On modeling the maximum duration of dry spells: a simulation study under a Bayesian approach
Dry spell and drought are hydrological phenomena with serious socioeconomic effects and, despite recent efforts, substantial scientific and statistical comprehension are still lacking—especially when considering their extreme events. Such events are usually modeled using the generalized extreme value (GEV) distribution, whose prediction performance, at least under a Bayesian approach, remain poorly understood when fitted to a discrete series (the simplest way to record dry spell occurrence and duration). Thus, in this study, we aim at evaluating point and interval prediction performances of the GEV distribution when fitted to dry spell data, using computer simulations of different realistic scenarios (variations in the number of days per dry spells, number of dry spells per year, sample sizes, and available prior information). While sample size increase produced generally expected results over point performance (i.e., stronger bias in small samples), counterintuitive patterns arose when we evaluated the accuracy of prediction credible intervals. We also found a positive correlation between prediction bias and the GEV shape parameter estimate, a fact we believe to be related to the discrete nature of the data. Furthermore, we noticed the best interval performances occurred in increasing levels of information rendered by prior distributions. Finally, we consider all these results to be general enough to apply to different extreme discrete phenomena, since we found no effect of neither the duration nor the frequency of dry spells. Although typical issues in discrete data (e.g., overdispersion) and time series data (e.g., trend) should be considered in future investigations, one must be aware that whenever attempting to fit dry spell duration series to the GEV distribution in the absence of substantial prior information will frequently lead to underestimated predictions—the worst kind for dry spell strategic management—which may further compromise scientists, practitioners, and their community responsibilities.
The authors thank Mr. Fábio F. Marchetti for his kind and insightful considerations.
This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.
- Assis JMO (2012) Análise de tendências de mudanças climáticas no semiárido de Pernambuco 166Google Scholar
- Geweke J (1992) Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds) Bayesian statistics 4. Clarendon Press, Oxford, p 859Google Scholar
- IBGE (2010) Brazilian socio-economic database. In: Munic. Soc. Indic. https://goo.gl/kS64D6. Accessed 10 Sep 2017
- IBGE (2013) Brazilian socio-economic database. In: Vectorial SHP files Polit. Div. Brazil (in Port. https://goo.gl/JDuRiA. Accessed 17 Aug 2018
- McKee T, Doesken NJ, Kleist J (1993) The relationship of drought frequency and duration to time scales. 179–184Google Scholar
- Paixão Junior BR, Estrela F, Cruz G, Lima M (2010) CodeGeo. In: Brazil shapefiles download (in Port. https://goo.gl/qkfPCp. Accessed 17 Aug 2018
- Pasarić Z, Cindrić K (2018) Generalised Pareto distribution: impact of rounding on parameter estimation. Theor Appl Climatol. https://doi.org/10.1007/s00704-018-2494-5
- Pérez-Sánchez J, Senent-Aparicio J (2017) Analysis of meteorological droughts and dry spells in semiarid regions: a comparative analysis of probability distribution functions in the Segura Basin (SE Spain). Theor Appl Climatol 133:1–14. https://doi.org/10.1007/s00704-017-2239-x CrossRefGoogle Scholar
- Plummer M, Best N, Cowles K, Vines K (2006) CODA: convergence diagnosis and output analysis for MCMC. R News 6:7–11Google Scholar
- R Core Team (2017) R: a language and environment for statistical computingGoogle Scholar
- Smith RL (2003) Statistics of extremes, with applications in environment, insurance and finance. In: Finkenstadt B, Rootzen H (eds) Extreme values in finance, telecommunications, and the environment, 1st edn. Chapman and Hall/CRC, pp 1–78Google Scholar
- Stephenson AG (2002) evd: extreme value distributions. R News 2:31–32Google Scholar
- Vicente-Serrano SM, Beguería-Portugués S (2003) Estimating extreme dry-spell risk in the middle Ebro valley (northeastern Spain): a comparative analysis of partial duration series with a general Pareto distribution and annual maxima series with a Gumbel distribution. Int J Climatol 23:1103–1118. https://doi.org/10.1002/joc.934 CrossRefGoogle Scholar