The Statistical Face of a Region Under Monsoon Rainfall in Eastern India

A region under rainfall is a contiguous spatial area receiving positive precipitation at a particular time. The probabilistic behavior of such a region is an issue of interest in meteorological studies. A region under rainfall can be viewed as a shape object of a special kind, where scale and rotational invariance are not necessarily desirable attributes of a mathematical representation. For modeling variation in objects of this type, we propose an approximation of the boundary that can be represented as a real valued function, and arrive at further approximation through functional principal component analysis, after suitable adjustment for asymmetry and incompleteness in the data. The analysis of an open access satellite dataset on monsoon precipitation over Eastern Indian subcontinent leads to explanation of most of the variation in shapes of the regions under rainfall through a handful of interpretable functions that can be further approximated parametrically. The most important aspect of shape is found to be the size followed by contraction/elongation, mostly along two pairs of orthogonal axes. The different modes of variation are remarkably stable across calendar years and across different thresholds for minimum size of the region. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

降雨区是指某一特定时刻内存在正降水量的连续空间区域。这类区域的概率特性是气象学研究中的热点问题。降雨区可被视为一类特殊的形状对象（shape object），其数学表征未必需要具备尺度不变性与旋转不变性。针对这类对象的形状变异建模需求，本文提出一种可通过实值函数表征的边界近似方法，并在对数据中的非对称性与不完备性进行适当校正后，进一步通过函数主成分分析（functional principal component analysis）实现精细化近似。针对东印度次大陆季风降水的开放获取卫星数据集开展分析后，本文通过少量可解释函数即可解释降雨区形状的绝大多数变异，且这些函数还可进一步通过参数化方式进行近似。研究发现，降雨区形状的首要影响因素为区域尺寸，其次为收缩或拉伸特性，且这类变异主要沿两对正交轴展开。不同的变异模式在历年以及区域最小尺寸的不同阈值下均表现出显著的稳定性。本文的补充材料（含可用于复现研究的标准化材料说明）可通过在线补充资源获取。