*3.3. Initial Condition Specification*

For the 19-month hindcast initial condition specification, the salinity and temperature fields were developed for 1 April 1979 using the joint NOS and USGS historical circulation survey conductivity-temperature-depth (CTD) datasets and the model was started from rest. The quasi-operational nowcast/forecast system started in the middle of March 2013 when a climatological temperature and salinity file (with adjustment from observation) was used as the very first initial condition. For each nowcast/forecast cycle, the COMF-HPC will automatically find the most recent restart file as this cycle's initial condition (SFBOFS has four cycles a day). The details of the HPC-COMF can be found in Zhang *et al.* [17].

### *3.4. Surface Forcing Specification*

For hindcast scenario, the North American Regional Reanalysis (NARR) 2007 datasets with 32 km spatial and 3 h temporal resolution were interpolated to the model grid to provide 10 m winds, sea level atmospheric pressure, and 2 m fluxes of downward shortwave radiation and net total heat flux. For the nowcast and forecast, the COMF-HPC will automatically find the most recent NAM4 (North American Mesoscale Model 4 km resolution) results in NCEP's data tank to get the necessary input surface forcings.

#### **4. Tidal Simulation**

The tide scenario simulation is the standard first step for all OFS' development. This is due in good measure to the fact that water level is the first priority for safe navigation, and tide and tidal current are the dominant dynamic processes in most coastal waters. For the tide scenario, the model setup for the four forcing specifications as mentioned in the previous section is similar to that for hindcast scenario. The slight differences can be found below.

#### *4.1. Short Term Experiment: 1–15 April 1979*

A three-dimensional simulation approach including baroclinics was used to capture the influence of internal waves on the tidal dynamics following [37,38]. The slight model setup difference from hindcast scenario is: winds were set to zero and the sea level atmospheric pressure set to 1013 mb. River flow conditions are used for all rivers. The April 1979 NOS and USGS historical circulation survey data were used to compare the model results with the observation.

To develop initial salinity and temperature conditions on 1 April 1979 (and on 1 September 1980 for the later extended experiment case), the available CTD and CT time series data were placed on a coarse unstructured grid of order 50 elements. An interpolation program was developed in which each FVCOM grid node was assigned a given element and the salinity/temperature value interpolated from the node values at the appropriate depths. This program allows the initial density condition to be developed for the tidal and hindcast simulations.

To calibrate the bottom roughness, the approach of Cheng *et al.* [15] was used, in which the bottom roughness is made a function of water depth as in Table 1. To reduce the amplitude of the simulated water level response at Port Chicago, the bottom friction was further increased above Carquinez Strait as noted in Table 1. The water level response with respect to MLLW at Port Chicago for Experiments 1 and 2 is similar (See Figure 4). Results for Experiments 5 and 7 show very minor improvement in the agreement with water level observations at Port Chicago in the order of a 2 cm reduction in RMSE. Experiments 3, 4, and 6 were unstable, due to large horizontal gradients in bottom roughness during the wetting/drying cycle.

**Table 1.** Delta Inflow Bottom Friction Experiment Summary. The scale factor was used to multiply bottom roughness in model domain above Carquinez Strait. The tapered scale factor ranges from 1 to the full value in a linear fashion from Carquinez Strait to the river inflows based on longitude. The bottom roughness sets are given in the second table. The HA amplitude reduction corresponds to reducing the amplitudes of the offshore boundary harmonic constants.


Three additional Experiments 8–10 were conducted in which the river stage at Rio Vista and at Antioch was reconstructed from NOS harmonic constituents. Experiment 8 used the Experiment 7 bottom roughness specification. Experiment 9 included a 20 cm offset for the San Joaquin River and a 22 cm offset for the Sacramento River. In Experiment 10, the Experiment 9 offsets were retained and the Set 1 Bottom Roughness z0 values were used. Note in these stage experiments the Oregon State University Tidal Data Inversion, OTIS Regional Tide Solutions [35] harmonic analysis results were reduced by 5% for the four ocean open boundary stations. Note the Sa and Ssa harmonic constituents derived from San Francisco water level analysis were used at these stations. All other open boundary node water levels were derived via linear interpolation of values from two of the stations surrounding the node.

**Figure 4.** Comparison of modeled versus predicted water level at Port Chicago with flow boundary condition over the period 1–15 April 1979.

In SFBOFS, we assume that the model datum is equal to the North American Vertical Datum of 1988 (NAVD88) minus 0.955 m (this resultant level is close to the MSL at open ocean boundary). Therefore, an additional field, model datum minus mean sea level, was developed. In San Francisco Bay, NAVD88 data were available from Point Reyes up to the river inflow locations.

A program was developed to access the VDATUM database and to interpolate onto the SFBOFS grid the following four datum fields: MLLW to MSL, MLW to MSL, MHHW to MSL, and MHW to MSL. In addition, the specification of the model datum (MD) to MSL allows the model predicted water level results to be presented with respect to all of the tidal datums. MSL, MLLW, NAVD88 and MSL-MD of key stations are listed in Table 2.

**Table 2.** Water Level Vertical Datums. Note tidal datums and NAVD88 are with respect to gage zero. Model Datum (MD) is given with respect to MSL. Note at the up estuary stations, MSL is above the model datum, while at the entrance to the Bay, MSL and the model datum are coincident. Using the table, it is possible to determine MLLW with respect to MD.


Note that MSL-MD difference increases from the Bay entrance to Antioch and Rio Vista. The MSL at Antioch and Rio Vista are 0.20 and 0.22 m above model datum, respectfully. The digital relationships among the different tidal datums, the model datum and NAVD88 are helpful in correctly comparing model results with measured water level data. The Experiment 10 water level response at Port Chicago with respect to MLLW is shown in Figure 5. Note by using the stage boundary condition with the offsets in Experiment 10, the agreement with observations is reduced from 19 cm in Figure 4 with the flow boundary condition to 9 cm RMSE. This is due in large measure to the improvement in the simulated tidal range.

### *4.2. Extensive Tidal Calibration*

For further calibration, the model setup used for the short term tidal experiment was used over an extended 19-month simulation from April 1979 through October 1980. Meteorological forcings were specified by setting the wind speed to zero and the sea level atmospheric pressure to 1013 mb over the entire model domain. A nudging of both salinity and temperature to specified climatological values was used along the open ocean boundary. The nineteen month simulation was completed in 38 segments of approximately 15 days' duration each, with each segment restarted from the previous segment's final fields.

**Figure 5.** Comparison of modeled *versus* predicted water level at Port Chicago with stage boundary condition and 5% harmonic amplitude reduction over the period 1–15 April 1979.

In Table 3, simulation segment results for water surface elevation are compared respectively to harmonic predictions in terms of RMS error and Willmott relative error [39], which is given by *<(abs(Y-X))2>/<(abs(Y-<X>)+abs(X-<X>))2*>, with *Y* the model prediction and *X* the observation. Station locations can be found in Figure 6. In addition, model and predicted means are compared with respect to station MLLW. In general, the water level RMS errors do not exceed 15 cm and are consistent from month to month from Port Chicago in Suisun Bay through San Pablo and mid-Bay regions, as well as in the offshore and southern regions of San Francisco Bay. At Coyote Creek, at the southern end of South Bay, while the means are in close agreement, the RMS errors range from 13 to 22 cm and often exceed 15 cm. The adjustment of the bottom friction over salt marsh regions undergoing wetting and drying may need further consideration. In Table 4, principal component direction currents at mid layer (k = 10) are compared respectively to harmonic predictions in terms of RMS error and Willmott relative error. In addition, model and predicted mean currents are given. Current amplitude RMS errors are consistent from month to month and are generally less than 35 cm/s. Willmott relative errors are less than 10% except at C-33.

A more formal skill assessment has been performed in two parts. In part one, harmonic analysis was used to compare water level and principal component current strengths for the M2, S2, N2, O1, and K1 tidal constituents. NOS accepted harmonic constants are compared with tidal simulation results in Table 5. Favorable comparisons were obtained for all constituents at all stations. In Table 6, model principal component current strengths are compared with NOS harmonic constants. Again, comparisons are favorable for both amplitude and phase at most stations except at Station C-18 for the M2 amplitude. In part two, model and predicted means, root mean square error, standard deviation of the error, and central frequency (at reference levels of 15 cm for water level and 26 cm/s for current) were considered. In Table 7, water level skill assessment results are given with favorable comparisons exhibited for means and RMSE at all stations with the exception of Coyote Creek, where the water level error exceeded 15 cm 33.9% of the time. In Table 8, principal component current strength skill assessment results are shown with favorable results observed at most stations except again at Station C-18.

**Figure 6.** NOS and USGS Historical Circulation Survey Water Level, Current, Salinity, and Temperature Stations. Note current meters were collocated with conductivity-temperature sensors. Note the location of Point Reyes is shown in Figure 1.

The heat flux algorithm generates no excessive temperatures and produces accurate seasonal heating and cooling [22]. No comparisons with observed salinity are made, since meteorological forcings are not included. However, the simulated salinity gradients are reasonable and a density front is present with the inclusion of the freshwater inflows [22]. The salinity structures through the entrance are in line with climatological values. In the next section, all forcings will be turned on for the hindcast simulation and the model skill assessment will be conducted for further validation.






**Table 3.** *Cont.* **Table 4.** Principal Current Direction Mid-Level Current Speed Tidal Calibration: April 1979–October 1980. For each box, the first column of values corresponds to the first 15 days of the month, with the second column of values denoting the remaining portion. Within each column: Row 1 corresponds to the RMSE in cm/s. Row 2 corresponds to the Willmott Relative Error in percent. Row 3 corresponds to the model mean in cm/s. Note the predicted mean current speed is zero. 


**Table 5.** Harmonic Analysis of 19-month tidal simulation water level comparison to NOS accepted tidal constituents. Accepted constituentvalues of amplitudes (m) and phase (degrees) minus model predictions. Note negative amplitude differences denote an under prediction of tidal water level constituent amplitudes, while positive phases denote a lag in tidal water level constituent propagation. 


**Table 6.** Harmonic Analysis of 19-month tidal simulation principal current direction current comparison to NOS accepted tidal current constituents. Accepted constituent values of amplitudes (m/s) and phase (degrees) minus model predictions. Note negative amplitude differences denote an under prediction of tidal current constituent amplitudes, while positive phases denote a lag in tidal current constituent propagation. Along with station id measurement, depths are given in parenthesis with observed/model principal component directions given following the depth information. 




**Table 8.** Nineteen-month Tidal Simulation Principal Component Direction Current Strength Skill Assessment Results. Note measurement depth given in parenthesis followed by observed/model principal current direction. RMSE is root mean square error, SD is standard deviation of the error; e.g., model minus observation, and CF is central frequency of the errors with respect to a reference level of 0.26 m/s. 

