A Monte Carlo Test of Load Calculation Methods,
Lake Tahoe Basin, California-Nevada


Robert N. Coats, Fenjing Liu, and Charles R. Goldman


The sampling of streams and estimation of total loads of nitrogen, phosphorus and suspended sediment play an important role in efforts to control the eutrophication of Lake Tahoe. We used a Monte Carlo procedure to test the accuracy and precision of four methods of calculating total constituent loads for nitrate-N, soluble reactive P, particulate P, total P, and suspended sediment, in Blackwood Creek, for two water years. The methods tested were two forms of the BealeÕs Ratio Estimator, the Period Weighted Sample, and the Rating Curve. The BealeÕs Ratio Estimator calculates load by multiplying discharge-weighted mean concentration by total discharge in a given time interval, and adjusting the result using a factor that incorporates the ratio of covariance of load with discharge to the variance of discharge. In the Period Weighted Sample method, two successive samples of concentration are averaged, and the result multiplied by the cumulative discharge between sampling times, with the results for each interval summed over the water year. The Rating Curve method uses a regression of log of instantaneous concentration vs. log of instantaneous discharge to estimate daily concentration, which is then used with daily discharge to estimate daily load. Intensive sampling in 1985 (a dry year) and 1986 (a wet year) provided a basis for estimating loads by the "worked record" method, for comparison with estimates based on re-sampling at the lower intensity that characterizes the present monitoring program.

Figure 1 shows the relationship between sample size and Root Mean Square Error (a measure of both accuracy and precision). The results show that 1) the Period Weighted Sample method was superior to the other methods for all constituents, for 1985; 2) For total P, particulate P and suspended sediment, the Rating Curve gave the best results in1986; 3) For soluble reactive P and nitrate-N, the Period Weighted Sample method was best in both 1985 and 1986; 4) The precision of all methods for total P is low; with 30 samples per year (typical the present sampling program) the 95 percent confidence limits on the estimate of total P load for 1986 would be +/- 59 percent of the load estimate. Modification of the present sampling program and load calculation methods may be necessary to improve the precision and accuracy of estimates of total P loads in basin streams.



Figure 1. Relationships between sample size and Root Mean Square Error, for total phosphorus, particulate phosphorus, suspended sediment, soluble reactive phosphorus and nitrate-nitrogen. _ Rating Curve; _ Period-weighted Sample; _ BealeÕs Ratio Estimator; _ Stratified BealeÕs Ratio Estimator