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[1] This article presents the modeling of multivariate extreme values using copulas. Our approach allows us to model the dependence structure independently of the marginal distributions, which is not possible with standard classical methods. The methodology has been applied on two different problems in hydrology. The first application is concerned with the combined risk in the framework of frequency analysis. Four copulas have been tested on peak flows from the watershed of Peribonka in Québec, Canada. The second application relates to the joint modeling of peak flows and volumes. Three copulas have been applied to the watershed of the Rimouski River in Québec, Canada. This approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology.

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[1] The objective of the present study is to develop efficient estimation methods for the use of the GEV distribution for quantile estimation in the presence of nonstationarity. Parameter estimation in the nonstationary GEV model is generally done with the maximum likelihood estimation method (ML). In this work, we develop the generalized maximum likelihood estimation method (GML), in which covariates are incorporated into parameters. A simulation study is carried out to compare the performances of the GML and the ML methods in the case of the stationary GEV model (GEV0), the nonstationary case with a linear dependence of the location parameter on covariates (GEV1), the nonstationary case with a quadratic dependence on covariates (GEV2), and the nonstationary case with linear dependence in both location and scale parameters (GEV11). Simulation results show that the GLM method performs better than the ML method for all studied cases. The nonstationary GEV model is also applied to a case study to illustrate its potential. The case study deals with the annual maximum precipitation at the Randsburg station in California, and the covariate process is taken to be the Southern Index Oscillation.

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The use of statistical models to simulate or to predict stream water temperature is becoming an increasingly important tool in water resources and aquatic habitat management. This article provides an overview of the existing statistical water temperature models. Different models have been developed and used to analyze water temperature-environmental variables relationship. These are grouped into two major categories: deterministic and statistical/stochastic models. Generally, deterministic models require numerous input data (e.g., depth, amount of shading, wind velocity). Hence, they are more appropriate for analyzing different impact scenarios due to anthropogenic effects (e.g., presence of reservoirs, thermal pollution and deforestation). In contrast to the deterministic models, the main advantage of the statistical models is their relative simplicity and relative minimal data requirement. Parametric models such as linear and non-linear regression are popular methods often used for shorter time scales (e.g., daily, weekly). Ridge regression presents an advantage when the independent variables are highly correlated. The periodic models present advantages in dealing with seasonality that often exists in periodic time series. Non-parametric models (e.g., k-nearest neighbours, artificial neural networks) are better suited for analysis of nonlinear relationships between water temperature and environmental variables. Finally, advantages and disadvantages of existing models and studies are discussed.