To evaluate the performance of the four different vertical mixing parameterizations, model results were compared against time series of the observed data for potential temperature (θ), salinity (S), the East–West and North–South horizontal velocities (u and v, respectively), and temperature diffusivity (K
T). To reduce the number of figures in this document, we will focus on potential temperature, θ and the temperature diffusivity, K
T or K
ρ
. Since the vertical temperature diffusivity depends on the stratification and vertical shears in the horizontal velocities, the Brunt–Väisäla frequency, N, the vertical shears, U
Z and V
Z, the turbulent kinetic energy, k, and the length or dissipation scale, l, were also investigated. The key criteria for the evaluation were the depths of the surface mixed layer, the potential temperature field over time, and the vertical temperature diffusivity. The surface mixed layer depth, smld, was defined as a 0.2 °C difference from the surface, i.e. a reference depth of 0 m (Fig. 1b).
During the FLX91 experiment, the winds were strong the first day, weak during day 1.5–2.5, then building to 15 m/s (30 kts) during the second storm from day 2.5 to 5.5 (Fig. 1a). Since the winds were being ramped up during day 1 in the simulations, the strong winds of day 1 did not induce as much mixing as they would have at full strength and the day 1 response should be ignored.
The observed surface mixed layer depth (smld) (red in Fig. 1b) was a few meters deeper than that of the model results for NN (blue), MY (cyan), and GLS (black) and generally shallower than LMD (green). The general trend for the observed smld was matched by NN, MY, and GLS, but not LMD. The LMD smld was too deep and too constant to match the observations. The LMD smld was roughly around 50 m by 0.5 days and remained at that depth until 4 days. The smld for the other schemes were less than 20 m and so were the observed smld (Fig. 1b). Around 4 days, the wind strengthened suddenly, and the observed smld increased rapidly to fluctuate around 30 m. The fluctuations were strong, primarily ranging from the surface to 60 m, but once reaching 90 m. The smld’s of all mixing schemes increased at this time, but those of LMD dove ~ 20 m deeper than those of the other mixing schemes. LMD was also a bit slower to respond to the stronger winds. GLS was a bit too shallow and did not match as well as MY or NN. Neither MY or NN went as deep for the deep excursions as the observations. None of the vertical mixing parameterizations responded as quickly as the observations, although the simulation results were output at the same time interval as the observations.
Inspection of the potential temperatures from the model simulations (Fig. 2a–k) compared to the observations (Fig. 2l) shows that NN (Fig. 2a, e, i) and MY (Fig. 2b, f, j) simulated the observed potential temperature structure the best. LMD (Fig. 2d, h, 25 levels not shown) mixes the water column too much and does not show the warm surface layer forming like the other parameterizations. Note the results from the 25-level simulation for LMD are not shown as they were nearly identical to those with 50 levels. GLS (Fig. 2c, g, k) does not mix the warm surface water as much as occurred in the observations.
The vertical resolution did not appear to make much difference for the surface 40 m; however, the thermocline at 120–190 m thickened with fewer levels (Fig. 2). The potential temperatures with the coarse vertical structure, 25 levels, (Fig. 2i–k) actually matched in the thermocline region better than the higher resolution simulations, 100 and 50 levels, (Fig. 2a–h). The salinity structure between the simulations was essentially equivalent (not shown) with the observations having higher temporal variability.
Model estimates of temperature diffusivities varied widely between LMD and the other vertical mixing parameterizations (Fig. 3). LMD had much higher temperature diffusivities than the observations (Fig. 3l) at all vertical resolutions (Fig. 3d, h, 25 levels not shown). Temperature diffusivities generated by the simulations for the other mixing parameterizations (Fig. 3a–c, e–g, i–k) were higher near the surface and lower below 40 m than the observations (Fig. 3l) at all vertical resolutions. The observed temperature diffusivities are much more variable with time; however, the magnitudes are roughly equivalent, except below 40 m where the models are less diffusive. There are two reasons the models are less diffusive below 40 m. First, the stratification, as characterized by N, is too low for all resolutions (not shown). Second, the velocity shears are too low (not shown). The latter is due to the high vertical resolution of the observations compared to the model resolution, centimeters compared to meters. The shear stress at the surface from the wind matched between the observations and the model simulations for all vertical mixing parameterizations; however, this shear stress did not propagate vertically in the water column below 40 m in the model simulations. To see if the low diffusivity below 40 m affected the results, the background diffusivity was increased to 10−5 m2 s−1 for simulations with the NN and MY schemes with 100 levels. These simulations did not show appreciable differences in the smld or potential temperatures (not shown).
Investigation of the distribution of the temperature diffusivities between the different vertical mixing parameterizations had a typical 2 peak distribution with 1 large peak near the molecular diffusivity 10−6 m2 s−1 and another between 10−2 and 10−1 m2 s−1 (Fig. 3). In the log distribution, the observations had a temperature diffusivity distribution, which generally decreased with larger magnitudes (red line in Fig. 4). The temperature diffusivity distributions for the simulations behaved differently. LMD had several peaks and a gap at low diffusivities (green line in Fig. 4). NN, MY, and GLS all had peaks between 10−2 and 10−1 m2 s−1 and NN and GLS roll off around 0.3 (10−0.5). MY responds most similarly to the observations; however, all mixing parameterizations are missing many values between 10−6 and 10−4 m2 s−1.