Transient stochastic downscaling of quantitative precipitation estimates for hydrological applications
Rainfall fields are heavily thresholded and highly intermittent resulting in large areas of zero values. This deforms their stochastic spatial scale-invariant behavior, introducing scaling breaks and curvature in the spatial scale spectrum. To address this problem, spatial scaling analysis was performed inside continuous rainfall features (CRFs) delineated via cluster analysis. The results show that CRFs from single realizations of hourly rainfall display ubiquitous multifractal behavior that holds over a wide range of scales (from ≈1. km up to 100's. km). The results further show that the aggregate scaling behavior of rainfall fields is intrinsically transient with the scaling parameters explicitly dependent on the atmospheric environment. These findings provide a framework for robust stochastic downscaling, bridging the gap between spatial scales of observed and simulated rainfall fields and the high-resolution requirements of hydrometeorological and hydrological studies.Here, a fractal downscaling algorithm adapted to CRFs is presented and applied to generate stochastically downscaled hourly rainfall products from radar derived Stage IV (~4. km grid resolution) quantitative precipitation estimates (QPE) over the Integrated Precipitation and Hydrology Experiment (IPHEx) domain in the southeast USA. The methodology can produce large ensembles of statistically robust high-resolution fields without additional data or any calibration requirements, conserving the coarse resolution information and generating coherent small-scale variability and field statistics, hence adding value to the original fields. Moreover, it is computationally inexpensive enabling fast production of high-resolution rainfall realizations with latency adequate for forecasting applications. When the transient nature of the scaling behavior is considered, the results show a better ability to reproduce the statistical structure of observed rainfall compared to using fixed scaling parameters derived from ensemble mean analysis. A 7-year data set of 50 hourly realizations of downscaled Stage IV rainfall fields at 1. km resolution for the IPHEx domain is publicly available from iphex.pratt.duke.edu.The value of the downscaled products is demonstrated through hydrological simulations of two distinct storm events in the Southern Appalachians, a winter storm that caused multiple landslides and a summer tropical event that caused flashfloods. The simulations are forced by the entire span of plausible fractally downscaled rainfall fields at two distinct resolutions (1. km and 250. m). The results show very good skill against the observed streamflow, especially with regard to the timing and peak discharge of the hydrograph, and the accuracy is enhanced by increasing the target downscaling resolution from 1. km to 250. m. Probabilistic simulations of both events capture the observed behavior indicating that the proposed CRF-based stochastic fractal interpolation provides a generalized framework for producing fast and reliable probabilistic forecasts and their associated uncertainty for extreme events and risk management of hydrometeorological hazards, as well as long-term hydrologic modeling.
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