HR: 1330h
AN: H12B-0983    [PDF]
TI: Effects of Calibration Period and Trend Terms on Regression Model Based Streamwater Constituent Load Estimates
AU: * Aulenbach, B T
EM: btaulenb@usgs.gov
AF: U.S. Geological Survey, Peachtree Business Center 3039 Amwiler Road, Suite 130, Atlanta, GA 30360-2824 United States
AB: An analysis was done to measure the effects of model calibration period length and model form on streamwater constituent load estimates. Selected regression models were applied to nitrate-plus-nitrite concentration data collected for the USGS National Stream-Quality Accounting Network Program at the Mississippi River at St. Francisville, La., from July 1967 through June 2003. Model calibration periods were varied from four to twelve years with each calibration period modeled at 1-year increments throughout the period of record, thereby producing multiple estimates of daily loads which were then compiled on an annual basis for each model. The regression model estimates the log of streamwater load as a function of the log of flow and flow-squared terms, sine and cosine seasonal terms, and long-term trend terms. Both linear and second order polynomial long-term trend model forms were used. A Minimum Variance Unbiased Estimator is used to correct for log back transformation bias correction. The root mean squared error (RMSE), expressed as a percentage of the annual load estimate, is used to assess the accuracy of the annual load estimates. Load estimates for a given year for models with the same calibration period length and model form are similar, except when the estimate is from the beginning or end of the calibration period. RMSEs are always lowest in the middle of the calibration period and highest at the beginning and end of the calibration period, with average increases in RMSE for each set of models with the same calibration period length and time-term combination ranging from 31% to 58% higher than the RMSE at the center of the calibration period. The r$^{2}$s of the polynomial trend models were higher than the linear trend term models, but only minimally. Despite improvement in r$^{2}$s, the RMSEs were higher for the polynomial time-term models, especially at the beginning and end of the calibration periods, indicating that the inclusion of the time-squared term may produce larger variance in load estimates. Longer calibration periods produced lower RMSEs for both linear and polynomial long-term trend models. It is suggested that as the calibration period increases, the long-term time terms will not accurately model temporal changes in the relation between concentration and discharge. However, the RMSE appears to be more sensitive to the increase in the number of samples in the calibration set in that RMSE decreases as calibration period increases. The results of this analysis alludes to the importance of residual analysis, in addition to model r$^{2}$s and RMSEs, to ensure that model form is appropriate for the data because calculations of RMSE assume that the error is due to sampling and not due to the lack of model fit.
DE: 1871 Surface water quality
SC: Hydrology [H]
MN: 2003 Fall Meeting