Application of index number theory to the construction of a water quality index: Aggregated nutrient loadings related to the areal extent of hypoxia in the northern Gulf of Mexico

Numerous studies have linked individual nutrient loadings from the Mississippi and Atchafalaya Rivers to the growth of the hypoxic, or oxygen depleted, zone in the northern Gulf of Mexico. However, in the discussion of policy to remediate Gulf hypoxia, it is beneficial for stakeholders and policymakers to obtain a single measure for water quality that characterizes information from multiple water pollutants. This study aggregates loadings from six nutrients measured at the entrance to the Gulf of Mexico into a single time-varying index of water quality. The index is constructed using traditional index number theory originating from economic production theory, mainly, Shephard's distance functions calculated using data envelopment analysis (DEA). The methodology is an advance over other index construction schemes because the determined metric weights are endogenous, calculated from the data itself, and do not require external user input. To validate the index, May values of the index are used within a statistical regression model to model the areal extent of Gulf hypoxia using mid-July cruise measurements from 1985 to 2013, excluding 1989 when no cruise data were available. Regression results (R2adj = 0.81) suggest the index is successful at aggregating multiple pollutants into a single measure of water quality and may be useful for tracking their aggregated effect on the growth of the hypoxia area in the northern Gulf of Mexico. Calculation of the water quality index described here is automatic in the sense that no human intervention is required for variable selection, statistical analysis or assignment of weights. This is very useful for specifying a water quality objective in a multiple objective optimization for watershed management.