Introduction

The Puget Sound basin encompasses the 13,700-square-mile area that drains to the Puget Sound and the adjacent marine waters of Washington State, which are home to numerous species of fresh and marine organisms. More than 4 million people live within the basin, with numbers continuing to increase, who rely on the basin’s ecosystem. As populations and anthropogenic activities within the basin have increased, the wellbeing of several aquatic organisms and ecosystem processes have been impacted (Puget Sound Info, 2022). The Puget Sound Partnership was created by a Washington State statute (Washington State Legislature, 2007) to implement a science-based recovery of the Puget Sound to help address these impacts. As part of the recovery, the Partnership developed the Puget Sound Vital Signs as measures of ecosystem health that guide the assessment of progress toward Puget Sound recovery goals (Puget Sound Partnership, 2020). Each of these components is represented by one or more indicators of the condition of the Puget Sound.

In 2015, the Puget Sound Partnership Leadership Council adopted a Drinking Water Vital Sign associated with human health and quality of life, recognizing these characteristics as integral to the sustainability of Puget Sound recovery efforts. Recommendations for two complimentary drinking-water indicators were developed by a Puget Sound Partnership led team in 2019 and adopted by the Science Panel and Leadership Council in May 2019. Both indicators are focused on drinking-water quality and include:

The U.S. Geological Survey (USGS) led the development of the second indicator as described in this report.

For this study, groundwater vulnerability refers to the relative ease with which a contaminant applied at or near the land surface can migrate to the aquifer of interest for a given set of land-use practices. Nitrate concentration data were selected for evaluation because elevated nitrate concentrations are typically caused by anthropogenic activities (for example, cropland fertilization, lawn and garden fertilization in urbanized areas, domestic on-site sewage disposal; Williamson and others, 1998; Ebbert and others, 2000), excess nitrate concentrations can impact drinking water and human health (Winter and others, 1999; Tesoriero and others, 2013; Ward and others, 2018; Stayner and others, 2021), and nitrate concentration data are relatively common compared to the frequency of analysis for other constituents commonly associated with anthropogenic activities, such as pesticides or volatile organic compounds. For example, the Washington State Department of Health (WDOH) requires that public water supply systems regularly measure nitrate concentrations. Thus, as a widespread contaminant, nitrate concentrations are an important indicator of environments that are susceptible to contamination. However, such testing is only required by WDOH for relatively large (Group A—more than 15 connections or more than 25 people) public water supply systems and, as a result, citizens and public health officials have only limited information about the potential exposure to elevated nitrate concentrations for people whose primary drinking-water sources are small systems or domestic wells. To assist the Partnership, the USGS developed a series of temporally based maps that show groundwater vulnerability to elevated nitrate concentrations. These maps and the associated models used to create them provide a regional scale understanding of groundwater vulnerability to anthropogenic contamination, and how that vulnerability has changed over time with changes in land use and other variables. The results of the project will also inform decisions on how best and how frequently to report on this indicator of groundwater vulnerability as defined as the probability of exceeding specific nitrate concentrations at specific well depths throughout the Puget Sound basin in future years.

Description of Study Area

The Puget Sound basin contains a varied landscape that ranges from more urbanized and agricultural areas in the lowlands and alluvial valley foothills adjacent to the Puget Sound and forested areas in the rolling hills and steep mountains surrounding the lowlands (fig. 1). The mild rainy marine climate, densely forested slopes, volcanic peaks, migrating salmon, and islands and shores of Puget Sound are all defining features of the basin, as are the cities and farms and expanses of forest. The rivers and streams in the basin drain from many separate watersheds directly into Puget Sound. Although each of these watersheds is unique, and the quality of water in the streams is influenced to varying degrees by a range of environmental factors, the watersheds share many common characteristics, and the range of water-quality conditions are similar and comparable. The natural and human factors that have a large-scale or regional influence on water quality in the Puget Sound basin define the basin's environmental setting. Mountainous and forested lands can be found to the east and the west of the basin, with the Puget Sound basin lowlands located within the middle of the basin.

The Puget Sound Regional Aquifer System, contained largely within the Puget Sound lowland and the upper reaches of the adjacent alluvial valleys, is composed primarily of unconsolidated sediments that can be locally more than 3,000 feet (ft) thick. Coarse-grained outwash and alluvial deposits have significant water-bearing capacity and form the major aquifers in the Puget Sound basin (Frans, 2008). Most domestic and large-capacity public supply wells are screened in these units that can extend up stream in the floodplains of larger river systems in the Puget Sound basin. Fine-grained interglacial, lacustrine and till deposits are layered between the coarse-grained deposits and serve as confining and semi-confining units. A more detailed description of the hydrogeology of the Puget Sound can be found in Staubitz and others (1997).

Methods of Investigation

Similar to the previous USGS vulnerability assessments (Tesoriero and Voss, 1997; Frans, 2000, 2008), maps showing the probability of elevated nitrate concentrations in groundwater at multiple depths selected by the authors to represent the relationship between depth and vulnerability to elevated nitrate concentrations during specific time periods in the Puget Sound basin were developed in several steps:

Compilation of Nitrate Concentration Data into a Response Variable

The binary response variable of nitrate concentrations exceeding or not exceeding 2 mg/L was computed from data archived in the WDOH Sentry public-water supply system database (Washington State Department of Health, 2020). The dataset provided to us by WDOH contained more than 16,500 nitrate concentration analyses from more than 2,900 pre-treatment samples collected for Group A wells from 2000 through 2019, along with selected metadata about the wells. Well depths ranged from very shallow wells and springs to a maximum depth of 1,600 ft. The median well depth was 200 ft, and the 25th and 75th percentile well depths were 133 and 303 ft, respectively. Because nitrate concentrations and land-use characteristics would be expected to have changed over time, the dataset was divided into four time periods: 2000–04, 2005–09, 2010–14, and 2015–19. The number of wells in each time period ranged from 868 in the 2005–09 time period to 1,815 in the 2010–14 time period and were evenly distributed throughout the study area for each time period. More than 70 percent of the wells were represented by more than one period. For each unique well, multiple samples were possible within each of the four time periods. If multiple results for a well were available within a time period, an average nitrate concentration was calculated and converted into the binary response form (exceeding 2 mg/L or not). The locations of the wells within the final dataset for each time period are shown in figure 2.

Logistic Regression Model Results

Using the stepwise logistic regression modeling procedures described in section, “Methods of Investigation,” separate models were developed to estimate the probability that groundwater would exceed 2 mg/L within each of the four specified time periods. The stepwise modeling procedure tested all possible combinations of the explanatory variables and, for each time period, the most significant model was selected based on the log-likelihood ratio, McFadden’s rho-squared, the p-values for each variable included in the models, and the prediction efficiency of each model. For each model, the correlations between explanatory variables were examined to ensure that no unacceptable multicollinearity existed, which is a required assumption associated with a statistically valid logistic regression model.

Statistically significant models were found for each time period (table 2). For all of the models, the McFadden’s rho-squared values were greater than or equal to (≥) 0.20. Rho-squared values tend to be smaller than R² values often used to evaluate linear regression results, so values from 0.2 to 0.4 are generally interpreted to indicate good results (SPSS, Inc., 2000). Of additional value in evaluating the models are the highly significant p-values that were all less than (<) 0.0001, indicating that all of the included explanatory values were significant. Prediction efficiencies were also very high for each model, ranging from 88.1 to 90.1 percent.

The significant explanatory variables within each of the models were similar for all four time periods. For example, well depth and the percent of agricultural land cover within a 4,000-m buffer around a well were consistently highly significant in each model as shown by their very low p-values (table 3). For all models, one of the measures of urban land cover around the well (percent within either a 500- or a 1,000-m buffer) was significant. The consistent significance of well depth, percent agricultural land cover within 4,000 m of a well, and percent urban land cover within 500–1,000 m of a well across all four time-period models suggests that these explanatory variables have been consistent controlling factors of groundwater vulnerability to elevated nitrate concentrations over time. Saturated hydraulic conductivity was a significant explanatory variable in all except the 2005–09 model, whereas average annual precipitation was a significant explanatory variable only in that 2005–09 model. Together those results suggest that an explanatory variable that characterizes the ability of nitrates applied to the land surface to be transported through the soil to the wells is an important variable. The percent wetland within 500 m of a well and percent forest cover within 4,000 m of a well was significant in only one of the four time periods.

In addition to the significance levels of the test statistics, the positive and negative signs of the model coefficients are also extremely insightful (table 3). For example, well depth coefficients were all negative, indicating that as depth increases, the probability of elevated nitrate concentration decreases. A reduced probability of elevated nitrate concentrations in groundwater is to be expected with increasing well depths and has been documented in previous modeling efforts (Tesoriero and Voss, 1997; Frans, 2000, 2008). The significant model coefficients for well depth are consistently negative across all time periods. While significant for all time periods, the well depth model coefficients are decreasing over time which may indicate a delayed response of deeper groundwater to nitrate application or changes in denitrification potentials in overlying soils (Tesoriero and others, 2013). The coefficients for the percent agricultural cover and the percent urban cover in the well buffers were consistently positive, indicating that increases in these land covers coincide with increased probabilities of elevated nitrate concentrations. Positive coefficients for the saturated hydraulic conductivity variable suggest that greater soil permeability coincides with greater probability of elevated nitrate concentrations. Finally, the few significant wetland and forest land cover explanatory variables had consistently negative coefficients, reflecting the likely lower loading of nutrients to these land covers as well as the expected increase in processing and uptake of nutrients in those land covers. The magnitudes of all coefficients were the same among models for all four time periods, suggesting that the influence of these explanatory variables on groundwater vulnerability has been consistent over time. In addition to the consistency of explanatory variables over time, the significant variables identified in this study were similar to those found in previous studies using a similar approach (Tesoriero and Voss, 1997; Frans, 2000, 2008).

Evaluation of Model Performance

To further evaluate the performance of the models presented in table 3, a series of comparisons between the measured and predicted probabilities of elevated nitrate concentrations for wells included in the model calibration datasets were performed using linear regression (fig 3). Wells from the model development datasets for each of the four time periods were sorted from low to high predicted probabilities of elevated nitrate concentrations as calculated using their reported well depths and the models presented in table 3. After sorting the data by predicted probabilities, wells were equally distributed between 10-percent quantiles of probability. A mean predicted probability was calculated for each decile and plotted against the observed probability for the decile (fig. 3). For all time-period models, the differences between measured and predicted probabilities of elevated nitrate concentrations were very small as indicated by the high adjusted R² values and the close fit to the 1:1 line. The strongest relation was observed in the 2015–19 model, which had an R² value of 0.99.

To validate the models for each of the four time periods, the predicted probabilities of elevated nitrate concentrations for wells in the validation datasets were computed and compared to the observed probabilities using the same approach as described for the model calibration datasets presented in figure 3. As with the calibration data, the differences between predicted and observed probabilities of elevated nitrate concentrations in the validation data were generally small (fig. 4). For example, predicted values averaged 0.6 and 1.7 percent less than observed probabilities for 2000–04 and 2015–19 validation data, respectively. For 2005–09 and 2010–14 data, predicted probabilities averaged 1.7 and 2.1 percent greater than observed values, respectively.

Probability of Elevated Nitrate Concentrations in Groundwater of the Puget Sound Basin

The logistic regression models presented in table 3 were used to create maps showing the probability of finding elevated nitrate concentrations in groundwater throughout the Puget Sound basin during each of the four time periods (figs. 5, 6). To generate the maps, a 500 × 500-m grid was constructed that covered the entire Puget Sound basin. A hypothetical well was assigned to the center of each grid cell resulting in 171,538 such wells within the basin. For each hypothetical well and each of the four time-periods, the significant explanatory variables included in each of the time specific models were calculated using GIS and other data and attributed to each hypothetical well. For each of the 171,538 hypothetical wells, the significant explanatory variables included in each of the time specific models was used to calculate the probability of finding elevated nitrate concentrations and assigned to the 500 × 500-m grid for the hypothetical well. It should be noted that explanatory variables used in each of the time-specific models were not constrained to the 500 × 500-m grid but were allowed to use GIS explanatory data as defined in each of the models (that is, percentage of agricultural land cover within 4,000 m of well). For some of the explanatory variables, data were not available for the entire area of interest; areas with missing data were typically located within the national parks, wilderness areas, and higher-elevation forested areas with limited groundwater resources. Selected other hypothetical well locations also had missing explanatory data, such as average annual precipitation. Probabilities of elevated nitrate concentrations were not estimated in those areas with missing data. Other smaller, dispersed areas were missing saturated hydraulic conductivity data, but spatial kriging methods within ArcInfo (Krivoruchko and Gribov, 2019) were used to extrapolate saturated hydraulic conductivity for those areas from nearby data.

Maps of estimated probabilities of nitrate concentrations exceeding 2 mg/L generated from hypothetical wells located at 150 and 300 ft in each of the 171,538 grid cells were produced for well depths of 150 and 300 ft for each of the four time periods, resulting in the set of eight maps (figs. 5. 6). The data used to generate these maps can be found in Wright and others (2023). The selection of the 150- and 300-foot (ft) depth were selected based on previous work (Tesoriero and Voss, 1997; Frans, 2000, 2008) and were representative of the range of well depths in the datasets used to create the models. For both the 150- and 300-ft depths, the highest probabilities of elevated nitrate concentrations are most common in the areas of high urban and agricultural activity. Whereas the geographic areas with elevated probabilities of nitrate were similar for both depths, the probabilities were lower at the 300-ft depth. The highest probabilities of elevated nitrate concentrations beneath the urban and agricultural areas at the 150-ft depth ranged from 87 percent in 2000–04 to 96 percent in 2015–19. At 300 ft deep, the highest probabilities ranged from 67 percent in 2000–04 to 90 percent in 2015–19. Conversely, regions with little agriculture or urban land use had lower probability of elevated nitrate concentrations. These types of maps could be generated for any depth of interest, with probabilities of elevated nitrate concentrations expected to decrease with increasing well depth at any individual location.

Modeled probabilities of elevated nitrate concentrations at both the 150- and 300-ft depths were less than 10 percent for more than 75 percent of the modeled area of the Puget Sound basin across all time periods (fig. 7). However, there were several locations with relatively high probabilities and other locations with differences in probabilities among time periods. A nonparametric Kruskal-Wallis test was performed for both the 150- and 300-ft depths to compare differences between modeled probabilities for each of the four time periods. These tests found significant differences between time periods (table 4). At the 150-ft level, mean probabilities for the first three time periods were comparable, but probabilities for the 2015–19 period were higher. A similar result was found at the 300-ft level.

Although most modeled probabilities were less than 50 percent, values greater than this level may be of greater interest to water purveyors, regulators, and land managers. Figure 8 summarizes the subset of modeled probabilities that are equal to or greater than 50 percent for each time period at the 150- and 300-ft depths. The probabilities of elevated nitrate concentrations were less than 70 percent for more than 75 percent of this subset of samples for every time period at both the 150- and 300-ft depths. Similar to the nonparametric Kruskal-Wallis test done on all of the modeled results, mean values for the subset of probabilities equal to or greater than 50 percent were significantly different with time at both well depths (table 5). Unlike the mean probabilities for all of the modeled results, mean values for this subset of probabilities for the most recent three time periods were similar, and the mean value for the 2000–04 time period was lower at both the 150- and 300-ft depths. It is important to restate that these results are for a small subset of wells with precited probabilities equal to or greater than 50 percent and do not represent results of the Puget Sound basin as a whole, but rather select locations that may be of greater interest to water purveyors, regulators, and land managers.

Temporal Changes in the Probability of Elevated Nitrate Concentrations

Comparing modeled probabilities across the time periods, particularly probabilities greater than 50 percent, provides insight into changes (trends) in groundwater vulnerability at the scale of the Puget Sound basin, although it does not provide insight into changes at specific locations. To examine changes more explicitly in the probability of elevated nitrate concentrations at specific locations over time, a series of change maps was generated (figs. 9, 10). To create these maps, each hypothetical well location with a predicted probability of elevated nitrate concentrations equal to or greater than 50 percent was identified for each model time period, and the modeled probability at that location was compared across adjacent time periods. For all the pairwise comparisons, the probability of elevated nitrate concentrations had to be at least 50 percent or greater for at least one of the two time periods. These comparisons were done separately for wells at the 150- and 300-ft depths. The change maps generated for 150-ft-deep wells (fig. 9) showed inconsistent changes over time. For example, the changes from 2000–04 to 2005–09 were mostly increased probabilities of elevated nitrate concentrations (fig. 9A), changes from 2005–09 to 2010–14 were mostly decreased probabilities (fig. 9B), and changes from 2010–14 to 2015–19 included a more even mixture of increased and decreased probabilities (fig. 9C). In contrast, at the 300-ft depth, probabilities of elevated nitrate concentrations generally increased between all the time periods (fig. 10A-C). The difference in responses between the 150- and 300-ft wells suggests that the probability of elevated nitrate concentrations in shallower wells is more dynamic than it is in deeper wells. The reduced fluctuation of nitrate concentration in the deeper wells is likely given increased mixing, dispersion, denitrification, and (or) other processes. The general increase in the probability of detecting elevated nitrates at the 300-ft depths over time suggests that the deeper wells are receiving a consistently greater fraction of groundwater affected by anthropogenic nitrate loads and suggests that a time delayed front of anthropogenically impacted waters are migrating to the 300-ft depths across a broad area. Previous studies have seen similar processes occur (Levy and others, 2021).

Although the boxplots in figures 7 and 8 show course temporal changes in the modeled probabilities across the four time periods, they represent the distributions of probabilities across very large and relatively noisy datasets. To examine temporal trends in the data in greater detail, predicted probabilities within each time period at 150- and 300-ft depths were sorted from low to high and assigned to one of ten quantiles, each quantile with 10 percent of the values. The distributions of predicted probabilities within each of those ten quantiles were plotted for each of the four time periods for 150-ft and 300-ft-deep wells. The distribution patterns for 150-ft wells in quantiles 1–6 (figs. 11, 12) show low probabilities of elevated nitrate concentrations, generally less than 5 percent. These distributions for quantiles 1–6 were consistent across time periods in that median probabilities within the 2000–04 and 2015–19 time periods were higher than median probabilities in the intervening 2005–09 and 2010–14 periods. The distribution patterns for 150-ft wells in quantiles 7–10 showed increasingly higher probabilities of elevated nitrate concentrations, with probabilities that generally exceeded 20 percent in the uppermost 10th quantile (fig. 12). Compared with patterns for the lower quantiles, the differences in distributions shifted across the time periods in the higher quantiles, particularly in the 9th and 10th quantiles, where median probabilities for the 2000–04 time period were the lowest and gradually increased in the subsequent time periods. Very similar patterns were found in the predicted probabilities for the hypothetical 300-ft-deep wells (figs. 13, 14).

The patterns observed in figures 11 and 12 indicate that, at both the 150- and 300-ft well depths, changes in the probabilities of finding elevated nitrate concentrations in groundwater over the past two decades have been inconsistent across time periods and across ranges of predicted probability. This analysis shows that the highest probabilities of finding elevated nitrate concentrations seem to have generally increased over the four time periods, whereas the more moderate probabilities (represented by the 4th–6th quantiles in figures 11 and 12) seem to have generally decreased over at least the first three same time periods. The highest probabilities for finding elevated nitrate concentrations on these quantile plots are nearly all less than 10 percent for the first 8 quantiles, and less than 25 percent for the 9th quantile, further indicating how much of the Puget Sound basin area has relatively low predicted probabilities of elevated nitrate concentrations. Only in the 10th quantile do probabilities become consistently greater than greater than 25 percent, which may be the probabilities of most interest to water-quality managers.

An additional quantitative method to examine these temporal trends across the range of predicted probabilities is with quantile regression, as described in section, “Analytical Approaches for Evaluating Trends in Predicted Probabilities.” Although quantile regression has many similarities to traditional regression, it does not have the same restrictive assumption regarding uniform variation and thus allows one to examine relationships between variables outside the mean of the data. For this analysis, the independent variables were the four time periods, and the dependent variable was the predicted probability of elevated nitrate concentrations in 150- and 300-ft-deep wells. Quantile regressions were examined for the lower 5th quantile through the 95th quantile of probabilities by 5 percent increments. A simple way of thinking about this analysis is that a correlation line between the independent variable (time period) and the dependent variable (probability of elevated nitrate concentrations) is calculated for each of the 19 defined quantiles. Like simple linear regression, intercept and slope coefficients are generated. For this analysis, the slope coefficient is of most interest because it indicates of the rate of change in the probabilities of elevated nitrate concentrations over time for various ranges of the predicted probabilities.

The slope coefficients for these analyses (table 6) for all 19 quantiles for 150- and 300-ft-deep wells were all statistically significant at the p <0.0001 level. A positive slope value indicates an increasing trend in the probability of elevated nitrate concentrations over the four time periods, whereas a negative slope indicates a decreasing trend. For both well depths, the largest increasing trends (largest positive slope values) were found in the highest quantiles, which are associated with the highest predicted probabilities for elevated nitrate concentrations. These results indicate that the higher probabilities of elevated nitrate concentrations (quantiles 70–95 percent) have been increasing from 2000 to 2019. Such increases in nitrates for those wells with high probabilities may be due to continued anthropogenic sources of nitrates in the modeled areas around the wells and (or) a lag in the delivery of excess nitrate to these wells. When presented graphically (fig. 15), the increase in slope values is obvious. These analyses indicated that over the time periods examined, the abundance of wells with moderate probabilities of elevated nitrate concentrations (about 30–60 percent) has declined, whereas the abundance of wells with higher probabilities (greater than [>] 70 percent) has increased. Although the abundance of hypothetical wells with high probabilities of elevated nitrate concentrations seems to have increased over time, most of the hypothetical wells (30–60 percent quantiles) have small decreases in probabilities of elevated nitrate concentrations.

Summary

To help develop a Drinking Water Vital Sign for the Puget Sound Partnership, existing data from large public water supply system (Group A) wells contained within the Washington State Department of Health (WDOH) Sentry database were used to create temporal groundwater vulnerability models and maps to spatially and temporally characterize the vulnerability of groundwater to elevated nitrate concentrations, defined as exceeding 2 milligrams per liter (mg/L). Statistically significant logistic regression models were created for four time periods: 2000–04, 2005–09, 2010–14 and 2015–19. In addition to the nitrate concentrations and well depth information for the Group A wells contained within the Sentry database, publicly available land cover, soil characteristics, and precipitation data were also used in the statistical model development.

The significant explanatory variables within each of the models were similar for all four time periods. For example, well depth and the percent of agricultural land cover within a 4,000-meter buffer around a well were consistently highly significant in each model. For all models, one of the measures of urban land cover around the well was significant. The consistent significance of well depth and percent agricultural and urban land cover around the well across all four time-period models suggests that these explanatory variables have been consistent controlling factors of groundwater vulnerability over time. Saturated hydraulic conductivity was also a significant explanatory variable in all except the 2005–09 model, whereas average annual precipitation was a significant explanatory variable only in that 2005–09 model. Together these results suggest that an explanatory variable that characterizes the ability of nitrates applied to the land surface to be transported through the soil to the wells or a dilution effect are important predictors of groundwater vulnerability to nitrates. The positive or negative signs of the model coefficients for each of the statistically significant variables in the models were appropriate and easily explained by our mechanistic understanding of hydrologic principles. For example, well depth coefficients were all negative, indicating that as depth increases, the probability of elevated nitrate concentration decreases. A significant negative coefficient for average annual precipitation in the 2005–09 model suggests that increasing mean annual precipitation during this time reduced the probability of finding elevated nitrate in a well perhaps due to dilution or a flushing effect that removed anthropogenic sources of nitrate from the area around a well. Future modeling efforts may want to consider adding an explanatory variable that measures the intensity and timing of precipitation to better reflect the mechanisms by which precipitation might recuse or enhance the probability of elevated nitrates in a well. In addition to appropriate and explainable signs for each of the model parameter estimates, the magnitudes of all coefficients were all similar, suggesting that the influence of these explanatory variables on groundwater vulnerability has been consistent over time.

Applying the logistic regression vulnerability models developed for each time period to hypothetical wells of 150- and 300-feet (ft) depth throughout the Puget Sound generated vulnerability maps that produced the highest probabilities of elevated nitrate concentrations in aquifers in the areas of high urban and (or) agricultural activity. Although geographic locations of elevated probabilities of nitrate concentrations were consistent at both the 150- and 300-ft depths, the probabilities were lower at the 300-ft depths. Regions with little agriculture or urban land use had lower probabilities of elevated nitrate concentrations. Modeled probabilities of elevated nitrate concentrations at both the 150- and 300-ft depths were less than 10 percent for more than 75 percent of the modeled area of the Puget Sound basin across all time periods. However, there were several locations with relatively high probabilities and differences in probabilities between time periods.

Although most modeled probabilities throughout the Puget Sound basin were less than 50 percent, values greater than this level may be of greater interest to water purveyors, regulators, and land managers. Comparing modeled probabilities across the time periods, particularly probabilities greater than 50 percent, provides insight into changes (trends) in groundwater vulnerability at the scale of the Puget Sound basin. To examine changes in the probability of elevated nitrate concentration at specific locations over time, a series of change maps was generated. The change maps generated for 150-ft-deep wells showed inconsistent changes over time. For example, the changes during 2000–04 and 2005–09 were mostly increased probabilities of elevated nitrate concentrations, changes during 2005–09 and 2010–14 were mostly decreased probabilities, and changes during 2010–14 and 2015–19 included a mixture of increased and decreased probabilities. In contrast, at the 300-ft depths, probabilities of elevated nitrate concentrations generally increased between all of the periods. The difference in responses between the 150- and 300-ft wells suggest that the probability of elevated nitrate concentrations in shallower wells is more dynamic than it is in deeper wells. That is not unexpected in that deeper wells are known to respond to land surface changes more slowly and may not be as representative of current anthropogenic changes.

To examine temporal trends in the data in greater detail, predicted probabilities within each time period at 150- and 300-ft depths were sorted from low to high and assigned to quantiles. When the sorted data were placed into one of 10 quantiles with each quantile representing 10 percent of the data, the predicted probabilities within the first 6 quantiles for 150-ft wells showed low probabilities of elevated nitrate concentrations, generally less than 5 percent. The distribution patterns in quantiles 7–10 showed increasingly higher probabilities of elevated nitrate concentrations, with probabilities that generally exceeded 20 percent in the uppermost 10th quantile. Very similar patterns were found in the predicted probabilities for the hypothetical 300-ft-deep wells.

For the predicted probabilities at the 150- and 300-ft well depths, changes in the probabilities of finding elevated nitrate concentrations in groundwater over the past 2 decades have been inconsistent across time periods and across ranges of predicted probability. The modeling results show that the highest probabilities of finding elevated nitrate concentrations seem to have generally increased over the four time periods, whereas the more moderate probabilities (represented by the 4th–6th quantiles in figures 11 and 12) seem to have generally decreased over at least the first three same time periods. The highest probabilities for finding elevated nitrate concentrations at most wells are less than 10 percent demonstrating how much of the Puget Sound basin area has relatively low predicted probabilities of elevated nitrate concentrations.

Quantile regression was used to further examine temporal trends in predicted probabilities of elevated nitrate concentrations. For this analysis, the independent variables were the four time periods, and the dependent variable was the predicted probability of elevated nitrate concentrations in 150- and 300-ft-deep wells. Quantile regressions results were examined for the lower 5th quantile through the 95th quantile of probabilities by 5-percent increments. This analysis resulted in 19 slope and significance estimates for each quantile. The slope coefficient is of most interest because it is an indication of the rate of change in the probabilities of elevated nitrate concentrations over time for various ranges of the predicted probabilities. A positive slope value indicates an increasing trend in the probability of elevated nitrate concentrations over the four time periods, whereas a negative slope indicates a decreasing trend.

For both 150- and 300-ft well depths, the largest increasing trends (largest positive slope values) were found in the highest quantiles, which are associated with the highest predicted probabilities for elevated nitrate concentrations. These results indicate that wells with predicted higher probabilities of elevated nitrate concentrations have increased during 2000–19. Such increases in nitrates for those wells with high probabilities may be due to continued anthropogenic sources of nitrates in the areas around the wells and (or) a lag in the delivery of excess nitrate to these wells. For most of the modeled wells that had moderate probabilities of elevated nitrate concentrations, a slight but significant decline in the probability was observed over the time period examined.

The maps and statistical analysis presented in this study provide valuable and informative evaluation of the vulnerability of groundwater in the Puget Sound basin to elevated nitrate concentrations and effectively meet the goals of the study. Nevertheless, as addressed in previous vulnerability mapping exercises, limitations exist and should be noted. The probability maps do not represent measured nitrate concentrations of groundwater, but rather they present the probability that nitrate concentrations exceed 2 mg/L. The probability estimates have inherent uncertainty due to potential errors in the WDOH nitrate concentration data contained within the Sentry database and numerous GIS-based explanatory variables. Errors also arise from the formulation of the logistic regression models and their associated coefficient estimates. As noted in Frans (2008), higher resolution data for all the explanatory variables, particularly for saturated hydraulic conductivity and nitrate application data, would reduce the model error and improve predictions. Additional and (or) alternative explanatory variables not included in the modeling effort could also improve the predictions. The maps and predicted probability analyses in this report are intended for regional scale use and have limitations for use at the field scale given the scale of the explanatory variables. Many unaccounted-for field-scale complexities affect the concentration of nitrate in groundwater and in water produced by a given well. For example, the models do not account for point sources of nitrate or the observed flow pathways that water follows from the land surface to a shallow or deep well screen. Although a particular well may be installed in a region with an estimated high probability of elevated nitrate concentration, the well may in fact yield water with low nitrate concentration due to complexities that cannot be represented in regional-scale models such as those developed in this study.

Although there are always limitations to a statistical model, the models and predictions from this study are a viable indicator for the Puget Sound Partnership’s Healthy Human Population – Drinking Water Vital Sign. One benefit of the logistic regression modeling approach presented here is that the modeling framework can be implemented rapidly as new regional land-cover, anthropogenic data and climatic data are generated (land cover, population density, precipitation, etc.). Significant explanatory variables for each of the models from the four time periods were similar in both the type of variable (for example, percent agriculture within 4,000 meters of a well) and the magnitude of the model coefficients, indicating that future estimates of groundwater vulnerability can be estimated from a narrow suite of explanatory variables, facilitating comparisons among model predictions over time. For this study only two groundwater vulnerability depths were considered, but the current models and potential future models can be used to examine multiple depths, further enhancing the use of this model framework as a Vital Sign indicator. An additional benefit of the logistic regression approach for evaluating groundwater vulnerability is the ability to examine different vulnerability probabilities from the model output to assess temporal trends. This report presents several graphical and empirical approaches for examining the ranges and trends in the probabilities of exceeding nitrate concentrations greater than 2 mg/L in groundwater in the Puget Sound basin.