For the study conducted on the Metropolitan Toronto and Region Watershed, mass balance approaches were effective for calculating average concentrations of chloride and sodium in the base-flow discharge for steady state conditions. Until steady state occurs, methods of tracking NaCl transport in specific areas were introduced to accomodate varying characteristics . Each model gives its own prediction when steady state, (salt inputs are balanced by salt output), will be reached.
FLOWPATH (Franz and Guiguer, 1990) is a two-dimensional, finite-difference model that can simulate horizontal, steady-state ground water flow and perform particle tracking in heterogeneous, anisotropic, confined or unconfined and leaky aquifers. (GSA TODAY, December, 1993) This model was applied to the rather large section, 460 km2, of the greater Toronto area. Data came from 8000 well records. The records helped create the potentiometric surface and allowed calibration of the model. By using a reverse particle tracking method, particles were released in the discharge boundaries of Lake Ontario and terminal streams. By plotting travel times of particles moving upgradient, isochrones were developed to estimate flow lines of equal times to discharge points. Highly soluble contaminants released from the central section will take more than 100 yr to leave the system, whereas those released only a few kilometers will have a much shorter time of about 5 yr. If road salt is applied evenly in the area, steady state can be estimated through these isochrones. Steady-state for average chloride concentrations will be reached within 200 yr of initial salt application.
Another method using three-dimensional analytical solutions was developed to account for the movement of contaminant plumes within time and space. The first equation, the finite source solution (modified after Taylor and Howard, 1988), is better applied for single, isolated releases of a chemical (e.g., the use of a snow-salt dump for one season). The second equation works well for areas where salt is applied for a longer time. This solution emphasizes a continuous one-dimensional, x , steady-state flow field. These equations can be applied to spreadsheet programs like LOTUS 123. In one case, done on the downtown Toronto area, chloride was added to a 300 m length of a two-lane highway at a rate of 21.5 kg/m/yr. Slightly more that half enters the sandy subsurface beneath the road where it forms a contaminant plume after mixing with ground water. The chloride concentrations at the top of the aquifer (z =0 m) and in the center of the plume (y =0 m) vary with time as a function of the distance (x ) along the flow line. The highest levels of contamination, from 1000-3000 mg/L, lay directly on the sides of the highway. Steady-state occurs within 10 yr here, but more distant sites will not see steady-state conditions for 100 yr or more. This analytical approach is useful for finding quick answers, but its flaws include the assumption of stead-state flow at constant velocity and the aquifer containing the same material throughout its domain. Therefore, it is not very accurate for large distances; there are too many factors which cannot accurately be accounted for in equations.
The final approach, AQUA, stresses the importance of recharge as a diluting mechanism for road salt. This two-dimensional, finite element model simulates ground-water flow and mass transport in heterogeneous and anisotropic, confined or unconfined aquifer systems under steady-state and transient flow conditions. (GSA TODAY, December, 1993) AQUA was used on a much smaller area (2 km by 1 km parcel containing three 10-m-wide roadways) in a small subcatchment in the Highland Creek basin. The roads are located perpendicular to direction of flow and the aquifer (5 m) is recharged is recharged everywhere at a rate of 160 mm/yr. Highest concentrations were found nearest the ground-water divide, where little water is available for dilution to occur. Plume concentrations increase as time and salt input increases. Steady-state happens after just 30 yr, extremely shorter than predictions by FLOWPATH. However, the prediction is reasonable because of the small area studied. Concentrations of chloride within 200m of the salted highway are two to three times of the discharging base flow. (GSA TODAY, December, 1993)