Non-parametric Kernel-Based Estimation of Probability Distributions for Precipitation Modeling
This work addresses the need for flexible and accurate precipitation modeling in climatology and hydrology, though it is incremental as it builds on existing kernel density estimation techniques.
The authors tackled the problem of accurately modeling precipitation probability distributions across different time scales by deriving non-parametric kernel-based cumulative distribution function (CDF) estimates, showing that their adaptive plug-in bandwidth method (KCDE) provides better estimates than standard empirical and kernel-based approaches using synthetic and real data from Crete.
The probability distribution of precipitation amount strongly depends on geography, climate zone, and time scale considered. Closed-form parametric probability distributions are not sufficiently flexible to provide accurate and universal models for precipitation amount over different time scales. In this paper we derive non-parametric estimates of the cumulative distribution function (CDF) of precipitation amount for wet periods. The CDF estimates are obtained by integrating the kernel density estimator leading to semi-explicit CDF expressions for different kernel functions. We investigate an adaptive plug-in bandwidth (KCDE), using both synthetic data sets and reanalysis precipitation data from the Mediterranean island of Crete (Greece). We show that KCDE provides better estimates of the probability distribution than the standard empirical (staircase) estimate and kernel-based estimates that use the normal reference bandwidth. We also demonstrate that KCDE enables the simulation of non-parametric precipitation amount distributions by means of the inverse transform sampling method.