A nonparametric nonhomogeneous hidden Markov model for downscaling of multisite daily rainfall occurrences

Abstract

A K‐nearest‐neighbor (KNN)‐based nonparametric nonhomogenous hidden Markov model is developed and applied for spatial downscaling of multistation daily rainfall occurrences using four atmospheric circulations variables (mean sea level pressure (MSLP), east‐west gradient of MSLP, north‐south gradient of geopotential height at 700 hPa, and total precipitable water content) over a network of 30 rain gauge stations near Sydney, Australia. The proposed model generates rainfall occurrence conditional to a continuous weather state and the average rainfall occurrence over the previous day. The current day weather state is defined conditional to the previous day weather state and selected atmospheric variables. For each day a weather state is specified on the basis of the spatial rainfall occurrence distribution over the study region. The spatial rainfall distribution is represented on the basis of the wetness fraction for the region and its location from a fixed origin. The relative influence of each predictor variable on the conditional probability density function is ascertained by including an influence weight in the distance calculation. The influence weights are optimized by maximizing the likelihood score in leave‐one‐out cross validation. Rainfall occurrences at stations are estimated in a leave‐6‐years‐out cross validation using the optimized influence weights. Results from the proposed model are compared with the weather state–based parametric nonhomogeneous hidden Markov model (NHMM) and a standard KNN model. Results of the study show that introduction of a weather state in KNN simplifies the representation of spatial rainfall distribution structure, while conditioning on the atmospheric variables and previous day weather state helps represent the temporal structure of the rainfall process over the study region. The continuous weather states adopted in the proposed model are more successful in capturing the day‐to‐day rainfall characteristics in comparison to discrete state NHMM. The grouping of continuous weather states into a few discrete categories is shown to correspond to the dominant synoptic‐scale features of rainfall distribution.