Comparison of statistical methods for estimation of nutrient load to surface reservoirs for sparse data set: application with a modified model for phosphorus availability

Nutrient budget models for lakes and reservoirs critically respond to the input pollutant loading, yet little consensus exists on how to estimate the load, particularly for the common but challenging case of sparse nutrient concentration measurements and abundant input flow data. A statistical load calculation using cluster (in this case, annual) mean concentration and stratified (monthly) flow was compared to estimates by sample mean and ratio estimator methods for phosphorus loading to Whitney Reservoir in North Central Texas. The results varied considerably for the various estimator methods during the six-year study period with the cluster and stratified mean approach estimating extreme high loading periods not captured by the other methods. The variable loading patterns were then tested in phosphorus budget model simulations for Whitney Reservoir that considered vertical stratification of the water column, water–sediment phosphorus interaction, and seasonal variations in water quality. For independently determined settling, interlayer dispersion, recycling rates, and sediment burial rates estimated for the respective loading calculation, the cluster and stratified mean loading pattern provided a better statistical fit of phosphorus concentration measurements in the epilimnion than when ratio estimator load calculations were used. The two loading functions described hypolimnion concentration data equally well. The lesson of this exercise is that various methods of load estimation should be examined in order to develop as reliable a management model as possible when only a sparse data set is available for calibration.