Mixed memory, (non) Hurst effect, and maximum entropy of rainfall in the tropical Andes

摘要: Abstract Diverse linear and nonlinear statistical parameters of rainfall under aggregation in time the kind temporal memory are investigated. Data sets from Andes Colombia at different resolutions (15 min 1-h), record lengths (21 months 8–40 years) used. A mixture two timescales is found autocorrelation autoinformation functions, with short-term holding for lags less than 15–30 min, long-term onwards. Consistently, variance exhibits scaling regimes separated 15–30 min 24 h. Tests Hurst effect evidence frailty R / S approach discerning high resolution rainfall, whereas rigorous tests short-memory processes do reject existence effect. Rainfall information entropy grows as a power law time, ( T ) ∼  β 〈 〉 = 0.51, up to timescale, MaxEnt (70–202 h), which saturates,  = 0 Maximum reached through dynamic Generalized Pareto distribution, consistently maximum information-entropy principle heavy-tailed random variables, its asymptotically infinitely divisible property. The dynamics towards limit distribution quantified. Tsallis q -entropies also exhibit laws , such that ) ) ⩽ 0  ⩽ 0, ) ≃ 0.5  ⩾ 1. No clear patterns geographic within among studied, confirming strong variability tropical Andean rainfall.