Deseasonalisation of hydrological time series through the normal quantile transform

A procedure for deseasonalising hydrological time series is presented which is based on applying the normal quantile transform (NQT). The scientific literature recently presented examples of utilisation of the NQT that makes the cumulative distribution function (CDF) of the transformed hydrological variable Gaussian. The technique proposed here assumes that the CDFs of variables that form a seasonal time series are non-stationary and periodic; hence the NQT formulation is allowed to be periodic as well. The year is divided into a number of non-overlapping periods, each one characterised by an individual expression for the NQT. The latter is estimated empirically by applying a robust approach that avoids abrupt changes of the transformation through time. The resulting transformed time series is characterised by a single, stationary CDF which is no longer affected by the periodicity. The proposed technique is applied to deseasonalise hydrographs of mean daily flows observed in Italy and the United States.