U.S. Geological Survey

Data Series 152

National Water-Quality Assessment Program

Water-Quality, Streamflow, and Ancillary Data for Nutrients in Streams and Rivers Across the Nation, 1992–2001

Estimation of Nutrient Loads

The loads of selected nutrients at National Water-Quality Assessment Program sites were estimated using multiple-regression analysis. The specific method used for model calibration and load estimation is described by Runkel and others (2004). Separate regression models were developed for ammonia, nitrate, total nitrogen, orthophosphate, and total phosphorus at each site. Concentrations of total nitrogen (TN) were computed using the analytic results for dissolved nitrite plus nitrate (NO₂+NO₃), and for total Kjeldahl nitrogen (TKN), which includes organic nitrogen and ammonia. If neither NO₂+NO₃ nor TKN was censored, total N was simply their sum. If one or the other was less than a method detection limit (MDL), the following rules were applied:

• If TKN is not censored and NO₂+NO₃ is censored, then
  TN = TKN + 0.5 x (MDL for NO₂+NO₃)
• If TKN is censored and NO₂+NO₃ is greater than 0.20, then
  TN = (NO₂+NO₃) + 0.5 x (MDL for TKN)
• If TKN is censored and NO₂+NO₃ is less than 0.20, then
  TN = (< 0.20)

The most common detection limits during water years 1992–2001 were 0.2 mg/L for TKN and 0.05 mg/L for NO₂+NO₃.

The dependent variable in each model was the natural logarithm of the constituent load, computed as the product of a measured concentration and the mean daily streamflow for the date of sample collection. The explanatory (independent) variables were selected from a set of potential predictor variables:

• natural logarithm of streamflow, log (flow)
• log (flow) squared
• time, in decimal years
• sine of time
• cosine of time
• time squared

The variables log (flow) and time were centered by subtracting the mean from each value. Thus the squared values of these variables are fit to a parabolic curve with an inflection point near the mean.

For each constituent at each site, models were fit using all possible combinations of these variables, and the best model was selected on the basis of the Akaike Information Criteria (Akaike, 1981). The sine and cosine terms, which account for seasonality, were always included together if either was selected.

Because nutrient concentrations included censored values, regression coefficients were determined by an adjusted maximum-likelihood estimation (AMLE) method (Cohn and others, 1992). The AMLE method corrects for bias in the standard maximum-likelihood (MLE) regression coefficients and also incorporates a factor that minimizes the bias that can occur when estimated logarithms of constituent load are retransformed to original units. For some constituents, the AMLE method failed, but a standard MLE model was successful. In these cases, retransformation bias was corrected using the method of Bradu and Mundlack (1970).

If an AMLE or MLE model was selected, daily streamflows at the site were used to estimate daily nutrient loads for specified water years of the high-intensity sampling period. Nutrient concentrations were calculated for each date as a ratio of the daily load and streamflow. The daily estimates can have large errors, but positive and negative errors in the daily values tend to cancel out when loads are summed over a longer time period. Thus annual loads tend to have a greater accuracy. The time periods used for calibration of the models and for estimation of daily loads and concentrations are:

Complete descriptions of model calibration, selection, and application are in the report: Nutrients in Streams and Rivers Across the Nation — 1992–2001 (D.K. Mueller and N.E. Spahr, U.S. Geological Survey, written commun., 2005). Model coefficients are in the load-model coefficients file.