Estimation des courbes Intensité-Durée-Aire-Fréquence (IDAF) de la région de Tunis dans un contexte multifractal

Hanen Ghanmi 1
1 SPACE - LATMOS
LATMOS - Laboratoire Atmosphères, Milieux, Observations Spatiales
Abstract : Due to its geographical position, Tunisia is subject to the influence of two climates, Mediterranean on the north and Saharan on the South, which are responsible for a significant spatio-temporal variability of rainfall. Particularly in recent years, sudden and intense rainfall that occurred in the area of Tunis, subject of our study, caused flooding with catastrophic consequences. This extreme variability of the rainfall field encouraged and motivated us to study the rainfall in this area. Multifractal analysis has shown its relevance in the characterization of geophysical process at high variability as the process of rainfall. Accordingly, in a first aspect, we investigated the occurrence of rainfall in monofractal context. We also studied the intensity of rainfall using the multifractal approach. The mono-fractal analysis has enabled us to emphasize firstly the particular behavior of the Mediterranean rainfall regime of Tunis area, characterized by a long dry season followed by a short rainy season. Then this analysis gave us an idea about the origin of intense rainfall which is likely due to isolated and convective cloud structures with low lifetime. Finally it showed a significant change in the fractal dimension of the support of rainfall during the last century. The spectral analysis and the study of the structure function have identified three regimes of scale invariance namely micro-scales, mesoscale and synoptic scale. Unlike the last two regimes, the process of rain during the first regime is non-conservative. In this case the rainfall intensity is not a pure multiplicative cascade. It results from a fractionally integrated multifractal cascade. However, it is recognized that the methods conventionally implemented to estimate the parameters of the universal multifractal model (MU) give rise to biased parameters in the case of rainfall. This is due to the intermittent nature of this process. The bias correction methods presented in the literature do not solve the problem in the case of time series recorded in Tunis given the importance of periods without rain, in other words, the intermittency of rainfall signal. For this reason, an empirical method of bias correction based mainly on the use of percentage of zero in a sequence of non-continuous rainfall has been proposed. For micro-scales, after bias correction, the parameters obtained are consistent both with those obtained on some events of continuous rain and those recently published on the properties of rainfall at fine scale. The establishment of curves (Intensity Duration Frequency) IDF, which links the return period, the intensity and duration of the rainfall, is a prerequisite for the design of hydraulic structures. Their development requires the availability of observations at sufficiently fine scales (5 minutes) and sufficiently long periods. Time series observed over sufficiently long periods (total daily rainfall and maximum annual rainfall intensities for fixed durations) allowed us to test the hypothesis of simple scale invariance of maximum annual rainfall intensities for different tipping bucket raingauge stations in Northern Tunisia. This assumption, combined with Gumbel modeling of maximum rainfall intensities allowed us to define a methodology for IDF curves development from the daily rainfall totals. A regionalization formula valuable for Northern Tunisia which involves the percentile 90% of the annual maximum daily rainfall was established and validated. This regionalization formula applied to daily data collected by the national hydrological service (DGRE) in 41  raingauges in the area of Tunis, combined with the assumption of simple scale invariance has enabled us to develop IDF curves of  raingauges in the area of Tunis for unobserved sites. A comparison between the slopes of IDF curves derived from probabilistic empirical Montana and American models established by adjusting statistical laws with the classical method and those derived from the highest-order of singularity and from the divergence moments order deduced of parameters of the universal multifractal model was conducted. The results are generally comparable. Thus, the parameters of the multifractal model lead to a consistent estimation of the slope of the IDF curves. Therefore, IDF curves were further used to create maps of rainfall quantiles for different durations and different return periods through the ArcView geographic information system software and using kriging as a spatial interpolation method. As a result, maps of quantiles gave an estimation of surfaces receiving rainfall quantile exceeding a fixed threshold, as a way for IDAF establishment. Moreover, in order to estimate curves IDAF (Intensity Duration Area Frequency) we used another approach proposed by De Michele et al. (2011) which refers to multifractal approach. It assumes that the maximum annual rainfall is distributed according to a log-normal distribution and the chronology of events of intense rainfall follows a Poisson distribution. It has been concluded that the Tunis Manoubia station verifies both assumptions for durations below two hours. Thereafter IDAF curves for durations less two hours, for return period less or equal to 100 years and for areas ranging to up to tens of km2 were estimated with reference to the empirical abatement coefficients of NERC (1975).
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Hanen Ghanmi. Estimation des courbes Intensité-Durée-Aire-Fréquence (IDAF) de la région de Tunis dans un contexte multifractal. Physique Atmosphérique et Océanique [physics.ao-ph]. Uiversité Versailles Saint-Quentin-en-Yvelines; Université Tunis El Manar, 2014. Français. ⟨tel-01135837⟩

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