Methods

Site selection, data compilation, and data modification preceded trend analysis. The seasonal Kendall test or Tobit regression was used to detect monotonic trends.

Site Selection

Sites were selected for trend analysis from NWIS using data-summary functions of the SPARROW (Spatially Referenced Regression on Watershed Attributes) surface water-quality program (Schwarz and others, 2006) and a review of nutrient-concentration trend scatterplots. The SPARROW model consists of a nonlinear regression equation describing the transport of contaminants from point and nonpoint sources on land to rivers and through the stream and river network. The NWIS stations with continuous streamflow and water-quality records since 1975 and sites with recent (2004) record and at least 10 years of record were identified. Analysis was completed for 44 NWIS sites in this study (fig. 1; table 1).

Site selection for the STORET sites was determined by the requirements of the trend-analysis program S-ESTREND (Schertz and others, 1991; Slack and others, 2003). Parametric and nonparametric statistical trend tests used in S-ESTREND are constrained by number of observations and censoring of values. The 290 sites were selected using the automated constraints within the program. Sites were determined to have sufficient data for trend analysis using the seasonal Kendall test if the data record spanned a minimum of 5 years, the minimum number of detected observations was three times or greater the number of designated seasons and at least 10, and a minimum of one observation per year must have been present in the beginning and ending fifths of the record. Site records were determined to have sufficient data for trend analysis using the Tobit regression (used if the dataset had more than one reporting level) if each data record spanned a minimum of 5 years, the minimum number of detected observations in the record was at least 10, a minimum of 20 percent of the total number of observations in the record were detected observations, and a minimum of one observation per year must have been present in the beginning and ending fifths of the record. Sites were selected to allow evaluation of the periods 1975–1985, 1985–1995, 1993–2004, and 1975–2004.

Data Modification

In an effort to create more complete datasets, related properties or constituents in the NWIS dataset were combined. Field and laboratory alkalinity, pH, and specific conductance were each combined by preferentially selecting the field measurement when available but using the laboratory measurement when field values were not available. In a similar manner, the flow dataset was populated first by instantaneous discharge, and alternatively by daily mean discharge.

Flow data were not obtained from the STORET dataset, so a routine was implemented that assigned a streamflow value from a selected nearby USGS streamgaging station (Cassingham and Terziotti, 2006). The National Hydrography Dataset Plus (NHD-Plus) was used to match ungaged water-quality sites with nearby USGS streamgaging stations. If any streamgaging stations were within the upstream or downstream catchment areas of the ungaged water-quality site, drainage areas were compared to determine if they were within a threshold. The criterion for an acceptable match between a streamgaging station and an ungaged water-quality site was a drainage area pairing ratio between 0.75 and 1.25. When a matched pair was determined, streamflow values were added to the water-quality dataset.

Modification Related to Censoring Levels

Trend-test methods and the choice of an appropriate test are often affected by censoring (less-than or nondetection values) within datasets. Large amounts of censoring or censoring at different reporting levels are two important factors to consider in choosing an appropriate trend test or removing a site from consideration. Analytical methods and performance may change through time, resulting in reporting levels that change as well. No effort was made to re-censor data to a common reporting level when the cause of reporting-level variability was a result of method changes or analytical performance. Efforts were made, however, to ensure that reporting levels, also referred to as censoring levels, were used in a consistent manner and re-censoring techniques were applied to account for reporting-level variability that was caused by inconsistent usage.

Historically, the USGS National Water Quality Laboratory (NWQL) has used the minimum reporting level (MRL) in laboratory analyses; MRL is defined as the smallest measured concentration of a substance that can be measured reliably by using a given analytical method (Timme, 1995). The reliability of the measured concentration can be determined by statistical methods or subjective criteria, including the analyst’s judgment (Childress and others, 1999). Since the MRL definition is not specific, beginning in 1996 the NWQL began censoring data at the laboratory reporting level (LRL). The LRL is established by using a consistent statistical method that reduces the chances of reporting false negative results. The LRL is generally twice the method detection level (MDL), which is described as the minimum concentration of a substance that can be measured and reported with 99-percent confidence that the analyte concentration is greater than zero (Childress and others, 1999). This change in reporting level may create an artificial upward trend, especially in heavily censored datasets. Therefore, all USGS NWIS data censored with an LRL were re-censored with an MDL, by dividing by 2 (Mueller and Spahr, 2005). Laboratory-estimated values were assumed to be the actual values.

Similar to other constituents, ammonia has had multiple reporting levels because of changing analytical methods over the last 15 years. However, the NWQL evaluated historical data and recommended re-censoring to a common level; thus, all censored ammonia data were re-censored to less than (<) 0.02 milligram per liter (mg/L; Mueller and Spahr, 2005).

Modifications to censoring levels were performed only on the USGS NWIS dataset due to the availability of reporting-level history and usage. It was not feasible to modify censoring levels for the STORET dataset because of the multiple sources of data, greater variation of laboratory methodologies and quality-control procedures, and lack of reporting-level history and usage. Changes in analytical methods over time are some of the most difficult aspects of developing long-term records for trend analysis. The historical knowledge of the NWIS database allowed better standardization of the datasets than possible with the STORET dataset.

Trend-Analysis Methods

Trends were determined by using the seasonal Kendall test (Hirsch and others, 1982; Helsel, 1993b) and Tobit regression (Schertz and others, 1991). The seasonal Kendall test adjusts for seasonal variability by comparing seasonally grouped constituent concentrations adjusted for the effects of streamflow with LOWESS (LOcally WEighted Scatterplot Smoothing) smoothed curves. Tobit regression is appropriate for examining records that include censored data and multiple reporting levels. Statistical tests for trends in water quality over time were performed by using S-ESTREND, version 1.1 (Slack and others, 2003).

If the dataset contained less than 5 percent censored values and only one reporting level, the seasonal Kendall test for uncensored data was used. This nonparametric test calculates trends on the flow-adjusted concentrations.

If the dataset contained greater than 5 percent censored values and only one reporting level, the seasonal Kendall test for censored data, which has no flow adjustment, was used. This nonparametric test requires the user to select a value for the censoring level detection, in which case one-half the reporting level was selected. Because the seasonal Kendall test for censored data has no flow adjustment, care must be taken to avoid comparing the results of the test with results of trend tests using flow adjustment. Trends detected with the seasonal Kendall test for censored data may be due to trends in flow. Results of this test are not reported here, except for the ammonia results, because the high numbers of censored ammonia values in most cases only allowed analysis by the seasonal Kendall test for censored data or Tobit regression.

Finally, if the dataset had more than one reporting level, the Tobit regression model was selected. The Tobit trend test is a parametric regression model that incorporates flow and seasonality. When using the Tobit trend test, a log transformation of flow and constituent values was used, seasonal terms were included, and the criterion was applied that a minimum of 20 percent of the data must be above the detection limit to run the test.

The particular trend test used for each site, period, and constituent are given in Staub and others (2009). The trend test used is an indication of the frequency of censored values or multiple reporting levels in the data. Ammonia, ammonia plus total organic nitrogen, and total phosphorus were the constituents often associated with many censored values, such that even robust trend-analysis techniques for these constituents may not be able to produce a statistically valid trend (Helsel, 1993a).