Prédétermination des débits maximaux de crue par simulation Monte-Carlo de la pluie nette

Une méthodologie a été proposée pour la prédétermination des débits à partir de la pluviométrie. Il s’agit d’associer, en entrée, les simulations Monte Carlo de hyétogrammes de pluie nette avec un modèle d’hydrogramme unitaire à base de géomorphologie pour obtenir des hydrogrammes simulés en sortie. À la fin des simulations, l’analyse statistique des sorties permet d’apprécier l’étendue de la variabilité de la réponse du bassin aux événements pluvieux et de caractériser les débits et les temps de pointe. Un total de 44 simulations ont été menées pour chacun des 15 événements observés pour un petit bassin versant situé en Tunisie centrale. L’analyse des hydrogrammes générés a montré une assez faible dispersion des débits de pointe, d’une simulation à l’autre, pour un événement donné, et a mis en évidence la dissymétrie des distributions des débits et temps de pointe. L’exploitation des résultats de l’ensemble des simulations permet de dégager des relations empiriques caractérisant le comportement du bassin selon les débits de pointe, les temps de pointe, les temps de base et les volumes écoulés.The predetermination of peak discharges and flood volumes of ungauged basins is an important aspect of the management of surface waters, protection against floods, water supply, etc. In this study, a method is proposed for the predetermination of discharges from rainfall data. The method associates effective rainfall obtained from Monte Carlo Simulations (MCS) with a unit hydrograph based on geomorphology. The unit hydrograph (UH) based on geomorphology is selected knowing that the parameters can be obtained from topographic charts, soil charts and ground occupation charts, as well as from soil data. The UH used was produced from the Nash cascade model in which the scale and shape parameters were taken from the literature. These parameters depend on the hydrographical network, the Horton ratios and the average peak flow velocity, which is assumed to be constant throughout the network and with respect to time. The average peak flow velocity can be expressed as a function of 1) geomorphologic parameters such as the total surface area of the basin, the slope of the highest order stream, the Manning-Strickler coefficient, the width of the channel, the kinematic wave parameter of the highest order stream and the length of the main channel, and 2) the effective rainfall intensity and duration.With respect to effective rainfall intensities, the idea is to consider the effective rainfall as a vector of the parameters of the hydrological model, and then to use the MCS method to generate the corresponding components. The proposed simulation framework includes: 1) the specification of the data for which the geomorphologic parameters and the time increments are fixed for all simulations, whereas the duration of the total rainfall and the effective rainfall volume vary from one event to another, and constitute constraints determining whether or not simulations should be rejected, 2) the random drawing of effective rainfall intensities and durations, 3) the computation of resulting hydrographs and 4) the analysis of the simulated hydrographs, where the hydrographs are first simulated for each event and then simulated in their entirety to highlight indicators to characterize outputs.In order to statistically interpret the simulated hydrographs, the generated peak discharges were classified for each event, and their 25th, 50th and 75th percentiles were analyzed. The same treatment was applied to the simulated times to attain peak values. The use of the 25th and 75th percentiles makes it possible to evaluate the extent of the 50% interval of the simulated discharges, whereas the median and the mode make it possible to position values representative of the distribution of the generated discharges. The hydrographs are assumed have the same “recurrence” as their peak discharge. Hydrograph generation by the MCS method is a two step process: 1) the generation of effective rainfall intensities based on the assumption that the total volume is observed, and 2) the convolution of the unit hydrograph resulting from each interval of effective rainfall.The study site, Saddine1, is a small catchment with a surface area of 384 hectares. It is located adjacent to Makthar in Tunisia (northern latitude 35°48’06’’ and longitude 9°04’ 09’’) in a mountainous zone. The catchment is controlled by a small headwater dam and was monitored from 1992 to 1999. Observed over periods of five minutes, the maximum rainfall intensity was 324 mm/h and the minimal intensity was 10 mm/h. The maximum total rainfall recorded for an event was of 106 mm. The longest duration for an event was of approximately 5 hours (299 min) and shortest was 12 minutes. A great disparity in the volumes was also noted: the maximum volume observed was 67,200 m3 whereas the minimum was 1,275 m3. The peak discharges of the recorded hydrographs were very variable with a minimum/maximum ratio of about 1/1370. Indeed the maximum discharge observed was 85.6 m3/s, and the minimum discharge only 0.062 m3/s. The time to attain peak flows for the rainfall events varied from 10 to 120 minutes. The effective rainfall intensities were calculated using the infiltration index method, ϕ, which remains a method still largely used in spite of its rudimentary character. The effective rainfalls estimated for each event varied from 0.3 mm with 17.5 mm.Before using the MCS, the model was calibrated. The results of the calibration analysis showed that the calculated hydrographs were reasonable comparable to the observed hydrographs. In addition to the shape, the peak discharge and the peak time reconstitutions were satisfactory. A total of 44 simulations were carried out for each of the 15 events observed, of which 13 allowed for the identification of the distributions of effective rainfall intensities and durations. The remaining two events were used for the validation of the approach. The analysis of the generated hydrographs showed a rather weak dispersion of the peak output from one simulation to another, for a given event. Moreover, the discharges and times to attain peak discharge resulting from the generated hydrographs followed a dissymmetrical distribution. The observed values of the peak discharges and times to attain peak discharge represent realisations of output simulations with different probabilities of occurrence. In order to capitalize on the model, relationships between simulated peak discharges, times to peak discharge, base times and volumes were constructed

Evaluating the MSG satellite Multi-Sensor Precipitation Estimate for extreme rainfall monitoring over northern Tunisia

Knowledge and evaluation of extreme precipitation is important for water resources and flood risk management, soil and land degradation, and other environmental issues. Due to the high potential threat to local infrastructure, such as buildings, roads and power supplies, heavy precipitation can have an important social and economic impact on society. At present, satellite derived precipitation estimates are becoming more readily available. This paper aims to investigate the potential use of the Meteosat Second Generation (MSG) Multi-Sensor Precipitation Estimate (MPE) for extreme rainfall assessment in Tunisia. The MSGMPE data combine microwave rain rate estimations with SEVIRI thermal infrared channel data, using an EUMETSAT production chain in near real time mode. The MPE data can therefore be used in a now-casting mode, and are potentially useful for extreme weather early warning and monitoring. Daily precipitation observed across an in situ gauge network in the north of Tunisia were used during the period 2007–2009 for validation of the MPE extreme event data. As a first test of the MSGMPE product's performance, very light to moderate rainfall classes, occurring between January and October 2007, were evaluated. Extreme rainfall events were then selected, using a threshold criterion for large rainfall depth (>50 mm/day) occurring at least at one ground station. Spatial interpolation methods were applied to generate rainfall maps for the drier summer season (from May to October) and the wet winter season (from November to April). Interpolated gauge rainfall maps were then compared to MSGMPE data available from the EUMETSAT UMARF archive or from the GEONETCast direct dissemination system. The summation of the MPE data at 5 and/or 15 min time intervals over a 24 h period, provided a basis for comparison. The MSGMPE product was not very effective in the detection of very light and light rain events. Better results were obtained for the slightly more moderate and moderate rain event classes in terms of percentage of detected events, correlation coefficient, and ratio bias. The results for extreme events were mixed, with high pixel correlations of R=0.75 achieved for some events, while for other events the correlation between satellite and ground observation was rather weak. MPE data for northern Tunisia seem more reliable during the summer season and for larger event scales. The MSGMPE data have demonstrated to be very informative for early warning purposes, but need to be combined with other near real time data or information to give reliable and quantitative estimates of extreme rainfall

<i>SPI-3</i> Analysis of Medjerda River Basin and Gamma Model Limits in Semi-Arid and Arid Contexts

The Standardized Precipitation Index SPI-3, associated with three months of rainfall accumulation, is a drought index for detecting immediate drought impacts. The two-parameter gamma distribution, recommended by the World Meteorological Organization as the underlying distribution for estimating SPI, has shown limits in semi-arid and arid conditions with respect to the normality test for the resulting SPI series. Our purpose was to evaluate its relevance for the Medjerda River Basin (Tunisia), a transboundary basin where the climate classes are temperate, dry, and hot summer, as well as arid hot desert and arid hot steppe. When analyzing the time series of 144 stations from 1950 to 2018, we found that the normality Shapiro–Wilk test was rejected in 17% of the cases, which agreed with the literature review results. The transition season (August, September, and October) had the highest rejection percentage. Three factors were identified to explain the deviation from normality. We first identified the rate of occurrence of completely dry (zero rain) three-month periods. The higher the rate of occurrence was, the higher that the probability was of its rejecting the normality test. High sample skewness was the second influencing factor. Finally, a series where the Grubbs’ test of identifying outliers was rejected was more likely to show the SPI-3 series deviating from normality

Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate

International audienceThe scale invariance of rainfall series in the Tunis area, Tunisia (semi-arid Mediterranean climate) is studied in a mono-fractal framework by applying the box counting method to four series of observations, each about 2.5 years in length, based on a time resolution of 5 min. In addition, a single series of daily rainfall records for the period 1873-2009 was analysed. Three self-similar structures were identified: micro-scale (5 min to 2 d) with fractal dimension 0.44, meso-scale (2 d to one week) and synoptic-scale (one week to eight months) with fractal dimension 0.9. Interpretation of these findings suggests that only the micro-scale and transition to saturation are consistent, while the high fractal dimension relating to the synoptic scale might be affected by the tendency to saturation. A sensitivity analysis of the estimated fractal dimension was performed using daily rainfall data by varying the series length, as well as the intensity threshold for the detection of rain

Study of the occurrence of rain in the Tunis area in a mono-fractal framework

International audienceLess study concern the scale variability of the rainfall field in North Africa (Mediterranean climate), where the climate differ significantly from the Sahelian Africa (monsoon climate). This paper undertakes a study of the occurrence of rain in the region of Tunis in a mono-fractal framework. The box-counting method is applied to four series of observations of a continuous period of two and a half years, based on a minimum resolution of 5 min and belonging to the semi-arid bioclimatic stage. These series are characterized by strong intermittency. Using the sensor detection threshold, two self-similar structures were detected: micro-scale (5min- 2 days) with fractal dimension 0.44 and a synoptic-scale (one week - eight months) with fractal dimension of 0.9. This last value is probably overestimated by the presence of the saturation of the available space by rain (fractal dimension equal to one) for period longer than eight month. Due to the length of the dry period observed, the length of this saturation period differs from other studies performed in other area. Between the two self-similar structures a transitional regime corresponding to a meso-scale (2 days- one week) could be distinguished. The increase of the threshold would allow to 'filter' the frontal structure so as to keep only the convective structures, a sub micro-scale structure (5mn - 1h 20) has been detected with 0.3 mm/5mn intensity threshold. These results may reflect the influence of two distinctive types of convective showers and original front controlling these series