Persistence in Physical Systems: An Application to Soil Moisture Memory

Several physical variables and fluid systems exhibit memory effects arising from their internal dynamics and interactions with external forcings. Various existing techniques are either complex or face limitations due to the usual nonlinear nature of the time series, typically overestimating memory timescales. We overcome this by considering a nonparametric, model-free framework grounded in information theory, with methodological modifications to estimate memory timescales. We show that there is a good agreement between the estimated memory and the known Markov order of some synthetic time series. Leveraging this method, we analyzed observational and reanalysis datasets of soil moisture (SM) time series over India's core monsoon zone and quantified SM memory. Results indicate that SM behaves as a finitary, higher order Markov process, revealing a memory timescale of ∼35  days on core monsoon zone. The proposed treatment offers methodological simplicity and generalization beyond conventional linear approaches for analyzing stationary time series.