Model Version and Run Time

CE-QUAL-W2 undergoes regular development, incorporating bug fixes and new features. The model software used for the LWSC model was labeled as version 4.5 and was compiled on April 8, 2021, by the developers at Portland State University (Wells, 2021). More recent releases of version 4.5 are available and this updated software could be applied to the LWSC model.

The model runtime for the 2014–20 model was 9 hours and 25 minutes on a laptop with a 12th-generation Intel Core i7 1.8-gigahertz processor and 32 gigabytes of random-access memory. The average model timestep was 11 seconds.

Model Grid

An accurate representation of the bathymetry of a waterbody is important in simulating water temperature and salinity because the bathymetry affects the modeled surface area, depth, volume, water age, and travel time. A CE-QUAL-W2 model grid was formed from model segments that connect in the direction of flow (fig. 2). Each segment has layers of defined height that typically decrease in width from the top of the grid to the channel bottom, approximating a cross-sectional shape of stacked rectangular layers that are laterally integrated (example segment cross-sections are documented in WEST Consultants, Inc., 2017). A series of segments are grouped into “branches” and groups of branches into “waterbodies” that define specific reaches.

The LWSC model grid consisted of one waterbody, seven branches, and 108 segments. Layer height was 0.5 meters (m) throughout. Branch 1 was the main-stem Lake Washington Ship Canal, with 70 of the model segments. These segments had an average segment length of 129.7 m, with a minimum of 15.7 m and maximum of 426.7 m. Added together, the length of these main-stem LWSC model segments is 9.2 kilometers (km; 5.7 miles [mi]), which matches the actual length of the Lake Washington Ship Canal, as estimated in Google Earth. The deepest model segments were segments 63 and 64 near sampling site LLLW (Large Locks site; figs. 1, 2). During the model run, the maximum water depth at segment 64 was 16.7 m (54.8 feet [ft]).

The model branch that Lake Union comprises includes model segments 79–88 (fig. 2) and is also one of the deeper areas of the model grid. The Lake Union model branch connects to the main stem at model segment 18. Lake Union is reported to represent most of the surface area and volume of the Lake Washington Ship Canal (King County, 2017). That source reports the total Lake Washington Ship Canal volume as 32.1×10⁶ m³ and Lake Union volume as 23.4×10⁶ m³ (73 percent of total). The model grid, considered at a typical water-surface elevation, indicates the main-stem ship canal branch volume as 34.3×10⁶ m³ and the Lake Union volume (including the Lake Union model branch and the main-stem segments typically considered as part of Lake Union) as 21.3×10⁶ m³ (62 percent of total). Although some difference exists between these values, these Lake Union volumes estimated by King County and as represented in model grid are relatively close. Some uncertainty is inherent in this comparison; for example, the King County (2017) report did not note the water-surface elevation that was considered in that calculation.

Outflow Structures and Withdrawals

The main-stem branch terminates at the Ballard Locks spillway. At this location, outflow occurs over the spillway, through smolt flumes, and through surface flow into the fish ladder. These three outflow time series were combined into one time-series boundary condition for the model, with an assigned centerline elevation of 4.5 m for the structure outflow. This approach would make sense if all three outflows released water from the Lake Washington Ship Canal at the same elevation. The smolt flume was constructed at the spillway, so releases from the spillway and smolt flume did occur at the same elevation. The fish ladder, however, released water from the Lake Washington Ship Canal from a higher elevation (U.S. Army Corps of Engineers, 2017), and that outflow time series could be implemented separately in the model. The surface freshwater fish ladder flow was relatively small (23 cubic feet per second most of the year), so changing this may not have much of an effect on overall model results. However, for waterbodies that undergo thermal or water-quality stratification, the elevation at which water is released or withdrawn from a waterbody can affect conditions downstream and in the waterbody itself (Casamitjana and others, 2003; Sullivan and Rounds, 2005; Carr and others, 2020). The outflows at the large locks and saltwater drain were modeled as withdrawals, and the outflows from the small locks were modeled as structure releases.

Model Inputs and Parameters

Meteorology

Most data for the model’s meteorological input file came from a site on the roof of the University of Washington’s Atmospheric Sciences-Geophysics (ATG) Building, about 1 km north of the Lake Washington Ship Canal. These input data included air temperature, dew-point temperature, wind speed, wind direction, and solar radiation. Cloud-cover data for model input came from the King County International Airport Metar site, about 12 km south of the Lake Washington Ship Canal. All meteorological model inputs were configured for an hourly timestep.

Some unexpected anomalies were noted in some of the meteorological data. For instance, the minimum wind speed values were near 0 meter per second (m/s) for the first years of the dataset, but the minimums shifted upward to a new baseline greater than 1 m/s in the later years (fig. 3). The annual maximum solar radiation rate also varied over the years, which is unusual (fig. 3). University of Washington personnel were contacted as part of this review, and they noted that the ATG dataset underwent minimal quality assurance (David Warren, University of Washington, written commun., May 9, 2024).

Other nearby meteorological datasets could be compared to the ATG dataset. If higher-quality meteorological data were identified, those replacement data could be used in the model, or could be used to correct the ATG dataset. The presence of anomalies in the model inputs, however, is problematic and is worth further investigation. Wind and air-temperature data from the Metar site and the Lake Washington profiling buoy were already tested during model development according to the model documentation (WEST Consultants, Inc., 2017).

Upstream Boundary

The upstream boundary of the model was at the Montlake Cut, near Union Bay and the outflow of Lake Washington (fig. 1). This inflow into the model was set up as an external head (stage) boundary in the model. Three model input files defined that boundary condition: water-surface elevation, water temperature, and water quality (salinity). The water-temperature input file was created using data from a profiling buoy in Lake Washington, at an approximately 3-hour frequency. The input file for upstream water quality set the salinity time series as 0 ppt at all depths for the entire simulation.

The same profiling buoy in Lake Washington that measured water temperature also measured specific conductance. Example data from 2018 are shown in figure 4. Specific conductance can be used to estimate salinity or total dissolved solids (Hem, 1985) and could be used to create a more realistic estimate of inflow salinity for the model; that more-realistic salinity would still likely be low, but nonzero.

Flow and Water Age

The Lake Washington Ship Canal water-surface elevation varied from 5.0 to 5.8 meters North American Vertical Datum of 1988, with minimums during the winter holding period, which often begins on December 1 (U.S. Army Corps of Engineers and WEST Consultants, Inc., 2023), and maximums in late May through early summer. Modeled water-surface elevations echoed this annual pattern in water-surface elevation (WEST Consultants, Inc., 2017; Rinehimer and Walton, 2022).

The LWSC model simulated water age, an estimate of residence time, for each model segment and layer (figs. 5–6). In an example year (2019), modeled volume-average water age of the Lake Washington Ship Canal was less than (<) 30 days from November through mid-June (fig. 5). Water age of the main-stem Lake Washington Ship Canal near Lake Union increased to more than (>) 30 days in late June and July. In mid-August through mid-October, the main-stem reach from Lake Union to the Ballard Locks had lower throughflow and greater resulting water age of >30 days. Some differences in the modeled water age occurred vertically through the water column at some times and locations (fig. 6).

Modeled water velocity in the Lake Washington Ship Canal was mostly positive, in the downstream direction toward the Ballard Locks (fig. 7). There were times and locations in the model with negative velocity, indicating flow in the upstream direction. This could occur as saline water was brought into the Lake Washington Ship Canal from the Ballard Locks (fig. 7, top), or during periods when overall flows were low (fig. 7, bottom).

Easthouse (1993) studied circulation patterns in Lake Union and found no definitive pattern. Instead, four possible circulation patterns could occur, including (1) east-west flow in winter and spring, (2) north-south flow, (3) minimal circulation during summer low flow, and (4) southeast to northeast flow (rare). The two-dimensional CE-QUAL-W2 model simulated Lake Union water velocity in the south-north and north-south directions, varying between layers at different times (fig. 7). In the model, Lake Union connected to the east-west flow (and occasional instances of west-east flow) of the main-stem Lake Washington Ship Canal at the northernmost segment of the Lake Union branch.

Water Temperature

Modeled water temperature in the Lake Washington Ship Canal followed an annual cycle, with cool temperatures in late autumn through early spring and warm temperatures in summer (figs. 5; 8–13). Some vertical stratification in modeled water temperature could occur in spring through autumn (fig. 8).

The model simulated water temperature well in the Lake Washington Ship Canal. Compared to measured water temperature at five locations along the Lake Washington Ship Canal, the model was able to simulate the seasonal and daily variation in water temperature well at different depths in the water column (figs. 9–13). At all sites, the model underpredicted water temperature, calculated as an average over the modeled period, as shown with negative bias metrics at each site and depth (table 1). However, calculation of goodness-of-fit statistics that compared model output to measured values at the same location and time produced MAE values that were mostly <1 °C (table 1); these values indicate that overall, the model simulated water temperature well. The only site and depth with MAE >1 °C was the Gas Works Park monitoring site (GWLW) at 44 ft.

Salinity

Modeled salinity varied between the freshwater input at Montlake Cut upstream to the saline waters from exchange at the downstream Ballard Locks location (figs. 5; 9–13; 14). The saline water had higher density than the fresh water and the model simulated it entering from the locks and then moving to the channel bottom because of that density difference (fig. 14).

In many periods, elevated salinity was not noted in the most upstream reach of the Lake Washington Ship Canal. However, during a period in late summer of 2014, elevated salinity (greater than 2 ppt at depth) was measured as far upstream as the University Bridge site (UBLW; figs. 9–13). The especially high concentration of salinity in the Lake Washington Ship Canal in that year was thought to be related to a false-locking study from July 28 to September 12, 2014 (Easthouse and Emry, 2015). False lockings were additional lock operations when boats were not present and were a possible strategy to benefit migrating salmon (U.S. Army Corps of Engineers, 2012). The model was able to simulate some part of the upstream movements of salinity under those conditions, but not the full extent.

The model’s baseline salinity was too low compared to measured salinity (figs. 9–13). The model baseline was at or near zero, whereas the measured data had a baseline salinity ranging from about 0.1 to 0.5 ppt (100–500 mg/L). This difference could be caused by the fact that the model’s upstream boundary salinity was set to 0 ppt along with the absence of any within-reach tributaries. Although freshwater sources of salinity were much lower in dissolved solids concentration, compared to the seawater inputs from the locks, the simulation of baseline salinity could be improved by updating the estimate of the upstream boundary salinity conditions and possibly adding within-reach tributaries to the model, if any data for such tributaries can be found.

Goodness-of-fit statistics were calculated from the comparison of modeled salinity to measured data at the same location (table 2). The model underpredicted salinity compared to measured values, as shown by the bias statistic. MAE values ranged from 0.04 to 3.62 ppt.