Alternative probabilistic exponential distributions for modelling rainfall intensity in Australia

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Conference Proceeding
MODSIM 2005 - International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, Proceedings, 2020, pp. 1709-1715
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© MODSIM 2005 - International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, Proceedings. All rights reserved. Most runoff and soil erosion models take into account rainfall intensity, since higher storm intensities lead to greater runoff and losses of soil due to erosion. Accurate prediction of soil erosion requires rainfall intensity data with a high temporal resolution. This places a restriction on the simulation of soil erosion, since high temporal resolution data are usually not available. One way to overcome this problem is to synthesise storms using a stochastic rainfall intensity distribution. It has been common for past authors to employ an exponential relationship between rainfall intensity and the frequency of occurrence of that rainfall intensity. The motivation for using an exponential relationship between rainfall intensity and its frequency is based on the log-normal distribution for the recurrence interval between various rainfall depth and duration measurements. For those authors assuming an exponential relationship between rainfall intensity and its frequency, it has been traditional to formulate the distribution in terms of the amount of time for which rain falls at a particular intensity. The drawback of this approach is that the parameter for this distribution is strongly influenced by rain falling at a low intensity over long periods of time. Clearly this type of rainfall has little impact on runoff and soil erosion rates. An alternative distribution for simulating rainfall intensity has been proposed that considers the depth of rain that falls at a particular intensity, rather than the duration for which rain falls at a particular intensity. The advantage of this formulation for simulating the temporal pattern of rainfall is that this distribution's single parameter is strongly influenced by high rainfall intensity. In addition, parameter values for the proposed distribution can be readily estimated using intensity data collected with tipping bucket rain gauges. The question that motivated this research was which of the two distributions better simulates rainfall intensity data over a range of Australian climates? It thus follows that the aim of this paper was to test two exponential probabilistic rainfall intensity distributions, one in the time domain and the other in the rainfall domain. Ten sites were considered in this work, namely; Adelaide, Alice Springs, Brisbane, Cairns, Canberra, Darwin, Hobart, Melbourne, Perth and Sydney. The two distributions were compared in terms of goodness of fit via the Kolmogorov-Smirnov test statistic. The Kolmogorov-Smirnov test was used to perform all goodness of fit assessments, since it does not assume a distributional form for its test statistic. In addition, the Kolmogorov-Smirnov test possesses a higher power relative to the chi-square test. Based on comparison of the p-values for each of the distribution fits, the rainfall domain distribution provided a superior fit than the duration domain distribution for almost all of the three hundred fits. A paired t-test testing for equality between the mean number of null hypothesis acceptances for each site and for both distributions was found to be highly significant. Storm depth at high rainfall intensity tended to be predicted more accurately with the rainfall domain distribution then was storm duration with the duration domain distribution. It should be mentioned however, that a rigorous test of goodness of fit at high rainfall intensity was outside the scope of this study and hence was not considered. The results of this study have implications for the simulation of runoff and soil erosion, since this new distribution can replicate rainfall intensity data with greater accuracy and should lead to improved runoff and soil erosion models.
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