For this report, the Puget Sound region refers to watersheds draining into the Washington State waters of the Salish Sea (fig. 1). Ecology has grouped all contributing watersheds by Water Resource Inventory Areas (WRIAs) based on information regarding water availability, regulations, and water use (Washington State Department of Ecology, 2019a).

The Puget Sound region includes 19 WRIAs with various land cover patterns that affect the delivery of nutrients to streams. The major land cover types in the Puget Sound region are forested (62 percent), grassland/scrubland (12 percent), and urban land (12 percent) based on the 2019 National Land Cover Database (NLCD; Dewitz and U.S. Geological Survey [2021]; refer to fig. 1.1). Urban land, including major cities and urban areas (for example, the Cities of Seattle and Tacoma), is concentrated along coastal shoreline areas and estuaries, whereas the headwaters are mostly forested. Areas of agricultural land can be found in the northern watersheds, such as the lower Nooksack and Skagit Rivers, and in a few areas in southern watersheds, such as the lower Nisqually and Deschutes Rivers.

Rivers are relatively short and steep from the Cascade Range crest to the coastal lowlands. Streamflow patterns are influenced by several factors, including reservoir storage, wet winters, dry summers, and seasonal snowmelt at higher elevations (refer to Figueroa-Kaminsky and others [2022] for more details).

The analytical mass-balance framework for the TN and TP models was guided by the approaches and findings in Schmadel and others (2021, 2024) to produce seasonal nutrient load estimates for every E2NHDPlusV2 stream reach across the Puget Sound region. Seasonally varying nutrient loads transported through a reactive river reach were estimated as the summation of load entering from the upstream end of the reach and load generated within the reach’s catchment (after Schmadel and others, 2024):Lout,t,i=Lin,t,i+LI,t,i+LS,t,iDj,t,i(1)where

A net decay of nutrients was estimated each period based on seasonal streamflow. For lakes and reservoirs, hereafter, waterbodies (j = 2), the aquatic decay function was:Dj=2,t,i=exp−νf,j=2AiQt,i(2)where

For a stream reach (j = 1), the aquatic decay function was updated to:Dj=1,t,i=exp−νf,j=1τt,idt,i(3)where

The net unit-area rate of biogeochemical reactions that remove and replenish TN or TP is represented by ν_f, in units of meters per day [m/d] and assumes that the load in each reach decreases over time as a constant percentage (first-order decay conditions) in a waterbody (eq. 2) or stream channel (eq. 3; Alexander and others, 2000).

For streams draining watersheds in the Puget Sound region, other factors such as stream temperature, in addition to travel times, may affect decay (Sheibley and others, 2015). Therefore, the hypothesis that the mean uptake velocity (v₀; meters per day [m/d]) varied seasonally and spatially due to water temperature was tested by estimating v_f as (after Schmadel and others [2020, 2021]):vf,j=1,t,i= v0+βTlnTt,i−lnT¯(4)where

Mean seasonal water temperature, T, was mean-centered to provide a meaningful estimate of v₀ and log-transformed to add model calibration stability and reduce the dependence on the shape of the distribution. A positive value of β_T, for example, implies an increase in uptake velocity caused by a temperature above the mean temperature.

Load delivered from an incremental catchment to the edge of a stream or waterbody reach was estimated, assuming all mass (except mass from point sources) passed through and completely mix in a storage repository with some fraction retained each season, as (after Schmadel and others, 2024):LI,t,i=∑n=1NαnIn,t,ifI,n,t,i(5) LS,t,i=αSLt−1,ifS,t,i(6)where

The α_S coefficient represents the mean strength of storage retention where a value approaching zero implies no storage effects whereas a value approaching one would imply that all inputs are retained and accumulate in storage with little delivery to streams. The amount of mass retained simultaneously depends on the amount released; a higher release fraction leads to an immediate lowering of the storage retention fraction. As mass passes through the storage repository and is delivered to the stream, ln(α_S) is negative and provides an estimate of the mean storage retention rate each season (and its inverse is a retention timescale) of mass. An estimate of the previous period instream load is required to initiate storage lag in equation 6; the initial condition solution from Schmadel and others (2024) was used to estimate L_t=0.

The land-to-water delivery functions further mediate seasonal and spatially explicit effects on the delivery of source inputs to streams (after Schmadel and others, 2024):fI,t,n,i=exp∑mθmXm,t,i(7) fS,t,i=exp∑mγmXm,t−1,i+∑dβdXd,t,iXd,t−1,i(8)where

Model coefficients of the TN and TP models were calibrated through nonlinear weighted least-squares regression using the seasonal loads (kg/season) estimated at 49 TN stations and 47 TP stations (fig. 3). Across 64 seasons, a total of 2,951 TN load observations and 2,834 TP load observations were used in calibration of the TN and TP models, respectively. For every load observation, there was a model residual (calculated as observation minus prediction) used to examine patterns in model error.

Seasonal patterns in model residuals were examined for heteroscedasticity and serial correlation following Schmadel and others (2021, 2024). To examine for heteroscedasticity, squared residuals were regressed against specified binary seasonal variables (one if winter, zero otherwise) to produce predicted squared residuals as a function of season. Models with significant seasonal patterns in the squared residuals were recalibrated by weighting the observations by the inverse of the predicted squared residuals to reduce potential bias due to heteroscedasticity solely caused by seasonality. Once weighted, bootstrap resampling with 100 iterations was then performed to estimate 90 percent confidence intervals on the load predictions.

Serial correlation in the residuals can cause a bias in estimated standard errors of coefficients. Its effects were quantified for improved interpretation of source pathway and uncertainty. Serial correlation can artificially reduce a coefficient p-value by indicating significance based on the previous period value instead of by the underlying process that drives nutrient fate and transport. This potential bias may limit the amount of constant explanatory variables possible in a dynamic model, as a constant variable does not change throughout the 64 periods. Following Schmadel and others (2024), standard errors (and associated t-values and p-values) of the model coefficients were therefore corrected for serial correlation by performing a first-order autoregressive analysis of the model residuals assumed independent across stations.

Another potential validation step considered is a withholding of some calibration data for further assessment of error and the model’s ability to simulate loads at unmonitored locations. However, withholding calibration stations is not common practice in SPARROW modeling because each developed model is already limited in the number of stations necessary to represent the gradients across a region. Thus, removal of any stations (for example, 10 percent of stations) may cause a large portion of the model domain to go unrepresented. In the Puget Sound region, of the WRIAs that contained calibration stations, many contained only one station near the basin outlet. Excluding any one single station could result in a different model interpretation because less of the region is represented—withholding stations to test model performance in unmonitored locations is not trivial as each station represents different upstream information. However, each station had a unique leverage on the estimation of coefficients and certain calibration stations were more important to represent gradients across WRIAs than others. For example, some stations more densely packed in urban areas may not necessarily provide new information. It was found, however, that exclusion of any calibration station near urban areas (for example, in King County, Washington; fig. 3) provided a model with higher error in the urban source pathway coefficient. Calibration stations close to one another could be excluded if they provide redundant information; however, stations 09A080 and KCM-3106 on the Green River are located on the same model reach but provided different load values as there is a stormwater outfall in between. Thus, 09A080 was artificially moved to the next upstream reach and both stations were kept in the models.

The interactions between source inputs and land-to-water delivery variables were assumed and set within the TN and TP models. To set source input coefficients to per-year units for comparison purposes to previous estimates, constant source input variables or variables expressed at an annual timescale (for example, urban land or animal count), were divided by four, or by the number of timesteps in 1 year. Red alder tree coverage was the exception; red alder tree coverage was divided in half under the assumption that deciduous forests fix nitrogen for half of the year and decompose and leach the other half of the year. Precipitation in the TN model was assumed to interact with all nonpoint sources except for atmospheric deposition—precipitation was already used in the calculation of atmospheric deposition and setting an interaction with precipitation could cause a double-counting effect. Precipitation in the TP model was set to interact with all nonpoint sources. ET was tested in both models; the specification set for the TN model (after many test models) was a season-to-season change in ET interacting with the storage lag source. In the TP model, the previous season precipitation and ET variables were set to interact with the storage lag source, but also, the current period ET was set to interact with crop fertilizer and septic. The indication was that precipitation increases TN and TP delivery (positive coefficient) whereas ET represents a loss process (negative coefficient). The additional interaction between ET and septic in the TP model suggested that some of the TP in septic leachate was removed in its transport to streams.

Soil and catchment attribute variables also interacted with source inputs. Clay content was assumed to interact with all source inputs in both models (except for upland geologic material in the TP model because soil properties are already included in that variable calculation). Organic content was included in the TN model and interacted with all nonpoint sources whereas soil erodibility (K-factor) interacted with all nonpoint sources in the TP model (but again did not interact with upland geologic material). Additional soil and catchment variables included only in the TP model were small stream density (Schmadel and others, 2020) and mean catchment slope (Wieczorek and others, 2018) to represent channel erosion processes.

Interaction between atmospheric deposition and urban sources could cause feedback noise in the TN model (Conrad-Rooney and others, 2023), potentially increasing uncertainty in both source terms. Therefore, to break up some collinearity and better isolate the two assumed independent source pathways, the density of stormwater outfalls interacted with the urban source term in the TN model. Furthermore, to represent dynamic effects caused by outfalls, their density was scaled by rainfall intensity expressed as the ratio of seasonal precipitation to long-term mean precipitation.

Point-source data included permitted treated wastewater from municipal and industrial facilities and fish hatchery operations. These point sources were lumped into a single source type in the models, represented by one coefficient. Furthermore, because nearly two-thirds of the point sources discharged into streams and marine waters at locations downstream of calibration stations, the point-source coefficient was set to α_n=1 (eq. 5) to prevent overestimation of this source (after Schmadel and others, 2024). Mass inflow from Canada was treated as its own source also with its source coefficient set to α_n=1, which was based on the nearest calibration station data scaled by the ratio of drainage areas between the station and the Canadian border.

Aquatic decay in streams was specified with seasonal hydraulic load. All streamflow conditions were represented in the TN aquatic decay expression. Aquatic losses of TP in streams were set to occur only when seasonal streamflow was less than the annual mean, because streams under high flow conditions are hypothesized to not be net sinks of TP (Valett and others, 2022). Water temperature was added as an additional process to TN stream decay (eq. 4) but not for TP.

Model quality objectives for this study, defined in more detail by Figueroa-Kaminsky and others (2022), were, in summary, to:

Model results are summarized in this report and accessible and viewable via a mapper (U.S. Geological Survey, 2025).

Regression statistics (tables 2–7) and diagnostic plots (fig. 7A–H; figs. 8 and 9) indicated that TN and TP models simulated loads. The RMSE was like that from previous larger-scale static annual models that encompass the Puget Sound region (Wise, 2019). The RMSE of the seasonal TN model in natural logarithmic space was 0.470 (compared to 0.538 in the static model) and RMSE of the seasonal TP model was 0.648 (0.615 in the static model). Overall mean error was interpreted as plus or minus 50 percent and 72 percent of the simulated TN and TP loads, respectively (tables 4 and 7). The TN and TP models were shown to explain 95 percent and 93 percent (82 percent and 71 percent by yield) of the variability in the observed loads, respectively (R² in tables 4 and 7). The Nash-Sutcliffe efficiency (NSE) in real space further indicated that the TN model performed efficiently at 88 percent NSE; although the TP model performance was much less at 45 percent NSE, that efficiency is still considered satisfactory (tables 4 and 7; Moriasi and others, 2007).

Residuals of the TN load in natural logarithm space (calculated as ln[observed] minus ln[predicted]) were mostly less than one (as absolute values; fig. 7C), which indicated good agreement between prediction and observation. Likewise, residuals remained small for high yields—for example, a large negative residual corresponding to a high yield is an indicator that a source is over predicted. If a point-source discharge location was incorrect (for example, the location was assigned to discharge upstream of a calibration station but is actually located downstream of the calibration station), an error associated with a high yield prediction would be an indicator of that mismatch. Residuals of the TN and TP models were void of that mismatch indicator.

In absolute terms, the larger TN model residuals occurred mostly during summer low flows whereas the TP model residuals were largest during winter and fall high flows (fig. 7C–H). Most calibration stations had a mix of positive and negative residuals, indicating that homoscedasticity in error was achieved (figs. 8 and 9). The TP model typically underpredicted loads discharging from the headwaters of the Nooksack River during winter and fall yet tended to overpredict loads from agricultural streams in the lower Skagit River (figs. 1 and 9). At a few stations, while still capturing dynamic signals in loads, the model tended to underpredict in, for example, the Deschutes and Puyallup-White WRIAs and overpredict in the Skokomish-Dosewallips WRIA. Weighting of those stations was tested using the inverse of their squared residuals, but an improvement to prediction accuracy was not found. For the TN model, residuals at stations were also mostly a mix of positive and negative values with many stations nearly matching observations (fig. 8). However, both models consistently underrepresented load exported from the Deschutes River. The Deschutes River exported only 0.4 percent and 1.3 percent of the TP and TN load, respectively, to marine waters from the entire Puget Sound region (app. 2; tables 2.1 and 2.2); thus, smaller loads are likely to have higher uncertainty because they have less effect on the overall model calibration.

A slight seasonal pattern was found in the squared residuals of the models, and seasonal weights were applied. The highest weights were applied to spring, winter, fall, and lowest to summer. However, that weighting had only marginal improvements to the largest squared residuals of the TP model.

Serial correlation had significant effects on artificially reducing the model coefficient standard errors, suggesting that a mean 51 to 54 percent of the current period residual can be explained by the previous period residual (tables 3 and 6). After correcting for serial correlation effects, the animal feeding operations source coefficient for the TN model increased in error and went from a p-value of less than (<) 0.0001 to 0.0005 (table 2). A p-value above 0.2 starts to become a concern in which the source coefficient may no longer be distinguishable from zero after accounting for serial correlation bias. It was interpreted that the animal feeding operations were still a TN source pathway, but the uncertainty in that pathway was instead estimated to be larger relative to other TN sources. For the TP model, serial correlation had a notable effect on more than one source coefficient. Coefficients for animal feeding operations and on-site wastewater treatment were still statistically different from zero and therefore considered representative of those source pathways, but adjusting for serial correlation provided a more representative estimate of error for those source coefficients. The largest effect was on the on-site treated wastewater coefficient, increasing the p-value from <0.0001 to 0.0015 (table 5). If an important source is not represented by the model, its contributing mass will shift to another source coefficient in model estimation to balance, potentially causing an overestimation of another source component. Therefore, while accounting for uncertainty, all source coefficients were kept, preventing any unfair assignment to any single source pathway.

Seasonal variability in observed load was represented by the TN and TP models. Model simulations were in agreement with observations at many stations as indicated by the observations falling within the estimated 90 percent confidence intervals of the simulations, and confidence intervals tended to be smaller for TN compared to TP (figs. 10 and 11). There were some cases, particularly for some TP stations, where the model simulation was generally close in magnitude to the observation, but with some disagreement between timing that tended to correct itself from upstream to downstream stations (for example, TP station 01A120 to 01A050; fig. 11).

As another general validation check, simulations were compared to annual load observations used in the previous annual SPARROW models (Wise, 2019), which were divided by four to convert units to kilograms per season for comparison. Magnitudes were in close agreement, yet annual estimates were on the higher end (horizontal lines in figs. 10 and 11). However, the seasonal load simulations produced a much larger range of extremes, oscillating by an order-of-magnitude each year—marine waters experienced their highest nutrient loading in winter and fall.

Flow-weighted concentrations estimated from the model simulations (seasonal load divided by seasonal streamflow) were also compared to in situ continuous nitrate observations at three sites in the Nooksack WRIA (fig. 12A–C). Three locations in the Nooksack WRIA have records of continuous in situ observed nitrate, which were downloaded from NWIS under p-code 99133 (U.S. Geological Survey, 2022): 12211390 Kamm Creek at Kamm Road near Lynden, Washington (fig. 12A); 12212050 Fishtrap Creek at Front Street at Lynden, Washington (fig. 12B); and 12213100 Nooksack River at Ferndale, Washington (fig. 12C). The magnitude and timing of nitrate concentrations were comparable to the model simulations at Ferndale, Washington, near the mouth of the Nooksack River (fig. 12C)—high concentrations during winter followed by low summer concentrations indicated times of possible nitrogen depletion. Discretely measured concentrations at station 01A050 from 2009 through 2020 indicated that a mean 83 percent of the measured TN concentration was comprised of nitrate plus nitrite. The simulated seasonal TN concentrations were all slightly above the in situ nitrate concentrations, indicating agreement between simulated and observed at that station. However, a composition of mostly nitrate is less likely up toward forested headwaters as more organic and particulate forms of nitrogen are possible. Discrete observations further revealed that a pulse of ammonia plus ammonium occurred each winter (fig. 12C).

Moving upstream into tributaries affected by agriculture and urban development, concentration magnitudes were also comparable in Fishtrap Creek (fig. 12B). Generally comparable magnitudes indicated that source pathway representation was achieved in Fishtrap Creek; however, there was some mismatch in the timing of seasonal peaks and troughs that suggests that the model simulation was out of phase with TP source delivery from some headwater tributaries. In the adjacent Kamm Ditch tributary (referred to as Kamm Creek in the USGS site name), observed nitrate was consistently higher than the model simulations, yet timing appeared consistent. This indicated that, although dynamic drivers were perhaps well represented, the model likely under-represented or did not include a source pathway from Kamm Ditch. The TN and TP models would likely benefit from additional calibration stations in those tributaries.

The model coefficients can be interpreted as seasonal and annual flux rates (tables 2 and 5), which directly demonstrates the value of applying a statistical-physical approach for improved process and source pathway interpretation. The mean annual mass from animal feeding operations was estimated at a mean rate from 2005 through 2020 of about 8.4 kg of TN and 2.3 kg of TP delivered per animal per year (coefficients 8.37 and 2.29 in tables 2 and 5, respectively). Interactions with land-to-water delivery variables suggested that delivery was increased in winter and fall during higher precipitation (positive coefficient). Similarly, the models estimated that a mean rate of 4.5 kg of TN and 0.2 kg of TP leached from each household on a septic system each year, and leachate delivery also increased when catchments were wetter.

Urban land was estimated to contribute 802 kg TN and 79 kg TP additional mass per square kilometer per year (tables 2 and 5). Based on the relative magnitudes of model coefficients, more TP came from urban land compared to TN while more TN came from septic systems compared to TP. In the TN model, the density of stormwater outfalls was found to inversely interact with urban land. During higher precipitation intensity, a negative interaction implies two possible pathways: (1) more diluted stormwater that went through the outfalls and (2) more mass that was carried from the atmospheric deposition pathway with precipitation falling on impervious surfaces. A significant coefficient identified for urban land and atmospheric deposition source pathways indicated that there were urban sources in addition to atmospheric—those urban sources not emitted into the atmosphere nor delivered from the atmosphere via impervious surfaces. The TN model further suggests that a mean annual 0.36 kg TN was produced by each square meter of red alder trees (table 2).

The storage lag coefficients for the TN and TP models were 0.25 and 0.29, respectively (tables 2 and 5). Those values represent the fractions of source inputs retained or lagged each season, which provided the mean strength of seasonal storage lag across the Puget Sound region for all predictions from 2005 through 2020. Model results suggest that nearly a quarter of contemporaneous nonpoint TN and TP source inputs were lagged in storage repositories each season and delivered to streams in later seasons, with a slightly larger storage effect estimated by the TP model. Nutrient load released from storage was highest during winter and fall. In the TN model, a positive change in ET from one season to the next was found to decrease the storage lag contribution (negative coefficient; table 2), indicating a loss of stored TN was represented by changes in ET where an increase in ET suggests a loss of stored TN. For the TP model, precipitation and ET from the previous season were found to inversely interact with the storage lag (negative coefficients, table 5). When the previous season had high precipitation or high ET, the model suggests that TP retained in storage was reduced. A negative ET coefficient may represent nutrient losses by processes including plant uptake and crop harvest.

The estimated net decay rate in streams was larger for TN compared to TP (0.31 compared to 0.19 m/d, respectively; tables 2 and 5). Stream decay in the TN model was found to have an additional interaction with water temperature. The mean TN uptake velocity in streams was 0.31 m/d but was estimated to increase when water temperature rose above the regional mean, and decreased when water temperature was below the mean, providing improved timing and spatial specificity, ranging from 0.20 m/d in the winter to 0.44 m/d in the summer (fig. 13A).

Waterbody decay was estimated for both models and had a larger effect on TP losses compared to TN. The estimated settling velocities of 4.1 meters per year (m/y) for TN and 31 m/y for TP (tables 2 and 5) were comparable to field values found in moderate size lakes and reservoirs (Cheng and Basu, 2017). However, after accounting for serial correlation, it was unclear whether an estimate of 4.1 m/y was statistically different from zero; thus, the TN model suggests that waterbodies were not a primary loss pathway, which is a consistent result with previous models (Wise, 2019). Waterbodies had a clearer effect on the TP model (table 5), but serial correlation affected their estimation, suggesting that there were additional seasonal changes to waterbodies not explicitly captured by seasonally changing streamflow.

Annual nutrient loads discharged from watersheds to marine waters from 2005 through 2020 were comprised of several different sources transported from different locations and times, but the dominant contributing individual source also varied by catchment (figs. 14 and 15). Moving downstream from the headwater catchments, the dominant source of TN load shifted from red alder trees and atmospheric deposition to urban and agricultural sources, with point sources from treated wastewater contributing the largest load in several coastal locations (fig. 14). These findings are generally consistent with previous nutrient syntheses indicating large human effects near coastal areas (Ahmed and others, 2019; McCarthy, 2019). Dominant TP sources followed a similar pattern, shifting from predominantly non-human geologic sources in the headwaters, such as soil erosion, to predominantly human-driven sources, such as urban runoff, in valleys and coastal areas (fig. 15). However, in some areas where urban land was the dominant source pathway of TP, on-site treated wastewater systems were the dominant source pathway of TN (figs. 14 and 15).

Aggregated by WRIA, the average load and relative source composition varied by basin (figs. 16A–C and 17A–C). The largest overall TN load discharged to marine waters was from the Cedar-Sammamish, Duwamish-Green, Snohomish, and Nooksack WRIAs (>4 gigagrams per year (Gg/y)], WRIAs 1, 7, 8, and 9; fig. 16A). TN sources in the Nooksack WRIA, for example, were a mix of red alder trees, animal feeding operations, crop fertilizer, and the storage lag of those sources, but the Cedar-Sammamish and Duwamish-Green WRIAs were mostly comprised of permitted treated wastewater discharge. Yield, or load delivered per drainage area, further indicated that the Chambers-Clover WRIA (422 square kilometers (km²), table 2.1) was one of the highest yielding WRIAs due to the outsized contribution of permitted treated wastewater (fig. 16B). For context, the Chambers-Clover WRIA is only a third of the size compared to the Cedar-Sammamish (1,688 km²) and Duwamish-Green (1,361 km²) WRIAs. The contribution of nitrogen fixed by red alder trees comprised a substantial portion of TN load in most watersheds; modeling results suggest that TN sources in the Lyre-Hoko WRIA were mostly from fixation of atmospheric nitrogen. In the Deschutes, Kennedy-Goldsborough, and Kitsap WRIAs, the larger sources of TN suggested by the model were from on-site treated wastewater combined with urban land (fig. 16C).

The largest mean TP load discharged to marine waters was estimated from the Snohomish WRIA (>0.6 Gg/y; fig. 17A)—a mix of permitted treated wastewater, upland geologic material, animal feeding operations, urban land, on-site treated wastewater, and fertilizer—yet the highest yields were again from the Cedar-Sammamish and Duwamish-Green WRIAs, mostly from permitted treated wastewater (fig. 17B). In the Nooksack and Lower Skagit-Samish WRIAs, animal feeding operations and crop fertilizer comprised almost half of the TP load discharged to marine waters (fig. 17C). Compared to TN, the relative contributions of TP from animal feeding operations were more while crop fertilizer was less (figs. 16 and 17).

There was strong seasonal variation in the TN and TP yield across the Puget Sound region with the highest yields predicted during the winter and fall followed by spring and summer (figs. 18 and 19). High yields were dense near coastal areas but also extended to locations far upstream, especially for TP. TN and TP yields during the summer were mostly driven by pockets of crop fertilizer and animal feeding operations.

As the incremental loads accumulated downstream, the final TN and TP load discharged to marine waters at the mouths of 14 major rivers fluctuated by nearly an order-of-magnitude in each river each season from 2005 through 2020 (figs. 20A and 21A). The Snohomish and Skagit Rivers discharged the largest TN and TP loads, yet the Samish River was shown to have the highest TN and TP yields and concentrations (figs. 20B, C and 21B, C). The range in load, yield, and concentration varied by orders-of-magnitude across rivers, yet the seasonal trend appeared mostly stable throughout the 16-year period of record. The exception was the Green River, which had its highest TN and TP yields and concentrations in 2006 and 2007 (figs. 20B, C and 21B, C). A breakdown by source indicated that the main cause of seasonal fluctuations of load in the Duwamish-Green WRIA was treated permitted wastewater discharge with higher inputs in 2006 and 2007 (figs. 16C and 17C).

TN and TP yield by WRIA provided an indication of which watersheds may be most affected by seasonal variability in loads. The Samish River stands out; its seasonal loads, compared to the other 13 example rivers, lie somewhere in the middle, yet its yields and concentrations were some of the highest in the Puget Sound region, and they stayed high throughout the year (for example, concentrations approached 1 milligram per liter [mg/L] of TN and 0.3 mg/L of TP; figs. 20C and 21C). The TP model tended to overpredict load from the Samish River (figs. 9 and 21), and even after considering confidence bounds, the predicted yield and concentration were still high relative to other rivers. For context, a TN concentration threshold of 0.5 mg/L of TN has been noted in other locations as a level at which biogeochemical processes start to become saturated and stop decaying nitrogen (Schmadel and others, 2020). In the Puget Sound region, there is evidence that stream uptake rates of nutrients have been reduced in areas of high concentrations (Sheibley and others, 2015), but that concentration effect was not explicitly quantified in the TN and TP models.

TN loads discharged to marine waters were consistently the largest during winter (fig. 22). Fall TN loads were also consistently large, but slightly lower compared to winter. In locations with high TN sources from red alder trees, the models suggest that leachate from fixed nitrogen was highest in winter and fall (for example, Nooksack and Skagit Rivers; fig. 22). The TN load from storage lag was highest during winter followed by fall, yet its relative contribution comprised half of the TN load during summer when loads were lowest. The largest relative TN aquatic losses also occurred during the summer when travel times and water temperature were highest.

TP load was also consistently highest in winter followed by fall; however, model results suggested that TP load from the Nooksack River was more often higher in fall than in winter (fig. 23). The seasonal lag of all nonpoint sources comprised 25–50 percent of total TP load with the highest relative contributions during spring and summer—a fraction of the larger magnitude fall and winter fluxes was lagged in delivery until the spring and summer seasons. In the Nooksack River, the components of storage lag were mostly from animal feeding operations, upland geologic material, and crop fertilizer. In the Skagit River, upland geologic material followed by urban land, and their lagged components, were the main contributors to TP load. The largest relative TP aquatic losses occurred during the summer when travel times were highest but were nearly four times lower than the relative losses of TN by aquatic decay (figs. 22 and 23).

Compliance with DO standards in the bottom layers of marine waters depends on nutrient reductions to upstream freshwater sources. This includes reductions in discharge from wastewater treatment plants into marine waters and reductions from other sources of nutrient inputs from watersheds (Mohamedali and others, 2011; Ahmed and others, 2019). The SSM suggests that marine waters of the Salish Sea are TN limited whereas freshwaters are more typically TP limited—higher TP yield can result in increased primary productivity and thus higher delivery of organic carbon loads (Ahmed and others, 2019). Thus, any reduction of TN should be considered with TP and vice versa. Predicting the time of year marine inlets are most vulnerable to low marine DO concentrations requires information regarding when and where TN and TP loads are delivered from the Puget Sound region. In other words, representation of the temporal variability of nutrient delivery across the region may be more important to Ecology’s PSNSRP than a mean spatial distribution of loads previously provided at annual timesteps when dynamic loads are likely to contribute to low marine DO. The seasonal TN and TP models developed here help inform the regional assessment of major sources, demonstrate how loads and concentrations varied seasonally and spatially, and define the primary drivers of those loads, including lagged components beyond what was capable from previous annual approaches (figs. 22 and 23). The dynamic SPARROW models are useful for evaluation and implementation of nitrogen reduction actions initiated in the PSNSRP, and perhaps more broadly for watershed management to meet approved freshwater DO TMDLs. The U.S. Environmental Protection Agency’s River Basin Export Reduction Optimization Support Tool (RBEROST; Chamberlin and others, 2022) is an example of a tool that can incorporate the dynamic SPARROW output to help managers identify best management practices (BMPs) to reduce nutrient loading from the Puget Sound region on a seasonal basis.

The dynamic modeling approach described in this report linked many unique datasets to physically based equations through statistical coefficients that provided useful interpretation of nutrient source pathways and processes accumulating throughout the stream network (tables 2 and 5). For example, the TN model quantified mass delivery rates estimated from animal feeding operations and on-site treated wastewater systems at 8.4 kg of TN per animal per year and 4.5 kg of TN per household per year, respectively (table 2). For TP, the rate of mass from animal feeding was relatively higher than for septic systems (2.3 kg of TP per animal and 0.2 kg TP per household per year, respectively; table 5), suggesting that more TN comes from septic compared to TP while more TP comes from animal feeding operations compared to TN, which is similar to patterns found in other locations in the Cascade Range (Anderson, 2002).

Urban land was treated as a lumped coverage source pathway, estimated to yield an additional 802 kilograms per square kilometer per year (kg/km²/y) TN and 79 kg/km²/y TP (tables 2 and 5). Compared to previous approaches, those urban values were generally higher (246 kilograms per year [kg/y] TN and 12 kg/y TP in the Pacific region model by Wise [2019]; 122 kg/y TN and 64 kg/y TP in the Midwest model by Robertson and Saad [2019]; and 150 kg/y TN and 24 kg/y TP in the Illinois model by Schmadel and others [2024]). Differences in urban coefficients could reflect some regional variation; the models developed for the Puget Sound region were much smaller in spatial size than previously attempted. Urban land comprised 12 percent of the Puget Sound region where coefficients represent the relative mean contributions for this region. Additionally, in the TN model, a new variable that represents stormwater outfall density interacted with the urban source variable, which caused the mean urban TN yield to nearly double from around 400 to over 800 kg/km²/y. The larger coefficient value suggests that, during higher precipitation intensity, more diluted stormwater went through the outfalls. It also suggests that additional source pathways are represented from atmospheric deposition with precipitation falling on impervious surfaces. A negative coefficient identified for stormwater outfall density indicated that sources from urban areas were reduced during higher precipitation, and other sources like atmospheric deposition were more dominant, but it also indicated that urban areas may be a dominant source during drier periods. A negative coefficient also suggests that there may be some potential effects of recently implemented BMPs in the stormwater conveyance systems (Figueroa-Kaminsky and others, 2022) but were not explicitly represented by the model.

TN leachate from red alder tree nitrogen fixation was estimated as 0.36 kg of TN fixed and produced by each square meter of trees per year (table 2), a value comparable to previous SPARROW applications (0.27 kilograms per square meter per year [kg/m²/y TN], Wise [2019]) and field estimates of fixation rates (0.31 kg/m²/y of nitrogen [N], Compton and others [2003]). However, that value does not directly translate to the TN flux exported from a watershed—fixed TN is accumulated and decomposed in the soils and later leached out. Therefore, across all WRIAs, the mean yield estimated by the TN model was 200 kg/km²/y N produced by red alder trees (fig. 16). For watersheds dominated by red alders, the mean yield increased to over 2,000 kg/km²/y N. Likewise, Compton and others (2003) further estimated that the fixation rate of 0.31 kg/m²/y N in watersheds dominated by red alder trees could yield between 2,600 and 3,900 kg/km²/y N from a watershed. The TN model’s representation of red alder tree fixation compared well to field measurements, but it is possible that the correlation to the coverage dataset represented more than just red alder trees and included additional nitrogen-fixing species such as lichens and maples (Compton and others, 2003). Further tests with the TN model using other vegetation datasets could be fruitful toward improved source pathway representation. However, inclusion of red alder tree coverage as a source input dataset greatly improved the TN model performance and was far better compared to other similar datasets such as NLCD forested cover.

The storage lag coefficients for the TN and TP models were 0.25 and 0.29, respectively (tables 2 and 5), indicating that 25 percent and 29 percent of contemporaneous nonpoint TN and TP source inputs were lagged in storage repositories each season and delivered to streams in later seasons, respectively. That estimate suggests that mean seasonal flux of nutrients was relatively fast in which a large portion of any source input passing through the storage repository got flushed through each year. Likewise, the relative contribution of storage lag was lowest during high load and streamflow conditions, yet retention caused an increased lagged contribution of mass as watersheds dried out. Models quantify a bulk retention rate and thus caution should still be exercised if used to interpret lagged timescales as that retention rate currently lumps many timescales. For example, urban nonpoint sources may be stored very briefly (a lower α_S with a faster timescale and lower lag effect [eq. 6]) compared to agricultural sources more connected to groundwater (a larger α_S with a slower timescale). If the stream or waterbody was also contributing to temporary storage instead of operating solely as a sink, α_S could be further biased toward faster timescales. Additional parsing or representation of different types of storage retention may be an area for improved nutrient prediction.

The relative net aquatic decay of TN and TP in streams was highest in summer during the longest travel times (figs. 22 and 23). TN and TP instream decay rates were comparable to the empirical estimates by Sheibley and others (2015) for nitrate (0.59 m/d) and orthophosphate (0.36 m/d) in the Puget Sound region. Consistent with field studies elsewhere (Miller and others, 2016), instream decay of nitrogen increased with water temperature, mostly during summer (fig. 13A). Sheibley and others (2015) found additional loss explanation with channel attributes. For example, they noted higher decay with higher sinuosity yet lower decay in channels with higher slopes, particularly for phosphorus. The SPARROW models are flexible in that more terms could be added and tested (refer to eq. 4). For example, adding slope in the TP model stream decay expression could improve explanation. However, slope has already been factored into the estimate of TP loss with Jobson velocity and depth derived from streamflow. Likewise, higher streamflow did not return significant instream TP decay (table 5).

Aquatic nitrogen and phosphorus storage may be temporary (Valett and others, 2022), especially in spring and summer associated with seasonal stratification in reservoirs and uptake by algae and aquatic vegetation or permanently removed through processes such as denitrification (Harvey and others, 2013). In addition, particulate phosphorus is often stored seasonally or longer in reservoirs, especially after dam construction, which at later times becomes susceptible to releases with increased sediment infill or following summer stratification and changes in sediment from reduction-oxidation processes (Posch and others, 2012). Processes related to dam removal were not explicitly represented by the TN and TP models. For example, a dam was removed on the Elwha River in 2013, and the downstream calibration station reflected a large increase in downstream TP load while TN load was less affected. That increase in TP load was likely mass previously stored in the reservoir and not explicitly accounted for in the model. Therefore, that downstream calibration station was excluded from the TP model—another dataset or process such as suspended sediment could improve representation of mass stored and released. Both models tended to over predict load from the Skokomish-Dosewallips WRIA, which is an indication that upstream influences from, for example, Lake Cushman, perhaps were not well represented (figs. 8, 9, and 1.1).

The modeling approach described in this report has proven useful for quantifying seasonal sources and drivers of nutrient load across the region but also identified challenges, limitations, and possible areas for improvement. Across the Puget Sound region, the overall mean error was 50 percent for the TN simulated load and 72 percent for the TP simulated load (tables 4 and 7). Although those results are considered promising, compared to the TN model, the TP model source pathways were more challenging to identify—possibly due to a lack of representation of erosion caused by human activity and high precipitation—and coefficients still contained large levels of uncertainty after adjusting for effects of serial correlation. There may be additional processes like mass stored and released by reservoirs not explicitly represented. Likewise, load estimation of the calibration data consistently returned higher errors for TP compared to TN, especially using the WRTDS_K approach. Also compared to the TP model, calibration of the TN model seemed more straightforward where most of the variation in calibration load data could be explained using only the source pathway variables interacting only with seasonal precipitation.

If error is large in any one source pathway, an option is sometimes to lump that pathway with another or altogether exclude one of the pathways. If a pathway is excluded, error in other coefficients might decrease, but the model will likely inaccurately assign mass to a defined pathway. For example, excluding the septic source pathway from the TP model could cause the animal feeding pathway coefficient to increase, sometimes by ten-fold; that animal feeding pathway coefficient would have a smaller standard error and p-value by excluding the septic source pathway, but it would not necessarily produce a better model if septic systems are in reality an independent source pathway—a higher animal feeding coefficient may increase just to compensate for the model missing septic contributions.

Regional-scale modeling is an efficient way to simulate water quality in streams but requires simplifications of processes and thus that may not account for specific conditions at unique locations. Likewise, a model can lack process representation if a key dataset is missed, or if data are not sufficient to separate and track a unique source pathway. For example, a mismatch in timing between simulation and observation at a few locations indicated a potential missing source pathway or land-to-water delivery information such as erosion rates during high precipitation. At the TP stations 01A120 and 01A050, for example, the TP model mostly missed the timing of observed load for 2007 through 2009 and then again in 2013 and 2014, but the model was nearly representative of instream load for 2017 through 2020 (fig. 11). It could be that some process or change in land use or management in the Nooksack WRIA occurred during the modeling period that affected TP load more so than TN load but was not explicitly represented by data and model coefficients. Management activities and BMPs not explicitly represented with data and coefficients, such as the inclusion of a dataset representing stormwater detention ponds, are areas to look for improvements. Similarly, as dam removal on the Elwha River caused large effects on instream TP load, sudden release of stored TP in reservoirs was not a process explicitly represented. Sediment transport processes are likely candidates for improving the TP load representation, but dam removal on the Elwha River was unprecedented and unlikely to represent any viable management actions for the region. Although independence in data is a limiting assumption, the SPARROW framework is uniquely suited for improvements to process representation and model error by its ability to include new interactions, processes, or datasets. Data representing the amount of stored mass in a reservoir, the age of the stored mass, together with dam release rates, potentially could improve model representation of TP load. However, the Elwha River contributed a smaller fraction of TP mass relative to some of the other WRIAs (1.5 percent of regional total; fig. 17; table 2.2), and thus additional data added to the Elwha-Dungeness WRIA may improve local accuracy but not necessarily improve overall model performance across the region.

A comprehensive quantification of source attribution and accumulation across space and time is helpful to assess where and how nutrient reductions could be most effective, but several limitations in the TN and TP models were identified. Although the models are useful to identify where error is low and high, and perhaps identify where other data are needed, the lumped process representation and seasonal timestep could be improved through further parsing of the lumped storage lag into more bins of different timescales (for example, nutrients lagged in groundwater versus in soils; Miller and others, 2024), integration of other data (for example, estimates of groundwater discharge), integration with other models (for example, transit time distribution of the subsurface or machine learning techniques), and with updated expressions of aquatic decay and wetland losses to potentially allow for estimation of any net sources from streams and waterbodies.

Better data integration, improvements to data processing and assumptions, or simply considering more data to test in calibration could improve process representation and quantification of source pathways. A first step could be increasing the number of calibration stations. The goal for the Puget Sound region, which is consistent with most water-quality models, was to include as many calibration stations as possible to reduce the weight of any single station used to explain error and comprehensively represent observed instream mass across space and time (in other words, represent gradients of the region). Coverage of calibration stations for the Puget Sound region was considered sufficient to represent variability across the region, but a few smaller WRIAs did not contain monitored data and half of the WRIAs contained only one or two stations mostly located low in the basin far away from headwaters (fig. 3). A few more calibration stations located more toward headwaters could improve process representation by explaining more variability and thus accuracy of simulation timing and magnitude or could further indicate if and where source pathway data may be missing or even misleading. There was consideration of expanding the model domain size to include more calibration stations and gradients. However, there is value in having Puget Sound region-specific models for faster simulations and more focused data collection and compilation efforts, which may allow for identification of source pathways unique to the region that might not otherwise be identified with a larger scale model. There were just enough stations to cover most of the region; a larger scale model may better represent variability in climatic and atmospheric drivers, but in exchange it may provide less isolated source information.

The effort to compile data for the TN and TP models was comprehensive yet there were still many datasets not used in the TN and TP models for a variety of reasons. While there are many other areas of potential data improvements to consider, more data do not always indicate that a better model is possible. For example, other data types may contain strong serial correlation—adding more constant variables can increase noise or cause issues with multicollinearity if also correlated with similar datasets. Other data types considered in the models included permeability, historical wildfire extent, mean percentage snow cover, and tile drainage, yet none were found significant or to improve models. There may be additional sources from springs (Rohde and others, 2024), but the springs dataset correlated well in space with urban cover. It is possible the urban source pathway contains a spring component, but it also may be coincidence that urban development falls closely where springs discharge into valleys at mountain fronts. Therefore, more exploration into those possible source pathways, and whether they would be considered separate or interacting pathways, could improve interpretation of the urban pathway.

Likewise for stormwater outfalls as both dilution and source delivery pathways, the explicit collection area for each outfall was not directly mapped or estimated. More data processing, and perhaps collection, would be needed to better isolate and represent the outfall component, but outfall size and collection area variables established consistently across the region could improve outfall representation in the models. Concentrations have been collected in some outfalls and such data would help quantify fluxes (Figueroa-Kaminsky and others, 2022), but those data would be needed consistently and comprehensively to represent outfall effects in the models. It is possible that the TN model is also picking up BMPs in the stormwater conveyance systems and it could be useful to separate and quantify the effects of BMPs, but that also would require additional data and further testing to establish a clear and significant statistical interaction to be a consistent variable used to represent a particular BMP (Detenbeck and others, 2018). Inconsistencies in datasets like BMPs or stormwater outfalls instead could be expressed as noise error and thus further limit model interpretation.

Near-term improvements to aquatic decay functions could be made using datasets such as reservoir volumes and operations, showing possible stratification, and improved local streamflow estimated through better dynamic estimation of water use and diversions. Net aquatic TN losses were occurring in streams with additional evidence that rates increased with water temperature (table 2; fig. 13A). Net TN losses in waterbodies, however, were not as clearly identified, suggesting that waterbodies were not removing much TN relative to streams. TP decay coefficients were difficult to identify for streams—if the overall net effect of streams was near zero, even if gross aquatic losses and sources are present, it is unlikely to identify a model coefficient different than zero. However, once the TP stream decay coefficient was set to estimate a loss for streamflow conditions below the annual mean, which assumes losses are occurring during lower streamflow, a significant stream decay process was quantified. Differences in net decay rates during different hydrologic conditions suggest that some temporary storage of mass in streams and waterbodies was likely occurring, particularly for TP. Although a net decay assumption is a model limitation, some reality in varying decay rates was still mimicked based on adjustments with streamflow and water temperature.

The seasonal mass balance representation of streams from headwaters to marine-water discharge points by source is important information to support Ecology’s nutrient reduction plan. Certainly, there are limitations with process representation and simulation accuracy, but the modeling approach directly provided real, interpretable values. A mass balance has been a cornerstone upon which interpretation depends. Although model uncertainty can be high when zoomed into unique reaches (50–72 percent mean error), an ability to quantify uncertainty in space and time is a strength—the models and their residuals can be useful toward identifying locations where data and understanding are lacking. The seasonal mass balance simulations also provide a dataset for further analyses or modeling. For example, seasonal loads could provide boundary conditions, or a point of comparison, for more localized and detailed water-quality studies.

Improvements to simulation accuracy and resolution of nutrient conditions may be possible with a machine learning (ML) modeling approach, capable of producing results at a daily timestep (Basu and others, 2023). Common critiques of ML models, however, are limited process interpretability and possible overparameterization as sometimes hundreds of variables are used (Maier and others, 2024). If the most important information is daily simulations of instream nutrient concentrations entering marine waters, an ML model might be favorable. However, some type of ML-mechanistic hybrid modeling framework may be the most useful approach to support Ecology’s needs of dynamic knowledge of nutrient delivery to marine waters by major source pathway. Next steps that build on the models developed here need to retain interpretable mass-balance information that include estimation of aquatic processes.