From fractals to stochastics: Seeking theoretical consistency in analysis of geophysical data

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.

[doc_id=1749]

[English]

Fractal-based techniques have opened new avenues in the analysis of geophysical data. On the other hand, there is often a lack of appreciation of both the statistical uncertainty in the results, and the theoretical properties of the stochastic concepts associated with these techniques. Several examples are presented which illustrate suspect results of fractal techniques. It is proposed that concepts used in fractal analyses are stochastic concepts and the fractal techniques can readily be incorporated into the theory of stochastic processes. This would be beneficial in studying biases and uncertainties of results in a theoretically consistent framework, and in avoiding unfounded conclusions. In this respect, a general methodology for theoretically justified stochastic processes, which evolve in continuous time and stem from maximum entropy production considerations, is proposed. Some important modelling issues are discussed with focus on model identification and fitting, often made using inappropriate methods. The theoretical framework is applied to several processes, including turbulent velocities measured every several microseconds, and wind and temperature measurements. The applications shows that several peculiar behaviours observed in these processes are easily explained and reproduced by stochastic techniques.

Full text is only available to the NTUA network due to copyright restrictions

PDF Additional material:

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, On the quest for chaotic attractors in hydrological processes, Hydrological Sciences Journal, 51 (6), 1065–1091, doi:10.1623/hysj.51.6.1065, 2006.
3. D. Koutsoyiannis, A random walk on water, Hydrology and Earth System Sciences, 14, 585–601, doi:10.5194/hess-14-585-2010, 2010.
4. D. Koutsoyiannis, Some problems in inference from time series of geophysical processes (solicited), European Geosciences Union General Assembly 2010, Geophysical Research Abstracts, Vol. 12, Vienna, EGU2010-14229, doi:10.13140/RG.2.2.13171.94244, European Geosciences Union, 2010.
5. S.M. Papalexiou, D. Koutsoyiannis, and A. Montanari, Mind the bias!, STAHY Official Workshop: Advances in statistical hydrology, Taormina, Italy, doi:10.13140/RG.2.2.12018.50883, International Association of Hydrological Sciences, 2010.
6. 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.
7. Y. Markonis, and D. Koutsoyiannis, Climatic variability over time scales spanning nine orders of magnitude: Connecting Milankovitch cycles with Hurst–Kolmogorov dynamics, Surveys in Geophysics, 34 (2), 181–207, doi:10.1007/s10712-012-9208-9, 2013.
8. 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.
9. D. Koutsoyiannis, Climacogram-based pseudospectrum: a simple tool to assess scaling properties, European Geosciences Union General Assembly 2013, Geophysical Research Abstracts, Vol. 15, Vienna, EGU2013-4209, doi:10.13140/RG.2.2.18506.57284, European Geosciences Union, 2013.
10. 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.
11. D. Koutsoyiannis, Random musings on stochastics (Lorenz Lecture), AGU 2014 Fall Meeting, San Francisco, USA, doi:10.13140/RG.2.1.2852.8804, American Geophysical Union, 2014.
12. D. Koutsoyiannis, and A. Montanari, Negligent killing of scientific concepts: the stationarity case, Hydrological Sciences Journal, 60 (7-8), 1174–1183, doi:10.1080/02626667.2014.959959, 2015.
13. 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.
14. 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.
15. 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.
16. P.E. O’Connell, D. Koutsoyiannis, H. F. Lins, Y. Markonis, A. Montanari, and T.A. Cohn, The scientific legacy of Harold Edwin Hurst (1880 – 1978), Hydrological Sciences Journal, 61 (9), 1571–1590, doi:10.1080/02626667.2015.1125998, 2016.
17. Y. Markonis, and D. Koutsoyiannis, Scale-dependence of persistence in precipitation records, Nature Climate Change, 6, 399–401, doi:10.1038/nclimate2894, 2016.
18. 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.

Our works that reference this work:

1. D. Koutsoyiannis, Entropy production in stochastics, Entropy, 19 (11), 581, doi:10.3390/e19110581, 2017.
2. 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.
3. I. Tsoukalas, C. Makropoulos, and D. Koutsoyiannis, Simulation of stochastic processes exhibiting any-range dependence and arbitrary marginal distributions, Water Resources Research, 54 (11), 9484–9513, doi:10.1029/2017WR022462, 2018.
4. 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.
5. 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.
6. D. Koutsoyiannis, Time’s arrow in stochastic characterization and simulation of atmospheric and hydrological processes, Hydrological Sciences Journal, doi:10.1080/02626667.2019.1600700, 2019.

Tagged under: Hurst-Kolmogorov dynamics, Course bibliography: Stochastic methods, Determinism vs. stochasticity, Scaling, Stochastics