Abstract
We use the principle of maximum entropy to propose a parsimonious model for the generation of simulated rainfall during the wettest three-month season at a typical location on the east coast of Australia. The model uses a checkerboard copula of maximum entropy to model the joint probability distribution for total seasonal rainfall and a set of two-parameter gamma distributions to model each of the marginal monthly rainfall totals. The model allows us to match the grade correlation coefficients for the checkerboard copula to the observed Spearman rank correlation coefficients for the monthly rainfalls and, hence, provides a model that correctly describes the mean and variance for each of the monthly totals and also for the overall seasonal total. Thus, we avoid the need for a posteriori adjustment of simulated monthly totals in order to correctly simulate the observed seasonal statistics. Detailed results are presented for the modelling and simulation of seasonal rainfall in the town of Kempsey on the mid-north coast of New South Wales. Empirical evidence from extensive simulations is used to validate this application of the model. A similar analysis for Sydney is also described.
Highlights
We propose a model for seasonal rainfall using the principle of maximum entropy
This is one more reason why the calculation of a checkerboard copula of maximum entropy, as we propose in this paper, may be a more computationally efficient way to generate the required correlations
We argue that if we have a single sample of independently generated monthly rainfall totals and if only the sample mean of the observed values and the sample mean of the logarithm of the observed values are used as constraints on the model, the principle of maximum entropy tells us that the maximum likelihood gamma distribution is the best model for the random generation of monthly totals
Summary
We propose a model for seasonal rainfall using the principle of maximum entropy. There is consensus amongst climate scientists that summer and autumn rainfall in eastern Australia is influenced on a recurring basis by the quasi-periodic seasonal climatic events, El Niño and La. Niña. It is not especially surprising to find a positive correlation for monthly rainfall in Kempsey during the period. Our aim is to construct a parsimonious model for a vector-valued random variable X = (X1 , X2 , X3 ) ∈ R3 that can be used to simulate typical monthly rainfall time series for February-March-April in Kempsey. We will show that the key observed seasonal statistics lie well within the commonly accepted empirical confidence intervals established by repeated simulations with our proposed model. Our results show that even seemingly significant trends in the observed data could be due to chance alone
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
