Nitrate Response Functions for Watersheds

Groundwater flow models are often used to assess the impact of non-point source contaminants, and in particular nitrate, on river and well water quality. When using a particle tracing approach, the nitrate response function at a stream or well, 퐶(푇)[M/L3], can be generated by tracking nitrate inputs on a particle-by-particle basis. This methodology accounts for spatial and temporal variations in nitrate concentrations in groundwater recharge, as well as denitrification in the subsurface (Kauffman et al. 2001). Conversely, C(T)may be calculated using the convolution integral:퐶(푡)=∫퐶௜௡(푡−푇)푓(푇)푒ି௞்푑푇∞଴(1)where f(T) [1/T]is the transit time distribution for groundwater, 퐶௜௡(푡−푇)[M/L3]is the spatially averaged nitrate input concentration, and k [1/T] is the first order rate of denitrification in the subsurface(Malowzewski and Zuber 1982).The exponential lumped parameter model (ELPM) is one option that can be used to estimate f(T)as well asits integral, the cumulative frequency distribution (CFD) of transit times (Haitjema 1995a). The advantage of the ELPM is that it is based off of spatially averaged hydrologic properties and hence easy to calculate; it also appears to be very robust, at least for large regional watersheds. We compared the performance of the ELPM with MODFLOW-MODPATH models developed for the Kirkwood-Cohansey Aquifer System (Kauffman et al. 2001) and Delmarva Watersheds (Sanford and Pope 2013). For large regional watersheds comprised of a single sand and gravel aquifer, the CFDs generated by the ELPM and MODPATH are similar (Figure 1). In all cases, the ELPM exhibits fewer transit times in the very short and very long ranges, primarily due to the presence of weak sinks. It is noted that, while the weak sink influence on the MODPATH CFD is small for these large regional watersheds, it is more pronounced for smaller sub-watersheds.