The unscented Kalman filter (UKF)-based algorithm for regional frequency analysis of extreme rainfall events in a nonstationary environment

Abstract

In regional frequency analysis, extreme rainfall patterns in a nonstationary environment are characterized by the time-dependent regional growth curves, in which location and scale parameters are the weighted values of at-site estimates from the sites within a homogeneous group. However, under different climate change scenarios, the monotonic trend assumption about these two regional growth curve parameters can be questionable. To consider the non-monotonic change behavior of extreme rainfall events in regional frequency analysis, an unscented Kalman filter-based regional approach is proposed for location, scale and shape parameters estimation using the scaled datasets within a homogeneous group at different temporal states or periods. To consider nonlinear relationships for the parameters in state transition function (STF) and measurement function (MF) between sequential temporal periods, the unscented Kalman filter (UKF) is applied for the filtering of state estimates in the proposed methodology. To avoid the degradation of UKF performance which is caused by inaccurate state and measurement noise covariances, a Monte Carlo simulation-based procedure is proposed for their noise estimations. To reduce the parameter uncertainty associated with the distribution fitting process and consider the spatial correlations amongst the stations within a homogeneous group, balancing resamples are used to improve state estimates in regional frequency analysis. This UKF-based approach addresses the non-monotonic change behavior of the extreme rainfall events in a nonstationary environment, and fills the gap of considering spatial correlation for dynamic state estimation in regional frequency analysis. This proposed methodology was successfully applied to three homogeneous groups in Canada, and goodness-of-fit tests were used to validate the parameter estimates and prove the superiority over traditional covariate approach for providing effective rainfall quantile estimates in the upper tail of the distribution.