Rib is expressed in:
𝑅𝑖𝑏 = (𝐵𝑟− 𝐵(𝑑))𝑑 (𝑉𝑟2− 𝑉2(𝑑)) + 𝑉𝑡(𝑑)
Br and Vr are mean buoyancy and velocity, d is depth and Vt include other effects such as
convection or non-local entrainment. The depth of OBL is at where Rib equals to critical
value Ric. Due to the strong eddy diffusivity, the vertical structure in OBL is almost
We use KPP in one-dimensional Regional Oceanic Modeling System (ROMS;
Shchepetkin and McWilliams 2005) to simulate the evolution of the upper ocean structure.
Float measurements in the upper 200 m are averaged from 12th Dec 1:00 p.m. to 13th Dec
6:00 a.m. as the initial conditions. Below 200 m, the missing measurements of
temperature, and salinity and horizontal current are compensated with Hycom data.
AL9207 and AL9209 do not have the current data so the initial conditions are completely
filled with Hycom data. The forcing term utilize buoy measurements, including wind, air
temperature, humidity, air pressure, shortwave, and longwave radiation. The run starts on
the 13th Dec when was one day before the arrival of MJO. The temporal resolution is 600
s. The default setting of mixing parameters critical gradient Richardson number equal 0.7
and critical bulk Richardson number equal 0.3. The vertical resolution is about 1 m from
110 m depth to the ocean surface.
5.2 Simulating mixed layer depth deepening
The simulation of surface MLD is compared to the observation (Fig. 12). To avoid
the impact of eddy which is located at the south of floats after 15th Dec, the comparison
focuses on 13th to 14th when the westerly wind rose up. The model does not predict the
MLD deepening during the MJO active phase as that observed by the three floats. On
AL9207 and EM8487, the result of MLD deepening rate is underestimated with a
difference of 5 m to the observations. Because the change of MLD is affected by the
turbulence simulating, some previous studies suggested some factors, including
resolution and KPP parameter (Critical Bulk Ri, Critical Gradient Ri), affect MLD
performance in KPP. Therefore, the sensitive test of the resolution, KPP parameter will
be described in the following section.
Fig. 12: (a)–(c) Simulations of MLD deepening at the different initial conditions of three
floats in KPP (blue line), with the comparison to the float observation (black line).
5.3 Effects on vertical resolution in the upper ocean
Vertical resolution is required to capture a small scale, such as vertical mixing
features in the equatorial ocean (Jia et al., 2021). Woolnough et al. (2007) and Bernie et
al. (2008) have proposed that increasing vertical resolution to around 1 m is critical for
simulating SST variations during the MJOs. In this study, the vertical resolution of 1 m,
2 m, and 4 m in upper 110 m are used in MLD deepening simulation (Fig. 13). In the
model, the MLD of AL9207 shallows about 5 m on Dec 13th at 12 p.m., and the MLD
maintains about the same depth in the following days. The MLD does not change
significantly in the three floats during the MJO. Furthermore, there is no significant
difference between high resolution and coarse resolution on MLD. The results
demonstrate that the vertical resolution apparently does not act on MLD performance in
Fig. 13: Different vertical resolutions on simulations of MLD (a)–(c) at AL9207, AL9209,
and EM8487 (blue: 4 m; orange: 2 m; yellow: 1 m), with the comparison to the float
observation (black line).
5.4 Parameters in the KPP mixing scheme
In the KPP, the parameters Ri0and Ric directly affect the vertical diffusivity Kρ within
and below the OBL, and these may result in difference of turbulence simulating. The
effects of these two parameters are studied.
Ri0 is increased from 0.7 to 1, resulting in stronger turbulence induced by shear at
the base of OBL (Fig. 14). However, the KPP still fails to simulate the MLD deepening
depth. The values of Ri0 are tested to make the simulated MLD similar with the
observation depth. The model results are not similar to the observation unless Ri0 of 5
was used. Although strengthening and extending the turbulent mixing at the base of OBL
can obtain a similar result to observation, the value is too large and not real in general
ocean conditions. Moreover, when Ri0 decreases from 0.7 to 0.3, more challenged to
induce shear instability. The MLD is not significantly variable, either.
On the other hand, increasing the Ric from 0.3 to 0.7 forces the KPP to simulate a
thicker OBL (Fig. 15). That is, increasing the Ric value may enhance wind effect on
destratifying all stratification to a deeper layer. When wind forcing became stronger at
about 13th 12 pm UTC, different Ric used in the model will cause the variations of
simulated MLD. When Ric equals 0.5, MLD is similar to the observation on AL9209. On
AL9207 and EM8487, the results by tuning Ric to 0.7 can also make simulation of MLD
close to the observation MLD when the wind field increases. In short, by modifying the
parameters Ric can reach a deeper KPP boundary layer and simulate a similar MLD
variation of observation when the wind started. However, the value between 0.5 or 0.7
does not correspond to typical ocean conditions (Geernaert 1990). Because the observed
change of MLD is due to the wind-driven shear instability, the momentum flux during the
model simulation can also significantly affect the ocean current. Therefore, the next
section will discuss the sensitive test of momentum flux.
Fig. 14: Different gradient Richardson number on simulations of MLD (a)–(c) at AL9207,
AL9209 and EM8487 (blue: Ri0 = 0.4; orange: Ri0 = 0.7; yellow: Ri0 = 1), with the
comparison to the float observation (black line).
Fig. 15: Different bulk Richardson number on simulations of MLD (a)–(c) at AL9207,
AL9209 and EM8487 (blue: Ric = 0.3; orange: Ric = 0.5; yellow: Ric = 0.7), with the
comparison to the float observation (black line).
5.5 Summary of MLD simulation by using KPP
We use KPP in one-dimensional ROMS to simulate the MLD deepen under the buoy
wind measurement. With the default parameters set in KPP, the MLD deepening depth do
not simulate well on MLD deepening. In the model, MLD does not change significantly
in the first two MJO days. Because the vertical resolution, critical gradient Ri, and critical
bulk Ri can affect MLD performance in KPP, the sensitive tests are performed to explore
these factors' effects on MLD simulations. The vertical resolution and critical gradient Ri
do not affect apparently on the MLD. Although tuning critical to 0.7 bulk Ri can obtain
similar MLD, this high value of 0.7 does not correspond to typical ocean conditions.
Therefore, adjusting the parameters in the KPP may not be appropriate for simulating the
observed MLD deepening during the MJOs. Other factors will be discussed in the section.