La modélisation stochastique des pluies horaires et leur transformation en débits pour la prédétermination des crues

Abstract

A statistical approach was developed for the study of frequency distributions of hydrologic variables. The Simulated HYdrographs for flood PRobability Estimation (SHYPRE) method uses observed values to describe hydrological phenomena and successfully reproduces observed-values statistics. SHYPRE combines a stochastic model for generating hourly rainfall with a model that transforms rainfall runoff into discharge. The rainfall generation model is a stochastic model that uses a geometric description of temporal rainfall signals, the so-called direct approach. The model assumes that a rainfall event is a random and intermittent process (series of dry and rainy events) describable by stochastic laws. Generation of a temporal rainfall signal has two stages. First, descriptive analysis of hyetographs indicates which variables best represent the internal temporal structure of observed hourly rainfall episodes; the model hypothesizes that each descriptive variable is independent and definable by a theoretical probability distribution fitted to observed values. Second, rainfall episodes are generated using descriptive variables derived randomly (using the Monte Carlo method) from their probability distributions. The hydrological model is a lumped conceptual model with three parameters on an hourly time step. The model operates in event mode, which is to say it is calibrated for each independent flood event. Parameters are independent of rainfall for all observed floods. Parameter independence, which is also analysed, makes it possible to randomly generate flood events for any simulated rainfall event. Parameters for each model are estimated from hourly rainfall and runoff information. Each simulated hyetograph is transformed into a flood by the hydrological model. Thus, numerous different flood events are simulated over a given period, an improvement over standard design floods that yields full hydrological temporal data and allows better evaluation of hydrologic risks. The rainfall model was calibrated with 50 rain gauge stations located on the French Mediterranean seaboard and simulations were performed for each. Observed and calculated values were compared for means and different quantiles of test variables (maximum rainfall in 1 to 72-hour periods). Results were good throughout the study zone. At stations with significantly different rainfall, mean deviation of test variables was between - 10% and + 10%. A good match was obtained between simulated and observed rainfall quantiles (with a fitted Gumbel probability distribution) in the observable frequency range up to the decennial return period. Simulated rainfall events were then transformed into hourly flow events. Maximum discharges of different duration were extracted from simulated hydrographs and compared with maximum observed discharges, and run by simple empirical transfer of simulation values. The entire frequency range required no new hypotheses about the probability distributions of discharges of different durations. The model reproduced flood discharge quantiles in the observed frequency range. SHYPRE yields useful temporal data, namely hyetograph and flood shapes. For example, in hydraulic studies this information allows estimation of construction-site effects as well as the study of their downstream discharges. Moreover, temporal data generated by the model can replace single-design rainfall or floods. It allows better estimates of flood volume, a significant gain, for whereas peak discharges of exceptional floods can be estimated hydraulically (using flood high-water marks), runoff volume data are generally unavailable. SHYPRE handles extreme-value samples with relative stability, a robustness arising from two features: The rainfall model examines hourly rainfall descriptors and temporal and quantitative rainfall data are reproduced by analysis of an average of several thousand storms per station. The large number of variables and values analysed ensures the accuracy of rainfall-model parametric calibration and reduces extreme-value sampling problems. - The parametric independence of the rainfall-runoff model from rainfall allows it to produce results not especially influenced by severe flood observations. Thus, calibration is not affected by discharge sampling problems and is therefore much more stable than simple statistical operations on discharges (for which, moreover, extreme-flood observation is essential). SHYPRE yields different estimations of flood quantiles of common to rare frequencies as well as complete temporal flood data. Moreover, it provides more stable estimates of flood quantiles than statistical distributions fitted on observed values, even for frequent events. The improvement stems from better use of rainfall data and from the parametric design stability of the rainfall model and rainfall-runoff model. While the rainfall model is essential to SHYPRE, the rainfall runoff model is also important: it avoids certain weaknesses of existing methods that put extreme discharges and rainfall statistics in linear relationships (problematic with common and rare quantiles in particular), and it generates more realistic flood events.