Testing for multivariate trends in hydrologic frequency analysis

Hydrological frequency analysis (HFA) relies on a number of assumptions on the data series, especially independence, homogeneity and stationarity. In the univariate setting, these assumptions are generally checked before the modeling step. During the last decade, multivariate HFA approaches have gained popularity since most hydrological events can be described through a number of dependent characteristics, e.g. peak, volume and duration for floods. However, checking the above assumptions remains neglected in the multivariate HFA literature whereas the focus is directly on the modeling. For a reliable analysis and accurate results, these assumptions should also be checked prior to modeling in the multivariate setting. The present paper attempts to start bridging this gap in the multivariate HFA by highlighting the importance of the testing step and focusing on the review and application of nonparametric tests for monotonic trends. The presented multivariate trend tests are usually developed and employed to treat water quality data. In the present work, two types of multivariate applications are performed, multi-variable for flood attributes and multi-site for different locations. The results indicate that, in both types of applications, the univariate and multivariate tests led to the detection of different trend signals. It is hence recommended to jointly apply univariate and multivariate trend tests in order to capture all existing trend components and guide the user towards the appropriate models.