Multiscale Statistical Properties of a High-Resolution Precipitation Forecast

Small-scale (less than ∼15 km) precipitation variability significantly affects the hydrologic response of a basin and the accurate estimation of water and energy fluxes through coupled land–atmosphere modeling schemes. It also affects the radiative transfer through precipitating clouds and thus rainfall estimation from microwave sensors. Because both land–atmosphere and cloud–radiation interactions are nonlinear and occur over a broad range of scales (from a few centimeters to several kilometers), it is important that, over these scales, cloud-resolving numerical models realistically reproduce the observed precipitation variability. This issue is examined herein by using a suite of multiscale statistical methods to compare the scale dependence of precipitation variability of a numerically simulated convective storm with that observed by radar. In particular, Fourier spectrum, structure function, and moment-scale analyses are used to show that, although the variability of modeled precipitation agrees with that observed for scales larger than approximately 5 times the model resolution, the model shows a falloff in variability at smaller scales. Thus, depending upon the smallest scale at which variability is considered to be important for a specific application, one has to resort either to very high resolution model runs (resolutions 5 times higher than the scale of interest) or to stochastic methods that can introduce the missing small-scale variability. The latter involve upscaling the model output to a scale approximately 5 times the model resolution and then stochastically downscaling it to smaller scales. The results of multiscale analyses, such as those presented herein, are key to the implementation of such stochastic downscaling methodologies.