A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall

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.



Generating fine-scale time series of intermittent rainfall that are fully consistent with any give coarse-scale totals is a key and open issue in many hydrological problems. We propose a stationary disaggregation method that simulates rainfall time series with given dependence structure, wet/dry probability, and marginal distribution at a target finer (lower-level) time scale, preserving full consistency with variables at a parent coarser (higher-level) time scale. We account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths. This approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean, variance, and autocorrelation function (ACF) for a mixed-type stochastic process in terms of mean, variance, and ACFs of both continuous and discrete components, respectively. To achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse-scale totals, the generated lower-level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model. To assess model performance, we study rainfall process as intermittent with both independent and dependent occurrences, where dependence is quantified by the probability that two consecutive time intervals are dry. In either case, we provide analytical formulations of main statistics of our mixed-type disaggregation model and show their clear accordance with Monte Carlo simulations. An application to rainfall time series from real world is shown as a proof of concept.

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Our works referenced by this work:

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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. 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.
3. 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.
4. F. Lombardo, F. Napolitano, F. Russo, and D. Koutsoyiannis, On the exact distribution of correlated extremes in hydrology, Water Resources Research, 55 (12), 10405–10423, doi:10.1029/2019WR025547, 2019.

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Tagged under: Stochastic disaggregation, Rainfall models, Papers initially rejected