Quantifying the Temporal Inequality of Nutrient Loads with a Novel Metric

Inequality is an emergent property of many complex systems. For a given series of stochastic events, some events generate a disproportionately large contribution to system responses compared to other events. In catchments, such responses cause streamflow and solute loads to exhibit strong temporal inequality, with the vast majority of discharge and solute loads exported during short periods of time during which high-flow events occur. These periods of time are commonly referred to as "hot moments". Although this temporal inequality is widely recognized, there is currently no uniform metric for assessing it. We used a novel application of Lorenz Inequality, a method commonly used in economics to quantify income inequality, to quantify the spatial and temporal inequality of streamflow and nutrient (nitrogen and phosphorus) loads exported to the Chesapeake Bay. Lorenz Inequality and the corresponding Gini Coefficient provide an analytical tool for quantifying inequality that can be applied at any temporal or spatial scale. The Gini coefficient (G) is a formal measure of inequality that varies from 0 to 1, with a value of 0 indicating perfect equality (i.e., fluxes and loads are constant in time) and 1 indicating perfect inequality (i.e., all of the discharge and solute loads are exported during one instant in time). Therefore, G is a simple yet powerful tool for providing insight into the temporal inequality of nutrient transport. We will present the results of our detailed analysis of streamflow and nutrient time series data collected since the early 1980's at 30 USGS gauging stations in the Chesapeake Bay watershed. The analysis is conducted at an annual time scale, enabling trends and patterns to be assessed both temporally (over time at each station) and spatially (for the same period of time across stations). The results of this analysis have the potential to create a transformative new framework for identifying "hot moments", improving our ability to temporally and spatially target implementation of best management practices to ultimately improve water quality in the Chesapeake Bay. This method also provides insight into the temporal scales at which hydrologic and biogeochemical variability dominate nutrient export dynamics.