Spatio-temporal relationships between rainfall and convective clouds during Indian Monsoon through a discrete lens

The Indian monsoon, a multi-variable process causing heavy rains during June-September every year, is very heterogeneous in space and time. We study the relationship between rainfall and Outgoing Longwave Radiation (OLR, convective cloud cover) for monsoon between 2004-2010. To identify, classify and visualize spatial patterns of rainfall and OLR we use a discrete and spatio-temporally coherent representation of the data, created using a statistical model based on Markov Random Field. Our approach clusters the days with similar spatial distributions of rainfall and OLR into a small number of spatial patterns. We find that eight daily spatial patterns each in rainfall and OLR, and seven joint patterns of rainfall and OLR, describe over 90\% of all days. Through these patterns, we find that OLR generally has a strong negative correlation with precipitation, but with significant spatial variations. In particular, peninsular India (except west coast) is under significant convective cloud cover over a majority of days but remains rainless. We also find that much of the monsoon rainfall co-occurs with low OLR, but some amount of rainfall in Eastern and North-western India in June occurs on OLR days, presumably from shallow clouds. To study day-to-day variations of both quantities, we identify spatial patterns in the temporal gradients computed from the observations. We find that changes in convective cloud activity across India most commonly occur due to the establishment of a north-south OLR gradient which persists for 1-2 days and shifts the convective cloud cover from light to deep or vice versa. Such changes are also accompanied by changes in the spatial distribution of precipitation. The present work thus provides a highly reduced description of the complex spatial patterns and their day-to-day variations, and could form a useful tool for future simplified descriptions of this process.