Rainfall downscaling in time: Theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades

F. Lombardo, 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.

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[English]

During the last three or four decades, intensive research has focused on techniques capable of generating rainfall time series at a certain time scale which are (fully or partially) consistent with a given series at a coarser time scale. Here we theoretically investigate the consequences on the ensemble statistical behaviour caused by the structure of a simple and widely used approach of stochastic downscaling for rainfall time series: discrete Multiplicative Random Cascade (MRC). We show that synthetic rainfall time series generated by MRC models correspond to a stochastic process which is non-stationary, since its temporal autocorrelation structure depends on the position in time in an undesirable manner. Then, we propose and theoretically analyze an alternative downscaling approach based on the Hurst-Kolmogorov process (HKp), which is equally simple but is stationary. Finally, we provide Monte Carlo experiments, which validate our theoretical results.

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See also: http://dx.doi.org/10.1080/02626667.2012.695872

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Featured article of Hydrological Sciences Journal.

For this article the authors Federico Lombardo and Elena Volpi received the 2013 Tison Award of the International Association of Hydrological Sciences (IAHS), which is granted to young scientists (under 41) for an outstanding paper published by IAHS in the last two years.

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.
2. 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.
3. F. Lombardo, E. Volpi, D. Koutsoyiannis, and F. Serinaldi, A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall, Water Resources Research, 53 (6), 4586–4605, doi:10.1002/2017WR020529, 2017.
4. 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.
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6. I. Tsoukalas, A. Efstratiadis, and C. Makropoulos, Building a puzzle to solve a riddle: A multi-scale disaggregation approach for multivariate stochastic processes with any marginal distribution and correlation structure, Journal of Hydrology, 575, 354–380, doi:10.1016/j.jhydrol.2019.05.017, 2019.
7. 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.

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

Other works that reference this work (this list might be obsolete):

1. Resta, M., Hurst exponent and its applications in time-series analysis, Recent Patents on Computer Science, 5 (3), 211-219, 2012.
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5. De Luca, D., Analysis and modelling of rainfall fields at different resolutions in southern Italy, Hydrological Sciences Journal, 10.1080/02626667.2014.926013, 2014.
6. Pavlopoulos, H., and W. Krajewski, A diagnostic study of spectral multiscaling on spatio-temporal accumulations of rainfall fields based on radar measurements over Iowa, Advances in Water Resources, 74, 258-278, 10.1016/j.advwatres.2014.10.001, 2014.
7. Licznar, P., C. De Michele and W. Adamowski, Precipitation variability within an urban monitoring network via microcanonical cascade generators, Hydrol. Earth Syst. Sci., 19 (1), 485-506, 2015.
8. Müller, H. and U. Haberlandt, Temporal Rainfall Disaggregation with a Cascade Model: From Single-Station Disaggregation to Spatial Rainfall, J. Hydrol. Eng., 10.1061/(ASCE)HE.1943-5584.0001195, 04015026, 2015.
9. Kianfar, B., S. Fatichi, A. Paschalis, M. Maurer, and P. Molnar, Climate change and uncertainty in high-resolution rainfall extremes, Hydrology and Earth System Sciences Discussions, doi:10.5194/hess-2016-536, 2016.

Tagged under: Hurst-Kolmogorov dynamics, Stochastic disaggregation, Rainfall models