Stochastic similarities between the microscale of turbulence and hydrometeorological processes

P. Dimitriadis, D. Koutsoyiannis, and P. Papanicolaou, Stochastic similarities between the microscale of turbulence and hydrometeorological processes, Hydrological Sciences Journal, 61 (9), 1623–1640, doi:10.1080/02626667.2015.1085988, 2016.



Turbulence is considered to generate and drive most geophysical processes. The simplest case is the isotropic turbulence. In this paper, the most common three-dimensional power-spectrum-based models of isotropic turbulence are studied in terms of their stochastic properties. Such models often have a high-order of complexity, lack in stochastic interpretation and violate basic stochastic asymptotic properties, such as the theoretical limits of the Hurst coefficient, in case that Hurst-Kolmogorov behaviour is observed. A simpler and robust model (which incorporates self-similarity structures, e.g. fractal dimension and Hurst coefficient) is proposed using a climacogram-based stochastic framework and tested over high resolution observational data of laboratory scale as well as hydrometeorological observations of wind speed and precipitation intensities. Expressions of other stochastic tools like the autocovariance and power spectrum are also produced from the model and show agreement with data. Finally, uncertainty, discretization and bias related errors are estimated for each stochastic tool, showing lower errors for the climacogram-based ones and larger for power-spectrum ones.

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Our works referenced by this work:

1. D. Koutsoyiannis, A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series, Water Resources Research, 36 (6), 1519–1533, doi:10.1029/2000WR900044, 2000.
2. D. Koutsoyiannis, Climate change, the Hurst phenomenon, and hydrological statistics, Hydrological Sciences Journal, 48 (1), 3–24, doi:10.1623/hysj., 2003.
3. D. Koutsoyiannis, Hurst-Kolmogorov dynamics and uncertainty, Workshop on Nonstationarity, Hydrologic Frequency Analysis, and Water Management, Boulder, Colorado, USA, doi:10.13140/RG.2.2.36060.39045, International Center for Integrated Water Resources Management, US Army Corps of Engineers, United States Geological Survey, US Department of the Interior - Bureau of Reclamation, National Oceanic and Atmospheric Administration, US Environmental Protection Agency, Colorado State University, 2010.
4. D. Koutsoyiannis, Hurst-Kolmogorov dynamics as a result of extremal entropy production, Physica A: Statistical Mechanics and its Applications, 390 (8), 1424–1432, doi:10.1016/j.physa.2010.12.035, 2011.
5. S.M. Papalexiou, 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.
6. D. Koutsoyiannis, Encolpion of stochastics: Fundamentals of stochastic processes, doi:10.13140/RG.2.2.10956.82564, Department of Water Resources and Environmental Engineering – National Technical University of Athens, Athens, 2013.
7. D. Koutsoyiannis, Hydrology and Change, Hydrological Sciences Journal, 58 (6), 1177–1197, doi:10.1080/02626667.2013.804626, 2013.
8. F. Lombardo, E. Volpi, and D. Koutsoyiannis, Effect of time discretization and finite record length on continuous-time stochastic properties, IAHS - IAPSO - IASPEI Joint Assembly, Gothenburg, Sweden, doi:10.13140/RG.2.2.29955.71206, International Association of Hydrological Sciences, International Association for the Physical Sciences of the Oceans, International Association of Seismology and Physics of the Earth's Interior, 2013.
9. 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.
10. D. Koutsoyiannis, Reconciling hydrology with engineering, Hydrology Research, 45 (1), 2–22, doi:10.2166/nh.2013.092, 2014.
11. P. Dimitriadis, and D. Koutsoyiannis, Climacogram versus autocovariance and power spectrum in stochastic modelling for Markovian and Hurst–Kolmogorov processes, Stochastic Environmental Research & Risk Assessment, 29 (6), 1649–1669, doi:10.1007/s00477-015-1023-7, 2015.
12. D. Koutsoyiannis, Generic and parsimonious stochastic modelling for hydrology and beyond, Hydrological Sciences Journal, 61 (2), 225–244, doi:10.1080/02626667.2015.1016950, 2016.

Our works that reference this work:

1. P. Dimitriadis, and D. Koutsoyiannis, Stochastic synthesis approximating any process dependence and distribution, Stochastic Environmental Research & Risk Assessment, 32 (6), 1493–1515, doi:10.1007/s00477-018-1540-2, 2018.
2. D. Koutsoyiannis, P. Dimitriadis, F. Lombardo, and S. Stevens, From fractals to stochastics: Seeking theoretical consistency in analysis of geophysical data, Advances in Nonlinear Geosciences, edited by A.A. Tsonis, 237–278, doi:10.1007/978-3-319-58895-7_14, Springer, 2018.
3. P. Dimitriadis, K. Tzouka, D. Koutsoyiannis, H. Tyralis, A. Kalamioti, E. Lerias, and P. Voudouris, Stochastic investigation of long-term persistence in two-dimensional images of rocks, Spatial Statistics, 29, 177–191, doi:10.1016/j.spasta.2018.11.002, 2019.

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