资源环境科技发展态势分析平台

Generating fine-scale time series of intermittent rainfall that are fully consistent with any given 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.

Plain Language Summary Rainfall is the main input to most hydrological systems. A wide range of studies concerning floods, water resources and water quality require characterization of rainfall inputs at fine time scales. This may be possible using empirical observations, but there is often a need to extend available data in terms of temporal resolution satisfying some additive property (i.e. that the sum of the values of consecutive variables within a period be equal to the corresponding coarse-scale amount). Hence, rainfall disaggregation models are required. Although there is substantial experience in stochastic disaggregation of rainfall to fine time scales, most modeling schemes existing in the literature are ad hoc techniques rather than consistent generalized methods. This is mainly due to the skewed distributions and the intermittent nature of the rainfall process at fine time scales, which are severe obstacles for the application of a theoretically consistent scheme to rainfall disaggregation. We propose a consistent disaggregation model that first generates lognormal time series of rainfall depths based on a random cascade structure. Then, such time series are multiplied by binary sequences (i.e., rainfall occurrences) to obtain intermittent rainfall time series with known summary statistics.