Theoretical Predictability Limits of Spatially Anisotropic Multifractal Processes: Implications for Weather Prediction

Abstract

Abstract A correlation spectrum‐based approach is used to express the theoretical predictability limits of multifractal processes as an analytical function of their anisotropy parameters. This spatially anisotropic power law function is then used to investigate the general impact of anisotropy on the predictability of atmospheric fields in the weather regime. The investigation reveals that (i) vertical stratification of a field increases and decreases its super and subsphero‐scale predictability limits, respectively; (ii) trivial horizontal anisotropy slightly improves predictability at all scales; and (iii) horizontal anisotropy together with vertical stratification significantly enhances its predictability over almost the entire scale range. Applying these general results to the case of horizontal wind fields suggests that the interplay between spatial‐anisotropy and atmospheric predictability could account for improvements in forecast skill, commonly observed during the occurrence of rotating thunderstorms and breaks in the Indian summer monsoon.

Keywords

• complexity
• chaos
• uncertainty
• storm‐scale atmospheric predictability
• multifractals
• space‐time scaling laws of turbulence