Modeling Monsoon‐Affected Rainfall of Pakistan by Point Processes

Abstract

Statistical analysis showed that monsoon reduced the variabilities of rainfall occurrences in Rechna Doab, an important agricultural region of Pakistan; but besides rainfall depths, it had little effect on other rainfall properties. Among the point‐process models explored, two continuous‐time models (Neyman‐Scott clustering or white noise [NSWN] and Rectangular Pulses models, [RPM]) and a discrete‐time model (Markov renewal [MRM]), NSWN is non‐Markovian, RPM is Markovian, and MRM is semi‐Markovian. Based on the variance ratio, variance at an arbitrary time scale to variance at daily time scale, none of the models calibrated (three out of six cases reported) was consistently better than others. However, after recalibrating them with data from six stations mixed together, only MRM predicted variance ratios that are consistent with their empirical counterparts. This is probably because MRM could account for the time discreteness of the rainfall sample process and accommodate data of high variabilities. Applying continuous point‐process models to time scales higher than daily and different from those used in calibration is discouraged, particularly the latter.