Air-sea gas transfer rate for the Southern Ocean inferred from 222Rn concentrations in maritime air and a global atmospheric transport model

Authors


Abstract

[1] Measurements of atmospheric 222Rn activity were made on board the icebreaker Shirase during the summers of 2004 and 2005, between 32°S and 69°S. Global atmospheric 3-D model calculation of 222Rn were conducted using hypothetical emissions from ocean and land including the Antarctic continent. Oceanic emissions were estimated based on wind speed parameterizations from the literature and by using radium in the ocean as a surrogate of surface radon concentrations. Modeled results suggest that a significant part of the measured activities originate from a release from the ocean and the Antarctic continent. Based on regression analysis, we investigated the power-law description of wind speed that best fits the measured concentrations. The correlation, root mean square errors, and emission from the Antarctic continent suggest that a 3.5 power law best fits the measured activities. However, the merit of this choice is not statistically significant, and the proportionality factor that scales a wind speed description with a flux depends on the dilution of radon in the mixing layer of the ocean. These weaknesses, therefore, pose a limitation for the application of the current parameterization to the other gases.

1 Introduction

[2] Quantitative evaluations of the exchange velocity of gas between the atmosphere and the ocean are required to assess the temporal and spatial variations in atmospheric compositions. Air-sea gas exchange at a specific point can be expressed by a Fickian flux equation:

display math(1)

where K is the transfer velocity and ΔC is the effective concentration difference between the air and the ocean. Historically, the air-sea gas transfer has been evaluated using an eddy correlation method [McGillis et al., 2001a, 2001b, 2004; Edson et al., 2011], a radon deficit method [Broecker and Peng, 1971; Peng et al., 1979; Smethie et al., 1985; Kawabata et al., 2003; Bender et al., 2011], and a dual deliberate tracer method [Ho et al., 2011]. The effects of environmental forcing on this transfer velocity have also been studied, e.g., surface wind [Peng et al., 1979; Wanninkhof and McGillis, 1999; McGillis et al., 2001a, 2001b, 2004], waves [Toba and Chaen, 1973; Zhao et al., 2003; Frew et al., 2007], bubbles [Woolf et al., 2007], boundary layer dynamics [Jeffery et al., 2007; Rutgersson et al., 2011], surfactants [Soloviev, 2007; Wurl et al., 2011], and rain [Zappa et al., 2009]. Some reviews have discussed the relative contributions and a level of understanding of these processes [Wanninkhof et al., 2009; Johnson et al., 2011]. However, the particular concern of this study is to quantify the retardation of gas exchange at low to middle wind, which is possibly due to surfactants, and to quantify the enhancement of gas exchange at high wind, which is possibly due to air bubbles.

[3] The development of a chemistry transport model has enabled an approach that seeks consistency between the air-sea gas exchange rate and the concentrations of the gas in the model. One example is 222Rn, which is a natural progeny of Ra. The activity concentrations of 222Rn in the maritime air over the Southern Ocean could be comprised of air from three sources: the major continents (excluding the Antarctic continent) (MC), the Antarctic continent (AC), and the ocean (OC). Emissions over ice-free land have been measured and summarized by Schery and Wasiolek [1998], and measurements of 222Rn at stations on the Antarctic continent indicate that 222Rn is released from bare soil on the Antarctic continent [Pereira, 1990; Tositti et al., 2002; Ilic et al., 2005]. Sea water containing 226Ra which is distributed as a result of biogeochemistry cycling also releases 222Rn into the ocean where it remains, making the partial pressure of 222Rn in the ocean larger than the partial pressure of 222Rn in the atmospheric layer just above the ocean. In fact, the degassing of 222Rn from the ocean to the atmosphere has been used to estimate air-sea gas exchange, based on vertical profiles of 222Rn and 226Ra in the ocean [Broecker and Peng, 1971; Peng et al., 1979; Smethie et al., 1985; Kawabata et al., 2003; Bender et al., 2011]. If the lifetime of 222Rn were long enough, for example, 1 year, it would be unrealistic to detect the effect from the AC and OC, because the emissions from these sources are a few orders of magnitude less than those from the MC. Owing to its short life time, half-life time of 3.824 days, a few days after leaving the continent, the activity concentrations of 222Rn released from the MC become comparable with or less than those of the air mass stationary over the ocean. However, although an elevated activity concentration of 222Rn over the ocean is considered an indicator of an air mass that passed over the continental boundary layer [Lambert et al., 1970, 1982; Gros et al., 1998], in addition to continental fetch, higher than average emissions at oceanic fetch can cause elevated radon concentrations.

[4] Using a global advection-diffusion model, the current study subtracts from the measured activity concentrations, all the activity concentrations of 222Rn, which are suspected of having an MC origin, and categorizes them as “known.” The remaining component of 222Rn activity concentrations is then used in the inverse calculations. Total activities originating from the MC, AC, and OC are recovered in the synthesized concentrations to perform a regression analysis using the measured concentrations. The advantage of using this current method is that it takes into account both the fetch dependencies and the variations of wind speed discussed by Wanninkhof [1992] and relies on the accuracy of surface wind fields and the advection diffusion process in the atmospheric 3-D chemistry transport model. All experimental details and the inverse method set-up are described in the next section. Results of the regression analysis and the conclusions follow.

2 Method

2.1 Consistency of Flux and Concentrations

[5] Previous studies using the radon deficit method [Broecker and Peng, 1971; Peng et al., 1979; Smethie et al., 1985; Kawabata et al., 2003; Bender et al., 2011] have examined the radon concentrations within the water column, deduced the flux from the radon lost to the atmosphere, and then related this to the wind speed history at that particular location. However, in this study we take a new approach and track the radon concentration in the air parcels using the atmospheric transport model. We then deduce the flux by matching the modeled and observed atmospheric radon concentrations and then relate this to the wind speed over the parcel trajectory.

2.2 Cruise

[6] The locations of the ship and 222Rn concentrations averaged over each day are shown in Figure 1 for two expeditions in the austral summer. The 46th (2004–2005) and 47th (2005–2006) Japanese Antarctic Research Expeditions (JARE) using the icebreaker Shirase were designed to perform oceanographic and atmospheric measurements between Australia and the Antarctic continent [Tasaka et al., 2011]. The southbound cruise of the 46th JARE left Fremantle (115°44'E, 32°02'S) on 3 December 2004, and arrived at Syowa station (39°35'E, 69°00'S) on 17 December 2004. The northbound leg left Syowa station on 10 February 2005, and arrived in Sydney (151°12'E, 33°52'S) on 19 March 2005. The southbound cruise of the 47th JARE took place between 5 and 19 December 2005, using a similar route to that of the 46th JARE. The northbound leg was from 8 February to 17 March 2006. The ship's hourly location and measured activity are available from the web site (http://133.66.77.213/moodle/course/view.php?id=21). A quick guide to acquire the data set is given in the supporting information.

Figure 1.

Track of the ship during the 46th and 47th JARE cruise along with the daily concentrations of 222Rn. (a) 3 to 17 December 2004; (b) 10 February to 19 March 2005; (c) 5 to 19 December 2005; and (d) 8 February to 17 March 2006. The two areas [A] and [B], surrounded by solid lines in Figure 1a, are described in section 3.2.

2.3 Measurements

[7] Air was sampled using an inlet pipe (1.5 m long) at a height of 14 m above the sea surface, from a porthole onboard the Shirase. Unlike previously used radon monitors, which were based on the scintillation of alpha particles, the current instrumentation is based on the electrostatic precipitation of 222Rn decay products, followed by instantaneous alpha-spectrometry on the surface of a PIN photodiode detector [Tasaka et al., 2011] and presents a better time resolution, sensitivity, and lower noise [Ui et al., 1998]. This method requires continuous air aspiration into a 70 L diffusion chamber made of stainless steel. The flow rate was 8 L min−1. A diagram of the instrument is presented in the supporting information.

[8] Alpha pulse counts were recorded onboard the Shirase every 10 min during the cruise. These counts include background noise, and thus, the inner surface of the diffusion chamber is polished to minimize background noise. The amount of background noise was estimated from a control experiment conducted at an onshore laboratory after the expedition and was then subtracted from the original count. However, as a result of extremely low activity, the hourly activity sometimes appears negative after this correction, and we therefore used daily integrated counts to avoid these negative values. The lower limit of the measurement for the daily concentration was estimated as 7.7 mBq m−3. Calibration was performed using an ionized chamber that was evaluated in an international comparison of the instrument [Shimo et al., 1997].

2.4 Global 3-D Atmospheric Transport Model Setup

[9] A global atmospheric 3-D chemistry transport model, Simulator of Trace Atmospheric constituents on a Global scale (STAG), is used to produce global distributions of 222Rn activity concentrations and is driven by wind, temperature, and surface pressure analyzed at the European Centre for Medium-Range Weather Forecasts (ECMWF). The horizontal grid interval is 1.125° in both east-west and north-south directions. Vertical layers belong to a sigma-pressure hybrid system conforming to the ECMWF model vertical grid system (http://www.ecmwf/int/products/data/technical/modellevel/model-def-60.html). There are 60 vertical layers between the surface and the top (at about 64 km), and the highest resolution near the surface is about 20 m. The model input and output have a temporal interval of 6 h. Advection is calculated using a semi-Lagrangian scheme, as described by Taguchi [1996] and in the supporting information. The model is equipped with a total mass conservation fixer, which compensates for an error in the total amount of constituents in the model caused by the loss of significant digits. This error is unavoidable because as long as the winds and constituents are represented by a limited number of digits, significant digits of concentrations are lost in the computation. The total mass fixer is indispensable for long-term integration, but is not relevant for integration times of less than a year. In fact, in this study it was turned off, because we realized that the mass fixer disturbs the linear additive characteristics, which are mandatory for the inverse method. Diffusion in the boundary layer is represented in a nonlocal planetary boundary layer scheme that specifies the homogeneous mixing ratio below the top of the boundary layer. This boundary layer diffusion is a determinant in this study and will be described later. The model has previously been applied to 222Rn and other species [Wada et al., 2007; Law et al., 2008; Patra et al., 2008; Sawa et al., 2008; Taguchi et al., 2011].

[10] The procedures used to determine daily mean activity concentrations along the track of the ship in this model, are as follows: (A) The hourly meteorological data are read on a grid system (at approximately 35 km intervals in this study) and are interpolated to a model grid system (at approximately 100 km intervals); (B) Using a hypothetical equation, the flux of 222Rn from the ocean to the atmosphere at each point is estimated with a time resolution of 1 h; (C) The hourly fluxes are accumulated for 6 h, to produce a 6 hourly flux; (D) The emissions during 6 h are applied to the atmospheric boundary layer of the model to generate 3-D distributions of 222Rn activity concentrations after 6 h; (E) Activity concentrations at the exact location of the ship, at the exact time of the hourly observations, are obtained by spatial interpolation at two individual 3-D distributions at consecutive 6 h intervals, followed by a temporal interpolation between the two values; (F) The daily activity is produced by collecting 24 activity concentrations. For sources originating from MC and AC, the steps from (D) to (F) are performed using a constant emission.

[11] The planetary boundary layer (PBL) of the atmosphere is located at the bottom of the atmosphere and acts as an entrance into the global atmosphere for any materials released from the surface of the Earth. The procedure in the model for supplying material to the PBL (hereafter called “the input scheme”) is described below. The mass of 222Rn to be supplied to the atmosphere for a specific grid point is determined from the flux distribution. The concentration increment due to the flux of 222Rn to vertical layers in the PBL within the model (hereafter called “the input increment”) is determined from the mass of 222Rn and the mass of air in the PBL. The top of the PBL is defined as the lowest layer where the bulk Richardson number, which is a function of the vertical profile of temperature and the wind speed at that point, exceeds 0.25 [Troen and Mahrt, 1986]. In stable conditions, when the PBL height (BLH) is estimated at less than four levels, roughly 150 m, we then set the fourth layer as the top of the PBL, because inversion layers extremely close to the surface may not continue for 6 h. The PBL used in the model was compared with observations on land by Taguchi [1996].

[12] Because the BLH is a function of wind speed, the input increment is not necessarily higher in high wind conditions, even if the flux is increased by the wind. Let us compare two cases, using wind speeds, U1 and U2, and assume a BLH of H1 and a flux of F1 for a wind speed U1. The input increment C1 is proportional to F1/H1 in the input scheme. Suppose that the BLH is then increased to H2 for a wind U2(> U1). If the flux is constant regardless of the wind speed, the input increment C2 may be reduced, because the air mass in the PBL(U2) is greater than that in the PBL(U1). The input increment C2 would be less than C1, as long as F2 is less than F1H2/H1. Only when a flux F2 is larger than F1H2/H1 does C2 become larger than C1. The BLH used in STAG are described in section 3.2 as a function of the surface wind.

[13] Numerical simulations using STAG were conducted over two 5 month periods, starting on 1 November 2004 and 1 November 2005, respectively. Initial conditions for these runs were zero over the whole model domain. We also conducted a time integration over a longer period, but did not observe any difference when using these 5 month integrations.

2.5 Emissions of 222Rn From the Major Continents (MC)

[14] The geographical distributions of the emissions from the MC in the present study are similar to those used in the World Meteorological Organization intercomparison experiments [Jacob et al., 1997]. Specifically, the flux density of radon from the ground between 60°S and 60°N (excluding Australia) is specified as 21 mBq m−2 s−1(1 atom cm−2 s−1). Over Australia, monthly mean flux distributions [Grant et al., 2008; Griffiths et al., 2010] are adopted because the flux is calibrated against in situ measurements. The annual emission of the MC is 15.1 kg yr−1.

2.6 Emissions of 222Rn From Ocean (OC)

[15] The emission of 222Rn from the sea surface at a point was estimated using the modified version of the equation given by Schery and Huang [2004]. The original formula is

display math(2)

where Fav is the average radon flux in mBq m−2 s−1, aRn is a proportionality factor as discussed by Wanninkhof [1992], uav is the monthly mean wind speed in m s−1at 10 m above the sea surface, Sc is the Schmidt number and [Ra] is the radium concentration below the radon deficit area (submixed layer) [Peng et al., 1979] in units of mBq m−3. This formula assumes that 222Rn activities in the atmospheric marine boundary layer are effectively zero.

[16] The hourly emission of radon from the sea surface (FH) was estimated as a function of sea ice, wind speed, sea surface temperature (SST), and radium contents in the submixed layer:

display math(3)

where aRn is now a constant to be solved, u is the hourly wind speed in unit of m s−1 and f(u) is a nondimensional function of wind speed, 981 is the Schmidt number at 20°C, and other symbols are the same as those in equation (2). For a power-law case, using p as the power-law dependency on wind speed, the formula f(u)=up is used. For a Liss and Merlivat [1986] case, f(u) is a piece-wise linear function given by Wanninkhof et al. [2009]; f(u)=0.17u(u<3.6 m s−1), f(u)=2.85u−9.67 (3.6<u<13), f(u)=5.9u−49.3 (13<u). The combined equation, aRnf(u), is called k-U10 relation hereafter.

[17] We adopted a ground heat flux, a wind at an elevation of 10 m, and an SST compiled by the Climate Forecast System (CFS, http://cfs.ncep.noaa.gov/) [Saha et al., 2010]. The CFS provides global distributions of such meteorological data for unprecedented hourly time intervals at 1152×576 points on the Gauss grid. The data consist of the product of a four-dimensional data assimilation system at 6 h intervals, and hourly predictions up to 6 h. Ground heat flux, winds, and SST are generated for the STAG grid system using spatial linear interpolation. If a CFS grid over the ocean has a ground heat flux, we consider that this CFS grid is covered with sea ice, and, therefore, the flux of 222Rn is zero on the STAG grid associated with this CFS grid. We used a formula for the Schmidt number and a horizontal distribution of 226Ra given by Schery and Huang [2004]. The Schmidt number is expressed in terms of SST. Within each oceanic basin, the 226Ra distribution is a function of latitude.

[18] The quality of CFS winds is evaluated using the ship wind at hourly locations. Figure 2 shows scatterplots of the CFS wind and the ship winds at the hourly ship location. The mean bias during the cruise is less than 0.001 m s−1for the individual components, east-west and north-south, and the root mean square errors are about 3 m s−1. Correlations between CFS wind and the ship wind are 0.90 for east-west and 0.88 for north-south. The annual mean wind speed of the CFS over the global ocean was 7.5 m s−1in 2005.

Figure 2.

Scatterplots of the hourly (a) westerly wind; and (b) southerly wind, both measured onboard the Shirase and from the CFS data set interpolated to the location of the ship. A line indicates where the CFS wind and the ship wind agree with each other.

[19] Flux from the sea using k-U10 relations used in literature are estimated and adopted in the STAG. In the preliminary study, the measured activities are compared with the model output using emissions from MC and OC with aRn=0.31 for quadratic [Wanninkhof, 1992], aRn=0.028 for cubic [Wanninkhof and McGillis, 1999], and aRn=1 for Liss and Merlivat [1986]. In Figure 3, the daily mean activity concentrations in Figure 1 are shown again in dots, with one standard deviation for each day in vertical lines. The solid curve shows the simulations using the emissions from the MC only. Dashes and dotted curves indicate the simulations using the MC with the OC estimated from three k-U10 relations.

Figure 3.

Daily 222Rn activity observed on the ship and standard deviations. (a) 3 to 17 December 2004; (b) 10 February 2005 to 19 March 2005; (c) 5 to 19 December 2005; (d) 8 February 2006 to 17 March 2006. Simulated activity is drawn for the: major continents (MC, solid line), Wanninkhof [1992] (dashed line), Wanninkhof and McGillis [1999] (dotted line), and Liss and Merlivat [1986] (dashed and dotted lines). Note that the emission from the Antarctic continent is not included here.

[20] Some elevated radon concentrations are observed at the same time as those in the MC-only simulations, such as on 6 December 2004 and 25 February 2005. Although the timing of elevated concentration events agree with each other, the magnitude of the concentration is significantly less than the observation. The model shows that the footprint of the former event is from the South American continent on 23 November 2005, and that the footprint for the latter event is from the same continent on 17 February. The method for determining the footprint is described in Taguchi et al. [2002] and the supporting information.

[21] To explain the gap between the model and the data using the MC only, a magnification of emissions from the MC is necessary of an order of approximately ten times, particularly over the South American continent. However, such large emissions are unrealistic. Figure 3 demonstrates that the inclusion of the OC, estimated using three methods, significantly fills the gap between the model and the data especially at an elevated concentration event simulated from the MC. Elevated concentration events of the MC indicate that the air mass which made contact with the land arrived at a speed which was fast enough to retain a high concentration of 222Rn. This suggests that the wind which transported the air mass was strong, and that the flux of 222Rn from the ocean was enhanced by the wind. It is noticeable that the curves of the two OC schemes [Wanninkhof, 1992; Wanninkhof and McGillis, 1999] are close together and almost undistinguishable, but that a huge gap remains between the model and the observations, on dates such as 3 March 2006 and 13 March 2006. Modeled results by Liss and Merlivat [1986] indicate that the flux produced with this scheme is too weak, and this will be discussed in section 3.2 .

[22] There are some high-concentration events irrelevant to the MC, such as 7–10 March 2005, 10–14 December 2005, 1–4 March 2006, and 12–14 March 2006. In these periods, neither the MC nor the OC produced elevated concentrations, which suggests that the filling of gaps cannot be achieved by a simple modification of wind speed parameterization. An alternative method using the AC will be discussed below.

2.7 Inverse Method Setup

[23] The inverse method, used to estimate the emission of a constituent by combining a global advection diffusion model with an atmospheric composition measurement, is similar to that used in the estimate of the emission scenario in a nuclear plant accident [Stohl et al., 2012]. A source receptor relationship is established using the model, and a source scenario that fits the observed activity concentrations in the least square sense is sought, as below. A linear fit is considered for M unknown emissions (xi,i=1,MM=33). We applied a code called the “nonnegative least square” (NNLS) in R [R Development Core Team, 2011]. This code gives a solution x from the linear fitting of model concentrations z and observations y. A set of model concentrations z is expressed using a matrix G:

display math(4)

where G is an M×Nmatrix. Each column of G is assembled with daily concentrations simulated by STAG using a component of a source in the AC or OC. Details of the source are described later. The code solves for x with the condition (xi≥0) to minimize w below:

display math(5)

where N is the number of observations (N=106).

[24] Emissions from the Antarctic continent were investigated by dividing the emission area into 32 segments, as shown in Figure 4. Potential grid points were selected corresponding to the Normalized Difference Snow Index (NDSI) provided from the National Snow and Ice Data Center of NOAA [Haran et al., 2005; Scambos et al., 2007], based on the satellite measurement in the austral summer of 2003 to 2004. The data is given on a polar stereo projection map with 8056×6964 pixels south of about 70°S. Pixels with NDSI exceeding 3500 are counted in each area covered with a 1.125°×1.125° grid. Potential emissions in a grid are given proportional to the rate of counted pixels in each grid. Although outcrops around some Antarctic stations, presented on the web site of the stations are included in the potential emission distributions using 3500 as a threshold, the position and the size of outcrops are highly uncertain. Any deficiencies in the OC are possibly dissimilated by the AC. Therefore, a solution giving the least size of the AC is assumed to be the best.

Figure 4.

Area of the Antarctic continent (AC) examined by the inverse method. Each segment contains grid points estimated from normalized difference snow index of the MODIS Mozaic of Antarctic Image Map.

[25] The air-sea gas exchange of 222Rn was examined for eight types of power-law (0, 1, 2, 3, 3.5, 4, 5, and 6) dependencies of wind and a combination of linear dependencies of wind [Liss and Merlivat, 1986]. This flux may be examined on an arbitrary scale, but in practice, 0.1 kg yr−1, which corresponds to 0.0532 mBq m−2 s−1for an ocean area of 3.39× 1014 m2, is used. Figure 5 depicts the transfer velocity, k-U10, relation. The flux is zero for calm conditions, except in the case of null wind dependency. The aRns obtained from the inverse calculation for each f(u) is described in section 3.2 and Table 1.

Figure 5.

Air-sea gas transfer velocity as a function of hourly wind speed. Each curve of k-U10 is scaled with a proportionality factor estimated from the solution in section 3.2. It is assumed that the flux is zero at zero wind speed, except for the case of null dependency on wind speed. The vertical axis is adjusted to express the value at 20°C.

Table 1. Summary of Inversion and Comparison Between Simulated Concentrations and Observationsa
f(u)aRnrBiasRMSEOCAC
 Standard PBL     
  1. af(u), a function of u in the equation (3); aRn, proportionality factor [cm h−1]; r, correlation between STAG and the observations; Bias, mean differences between STAG and the observations [mBq s−1]; RMSE, root mean square errors [mBq s−1]; OC, annual emission of 222Rn from the Ocean [kg222Rn yr−1], AC, annual emission of222Rn from the Antarctic continent [kg222Rn yr−1].
u020.280.654−2.818.60.1310.041
u3.2650.753−1.315.90.1560.015
u20.35220.799−1.114.50.1500.009
u33.153×10−20.813−1.414.20.1400.010
u3.58.968×10−30.813−1.714.10.1350.008
u42.485×10−30.810−2.014.40.1310.015
u51.788×10−40.800−2.614.90.1270.022
u61.197×10−50.784−3.315.50.1260.029
LM862.5630.811−1.014.20.2020.022
 ERA- Interim + 500 m     
u033.070.690−1.417.40.2130.037
u4.4720.771−0.415.30.2130.024
u20.45000.794−0.614.60.1910.021
u33.386×10−20.793−1.214.70.1700.024
u3.51.071×10−20.788−1.514.90.1610.026
u42.921×10−30.782−1.815.20.1550.029
u52.045×10−40.766−2.515.80.1450.034
u61.338×10−50.749−3.216.40.1410.026
LM862.4910.795−0.514.20.2030.022

3 Results

3.1 Antarctic Continent and Ocean

[26] We first examined the MC + AC and ignored values from the OC. Emissions from 32 segments of the Antarctic continents (AC) in Figure 4 were solved, and annual emission from the AC were obtained to be 0.149 kg yr−1. Using the solution, the correlation between the observed and the total daily activity concentrations simulated from synthesized emissions are shown in Figure 6, with the error bar corresponding to a 90%confidence level, estimated using the bootstrap analysis. The results of the MC + AC shown on the left side indicate that the mean correlation is higher than that in the MC only case (r=0.3). Therefore, emissions from the AC are suggested to be significant.

Figure 6.

Correlations between the observed and the simulated daily activity concentrations for different wind speed dependencies in different combinations of the components. The error bar is the 90% confidence level derived from a bootstrap analysis. Four combinations of the components are considered: Major continents (MC) and the Antarctic continent (AC) (short dashed line); MC and ocean (OC) estimated from Liss and Merlivat [1986], (dashed line); MC, AC, and OC from Liss and Merlivat [1986] (dotted line); and power-law dependencies (solid lines). Variations in correlations due to local variations in 226Ra for the 3.5 power-law case are indicated with arrows based on a series of Monte Carlo experiments. See text for details.

[27] Second, we examined the MC + OC and ignored values from the AC. Emissions from the ocean for each f(u) were evaluated. However, we have only displayed the case of Liss and Merlivat [1986] on the left-hand side in Figure 6, because the solutions for other f(u) exhibited similar correlations. The correlation in this case is higher than that in the MC only case, which suggests that emissions from the OC are significant.

3.2 Power-Law Dependency for Wind Speed

[28] Emissions from the OC for each power-law case were solved simultaneously with those of the AC. The proportionality factor aRn in the hypothetical equation (3) are listed in Table 1. Daily total activity concentrations of MC + OC + AC are produced using aRns and are compared with the observations in terms of the correlations (Figure 6). The range of correlations for the total concentrations of the three components (MC + AC + OC) for power laws between two and six are higher than the ranges in the case of both of the MC + OC, and the MC + AC. The range of the confidence level indicates that no power law is definitely superior to any other. Therefore, a power-law dependency higher than cubic [Monahan, 1971; Monahan and Spillane, 1984] could not be ruled out. In Table 1, aRn of Liss and Merlivat [1986] is shown to be more than twice. Such a large correction to the original formula is consistent with a small flux at a low wind regime shown in Figure 5.

[29] The uncertainty which is due to the uncertainty in the 226Ra content, is estimated in two ways, from a global and a local perspective. Surface concentrations of 222Rn are supposed to be less than the equilibrium to 226Ra, due to degassing from the ocean. Using the global perspective, the constant aRn in Table 1 needs to be multiplied by 1.43 if [Rn]/[Ra] ∼ 0.7 suggested by Smethie et al. [1985] and Schery and Huang [2004] represents the oceanic fetch relevant to the simulations. For local variations in 226Ra content, we performed a series of Monte Carlo experiments, specifying some fluctuations in 226Ra. We perturbed 226Ra contents among 10°×10° patches and applied 30%variations to the 226Ra content for each patch. All grid points inside a patch are scaled using a single factor. For example, if the original value in a patch is 1000, then a value is picked between 700 and 1300 using a homogeneous random number and is used for the whole period. No spatial correlations are considered among the patches. After applying this modification to 226Ra, emissions from the OC were generated for the 3.5 power-law case using the aRn in Table 1. Global 226Ra distributions were prepared for 100 cases, and corresponding simulations were conducted to produce daily activity concentrations. Correlations between the measured concentrations and the synthesized concentrations ranged between 0.809 and 0.817 for 100 cases. A similar range in the correlations for different power-law dependencies is expected.

[30] Daily mean concentrations in Figure 1 are shown again in Figure 7, with the modeled results using emissions synthesized from the solutions. The model outputs for different power-law dependencies are drawn in different line patterns. Some gaps in the model and observational in Figure 3 are filled in Figure 7, for example, 13 February 2005, 7–10 March 2005, 10–19 December 2005, and 12–14 March 2006.

Figure 7.

Same as Figure 3, except for synthesized activity concentrations developed from the solutions. Results of STAG using aRn in Table 1are drawn. The bold solid curve stands for the 3.5 power law, a dotted curve for Liss and Merlivat [1986], and dot and dash curves for other power laws. The surface wind and PBL height relation is examined when activity concentrations are increased with an increasing order of (A) power law; and (B) vice versa in Figure 7a. See text for details.

[31] Let us examine two periods, labeled (A) and (B). On (A) 6 December 2004, the model output for zero dependency (dotted line) is drawn in the lowest position, and that for the sixth power law (dashed line) in the highest position, except the case using Liss and Merlivat [1986]. In contract, on (B) 13 December, the output for zero dependency is located in the highest position and that for the sixth power law is in the lowest. Based on the k-U10 relation in Figure 5, a scenario where the air mass at (A) experiences a high wind region, and that at (B) a low wind region, is speculated. Therefore, wind speed in the footprint of these cases, including BLH, is examined to confirm this result.

[32] Hourly horizontal winds in the CFS and BLH in the model were collected for 6 days at the respective footprint and are shown in Figure 8. The footprint of the air mass at (A) and (B) in Figure 7a was detected with the tagged simulation, using emissions from the OC with null dependency on wind speed. Tagged simulations were conducted with a 10°×10° size patch. As a consequence of mixing, no single patch represents the bulk of the concentration. Rather, the footprint was spread among several 10°×10° patches, indicated as [A] and [B], surrounded by solid lines in Figure 1. Each area, comprising five to six patches, represents more than 70%of the activity concentrations of (A) and (B), respectively. Wind speed at area [A] and [B] is 9.0±3.0 m s−1, and 7.6±3.1 m s−1, respectively. Variations of wind speed are consistent with the speculation, while the wind speed at (A) is not located in the wind range where k-U10 increases with the power law in Figure 5. A possible explanation for this is that the footprint for air mass (A) may be narrower and the corresponding wind speed higher than these six patches. Figure 8 shows that higher BLHs are more abundant in area [A] compared with [B], simply reflecting the difference of the wind speed at a respective area and term. The tendency for the height of the BLH to increase with increasing wind speed, reflected in the slope of the regression, is in agreement between [A] and [B].

Figure 8.

Boundary layer height in STAG and wind speed for two periods: (a) 1–6 December 2004 and (b) 8–13 December 2004. The sampling time for each case corresponds to the time for which a wide response because of a power-law dependency is detected, as shown in Figure 7a. The corresponding time and areas are detected using a method described in Taguchi et al. [2002] and indicated as [A] and [B] in Figure 1. Because the boundary layer height is defined on the model level, the altitudes of the boundary layer are clustered on the model altitudes. The linear regression of wind speed and boundary layer height is shown at the bottom right corner.

[33] The results of model-data mismatch using revised emission distributions are listed in Table 1 in terms of mean bias, root mean square errors, and total emission of OC and AC for each wind speed dependency. The mean bias for all cases is lower than the minimum detection limit. Annual emission from the OC is twice as much as that by Schery and Huang [2004] (0.0382 mBq m−2 s−1). The root mean square errors and total emission from AC are found to be the minimum at a power law of 3.5. Because the model attains the highest correlation with less subsidiary emissions from the Antarctic continent, a 3.5 power law is considered superior to the third or fourth power laws.

[34] Because the BLH in the model has a crucial role in determining aRn in equation (3), BLH-STAG was compared with the vertical profile of temperature and humidity observed over the ocean. Detailed vertical profiles (10 m vertical resolution) of temperature and humidity were obtained from the Variability of the American Monsoon Systems Ocean Cloud Atmosphere Land Study (VOCALS, http://www.esrl.noaa.gov/psd/psd3/synthesis/) [de Szoeke et al., 2010]. If a BLH was defined with a bulk-Richardson number, which is the method adopted in STAG, no systematic difference was found. However, if a BLH was defined using a humidity profile, such as the height where the humidity drops sharply, the BLH-STAG was lower than the BLH-VOCALS-Humidity. Global distributions of BLH are defined using the GPS occultation method (BLH-GPS), which relies on the sharp decrease of humidity and are compared with the BLH estimated in the Interim Reanalysis of ECMWF (BLH-ERA) [Ao et al., 2012]. Results showed that BLH-ERA is found to be lower than BLH-GPS by 500 m. It is not clear at this moment whether or not the sharp decrease of humidity corresponds to the height of the active vertical mixing of the materials released from the surface. To assess the effect of this potential bias in the STAG model, BLH-STAG was replaced with the BLH-ERA, adding 500 m over the whole globe. The results of this set of simulations are listed in Table 1. Note that aRn is increased by 10%–30%, which demonstrates how crucial the BLH specifications are in determining aRn. These increases also demonstrate that the aRn obtained in this study is specific to the model and is not applicable for use in other models without calibrations. Correlations and root mean square errors are degraded compared with the standard case, which indicates that the BLH used in the STAG has the advantage of reproducing the concentration distributions in the atmosphere much more closely.

4 Conclusions

[35] On the basis of using temporally and spatially high-resolution wind fields, a global 3-D atmospheric chemistry transport model and 222Rn measurements over the Southern Ocean, we investigated the power-law dependency of air-sea gas exchange on wind speed. Radon flux estimated from the parameterization of Wanninkhof [1992] and Wanninkhof and McGillis [1999] produced the modeled concentrations comparable to the observations. On the other hand, to fit the model results using the parameterization of Liss and Merlivat [1986] with the observations, the oceanic flux needs to be doubled. We found that the highest correlation is obtained for a 3.5 power law, with a huge uncertainty between the quadratic and the sixth power law. We noticed that the preference of the power law depends on the wind speed dependency of the planetary boundary layer specified in the atmospheric model. The most significant point of this study is that a power- law dependency with wind does not produce statistically significant differences in the simulated concentrations in the current atmospheric transport model if an appropriate scaling factor is applied in the flux calculations. In other words, a higher than cubic power law could not be ruled out. If we take into account root mean square errors and the size of subsidiary emissions, the 3.5 power law has an advantage over other dependencies. However, the scaling factor depends on the reduction rate of 222Rn in the surface ocean, which poses a limitation of the application of the current scheme to other gases.

Acknowledgments

[36] The authors express their gratitude to the crew member of the icebreaker Shirase, especially those on the 46th and 47th JARE cruise. Expeditions were conducted as part of a project of the National Institute of Polar Research. Digital data for monthly emissions for the Australian Continent are provided from Griffiths. Funding for this project was supported by the grants-in-aid for creative scientific research (2005/17GS0203) and (16310007) of the Ministry of Education, Science, Sports and Culture, Japan.