Return period analysis of weakly non-stationary processes with trends

Abstract. Traditional return period analysis represents an essential tool for practitioners to assess the magnitude and occurrence of extreme events. The analysis considers stationary time series and assumes independent and identically distributed events. However, many environmental processes exhibit time-varying changes due to signal trends or shifts, leading to non-stationary behaviors. Although several approaches have been proposed in the literature and a formulation exists for the return period under non-stationarity, its practical use is often hampered by the high computational time. This work proposes a novel framework to estimate the return period by extending the simpler stationary formulation to weakly non-stationary processes, whose definition is derived by imposing a condition that limits the maximum change of the return period over a given timeframe. We rely on the General Extreme Value (GEV) distribution, allowing for time-varying parameters due to signal trends. The approach yields closed-form solutions for the maximum permitted trends in the GEV parameters (mean, variance, frequency, or magnitude) satisfying the weak non-stationarity hypothesis. Specific attention is paid to the case of the Gumbel distribution, for which the limit solutions are derived for the case of linear trends. We show that the approximation error is minor (approximately 5 % for the best tested parameters), compared to the more complex fully non-stationary solution, thus making the proposed framework a computationally efficient tool for practitioners.