**4. Discussion**

This novel application of Lorenz Inequality and corresponding *G* demonstrates the utility of leveraging an analysis commonly used in economics for quantifying income inequality for quantifying the temporal inequality of contaminant loads and establishing a framework for temporal targeting of "hot moments" to achieve load-reduction goals. Earlier efforts to apply Lorenz Inequality to hydrology and water-quality data have helped to explain the effects of scale (both temporal and spatial) on the degree of temporal inequality exhibited by discharge and loads, with higher inequality in smaller headwater catchments and lower inequality in larger watersheds as well as higher inequality when finer temporal resolution data (e.g., daily scale) are used to generate the Lorenz Curves compared to coarser temporal scales (e.g., monthly) [11]. Further, across the Chesapeake Bay, a wide range of temporal inequality was documented for 108 stations in the Chesapeake Bay Nontidal Network, with *G* ranging from 0.24–0.60 for flow, 0.18–0.69 for TN, 0.36–0.92 for TP, and 0.39–0.90 for total suspended sediment [15]. However, the results of the previous analysis across the Chesapeake Bay watershed were for the entire 2010–2018 period since the TMDL was enacted, limiting the utility of those results for decision making at the annual scale.

Here, the results of this temporal inequality analysis demonstrate the potential effectiveness of targeting "hot moments" to achieve load-reduction goals in impaired surface water bodies. For catchments with a high degree of temporal inequality (i.e., G approaching 1), this temporal targeting is especially important, as failing to adopt conservation practices that do not adequately reduce loads during high-flow conditions may prevent load-reduction goals from being met. Conversely, in catchments with low degrees of temporal inequality, the period of time over which the targeted load is exported is longer, and spatial targeting may be more effective than temporal targeting for meeting load-reduction goals, with more opportunities available to effectively reduce the load over the course of a year. The implications of this analysis may be helpful in understanding difficulties in meeting water-quality-restoration goals in long-impaired watersheds, such as the Chesapeake Bay.

The results demonstrate that while in some years, load-reduction goals are only a small portion of the overall load exported and may easily be met by targeting a few storm events, in other years, loads are actually less than the targeted load, and even if 100% of the annual load were effectively mitigated, the annual load-reduction goal could not be met. Viewing these expectations through the lens of temporal inequality can be helpful in understanding how easy or difficult achieving load-reduction goals will be in a given watershed since the higher the value of *G*, the more difficult it will be to reduce loads without capturing and treating high-flow conditions. When the *G* is relatively low, as is often the case for TN [15], it is because export of the constituent of interest occurs largely during baseflow conditions, and therefore, achieving load reduction without effectively treating high-flow conditions may be possible. In these cases, conservation practices that help reduce groundwater concentrations, such as cover crops and other nonstructural best management practices (BMPs), may be most effective in meeting load-reduction goals. However, when *G* is high, as is often the case for TP [15], it is because export of the constituent of interest largely occurs during high-flow conditions, and therefore, if these events are not effectively treated, meeting the load-reduction goal may not be possible. In these cases, conservation practices, such as riparian buffers, vegetated filter strips, and detention basins, may be most effective in meeting the load-reduction goals. Water-quality BMPs are often vegetative and therefore are mainly effective in managing low-flow events over only the portion of the year when the plants are actively growing and are not dormant. The portions of the year during which water-quality BMPs are effective should align with months during which large portions of annual loads are exported. This may require landowners to consider designing BMPs to manage high-flow events or a combination of low-flow BMPs that are effective over a longer time interval.
