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

Abstract

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.

摘要

随着星载降水雷达探测数据的不断增多, 提高星载雷达观测数据的分辨率非常重要, 尤其对于小尺度的灾害性天气预报和气候建模, 这些天气常常与强降水及局部极值关联。本文研究了天气雷达反射率数据的小波域统计特征, 并对其进行了隐马尔可夫树(HMT)建模, 进而提出一种基于HMT先验建模的星载雷达反射率数据小波域高分辨率插值方法。对于雷达降水回波, 小面积的强降水对流单体常常群簇出现在一片缓慢变换的弱降水中, 从而常表现出明显的多尺度统计特性, 如非高斯边缘分布和尺度间的依赖性等。小波域HMT模型能很好地刻画雷达降水回波的小波系数统计特征, 它采用混合高斯模型(GMM)刻画尺度内各子带系数的概率分布, 并利用多尺度马尔科夫过程来表示尺度间的小波系数变化规律。通过最大期望值算法确定GMM的状态概率, 其他的模型参数, 如尺度间的方差退化率, 从高分辨率地基雷达反射率数据中学习和估算得到。在确定先验模型参数的基础上, 通过局部维纳滤波估计得到雷达反射率数据更小尺度的小波系数。应用TRMM星载雷达降水数据对此插值算法进行实验, 结果表明, 该算法能很好地提高数据空间分辨率, 并最优重建雷达图像中的局部极值和变化细节。