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Selection of the best fit probability distributions for temperature data and the use of L-moment ratio diagram method: a case study for NSW in Australia

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Abstract

This paper explores different goodness-of-fit (GOF) criteria’s used in the various fields of science to compare candidate probability density functions (pdfs) to annual maximum temperature records and discusses their usefulness and drawbacks. The L-moment ratio diagram method is also proposed as alternative approach for the GOF of the pdfs. The advantage this method allows for an easy comparison of the fit of many pdfs for several stations on a single diagram. To gain knowledge about higher order moments (i.e. shape, skewness and kurtosis) of the station data set, plotting the position of a given temperature data set in L-moment ratio diagram space is prompt and effective and can provide a useful addition to the GOF criterion. Both the L-moment ratio diagrams and many GOF criteria are used on real data to assess the fit of the pdfs for temperature data in the state of New South Wales, Australia. The analysis of the L-moment ratio diagrams reveals that the generalized extreme value and normal distributions generally fit best the annual maximum temperature series. The other two- and three-parameter distributions also showed viable fits in some instances. Results obtained from L-moment diagrams, temperature frequency histograms, cumulative density plots and the simulation study are compared with those obtained from GOF statistics, and a good agreement is generally observed between all these approaches. In conclusion the L-moment ratio diagram can represent a simple, effective and efficient approach to be used as a complementary method along with the traditional GOF criteria.

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Acknowledgments

The author would like to thank the Bureau of Meteorology, Australia, for their website where the data for this study was obtained.

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  1. Cumberland Council, 16 Memorial Avenue, P.O. Box 42, Merrylands, NSW, 2160, Australia

    Khaled Haddad

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Appendix

Appendix

Fig. 9
figure 9

Temperature frequency histogram and CDF plot for station Bathurst. a Two-parameter distribution. b Three-parameter distribution

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Fig. 10
figure 10

Temperature frequency histogram and CDF plot for station Parramatta. a Two-parameter distribution. b Three-parameter distribution

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Fig. 11
figure 11

Temperature frequency histogram and CDF plot for station Sydney. a Two-parameter distribution. b Three-parameter distribution

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Fig. 12
figure 12

Temperature frequency histogram and CDF plot for station Liverpool. a Two-parameter distribution. b Three-parameter distribution

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Fig. 13
figure 13

Temperature frequency histogram and CDF plot for station Wollongong. a Two-parameter distribution. b Three-parameter distribution

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Haddad, K. Selection of the best fit probability distributions for temperature data and the use of L-moment ratio diagram method: a case study for NSW in Australia. Theor Appl Climatol 143, 1261–1284 (2021). https://doi.org/10.1007/s00704-020-03455-2

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