Studying Scale Invariance in Remotely Sensed Rainfall

降雨是由高度非线性的大气过程产生的，并且在大范围尺度上起作用和相互作用。水文学家、气象学家和气候学家面临的主要挑战之一是测量、模拟和预测不同尺度上降雨所表现出的极端变化的性质。最近的研究表明，令人兴奋的是，降雨可能表现出尺度/多尺度特征，即，除了与尺度有关的一个或多个因素外，小尺度波动在统计上与大尺度波动相似。在不同尺度的高度不规则的降雨模式中存在这样一个隐藏结构，将提高我们对降雨过程的理解，并将显著影响我们对降雨建模、测量和预测的方法。本研究的目的是建立一个新的理论框架，用于识别和研究遥感降雨中尺度不变关系的存在。我们的方法，基于多分辨率小波分析，不同于当代的方法。该方法更为通用，其主要优点是能够有效地处理时空降雨场的非平稳性/非均匀性和各向异性，这些都是时空降雨场的重要特征。我们的空间降雨方法的初步实施已经给出了非常有希望的结果，并为数据分析指明了新的方向，这些数据分析具有从复杂的非均质各向异性空间降雨场中揭示简单结构的潜力。此外，作为本研究的一部分，将探讨使用尺度概念进行亚网格尺度参数化和独立于分辨率的降雨估计的可能性。

Rainfall is produced by atmospheric processes which are highly nonlinear and operate and interact at a wide range of scales. One of the main challenges to hydrologists, meteorologists and climatologists is to measure, model and predict the nature of the extreme variability exhibited by rainfall at different scales. Recent research has indicated the exciting possibility that rainfall may exhibit scaling/multiscaling characteristics, i.e., small scale fluctuations are statistically similar to large scale fluctuations except for one or more factors related to scale. The presence of such a hidden structure in the highly irregular patterns of rainfall at different scales will improve our understanding of the rainfall process and will significantly influence our approach to rainfall modeling, measurement and prediction. The goal of the proposed research is to develop a new theoretical framework for identifying and studying the presence of scale invariant relationships in remotely sensed rainfall. Our approach, based on multiresolution wavelet analysis, is different from contemporary approaches. It is more general and has the major advantage of being able to handle non-stationarity/inhomogeneity and anisotropy efficiently, all of which are important characteristics of space-time rainfall fields. Preliminary implementation of our approach to spatial rainfall has given very promising results and has pointed out new directions for data analysis which have the potential of unraveling simple structures from the complex non-homogenous anisotropic spatial rainfall fields. Also, as part of this research, the possibility of using scaling concepts for subgrid scale parametrization and resolution- independent rainfall estimation, will be explored.