  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 data set on monsoon
precipitation over Eastern India 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.
