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• • 1.5k Downloads • Abstract This paper presents an application of a cellular automaton-based run-off model (RUICELLS) to a series of small dry valleys in the Seine-Maritime department, northern France, to better assess their susceptibility to flash flood. These muddy floods shortly follow high rainfall (50–100 mm in less than 6 h) and occur in very small areas (. Flash floods in northern France (Masson; Devaud; Merle et al.; Arnaud-Fassetta et al. ) induce serious risk conditions on populated outlets, especially in the Seine-Maritime department (Delahaye et al.; Douvinet, 2014; Douvinet et al. These hazards are generated shortly after rains ranging from 50 to 100 mm in less than 6 h and occur in small dry valleys (. AThis information has been extracted from the files related to the French recognition of the “state of natural disaster” (CATNAT database) bStandard Threshold Deviation (STTD) for the slope systems (automatically calculated by ESRI ®Arc Gis 9.8) cThis Gravelius index represents the fraction between the perimeter of one basin and the perimeter of a circle having the same surface dThe number of asterics indicates the number of victimes recorded after the flash flood events (from Douvinet, ) 3 Materials and methods. The spatial domain is discretized as a Triangular Irregular Network (TIN), based on the Digital Elevation Map (DEM) according to square grid (Fig.

Two techniques are available to create a lattice: a function obtained by the calculation of differences between neighbouring cells (Laurent et al. ), or the meshing in finite elements which gives a continuous interpolation between points of the DEM. We have chosen the latter, which gives for each point its elevation and its vector normal to the surface (Fig. B), allowing the calculation of every measure of size related with the local shape of the terrain (slope angle, exposition, run-off vector, surfaces, volumes, and flows). Consequently, we have divided each square cell into two triangles, choosing one of the diagonals to define the triangle (Fig.

This choice is relevant because the diagonals do not cross at the same height. To improve the outflow, the diagonal with the minimum height at the crossing point and with no risk of obstructing a stream channel have been chosen. The steepest downward link determines the flow direction, analogues to D1 and D8 algorithms for other square lattices (O’Callaghan and Mark; Tarboton ). The TIN structure, due to its linear applications, offers the simplest finite elements model and a substantial gain if we operate on a PC with a very large amount of cells. Importantly, this spatial structure overcomes one of the main disadvantages of many CA models, namely that flow directions are constrained to 45° intervals at any cell. Fig. 2 Rules and main characteristics of RUICELLS (modified from Delahaye et al. ) In order to access the geometric information, the topological graph applied on the TIN structure is composed of three main features: node, arc, or triangle (Fig.

D), inducing the following relational tables. The arcs play a major role: each arc is connected to two nodes and two triangles, and a morphological attribute may be given to it by the relative heights of the former and the relative slope angles of the latter. Comparing the heights of two nodes, we can see if the connecting arc is downhill, uphill, or flat. As for the triangles, two of them (side by side) may be also, individually, downhill, uphill, or flat. An arc whose final node is lower than the initial one is downhill but if its two neighboring triangles are downhill towards it, it equals a downhill thalweg (Fig. The typology gives 3 3 = 27 theoretical possibilities. After eliminating some rare and specific situations, we have kept several attributes for the arcs.

The “external limit” has been introduced to handle with the limits of the studied area. The “flat” is attributed to the limit between two flat triangles. It must be stressed that these attributes are purely local: if an arc equals a downhill thalweg, there is no continuity for the downstream arcs (Douvinet et al., ). Yet its knowledge is important to determine the run-off process, which is linear along this arc, while if the arc attribute is left slope, the run-off is a sheet flow and its direction transversal. A large thalweg is formed by a certain amount of triangles, in which there is a sheet flow transversal to the arcs (Fig. The local attributes of arcs are no longer sufficient to shape the network.

Then, the links between the elements (poles, arcs, and triangles) of the topological graph must be taken into account. The resulting graph is more complex than one oriented dual topological graph because it connects together poles, arcs, and triangles. A water drop laid on a triangle can flow towards the neighbouring triangle (if the connected arc is a left slope, Fig. D) or in the arc itself if it is a downhill thalweg. This drop can also be stopped in a pole if it arrives in a closed depression (Fig. Additional complications may arise in certain conditions.

For example, channel streams in dry valleys are mostly ephemeral, using the pre-existing drainage networks (Fig. Fb): the thalwegs may not have a continuous declivity but can consist of a sequence of little slopes creating a series of discontinuities in the flow. Another problem derives from the DTM: its 25 m horizontal resolution smoothes out several features (e.g. Small gulleys) that occur in many of the basins and the vertical precision of one meter for the elevation data produces, in approximately flat areas, a large number of horizontal triangles in which the calculation of the vector of greater slope angle is not easy to calculate.

When the water flows on grass or on cultivated area, the common mathematic models (such as Saint–Venant 1D or 2D) are also not useful because laminar flow does not really exist. Thus, the effects of gravity are computed with energy-based calculations, and velocity of flows does not directly depend on its mass. Two types of GIS data were used to produce the LUM. The Corine Land Cover (CLC) permits to delineate real-world objects (lakes, cultivated fields, meadows, forests, industrial areas, and natural areas). The CLC (with 46 hierarchical levels of classification) has been produced by the Agency of Development at the European scale and is derived from satellite images. By itself, these data are insufficient as it does not accurately delineate very small areas (. Name of land-use type in the CLC–GPBF database AREHN (2005) Cerdan et al.

( ) Delahaye et al. Fig. 4 One simulation fallout obtained on the basin of Mesnil-Val (9.88 km 2), permitting to simulate and to map the potential hydrological response for a storm event of 50 mm in 1 h 3.5 Limits for the modelling performance assessment Normally, after a model is developed, it is tested before being put to use as a predictive or explanatory tool. This is a form of quality assurance, and it involves the simulation of a situation for which observed data are available (Van de Wiel et al. For this instance, the model parameters have been only calibrated for the 1997, June 16th event (Delahaye et al. ), through the simulation of the diffusion of the run-off process in two basins. In these two cases, the major simulated areas sensitive to the run-off processes equal to the real production areas and the divergence with the observations is only important in the upstream southern part of a basin. The simulation, indeed, locates a major flow, which has not been observed in this area; this is due to the fact that the simulation has not taken into account the influence of the highway crossing the upstream part of the basin.

This highway stopped the flow and produced a flood leveling, generating retentions of water along many embankments. The observation shows the limits of the model, but stresses also the efficiency of such a tool to evaluate the incidence of an implement on the hydrological behaviour of a basin. Doctrine Of The Knowledge Of God Pdf more. On the other hand, these results show the accuracy of this approach and how, starting from a simple data set, it is possible to set-up a cartographic presentation of the run-off dynamics. Simulations also give a good agreement in comparison with estimations proposed by more complex hydrological models (GR4J, STREAM, and LISEM) and those derived from water deposits (Merle et al. Our simulations cannot be verified quantitatively due to a lack of independent data. Validation occurs only on a scenario basis, and it is always possible to attribute errors of the simulations to inaccuracy of the initial or external forcing conditions, rather than to inaccuracy of the model’s hypotheses (Van de Wiel et al.

Even though Begueria ( ) use, for example, confusion matrices to compare modelling and recorded events in true or false positives or negatives information (Kappes et al. ), the low availability of hydrological data of events renders such approach impractical. Lacking an independent quantitative validation, these first modelling results are only evaluated in a qualitative way, which necessitates a careful interpretation (see Sect. 5.1).

4 Results and susceptibility assessment. Simulations are analyzed for three main variables that characterize basin susceptibility of flash flooding: peak flow discharge (Q), peak unit discharge (Q s), calculated by dividing Q by the basin size and lag time (T), i.e. The duration between the beginning of rainfall and the onset of peak discharge (and not the time between the onset of peak rainfall and the onset of peak discharge, due to the simulation configuration), for each of the 148 studied basins and each of the 16 rainfall intensities. Even though results are available on each basin, they are presented here in aggregated form, i.e. At large scale, to facilitate the susceptibility analysis. 4.1 Peak flow discharges. Fig. 5 Evolution of the peak flow discharges simulated by RUICELLS over the 148 studied basins, according to different intensities varying from 30 mm ( a), 40 mm ( b) and 50 mm ( c) in 1 h to 50 mm in 2 h ( d) Similarly, the susceptibility decreases for rainfalls more spread over time.

For example, for storm with 50 mm in 2 h, only 33 basins have Q >4 m 3/s (Fig. D) and 6 basins have values up to 7 m 3/s. In terms of land use, susceptibility to flash flooding is higher in basins where percentages of sugar beet, corn, maize, and flax are important. These basins are subject to flash flooding at 30 mm in 1 h, and even react to lower intensity storm events of longer duration (e.g. 40 mm in 2 h or 50 mm in 3 h). Conversely, the peaks of discharges of other basins, in which cultivated areas are more dispersed, suddenly increase (>7 m 3/s) for more intense storm event of 50 mm in 1 h. Grasslands are sufficient to reduce the run-off production coming from upstream parts for gentle rainfall intensities (10 km 2).

Download Lungi Dance Video Mp4. Flash floods from similar events, but occurring over more isolated basins (such as in the eastern part of the department), are easier to manage and to prevent. In a qualitative way, the comparison with historic flash floods occurrences (over the period 1983–2005) shows a good correlation with the highest Q values: the three basins identified as the most susceptible in our simulations for storm events of 40 mm in 1 h, also have historically observed flood events). However, the validations are not systematic. For example, flood events have been observed in 12 of the 21 basins identified, as the most sensitive for 50 mm in 1 h, while the results for 30 mm in 1 h, as well as for 50 mm in 2 h, are a less successful indicator.

Therefore, the Q values need to be divided by the basin size, since weak peak flow discharges do not have the same hydrological significance in small and large basins. 4.2 Peak unit discharges.

Previous studies carried out on Mediterranean floods (Gaume et al. ) highlighted that surface flows become strongly erosive when peak unit discharges ( Q s) exceed at least 0.7 m 3/s/km 2. An earlier study (Douvinet and Delahaye ), carried out a few days after several flash floods on five areas in northern France, permitted to estimate a threshold of 1 m 3/s/km 2 for minor erosion forms and of 1.5 m 3/s/km 2 for major incisions on soils (gullies) or roads (destruction of network infrastructure). Thus, the analysis of simulated Q s takes into account these thresholds. Occurrence of peak unit discharges strongly increases with rainfall intensity. For storm events with 30 mm in 1 h, only 7 basins have Q s >1 m 3/s/km 2; at 40 mm in 1 h, 26 basins present Q s exceeding this threshold (Fig.

A), whereas 64 basins do so at 50 mm in 1 h (Fig. Another important question facing flood forecasters concerns the time they can have to alert the local authorities and the population for evacuation or for protection in areas at risk. The French Ministry of Environment and the General Delegation on Majors Risks (DGPR ) focus on this point after dramatic flash floods occurred in the western coastal part of France (49 deaths in February 2010) as well as in the southern part (25 fatalities in June 2010). To address this question, lag time, i.e. The time separating the beginning of rains and the occurrence of peak-flow discharge, was computed. Hydrologically, this differs from the time of concentration but it equals the duration of increasing flow (i.e. The rising limb of an hydrograph).

The modelling results underline an increasing number of basins with short lag times as rainfall intensity increases. Eleven basins responding 40 mm in 1 h (Fig.

A) present short lag times (i.e. In less than 2 h) and only one of these (the Hanouard basin) has high Q, high Q s, and short T. In contrast, 42 basins showing susceptibility for events with 50 mm of rainfall in 1 h, and cumulating discharges up to 4 m 3/s (Fig. B), have lag times less than 3 h, 22 of which have lag times.

Fig. 7 Evolution of the lag times simulated by RUICELLS over the most sensitive basins (with peak discharges >4 m 3/s) for storm events of 40 mm ( a) and 50 mm ( b) in 1 h Several basins with peak flows ranging from 4 to 7 m 3/s present the smallest lag times. The forecasters need to pay attention a greater attention on these as they can simultaneously produce several flash floods. Fortunately, all these identified basins very unlikely generate high flows at the same moment, since a storm event with 50 mm of rainfall in 1 h is very unlikely to occur over the entire Seine-Maritime. However, such storms can threaten this area in the future (following the predictive scenario 2.a; GIEC 2009) and can affect multiple basins locally if they are within close proximity. On the other basins, lag time increases with basin size, and forecasters should have more time (>3 h) for alert. In a qualitative way, the comparison with historic flash floods occurrences (over the period 1983–2005) shows bad correlations (whatever the rainfall intensities) because only a few number of basins with historical floods present small lag times. Hence, this parameter is of paramount importance for forecasters, but seems to be the less useful to explain the flash flooding susceptibility (Fig.

5 Discussion. The model’s success in identifying flash flooding over a majority of basins where historical flooding indeed was observed indicates that it can be used to anticipate the flash floods in the Seine-Maritime department. However, since the simulations cannot be completely validated, care must be taken in interpreting the results. 5.1 Validation efforts and limits The modelling validation is a fundamental step because this determines both the quality of the approach and the credibility of simulation results.

In this study, the validation remains difficult due to the relatively low number of basins (38) affected by previous flash flood events (over the period 1983–2005). If we focus on the simulations obtained on these 38 basins, 17 (46%) have peak unit discharges up to 0.7 m 3 s −1 km −2 and 24 (63%) have a peak flow discharge up to 4 m 3 s −1, for a rain of 50 mm in 1 h. Even if these results indicate that the model is successful in identifying flash flooding in most of these basins, this also indicates that a number of basins where historical flooding was observed did not experience flooding in simulations (14 out of 38, or 37%). The identification of such differences can be explained by three arguments: (1) the real rains were more intense than our maximum intensity rainfall scenario (50 mm in 1 h)—by running simulations with higher intensities (i.e.

From 60 to 100 mm in 1 h), we observe that all the 38 basins present high sensitivities for a rain up to 78 mm in 1 h; (2) a higher sensitivity to run-off and flash floods (even though the peak unit discharge does not exceed 0.7 m 3 s −1 km −2) because of a strong human settlement in the outlets—this hypothesis is attested on 9 basins out of the 14 studied; (3) the simulations underestimate the impact of the “built” environment in LUM. Alternatively, how can we explain the identification of other basins for which the simulations indicate flash flood susceptibility, but where no historical observations are present?

If we trust in local observations on “non-affected” basins, provided by stakeholders or risk managers, 35 basins (32%) have known local problems (flooded roads, small erosions) after intense rains. If we consider this additional information, the flash flood susceptibility is confirmed on 59 basins (57% of the 148 studied basins). Finally, if the critical rain is recorded in the future, we should survey the basin reactivity and then see if the simulation results can be validated a posteriori. 5.2 Advantages and limitations for anticipation Anticipation of flash floods in small basins becomes urgent, since they induce rare, violent and sudden impacts on inhabited outlets.

Furthermore, the local population is unaware of the possible flash flooding risk to which they are exposed. The other models developed earlier, such as STREAM, LISEM, or W.

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