We select a case study of a significant weather event that occurred off the US West Coast during 4–8 November 2020. A strong low pressure system [mean sea level pressure (MSLP) of 976 hPa] initially impacted the western Canadian coast on 4 November (Fig. a). The low pressure weakened while the cold front moved southward on 5 November. By 6 November, a strong maritime high pressure system with a MSLP of 1040 hPa built in behind the cold front while the cold front moved farther south over central California. Lower surface pressures were analyzed near the coast. Finally, by 7 November the cold front had moved farther south and the high pressure ridge covered a larger oceanic region behind the front. The NASA MODIS composites initially showed some high cirrus and low stratus clouds near the California coast ahead of the front (Fig. b, 4 and 5 November). After the front passed on 6 November, a convective cumulus and stratocumulus cloud field exists over the ocean as the colder air surged south (Fig. b, 6 and 7 November).

The Coupled Ocean Atmosphere Wave Sediment Transport (COAWST) model was used to simulate this event. We used two-way coupling between the Weather Research and Forecasting (WRF) Model and Wavewatch III (WW3) in the COAWST modeling system, accomplished through the Model Coupling Toolkit . Every 30 min, the WRF model 10 m zonal and meridional velocities are passed to WW3 and the wave characteristics (significant wave height, wave period, and wavelength) are passed to the WRF model surface-layer parameterization. In the surface-layer parameterization, the time-varying surface roughness length is calculated from the wave parameters , with a specified Charnock parameter relation. The momentum stress vector accounts for the directional discrepancy between wind vectors and wave fields. More details on the wave-atmosphere coupling in the COAWST model can be found in , , and . Lateral and initial boundary conditions were from the European Center for Medium Range Weather Forecasting Reanalysis version 5 (ERA5; ) at 3-hourly frequency. The numerical simulations were initialized at 00:00 UTC 4 November 2020 and integrated to 00:00 UTC 8 November 2020 (96 h). Two domains were used: an outer domain (d01) with Δx=2 km (638×755 points) and inner domain with Δx=400 m (691×776 points) [factor of 5 reduction in grid spacing]. One-way nesting was used; the inner domain did not feed back to the outer domain in the inner domain imprint region. On both WRF domains, ninety vertical levels were used. The model time step on the WRF model d01 was 10 s and the time step on d02 was 2 s. The model top was 50 hPa. To help constrain the large-scale evolution with the analysis, large-scale Newtonian relaxation to the ERA5 reanalysis was applied on the WRF model d01 with nudging coefficients of 3×10-4 s⁻¹ for winds and potential temperature (1/e damping time of 0.93 h), and 3×10-5 s⁻¹ for water vapor mixing ratio (1/e damping time of 9.3 h). Newtonian relaxation was not applied within the boundary layer.

On the WRF model d01, the Yonsei University (YSU) PBL parameterization was used. On the WRF model d02, two WRF model simulations were executed using different PBL parameterizations: YSU and the 3D PBL parameterization with the PBL approximation. Aside from the PBL parameterization, both d02 WRF model simulations used common physical parameterizations: aerosol-aware Thompson-Eidhammer microphysical parameterization , Rapid Radiative Transfer Model Global (RRTMG) shortwave and longwave radiation parameterization , the unified Noah land surface model , and the revised MM5 surface layer parameterization . The single WW3 domain was approximately the same size as the WRF model d01 and had a grid spacing of Δx=2 km. While inclusion of ocean coupling (and three-way feedback) would be more realistic, our primary goal was to understand differences in 1D and 3D PBL parameterizations with atmosphere/wave coupling only without the added complexity of oceanic processes. In future work, we will include ocean coupling to understand the impact of sea surface temperature changes and ocean currents.

Since the focus was analysis of the different PBL parameterizations on the innermost domain in the “gray zone” with Δx=400 m, more details of the parameterizations are given here to understand their behaviors. In the first-order-closure YSU PBL parameterization, SGS vertical mixing is treated through a prescribed eddy-viscosity profile dependent on the surface fluxes (a so-called K-profile parameterization). Nonlocal vertical mixing is accomplished through a gradient correction term. The 3D PBL parameterization is based on the local, 1.5-order prognostic turbulence kinetic energy (TKE) closure Mellor-Yamada SGS model . The 3D PBL parameterization calculates the Reynolds stresses and fluxes in the Mellor-Yamada level 2.5 model, and both horizontal and vertical mixing is treated through the grid-scale turbulent stress and flux divergences. Thus it does not use the 2D Smagorinsky deformation-based grid-scale mixing in the horizontal directions like 1D PBL parameterizations such as the YSU parameterization. There are two variants of the 3D PBL parameterization : the full application and an approximation. In the 3D PBL approximation, horizontal derivatives of mean quantities are neglected in the Mellor-Yamada model. The 3D PBL parameterization can be applied in simulations with horizontal grid spacings of O(100–1000 m) (the “gray zone”) where 3D effects are important since the most energetic turbulent eddies are neither fully parameterized nor fully resolved. Implementation of the 3D PBL parameterization in the COAWST modeling system involved adding and modifying several WRF model dynamics and physics FORTRAN codes and compiling and linking with the Intel Math Kernel Library (MKL), needed for linear algebra problems described in Eqs. (19) and (22) of . Due to computational expediency, we used the 3D PBL approximation for the simulation (henceforth labeled “3D PBL”).

The observations used in the evaluation are listed in Table  and shown geographically in Fig. . They consist of surface meteorological stations and buoys in the area of interest, as well the vertically profiling US Dept. of Energy Morro Bay lidar profiling buoy (MBY). One buoy outside the WRF model d02 (NDBC buoy 46013, located at [38.235° N, 123.317° W], approximately 80 km north of the WRF model d02 northern lateral boundary, is also used to evaluate the WRF model d01 inflow to the WRF model d02.

The large-scale evolution of this event on the WRF model d01 is shown in Fig. . The WRF model 10 m winds on both d01 and d02 fed back to WW3 in the WW3 domain (Δx=2 km; similar size to the WRF model d01), and the WW3 model fed back to the WRF model d01 and d02 with wind-wave-induced roughness changes. At 12:00 UTC 5 November, 10 m wind speeds were approximately 6–10 m s⁻¹ within the WRF model d02. Significant wave heights were approximately 2–2.5 m. As the simulated front passed around 12:00 UTC 6 November, wind speeds increased to 10–14 m s⁻¹ and significant wave heights increased to 3.5–4.5 m. By 12:00 UTC 7 November, wind speeds increased to 14–18 m s⁻¹ west of the WRF model d02 west lateral boundary, and significant wave heights increased further to peaks of 6–6.5 m. As the cold front moved south, 2 m air temperatures decreased approximately 3 °C from 12:00 UTC 6 November to 12:00 UTC 7 November (not shown). Overall there is a significant spatial correlation between the wind and wave fields, indicating this event is largely a wind-wave instead of a swell-wave event. For the remainder of the analysis, the focus will be on the WRF model d02 and differences between 1D and 3D PBL parameterizations.

Inspection of 24 h time means before and after the frontal passage on the WRF model d02 at z=10 m and z=206.5 m, the latter of which is one of the WRF model vertical levels that is within the typical range of hub heights for offshore wind turbines (z=75–225 m) , show persistent regions where consistent differences between the COAWST YSU and 3D PBL simulations existed (Fig. ). Prior to the frontal passage, near-surface winds in the COAWST YSU simulation were less westerly and stronger over the ocean than the COAWST 3D PBL simulation (Fig. a), while at z=206.5 m the COAWST YSU simulation had northwesterly winds that were weaker. Interestingly, there was a narrow central coastal band where the COAWST YSU simulation had 1–2 m s⁻¹ stronger onshore winds at 10 m a.g.l. (above ground level). Time-mean winds before the frontal passage over the ocean were approximately 10–14 m s⁻¹ in both simulations. The simulated front passed at approximately 12:00 UTC 6 November, and after the passage, time-mean wind speeds were much larger in both simulations, particularly in the southern portion of the WRF model d02 (approximately 14–18 m s⁻¹). The COAWST YSU simulation near-surface winds were stronger over the ocean (by approximately 0.5–1.5 m s⁻¹) (Fig. b). At z=206.5 m, the COAWST YSU simulation winds were also stronger over the ocean, but by only approximately 0.5 m s⁻¹ on average. Significant wave heights were approximately 1–3 m prior to the frontal passage and 4–6 m afterwards (Fig. ).

Instantaneous difference fields of the 10 m winds and significant wave heights on the WRF model d02 every 12 h are shown in Fig. . Prior to 10:00 UTC 6 November, the COAWST YSU simulation had 10 m winds that were stronger over the western part of the domain, and weaker near the coast. This simulation had significant wave heights that were approximately 0.1 m larger in the western portion of the domain and 0.1 m smaller near the coast. When the significant wave heights increased after the simulated frontal passage, COAWST 3D PBL simulation winds on average were weaker over the ocean, causing significant wave heights that were approximately 0.2–0.3 m lower than the COAWST YSU simulation.

The time-mean longitude-height vertical cross sections through the center latitude of the WRF model d02 (Fig. ) show that prior to the frontal passage the winds were strongest near the top of the boundary layer (sloping from z≈400 m to z≈250 m, moving from west to east, marked by the sharp potential temperature inversion) with weaker winds aloft. The COAWST YSU simulation had weaker winds (by approximately 1 m s⁻¹) within the boundary layer than the COAWST 3D PBL simulation on average (except for right near the surface, as seen in Fig. a). After the simulated frontal passage, the boundary layer deepened and momentum became more vertically well mixed. During this period, the COAWST YSU simulation had stronger winds below z≈500 m, and weaker winds above. This is possibly due to the nonlocal mixing in the YSU PBL parameterization during the more convective conditions, vertically mixing higher momentum air downward. The COAWST YSU simulation had greater water vapor content above the boundary layer than the COAWST 3D PBL simulation (Fig. c). After the frontal passage, the boundary layer deepened and water vapor became well mixed vertically (Fig. d). During this period, over the ocean, the COAWST YSU simulation had slightly less water vapor content below z≈500 m and greater content above. Vertical cross sections of cloud water content indicated a stratus cloud field below the inversion prior to the frontal passage in both simulations (Fig. e). The COAWST YSU simulation had greater cloud water content near the surface near the coast than the COAWST 3D PBL simulation. After the frontal passage, with cooler air advecting over the ocean, cumulus cloud fields developed in both simulations with bases above z≈1000 m (Fig. f). Differences arose due to phase offsets of individual cumulus cells.

Time series comparisons of wind speed and direction between the COAWST model d02 and d01 simulations and NDBC buoy observations are shown in Fig. . Since NBDC buoy 46013 was north of the WRF model d02, only the WRF model d01 time series is shown there. Overall, all simulations capture the wind speed and direction at the buoys well: in particular, the timing and magnitude of the wind speed increase between 12:00–18:00 UTC 6 November and the change in wind direction from northwesterly to more westerly near 06:00 UTC 7 November. Examining the overall biases and errors

Model time series were interpolated to the observational time grid to compute biases and errors.

Time series of simulated temperature and dewpoint (calculated using the standard formula from mixing ratio and pressure) in comparison to buoy observations are shown in Fig. . North of the WRF model d02, at NDBC buoy 46013, the WRF model d01 simulation had temperatures that were approximately 1–2 °C warmer than the observations. The simulated dewpoints were more consistent with the observations, although errors were larger during the decrease between 06:00–18:00 UTC 6 November. At buoy 46042 toward the northern part of d02, the COAWST YSU and 3D PBL simulations were also slightly warmer than the observations. The decrease in dewpoint of 4 °C between 06:00–18:00 UTC 6 November was captured well by all simulations, while between 12:00–18:00 UTC 7 November, all simulations were too dry. All simulations matched the observed temperatures well at buoy 46028 after 06:00 UTC 6 November. Interestingly, the COAWST 3D PBL simulation matched the observations best after 12:00 UTC 7 November, while the COAWST YSU d01 and d02 simulations were approximately 1 °C too warm. Similar to buoy 46042, the dewpoint drop is captured well by all simulations at buoy 46028 (although the minimum simulated dewpoints were slightly lower than the observations at 18:00 UTC 6 November). At buoy 46011, unfortunately there were no observations in which to verify the model simulations. Examining the overall biases and errors, no simulation was significantly better than another.

Figure  shows the evaluation of significant wave heights at the same buoys. At all buoys, the COAWST d02 YSU and 3D PBL simulations qualitatively captured the increase from 1–2 m near 00:00 UTC 6 November to 4–6 m near 12:00 UTC 7 November due to the near-surface wind increases. At buoy 46042, very minor differences existed between the simulations, while at buoys 46028 and 46011, the differences were slightly larger. At buoy 46042, both simulations had wave heights that were approximately 0.5 m too high between 18:00 UTC 5 November and 18:00 UTC 6 November, and wave heights approximately 0.5 m too low afterwards. At buoys 46028 and 46011, the COAWST 3D PBL simulation predicted slightly lower wave heights than the COAWST YSU simulation (by approximately 0.2 m) between 12:00 UTC 6 November and 06:00 UTC 7 November, and were more consistent with the observations. At buoy 46011, the simulations captured the general increasing trend and produced the two peaks evident in the observations, although a 6 h phase lag was apparent in the simulated second maximum relative to observations.

At the over-land stations farther north (MRY, SNS, and WVI), the peak simulated wind speeds were lower than observed (Fig. ). In particular, the observed maxima between 06:00–15:00 UTC 6 November were underpredicted at SNS and MRY. However, the simulations cannot be evaluated beyond 15:00 UTC 6 November due to missing observational data. The COAWST d02 simulations with Δx=400 m had higher wind speeds than the COAWST d01 simulation with Δx=2 km near the time of peak winds. At SPB, the model simulations generally overpredicted the wind speeds. At PRB, near 12:00 UTC 6 November, both COAWST d02 simulations overpredicted the wind speeds while the COAWST d01 simulation matched the observations better. Unfortunately, observations dropped out at all over-land stations during the peak of the wind event near 18:00 UTC 6 November to 00:00 UTC 7 November, and afterwards.

The COAWST simulated wind speed and direction at the Morro Bay lidar buoy (MBY) compared favorably in both the timing and magnitude (Fig. ). Prior to approximately 06:00 UTC 6 November, there was a stronger vertical gradient in both the simulations and observations, with weaker winds aloft and stronger winds near the surface. As the front moved through the domain near 12:00 UTC 6 November, wind speeds became more well mixed vertically. The timing of the wind maximum between 06:00–12:00 UTC 6 November was well captured by both COAWST d02 simulations. The second wind maximum near 09:00 UTC 7 November was also captured in both simulations, but more diffuse in time in comparison to the lidar observations. Wind directions were generally northwesterly near the surface and turning more northerly aloft before 12:00 UTC 6 November. Wind directions were more uniform vertically afterwards, and exhibited northwesterly flow. The turning of the flow to more westerly between 00:00–06:00 UTC 7 November was captured well by both COAWST simulations.

Since the COAWST simulations at Δx=400 m were in the “gray zone”, with partially resolved and parameterized TKE, it is appropriate to add an estimate of the resolved TKE to the SGS TKE in the PBL parameterizations (while noting the YSU PBL parameterization has no SGS predicted TKE) to compare to lidar velocity variance observations. Resolved TKE was estimated using an instantaneous horizontal domain average over the ocean as the mean to compute perturbations. Resolved plus SGS TKE is shown in Fig.  for both COAWST simulations. At 00:00 UTC6 November, higher TKE was confined near the coastline. As the simulated front passed near 12:00 UTC 6 November, a large area of increased TKE was evident near the Big Sur coast moving toward the MBY and 46027 buoys. TKE also increased over the ocean away from the coast. By 00:00 UTC 7 November, there was larger TKE in the northern part of the domain over the ocean and the southern coastal area. Examining the differences, the COAWST 3D PBL simulation had higher TKE over the ocean on average than the COAWST YSU PBL simulation.

The resolved plus SGS TKE from the COAWST simulations was compared to TKE at the Morro Bay lidar buoy (obtained from velocity variance observations) and shown in Fig. . Prior to 12:00 UTC 6 November, both simulations had significantly more TKE aloft above z=150 m, and slightly more TKE near the surface. It is possible that the missing lidar observations between z=200–250 m were due to the cloud base. Both simulations captured the increased TKE near 12:00 UTC 6 November, but the magnitudes were weaker than observed. Both simulations predicted the secondary peak approximately 6 h ahead of the observations near 12:00 UTC 7 November.

Finally, evolution of vertical profiles of winds and potential temperature are shown in Fig. . Prior to the frontal passage at 00:00 UTC 6 November, the wind speed peaked near z=200 m with a maximum around 15 m s⁻¹. The COAWST 3D PBL simulation matched the observations best at this time. The potential temperature profile showed a well-mixed boundary layer below z=150 m, with a strong inversion above. By 12:00 UTC 6 November, the boundary layer grew to z≈300 m, and the jet max moved upward to the boundary layer top with an increase in wind speed to approximately 25 m s⁻¹. Both simulations matched the lidar observations well below z=250 m. Finally, by 00:00 UTC 7 November, winds and temperature became very well mixed. The observed wind speeds were in between the COAWST YSU and 3D PBL simulations at this time.

To summarize the observational evaluation in Sect. 3.4 and 3.5, both the COAWST YSU and COAWST 3D PBL compare favorably with near-surface buoys measurements and vertical wind profiles from the Morro Bay lidar (MBY). TKE in both simulations is slightly underestimated in comparison to MBY. Errors in wind speed for both simulations are generally larger over land. Both simulations predicted the gradual increase in significant wave height well, with the COAWST 3D PBL simulation producing slightly reduced wave heights, matching the observations better. Vertical profiles (Fig. ) show the both simulations matched the observations well, with the COAWST 3D PBL simulation better producing the jet nose structure at 00:00 UTC 6 November than the COAWST YSU simulation.

A natural question that arises is to what extent are differences between the COAWST YSU and 3D PBL simulations due to the differences in vertical mixing treatment versus horizontal mixing treatment. Recall, the YSU parameterizaton uses a first-order, nonlocal, K-profile closure for SGS vertical mixing while the 3D PBL parameterization uses a 1.5-order, prognostic-TKE, local closure. Moreover, the YSU parameterization uses the 2D Smagorinsky parameterization in the horizontal directions while the 3D PBL parameterization does not. Therefore, a sensitivity test was carried out using the 1D version of the 3D PBL parameterization; a local, 1.5-order, prognostic TKE parameterization in the vertical direction . This parameterization also uses the 2D Smagorinsky parameterization; therefore, the precise role of differences in the vertical mixing treatment between the YSU PBL parameterization and the 1D PBL parameterization can be understood. The instantaneous differences in the wave and 10 m wind fields between the COAWST 1D PBL and 3D PBL simulations (Fig. ) are much smaller than the instantaneous differences between the COAWST YSU and 3D PBL simulations (Fig. ). Therefore, most differences between the 3D PBL and YSU parameterizations are due to the differences in vertical mixing treatment, rather than differences between the 3D PBL parameterization's heteorogeneous treatment of the horizontal Reynolds stress and flux divergence terms and the 2D Smagorinsky parameterization. We note however, that it is possible that more differences in the horizontal mixing would be present if the full 3D PBL parameterization were used, and this will be explored in future work. Recall, in the full 3D PBL parameterization, gradients of mean quantities in the Mellor-Yamada level 2.5 mode are not neglected, leading to more realistic representation of SGS mixing.