**1. Introduction**

Inequality is a ubiquitous, emerging property of complex systems. In catchments, the spatial and temporal inequality of hydrologic and biogeochemical responses lead to the emergence of "hot spots" and "hot moments", with the vast majority of these responses occurring during relatively short periods of time and in relatively small locations. While the importance of spatial and temporal inequality is widely recognized, the methods used to identify "hot spots" and "hot moments" are not well established, with the methodology employed to analyze spatial data generally disconnected and inconsistent with the methodology employed to analyze temporal data.

The quantification of "hot spots" has been more consistently reported in the literature than the quantification of "hot moments". By calculating area-normalized loads (or other nutrient-cycle responses, such as gaseous emissions), "hot spots" are identified as the locations over a given spatial extent of interest (i.e., field, catchment, or watershed) that have the highest loads per unit area. If an area of interest needs to be managed for water-quality impairment, for example, then decision makers can direct resources to a

**Citation:** Opalinski, N.; Schultz, D.; Veith, T.L.; Royer, M.; Preisendanz, H.E. Meeting the Moment: Leveraging Temporal Inequality for Temporal Targeting to Achieve Water-Quality Load-Reduction Goals. *Water* **2022**, *14*, 1003. https:// doi.org/10.3390/w14071003

Academic Editors: Nigel W.T. Quinn, Ariel Dinar, Iddo Kan and Vamsi Krishna Sridharan

Received: 15 February 2022 Accepted: 15 March 2022 Published: 22 March 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

relatively small number of places, knowing that implementing conservation practices in those locations will achieve a higher impact on load reduction than placing the same resources and practices in other areas. Crop nutritionists increasingly support this principle through management framework called "4R Nutrient Stewardship": right nutrient source at the right rate at the right time in the right place [1]. Previous research has shown that spatially targeting adoption of agricultural conservation practices at the field scale leads to larger load-reduction goals at the watershed scale [2–6]. It is also important to recognize and manage temporal inequalities, or "hot moments", such that resources can be targeted based on both spatial and temporal inequalities. However, no uniform metric for describing temporal inequality has been widely adopted despite the prevalence of temporal inequality documentation across small and large watersheds [7–10].

The need to quantify the degree of inequality in a system is not new. Perhaps nowhere has the degree of inequality been more routinely quantified than in economics. For more than a century, Lorenz Inequality and the corresponding Gini Coefficient (*G*) have been used to determine wealth distribution by quantifying the degree of income inequality in a population. Lorenz Inequality analysis was first applied to quantify the degree of inequality for streamflow hydrology and water quality in 22 locations in the Lake Okeechobee watershed [11] and has since been utilized globally at the continental scale to better understand how climate change is likely to affect flow regimes [12]. Additionally, the analysis has been applied to time series data for geogenic constituents, nutrients, sediment, and pesticides in more than 100 watersheds ranging from 2.5 km2 to 70,000 km2 and at time scales ranging from daily to annually [13–15].

Water-quality degradation of coastal water bodies due to the presence of excess nutrients is a leading global environmental concern [16], with agricultural activities identified as common contributors to degraded water quality [17]. The Chesapeake Bay is the third largest estuary in the world and has a watershed area spanning 166,000 km2 across seven jurisdictions. In 2010, a federally mandated Total Maximum Daily Load (TMDL) was established by the United States Environmental Protection Agency, designed to reduce nutrient and sediment loads and restore water quality to be in compliance with the Bay's designated use of fishing and swimming by 2025 [18]. To achieve mandated load-reduction goals, widespread adoption of conservation practices has occurred across the Chesapeake Bay watershed. However, current Chesapeake Assessment Scenario Tool (CAST) estimates of load reductions indicate that the Commonwealth of Pennsylvania (PA) in particular is behind the pace likely needed to meet the 2025 reduction goals [19]. Although a range of factors contribute to the overall water quality of the Chesapeake Bay, we argue that a failure to target load reduction during "hot moments" is a contributing factor. The Commonwealth of PA has established a four-tiered system for prioritizing spatial adoption of conservation practices, with each tier of counties needing to reduce 25% of the state's portion of the overall Chesapeake Bay TMDL in its current Watershed Implementation Plan [20]. Tier 1 consists of the two greatest "hot spot" counties that rank highest in nutrient and sediment loads, Tier 2 consists of five counties, whereas Tiers 3 and 4 consist of 16 and 20 counties, respectively. However, no efforts have been documented towards effectively target "hot moments".

The goal of this study is to demonstrate the impact that temporal variability from year to year can have on achieving load-reduction goals in an impaired watershed through the development of a decision-making framework for temporal targeting of "hot moments" during which the targeted load is exported. The framework consists of a novel application of Lorenz Inequality to link the temporal inequality of contaminant loads to the specific "windows of opportunity" and corresponding flow conditions necessary to target to achieve the desired load-reduction goals. The framework is demonstrated here using daily load and discharge data from eight impaired catchments in the Chesapeake Bay watershed. By comparing these loads on an annual basis with established load-reduction goals for each catchment, we determine the catchment-specific variability in percent reduction

needed from year to year and discuss how this framework enables watershed planners to understand and inform stakeholders of the risk of a watershed conservation plan.
