Applications of directional wavelets, Universal Multifractals and anisotropic scaling in ensemble nowcasting; a review of methods with case‐studies

Abstract

AbstractThis article begins with a review of the scale decomposition and stochastic noise generation aspects of the ensemble nowcasting process, as used in the Short Term Ensemble Prediction System (STEPS). Alternative methods are then suggested, with case‐study examples, which could lead to enhanced performance and may also be applicable in other fields. The standard FFT‐band‐pass‐filtering scale decomposition, essential to this process, is shown to be practically the same as a redundant Continuous Wavelet Transform (CWT). This immediately makes accessible a number of more advanced methods from the wavelet literature. Particular attention is given to directional wavelet transforms and their use for analysing anisotropic scaling behaviour, common in weather images. With a view to numerically efficient operational usage, the focus is then shifted to Discrete Wavelet Transforms (DWTs). While the standard DWT has a number of disadvantages, including limited orientational selectivity in two dimensions, the relatively recent Dual Tree Complex WT (DTCWT) overcomes most of these. Examples are given that show how its six‐fold directionality can be exploited, to create synthetic features that replace the unpredictable small‐scale parts of a (weather‐radar‐based) extrapolation nowcast with more realistic spatially varying anisotropy. Further, the Bounded Log‐normal Cascade noise model, as used in STEPS, is reconsidered and a proposal to use Universal Multifractal realizations is presented. For the noise parameters, some operationally viable estimation methods are considered, such as the Double Trace Moment technique and a structure‐function‐based approach, which could work on readily available DTCWT coefficients.