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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 ( B V ) 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.


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][5][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 a field and primary production in the ocean. Another important phenomenon triggered and enhanced by tropical cyclones is the phytoplankton bloom accompanied by nutrient pumping into the oligotrophic surface layer. Concentration of nitrate, phosphate, and chlorophyll a is observed to significantly increase after the occurrence of cyclonic disturbances [12]. In [13], after Typhoon Fengwong and Typhoon Sinlaku passed over the southern East China Sea in 2008, the in-situ particulate organic carbon flux was observed to experience a significant increase of about 1.7-fold and 1.5fold, respectively, compared to the recorded (140-180 mg cm −2 d −1 ) pre-typhoon concentration. The phytoplankton population growth was constrained by the light limitation and the grazing pressure. This increase of the surface chlorophyll a concentration might last 2-3 weeks before relaxing to pre-typhoon levels [14]. Because of the limitations imposed by in-situ point observations from ships or moored buoys along a typhoon's track, studies of the associated biological responses have become to more and more depend on the satellite observations. In the work of [15], satellite data are used as new evidence to quantify the contribution of tropical cyclones to enhance the ocean primary production. It was found that the peak of the chlorophyll a concentration enhancement tended to occur several days after the sea surface temperature cooling had achieved the maximum amplitude, after the typhoon's passage, see [16,17]. The extended region and concentration of primary production bloom tend to vary in response to the translation speed and intensity of typhoon. Weak slow-moving typhoons can cause enhanced concentrations of chlorophyll a, while strong fast-moving typhoon tends to cause more intense phytoplankton blooms over a larger geographic range, in the wake of the storm as discussed in [18]. Upwelling induced by tropical storms is within the region where the typhoon-induced enhancement of the chlorophyll a concentration occurs; please see [19]. The pre-existing cyclonic eddy is capable of strengthening the typhoon-induced nutrient pumping. However, the extent to which that upwelling contributes in the phytoplankton bloom is not clear yet. The development of biological models is helpful to investigate the relevant dynamic process of the nitrogen and carbon cycle in the ocean [20][21][22].
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 (B V ) term, as a function of wave number spectrum, was developed and applied in a global ocean circulation model [28,29]. This surface wave-induced vertical viscosity term also has a key role on the simulation of sea surface temperature cooling and the mixed layer deepening after typhoon's passage.
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 B V is incorporated into ROMS model to improve the accuracy of the simulation.

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 Δx (5.5-40 km) and Δy (3.6-37 km) and the minimum and maximum depths are 5 m and 5000 m, respectively (Figure 1). There are 80 layers in the vertical direction using the s-coordinate formulation. The western boundary is closed and the other three open boundaries are defined by the radiation boundary condition. 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 a field data are estimated from the SeaWiFS climatological seasonal data, and the nitrate (NO 3 ) and oxygen are estimated from the monthly climatological database of WOA09 [35,36]. The vertical structure of chlorophyll a is extrapolated from the surface chlorophyll a field using the Morel and Berthon [37] parameterization method. High concentrations of chlorophyll a are mostly distributed in coastal regions along the coastline of southern China and the Vietnam marginal continent, with values of over 1 mg cm −3 . By comparison, in the deep sea area, the concentration is less than 0.1 mg cm −3 . In most areas of the South China Sea, the NO 3 content is much smaller, less than 0.1 mmol Nm −3 in the deep ocean surface layer. The concentration of NO 3 increases with ocean depth. In the deep sea, with depths in excess of 800 m, the concentration of NO 3 can reach 40 mmol Nm −3 .
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 (NH 4 ), large and small detritus, and N-concentration are taken from the NO 3 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 a concentration multiplied by the respective ratios of 0.5, 0.2, 0.1, and 0.1, respectively.

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.

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 typhooninduced 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.   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).

Ocean currents
When 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: (1) where W represents the power in the units of W m −2 . Here, F represents the wind stress with (τ x , τ y ) the two components corresponding to the (x, y) coordinates, respectively. U(u, v) is the simulated surface current velocity and ζ represents the vorticity.   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.

Biological results
The monthly chlorophyll a concentration gridded datasets are obtained from the SeaWiFS observations, with a horizontal spatial resolution of 0.0417° × 0.0417°. Figure 7 shows the monthly distributions of surface chlorophyll a concentration on October 16 and November 16,2006 in the South China Sea. These two satellite images represent the pre-and post-typhoon situations for the primary production; it is evident that a phytoplankton bloom area exists around the location of the typhoon's wake after it had passed. Although the concentration of the chlorophyll a achieved high values, in excess of 4 mg cm −3 along the coast, the averaged concentration was about 0.09 mg cm −3 in the area that became the wake (the black box in Figure 7) before the appearance of Typhoon Cimaron. However, by November 16, the concentration in this area reached 0.85 mg cm −3 , which was much higher than the normal expected conditions, indicating that the maximum increase of chlorophyll a concentration was about 0.75 mg cm −3 at the location (17.02°N, 115.57°E) in the wake area. While the monthly dataset may be interpolated in both spatial and temporal dimensions, the detailed processes related to the development of the phytoplankton bloom triggered by Typhoon Cimaron are still not clear. The application of the biological numerical model can provide more details for the study of the subsurface water layers and can complement the limitations of the satellite remote sensing.  Figure 9). Figure 8 shows the simulated daily maximum surface concentrations of chlorophyll a and nitrate in the typhoon's wake area through October 28 to November 30. In the pre-typhoon condition, the nitrate concentration maintained a stable value of 0.03 mmol Nm −3 . During November 1-3, Cimaron lingered in locations that were quasistationary and caused strong mixing in the wave areas. Thus the nitrate concentration largely increased in the ocean surface layer in the wake, reaching a maximum of 1.24 mmol Nm −3 on November 3. By November 3, Cimaron had passed from this (wake) region. The surface nitrate concentration remained high, in excess of 1.1 mmol Nm −3 for an additional 3 days, from November 3-5, and then decreased to a rather stable level of 0.1 mmol Nm −3 from November 11 onwards.
Compared to the quick response of nitrate to Typhoon Cimaron, the response of the phytoplankton is a relatively slow process. The chlorophyll a concentration remained at the prety-phoon level of about 0.06 mg cm −3 for some time beyond November 3. Although the mixed layer depth deepened to its maximum on November 3, the chlorophyll a concentration was still increasing at that time, having increased slightly over the previous 2 days, as triggered by the upwelling induced by the approaching storm. Thereafter, the chlorophyll a concentration increased rapidly in early November, reaching a rate of 0.5 mg cm −3 d −1 , and attaining a maximum concentration of 1.76 mg cm −3 on November 7. The phytoplankton blooms occurred 5 days after Typhoon Cimaron's passage. The chlorophyll a concentration began to decrease from November 8 onwards, returning to a quasistable level of 0.3 mg cm −3 by November 18. The maximum concentration of chlorophyll a on November 16 was simulated at the value of 0.65 mg cm −3 , which was about 0.2 mg cm −3 less than the satellite observations. The surface ocean was restored to an equilibrium state again by about 10-20 days after the interruption that Cimaron introduced. Moreover, the concentrations of both nitrate and chlorophyll a in the resulting re-equilibrium of the ocean state are higher than those of the former pre-typhoon state.  Figure 7, in the typhoon wake are investigated with respect to the underwater impacts of Cimaron, comparing the pre-and post-typhoon profiles through October 28 to November 30 in Figure 9. Before the typhoon, the nutrient and phytoplankton in the surface layer are both at low concentrations, as the surface waters received strong light irradiation, which is not conducive to the growth and reproduction of the phytoplankton. Phytoplankton populations grow and reproduce mostly in the euphotic zone. The depth of the euphotic zone can be estimated from the chlorophyll a concentration of the surface layer, based on the assumption of Case-I waters; the equation is shown in [40]. After the typhoon's passage, cyclonic eddies caused by Typhoon Cimaron exhibited the upward doming of isopycnals from October 31 and the isopycnals were uplifted with high nutrient concentrations into the euphotic zone, which furthermore, had a positive influence on the photosynthetic performance. The chlorophyll a concentration in the surface layer increased and reached about 0.237 mg cm −3 on November 7 in Figure 9. Both the profiles of nitrate and chlorophyll a are significantly elevated after the typhoon's passage. The euphotic zone depth was estimated as 87.0 m before typhoon and 36.2 m after typhoon in the wake, with respect to the chlorophyll a concentrations obtained from the satellite for pre-and post-typhoon Cimaron. The euphotic zone was uplifted by 50.0 m in the wake of Typhoon Cimaron.

Discussion: effect of the wave-induced mixing
The mixed layer deepening induced by Typhoon Cimaron is underestimated in the threedimensional 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, B V into ROMS to investigate the effect of B V on the mixed layer deepening and ocean surface temperature cooling caused by Typhoon Cimaron.
The wave-induced mixing term B V , is added into ROMS, as part of the vertical kinematic viscosity, as expressed by Qiao et al. [29] ( ) ( ) ( ) ( ) where ω is the wave angular frequency, z is the vertical coordinate axis downward positive with z = 0 at the surface,k is the wave number, and E k represents the wave number spectrum including both wind wave and swell waves. B V can be calculated by the wave model. In this study, the wave-induced mixing term is directly derived from the Key Laboratory of Marine Science and Numerical Modeling (MASNUM) wave model [28] and is added into the vertical viscosity and diffusivity term of the K-profile parameterization (KPP) mixing scheme which is applied in ROMS. Because the wave mixing is dominant in the upper ocean layer, the B V term is confined to the range from 1000 m depth up to the surface. The weighting coefficient was set to 0.1 in our study, as suggested by Wang et al. [41]. In the wake of the typhoon, the vertical mixing was strengthened with the vertical viscosity coefficient of 0.1 m 2 s −1 from October 31 to November 2.   Figure 10 shows the maximum SST decrease in the wake of the typhoon, comparing the simulations by adding B V with the two sets of satellite observations. Under the effect of the strengthened mixing estimates, SST in the wake reached the lowest temperature on November 3 with a value that is consistent with both sets of satellite observations. The maximum SST decreases on November 2 and November 3, respectively, relative to the pre-typhoon conditions on October 28, which were 5.9°C and 6.2°C, which are close to the MWIR observations of 5.8°C and 6.3°C. Compared to the maximum temperature decreases without the B V term of 4.1°C on November 2 and 4.8°C on November 3 in the typhoon's wake, the wave-induced mixing can improve the SST cooling by 1.7°C on November 2 and 1.4°C on November 3. This is with a weighting coefficient of 0.1. The associated mixed layer deepening was increased by 30 m on November 3.

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 a in the wake increased from a pre-typhoon value of 0.1 mg cm −3 to a posttyphoon value of 0.65 mg cm −3 on November 16, which is close to the satellite observation of 0.85 mg cm −3 on November 16. The euphotic zone was uplifted by 50.0 m after Typhoon Cimaron's passage. Thereafter, the ocean restored to a new equilibrium state with higher concentrations of chlorophyll a and nitrate than those existing in the pre-equilibrium state in the wake area.