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Numerical experiments using hybrid coordinate ocean model (HYCOM) are designed to quantify the effects of wind wave-induced Coriolis-Stokes forcing (CSF) on mixed layer (ML) dynamics in a global context. CSF calculated by the wave parameters simulated by using the WaveWatch III (WW3) model is introduced as a new driving force for HYCOM. The results show that noticeable influence on ocean circulation in ML can be caused by CSF. Over most of the global oceans the direction of Stokes transport is different from that of the change in current transport caused by CSF. This is not unusual because CSF is normal to Stokes drift. However, the CSF-caused change in current transport and the wave-induced Stokes transport have the same magnitude. The seasonal variabilities of mixed layer temperature (MLT) and mixed layer depth (MLD) caused by CSF are analyzed, and the possible relationship between them is also given.

Ocean circulation is mainly driven by atmospheric forces through the ocean surface, for example, wind, heat, and fresh water. Wind blows at the ocean surface and produces gravity waves, transferring direct and indirect kinetic energies from atmosphere to ocean. Dynamics in the ocean surface mixed layer (ML) are influenced by the ocean surface waves mainly in three ways. First, wave breaking inputs turbulent kinetic energy (TKE) to turbulence. Second, the Langmuir circulations [

There is a mean Lagrangian volume transport produced in their propagation direction of monochromatic waves, the Stokes drift

where

where

In the classical Ekman layer model, the momentum equation describing the nonsteady state, ageostrophic current in the surface layer is [

where

where wave-induced stress is in the form of

This equation is consistent with Polton et al.’s [

Integration of (

in which

where

Current field in the upper layer is of great interest to oceanography community. By analyzing the analytical solutions to the standard Ekman layer model which includes CSF, Polton et al. [

where

The ocean surface boundary layer depth (BLD) is calculated by the bulk Richardson number

with the unresolved turbulent velocity shear

In (

In the KPP mixing strategy, estimation of MLD is diagnostically dependent on a temperature jump, for example, 0.3°C. The bottom of the ML is set to an interpolated depth where the density jump is equivalent to the temperature jump. Usually, BLD and MLD are similar, since KPP mixes strongly down to BLD and density should be relatively homogeneous throughout the whole layer. BLD and MLD are determined by different criteria, the former is by buoyancy and the latter by temperature. Note that buoyancy and temperature can be linked through density. Thus, the effects of CSF on MLD are similar to those on BLD.

The temperature conservation equation in HYCOM is given by

for temperature

The connection between CSF and the dynamics in ML can be examined through diagnosing the responses of key variables based on numerical experiment. Exp. 1 and Exp. 2, without and with CSF, are, respectively, designed using HYCOM to assess the effects of CSF on upper ocean circulation, MLT and MLD.

CSF in this study is computed using the wave parameters generated by WaveWatch III (WW3), a third-generation wave model of wide application. WW3 is configured on a horizontal grid field from 90°S to 90°N and from 180°W to 180°E, with a resolution of 2.5° in both latitude and longitude, generating a total of 144 × 73 horizontal grid points. Input winds are from ECMWF ERA40 Reanalysis data sets. The first frequency is set at 0.0418 Hz. With the frequency increment factor of 1.1, the number of frequencies is chosen to be 30. The directional resolution is 15°. Minimum source term time step is 600 s. Time interval of wind input is 86400 s. WW3 is spun up for 5 years, and then the 2001 actual year run is performed.

The configurations of HYCOM are mainly adopted from Deng et al. [

The starting point of examining CSF’s effect here is to analyze the current field in ML. The net forcing on the sea surface with the presence of CSF will be increased (decreased) when CSF having the same (opposite) direction as that of wind stress. For example, in the equatorial Northeast Pacific, the generally northward Stokes drift induces an eastward CSF which is against the westward winds, resulting in the decreased net forcing.

The simulated global current fields in ML, derived respectively from Exp. 1 and Exp. 2, are shown in Figures

(a) Annual-mean mixed layer current field of 2001 from Exp. 1, in which CSF is not included as a top boundary condition; (b) annual-mean mixed layer current field of 2001 from Exp. 2, in which CSF is considered; (c) annual-mean changes (results of Exp. 2 minus that of Exp. 1) in mixed layer current. Currents (m/s) are vertically averaged through the mixed layer.

Surface waves directly contribute to the volume transport in the upper layer, known as Stokes transport. We are wondering that through the action of CSF how much the variation of currents transport would be. As mentioned above the influence of surface wave is confined in the Ekman layer, here we compare the depth-integrated Stokes transport with the CSF-induced change in depth-integrated current transport in ML. The annual-mean depth-integrated Stokes transport ^{2} s^{−1}. At low latitudes, these differences are even smaller than 0.05 m^{2} s^{−1} (Figure ^{2} s^{−1}, with majority of the large values (maximum of ~10 m^{2} s^{−1}) occurring at westerly wind belt region, where relatively strong winds generate large waves. This result well verifies our hypothesis that when considering the effect of CSF on the ocean surface, wave-induced current transport in ML would be created. Furthermore, we notice that these changes are nontrivial; that is, the magnitude of

(a) Annual-mean depth-integrated wave-induced Stokes transport, ^{2} s^{−1}), simulated by WW3 model; (b) annual-mean depth-integrated wave-induced Stokes transport, ^{2} s^{−1}), calculated by ECMWF reanalysis wave variables; (c) the magnitude difference (m^{2} s^{−1}) between the WW3-based Stokes transport and ECWMF-based Stokes transport, with ECWMF-based ^{2} s^{−1}); (e) percentage change of

From Figures

The distribution of annual-mean MLT tends to be zonal (east-west), which is almost independent of longitude. The warmest water is near the equator (slightly higher than 29°C in the warm tongue), and the coldest water (about −1.8°C) locates close to the poles (Figure

(a) Annual-mean temperature field in the mixed layer of 2001 from Exp. 1; (b) annual-mean mixed layer depth of 2001 from Exp. 1. Mixed layer depth here is defined as the depth that has a 0.3°C temperature jump to the sea surface temperature. Temperatures (°C) are vertically averaged through the mixed layer.

The annual and seasonal variabilities of

Changes in mixed layer temperature in °C (a) and changes in mixed layer depth in m (b) due to the inclusion of CSF into HYCOM. Plots from top to bottom, in order, respectively show the annual-mean, spring-mean (Mar~May), summer-mean (Jun~Aug), fall-mean (Sep~Nov), and winter-mean (Dec~Feb) results.

As an important parameter that can be used to verify the capability of a numerical model in simulating the upper ocean phenomena, sea surface temperature (SST) can be directly measured with high accuracy by many marine instruments such as buoys. Observational array data of Tropical Atmosphere Ocean/Triangle Trans-Ocean Buoy Network (TAO/TRITON) are updated in real time and freely available to the research community. Here we use SST time series from TAO buoys which are deployed at the equatorial Pacific region to validate our simulation results. Figure

Daily SST (°C) time series in 2001 from TAO buoys (solid line) and those output from HYCOM simulations with CSF (cycle line) and without CSF (dash line) for 4 stations at equatorial Pacific, (0°N, 140°W), (0°N, 155°W), (5°S, 125°W), and (10°S, 10°W).

The effects of wave-induced CSF on ML dynamics are numerically quantified using HYCOM. Typically, surface-wave-associated Stokes depth is about 5 m in the open ocean [^{−1}, the Ekman depth is ~120 m). So, in the present analysis, we introduce the wave-induced CSF as a top boundary condition to modify the ML dynamics in the ocean circulation model. Serving as a correction to the upper ocean boundary conditions, CSF does not fundamentally change the structures of current field in ML. The change of current transport caused by CSF (^{2} s^{−1} and is comparable to wind-driven Ekman transport. Large values of ^{2} s^{−1}, in the same order as

In conclusion, the wave-induced CSF has a noticeable influence on the dynamics in ML. This effect is more pronounced over the westerly region where strong wind waves are present. The comparisons of SST with some available TAO buoy observations show that the simulated SSTs are generally improved with the contribution of CSF. Therefore, inclusion of CSF into the global ocean model is a sound step toward better representing the real ocean surface processes.

This work is supported by the National Natural Science Foundation of China (nos. 41206012, 41171304), China 973 Program (2012CB316206), China 908 Program (Chinese Offshore Investigation and Assessment), and program for public from State Oceanic Administration, China (200905030). The discussion with Ms. Qi Dongmei and suggestions from anonymous reviewers contributed significantly to the present work. The Global Tropical Moored Buoy Array temperature observations were obtained from the TAO Project Office of NOAA/PMEL