Maximum entropy methods for generating simulated rainfall

Julia Piantadosi; Phil Howlett; Jonathan Borwein; John Henstridge

doi:10.3934/naco.2012.2.233

Article Contents

2012, Volume 2, Issue 2: 233-256. Doi: 10.3934/naco.2012.2.233

This issue Previous Article On a family of means generated by the Hardy-Littlewood maximal inequality Next Article On Markovian solutions to Markov Chain BSDEs

Maximum entropy methods for generating simulated rainfall

1.
Centre for Industrial and Applied Mathematics, Mawson Lakes Campus, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, 5095
2.
Centre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308
3.
Data Analysis Australia Pty Ltd, School of Mathematics and Statistics, University of Western Australia, Crawley WA, 6009

Received: September 2011

Revised: March 2012

Published: May 2012

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Abstract

We desire to generate monthly rainfall totals for a particular location in such a way that the statistics for the simulated data match the statistics for the observed data. We are especially interested in the accumulated rainfall totals over several months. We propose two different ways to construct a joint rainfall probability distribution that matches the observed grade correlation coefficients and preserves the prescribed marginal distributions. Both methods use multi-dimensional checkerboard copulas. In the first case we use the theory of Fenchel duality to construct a copula of maximum entropy and in the second case we use a copula derived from a multi-variate normal distribution. Finally we simulate monthly rainfall totals at a particular location using each method and analyse the statistical behaviour of the corresponding quarterly accumulations.

Keywords:

Mathematics Subject Classification: Primary: 15B51, 60E05, 65C05; Secondary: 52A41.

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