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.

中文翻译：

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小波域星载雷达反射率的隐马尔可夫树和高分辨率插值统计建模

随着空间降水雷达数据的可用性不断增加，提高星载降水观测的分辨率非常重要，特别是对于与极端降水强度和梯度相关的局部尺度的灾害预测和气候建模。本文在小波域中使用隐马尔可夫树（HMT）研究和建模雷达降水反射率数据的统计特征。然后，提出了一种以HMT模型为先验信息的星载雷达反射率高分辨率插值算法。由于嵌入在较大且缓慢变化的元素中的小而短暂的风暴元素，雷达降水数据表现出独特的多尺度统计特性，包括非高斯结构和尺度到尺度的依赖性。HMT模型可以很好地捕捉雷达降水的统计特性，其中每个子带中的小波系数表征为高斯混合模型（GMM），从粗尺度到细尺度的小波系数采用多尺度马尔可夫描述过程。GMM 的状态概率是使用期望最大化方法确定的，其他参数，例如 HMT 模型中的方差衰减参数是从高分辨率地面雷达反射率图像中学习和估计的。使用先验模型，使用局部维纳滤波估计更精细尺度的小波系数。使用热带降雨测量任务卫星上的降水雷达数据验证插值算法，