Statistics of the simulated SSTs versus MWIR OI SSTs from October 30 to November 6, 2006.
Abstract
The physical dynamic and biological response processes to Typhoon Cimaron (2006) in the South China Sea are investigated through the three‐dimensional Regional Ocean Modeling System (ROMS). For sea surface temperatures, ROMS achieves a correlation of more than 0.84, with respect to satellite observations, indicating a generally high level of skill for simulating the sea surface temperature variations during Typhoon Cimaron (2006). However, detailed analysis shows that ROMS underestimates the sea surface temperature cooling and mixed layer deepening because of insufficient mixing in the model simulations. We show that the simulation accuracy can be enhanced by adding a wave‐induced mixing term (BV) to the nonlocal K‐profile parameterization (KPP) scheme. Simulation accuracy is needed to investigate nutrients, which are deeply entrained to the oligotrophic sea surface layer by upwelling induced by Typhoon Cimaron, and which plays a remarkable role in the subsequent phytoplankton bloom. Simulations show that the phytoplankton bloom was triggered 5 days after the passage of the storm. The surface ocean was restored to its equilibrium ocean state by about 10–20 days after the typhoon's passage. However, on this time‐scale, the resulting concentrations of nitrate and chlorophyll a remained higher than those in the pre-typhoon equilibrium.
Keywords
- Typhoon Cimaron
- SST cooling
- mixed layer deepening
- phytoplankton bloom
- wave‐induced mixing
1. Introduction
Tropical cyclones are extremely high wind events generated over tropical oceans, capable of producing strong mixing and entrainment, transient upwelling, and internal waves. The response of upper ocean water to typhoons can be conventionally divided into two stages, the forcing stage and the relaxation stage in [1, 2]. In the first stage, potential energy is injected into the surface ocean by strong typhoon winds. Two significant physical phenomena caused by typhoons are the mixed layer deepening and sea surface temperature cooling in the wake of the storm. Warm water in the ocean surface layers is transported outward from the typhoon center and downward to depths ranging from tens of meters to beyond a hundred meters; cold water upwells from the deeper ocean along the typhoon's passage [3]. The current velocity in the surface mixed layer can reach 2 m s−1 or more, responding to the intensity of the tropical storm winds [2]. The relaxation stage following a typhoon's passage is primarily due to the inertial gravity oscillations excited by the storm in its wake, where the ocean adjusts towards a new geostrophic equilibrium state [1, 4–6]. The work of [7] concluded that the inertial oscillations are predominantly locally generated and the surface winds account for a large part of the energy and variability of such oscillations near the ocean surface. The theory of geostrophic adjustment was further reviewed in [8]. The latter theory, which describes the nature of the difference between the baroclinic and barotropic responses of the ocean to a moving storm as caused by the difference in the gravity wave speed, was first pointed out in [9]. The storm‐induced oscillating wake is formed by the slow propagating, near‐inertial gravity baroclinic waves, while the fast propagating barotropic waves produce a broad area of convergent depth‐averaged currents with no discernible wake; the latter is determined entirely by the wind stress curl, with negligible effects due to the earth's rotation and ocean stratification [10]. The work of [11] confirmed that the mixed layer dynamics is associated with shear‐induced entrainment mixing, and forced by near‐inertial motions up to the third day after the passage of the storm.
Tropical storms also exert a strong influence on the oceanic chlorophyll
The ocean temperature cooling and mixed layer deepening caused by tropical storms, usually are underestimated in three‐dimensional ocean model simulations, because of the insufficient mixing [23, 24]. Improvements of the mixing estimates in the simulation leading to more realistic and reliable simulations may solve this problem. After the potential energy injected into the mixed layer by tropical storms, wave dispersion spreads energy in both the vertical and meridional directions from the mixed layer [1]. Surface waves have been measured and simulated and shown to play a certain role on enhancing the turbulence in the subsurface layer [25, 26]. In the work of [24], a surface wave model was coupled to a three‐dimensional ocean current model (POM), and some related estimates for transfer of momentum and wave energy are derived, assuming linear theory for vertically dependent wave motions. The effect of wave breaking on the simulation of sea surface temperatures and surface boundary layer deepening was investigated in [27]. A wave‐induced vertical viscosity (
In our study, a biological model is coupled to the three‐dimensional Regional Ocean Modeling System (ROMS) to investigate both the physical and biological process of Upper Ocean in response to Typhoon Cimaron (2006) which occurred in the South China Sea. Typhoon Cimaron formed over the Pacific Ocean east of the Philippines on October 28, 2006, and then propagated westward, entering the South China Sea on October 30. Thereafter, Cimaron moved to the northwest part of the South China Sea and remained quasistationary during November 1–2, moving southwest on November 3, and finally dissipating near the Vietnamese coast on November 7. Both the mixed layer deepening and sea temperature cooling are underestimated in the model simulation, in comparison to reliable estimates of mixed layer deepened (about 104 m) on November 3 using a one‐dimensional remote sensing model [30]. Therefore the wave‐induced mixing term
2. Materials and methods
ROMS is utilized to simulate the processes of Typhoon Cimaron, which influenced the South China Sea from October 29 to November 7, 2006. The model region covers the whole South China Sea including 0°–30°N, 99°–130°E. There are 220 × 100 orthogonal curvilinear grids with the horizontal resolution varying at Δ
The initial temperature and salinity conditions are taken from the 1/4° grid climatological temperature and salinity analyses of October from WOA01 to represent the pre-typhoon conditions in the South China Sea, which was discussed by Carton and Giese [31]. The climatological monthly data have 24 standard levels with depths varying from 0 to 1500 m and the seasonal data have 33 standard levels with depths from 0 to 5500 m. As the maximum depth in the model is 5000 m, the climatological monthly data are applied in the upper 1500 m and the climatological seasonal data (autumn) are applied from 1500 to 5000 m. The initial current velocity is set to zero in this study.
The lateral boundary conditions for temperature, salinity, sea level and current velocities are obtained from the 5‐day averages from the global simulations of the Simple Ocean Data Assimilation (SODA) dataset with horizontal resolution of 0.5° × 0.5° and 40 vertical layers [31]. The Kuroshio Current transport can be identified on the eastern boundary. The tidal amplitudes and phases used in this model are obtained from the TPXO Global Inverse solution database [32] with eight primary tide constituents (M2, S2, N2, K2, K1, O1, P1, and Q1) and two long‐period constituents (Mf and Mm).
The daily wind stresses are obtained from QuikSCAT satellite data. The effect of heat flux is considered as the surface boundary for momentum, although the heat flux can be neglected under the extreme meteorological phenomena such as tropical cyclones. The daily heat fluxes are obtained from the Objectively Analyzed air‐sea Fluxes (OAFlux) project which is an ongoing research and development project for global air‐sea fluxes [33]. To present the climatological heating or cooling trends, we computed the surface boundary conditions for temperature and salinity involving relaxation to its observed values. Corrections are made for the net surface heat flux in the model simulations, as discussed in [34].
For the biological model, the surface chlorophyll
Both the total inorganic carbon (TIC) and total alkalinity are obtained from the Carbon Dioxide Information Analysis Center. The detailed data information is given in work et al. [38]. The climatological seasonal dataset is used to generate the initial and boundary conditions. Ammonium (NH4), large and small detritus, and N‐concentration are taken from the NO3 estimates and multiplied by the respective ratios of 18/62, 0.1 and 0.1, respectively, while phytoplankton, zooplankton, large and small detritus, and C‐concentration are taken from the chlorophyll
3. Model validation
Two Optimally Interpolated (OI) SST daily products (including microwave plus infrared (MWIR) OI SSTs and microwave only TMI AMSRE SSTs) are used in comparisons with the simulated SSTs to validate the model accuracy. MWIR OI SST product is at 9 km resolution, while TMI AMSRE SST product is at 25 km resolution. The validation statistical parameters contain mean error (ME), mean absolute error (MAE), root-mean-square (RMS), and correlation coefficient (R). The formulas to calculate these statistical parameters are presented in [39].
The simulated SSTs (Figure 2) are compared with the satellite observations from October 30 to November 6. The validation region is set from 99°E to 120°E and from 0°N to 26°N. For validation of the simulation, the statistical parameters are displayed in Table 1 for MWIR OI and Table 2 for TMI AMSRE. The MEs of the simulated SSTs are less than 0.12°C, compared with the MWIR SSTs; for TMI AMSRE SSTs, the MEs are within 0.14–0.24°C. Negative signs indicate that the modelled SSTs are less than the observed SSTs. The MAEs are within the range from 0.4°C to 0.6°C, and the RMS errors are less than 0.9°C. The correlation coefficients between the MWIR OI SST and simulated SST are over 87% from October 30 to November 6, while the correlation coefficients validated with TMI AMSRE SSTs are over 84%. The high values of the correlation coefficients indicate that the simulated SSTs are within a reasonable range. Therefore, we have demonstrated that ROMS can generally reproduce the processes of Typhoon Cimaron in the South China Sea.
Oct 30 | Oct 31 | Nov 1 | Nov 2 | Nov 3 | Nov 4 | Nov 5 | Nov 6 | |
---|---|---|---|---|---|---|---|---|
ME (°C) | −0.12 | −0.12 | −0.09 | −0.04 | −0.01 | −0.00 | −0.09 | −0.10 |
MAE (°C) | 0.42 | 0.45 | 0.50 | 0.54 | 0.58 | 0.56 | 0.55 | 0.58 |
RMS (°C) | 0.56 | 0.61 | 0.69 | 0.76 | 0.88 | 0.81 | 0.78 | 0.80 |
R | 0.89 | 0.88 | 0.88 | 0.89 | 0.87 | 0.88 | 0.88 | 0.88 |
Oct 30 | Oct 31 | Nov 1 | Nov 2 | Nov 3 | Nov 4 | Nov 5 | Nov 6 | |
---|---|---|---|---|---|---|---|---|
ME (°C) | −0.23 | −0.24 | −0.21 | −0.14 | −0.14 | −0.17 | −0.21 | −0.16 |
MAE (°C) | 0.41 | 0.44 | 0.48 | 0.53 | 0.53 | 0.49 | 0.46 | 0.46 |
RMS (°C) | 0.53 | 0.58 | 0.71 | 0.77 | 0.78 | 0.71 | 0.68 | 0.67 |
R | 0.87 | 0.86 | 0.84 | 0.87 | 0.88 | 0.89 | 0.89 | 0.90 |
4. Results
4.1. Ocean temperatures
The ocean surface temperature distributions from October 31 to November 5, 2006 are shown in Figure 2. Cimaron entered the South China Sea on October 30, and the simulation of the typhoon‐induced wake suggests that the apparent temperature depression started on October 31. The wake of the typhoon occurred within the region from 15°N to 20°N and from 114°E to 119°E. Figure 3 shows the time series (daily) of the maximum SST decreasing in the typhoon‐induced wake, located at 18.51°N and 116.45°E, relative to the pre-typhoon conditions on October 28. Although bias exists between these two satellite SST observations, both satellite SSTs display the same trend in their variations in the SST cooling amplitude in the wake. The observed SST decreased to an extremely low value on November 3, by which time the ocean was in the forcing stage. Starting from November 3, SSTs had begun to increase, which defines the beginning of the relaxation stage towards a new equilibrium state, with the injection of potential vorticity into the wake by the typhoon winds [1]. Comparing model results to these two satellite SSTs which show that the maximum amplitude of the SST cooling appeared on November 3, with values of 5.1°C for TMI AMSRE and 6.3°C for MWIR OI, the simulated maximum SST cooling was 4.8°C on November 4 (Figure 3). Thus, the relaxation of surface temperature in the wake after the typhoon's passage is clearly underestimated in our simulations.
Figure 4 shows the comparison of the daily surface isotherms between MWIR OI observations and the model simulations from October 31 to November 5. The isothermal lines ranged from 22°C to 26°C with 1°C intervals. The distributions of the simulated surface isotherms in the wake area are quite consistent with the MWIR OI SSTs, which further demonstrate that the temperature simulations related to Typhoon Cimaron are well reproduced. The southward shift of the location of the maximum SST cooling in the simulation results compared to the satellite observations indicates another common issue during the forecasting of extreme weather conditions, which is the lack of high‐accuracy wind forcing observations. The simulated maximum mixed layer depth was about 53.2 m, located at (18.51°N, 116.44°E) on November 3, 2006 which is an underestimate compared with the maximum deepening of 104.5 m at (19.50°N, 116.26°E) estimated in work [30]. Underestimation of the mixed layer depth and SST cooling is a common problem in the numerical ocean model simulations because of insufficient mixing. To solve this problem, a parameterization of wave‐induced mixing is added to the model to improve the mixing estimates in this chapter (see details in Section 5).
4.2. Ocean currents
When Typhoon Cimaron entered the South China Sea on October 30, the upper ocean's response was almost instantaneous. Typhoon‐induced cyclonic currents caused divergence of upper ocean water over the surface areas by tens of kilometres (in scale) with cold water that is upwelled from the deeper ocean, accounting for the formation of a cold‐core eddy. The cyclonic currents flowed in a roughly circular motion around the mesoscale cold eddy, with the maximum velocity reaching 2.5 m s−1 at location (18.44°N, 115.3°E) on October 31. An alongshore current flowing through the Taiwan Strait into the South China Sea, driven by the northeast monsoon winds, was strengthened by the typhoon forcing on October 31 and November 1. The intrusion of Kuroshio Current meandering towards the South China Sea through the Luzon Strait was strengthened too, with the current velocity reaching 1.6 m s−1 north of the Philippines Islands on November 1.
A very large amount of potential and kinetic energy is injected into the ocean surface layer from the strong typhoon winds during the typhoon generation and development process. The power of the injected energy and the vorticity can be calculated using the following formulae:
where
Strong cyclonic currents caused by Typhoon Cimaron lasted for several days after typhoon's passage. Strengthened by the long‐lasting intense typhoon wind forcing, the cyclonic eddy generated by the cyclonic circulation reached a maximum positive vorticity of 3.56 × 10−5 s−1 at the location (116.8°E, 18.3°N) on October 30, and continued intensifying to 5.36 × 10−5 s−1 on October 31 and 5.07 × 10−5 s−1 on November 1 (Figure 5). Figure 6 shows estimates for the power of the injected oceanic kinetic energy from October 30 to November 4. The power input from the wind forcing was mostly located on the right side of the typhoon's track with maxima of 1.45 W m−2 on October 31, and 1.43 W m−2 on November 1 and 0.54 W m−2 on November 2. The power input was low in the typhoon's eye area where the winds were very weak. The initial oceanic state was changed under the effect of the strong typhoon winds. On October 30, there is a large region with negative kinetic energy injected by the typhoon, appearing on the right side of the typhoon's track; this suggests that the oceanic kinetic energy was decreased by the typhoon. Thus, the intense typhoon winds changed the original pre-typhoon sea state conditions. The maximum decrease in the oceanic kinetic energy in the wake of the typhoon was 0.83 W m−2. On October 31, the power reached a maximum value of 2.3 W m−2, and on November 1, this value was 2.0 W m−2.
From November 2 onwards, the injected energy into the wake region of the typhoon showed the decreasing tendency pattern. However, the vorticity of the current induced by typhoon persisted for a long time after typhoon's passage. The study presented here shows that the energy input induced by the typhoon winds was responsible for the ocean‐enhanced mixing processes.
4.3. Biological results
The monthly chlorophyll
Figure 8 shows the simulated daily maximum surface concentrations of chlorophyll
Compared to the quick response of nitrate to Typhoon Cimaron, the response of the phytoplankton is a relatively slow process. The chlorophyll
The vertical profiles of the density, both of chlorophyll
5. Discussion: effect of the wave‐induced mixing
The mixed layer deepening induced by Typhoon Cimaron is underestimated in the three‐dimensional ocean model simulations, which is a common situation in ocean model simulations. To strengthen the insufficient mixing, in our chapter, we incorporated the wave‐induced mixing term,
The wave‐induced mixing term
where
Figure 10 shows the maximum SST decrease in the wake of the typhoon, comparing the simulations by adding
6. Conclusions
A three‐dimensional simulation of the upper ocean in response to Typhoon Cimaron is investigated in this study, including both the physical and biological processes. The validation of SST was compared with two satellite observations, TMI AMSRE and MWIR OI SSTs, from October 30 to November 6. High correlation (over 84%) and low bias (between 0.4°C and 0.6°C) show that ROMS can reproduce the process of upper ocean response to Typhoon Cimaron quite well. Detailed analysis indicates that the surface cooling is underestimated due to the insufficient mixing in the ROMS model. To solve this problem, the wave‐induced mixing with a certain weighting coefficient was introduced into the KPP mixing scheme to improve the simulation of SST cooling. Values up to 6.2°C are obtained, which is close to the observed MWIR cooling estimate of 6.3°C on November 3, whereas the ROMS simulation without the wave‐induced mixing gives an underestimated cooling of 4.8°C. The simulation accuracy is enhanced by adding the wave‐induced mixing, which increases the SST cooling by 1.4°C and deepens the mixed layer by 30 m in the wake of typhoon.
A strong mesoscale ocean eddy, as characterized by the cyclonic currents, was caused by Typhoon Cimaron in the South China Sea. The water within the eddy diverged over surface areas on a scale of tens of kilometres. Under the divergent condition, cold nutrient‐rich water upwelled from deeper waters. The positive vorticity kept a high value over 5.0 × 10−5 s−1 on October 31 and November 1. Moreover, the concentration of nitrate in the surface wake area increased to a maximum during these 2 days, which indicates that upwelling played a key role on the phytoplankton blooming after typhoon's passage. The simulated maximum concentration of chlorophyll
Acknowledgments
We thankfully acknowledge funding support from the General Research Fund of Hong Kong Research Grants Council (RGC) under Grants CUHK 402912 and 403113, the Hong Kong Innovation and Technology Fund under the Grants of ITS/321/13, the direct grants of the Chinese University of Hong Kong, the National Natural Science Foundation of China under project 41376035, the Marine Environmental Observation Prediction and Response Network (MEOPAR), DFO's Aquatic Climate Change Adaptation Service (ACCASP), the PERD, and the Canadian Panel on Energy Research and Development.
Wave‐induced mixing | |
K1 | Lunisolar declinational diurnal tidal constituent |
K2 | Lunisolar declinational semidiurnal tidal constituent |
KPP | K‐profile parameterization |
M2 | Principal lunar semidiurnal tidal constituent |
MAE | Mean absolute error |
MASNUM | Key Laboratory of Marine Science and Numerical Modeling |
ME | Mean error |
Mf | Lunar fortnightly long‐period tidal constituent |
Mm | Lunar monthly long‐period tidal constituent |
MWIR OI | Microwave infrared optimally interpolated |
N2 | Larger lunar elliptic semidiurnal tidal constituent |
NH4 | Ammonium |
NO3 | Nitrate |
R | Correlation coefficient |
RMS | Root‐mean‐square |
ROMS | Regional Ocean Modeling System |
S2 | Principal solar semidiurnal tidal constituent |
SeaWIFS | Sea‐Viewing Wide Field‐of‐View Sensor |
SSTs | Sea surface temperatures |
SODA | Simple Ocean Data Assimilation dataset |
TIC | Total inorganic carbon |
TMI AMSRE | Tropical Rainfall Measuring Mission (TRMM) Microwave Imager and Advanced Microwave Scanning Radiometer |
TPXO | The OSU TOPEX/Poseidon Global Inverse Solution |
O1 | Principal lunar diurnal tidal constituent |
OAFlux | Objectively Analyzed air‐sea Fluxes |
P1 | Principal solar diurnal tidal constituent |
POM | Princeton Ocean Model |
Q1 | Major lunar elliptical diurnal tidal constituent |
QuikSCAT | NASA Quick Scatterometer Earth observation satellite |
WOA01 | World Ocean Atlas 2001 |
WOA09 | World Ocean Atlas 2009 |
References
- 1.
Gill AE: On the behavior of internal waves in the wakes of storms. J. Phys. Oceanogr. 1984; 14: 1129–1151. - 2.
Price JF, Sanford TB, Forristall GZ: Forced stage response to a moving hurricane. J. Phys. Oceanogr. 1994; 24: 233–260. - 3.
Leipper DF: Observed ocean conditions and Hurricane Hilda 1964. J. Atmos. Sci. 1967; 24: 182–196. - 4.
Bolin B: The adjustment of a non‐balanced velocity field towards geostrophic equilibrium in a stratified fluid. Tellus. 1953; 5(3): 373–385. - 5.
Pollard RT: On the generation by winds of inertial waves in the ocean. Deep‐Sea Res.. 1970; 17(4): 795–812. DOI: 10.1016/0011‐7471(70)90042‐2. - 6.
Veronis G: Partition of energy between geostrophic and non‐geostrophic oceanic motions. Deep‐Sea Res.. 1956; 3(3): 157–177. DOI: 10.1016/0146‐6313(56)90001‐6. - 7.
Pollard RT, Millard Jr RC: Comparison between observed and simulated wind‐generated inertial oscillations. Deep‐Sea Res.. 1970; 17(4): 813–821. DOI: 10.1016/0011‐7471(70)90043‐4. - 8.
Blumen W, Wu R: Geostrophic adjustment: frontogenesis and energy conversion. J. Phys. Oceanogr. 1995; 25: 428–438. - 9.
Geisler JE: Linear theory of the response of a two layer ocean to moving hurricane. Geophys. Fluid Dyn. 1970; 1: 249–272. DOI: 10.1080/03091927009365774. - 10.
Ginis I, Sutyrin G: Hurricane‐generated depth‐averaged currents and sea surface elevation. J. Phys. Oceanogr. 1995; 25: 1218–1242. - 11.
Black PG: The 3D oceanic mixed layer response to Hurricane Gilbert. J. Phys. Oceanogr. 2000; 30: 1407–1429. - 12.
Chang J, Chung CC, Gong GC: Influences of cyclones on chlorophyll a concentration and Synechococcus abundance in a subtropical western Pacific coastal ecosystem. Mar. Ecol. Prog. Ser. 1996; 140: 199–205. - 13.
Hung CC, Gong GC, Chou WC, Chung CC, Lee MA, Chang Y, Chen HY, Huang SJ, Yang Y, Yang WR, Chung WC, Li SL, Laws E: The effect of typhoon on particulate organic carbon flux in the southern East China Sea. Biogeosciences. 2010; 7: 3007–3018. - 14.
Babin SM, Carton JA, Dickey TD, Wiggert JD: Satellite evidence of hurricane‐induced phytoplankton blooms. J. Geophys. Res. 2004; 109: C03043. DOI: 10.1029/2003JC001938. - 15.
Lin I, Liu W, Wu CC, Wong TF, Hu C, Chen Z, Liang WD, Yang Y, Liu KK: New evidence for enhanced ocean primary production triggered by tropical cyclone. Geophys. Res. Lett. 2003; 30(13). DOI: 10.1029/2003GL017141. - 16.
Zheng G, Tang D: Offshore and nearshore chlorophyll increases induced by typhoon winds and subsequent terrestrial rainwater runoff. Mar. Ecol. Prog. Ser. 2007; 333: 61–74. - 17.
Shang S, Li L, Sun F, Wu J, Hu C, Chen D, Ning X, Qiu Y, Zhang C, Shang S: Changes of temperature and bio‐optical properties in the South China Sea in response to Typhoon Lingling 2001. Geophys. Res. Lett. 2008; 35: L10602. DOI: 10.1029/2008GL033502. - 18.
Zhao H, Tang D, Wang Y: Comparison of phytoplankton blooms triggered by two typhoons with different intensities and translation speeds in the South China Sea. Mar. Ecol. Prog. Ser. 2008; 365: 57–65. - 19.
Chang Y, Liao HT, Lee MA, Chan JW, Shieh WJ, Lee KT, Wang GH, Lan YC: Multisatellite observation on upwelling after the passage of Typhoon Hai‐Tang in the southern East China Sea. Geophys. Res. Lett. 2008; 35: L03612. DOI: 10.1029/2007GL03285. - 20.
Franks PJS, Wroblewski JS, Flierl GR: Behavior of a simple plankton model with food‐level acclimation by herbivores. Mar. Biol. 1986; 91: 121–129. - 21.
Fennel K, Wilkin J, Levin J, Moisan J, O'Reilly J, Haidvogel D: Nitrogen cycling in the Middle Atlantic Bight: results from a three‐dimensional model and implications for the North Atlantic nitrogen budget. Global Biogeochem. 2006; 20: GB3007. DOI: 10.1029/2005GB002456. - 22.
Powell TM, Lewis CVW, Curchitser EN, Haidvogel DB, Hermann AJ, Dobbins EL: Results from a three‐dimensional, nested biological‐physical model of the California Current System and comparisons with statistics from satellite imagery. J. Geophys. Res. 2006; 111: C07018. DOI: 10.1029/2004JC002506. - 23.
Ezer T: On the seasonal mixed layer simulated by a basin‐scale ocean model and the Mellor‐Yamada turbulence scheme. J. Geophys. Res. 2000; 105: 16843–16855. - 24.
Mellor G: The three‐dimensional current and surface wave equations. J. Phys. Oceanogr. 2003; 33: 1978–1989. - 25.
Sanford TB, Black PG, Haustein JR, Feeney JW, Forristall GZ, Price JF: Ocean response to a hurricane. Part I: observations. J. Phys. Oceanogr. 1987; 17: 2065–2083. - 26.
Craig PD, Banner ML: Modeling wave‐enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr. 1994; 24: 2546–2559. - 27.
Mellor G, Blumberg A: Wave breaking and ocean surface layer thermal response. J. Phys. Oceanogr. 2004; 34: 693–698. - 28.
Yuan Y, Qiao F, Hua F, Wan Z: The development of a coastal circulation numerical model: I. Wave‐induced mixing and wave‐current interaction. J. Hydrodyn. Ser. A. 1999; 14: 1–8. - 29.
Qiao F, Yuan Y, Yang Y, Zheng Q, Xia C, Ma J: Wave‐induced mixing in the upper ocean: distribution and application to a global ocean circulation model. Geophys. Res. Lett. 2004; 31: L11303. DOI: 10.1029/2004GL019824. - 30.
Pan J, Sun Y: Estimate of ocean mixed‐layer deepening after a typhoon passage over the South China Sea by using satellite data. J. Phys. Oceanogr. 2013; 43: 498–506. - 31.
Carton JA, Giese BS: A reanalysis of ocean climate using Simple Ocean Data Assimilation (SODA). Mon. Weather Rev. 2008; 136: 2999–3017. - 32.
Egbert GD, Bennett AF, Michael MGG: TOPEX/POSEIDON tides estimated using a global inverse model. J. Geophys. Res.. 1994; 99(C12): 24821–24852. - 33.
Yu L, Jin X, Weller RA: Multidecade global flux datasets from the Objectively Analyzed Air‐sea Fluxes (OAFlux) project: latent and sensible heat fluxes, ocean evaporation, and related surface meteorological variables, Woods Hole Oceanographic Institution, OAFlux Project Technical Report, OA‐2008‐01. Woods Hole, Massachusetts; 2008. 64 p. - 34.
Haney RL: Surface thermal boundary condition for ocean circulation models. J. Phys. Oceanogr. 1971; 1: 241–248. - 35.
Garcia HE, Locarnini RA, Boyer TP, Antonov JI, Baranova OK, Zweng MM, Johnson DR. World Ocean Atlas 2009, Volume 3: Dissolved Oxygen, Apparent Oxygen Utilization, and Oxygen Saturation. S. Levitus, Ed. NOAA Atlas NESDIS 70, U.S. Government Printing Office, Washington D.C.; 2010. 344 p. - 36.
Garcia HE, Locarnini RA, Boyer TP, Antonov JI, Zweng MM, Baranova OK, Johnson DR: World Ocean Atlas 2009, Volume 4: Nutrients (phosphate, nitrate, silicate). S. Levitus, Ed. NOAA Atlas NESDIS 71, U.S. Government Printing Office, Washington D.C.; 2010. 398 p. - 37.
Morel A, Berthon JF: Surface pigments, algal biomass profiles, and potential production of the euphotic layer: relationships reinvestigated in view of remote‐sensing applications. Limnol. Oceanogr. 1989; 34: 1545–1562. - 38.
Goyet C, Healy RJ, Ryan JP: Global distribution of total inorganic carbon and total alkalinity below the deepest winter mixed layer depths. 2000; NDP‐076, http://cdiac.ornl.gov/oceans/ndp_076/ . - 39.
Sun Y, Qiao F, Wang G, Ying X, Yang Y: Forecast operation and verification of MASNUM surface wave numerical model (in Chinese). Adv. Mar. Sci.. 2009; 27(3): 281–293. - 40.
Lee Z, Weidemann A, Kindle J, Arnone R, Carder KL, Davis C: Euphotic zone depth: its derivation and implication to ocean‐color remote sensing. J. Geophys. Res. 2007; 112: C03009. DOI: 10.1029/2006JC003802. - 41.
Wang Y, Qiao F, Fang G, Wei Z: Application of wave‐induced vertical mixing to the K profile parameterization scheme. J. Geophys. Res. 2010; 115: C09014. DOI: 10.1029/2009JC005856.