Advances in Meteorology

Volume 2015 (2015), Article ID 752947, 15 pages

http://dx.doi.org/10.1155/2015/752947

## Upper Ocean Thermal Responses to Sea Spray Mediated Turbulent Fluxes during Typhoon Passage

^{1}Key Laboratory of State Oceanic Administration for Marine Environmental Information Technology, National Marine Data and Information Service, State Oceanic Administration, Tianjin 300171, China^{2}College of Physical and Environmental Oceanography, Ocean University of China, Qingdao 266100, China^{3}Physical Oceanography Laboratory, Ocean University of China, Qingdao 266100, China^{4}Ocean Dynamical Laboratory, Third Institute of State Oceanic Administration, Xiamen 361005, China

Received 16 December 2014; Revised 30 January 2015; Accepted 18 February 2015

Academic Editor: Shaoqing Zhang

Copyright © 2015 Lianxin Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A one-dimensional turbulent model is used to investigate the effect of sea spray mediated turbulent fluxes on upper ocean temperature during the passage of typhoon Yagi over the Kuroshio Extension area in 2006. Both a macroscopical sea spray momentum flux algorithm and a microphysical heat and moisture flux algorithm are included in this turbulent model. Numerical results show that the model can well reproduce the upper ocean temperature, which is consistent with the data from the Kuroshio Extension Observatory. Besides, the sea surface temperature is decreased by about 0.5°C during the typhoon passage, which also agrees with the sea surface temperature dataset derived from Advanced Microwave Scanning Radiometer for the Earth Observing and Reynolds. Diagnostic analysis indicates that sea spray acts as an additional source of the air-sea turbulent fluxes and plays a key role in increasing the turbulent kinetic energy in the upper ocean, which enhances the temperature diffusion there. Therefore, sea spray is also an important factor in determining the upper mixed layer depth during the typhoon passage.

#### 1. Introduction

When the wind speed reaches a certain level, surface wave breaking produces large numbers of sea spray droplets in the air-sea interface. Wave breaking and sea spray significantly affect the turbulent mixing [1, 2] and turbulent fluxes [3], respectively, which play a key role in the upper ocean in the high wind speed condition (>25 m/s) [4] (e.g., typhoon). So the research method of sea spray has been concerned for several decades. Riehl (1954) [5] was the first to point that the sea spray evaporation provided a significant amount of heat. After twenty years, the sea spray problem caught high attention again [6–11]. Wu (1974) [10] observed sea spray’s concentration in the wind-wave tank and computed the evaporation of sea spray. Bortkovskii (1973) [9] simply evaluated the energy and evaporation of the sea spray droplet and claimed that it is a primary source for enhancing the sea-air interfacial transfer in the high wind speeds. In addition, Ling and Kao (1976) [11] introduced sea spray evaporation into the equation of heat transfer and found that sea spray is also the important humidity source. In recent years, much research has focused on the effect of sea spray by developing theories [12–16]. Anthes (1982) [12] proposed that the evaporation of sea spray droplets would enhance the sensible heat transfer. Zhang and Lou [13] and Lou and Zhang [14] analyzed the physical processes of the individual sea spray droplet to get the expressions of spray heat flux and water vapor flux. Hasse (1992) [15] simply estimated the spray’s impact by using three distinct arguments: the total surface area of sea spray droplet, an energy constraint, and the evaporation implied by the sea-salt aerosol. In recent years, much research has focused on the sea spray by the developing theories. Andreas [17–19] adapted Pruppacher and Klett’s [20] cloud microphysical equations to study the thermal and moisture evolution of sea spray droplets. Fairall et al. [21] predigested Andreas’s [17, 19] time scale and first incorporated a reasonable spray-based parameterization scheme into a simple model of the tropical cyclone boundary layer. So far, on the basis of the above studies, it is possible to calculate the sea spray induced heat flux using the actual observed data. At the same time, the sea spray heat algorithm presented by Fairall et al. [21] is basically valid for the high wind condition, since the sea spray generation function depends on wind speed and the whitecap areal fraction. In this study, the sea spray mediated heat flux is calculated following Fairall’s sea spray algorithm in the typhoon passage. However, the feedback mechanism between the sea spray and the atmosphere is not considered in Fairall’s sea spray algorithm. Therefore, the study will introduce the feedback mechanism into the air-sea heat flux algorithm, which is feasible for us to calculate reasonable sea-air heat fluxes under the typhoon conditions.

Both theoretical researches [22] and field observations [23, 24] reveal that the drag coefficient leveled off or even decreased in the high wind speed. Powell et al. [23] hypothesized that sea spray could significantly influence the transfer of momentum for the wind speed above about 34 m/s. On the basis of field observations [23], Makin [25] suggested that a thin air boundary layer adjacent to the surface goes into a regime of limited saturation by suspended sea spray droplets, and the thin layer restrains the momentum transfer from the wind to the ocean. In the meantime, Makin [25] revised the wind speed logarithmic profile by the sea spray influence and derived the sea surface dynamic roughness length including the effect of sea spray at high winds. Based on the above research results, it is expected to investigate the momentum effect of sea spray during the typhoon passage through the spray induced sea surface dynamic roughness length.

Although the effect of the spray induced heat flux on air-sea interface under high winds was demonstrated by numerical simulations over a decade [26–30], the momentum effect of sea spray is hardly considered. In addition, little attention has been paid to both heat and momentum conjunct effects of sea spray on the upper ocean temperature in the period of typhoon by the numerical simulations. The goal of the present study is to investigate the impact of sea spray mediated turbulent fluxes on the upper ocean over the midlatitude oceans during a typhoon passage, using the General Ocean Turbulent Model (GOTM) that contains comprehensive turbulent mixing parameterizations. The effects of sea spray are presented from two kinds of physics processes. On the heat aspect, the impact of sea spray is considered in the form of modifying air-sea surface heat fluxes by microcosmic way, based on the sea spray microcosmic physical model from Fairall et al. [21]. On the momentum aspect, the effect of sea spray is introduced by the sea surface aerodynamic roughness length to investigate its impact on the air-sea momentum flux. As a pilot study, we present a case study of typhoon cyclone and explore the effects of sea spray in the numerical simulations.

The remainder of this study is organized as follows: model description and the spray turbulent flux algorithms are presented in Section 2. The experimental design of the numerical simulations is described in Section 3. Section 4 discusses numerical results and analyzes related mechanisms according to the model results, followed by the conclusions in Section 5.

#### 2. Model Description

##### 2.1. The GOTM Model

To clearly address the issue raised from the last section and avoid the complexity of a general circulation model, a one-dimensional ocean numerical model, namely, General Ocean Turbulence Model (denoted by GOTM) [31], which has a potential capability to simulate the vertical mixing processes near the upper ocean, is employed in this study. General Ocean Turbulent Model (GOTM) is a one-dimensional water column model (see http://www.gotm.net/), which solves the transport equations of heat, salt, and momentum. The governing equations of GOTM are formulated aswhere and represent the mean potential temperature and salinity, respectively. and denote the molecular diffusivities of heat and salt, respectively. is the heat capacity of seawater. is a constant reference density resulting from the Boussinesq approximation. The source term of temperature in the right-hand side of (1) is the vertical divergence of solar radiation (). and denote temperature and salinity diffusion coefficient. In the current version of GOTM, we set equal to for simplicity.

We will use the - second turbulence closure model to simulate turbulence parameters [32]. Within the framework, is equal to . The nondimensional quantity is the function of nondimension stability parameter that describes the influence of stratification on turbulent mixing. is the turbulent kinetic energy and is the integral length scale, computed here from the dissipation rate . The transport equation for the turbulent kinetic energy follows immediately from the contraction of the Reynolds-stress tensor. The equation of can be written aswhere and are the turbulent production of by shear production and buoyancy generation, respectively, and is the dissipation term of turbulent kinetic energy. represents vertical diffusion terms. In - model, the rate of dissipation is balanced according towhere represents the sum of the viscous and turbulent transport terms. The model constants , , and are 1.44, 1.92, and 1.44, respectively.

##### 2.2. Air-Sea Flux Parameterizations

###### 2.2.1. COARE Model

To provide the external forcing for the GOTM, the surface fluxes in the air-sea interface are calculated from the mean model parameters using Monin-Obukhov Similarity Theory. The COARE version 2.6 bulk model turbulent fluxes of momentum , latent heat , and sensible heat arewhere is the air density; is the specific heat of air at constant pressure; is the latent heat of vaporization of water; is the potential temperature and is the specific humidity. is the mean horizontal wind speed and the subscript denotes the lowest model level, while 0 refers to the water surface. , , and are the drag coefficient, the transfer coefficient for the sensible heat, and the latent heat, respectively:

Here is the von Karman constant, while , , and are the roughness lengths for the velocity, temperature, and humidity, respectively. From laboratory studies it has proven convenient to characterize the surface and the flow regime by the roughness Reynolds number:where is the kinematic viscosity of air,where and , as the functions of , are roughness Reynolds number for temperature and moisture.

Based on the COARE model, the next section introduces the parameterization of sea spray. The key feature of sea spray parameterization is that the heat and momentum effects of sea spray are recognized by the microcosmic and macroscopical aspects, respectively. On the macroscopical aspect, the sea surface aerodynamic roughness length with the effect of sea spray is used to investigate the impact of the sea spray on the drag coefficient and air-sea momentum flux. On the microcosmic aspect, the effects of heat fluxes induced by sea spray are introduced by the Fairall et al. [21] spray heat algorithm (henceforth FA94). Hence, the model includes the parameterizations for both the interfacial and the sea spray fluxes.

###### 2.2.2. Sea Spray Affected Sea Surface Dynamic Roughness

In the original COARE version 2.6 bulk model, the Charnock relation is used to calculate the sea surface dynamic roughness length,where is Charnock constant and is set to 0.011 [33]. represents the acceleration due to gravity. Fairall et al. [33] pointed that the Charnock relation has been proven to work well for the low-moderate wind, and it is theoretically based and accurately for the interfacial turbulent fluxes for wind up to 10 m/s. When the wind speed reaches 11–13 m/s, the contribution of sea spray to the heat fluxes becomes significant. In other words, the Charnock relation does not contain sea spray droplets effect. Hence, the Charnock relation is still accurate for the interfacial turbulent fluxes when extrapolated to higher wind speeds.

For the high wind speed, the transfer coefficient for momentum flux decreases with the increasing of the wind, which is validated by the current field observations in the marine boundary layer [23, 24]. Based on the field measures [23], Makin [25] introduces the effect of sea spray into the wind speed logarithmic profile and further gives the sea surface dynamic roughness length including the effect of sea spray for high wind speed:where represents the correction parameterization indicating the effect of sea spray on the logarithm wind speed. The value of the terminal velocity is estimated about 0.64 m/s corresponding to a sea spray droplet radius of about 80 m [25]. is the height of the suspension layer in the regime of limiting saturation, which is proportional to and larger than the height of the breaking waves but smaller than the significant wave height by assuming that most of the spray at high wind speeds is produced by mechanical tearing by the wind from steep short waves. Hence, the height of the suspension layer in the regime of limiting saturation is about 1/10 of the significant wave height [25, 34]. In (10c), represents the nondimensionalized quantity of the height of the suspension layer in the regime of limiting saturation: It is found that the effects of sea spray are implied in the parameters and according to (10a), (10b), (10c), and (11).

For the low-to-moderate wind conditions (<25 m/s), depends on both the wave states and wind speeds [35–39]. Donelan [40, 41] argued that laboratory experiments could not represent field conditions for the same wave ages, so observations of the laboratory experiments and the field conditions should be discussed separately. To simulate the real open ocean, is derived from the real open ocean condition and Donelan [40] can represent most results of the foregoing researcher for the moderate wind speed:where is peak wave phase velocity.

For the full wind speeds condition, the including the effect of sea spray is calculated by combining the for moderate wind (12) and for high wind ((10a), (10b), and (10c)), using the 3/2 power law [42] and the relation between significant wave period and peak wave period: where is the wave age. When the impact of the sea spray droplets on the dynamics of the airflow at this regime is still small, should be equal to 1, and fully wind conditional roughness length (13) degrades the low wind conditional roughness length (12). However, the impact of the sea spray on the sea surface roughness is large enough (), which leads to the decrease of the roughness length and the drag coefficient.

###### 2.2.3. Spray Heat Flux Algorithm

The parameterization scheme for the sea spray heat fluxes used in this study follows FA94. This parameterization builds on earlier work on droplet microphysics and the associated timescales by Andreas [17, 19]. Thus, the spray droplet mediated sensible heat flux is proportional to the mass flux of all relevant spray droplets and the air-sea temperature difference: Here and are the density and specific heat of liquid water. is the whitecap areal fraction that is used to compute the sea spray droplet source number density spectrum. FA94 used the following form with the strong wind speed dependence:from Monahan and Muircheartaigh [43]. is all the relevant whitecap normalized droplet volume flux:where is the source spectrum per unit area of whitecap. Evaluation of is straightforward from three different data sources [44–46], whose value is equal to 5.0 × 10^{−6 }m/s, which is independent of meteorological conditions.

Using the above approach, the spray droplet mediated latent heat flux is expressed asHere is the saturation mixing ratio and spray droplets evaporate at their evaporating temperature , which can be regarded as a wet-bulb temperature modified for the effects of salinity and curvature, and not at the air temperature. Thus would be expected to be proportional to , rather than as given. The termwhere is the gas constant of dry air. The 10 m wind speed adjusted termBased on the Andreas [19] sea spray heat fluxes model, is set to 0.125 s^{−1} (given by FA94). The evaporation zone scale height is crudely defined as the height above the mean surface below which 67% of the total droplet evaporation takes place. is the evaporation zone scale height. Both measurements [47–49] and modeling studies [11, 50] confirm that the proper scaling height for the droplet evaporation zone is the mean wave height. For simplicity, FA94 considered mean wave height as the evaporation zone scale height.

FA94 argued that and represent upper limits and that the actual spray-dependent fluxes will be reduced by a factor due to the fact that mean profiles of and in the droplet zone do not remain logarithmic but are modified by the presence of the spray. Based on the numerical simulations [16, 51], the limited constant is about 0.5 (given by FA94). The equations for the spray sensible heat and latent heat flux areWe note that and are the spray droplet mediated fluxes that would occur if the sea spray does not alter the normal logarithmic profile of mean and in the droplet evaporation zone.

###### 2.2.4. Combined Turbulent Fluxes

The physical effects of sea spray between the air-sea interfaces are introduced from both the macroscopical and microcosmic ways. Concretely, the momentum (heat) effect of spray is introduced by the macroscopical (microcosmic) way.

Firstly, based on COARE 2.6 bulk model, the total air-sea momentum (including sea spray effect) is calculated by the sea surface dynamical roughness length with the sea spray effect at the full wind speeds (13); the interfacial air-sea momentum (excluding sea spray effect) is computed by the Charnock relation (9). Hence the sea spray induced momentum flux is

Secondly, the combined spray and interfacial fluxes constitute the boundary conditions. Andreas and DeCosmo [52] give the total sensible () and latent () heat fluxes as

Here, and are the interfacial latent and sensible heat fluxes that are computed by the COARE version 2.6 algorithms and described in Section 2.2.1. In (23a), term models the latent heat flux (or moisture flux) coming out the top of the spray droplet evaporation layer that spray has contributed. However, FA94 pointed out that because the atmosphere must supply all the heat to evaporate the droplets, these droplets are a sink for sensible heat. Hence, to conserve energy, this term in (23a) must appear with the opposite sign in the sensible heat equation (23b). The term in (23b) models the sensible heat that spray droplets give up in cooling from the ocean surface temperature to the temperature they have on returning to the sea surface. Thus, the term in (23b) adds more sensible heat to the layer because of the increased air-sea temperature different that results from the spray’s evaporative cooling of the layer.

Andreas [53] used the FA94 spray generation function to compute the spray heat fluxes and evaluate that the values of , , and are 3.3, 5.7, and 2.8 based on the HEXOS heat and moisture flux dataset. Hence coming by the above physics processes, the net sea spray contribution to the total sensible and latent heat fluxes can be estimated:

Hereafter, and are called sea spray induced sensible heat flux and latent heat flux, respectively.

#### 3. Experimental Design

Two experiments are designed to investigate the influence of sea spray in the upper ocean during the passage of typhoon Yagi. According to the descriptions in Section 2, the air-sea turbulent fluxes without the effect of sea spray are computed in Test 1. On the basis of Test 1, Test 2 introduces the effect of sea spray into the air-sea turbulent fluxes. Based on the GOTM model and KEO observations, the 1D GOTM is configured to the position of the KEO station with a 400 m depth and 1200 vertical layers with intervals of 0.33 m. To use the typhoon data, the simulation period is extended from September 17 to 29, 2006. Note that the ocean was initialized with the same temperature and salinity profiles from the KEO station in two cases. The numerical output such as air-sea momentum flux fields, heat fluxes fields, and sea temperature will be presented for sequent comparative analysis.

The Kuroshio Extension Observatory (KEO) is used in the GOTM model to simulate the typhoon Yagi, which is located at 32.4°N, 144.6°E and was first deployed in mid-June 2004. The measurements of KEO include 3 m air temperature, 3 m relative humidity, 3 m wind speed and direction, solar and long-wave radiation, rain rate, sea temperature profile, and sea salinity profile. The temporal resolution of all variables is 10 min, except for the radiations being 2 minutes. The observed layers of salinity and temperature are 1, 10, 15, 50, 75, and 400 m and 1, 10, 15, 25, 50, 75, 100, 150, 200, 300, 400, 450, and 500 m, respectively. The period of KEO variables used in the simulation is from September 17 to 29, 2006.

#### 4. Numerical Results

Figure 1 shows the track of typhoon Yagi on September 21–24 (color dots) and the distribution of sea surface temperature on September 23 (shade) in the study area (15–40°N, 130–150°E). As shown in Figure 1, the typhoon Yagi upgraded to a supper typhoon on September 22. Subsequently, Yagi moved towards northeast and passed KEO station on September 23, where a broad area of low temperature can be seen distinctly around the right of Yagi [54]. On September 24, Yagi left the sea region, and the low temperature lasted until September 27 (not shown).