Stochastic spatial-temporal models for rainfall processes

Abstract

© 2018 Dr. Nanda Ram AryalCurrently clustered rainfall models have been fitted using Generalized Method of Moments (GMM), because typically they have intractable likelihood func- tions. GMM fitting matches theoretical and observed moments of the process and thus is restricted to models for which analytic expressions are available for the moments. We show that Approximate Bayesian Computation (ABC) can also be used to fit clustered rainfall models. We also validate that ABC readily adapts to more general, and thus more realistic, variants of spatial- temporal rainfall models. ABC fitting compares the observed process with simulations and hence places no restrictions on the statistics used for the comparison. This opens up the possibility of fitting much more realistic stochastic rainfall models. The penalty we pay for this increased flexibility is an increase in computational time. Simulated Method of Moments (SMM) is used to initialize the ABC. This can also be used to estimate the weights of the distance measure in the ABC-MCMC setting. We found that our method requires much smaller computation time in comparison with what previous authors have suggested using a separate ABC step to estimate initialisation. A spatial-temporal rainfall model based on a cluster process is constructed by taking a primary process, called the storm arrival process, and attaching to each storm centre a finite secondary process, called a cell process. The total intensity at a point in R2 × [0, ∞) is the sum of the intensities of all cells active at that point. Typically, the model parameters are interde- pendent.This dependency produces complexity in model fitting procedures, and has also restricted further extension of the model, particularly finding theoretical expressions for the moments. Fortunately, ABC can be applied without having analytical expressions for the moments. We reparameterized the models and the parameters were log transformed to reduce dependence and skewness, also simplifies the chain proposal in MCMC steps. We also present two new stochastic spatial-temporal rainfall models that yield with better representation of observed rainfall processes, and also cap- ture the dependence between size and intensity for rain cells