Occurrence des sécheresses dans le bassin de la Medjerda (Tunisie)

La probabilité d'occurrence des sécheresses dans le bassin de la Medjerda (Tunisie) est calculée en se basant sur les totaux pluviométriques annuels de 35 postes sur une période de quarante ans. Les moments statistiques des volumes de déficits face à une demande en eau fixée sont estimés par la méthode des séries. Une fonction de répartition marginale des volumes de déficits est proposée, ainsi que des fonctions de répartition conditionnelles pour des durées sèches de un à six ans. Plusieurs lois de probabilité couramment utilisées en hydrologie sont étudiées. Des applications de ce modèle sont présentées.The probability of occurrence of drought in the Medjerda basin (Tunisia) is estimated using the stochastic process based on the measurement of total annual rainfalls taken in 35 stations over a period of 40 years.Marginal and conditional distributions of shortage volumes are analytically proposed at each location. Mean, standard deviation and skewness coefficients of shortage volumes are used for setting up a Person type III model. Then, similarly to I-D-F curves, drought duration curves are plotted within a given threshold. A general formulation of statistics of shortage volume population is given. It is expressed in terms of the position, the location and the scale parameters of the rainfall generator process, for a given threshold value. As an application, some useful distributions in hydrology are examined (Normal, Galton, Gamma, Weibull) and expected drought volumes are estimed.Model verification is performed using three stations of the basin for which the observed sample was extended to a period of 58 years. Comparison between observed and calculated statistics of shortage shows a good agreement. Expected shortage volumes are mapped using the average rainfall at each station as a threshold. A second threshold was based on an agricultural water demand. The corresponding water supply expected was mapped

Une approche floue pour la détermination de la région d'influence d'une station hydrométrique

La notion d'appartenance partielle d'une station hydrométrique à une région hydrologique est modélisée par une fonction d'appartenance obtenue en appliquant les concepts de l'analyse floue. Les stations hydrométriques sont représentées dans des plans dont les axes sont des attributs hydrologiques et/ou physiographiques. Les régions hydrologiques sont considérées comme des sous-ensembles flous. Une méthode d'agrégation par cohérence (Iphigénie) permet d'établir des classes d'équivalence pour la relation floue "il n'y a pas d'incohérence entre les éléments d'une même classe": ce sont des classes d'équivalence qui représentent les régions floues. La fonction d'appartenance dans ce cas est stricte. Par opposition, la seconde méthode de type centres mobiles flous (ISODATA) permet d'attribuer un degré d'appartenance d'une station à une région floue dans l'intervalle [0,1]. Celle-ci reflète le degré d'appartenance de la station à un groupe donné (le nombre de groupes étant préalablement choisi de façon heuristique). Pour le cas traité (réseau hydrométrique tunisien, débits maximums annuels de crue), il s'avère cependant que le caractère flou des stations n'est pas très prononcé. Sur la base des agrégats obtenus par la méthode Iphigénie et des régions floues obtenues par ISODATA, est effectuée une estimation régionale des débits maximums de crue de période de retour 100 ans. Celle-ci est ensuite comparée à l'estimation régionale obtenue par la méthode de la région d'influence ainsi qu'à l'estimation utilisant les seules données du site, sous l'hypothèse que les populations parentes sont des lois Gamma à deux paramètres et Pareto à trois paramètres.The concept of partial membership of a hydrometric station in a hydrologic region is modeled using fuzzy sets theory. Hydrometric stations are represented in spaces of hydrologic (coefficient of variation: CV, coefficient of skewness: CS, and their counterparts based on L- moments: L-CV and L-CS) and/or physiographic attributes (surface of watershed: S, specific flow: Qs=Qmoyen/S, and a shape index: Ic). Two fuzzy clustering methods are considered.First a clustering method by coherence (Iphigénie) is considered. It is based on the principle of transitivity: if two pairs of stations (A,B) and (B,C) are known to be "close" to one another, then it is incoherent to state that A is "far" from C. Using a Euclidean distance, all pairs of stations are sorted from the closest pairs to the farthest. Then, the pairs of stations starting and ending this list are removed and classified respectively as "close" and "far". The process is then continued until an incoherence is detected. Clusters of stations are then determined from the graph of "close" stations. A disadvantage of Iphigénie is that crisp (non fuzzy) membership functions are obtained.A second method of clustering is considered (ISODATA), which consists of minimizing fuzziness of clusters as measured by an objective function, and which can assign any degree of membership between 0 to 1 to a station to reflect its partial membership in a hydrologic region. It is a generalization of the classical method of mobile centers, in which crisp clusters minimizing entropy are obtained. When using Iphigénie, the number of clusters is determined automatically by the method, but for ISODATA it must be determined beforehand.An application of both methods of clustering to the Tunisian hydrometric network (which consists of 39 stations, see Figure 1) is considered, with the objective of obtaining regional estimates of the flood frequency curves. Four planes are considered: P1: (Qs,CV), P2: (CS,CV), P3: (L-CS,L-CV), and P4: (S,Ic), based on a correlation study of the available variables (Table 1).Figures 2, 3a, 4 and 5 show the clusters obtained using Iphigénie for planes P1 through P4. Estimates of skewness (CS) being quite biased and variable for small sample sizes, it was decided to determine the influence of sample size in the clusters obtained for P2. Figure 3b shows the clusters obtained when the network is restricted to the 20 stations of the network for which at least 20 observations of maximum annual flood are available. Fewer clusters are obtained than in Figure 3, but it can be observed that the structure is the same: additional clusters appearing in Figure 3 may be obtained by breaking up certain large clusters of Figure 3b. In Figure 3c, the sample size of each of the 39 stations of the network is plotted in the plane (CS,CV), to see if extreme estimated values of CS and CV were caused by small samples. This does not seem to be the case, since many of the most extreme points correspond to long series.ISODATA was also applied to the network. Based on entropy criteria (Table 2, Figures 6a and 6b), the number of clusters for ISODATA was set to 4. It turns out that the groups obtained using ISODATA are not very fuzzy. The fuzzy groups determined by ISODATA are generally conditioned by only one variable, as shown by Figures 7a-7d, which respectively show the fuzzy clusters obtained for planes P1-P4. Only lines of iso-membership of level 0.9 were plotted to facilitate the analysis. For hydrologic spaces (P2 and P3), it is skewness (CS and L-CS) and for physiographic spaces (P1 and P4) it is surface (Qs and S). Regionalization of the 100-year return period flood is performed based on the homogeneous groups obtained (using an index-flood method), and compared to the well-known region of influence (ROI) approach, both under the hypothesis of a 2-parameter Gamma distribution and a 3-parameter Pareto distribution. For the ROI approach, the threshold corresponding to the size of the ROI of a station is taken to be the distance at which an incoherence first appeared when applying Iphigénie. Correlation of the regional estimate with a local estimation for space P1 is 0.91 for Iphigénie and 0.85 both for ISODATA and the ROI approach. Relative bias of regional estimates of the 100-year flood based on P1 is plotted on Figures 9 (Gamma distribution) and Figure 10 (Pareto distribution). The three methods considered give similar results for a Gamma distribution, but Iphigénie estimates are less biased when a Pareto distribution is used. Thus Iphigénie appears superior, in this case, to ISODATA and ROI. Values of bias and standard error for all four planes are given for Iphigénie in Table 3.Application of an index-flood regionalization approach at ungauged sites requires the estimation of mean flow (also called the flood index) from physiographic attributes. A regression study shows that the best explanatory variables are watershed surface S, the shape index Ic and the average slope of the river. In Figure 8, the observed flood index is plotted against the flood index obtained by regression. The correlation coefficient is 0.93.Iphigénie and ISODATA could also be used in conjunction with other regionalization methods. For example, when using the ROI approach, it is necessary to, quite arbitrarily, determine the ROI threshold. It has been shown that this is a byproduct of the use of Iphigénie. ISODATA is most useful for pattern identification when the data is very fuzzy, unlike the example considered in this paper. But even in the case of the Tunisian network, its application gives indications as to which variables (skewness and surface) are most useful for clustering

Development of a method of robust rain gauge network optimization based on intensity-duration-frequency results

Based on rainfall intensity-duration-frequency (IDF) curves, fitted in several locations of a given area, a robust optimization approach is proposed to identify the best locations to install new rain gauges. The advantage of robust optimization is that the resulting design solutions yield networks which behave acceptably under hydrological variability. Robust optimization can overcome the problem of selecting representative rainfall events when building the optimization process. This paper reports an original approach based on Montana IDF model parameters. The latter are assumed to be geostatistical variables, and their spatial interdependence is taken into account through the adoption of cross-variograms in the kriging process. The problem of optimally locating a fixed number of new monitoring stations based on an existing rain gauge network is addressed. The objective function is based on the mean spatial kriging variance and rainfall variogram structure using a variance-reduction method. Hydrological variability was taken into account by considering and implementing several return periods to define the robust objective function. Variance minimization is performed using a simulated annealing algorithm. In addition, knowledge of the time horizon is needed for the computation of the robust objective function. A short- and a long-term horizon were studied, and optimal networks are identified for each. The method developed is applied to north Tunisia (area = 21 000 km2). Data inputs for the variogram analysis were IDF curves provided by the hydrological bureau and available for 14 tipping bucket type rain gauges. The recording period was from 1962 to 2001, depending on the station. The study concerns an imaginary network augmentation based on the network configuration in 1973, which is a very significant year in Tunisia because there was an exceptional regional flood event in March 1973. This network consisted of 13 stations and did not meet World Meteorological Organization (WMO) recommendations for the minimum spatial density. Therefore, it is proposed to augment it by 25, 50, 100 and 160% virtually, which is the rate that would meet WMO requirements. Results suggest that for a given augmentation robust networks remain stable overall for the two time horizons

Seasonal precipitation forecasting with large scale climate predictors: a hybrid ensemble empirical mode decomposition-NARX scheme

Much of northern Tunisia regularly experiences extremes of drought and flooding, with high rainfall variability. The development of reliable and accurate seasonal rainfall forecasts can provide valuable information to help mitigate some of the outcome of floods and enhance water management and monitoring, particularly for agriculture. Whether climate indices oscillations contain some information to be useful for hydrological forecasting is worth investigating. Ensemble monthly rainfall forecasts are carried out using a hybrid neural network model. The hybrid model called EEMD-NARX based on a non-linear autoregressive network with exogenous inputs (NARX) coupled to Ensemble Empirical Mode Decomposition (EEMD) method is developed in this work. First, the EEMD is performed to extract significant information from modes of variability (IMF) associated to climate indices and precipitation. Each IMF of selected indices as well as precipitation IMFs are then used as inputs to the NARX forecasting model to forecast each IMF of precipitation. To make forecasts operational, we reconstruct precipitation by summing of all forecasted IMFs to make comparison with observed precipitation in the Medjerda river basin located in north Tunisia. Results show that IMFs of MEI and SOI indices can be distinguished from a white noise at the 95 % level. It is also found that an oscillatory forcing coming from the Atlantic influences the precipitation in the Mediterranean basin. The results indicate that exogenous inputs like climatic indices improve the accuracy of forecasts in some in some precipitation stations. The correlation coefficient between observed and forecasted monthly precipitation is ranging from 0.7 to 0.8. EEMD allows extracting significant components from exogenous inputs like climate indices that help reducing predictive uncertainty as well as improving forecasts of a NARX model at longer lead-times.</p

Comparison of Actual Evapotranspiration assessment by satellite-based model SEBS and hydrological model BBH in northern Tunisia

Estimating actual evapotranspiration (AET) in agricultural semi-arid regions is important for crop yield and drought assessment. The Surface Energy Balance System (SEBS) model, a physically based energy balance model using satellite information is used to estimate AET at the 10 d scale, with a 3 km resolution. The bucket bottom hole (BBH) model, a conceptual daily water balance model is calibrated using the equifinality approach and run for simulating daily AET. Five watersheds located in northern Tunisia with areas varying between 56 and 448 km2 were calibrated using daily rainfall and potential evapotranspiration data as entry and river discharge as output data. Sets of model parameters fulfilling both absolute relative errors of simulated discharge less than 20 % and Nash–Sutcliffe coefficients greater than 0.75 were selected. Three years were selected for the comparison (2010, 2017, and 2018). For every year, six subperiods of 10 d are considered belonging to January, March, April, May, July, and September. Boxplots of AET-BBH estimations are plotted to achieve a comparison with AET-SEBS estimates. It is found that AET comparisons are well favorable for January, March, and April while less satisfactory for May and September. They do not match for July. AET-SEBS are much higher in comparison with AET-BBH estimates with an RMSE and MAE equal respectively to 17 and 19 mm 10 d−1. These results may help stakeholders to assess AET coming from different data sources and models.</p

Sensitivity of actual evapotranspiration estimation using the sebs model to variation of input parameters (lst, dssf, aerodynamics parameters, lai, fvc)

Actual Evapotranspiration (AET) is a key component of the water and energy balance and hydrological regime of catchments. A land surface energy balance system model (SEBS) was used to estimate the AET of the 160100-km² Medjerda river basin in Northern Tunisia. This model uses satellite data in combination with meteorological data. In this study, we investigated the sensitivity of the AET model output to five major input variables: the 30-minute Downward Surface Shortwave solar radiation fluxes (DSSF), and Land Surface Temperatures (LST), the roughness height for momentum transfer z0m, and the influence of the spatial resolution of satellite-based Leaf Area Index (LAI) and fraction of Vegetation Cover (FVC) estimates. The DSSF product was validated using a comparison to solar radiation estimates by the Angstrom formula based on in-situ station data. Gaps in the 15-min satellite-based land surface temperature time series were filled using a sinusoidal model on pixels containing meteorological stations. One-half to two standard deviations of the errors of the regression curves were applied to analyse the sensitivity of the SEBS output. Two methods to estimate the near surface aerodynamic parameter z0m were applied and compared. Maps of LAI and FVC derived from two sensors alternatively applied as an input to the SEBS model. A sensitivity analysis, performed in the first decade of May 2010, showed that SEBS model parameterization is quite sensitive in the forestland cover type. The difference can be up to 0.3 mm day−1. For agricultural land areas, representing an important percentage of the Medjerda basin, AET estimations based on the SEBS model proved to be used to satisfy the actual evapotranspiration estimates

Regionalization of IDF curves using the property of scale invariance

Networks of daily rainfall raingauges are often much dense than tippet bucket raingages networks. Consequently, it would be of high interest to make use of daily rainfall information assessing IDF curves for unobserved locations. The present work proposes achieving this goal by using the assumption of simple scale invariance. The simple scaling property is identified using the fitting of regression of log transforms of rainfall statistical moments of order q versus log transforms of rainfall durations (scale). In case where the relation of slopes versus moment orders is linear, "simple scaling invariance" is assumed (Gupta et Waymire, 1990). Yu et al. (2004), Bara et al. (2009) as well as Ceresetti et al., (2010) adopted the assumptions of simple scaling to maximum annual rainfall for durations in the interval 30 mn to 24 h. Thus, using 24h-rainfall totals, they suggested estimating quantiles of rainfall intensities of short durations using quantiles of 24 h rainfall. In the present work, series constituted by the N most important maximum annual intensities observed during N years in 15 stations are studied. Observed intensities for various time resolutions extending from 5 minutes to 24 h are available. The period of observation is 1950 to 2001. Two simple scale invariance behaviors are identified namely a scale regime in the interval [5 minutes - 30 minutes] and another in the interval [30 minutes - 24 hours] for all stations. The study focuses on durations in the interval [30 minutes - 24 hours]. The resulting scale exponents vary from k=0.55 to k=0.89 for the resolutions [30 minutes - 24 hours] and vary from k=0.40 to k=0.65 for [5 minutes - 30 minutes] resolutions. Furthermore, for regionalization purposes, a power low regression is fitted and cross-validated between the estimated scale exponents and 90th percentile of sample maximum annual daily rainfall

Seasonal precipitation variability in regional climate simulations over Northern basins of Tunisia

Northern Tunisia is the rainiest part of the country where most of the water management structures (dams, reservoirs, etc) are located. Its strategic situation with respect to surface water resources encourages the investigation of the climate change impacts projected by climate models. The goal of this study is first to compare the observed precipitation with climate model outputs, and then to evaluate the future changes projected by different climate models. The study area is subdivided into four regions: the upstream and downstream transboundary Medjerda basin, the northern coastal basins and the eastern coastal basins. A database provided by the Tunisian hydrological service includes 388 stations with complete monthly precipitation data over the period 1961-2000. An ensemble of Regional Climate Models (RCM) simulations provided by the European Union-funded project ENSEMBLES are used. Six RCM model runs (CNR-A, DMI-A, DMI-B, ICT-E, SMH-B and SMH-E) are analysed, for the control period 1961-2000 and two projection periods, 2011-2050 and 2051-2090. The models efficiency in reproducing seasonal precipitation amounts and variability is evaluated. A 1-km monthly precipitation reference grid is computed through the interpolation of rainfall observations during the period 1961-2000 with kriging techniques. Monthly precipitation series averaged over the four basins are built for comparison during the control period. The RCM outputs are evaluated with respect to the annual precipitation cycle and rainfall frequency distribution using robust statistics. For the control period, features of the seasonal regimes are well reproduced by all models. It is found that models underestimate seasonal precipitation on average by 20%. The discrepancy between model outputs and observations depends on the season. For the future, in summer and autumn the different models do not project major changes in the seasonal distributions. However, for winter and spring, all the models project a significant decrease of precipitations

Climate change impacts on hydrology in Maghreb countries ENVIMED/ MISTRALS Project “CLIHMag"

International audienc

Hydrological impacts of climate change in Morocco and Tunisia.

Regional climate modelling, heavy precipitation, flash-floods, droughts: Climate change impacts on the MediterraneanInternational audienc