Hurst scaling with crossover of a drought indicator: a case study in Belem and Manaus, Brazil

Humberto Millán (), Idalberto Macías and Jakeline Rabelo-Lima
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Humberto Millán: University of Granma
Idalberto Macías: Universidad Estatal Península de Santa Elena
Jakeline Rabelo-Lima: Amazonas State University

Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, 2022, vol. 110, issue 1, No 4, 69-93

Abstract: Abstract Some Amazonia regions are vulnerable to natural disasters. Hurst analysis of hydrological events can provide more information than classical statistical methods. The objectives of the present work were (1) to search for nonlinear signatures in rainfall and temperature using nonlinear time series methods and (2) to identify different Hurst scaling regimes in the Standardized Precipitation-Evapotranspiration Index (SPEI hereafter) at multiple resolutions using R/S analysis. Data sets of monthly rainfall and monthly mean temperature correspond to Belem (Pará state) and Manaus (Amazonas state), Brazil. The study covered a temporal scale of fifty-nine years (1961–2019). We selected 1-month, 3-month, 6-month, 9-month, 12-month, 24-month and 48-month SPEI timescales. The main analyses were conducted on detrended time series. Previous to rescaled range analysis (R/S hereafter) application, we explored nonlinear properties of each raw and residual time series through linear and nonlinear stationarity tests. Based on local means, the undetrended temperature and rainfall time series showed evidence of heteroscedasticity. Second-order statistics was stationary in all cases. Each rainfall and temperature time series showed deterministic components ranging from 0.78 to 0.83. Drought/extremely wet events are probably related to deterministic processes. We found two long-term correlation zones with scaling regimes separated by a crossover starting in March 1964. Short-scale regimes in SPEI1 to SPEI48 could be due to self-organized criticality or finite sample effect. Positive SPEI values can persist in Belem in the future, while memory effect of negative SPEI values in Manaus suggests trend-reinforcing of different drought types in the future.

Keywords: Determinism; Hurst scaling; Memory effect; Extreme events; Crossover (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11069-021-04937-w

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