A new framework for rainfall downscaling based on EEMD and an improved fractal interpolation algorithm

In this research, a novel framework is proposed for temporal downscaling rainfall records to address the problem of insufficient temporal resolution of rainfall during the refined hydrological simulation. This framework consists of three main steps: (1) The existence of the fractal features of the original rainfall series with different temporal scales (month, week, day, h) can be judged by the dominant frequency of Hilbert marginal spectrum, and geometric shape similarity of different time scales on the basis of the ensemble empirical mode decomposition (EEMD). (2) Based on the previous fractal interpolation theory, an improved algorithm that couples with a threshold to control the number of interpolation points for the specific interpolation intervals and a parameter to captures the high intermittentness of rainfall series is developed, which can achieve the conservation of the total rainfall quantity. (3) EEMD method is applied again to compare and evaluate the fit of the downscaled records to observed records from the perspective of IMF components, and various statistical indicators (e.g., root mean square error, correlation coefficient, Nash–Sutcliffe efficiency coefficient, fractal dimension) are applied to quantify the performance of improved fractal interpolation algorithm. Three sets of observed hourly rainfall series (from 2016 to 2018) of Chaohu city, Anhui, China, were investigated using the new framework, EF (EEMD + improved fractal interpolation algorithm). First, in order to validate the applicability of the EF framework, the observed hourly rainfall sets were aggregated into daily, weekly, and monthly sets and subsequently, the EF framework was employed to downscale above sets back into daily and hourly scale. Then, a long-duration rainfall event with hourly scale in early July 2016 was downscaled to 5-min time series using EF framework and equipartition method, respectively. Finally, simulation results based on MIKE URBAN software were compared for EF framework and equipartition method. The results of our work reveal that: (a) EEMD is a reasonable identification tool for fractal characteristics of rainfall records. (b) the improved fractal interpolation algorithm not only reasonably preserves key statistical indices (e.g., low-order moments, autocorrelation, power spectra), but also captures the overall trends and inherent details of the rainfall. (c) Based on the digital simulation and model analysis, the storm sewer peak flows obtained by the EF framework are larger than that of equipartition method.