A variety of nutrient sources transported by multiple flow paths contribute to the nutrient load entering Willow Creek Lake. In addition to Willow Creek, there are several smaller tributaries that contribute streamflow to the lake. As Spalding and others (1992) noted, groundwater interactions with the lake are likely another important contributor to nutrient loading. Nutrient load was computed as the product of volumetric flow rate and nutrient concentration and was applied to both streamflow and groundwater. A water balance approach was used to estimate the volumetric flow rates (hereinafter referred to as flow) for streams and atmospheric sources, with groundwater flow as the residual of that balance. Nutrient concentrations were determined from sampling data. Nutrient loading into and out of the lake was quantified using multiple techniques, all of which linked volumetric water flux along a flow path with nutrient concentrations. Surface-water inflows were estimated using the program LOADEST (Runkel and others, 2004). Using the streamflow record and sampling results, LOADEST builds a regression for nutrient loads based upon variables such as flow and time of year. Streamflow and nutrient concentrations were both log-transformed to ensure the statistical assumptions of the regression were met, including residual normality (Helsel and Hirsch, 2002). Regression equations were evaluated based upon statistical goodness of fit and avoided the use of quadratic relations to streamflow to prevent excessive extrapolation errors in the load estimates. The LOADEST model is described in Rus and others (2018).
Groundwater loading was estimated by assigning a static nutrient concentration to the groundwater flow component estimated from the water balance. Groundwater transport was assumed to be limited to the soluble forms of nitrogen (nitrate plus nitrite) and phosphorus (phosphate). Nutrient concentrations assigned to positive groundwater flow (into the lake) were taken as the unweighted mean of samples from wells in the shallow aquifer. Nutrient concentrations assigned to the negative groundwater flow (out of the lake) were estimated from concentrations measured in the lake. For phosphate, the level was assumed to be zero out of simplicity, as very few lake samples were above the detection limit for phosphate. Nitrate plus nitrite, however, was more complex, with a clear seasonal trend in the lake showing highest concentrations in early spring and lowest concentrations in late summer. Consequently, nitrate plus nitrite in the lake was estimated as a seasonal function of the day of the year that was derived from sample data.
Loads calculated at the North Tributary (NT) site had higher uncertainty than the other stream sites, presumably as a result of greater flashiness at the site relative to the other two. The load uncertainty at the NT site was particularly high with the sediment-associated nutrients of total Kjeldahl nitrogen, total phosphorus, and phosphate as phosphorus, with the average standard error being nearly equal to the average daily load. The greatest amounts of uncertainty were associated with the early spring periods, implying that the first flush of sediments from the ephemeral stream were dynamic and had a detrimental effect on the model performance.