Methods


The SPARROW Model


The SPARROW model is a hybrid statistical and mechanistic model for estimating the movement of mass through the landscape under long-term, steady state conditions (Schwarz and others, 2006). The model uses data describing catchment attributes (nutrient sources, landscape characteristics, and stream and water body properties) to explain the spatial variation in measured, mean annual stream load (expressed as kilograms per year). The measured, mean annual stream loads are the dependent variable (the calibration data set) for the model and the catchment attributes are the explanatory variables. In this report, the variables representing nutrient sources are called nutrient source terms and the variables representing the delivery of nutrients from land to water are called delivery terms. A calibrated SPARROW model can be used to predict water-quality conditions throughout a surface-water network, including areas where no water-quality data exists.


Model Input Data Sets


The input data sets used for this study were similar to those used to develop the RF1 SPARROW models for the PNW (Wise and Johnson, 2011). An important structural change from the earlier models was the use of the National Hydrography Dataset Plus (NHDPlus) as the surface-water drainage network for the models rather than the RF1 hydrologic network. Refinements also were made to many of the input data sets, including the calibration data set of mean annual nutrient loads, the estimates of nutrient sources, and the accounting of irrigation diversions, power returns, and discharge from large spring complexes.


Surface-Water Drainage Network


The NHD Plus Version 2 for Hydroregion 17 (Horizon Systems, 2013) was used to represent the surface-water drainage network in the models developed for this study. Hereafter, this data set will be referred to as the NHD. The NHD is a comprehensive set of digital spatial data that contains information about surface water features such as lakes, ponds, streams, and rivers (Simley and Carswell, 2009). The surface water features represented in the NHD largely correspond to the features on 1:100,000 scale USGS topographic maps. 


The NHD for the PNW is divided into 232,811 reaches, which vary in size from small, ephemeral streams that can go years without streamflow to the Columbia River with a mean annual streamflow of 9,575 cubic meters per second near its confluence with the Pacific Ocean (U.S. Geological Survey,  2012). The NHD identifies the incremental catchment for each reach. An incremental catchment is defined as the area that drains directly to a reach without passing through another reach. Most reaches in the NHD represent streams or inland water bodies, such as lakes and reservoirs. However, some reaches represent coastlines or closed basins, which do not have a surface water connection to other reaches in the NHD. In building the hydrologic framework for the SPARROW models, reaches representing streams, inland water bodies, and coastlines were retained, but reaches representing closed basins were eliminated from the network. The NHD contains minimal information on stream reaches and catchments in Canada, but does provide sufficient information to properly route surface water into the United States.


Irrigation and power networks in the PNW divert large amounts of water from streams and reservoirs, and these diversions needed to be accounted for to properly estimate nutrient transport through surface waters. The PNW SPARROW models included a reach attribute that simulated the diversion of streamflow in the drainage network. This was done by estimating the fraction of streamflow and, therefore, nutrient load that was delivered from one reach to the reach immediately downstream (based on long term average conditions). In the SPARROW model, nutrient load that is removed because of irrigation diversions is not explicitly accounted for as return flow through the modeling network, although many of the agricultural returns in the PNW are represented in the NHD drainage network.


Calibration Data Set


The calibration data set for the models consisted of mean annual TN and TP stream loads that were estimated from water-quality data obtained from Federal agencies, State regulatory agencies, one county government, and one water pollution control district and streamflow data collected primarily by the U.S. Geological Survey (USGS). Water-quality monitoring stations were selected as TN, TP, or both calibration stations if they were close enough to a nearby streamflow gaging station and met the minimum criteria for the number of TN and TP samples (20), seasonal coverage (3 samples per season), and period of record (last sample collected no later than 1995 if there were at least 5 years of data or last sample collected no later than 1999 if there were less than 5 years of data). The mean annual TN and TP stream loads were estimated using the USGS Fluxmaster model (Schwarz and others, 2006), which relates the loads measured at water-quality monitoring stations (the calibration stations) to measured streamflow, season, and time. There were 179 calibration stations where TN loads were estimated, 220 where TP loads were estimated, and 177 where both TN and TP loads were estimated. This resulted in a total of 222 calibration stations. A breakdown of the calibration stations by agency and location is provided in table 2.


The mean annual TN and TP stream loads were detrended to 2002 to account for differences in record length, hydrologic conditions, and sample size among the calibration stations (Preston and others, 2009). Differences between the calibration stream loads used in the PNW NHD SPARROW models and those used in the PNW RF1 SPARROW models (see Saad and others, 2011) were a result of closer examination of the water-quality and streamflow data used to estimate the loads. In one case, however, the difference was due to the inclusion of a water-quality monitoring station that was located on an NHD stream reach not represented in the RF1 network. 


Catchment Attribute Data


The catchment attribute data for computing explanatory information used in the PNW NHD SPARROW models consisted of nutrient sources, boundary loads, and land-to-water delivery factors.


Nutrient Sources


All nutrient sources considered in the PNW RF1 SPARROW models were considered in the PNW NHD SPARROW models. Fixation of nitrogen from the atmosphere in forested areas was represented by the area of forestland, and the weathering of geologic phosphorus was represented by the area of forestland and the area of scrubland plus grassland. The approach used to represent geologic phosphorus was similar to that used in other SPARROW applications (Smith and others, 1997; Alexander and others, 2008). Other nutrient sources considered for use in the models were (1) the discharge from permitted wastewater treatment facilities including fish farms and hatcheries (point sources), (2) the area of developed land to represent nonpoint urban sources, (3) the number of people living in areas not served by municipal sewage districts to represent nitrogen leaching from septic tanks, (4) the atmospheric deposition of nitrogen, (5) the application of farm and nonfarm fertilizer, (6) the application or deposition of livestock manure, and (7) the leaching of nitrogen from red alder trees (Alnus rubra). The methods used to estimate these nutrient sources are described in appendix A.


The TN and TP NHD models also accounted for nutrient loads from the largest spring complexes, which are collections of natural springs that discharge into or near a stream and contribute a substantial amount of the flow in that stream, and the nutrient loads associated with the return of water from off-stream power generation facilities. Spring complexes and power returns are not sources of nutrients, but are pathways for the return of nutrients to a stream. They are represented in the models as point sources because there is no mechanism within the NHD network or in the SPARROW model to accommodate these unique pathways for nutrient movement from the landscape to the stream. The methods used to estimate these loads also are included in appendix A.


Boundary Loads


Five of the calibration stations were on stream reaches with large upstream drainage areas that were primarily in Canada (Kettle River, Okanogan River, Columbia River, North Fork of the Flathead River, and Kootenai River; fig. 1). Because catchment attribute data for computing explanatory information in the Canadian part of the modeled area were not available, these five calibration stations were used as boundary conditions for the models. The TN and TP models were configured so that the load entering the stream network at these boundary reaches was equal to the measured mean annual TN and TP load and that the processes occurring upstream of and within their incremental catchments had no effect on the calibration of the TN and TP models. There also were 184 incremental catchments that included some Canadian land but that did not drain to a boundary reach. Incomplete attribute data for these catchments was expected to have little influence on the model calibrations, however, because they represented 0.23 percent of the area of the modeling domain.


Land-to-Water Delivery 


The delivery of nutrients from land to water was modeled by considering land cover, climate, soil properties, geology, and hydrology. Most of these landscape properties were compiled by the National Water-Quality Assessment Program (NAWQA) as part of a national effort and were summarized for each incremental NHD catchment (Michael Wieczorek, U.S. Geological Survey, written commun., June 11, 2011), and two landscape properties were compiled specifically for the PNW NHD SPARROW models (mean annual solar radiation and the extent of arid land irrigation). The methods used to compile the two data sets representing mean annual solar radiation and the extent of arid land irrigation are described in appendix A.


Nutrient Loss in Free-Flowing Streams and Impoundments


The SPARROW model can simulate the net effect of processes that lead to permanent nutrient loss (particulate settling and benthic denitrification) within surface waters. When modeling mean annual conditions an assumption is made that there is no net gain or loss of nutrients due to the growth and decay of aquatic plants (Schwarz and others, 2006). Nutrient loss in free-flowing streams is modeled in SPARROW using a first-order decay formulation that is a function of the time of travel for each reach (reach length divided by estimated mean annual velocity). As a result, the stream loss coefficient in the model is expressed as day^-1. Estimates of different instream nutrient-decay rates for different stream categories can be specified in the SPARROW model. In most SPARROW models developed for other parts of the United States, these stream categories were based on a gradient of mean annual streamflow, but they also can be based on stream type (for example, perennial or intermittent), temperature, or other measures that affect nutrient uptake and removal. Nutrient loss in impoundments such as lakes and reservoirs is modeled in SPARROW as an apparent settling velocity that is expressed in units of length per time and is a function of the areal hydraulic load (estimated mean annual streamflow through an impoundment divided by the surface area of the impoundment). As a result, the impoundment loss coefficient in the model is expressed as meters per year. All of the information needed to compute the parameters used to estimate nutrient loss was included with NHDPlus.


Model Calibration


The explanatory variables included in the TN and TP models represented statistically significant or otherwise important geospatial variables. The significance of the coefficients for each of the nutrient source terms (which were constrained to be positive) were determined by using a one-sided t-test and a significance level of 0.10. The significance of the coefficients for each of the delivery terms (which were allowed to be positive or negative, reflecting either enhanced or attenuated delivery, respectively) was determined by using a two-sided t-test and a significance level of 0.05. The significance of the coefficients for the variables representing nutrient loss in free-flowing streams and impoundments (which were constrained to be positive) was determined by using a one-sided t-test and a significance level of 0.10. Final model selection was based on the overall model fit by evaluating the yield R-squared (R²) and the root mean squared error (RMSE), and by evaluating the residuals for spatial patterns. The yield R-squared is the R-squared value for the natural logarithm of yield and is considered a better measure of goodness of fit than R-squared because it accounts for the effect of contributing area, which can explain much of the variation in stream load. The spatial patterns in model fit were evaluated by calculating and mapping the studentized residual for each calibration station. The studentized residual is equal to the model residual (the difference between the natural logarithm of measured load and predicted load) divided by an estimate of its standard deviation.


The SPARROW model uses a weighted nonlinear least squares (NLLS) regression to estimate model coefficients and provides a way to assess uncertainty in these estimated coefficients. Because of the nonlinear manner in which the estimated coefficients enter the model, this uncertainty needs to be evaluated using a bootstrap resampling method (Schwarz and others, 2006). The method is implemented through repeated estimation of the SPARROW model (200 times for these applications) to obtain a range of values for each coefficient, from which a mean value (the nonparametric bootstrap estimate) is estimated. The overall stability of each of the models was evaluated by comparing the NLLS estimates of the model coefficients to the nonparametric bootstrap estimates. The 90 percent confidence intervals for the NLLS coefficients in each model were generated by using the standard errors and a t-distribution with N-k degrees of freedom, where N was the number of calibration sites and k was the number of coefficients.


Analysis of Model Predictions


The predictions from the PNW NHD SPARROW models were analyzed and presented in three ways for this report. First, the models were used to estimate the mean annual incremental TN and TP yield for each of the 232,811 modeled catchments. Incremental yield is equal to the estimated stream load per unit area that is attributable to nutrient sources located exclusively within each incremental catchment, and is a useful tool for comparing the relative intensity of stream load between catchments because it normalizes for contributing area. The median incremental TN and TP yields were then calculated for each of the 22 six-digit hydrologic unit code (HUC6) watersheds (table 1) within the study domain. Second, the models were used to identify the largest local source of TN and TP (that is, the nutrient source contributing the most to the incremental TN and TP yield for each catchment). To simplify the presentation of the results, the nutrient sources were generalized into categories that represented similar activities or processes. The incremental catchments were then grouped together by their largest local source of TN and TP and the median incremental TN and TP yields for each group of catchments were calculated and analyzed for statistical differences in their median values using the Wilcoxan rank sum test with a Simes-Hochberg correction applied to the test values (Simes, 1986; Hochberg, 1988). Third, the models were used to estimate the contribution from each nutrient source to the total TN and TP loads predicted for each reach. Total load was the predicted load contributed from all upstream landscape nutrient sources. The Willamette and Snake Rivers were then used as examples to show how the relative contribution to total load from different nutrient sources varied along two large rivers.


First posted July 17, 2013