A random walk on water

Koutsoyiannis, D., A random walk on water, Hydrology and Earth System Sciences, 14, 585–601, 2010.



According to the traditional notion of randomness and uncertainty, natural phenomena are separated into two mutually exclusive components, random (or stochastic) and deterministic. Within this dichotomous logic, the deterministic part supposedly represents cause-effect relationships and, thus, is physics and science (the “good”), whereas randomness has little relationship with science and no relationship with understanding (the “evil”). Here I argue that such views should be reconsidered by admitting that uncertainty is an intrinsic property of nature, that causality implies dependence of natural processes in time, thus suggesting predictability, but even the tiniest uncertainty (e.g., in initial conditions) may result in unpredictability after a certain time horizon. On these premises it is possible to shape a consistent stochastic representation of natural processes, in which predictability (suggested by deterministic laws) and unpredictability (randomness) coexist and are not separable or additive components. Deciding which of the two dominates is simply a matter of specifying the time horizon and scale of the prediction. Long horizons of prediction are inevitably associated with high uncertainty, whose quantification relies on the long-term stochastic properties of the processes.

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Erratum in p. 589, left column, around the middle: the line "Eq. (1) (but not in Eq. (1), which represents..." should read "Eq. (2) (but not in Eq. (1), which represents...".

Our works referenced by this work:

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Our works that reference this work:

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Tagged under: Course bibliography: Hydrometeorology, Course bibliography: Stochastic methods, Climate stochastics, Determinism vs. stochasticity, Works discussed in weblogs, Entropy, Hurst-Kolmogorov dynamics, Scaling, Stochastics, Uncertainty