Generating synthetic rainfall using a disaggregation model

Synthetic rainfall data has a large number of uses. Specifically, the behaviour of a reservoir under most scenarios can be best understood when evaluated using a large number of synthetic inputs. These synthetic values are all equally probable to occur but many of them may not have appeared in the historical record. Stochastic weather generators produce these synthetic data that were statistically equal to historical records. Different approaches have been used to generate synthetic rainfall data, Markov Chains being the most frequently used method. One of the major drawbacks of the current models is that when synthetically generated daily rainfall is aggregated into monthly totals, it fails to demonstrate all statistical properties of monthly series. The same could be seen in seasonal and annual series as well. The above drawback is very significant in preserving the variance of the series. Since daily rainfall is the basis of higher order synthetic rainfall series, the preservation of all statistical properties should be a pre-requisite for its application in numerous hydrological, ecological and agricultural contexts. A disaggregation rainfall model is presented in this paper that overcomes the drawbacks of earlier models, which could not produce coinciding statistical moments at all the time scales discussed above. In this model first a seasonal value is generated; followed by monthly values to tally with the seasonal total; and finally, daily values to tally with the monthly totals. Daily, monthly and seasonal rainfall have a skewed pattern, on [0,∞). A Gamma distribution is often used in the literature to generate rainfall amounts due to its similarity to the above pattern. However, some of the values generated using the Gamma distribution are high and unrealistic as it has no upper bound. Use of Beta distribution from the same family overcomes this limitation. Upper and lower limits are found using an Extreme Value distribution. The correlation structure of the rainfall differs with the place and time. When generating synthetic rainfall both the independent and correlated cases were considered. Spearman’s correlation coefficient is used to find the correlation structure in the seasonal and monthly rainfall values while a Markov Chain is used to capture the underlying correlation in the daily rainfall. The KolmogorovSmirnov statistical test is used to check whether the simulated and observed values have statistically indistinguishable cumulative probability distributions. The model is demonstrated using data from two locations, Hume in New South Wales and Pooraka in South Australia.