Two-dimensional Hurst-Kolmogorov process and its application to rainfall fields

D. Koutsoyiannis, A. Paschalis, and N. Theodoratos, Two-dimensional Hurst-Kolmogorov process and its application to rainfall fields, Journal of Hydrology, 398 (1-2), 91–100, doi:10.1016/j.jhydrol.2010.12.012, 2011.



The Hurst-Kolmogorov (HK) dynamics has been well established in stochastic representations of the temporal evolution of natural processes, yet many regard it as a puzzle or a paradoxical behaviour. As our senses are more familiar with spatial objects rather than time series, understanding the HK behaviour becomes more direct and natural when the domain of our study is no longer the time but the two-dimensional space. Therefore, here we detect the presence of HK behaviour in spatial hydrological and generally geophysical fields including Earth topography, and precipitation and temperature fields. We extend the one-dimensional HK process into two dimensions and we provide exact relationships of its basic statistical properties and closed approximations thereof. We discuss the parameter estimation problem, with emphasis on the associated uncertainties and biases. Finally, we propose a two-dimensional stochastic generation scheme, which can reproduce the HK behaviour and we apply this scheme to generate rainfall fields, consistent with the observed ones.

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Our works referenced by this work:

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Our works that reference this work:

1. F. Lombardo, E. Volpi, D. Koutsoyiannis, and S.M. Papalexiou, Just two moments! A cautionary note against use of high-order moments in multifractal models in hydrology, Hydrology and Earth System Sciences, 18, 243–255, doi:10.5194/hess-18-243-2014, 2014.
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3. D. Koutsoyiannis, Knowable moments for high-order stochastic characterization and modelling of hydrological processes, Hydrological Sciences Journal, 64 (1), 19–33, doi:10.1080/02626667.2018.1556794, 2019.
4. G.-F. Sargentis, P. Dimitriadis, R. Ioannidis, T. Iliopoulou, and D. Koutsoyiannis, Stochastic evaluation of landscapes transformed by renewable energy installations and civil works, Energies, 12 (4), 2817, doi:10.3390/en12142817, 2019.
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6. D. Koutsoyiannis, Stochastics of Hydroclimatic Extremes - A Cool Look at Risk, Edition 2, ISBN: 978-618-85370-0-2, 346 pages, doi:10.57713/kallipos-1, Kallipos Open Academic Editions, Athens, 2022.

Works that cite this document: View on Google Scholar or ResearchGate

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1. Montanari, A., Hydrology of the Po River: looking for changing patterns in river discharge, Hydrology and Earth System Sciences, 16, 3739-3747, doi:10.5194/hess-16-3739-2012, 2012.
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Tagged under: Hurst-Kolmogorov dynamics, Rainfall models, Stochastics, Students' works