The transient behavior of scaling in the atmosphere: stratiform/convective transition and applications to sub-grid scale statistics

Multifractal behavior holds to a remarkable approximation over wide ranges of spatial scales in orographic rainfall and cloud fields. The scaling exponents characterizing this behavior are shown to be fundamentally transient with nonlinear dependencies on the particular atmospheric state and terrain forcing. In particular, a robust transition is found in the scaling parameters between non-convective (stable) and convective (unstable) regimes, with clear physical correspondence to the transition from stratiform to organized convective orographic precipitation. These results can explain two often reported scaling regimes for atmospheric wind, temperature and water observations. On the one hand, spectral slopes around 2-2.3 arise under non-convective or very weak convective conditions when the spatial patterns are dominated by large-scale gradients and landform. On the other hand, under convective conditions the scaling exponents generally fluctuate around 5/3, in agreement with the Kolmogorov turbulent regime accounting for the intermittency correction.

High-resolution numerical weather prediction (NWP) models are able to reproduce the ubiquitous scaling behavior of observed atmospheric fields down to their effective resolution length-scale, below which the variability is misrepresented by the model. The effective resolution is shown to be a transient property dependent on the particular simulated conditions and NWP formulation, implying that a blunt decrease in grid spacing without adjusting numerical techniques may not lead to the improvements desired.

Finally, the application of transient spatial scaling behavior for stochastic downscaling and sub-grid scale parameterization of cloud and rainfall fields is investigated. The proposed fractal methods are able to rapidly generate large ensembles of high-resolution statistically robust fields from the coarse resolution information alone, which can provide significant improvements for stochastic hydrological prediction and associated extreme event forecasting and risk management, and also for stochastic sub-grid parameterization of clouds with large potential to improve the current state-of-the-art cloud parameterization schemes.