Développements récents en matière d'analyse des chroniques d'événements hydrologiques : liaison en chaine, analyse spectrale

Professeur School of Civil Engineerig, Purdue University, Lafayette, Indiana (U.S.A.)

Résumé

The generation of hydrologic time series is the starting point of the systematic analysis for the study or the management of water resources developments. In general, the stationarity of the time series, at least to the second order is assumed. Hydrologic series are not necessarily stationary but may be made approximately stationary by the removal of the deterministic components that may exist, such as a trend, a periodicity, or persistence. The most common mathematical models for time series simulation are the autoregressive processes, the moving averages and the mixed processes. The auto- and cross-spectral analysis is a powerful method for the determination of mathematical models of hydrologic processes. The general appearance of the autospectrum indicates the type of process, for example, if a first or a second order autoregressive process is a suitable model, and the spectrum may also be used to determine the values of the model parameters. The crossed spectrum is useful to establish relationships between two time series such as the rainfall and runoff sequences. These series may be related, for example, by a simple regression. A continuous or a discrete linear system connecting the two series may be identified. With the latter model, the runoffs may be expressed as a weighed sum of antecedent precipitations. These techniques were applied to the study of rainfall and runoff in the Sioule basin, a tributary of the Allier River, in central France. The study was made for monthly, daily and bihourly data. A logarithmic transformation of the runoffs and a square root transformation of the rainfalls improved the relationships at the monthly and daily time scales. The periodicity was removed by normalization for the monthly data, and by filtering for the daily and bihourly data. Several mathematical models are proposed to simulate the time series of rainfall and of the runoff and the rainfall-runoff transfer in the Sioule basin for the three time scales.