Developments in statistics applied to hydrometeorology : imputation of streamflow data and semiparametric precipitation modeling.

Summary Precipitation and streamflow are the two most important hydrometeorological variables for watershed analysis. They provide fundamental information for integrated water resources management, such as drinking water supply, hydropower, flood or drought forecasting, or irrigation systems.In this PhD thesis two distinct problems are addressed. The first one is based on the study of river flows. In order to characterize the global behavior of a watershed, long time series of flows covering several decades are necessary. However, missing data in the series represent a loss of information and reliability, and can lead to misinterpretation of the statistical characteristics of the data. The method we propose to address the flow imputation problem is based on dynamic regression models (DRM), more specifically, multiple linear regression coupled with ARIMA-type residual modeling. Contrary to previous studies involving the inclusion of multiple explanatory variables or the modeling of residuals from a simple linear regression, the use of DRMs allows both aspects to be taken into account. We apply this method to reconstruct daily streamflow data at eight stations located in the Durance watershed (France) over a 107-year period. By applying the proposed method, we succeed in reconstructing the flows without using other explanatory variables. We compare the results of our model with those obtained from a complex model based on analogues and hydrological modelling and from a nearest neighbor approach. In the majority of cases, DRMs show better performance when reconstructing missing data periods of different sizes, in some cases up to 20 years.The second problem we consider in this thesis concerns the statistical modeling of precipitation amounts. Research in this area is currently very active because the precipitation distribution exhibits a heavy upper tail and, at the beginning of this thesis, there was no satisfactory method to model the full range of precipitation. Recently, a new class of parametric distribution, called the extended generalized Pareto distribution (EGPD), has been developed for this purpose. This distribution exhibits better performance, but it lacks flexibility in modeling the central part of the distribution. In order to improve the flexibility, we develop two new models based on semiparametric methods. The first estimator developed first transforms the data with the cumulative EGPD distribution and then estimates the density of the transformed data by applying a nonparametric kernel estimator. We compare the results of the proposed method with those obtained by applying the parametric EGPD distribution on several simulations, as well as on two precipitation series in southeast France. The results show that the proposed method performs better than the EGPD, with the mean integrated absolute error (MIAE) of the density being in all cases almost two times lower.The second model considers a semiparametric EGPD distribution based on Bernstein polynomials. More precisely, we use a hollow mixture of beta densities. Similarly, we compare our results with those obtained by the parametric EGPD distribution on simulated and real data sets. As before, the MIAE of the density is significantly reduced, this effect being even more evident as the sample size increases.