Stochastic Simulation Of Daily Rainfall Data Using Matched Block Bootstrap

Abstract

Characterizing the uncertainty in rainfall using stochastic models has been a challenging area of research in the field of operational hydrology for about half a century. Simulated sequences drawn from such models find use in a variety of hydrological applications. Traditionally, parametric models are used for simulating rainfall. But the parametric models are not parsimonious and have uncertainties associated with identification of model form, normalizing transformation, and parameter estimation. None of the models in vogue have gained universal acceptability among practising engineers. This may either be due to lack of confidence in the existing models, or the inability to adopt models proposed in literature because of their complexity or both. In the present study, a new nonparametric Matched Block Bootstrap (MABB) model is proposed for stochastic simulation of rainfall at daily time scale. It is based on conditional matching of blocks formed from the historical rainfall data using a set of predictors (conditioning variables) proposed for matching the blocks. The efficiency of the developed model is demonstrated through application to rainfall data from India, Australia, and USA. The performance of MABB is compared with two non-parametric rainfall simulation models, k-NN and ROG-RAG, for a site in Melbourne, Australia. The results showed that MABB model is a feasible alternative to ROG-RAG and k-NN models for simulating daily rainfall sequences for hydrologic applications. Further it is found that MABB and ROG-RAG models outperform k-NN model. The proposed MABB model preserved the summary statistics of rainfall and fraction of wet days at daily, monthly, seasonal and annual scales. It could also provide reasonable performance in simulating spell statistics. The MABB is parsimonious and requires less computational effort than ROG-RAG model. It reproduces probability density function (marginal distribution) fairly well due to its data driven nature. Results obtained for sites in India and U.S.A. show that the model is robust and promising.