Can a simple stochastic model generate rich patterns of rainfall events?

Papalexiou, S.M., D. Koutsoyiannis, and A. Montanari, Can a simple stochastic model generate rich patterns of rainfall events?, Journal of Hydrology, 411 (3-4), 279–289, 2011.



Several of the existing rainfall models involve diverse assumptions, a variety of uncertain parameters, complicated mechanistic structures, use of different model schemes for different time scales, and possibly classifications of rainfall patterns into different types. However, the parsimony of a model is recognized as an important desideratum as it improves its comprehensiveness, its applicability and possibly its predictive capacity. To investigate the question if a single and simple stochastic model can generate a plethora of temporal rainfall patterns, as well as to detect the major characteristics of such a model (if it exists), a data set with very fine timescale rainfall is used. This is the well-known data set of the University of Iowa comprising measurements of seven storm events at a temporal resolution of 5-10 seconds. Even though only seven such events have been observed, their diversity can help investigate these issues. An evident characteristic resulting from the stochastic analysis of the events is the scaling behaviours both in state and in time. Utilizing these behaviours, a stochastic model is constructed which can represent all rainfall events and all rich patterns, thus suggesting a positive reply to the above question. In addition, it seems that the most important characteristics of such a model are a power-type distribution tail and an asymptotic power-type autocorrelation function. Both power-type distribution tails and autocorrelation functions can be viewed as properties enhancing randomness and uncertainty, or entropy.

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Our works referenced by this work:

1. Koutsoyiannis, D., A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series, Water Resources Research, 36 (6), 1519–1533, 2000.
2. Koutsoyiannis, D., The Hurst phenomenon and fractional Gaussian noise made easy, Hydrological Sciences Journal, 47 (4), 573–595, 2002.
3. Koutsoyiannis, D., Climate change, the Hurst phenomenon, and hydrological statistics, Hydrological Sciences Journal, 48 (1), 3–24, 2003.
4. Koutsoyiannis, D., Statistics of extremes and estimation of extreme rainfall, 1, Theoretical investigation, Hydrological Sciences Journal, 49 (4), 575–590, 2004.
5. Koutsoyiannis, D., Statistics of extremes and estimation of extreme rainfall, 2, Empirical investigation of long rainfall records, Hydrological Sciences Journal, 49 (4), 591–610, 2004.
6. Koutsoyiannis, D., Uncertainty, entropy, scaling and hydrological stochastics, 1, Marginal distributional properties of hydrological processes and state scaling, Hydrological Sciences Journal, 50 (3), 381–404, 2005.
7. Koutsoyiannis, D., Uncertainty, entropy, scaling and hydrological stochastics, 2, Time dependence of hydrological processes and time scaling, Hydrological Sciences Journal, 50 (3), 405–426, 2005.
8. Koutsoyiannis, D., An entropic-stochastic representation of rainfall intermittency: The origin of clustering and persistence, Water Resources Research, 42 (1), W01401, doi:10.1029/2005WR004175, 2006.
9. Koutsoyiannis, D., On the quest for chaotic attractors in hydrological processes, Hydrological Sciences Journal, 51 (6), 1065–1091, 2006.
10. Koutsoyiannis, D., and A. Montanari, Statistical analysis of hydroclimatic time series: Uncertainty and insights, Water Resources Research, 43 (5), W05429, doi:10.1029/2006WR005592, 2007.
11. Koutsoyiannis, D., H. Yao, and A. Georgakakos, Medium-range flow prediction for the Nile: a comparison of stochastic and deterministic methods, Hydrological Sciences Journal, 53 (1), 142–164, 2008.
12. Koutsoyiannis, D., A. Montanari, H. F. Lins, and T.A. Cohn, Climate, hydrology and freshwater: towards an interactive incorporation of hydrological experience into climate research—DISCUSSION of “The implications of projected climate change for freshwater resources and their management”, Hydrological Sciences Journal, 54 (2), 394–405, 2009.
13. Koutsoyiannis, D., A random walk on water, Hydrology and Earth System Sciences, 14, 585–601, 2010.
14. 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.

Our works that reference this work:

1. Lombardo, F., E. Volpi, and D. Koutsoyiannis, Rainfall downscaling in time: Theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades, Hydrological Sciences Journal, 57 (6), 1052–1066, 2012.
2. Koutsoyiannis, D., Entropy: from thermodynamics to hydrology, Entropy, 16 (3), 1287–1314, 2014.
3. Dimitriadis, P., D. Koutsoyiannis, and K. Tzouka, Predictability in dice motion: how does it differ from hydrometeorological processes?, Hydrological Sciences Journal, doi:10.1080/02626667.2015.1034128, 2015.
4. Dimitriadis, P., D. Koutsoyiannis, and P. Papanicolaou, Stochastic similarities between the microscale of turbulence and hydrometeorological processes, Hydrological Sciences Journal, doi:10.1080/02626667.2015.1085988, 2015.
5. Koutsoyiannis, D., Generic and parsimonious stochastic modelling for hydrology and beyond, Hydrological Sciences Journal, 61 (2), 225–244, doi:10.1080/02626667.2015.1016950, 2016.
6. Iliopoulou, T., S.M. Papalexiou, Y. Markonis, and D. Koutsoyiannis, Revisiting long-range dependence in annual precipitation, Journal of Hydrology, doi:10.1016/j.jhydrol.2016.04.015, 2016.

Other works that reference this work:

1. Resta, M., Hurst exponent and its applications in time-series analysis, Recent Patents on Computer Science, 5 (3), 211-219, 2012.
2. Kane, I. L., and F. Yusof, Assessment of risk of rainfall events with a hybrid of ARFIMA-GARCH, Modern Applied Science, 7 (12), 78-89, 2013.
3. #Majumder, M., and R.N. Barman, Application of artificial neural networks in short-term rainfall forecasting, Application of Nature Based Algorithm in Natural Resource Management, 43-58, 2013.
4. Brigode, P., P. Bernardara, E. Paquet, J. Gailhard, F. Garavaglia, R. Merz, Z. Mic̈ovic̈, D. Lawrence and P. Ribstein, Sensitivity analysis of SCHADEX extreme flood estimations to observed hydrometeorological variability, Water Resources Research, 50 (1), 353-370, 2014.
5. Kormos, P.R., J.P. McNamara, M.S. Seyfried, H.P. Marshall, D. Marks and A.N. Flores, Bedrock infiltration estimates from a catchment water storage-based modeling approach in the rain snow transition zone, Journal of Hydrology, 525, 231-248, 2015.

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