Introduction
Flash floods are intense and sudden hydrologic responses of small basins to
huge rainfall events. During the past 20 years in southern France they
caused more than 100 fatalities and several billions euros of damages.
Although, numerous studies have been devoted to flash flooding, hydrologic
mechanisms generating flash floods are yet misunderstood. Specifically in
case of mixed, karst/non-karst basins, the role of the karst part of the
basin is generally unknown. In this context, the aim of this study is thus
to improve understanding of karst hydrosystems behaviour during flash
flooding. As generally karst basins boundaries are not superposed to those
of the surface watershed and have different dynamics, it seems interesting
to estimate two different floods: the surface flood and the underground
flood, both being finally blended in rivers. To this end, and as it is
generally impossible to achieve these measurement on flash floods downstream
of the basin, because of the intensity of flood, we propose in this study a
methodology which allows to propagate measurements made on or near karst
springs (lower discharge) to build discharge at the outlet of the considered
basin. First we propose to build a conceptual model of the hydrosystem
behaviour (surface watershed and underground basin) and a mathematical
expression of the mixture of the two kinds of water. After that, chemical
analysis of water near principal karst springs (if there are several
springs) allows to estimate relative karst and non-karst contributions to
flood. Third, floods coming from different parts of the watershed are
propagated towards the outlet using hydrologic models, and the model of
mixture elaborated in the first part is used to estimate the total
contribution of karst and no-karst parts of the flood. To illustrate the
methodology, a case-study is chosen on the Lez hydrosystem, well known for its
flash floods and important karst role. The Lez karst river crosses the
conurbation of Montpellier (400 000 inhabitants), providing great damages,
and is subjected to strongly heterogeneous and anisotropic water circulation
providing highly nonlinear hydrodynamic behaviour.
The paper is thus organized as follows: first, in Sect. 2, the Lez
hydrosystem is presented in order to introduce the design of the postulated
model and the rainfall-runoff series. In Sect. 3 the behaviour of the
hydrosystem is designed thanks to an original utilization of neural networks
modelling. In Sect. 4 the propagation of both karst water and surface
water is done up to the gauge station of Lavalette. Section 5 allows proposing
hydrographs visualizing karst and non-karst contributions. It must be
underlined that this study suffers from a lot of approximations and
uncertainties due to the lack of measurements; nevertheless it represents a
mandatory work preliminary to field works and exhaustive data acquisitions.
Targeted field works and measurements, combined with proposed methodology
will lead to more accurate estimation of karst contribution to floods, and
by this way, to flash flood forecasting improvement.
Case study: the Lez aquifer
The Lez aquifer is a Mediterranean karst system located in southeastern France,
upstream Montpellier (Fig. 1). The Lez Spring is the main outlet of this aquifer and the
Lez river crosses Montpellier conurbation. Several intermittent springs also
exist, among which the Lirou Spring is the most important. In this work we will
take in consideration the Lez watershed at Lavalette station, at the entrance of
Montpellier, about 120 km2, its sub-watershed, the
Triadou watershed, outlet
of the Triadou Spring, about 85 km2; and the hydrogeologic basin of
around 380 (Bérard, 1983) (Fig. 1).
Map of the Lez hydrosystem with location of Le Triadou and
Lavalette gauging station, Lez Spring and Lirou Spring.
Geological settings
As most of karst system, the Lez system is composed of karst and non-karst
components. The karst component is principally located in the northwestern
part of the system. It is composed of Cretaceous and Jurassic carbonate
rocks. These formations widely outcrop and form the calcareous plateaus of
both Causse de l'Hortus and Causse de Viols-le-Fort (Fig. 1).
The Causse de l'Hortus is a perched aquifer. The southeastern
part of the system, principally impervious, is composed of Eocene formations
as carbonates and clays, and tertiary formations as sandstones, and
conglomerates. The major Corconne fault crosses the Lez hydrogeological basin leading
to contrasted hydrogeological behaviours.
Hydrogeological settings
The principal aquifer stands in well karstified upper Jurassic and lower
Cretaceous limestones. Its bottom limit is the marl and marly limestone
layer of the Callovo-Oxfordian formation. Under this layer, thick from 20 to
150 m, stands the middle Jurassic limestone and dolomite aquifer
(Bérard, 1983; Marjolet and Salado, 1978). Tectonic
accidents affecting the Callovo-Oxfordian layer make water circulation
between the both aquifer possible. This water exchanges are not accurately
quantified. However, Caetano Bicalho (2010) and Marjolet and Salado (1978) has assessed proportion of water
at the Lez Spring coming from the deepest aquifer using both major and trace
elements measurements.
The principal aquifer outcrops at the South-West of Lez system (Causse de Viols-le-Fort). Its
upper boundary is the lower Valanginian, which outcrops on eastern and
northern parts of the Lez system (Fig. 1). The karst aquifer is thus confined
under these impervious layers. Infiltration downward aquifer mainly occurred
in its southwestern part.
Underground circulations
The Corconne Fault has contrasted roles: in the South part of the basin it behaves
as a dam between eastern and western parts of the aquifer. In the North
part, it has a drain role thanks to several sinkholes along the fault and
its satellites. Communication between northwestern part towards the
Lez Spring were proved by coloration experiments (Marjolet and Salado, 1978).
Based on these findings, a zone division of the Lez basin in four parts has
been proposed by Kong-A-Siou et al. (2013) (Fig. 1). The geological composition of each zone is assumed to be
“homogeneous”, which means that geological similarity is greater inside
each zone than outside. The eastwestern division is based on Corconne Fault. On the
western side of the basin, south-north division has been drawn based on
Causse de Viols-le-Fort boundary. On eastern side southnorthen division has been drawn
thanks to infiltration properties based on high density of fractures.
Climate and meteorology
The Lez climate is Mediterranean, characterized by two rainy seasons during
spring and autumn. Mediterranean rainy events are generally intense and
localized providing heterogeneous rainfalls. Heterogeneous rainfall
increases thus the sensitivity of the hydrologic response to the location of
the rainfalls. It is thus necessary to be able to consider the location of
rainfalls and the role of karst and non-karst parts of the basin on
infiltration properties.
Database
Database contains one-hour time step data: (i) rainfalls at 5 rain gauges
inside or near the basin in order to take into account the heterogeneity of
rainfalls, and discharges at Lavallette for 15 intense floods before 2010, and 3
intense floods after 2010. Moreover chemical data are available only for the
two last events of 2014 (Table 1). Table 1 focuses on the last events which
were investigated in the present work.
Dates, peak discharges at Le Triadou and Lavalette gauging stations and mean
cumulative rainfalls.
Peaks discharges at
Peaks discharges at
Mean cumulative
Dates
Lavalette (m3 s-1)
Le Triadou (m3 s-1)
rainfalls (mm)
29–30 September 2014
388
370
149
6–7 October 2014
538
445
143
Lez Flash floods at Lavalette
Operational flash flood forecasting and early-warning constitute an
important field of research (Borga
et al., 2011; Price et al., 2011). The task is difficult due to: (i) the lack
of knowledge about hydrological processes involved in flash flooding (ii) uncertainty
on the rain forecasts, (iii) great noise and uncertainty on
measurements especially for the flood peak. In karst system these
difficulties are increased due to the necessity to take into account
underground process as karst can reduce or increase flood, depending on its
saturation prior the event (Jourde et al., 2007; De Waele et al., 2010;
Bailly-Comte et al., 2012; Coustau et al., 2012)
at the Lavalette station.
Regarding the Lez floods at Lavalette and considering the high velocity of flash flood
genesis, it can be assumed that runoff is the major contributor.
Nevertheless, the karst contribution is significant and can worsen
significantly the flood. We thus propose a methodology able to estimate
separately karst flood and surface flood in order to design two different
predictors, for example with neural networks models, as shown by
Kong-A-Siou et al. (2011a). The methodology proposes several steps each one
achieved and described in this paper in a specific section: (i) establishment
of the conceptual model of the basin behaviour (surface and karst), (ii) chemical
analysis in order to quantify karst and non karst water, at key
points of the basin, were floods don't prevent from making measurements in
safe conditions, (iii) propagation of karst and non karst flood up to the
outlet of the watershed, and finally (iv) reconstitution of the both karst and
non karst floods.
Elaboration of the conceptual model of the Lez
hydrosystem
Conceptual modelling of the Lez hydrosystem behaviour using neural networks
(KnoX method) (Kong-A-Siou et al., 2013) proposed a method
able to estimate the contribution of each one of the four zones of the Lez
basin to the discharge at the Lez Spring, with daily time step. It appeared
that the two northern zones were the most contributory zones to the
discharge, sometimes with a 3-day time transfer. Darras et al. (2014)
revisited this work at different time and space scales: time step was the
hour and only flash floods on the whole basin at Lavalette were considered. The
discharge at Lavalette have thus been simulated using artificial neural network fed
by mean rainfall, for each of the four zones on several previous time steps,
and the previous observed discharge (feed-forward model). The time window
widths of previous rainfalls have been sized using method used by
Kong-A-Siou et al. (2011b). Table 2 shows
the temporal window width of each rainfall zone. Then, as proposed by
Kong-A-Siou et al. (2013), model parameters
have been analysed to establish contribution of each zone, at each time step
of their temporal window width.
Temporal window width and contribution of each zone to discharge at
Lavalette.
northwestern
northeastern
southwestern
southeastern
Discharge at
rainfall
rainfall
rainfall
rainfall
Lavalette
Temporal
window width
k to k-6
k to k-6
k to k-6
k to k-3
Only k-1
Contribution
to discharge
9 %
26 %
47 %
18 %
–
Median and total spread (%) of respectively northwestern,
northeastern, southwestern and southeastern zone contributions versus time.
One can note on Fig. 2 that northwestern zone (Causse de l'Hortus) has the least
contribution and, considering uncertainties on the data, can consequently be
excluded from the model. The main contributor is the southwestern zone
(almost 50 % on the whole rainfall contribution). The northeastern and
southwestern zones both show two peaks of contribution. It seems coherent to
attribute the first peak to the surface runoff and the second peak to the
karst one, which is slower. One can note that northeastern and southwestern
zones are both upstream Le Triadou. We thus assume that water at Le Triadou is composed of karst
and surface water. Moreover downstream Le Triadou the watershed is mainly impervious
(southeastern zone) with negligible karst/surface interaction, except the
contribution of the Lez spring. The conceptual behaviour of the hydrosystem for
flash flooding is thus the following: water coming from the northwestern
zone can be neglected, floods coming from both southwestern and northeastern
zones are composed of karst water and non-karst water, in unknown
proportions, presumably depending on location of rainfalls. The major
contribution comes logically from the southeastern impervious zone.
Blending model at Lavalette
Based on the previously presented conceptual understanding of the
Lez hydrosystem, a simple model of water blending is proposed. The Le Triadou blend is
expressed in Eq. (1):
QL=QTprop+QSprop+QR,
were QL is the discharge at Lavalette,
QTprop is the propagated discharge from Le Triadou to Lavalette,
Qsprop is the propagated discharge from Lez Spring to Lavalette and QR is the additional
runoff between Le Triadou and Lavalette. QL is known, QR is unknown,
QTprop and QSprop can be deduced from known
discharges at Le Triadou and Lez Spring by a propagation law.
To this end we estimated the distances (10 km) and slopes (3%) between the
both stations of Le Triadou and Lez Spring to the Lavalette station. It appeared that as both are
equivalent, the same propagation function is then applied to both
hydrographs. This propagation was performed using a convolution between the
hydrograph and a Gaussian function applied each time step on the 10 previous
time steps.
After that is could thus be possible to deduce the unknown surface runoff
between Le Triadou and Lavalette from Eq. (1). Unhopefully some negative values appeared which
are difficult to explain, as the watershed is essentially impervious in this
part of the hydrosystem. Nevertheless, because of the high uncertainty on
discharge estimation we proposed to smooth this additional runoff as shown
in Fig. 3. Figure 3 shows the smoothed hydrographs of additional runoff, of
the event on 29 September and 6 October 2014. One can note that the
additional runoff of the October event didn't necessitate smoothing. Maybe
this is due to the fact that soils were very wet thanks to the September
event.
Additional runoff between Le Triadou and
Lavalette.
In order to estimate karst contribution and runoff contribution to the
flood, and because this measurement was impossible to proceed at
Lavalette
station, Raynaud et al. (2015) proposed two functions to evaluate the karst
contribution of the discharge at Le Triadou during rise and decrease of the
hydrograph. Equations (2) and (3) provide the relation applied for the rise and
the recession of the hydrograph.
QTK=152.08QT-0.302,∀QT>15m3s-1,QTK=-17.59Ln(QT)+137.39,∀QT>15m3s-1,
where QTK is the karst component of the discharge at
Le Triadou and QT is the total discharge at Le Triadou.
One can thus see on Fig. 4 the repartition of karst and surface
contributions to the flood of the events of 29 September and 6 October 2014.
One can distinguish a kind of saturation of the karst contribution around
100 m3 s-1.
Karst and surface contributions for propagated floods of Le Triadou
according Eqs. (2) and (3).
Regarding the Lez Spring, one can consider that the discharge is fully karst
water as spring is situated in a principally impervious zone.
The karst and surface contributions at Lavalette are then calculated respectively
using Eqs. (4) and Eq. (5). Equation (4) expresses that the karst water at Lavalette comes from
the whole water of the Lez Spring and the karst part of the Le Triadou discharge, both
propagated. Regarding Eq. (5), it expresses that the non-karst water at
Lavalette comes from the surface runoff and the part of non-karst water propagated
from Le Triadou.
QLK=QTKprop+QSprop,∀QT>15m3s-1,QLS=QTSprop+QR,∀QT>15m3s-1,
where QLK and QLS are respectively the karst and surface
contributions at Lavalette and QTKprop and QTSprop
are respectively the karst and surface contributions of the discharge
propagated from Le Triadou to Lavalette.
Karst and surface contribution at Lavalette
The karst and surface contributions to the discharge at Lavalette were proposed for
both events of 29 September and 6 October 2014. The karst contribution and
runoff contributions were calculated respectively following Eqs. (4) and (5).
Fig. 5 shows hydrographs of the two events analysed splited between their
various origins. From bottom to top, contributions from: (i) Lez Spring (karst),
(ii) Le Triadou karst component, (iii) runoff between Le Triadou and
Lavalette and (iv) Le Triadou surface component.
Regarding the event of 29–30 September 2014, the sum of the four
contributions is sometimes higher than the discharge at Lavalette. This misfit is due
to the correction of the smoothed contribution of runoff between Le Triadou and
Lavalette that have been done before.
Karst and surface contributions to the discharge at Lavalette.
Discussion
Concerning both events, although the second event reaches a peak discharge
at 150 m3 s-1 upper than the first one, the karst contribution
reaches the same value, around 100 m3 s-1 in both cases. It seems
thus that saturation occurs for karst flood, which seems to be right. The
contribution from the Le Triadou surface component is equivalent in both events. The
main difference between both events is thus the contribution of runoff
between Le Triadou and Lavalette. The application of this method to other intense events could
confirm this behaviour of the karst during flash floods.
As the proposed methodology suffers from several approximations and
hypothesis due to the lack of measurements and knowledge about the
hydrosystem, we thought necessary to present the limitations of this work.
First, the main limitation of this study is the choice to estimate the karst
contribution at the discharge at Le Triadou as a part of the “total” discharge
(karst and surface). This induces thus a systematic synchronisation between
“total” discharge and karst contribution. Consequently, the
synchronization of karst and surface contributions at Lavalette is not well described
by this method while it is known that the karst contribution has a different
dynamic than surface contribution, which can be slower or faster depending
on the saturation of the hydrosystem prior the event and the rainfall
distribution. This drawback could be corrected by measuring directly karst
water at the Lirou and other springs. Secondly, the estimation of runoff by
difference between total discharge and karst discharge seems also to be
inaccurate, probably due to the previous approximation. Third, the
propagation of discharges towards the outlet of Lavalette adds uncertainties.
Nevertheless, this method seems to provide an acceptable estimation of karst
contribution at each time step. Future field works and data measurements
will allow to validate it and to establish accurate karst and non-karst
contributions at Lavalette outlet in order to be able to implement an operational
flood prediction model based on neural networks.