Statistical Modeling with a Hidden Markov Tree and High-resolution Interpolation for Spaceborne Radar Reflectivity in the Wavelet Domain

With the increasing availability of precipitation radar data from space, enhancement of the resolution of spaceborne precipitation observations is important, particularly for hazard prediction and climate modeling at local scales relevant to extreme precipitation intensities and gradients. In this paper, the statistical characteristics of radar precipitation reflectivity data are studied and modeled using a hidden Markov tree (HMT) in the wavelet domain. Then, a high-resolution interpolation algorithm is proposed for spaceborne radar reflectivity using the HMT model as prior information. Owing to the small and transient storm elements embedded in the larger and slowly varying elements, the radar precipitation data exhibit distinct multiscale statistical properties, including a non-Gaussian structure and scale-to-scale dependency. An HMT model can capture well the statistical properties of radar precipitation, where the wavelet coefficients in each sub-band are characterized as a Gaussian mixture model (GMM), and the wavelet coefficients from the coarse scale to fine scale are described using a multiscale Markov process. The state probabilities of the GMM are determined using the expectation maximization method, and other parameters, for instance, the variance decay parameters in the HMT model are learned and estimated from high-resolution ground radar reflectivity images. Using the prior model, the wavelet coefficients at finer scales are estimated using local Wiener filtering. The interpolation algorithm is validated using data from the precipitation radar onboard the Tropical Rainfall Measurement Mission satellite, and the reconstructed results are found to be able to enhance the spatial resolution while optimally reproducing the local extremes and gradients.