Fractal complexity evaluation of meteorological droughts over three Indian subdivisions using visibility Graphs

Evaluation of scaling properties and fractal formalisms is one of the potential approaches for modelling complex series. Understanding the complexity and fractal characterization of drought index time series is essential for better preparedness against drought disasters. This study presents a novel visibility graph-based evaluation of fractal characterization of droughts of three meteorological subdivisions of India. In this method, the horizontal visibility graph (HVG) and Upside-down visibility graph (UDVG) are used for evaluating the network properties for different standardized precipitation index (SPI) series of 3, 6 and 12 month time scales representing short, medium and long term droughts. The relative magnitude of fractal estimates is controlled by the drought characteristics of wet-dry transitions. The estimates of degree distribution clearly deciphered the self-similar properties of droughts of all the subdivisions. For an insightful depiction of drought dynamics, the fractal exponents and spectrum are evaluated by the concurrent application of Sand Box Method (SBM) and Chhabra and Jenson Method (CJM). The analysis was performed for overall series along with the pre- and post-1976-77 Global climate shift scenarios. The complexity is more evident in short term drought series and UDVG formulations implied higher fractal exponents for different moment orders irrespective of drought type and locations considered in this study. Useful insights on the relationship between complex network and fractality are evolved from the study, which may help in improved drought forecasting. The visibility graph based fractality estimation evaluation is efficient in capturing drought and it has vast potential in the drought predictions in a changing environment.

Keywords:  Drought, Fractal, SPI, Visibility Graph