Multivariate shift testing for hydrological variables, review, comparison and application

Hydrological frequency analysis (HFA) is commonly used for the assessment of the risk associated to hydrological events. HFA is generally based on the assumptions of homogeneity, independence and stationarity of the hydrological data. Hydrological events are often described through a number of dependent characteristics, such as peak, volume and duration for floods. Unfortunately, in this multivariate setting, the verification of the above assumptions is often neglected. When a shift occurs in a data series, it can affect the stationarity and the homogeneity of the data. The objective of this paper is to study tests for shift detection in multivariate hydrological data. The considered shift tests are mainly based on the notion of depth function, except for one test that is considered for comparison purposes. A simulation study is performed to evaluate and compare the power of all these tests with hydrological constraints. A flood analysis application is also carried out to show the practical aspects of the considered tests. The power of the considered tests is influenced by a number of factors, including the sample size, the shift amplitude, the magnitude of the series and the location of the shift in the series.