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

Summary Statistics

Nutrient-load model results were used to compute a number of summary statistics. These statistics include mean annual loads, yields, and concentrations for each nutrient constituent at each site, with the following exceptions. Two sites in the San Joaquin Valley of California were on sloughs draining the same area; therefore, streamflows and estimated loads were combined to indicate output from a single "site." Eighteen other sites had insufficient data for model calibration; 12 of these had fewer than 18 samples during the high-intensity period, and another 6 had no complete water year of daily streamflow values. The resultant summary data set includes statistics for five nutrient constituents at 481 sites. These data are in the summary data set.

For nutrients that could be fit to a regression model, mean annual load was estimated as the sum of the daily load values for the estimation period divided by the number of years. Mean annual yield was estimated by dividing the mean annual load by the upstream drainage-basin area. The flow-weighted mean concentration was calculated by dividing the total load over the estimation time period by the total streamflow. The time-weighted mean concentration was calculated as the average of the daily concentrations for the same time period. Time-weighted concentration is similar to flow-weighted concentration at many sites. However, at some sites where steamflow and load are affected by large storm events, the time-weighted concentration can differ from the flow-weighted concentration and represents the more common condition.

For some nutrients, the calculated mean concentrations were less than the most common detection limit. In these cases, the yield and load estimates were retained, but the mean concentration was revised to less than detection. Censored values reported in the summary data set can be converted to uncensored values by calculating the ratio of mean annual load and streamflow and multiplying by 0.00112 to convert the units to milligrams per liter.

In cases where a regression model could not be calibrated, the nutrient concentrations were plotted relative to streamflow and time. If there were no obvious curves or slopes in these relations, a mean concentration was computed. For nutrients with fewer than six uncensored concentrations, the flow-weighted and time-weighted mean concentrations were set to less than the most common detection limit. In these cases, load and yield were not calculated. For nutrients with more than six uncensored concentrations, a mean and standard error were computed using censored data techniques described by Helsel and Cohn (1988). If the standard error was less than 40 percent of the mean, the flow-weighted and time-weighted mean concentrations were set equal to the computed mean. Mean annual load was then calculated as the product of the flow-weighted mean, the total streamflow for the estimation period, and an appropriate units-conversion factor. Mean annual yield was estimated by dividing the load by the upstream drainage-basin area.

After all possible mean concentrations were determined, sites were ranked from low to high for flow-weighted and time-weighted concentrations of each nutrient. Percentiles were calculated from these ranks. The percentiles indicate the relative magnitude of the mean concentration at a site in comparison to those at all other National Water-Quality Assessment Program sites. The median nutrient concentration for all sites is the 50th percentile value. One-half of the sites have concentrations between the 25th and 75th percentile values.