A copula-based joint deficit index for droughts

Current drought information is based on indices that do not capture the joint behaviors of hydrologic variables. To address this limitation, the potential of copulas in characterizing droughts from multiple variables is explored in this study. Starting from the standardized index (SI) algorithm, a modified index accounting for seasonality is proposed for precipitation and streamflow marginals. Utilizing Indiana stations with long-term observations (a minimum of 80 years for precipitation and 50 years for streamflow), the dependence structures of precipitation and streamflow marginals with various window sizes from 1- to 12-months are constructed from empirical copulas. A joint deficit index (JDI) is defined by using the distribution function of copulas. This index provides a probability-based description of the overall drought status. Not only is the proposed JDI able to reflect both emerging and prolonged droughts in a timely manner, it also allows a month-by-month drought assessment such that the required amount of precipitation for achieving normal conditions in future can be computed. The use of JDI is generalizable to other hydrologic variables as evidenced by similar drought severities gleaned from JDIs constructed separately from precipitation and streamflow data. JDI further allows the construction of an inter-variable drought index, where the entire dependence structure of precipitation and streamflow marginals is preserved.