Precise Temporal Disaggregation Preserving Marginals and Correlations (DiPMaC) for Stationary and Nonstationary Processes

Hydroclimatic variables such as precipitation and temperature are often measured or simulated by climate models at coarser spatiotemporal scales than those needed for operational purposes. This has motivated more than half a century of research in developing disaggregation methods that break down coarse‐scale time series into finer scales, with two primary objectives: (a) reproducing the statistical properties of the fine‐scale process and (b) preserving the original coarse‐scale data. Existing methods either preserve a limited number of statistical moments at the fine scale, which is often insufficient and can lead to an unrepresentative approximation of the actual marginal distribution, or are based on a limited number of a priori distributional assumptions, for example, lognormal. Additionally, they are not able to account for potential nonstationarity in the underlying fine‐scale process. Here we introduce a novel disaggregation method, named Disaggregation Preserving Marginals and Correlations (DiPMaC), that is able to disaggregate a coarse‐scale time series to any finer scale, while reproducing the probability distribution and the linear correlation structure of the fine‐scale process. DiPMaC is also generalized for arbitrary nonstationary scenarios to reproduce time varying marginals. Additionally, we introduce a computationally efficient algorithm, based on Bernoulli trials, to optimize the disaggregation procedure and guarantee preservation of the coarse‐scale values. We focus on temporal disaggregation and demonstrate the method by disaggregating monthly precipitation to hourly, and time series with trends (e.g., climate model projections), while we show its potential to disaggregate based on general nonstationary scenarios. The example applications demonstrate the performance and robustness of DiPMaC.