Upper limits for road salt pollution in lakes

Widespread and increasing use of road deicing salt is a major driver of increasing lake chloride concentrations, which can negatively impact aquatic organisms and ecosystems. We used a simple model to explore the controls on road salt concentrations and predict equilibrium concentrations in lakes across the contiguous United States. The model suggests that equilibrium salt concentration depends on three quantities: salt application rate, road density, and runoff (precipitation minus evapotranspiration). High application combined with high road density leads to high equilibrium salt concentrations regardless of runoff. Yet if application can be held at current rates or reduced, concentrations in many lakes situated in lightly to moderately urbanized watersheds should equilibrate at levels below currently recommended thresholds. In particular, our model predicts that, given 2010–2015 road salt application rates, equilibrium chloride concentrations in the contiguous United States will exceed the current regulatory chronic exposure threshold of 230 mg L−1 in over 2000 lakes; will exceed 120 mg L−1 in over 9000 lakes; and will be below 120 mg L−1 in hundreds of thousands of lakes. Our analysis helps to contextualize current trends in road salt pollution of lakes, and suggests that stabilization of equilibrium chloride concentrations below thresholds designed to protect aquatic organisms should be an achievable goal.

Anthropogenic increases in salt concentrations of freshwaters are a widespread phenomenon with important implications for aquatic ecosystems, aquatic biota, and ecosystem services (Evans and Frick 2001;Kaushal et al. 2005Kaushal et al. , 2021;;Cañedo-Argüelles et al. 2013, 2019;Hintz and Relyea 2019;Kinsman-Costello et al. 2023).These increases-together with increases in alkalinity that share some of the same drivershave been recognized as part of an emerging global "freshwater salinization syndrome" (Kaushal et al. 2018(Kaushal et al. , 2021)).High salt concentrations can negatively impact aquatic ecosystems at multiple levels of organization, ranging from individual growth, reproduction, and survival to ecosystem-level nutrient cycling and energy flow (Hintz and Relyea 2019).
A leading cause of freshwater salinization in regions with cold winters is the application of road deicing salt (Thunqvist 2004;Kelly et al. 2008;Kaushal et al. 2018Kaushal et al. , 2021)).The use of salt for road deicing in the United States began in a few locations around the late 1930s, and rapidly spread and intensified as new jurisdictions took up the practice, the area of salted road surface grew, and the rate of salt application per unit of road increased (Jackson and Jobb agy 2005;Hintz et al. 2022b).Recent data suggest that annual usage of road saltmostly sodium chloride (NaCl)-is approximately 24.5 million tons in the United States, 7 million tons in Canada, and 0.15 to 2 million tons across several European countries (Arnott et al. 2020).
The intensification of road salt application has driven large and widespread increases in chloride concentrations in both surface and ground waters (e.g., Thunqvist 2004;Chapra et al. 2009;Likens and Buso 2010;Cassanelli and Robbins 2013;Kelly et al. 2018).A recent synthesis of long-term data from hundreds of lakes in North America demonstrated that increasing chloride trends are common; that there is substantial variation in current chloride concentrations and the rate at which they are changing; and that current trends suggest that many lakes may be at risk of reaching chloride concentrations that exceed regulatory guidelines for chronic exposure (Dugan et al. 2017).
These trends led us to wonder how high chloride concentrations might become in lakes influenced by road salting, and how that might vary across the landscape.To build insight about those questions we formulated and analyzed a simple model of lakes and their watersheds.We then used empirical estimates of the model parameters to predict equilibrium chloride concentrations in lakes under a wide range of conditions, and considered the implications of our findings for the management of road salt and the protection of freshwater ecosystems.Our analysis abstracts away some of the complexity of the real world and considers equilibrium conditions as a simple heuristic to help understand underlying patterns.

Model of road salt chloride in a watershed and lake
Road salt applied in a watershed is transported into and out of lakes by hydrologic fluxes.We used the following simple dynamic model of road salt chloride in the watershed (S W ; kg Cl À ) and road salt chloride in the lake (S L ; kg Cl À ) to describe these processes: Here, chloride is added to the watershed by application at rate α to roads, which are present at density δ across the area Table 1.State variables and parameters for a simple model of the mass of road salt (as chloride, Cl À ) in lakes and watersheds.Note that SI units are used in all cases; for example, "lane-m" is "lane-meters," which is different from the convention of reporting salt data in lane-miles in the United States.A lane is the width of road necessary for one car to move in one direction (so, e.g., a road that allows a car to move in each direction at the same time is a two-lane road).Lane width varies with road type and other conditions but is often $ 3.0-3.5 m.V Lake volume m 3 of the watershed, A. Precipitation that is not evaporated nor transpired becomes surface or subsurface runoff, r, which removes chloride from the watershed and delivers it to the lake, depending on ϕ, the relative chloride yield of the watershed per unit of runoff.Chloride in the lake is removed by hydrologic outflow.Descriptions and units for all the state variables and parameters of the model are provided in Table 1.

State variable or parameter
We made several simplifying assumptions in formulating this model.We ignored the distinction between surface and groundwater flows, treating all of the precipitation input to the watershed (net of evapotranspiration) as a single hydrologic flow path that moves from the watershed, to the lake, and then downstream.This allowed us to forego tracking the temporary but potentially long-term storage of chloride in soils or groundwater (Kelly et al. 2008).Instead the model mimics storage via ϕ, the parameter describing the proportion of the chloride currently in the watershed that is exported per unit of runoff; if ϕ is low the chloride in the watershed is exported very gradually (Fig. 1).We assumed that ϕ is constant; that the lake is exorheic, well-mixed on an annual scale, and has constant volume; and that direct precipitation on and evaporation from the lake are equal or negligible.Our model shares many assumptions and structural features with diverse previous models (e.g., Sonzogni et al. 1983;Bowser 1992;Novotny and Stefan 2010;Bailey et al. 2019;Dugan and Rock 2023), but combines a focus on the watershed-level features that determine water and chloride loads with a relatively abstracted and simple structure.It omits chloride derived either from natural weathering, which accounts for 0-10 mg Cl À L À1 in most lakes and much more in some naturally saline lakes (Last and Ginn 2005;Hintz and Relyea 2019); or from anthropogenic sources other than road salt, which can be significant (Kaushal et al. 2021).
Note that while the state variables in the model are masses of Cl À , the concentrations of Cl À in the lake (C L ) or in the lake's hydrologic inflow (C I ) can be calculated as: To facilitate interpretation we present results as concentrations of Cl À , converting units to mg L À1 .
The masses of road salt chloride in the watershed and the lake at equilibrium are given by: Substituting Eq. 3b into Eq.2a demonstrates that the equilibrium concentration of road salt chloride in the lake depends only on the rate of application to roads, the road density, and runoff: Comparing model predictions to empirical observations in one well-studied watershed suggests that predicted equilibrium chloride concentrations are plausible.Likens and Buso (2010) estimated annual chloride budgets for Mirror Lake, New Hampshire from the late 1960s through 2007, documenting the impacts of two roads that were built through the watershed around 1970.We used data from their paper, along with Eq. 4, to calculate the predicted equilibrium chloride concentration in the lake under two scenarios, assuming that engineering controls intended to prevent salt runoff to the lake from one of the roads were either 100% or 0% effective (see Supporting Information for details).Predicted equilibrium Cl À concentrations under these two scenarios were 0.6 and 31 mg L À1 , while the actual Cl À concentration was $ 3-4 mg L À1 in 2007 and has varied between 3 and 5 mg L À1 between 2008 and 2021 (see Supporting Information).
We applied the model in three ways to build insight into equilibrium road salt chloride concentrations in lakes.First, we solved the model through time to see how chloride concentrations approach equilibrium.Next, we explored general patterns in equilibrium chloride concentration across wide but realistic ranges of road salt application rate and road density, for three different values of runoff representing the range of climates across the northern United States.Finally, for each lake or reservoir larger than 1 ha in the contiguous United States (Cheruvelil et al. 2021;Lehner et al. 2022), we calculated the equilibrium road salt chloride concentration expected if salt application were to be held at reported 2010-2015 levels (Falcone et al. 2018).Details on each of these three model applications are provided in the Supporting Information.All of the code to reproduce our analyses is publicly available (Dugan and Solomon 2023).

Results
The equilibration of lake road salt chloride concentration to the rate of road salt application in the watershed may occur slowly (Fig. 1; see also e.g., Novotny and Stefan 2010;Dugan and Rock 2023).How slowly depends on several features of the lake's hydrologic setting, as indicated by Eq. 1b.These include runoff from the watershed; the ratio of watershed area to lake volume; and the extent of temporary storage in the watershed via slow hydrologic flow paths, which is represented in the model via the relative salt yield parameter, ϕ.During the approach to equilibrium, the increase in chloride concentration is essentially linear for many years or even many decades (Fig. 1).Furthermore, increases through time in road density or salt application rate shift the equilibrium concentration higher and delay equilibration (Eq.4; Fig. 1).
High road density combined with high salt application rates leads to high equilibrium chloride concentrations, regardless of regional runoff conditions (Fig. 2).For instance, even in a wet climate where high runoff dilutes salt inputs, equilibrium chloride concentration is > 200 mg Cl À L À1 if road density in the watershed exceeds 0.010 lane-m m À2 and application rate exceeds 10 kg Cl À (lane-m) À1 yr À1 (Fig. 2C).These are high but realistic values for both road density (Fig. 2D) and application rate (Dugan et al. 2017; note that 10 kg Cl À (lane-m) À1 yr À1 is equivalent to 29 US tons NaCl (lane-mile) À1 yr À1 ).In drier climates equilibrium chloride concentrations can exceed 200 mg Cl À L À1 even in watersheds with substantially lower road density or application rates (Fig. 2a,b).
If road salt application can be held at current rates or reduced, road salt chloride concentrations in many lakes situated in lightly to moderately urbanized watersheds should equilibrate at levels below 230 mg Cl À L À1 , the current U.S. Environmental Protection Agency threshold for chronic exposure (Fig. 2).In wet climates in particular, even watersheds with road densities of 0.014 m m À2 -a value typical of major suburbs such as Westchester County, New York or Middlesex County, Massachusetts-are predicted to have equilibrium road salt chloride concentrations below 230 mg Cl À L À1 if salt application rates are kept below 13.5 kg Cl À (lane-m road) À1 yr À1 .
Most of the lakes and reservoirs ("lakes") larger than 1 ha in the contiguous United States for which the model predicts high equilibrium road salt chloride concentrations, given reported 2010-2015 salt application rates, are in the Northeast and Midwest (Fig. 3).The road network is densely developed in many places within this region, and salt application rates are often high.Lakes larger than 1 ha with predicted equilibrium chloride concentrations in excess of the 230 mg Cl À L À1 threshold were most abundant in Illinois and Ohio, where they represented 9-10% of all lakes larger than 1 ha (Fig. 3b).Lakes with predicted concentrations above this threshold were also present in Indiana, Iowa, Kansas, Michigan, Minnesota, New York, Pennsylvania, and Wisconsin, where they represented < 0.1% to 1% of lakes larger than 1 ha, and in the District of Columbia, where they represented 17% of 12 lakes.Lakes with predicted equilibrium road salt chloride concentrations above the 120 mg Cl À L À1 threshold used as a water quality guideline in Canada were much more abundant: in Illinois and Ohio 23-28% of lakes had predicted concentrations above this threshold, and in several other states 1-7% of lakes were above this threshold (Fig. 3b).Across the contiguous United States, more than 9000 lakes (2%) were predicted to have equilibrium road salt chloride concentrations in excess of 120 mg Cl À L À1 .

Discussion
As our model emphasizes, the concentration of road salt chloride in a lake is ultimately controlled by the amount of salt applied in its watershed and by runoff.Increases in road salt application rates and road density, and gradual equilibration to those changes, have all contributed to the increases in chloride concentrations that have been observed in many surface waters since the widespread adoption of road salting in the mid-1900s.
Our analysis suggests that it should be possible in many places to stabilize average road salt concentrations at levels below the current EPA threshold (230 mg Cl À L À1 ) for protection of aquatic life.Simply limiting salt application rates to current business-as-usual levels might achieve this goal in watersheds which have low to moderate road density and mesic to wet climates, while reducing application rates may be particularly important where road density is high or increasing (Fig. 2).Emerging evidence suggests that it is possible to reduce application rates without degrading road safety, via changes in technology and practices (Kelly et al. 2019;Hintz et al. 2022b).Reduced application rates generate an ongoing cost savings for transportation authorities, but the upfront costs of implementing new technologies can be substantial.Programs to help defray upfront costs could accelerate the transition to lower application rates and pay substantial economic and environmental dividends.
An important question is whether stabilizing average road salt chloride concentrations at 230 mg Cl À L À1 would be sufficient to protect aquatic ecosystems from undesirable changes.There are at least five reasons for caution here.First, even concentrations well below this threshold may be many times higher than the background concentrations arising from natural weathering, and thus well outside the range that aquatic organisms were historically exposed to (Hintz and Relyea 2019).Second, this EPA chronic toxicity threshold was developed based on laboratory experiments with only three aquatic organisms, and there is increasing evidence that negative impacts on some aquatic organisms occur at chloride concentrations well below 230 mg L À1 , particularly in waters with low background concentrations of calcium, magnesium, and other ions (Elphick et al. 2011;Arnott et al. 2020;Dugan and Arnott 2022;Hintz et al. 2022a;Wersebe et al. 2023).Given this evidence it seems prudent to take a precautionary approach in managing road salt application and controlling road salt pollution.Regulatory agencies in some jurisdictions such as Canada and Michigan use lower thresholds of 120-150 mg Cl À L À1 .Third, road salt is only one of many potential contributors to salinization, along with other anthropogenic impacts such as irrigation runoff and accelerated mineral weathering (Kaushal et al. 2018).Fourth, we know very little about how salt mixtures from multiple sources will affect aquatic organisms (Kaushal et al. 2019).Fifth, even if average concentrations equilibrate below 230 mg Cl À L À1 , much higher concentrations may occur in the lake at some times and places, due to vertical concentration gradients during winter or high winter or spring chloride loads that are subsequently flushed (Novotny et al. 2008;Corsi et al. 2010;Novotny and Stefan 2010).More elaborate models than ours, whether existing or new, could help describe these temporary excursions from equilibrium and the more rare but important cases when very high levels of salt input induce permanent stratification and meromixis (Smol et al. 1983;Ladwig et al. 2023).In addition, further work is clearly needed to better understand both the acute and chronic effects of high chloride concentrations on aquatic organisms and ecosystems.
While the general conclusions of our analysis seem fairly robust, the lake-specific predictions of equilibrium road salt concentrations that we present in Fig. 3 should be interpreted with caution.Some model assumptions are clearly violated for some lakes.For instance, lakes where evaporation dominates hydrologic losses, which are common in semi-arid regions, will concentrate road salt inputs substantially beyond the levels predicted by the model and thus will be particularly sensitive to high road density and high salt application rates.Our lake-specific predictions also make a number of assumptions in addition to those embedded in the model structure, including that actual road salt application rates are held constant indefinitely at mean 2010-2015 levels as reported by Falcone et al. (2018), and that road density and runoff also remain constant.Furthermore, because our model's treatment of hydrologic flow paths is highly abstracted, it is probably best suited for considering how equilibrium road salt chloride concentrations vary across the landscape in response to road density, salt application rate, and climate, not for understanding detailed temporal dynamics within a given system.
Our model also assumes that the relative chloride yield of the watershed per unit of runoff (ϕ) is constant, and in particular that it does not vary with the amount of chloride in the watershed.This assumption, like others that our model makes, is a simplification of reality.While chloride does generally behave conservatively (particularly at long time scales and high input rates), it nonetheless can be immobilized in ecosystems by processes including adsorption onto iron and aluminum oxides, uptake by microbes and vegetation, and conversion to organic forms (Svensson et al. 2012).A more elaborate model might allow some sort of saturating increase in ϕ as the mass of chloride in the watershed increases, to mimic saturation of these immobilizing processes.This change would likely result in somewhat lower predicted equilibrium chloride concentrations for lakes in watersheds receiving low inputs of road salt, where immobilizing processes might play an important role.
Two additional extensions of the simple approach that we took here seem potentially valuable as next steps, in addition to the use of more elaborate hydrological and limnological models.First, additional efforts to compare the model predictions to data in places where salt inputs and lake chloride concentrations have been documented over many years, as in the Mirror Lake example that we considered, would help clarify the usefulness of the model as a heuristic.Second, it would be interesting to use the model to explore how other forms of global change-such as land use or climate changes that alter the balance of precipitation and evapotranspiration or the frequency with which road salt applications are necessarymight influence road salt concentrations in lakes.

Fig. 1 .
Fig. 1.Modeled trends in road salt chloride concentration in a lake through time.The relative yield of chloride from the watershed (φ) influences the rate at which the concentration of chloride in the lake approaches equilibrium.Dotted line: If the rate of salt application or the density of roads increases through time, chloride concentrations increase without reaching equilibrium.Solid line: Chloride concentration in the lake equilibrates rapidly to a constant rate of salt application in the watershed if relative yield from the watershed is high, as might occur because hydrologic flow paths to the lake are short or dominated by surface runoff.Dashed line: Equilibration to the same final concentration occurs slowly if relative yield from the watershed is low, as might occur if flow paths are dominated by slow groundwater flows.

Fig. 2 .
Fig. 2. (a-c) Equilibrium road salt chloride concentration varies with runoff (precipitation À evapotranspiration), road density, and road salt application rate.Panels give model predictions for dry, mesic, and wet climates (runoff = 0.02, 0.25, or 0.50 m yr À1 , corresponding roughly to the climates of Montana, Michigan, and Connecticut, USA), across ranges of road density and road salt application rate corresponding to empirically observed ranges.(d) Road density distribution for county-level administrative units in the contiguous United States.See text and Supporting Information for additional details.

Fig. 3 .
Fig. 3. (a) Predicted equilibrium road salt chloride concentration for 461,567 lakes and reservoirs ("lakes") larger than 1 ha in the contiguous United States.These predictions rest on a number of important assumptions, including that road density and salt application rate per lane-m of road remain constant at mean 2010-2015 levels, and that evaporation from and precipitation on the lake surface are equal or negligible; they should be interpreted with caution.(b) State-level summary of the abundance of lakes for which the predicted equilibrium road salt chloride concentration exceeds 120 or 230 mg Cl À L À1 .Results are shown for all states where at least 25 lakes have predicted equilibrium concentrations > 120 mg Cl À L À1 .Numbers printed above bars indicate relative abundance, that is, the proportion of lakes in the state that exceed each threshold; relative abundances <0 .01 are not shown.States are ordered left to right in decreasing order of the proportion of lakes in the state that exceed the 230 mg Cl À L À1 threshold.