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

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

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[English]

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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See also: http://dx.doi.org/10.1016/j.jhydrol.2010.12.012

Our works referenced by this work:

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15. Tyralis, H., and D. Koutsoyiannis, Simultaneous estimation of the parameters of the Hurst-Kolmogorov stochastic process, Stochastic Environmental Research & Risk Assessment, 25 (1), 21–33, 2011.
16. Koutsoyiannis, D., and A. Langousis, Precipitation, Treatise on Water Science, edited by P. Wilderer and S. Uhlenbrook, 2, 27–78, Academic Press, Oxford, 2011.

Our works that reference this work:

1. Lombardo, F., 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, 2014.

Other works that reference this work:

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.
2. Resta, M., Hurst exponent and its applications in time-series analysis, Recent Patents on Computer Science, 5 (3), 211-219, 2012.
3. De Michele, C., and M. Ignaccolo, New perspectives on rainfall from a discrete view, Hydrological Processes, 10.1002/hyp.9782, 2013.
4. van den Berg, M. J., L. Delobbe and N. E. C. Verhoest, Imperfect scaling in distributions of radar-derived rainfall fields, Hydrol. Earth Syst. Sci. Discuss., 10, 11385-11422, 10.5194/hessd-10-11385-2013, 2013.
5. Paschalis, A., P. Molnar, S. Fatichi and P. Burlando, A stochastic model for high resolution space‐time precipitation simulation, Water Resources Research, 49 (12), 8400-8417, 2013.
6. Paschalis, A., P. Molnar, S. Fatichi and P. Burlando, On temporal stochastic modeling of precipitation, nesting models across scales, Advances in Water Resources, 63, 152-166, 2014.

Tagged under: Hurst-Kolmogorov dynamics, Rainfall models, Stochastics