Bipartite Graphs: A Useful Tool for Monsoon Season
Some of the most devastating weather events have been recorded during the monsoon season in India. In Kolkata, pre-monsoon season occurs in April and May, a time in which life-threatening thunderstorms, hail, high winds, and occasional tornadoes cause much devastation. In order to decrease the extent of this devastation, better modeling of weather systems has been extensively researched.
To find a better model, this study used Graph Theory for forecasting thunderstorms, as this approach “can adopt all the complexity, nonlinearity, and inherent chaos of a system in its heuristic framework” (Chaudhuri 2). In this study, data was collected for 112 thunderstorms and 112 bipartite graphs were developed, where the two independent sets in each graph were VT and Vp, corresponding to vertices of time and vertices of other parameters related to thunderstorm tracking. An edge was created between VT and Vp if the parameter values for a specific day were above a certain threshold, indicating that a thunderstorm may be likely. The bipartite graphs were then connected to create a set of graphs for monsoon days, and the days where then plotted on two other sets of bipartite graphs. In effect, a nesting of graphs was created via complicated structural networks.
To analyze the data, eigenvalues for the bipartite graphs were computed, and other statistical probability computations were performed, but most of the presented data and mathematical discussion surpasses the scope of this class. Overall, the analysis showed that the bipartite modeling system was an efficient way to predict the severity of a thunderstorm 12 to 6 hours before the event. Furthermore, it was concluded that “the statistical approach does not provide any information regarding the severity of thunderstorms, while bipartite graph connectivity approach can be a useful tool to measure the strength of thunderstorms” (9). Further analysis of the bipartite graphs was used to classify the thunderstorms into three groups: severe, ordinary, and no thunderstorms, and the forecasts were accurate 96.8% of the time.
Although most of the information in this article delves much deeper into the statistics and mathematics related to bipartite graphs, the basis of the computations directly relates to INFO 2040, as bipartite modeling is a useful tool for modeling nodes and edges. In this case, the nodes were grouped into two sets of VT and Vp, with edges connecting the nodes in the sets if the eigenvalues related to the mathematics were above a certain threshold. As evident by the data, a simple model can become useful in a real-world setting when supplemented with various calculations. As such, the concepts that are covered in INFO 2040 provide a useful background in modeling very complicated systems, such as thunderstorms and weather events, and can be applied to weather forecasting as a means of diminishing the adverse effects of monsoon season in remote cities of India.
Chaudhuri S, Middey A. The Applicability of Bipartite Graph Model for Thunderstorms Forecast over Kolkata. Advances in Meteorology. 2009;2009:1-12. doi:10.1155/2009/270530. Accessed from hindawi.com. Accessed on September 18, 2014.