Tracing Time-Varying Characteristics of Meteorological Drought through Nonstationary Joint Deficit Index
Authors: Vinnarasi R. , Dhanya C. T. , Kumar Hemant 
Published: March 2023

Abstract
Standardized precipitation index (SPI) is one of the frequently used meteorological drought indices. However, the time-varying characteristics observed in the historical precipitation data questions the reliability of SPI and motivated the development of nonstationary SPI. To overcome some of the limitations in the existing nonstationary drought indices, a new framework for drought index is proposed, incorporating the temporal dynamics in the precipitation. The proposed drought index is developed by coupling the joint deficit index with the extended time sliding window–based nonstationary modeling (TSW-NSM). The proposed nonstationary joint deficit index (NJDI) detects the signature of nonstationarity in the distribution parameter and models both long-term (i.e., trend) and short-term (i.e., step-change) temporal dynamics of distribution parameters. The efficacy of NJDI is demonstrated by employing it to identify the meteorological drought-prone areas over India. The changes observed in the distribution parameter of rainfall series reveal an increasing number of dry days in recent decades all over India, except the northeast. Comparison of NJDI and stationary joint deficit index (JDI) reveals that JDI overestimates drought when frequent severe dry events are clustered and underestimates when these events are scattered, which indicates that the traditional index is biased toward the lowest magnitude of precipitation while classifying the drought. Moreover, NJDI could closely capture historical droughts and their spatial variations, thereby reflecting the temporal dynamics of rainfall series and the changes in the pattern of dry events over India. NJDI proves to be a potentially reliable index for drought monitoring in a nonstationary climate.

Significance Statement
Drought is one of the most severe natural disasters and is expected to intensify under a warming climate. There has been progress on developing newer methodologies to characterize drought severity under the changing climate. However, some limitations remain in capturing the temporal changes of the precipitation, especially the nonstationarity in variance (rapid increases in extreme precipitation versus the average precipitation). We propose an extension to the time sliding window approach to capture the nonstationarity in variance and mean while incorporating short-term (step-change) and long-term (trend) temporal dynamics. We apply the methodology to a subcontinent-sized heterogeneous country of India with gridded rainfall dataset (0.25° × 0.25°, 1901–2013) from the India Meteorological Department. We find that the majority of grids exhibit negative and positive trends in shape and scale parameters, respectively, which ultimately leads to an increase in the number of drier events, whereas a contradictory pattern is exhibited in the northwest Indian region (decrease in the number of dry days). The proposed index gives a potential framework for drought monitoring under the changing climate and can be extended to develop a multivariate nonstationary joint deficit index by incorporating other hydrological variables (e.g., soil moisture, diurnal temperature range, streamflow).