same trend is seen for flow depths, with median values of 20, 10 and 2 mm and 50, 15 and 5 mm for C, J and N and NK, M and K catchments, respectively.
The distribution of water-balance descriptors is presented in Fig. 6 (top
row) (i) by geology type (K: karst, M: mixed, NK: non-karst) and (ii) by
location for karst catchments only (C: Cévennes, J: Jura, N: Normandy).
Storm-flow and baseflow depths (
Distribution of hydrological descriptors, grouped by geology type (K: karst, M: mixed, NK: non-karst) and by location for karst catchments (C: Cévennes, J: Jura, N: Normandy). First row: water-balance descriptors; second row: hydrograph-shape descriptors; third row: lateral-exchange descriptors. Red dotted lines show the median value of karst catchments for the whole sample. Values beyond black dashed lines are represented on the lines.
Runoff coefficients are also significantly influenced by geology type,
Water-balance descriptors globally show that karst areas promote more
infiltration (lower
Distributions of hydrograph-shape descriptors are shown in Fig. 6 (middle
row) (i) by geology type and (ii) by study area for karst catchments only.
Median values of peak-flow variation normalized by rainfall (
Karst catchments have a median rise duration
The flood-wave celerity (
Figure 7 shows the peak-flow evolution towards catchments with karst. K
catchments globally align on the first bisector, showing in most cases low
peak-flow amplification. NK catchments mostly lie above the equation line of
Variation of peak flow (
To summarize, hydrograph-shape descriptors globally show that during the strongest storm events, karst areas tend to decrease peak-flow amplification and increase characteristic flood times, without impacting flood-wave celerity. It should be noted that this general pattern is associated with a large variability of hydrological response in K catchments with locally contrasting behaviour.
The distribution of lateral-exchange descriptors is shown in Fig. 6 (bottom
row). The component of peak-flow variation due to channel diffusivity
(
This trend is confirmed by the volume of lateral inflows (
Analysis of the simulated lateral hydrographs shows that the weak peak-flow
amplification of karst reaches is mostly due to a low exchange component
Figure 6 also shows the distribution of IGF
IGF
Table 2 shows for each descriptor the results of
Synthesis of
Storm-hydrograph shape is strongly related to geology type, with peak-flow
amplification reduced and locally attenuated. The longer characteristic
times for karst catchments (Fig. 6) have a statistical significance
regarding characteristic times. Only flood-wave celerity is not affected by
geology type. Karst influence is area specific for
Lateral-exchange descriptors show that peak-flow amplification in karst
reaches is limited, mostly due to its exchange component
The analysis of descriptor distribution (Fig. 6) and its statistical
significance (Table 2) shows that several factors affect flood processes at
the elementary catchment scale. Water-balance descriptors show that quick-
and slow-flow depths,
In addition, hydrograph descriptors show a reduction in peak-flow amplification on K catchments in all study areas, associated with an increase of characteristic times. This trend is consistent with previous work showing peak-flow attenuation in karst areas (De Waele et al., 2010; Charlier et al., 2019). The influence on characteristic times is area specific, with Jura catchments having greater inertia than Cévennes ones. This area-dependent nature of characteristic flood times may be partly explained by different karst settings and occurrence, but it is also linked with rainfall patterns. Cévennes catchments have a Mediterranean climate, with typical intense and short storm events triggering flash floods (Marty et al., 2013). The inertial events of Jura catchments can be explained by their great length compared to other areas: Cévennes and Normandy rivers hardly reach 150 km before reaching the sea or the Rhône, but the downstream Jura station is 400 km from the source along the Doubs river.
Finally, lateral-exchange descriptors show contrasting exchanges between different geology types, with more lateral inflow in NK catchments and more lateral outflow in K catchments. This agrees with previous studies on storm events in karst catchments highlighting river losses in karst reaches (Delrieu et al., 2005; Perrin and Tournoud, 2009; Bailly-Comte et al., 2012; Charlier et al., 2019). This trend accompanies a study-area variation, where the main aspect is a higher variability of exchanges for Cévennes catchments and a lower one for Normandy. This is probably related to the need of harmonizing spatial scales between gain–loss processes and gauging networks. In fact, earlier work (Toth, 1963; Schaller and Fan, 2009; Bouaziz et al., 2018; Fan, 2019) shows that the size of the investigated catchment affects the IGF importance, with greater areas being more likely to be self-contained. In the case of our study areas, as the median gauged areas are similar for each of them (Table 1), it might be explained by the generally thick soil and epikarst in Normandy, which is very reduced in the mountainous and Causses areas of Cévennes. Indeed, soil and epikarst are more likely to promote subsurface flow with closer zones of gains and losses, whereas exposed karst drains, as in the Cévennes, enlarge the spatial scale of IGF processes by connecting river losses to trans-catchment karst aquifers.
Hydrological processes have been shown to be influenced by physiographic
parameters such as karst occurrence. Nevertheless, other drivers can control
catchments hydrological response to storm events. As an example, Fig. 8
shows IGF
IGF
Figure 6 shows that storm events in K catchments in the Cévennes are
mostly associated with losing IGF
To discuss the spatial variability of IGFs, the median storm-event IGF
Main geological features in the three studied areas
In the Jura Mountains along the main Doubs river (Fig. 9, second row),
almost all elementary catchments have negative IGF
Normandy catchments (Fig. 9, third row) show less important IGF
Relationships between multi-annual water-balance-derived
IGF
Figure 9g to i show the percentage of area variation of the elementary
catchments, from the topographic catchment area to the theoretical area of the
hydrogeologically active catchment (i.e. without excess or deficit in water
balance). The area of such catchments is calculated from the IGF
Figure 9j to l show the same elementary catchment area variations
expressed in square kilometres [km
In this section, we compare a major missing term of the water budget,
alternately estimated by two approaches. First, at the annual scale, the
multi-annual IGF (noted IGF
Le Mesnil et al. (2020) assessed multi-annual values of IGF
Figure 10a shows some points with opposed annual IGF
Figure 11 represents
We carried out a spatialized analysis of 15 easily calculable descriptors characterizing water balance, hydrograph shape and lateral exchanges for a set of 20 storm-event data at the elementary catchment scale for each of the 108 gauging stations, controlling karst and non-karst regions. The results show that karst promotes higher water infiltration, with this water being mostly retained during storm events. Karst increases characteristic flood times and limits peak-flow amplification, without affecting flood-wave celerity much. This is interpreted to be due to an interbasin groundwater flow (IGF) loss that can be high at the storm-event scale, representing around 50 % of the discharge at a catchment outlet and 20 % of rainfall. A spatial variability of those effects is linked to differences in karst regions: binary karst catchments mostly attenuate floods, whereas extended karst plateaus undergo alternated losses and gains. Secondary factors include climatic influence (regional variability of rainfall-event intensity) and the spatial-scale match between gain–loss processes and spacing of the gauging network. A seasonal effect has also to be considered regarding IGF magnitude and direction.
The existence of karst hydrological specificities has been known for decades but has not been quantified to a large extent, especially regarding its impacts on flood processes at the scale of the river reach. Although some research had been done on this topic, it leads to hindered modelling performance in many cases. We have quantified several important parameters for a large set of catchments, for the first time, in a spatialized study based on event-scale processes, contributing to build a common understanding at regional scale of karst behaviour during storm events and thus improving modelling and forecasting capabilities in such terrains. Although our approach is based on karst areas, it stays generic, and we hope future work will investigate other relationships between the hydrological response and physiographic characteristics of catchments, such as soil types, land use, climate, etc.
At each gauging station, discharge values were filtered in order to separate
the quick (storm flow,
We chose this method as it provides consistent results, like those obtained
with graphical approaches (results not shown). It can easily be automated
and has only one
An inverse modelling approach is adopted for simulating lateral flow between
two gauging stations. This approach simulates the lateral flow
The diffusive wave equation (DWE), accounting for lateral flow, is an
approximation of the St-Venant equation that can be written as
Moussa (1996) extended the solution of the DWE under Hayami's hypotheses
(semi-infinite channel,
Under Hayami's conditions and assuming that lateral flow is uniformly
distributed along the channel, Moussa (1996) proposed a solution of the
inverse problem; this enables evaluation of the temporal distribution of
lateral flow
Effective rainfall
In the Thornthwaite method, water in the soil reservoir is directly
available for evapotranspiration, and precipitation produces effective
rainfall ( If If
The Dingman method is similar to the previous one, with an exponential law governing water extraction for evapotranspiration from the soil reservoir.
If If
The GR method is derived from the GR hydrological models (Edijatno et al., 1999) and involves a quadratic law for the water-level variation in the soil reservoir. The algorithm, summarized below, was then adapted to the BRGM “Gardenia” model (Thiéry, 2014), which has been used here.
If If Integration of the
differential variations provides expressions of B
The final
List of symbols.
Hourly
streamflow data were gathered from the “Banque hydro” database using a
script available at
RM and JBC were involved in conceptualization, funding acquisition and supervision. MLM gathered the data and designed the methodology with the help of JBC, RM and YC. MLM prepared the article with the help of all co-authors.
The authors declare that they have no conflict of interest.
The authors thank the Editor Jim Freer and three anonymous reviewers for their constructive comments.
The work was funded by the French Governmental Administration for Risk Prevention (DGPR), the Service Central d'Hydrométéorologie et d'Appui à la Prévision des Inondations (SCHAPI) and the French Geological Survey (BRGM).
This paper was edited by Jim Freer and reviewed by three anonymous referees.