Gas transfer across a gas–liquid interface is commonly parameterized as follows: F=KCwα-Ca, where F is the air–sea flux (mol m-2 s-1), Ca and Cw are bulk air- and water-side concentrations (mol m-3), and α is the dimensionless solubility (Cw/Ca at equilibrium). K represents the bulk gas transfer coefficient reflecting the physical processes limiting exchange on both sides of the interface, expressed in air-side units (m s-1). The reciprocal of K, or resistance, can be partitioned into water-side and air-side processes, where K-1=Rtotal=rw+ra=1kw+αka. In the case of gases like SO2 with very high effective solubility (α≫1) and negligible seawater concentration (see below), the air side dominates the total resistance (i.e., ra≫rw) so the gas transfer equation becomes F=ka[SO2]wα-[SO2]a≈ka[SO2]air, where ka is the air-side gas exchange coefficient (m s-1), also referred to as the deposition velocity. The transfer coefficient, ka (hereafter referred to as kSO2), encapsulates the physical processes controlling transport across the marine atmospheric surface layer to the air–sea interface. This transport is governed by (1) turbulence in the surface layer, (2) molecular diffusion close to the sea surface where turbulence is suppressed by molecular viscosity, and (3) the resistance to transfer across the air–sea interface at the water surface . The transfer coefficient can be expressed in terms of resistance to deposition, as follows: ka-1=rtotal=rturbulence+rdiffusion+rsurface. The turbulent resistance term, sometimes referred to as aerodynamic resistance, is often approximated by the momentum transfer coefficient (or drag coefficient) under the assumption that there is no diffusive barrier to momentum transfer. Diffusive resistance is usually conceptualized in terms of the surface renewal model, involving periodic exchange of patches of near-surface air by turbulent eddies, with deposition of a trace gas to the sea surface via non-steady-state diffusion . This model implies a dependency on molecular diffusivity, as follows: rdiffusion∝Scn, where Sc is the Schmidt number defined as the kinematic viscosity of air (ν) divided by the molecular diffusion coefficient (D) of the gas in air and n is a constant. Early studies of soluble gas deposition to the ocean suggested a Sc2/3 dependence based on boundary layer theory . Current gas transfer models parameterize gas transfer as a surface renewal process with a Sc1/2 dependence . Laboratory experiments using water-side-controlled gases show n ranging from 0.50 to 0.66 for smooth and rough flow conditions .

Interfacial surface resistance, i.e., resistance to air–sea gas transfer arising from physical–chemical interactions in a molecular scale layer at the surface, is included here for completeness. We are aware of no evidence that such processes are important at clean water surfaces for molecules such as SO2 or H2O (see Sect. 2.2.3). The sea surface is often “contaminated” by the presence of organic compounds and particulates collectively referred to as the sea surface (or marine) microlayer. One could hypothesize that a hydrophobic surface film of sufficient coverage and thickness could introduce resistance to the transfer of small polar molecules such as SO2 or H2O, but such effects have not yet been demonstrated. It is well known that the microlayer can alter the surface tension of the sea surface, dampening the formation of capillary waves and indirectly altering the turbulent and diffusive resistance to transfer of momentum and gases .

The interpretation of the SO2 air–sea flux measurements in this study is based on the following premises: (1) deposition of SO2 is controlled entirely on the air side of the air–sea interface and (2) surface ocean waters are always highly undersaturated in SO2 with respect to the overlying atmosphere. In this section we discuss the basis for these assumptions.

This study was conducted at Scripps Pier located in La Jolla, California, during April 2014. The local meteorology is characterized by a daily westerly sea breeze with occasional frontal systems that generally approach from the northwest. The pier structure extends 330 m from shore in the west–northwest direction and the water depth at the end of the pier is approximately 10 m. The end of the pier extends roughly 100 m past seaward of breaking waves. Meteorological sensors and air inlets were mounted at the end of a moveable 6 m boom mounted on the northwest corner of the pier. The boom was positioned to extend approximately into the prevailing winds. The sensing regions of the eddy covariance flux package and the air intake for SO2 detection were located approximately 10 m above the sea surface. The sensor height was corrected for changes in tidal range during the experiment. Instrumentation for sulfur dioxide detection, data acquisition, clean air generator, and pumps were located in a trailer located at the end of the pier. Three-dimensional winds and fast-response temperature measurements were measured using a Campbell CSAT 3 sonic anemometer, with data collection at 50 Hz. Water vapor and air density were measured using an open-path infrared gas analyzer (IRGA; LI-COR model LI-7500) at 5 Hz. The instrument was calibrated using a dew point generator (LI-COR model LI-610). Sea surface temperature was measured using a temperature probe array mounted on the pier with 9 probes vertically spaced by about 1 m. The sea surface temperature was taken to be the shallowest probe not exposed to air. Mean air temperatures were obtained from the NOAA meteorological station at the end of the pier.

For SO2 detection, the air sampling inlet was similar to that used by to measure DMS. The air inlet was a 0.25′′ O.D. PFA tee fitting mounted just behind the sonic anemometer sensing region. Air was drawn into the inlet at a flow rate of 8500 cc min-1 and dried by passage through two counterflow Nafion membrane driers (Perma Pure LLC model PD-625-24PP) connected in series just after the inlet. The air passed from the driers through a 0.25′′ O.D., 13 m long PFA Teflon tube to a chemical ionization mass spectrometer located in the trailer. In the trailer, 1000 cc min-1 of the 8500 cc min-1 airflow was drawn through the ionization source of the mass spectrometer. A 200 cc min-1 stream of ozonized dry air (Pen Ray UV lamp) was added to the 1000 cc min-1 prior to entry into the ionization source. A continuous flow of isotopically labeled gas standard (34SO2 in N2) was injected into the sampled air stream at the inlet tee. This gas standard was delivered to the inlet from an aluminum high-pressure cylinder located in the trailer, at a flow rate ranging from 1 to 10 cc min-1 from a 1/8′′ O.D. PFA tube.

All flow rates were controlled and logged using mass flow controllers interfaced to a PC. Air for the Nafion counterflow driers and ozone generator was supplied by a pure air generator and compressor (Aadco model 737-11), located in the trailer. Pumping for the air inlet and ionization source was provided by a carbon vane pump (Gast model 1023).

Atmospheric SO2 was detected using a laboratory-built chemical ionization mass spectrometer (CIMS) in negative ion mode. This instrument was described previously for positive ion measurements of dimethylsulfide . The instrument was modified for this study by replacing a set of conical declustering lenses with a multi-lens ion funnel of the design developed by . This resulted in an order of magnitude improvement in ion transmission over the prior configuration of the instrument. In the CIMS instrument, ionization was carried out in a 0.25′′ inch glass-lined stainless steel flow tube containing a 63Ni foil at 430 Torr and room temperature, with an airflow rate of 1000 cc min-1. Ions from the source enter the declustering region containing the ion funnel through a 250 µm diameter pinhole. The ion funnel is 127 mm long and consists of 100 concentric rings decreasing in diameter from 25.4 to 1.5 mm . A DC gradient of 3 V cm-1 was applied to transmit ions axially and two phases of radio frequency (RF; 2 MHz, 150 V p-p) were applied so that adjacent rings in the funnel were 180∘ out of phase. The ion funnel was operated at a pressure of 1 Torr. Ions exit the ion funnel via a 1 mm orifice into the first stage of a differentially pumped Extrel quadrupole mass filter (19 mm). Ions are detected using a dynode, ion multiplier, pulse amplifier/discriminator, and counting electronics (National Instruments model USB 6343). Ion counts were logged locally by the mass spectrometer control software and retransmitted as analog signals in real time with a fixed 2 s delay. The analog signals were logged by the multichannel data logger along with data from the meteorological sensors. Sulfur dioxide was detected in negative ion mode as SO5- (m/z 112), which was generated using the following reaction scheme previously described by . O2-+O3→O3-+O2O3-+CO2→CO3-+O2CO3-+SO2→SO3-+CO2SO3-+O2+N2→SO5-+N2 The addition of ozone minimizes the competing reaction O2-+SO2→SO4- and increases response to SO2 . When operating the ionization source at atmospheric pressure there was interference at m/z 112 from the CO4(H2O)2- cluster ion. This was essentially eliminated by dropping the pressure in the source to 430 Torr.

Isotopically labeled 34SO2 delivered to the air inlet served as an internal standard to account for any wall losses or variations in instrument sensitivity due to changes in ambient conditions. The flow rate of the gas standard was adjusted to achieve a 34SO2 level of roughly 100 pmol mol-1 after dilution into the ambient airflow. The gas standard was prepared in our laboratory in a high-pressure aluminum gas cylinder (Scott Marrin model 30A) and delivered via mass flow controller. These gas standards were calibrated in the lab against a gravimetrically calibrated permeation device using an inert dilution system described by . The isotopically labeled standard was detected at m/z 114. The ambient SO2 mixing ratio was calculated from the field data as follows: XSO2=S112S114fstdftotalXtank, where S112 and S114 are blank-corrected mass spectrometer signals, fstd and ftotal are the gas flow rates of the isotopic standard and inlet, and Xtank is the molar mixing ratio of 34SO2 in the compressed cylinder. Because the air stream was dried in the inlet tube prior to analysis, XSO2 represents the mixing ratio of SO2 in dry air. Blanks involved sampling air through a carbonate-impregnated filter to quantitatively remove ambient SO2. Whatman 41 filters for this purpose were soaked in 1 % sodium carbonate solution and dried prior to use. During this study the SO2 instrument exhibited sensitivity of approximately 150 Hz ppt-1.

The analog data streams from the meteorological and chemical sensors were filtered with a Butterworth filter and logged at 50 Hz using a National Instruments multichannel data logger. Post-processing consisted of (1) aligning the data to account for instrumental electronic delays and the delay due to the airflow transit time through the inlet tube; (2) rotating the 3-D winds for each flux interval into the frame of reference of the mean winds and to account for tilt in the sonic anemometer (1.3∘); (3) converting the data to geophysical units; (4) computing vertical fluxes of water vapor, sensible heat, SO2 and momentum; (5) applying a high-frequency correction to the SO2 fluxes to account for loss of fluctuations in the inlet tubing; and (6) applying various quality control criteria to filter the resulting data set for instrumental issues or unsuitable environmental conditions. Data processing was carried out using Matlab (Mathworks). The inlet delay for SO2 was determined experimentally in the laboratory prior to field deployments to be roughly one second. The measured delay was consistent with the offset required for maximizing the covariance between vertical wind and SO2 concentration. Sulfur dioxide was measured as a dry mixing ratio since the air stream was dried prior to entering the mass spectrometer and converted to concentration (mol m-3) using the dry air density. Water vapor concentrations measured by the LI-COR IRGA were corrected to account for air density fluctuations and converted to concentration (mol m-3). The saturation vapor pressure of seawater at the sea surface temperature was calculated following . The mean air temperature was corrected for the adiabatic lapse rate, and the sonic temperatures were corrected for humidity. SO2, water vapor, temperature, and winds were corrected to 10 m height and neutral stability using COARE . The data set was subdivided into 13 min flux intervals for processing. The resulting data consisted of means and variances for air temperature, relative humidity, SO2, and seawater surface temperature. Fluxes of momentum (Reynolds stress, τ), water vapor, sensible heat, and SO2 were calculated for each interval according to FSO2=w′CSO2′‾,FH2O=ρ‾w′XH2O′‾,Fmom=ρ‾(w′u′)2‾+(w′v′)2‾,FSH=ρ‾cpw′T′‾, where u, v, and w are the winds; cp is the heat capacity of air and ρ is air density in kg m-3; and the other variables are defined previously. T is the air temperature corrected for humidity and the adiabatic lapse rate. Primed quantities with overbars represent the ensemble average of the fluctuations about the mean.

Transfer velocities were computed following Eqs. (1) and (3), as follows: kSO2=-FSO2[SO2]a,kH2O=FH2O(Xs‾-XH2O‾)ρdry‾,kmom=FmomU10ρ‾,kSH=FSH(Ts‾-T‾)ρ‾cp‾. Xs is the calculated mixing ratio of water vapor corresponding to the saturation vapor pressure of water at the sea surface temperature.

High-frequency fluctuations in the mixing ratio of SO2 are attenuated during the passage of ambient air through inlet tubing and membrane driers. The attenuation characteristics of the inlet used in this study were characterized by interrupting the addition of an SO2 gas standard to the airflow, resulting in an exponential decay of the SO2 signal. A decay constant (K) was obtained from the slope of a linear regression to a plot of log(SO2) vs. time. The attenuation of the inlet was modeled as a first-order low-pass Butterworth filter with a cut-off frequency, Fc=K/(2p), of about 1.5 Hz. A high-frequency correction factor or gain, G, was computed for each flux interval by applying the filter to the sonic temperature time series data and taking the ratio of the filtered and unfiltered fluxes as follows: G=Funfiltered/Ffiltered. Linear regression of the gain against wind speed yielded G=0.005U10+1.018. The SO2 flux for each interval was multiplied by the gain using this relationship and the mean wind speed for the interval.

Several quality control criteria were applied to the data to identify and eliminate flux intervals collected under unsuitable conditions or with instrumental problems. They are described as follows.

Co-spectral shape: a cumulative sum of co-spectral density, normalized to the total flux, was computed for each flux interval, summing from low to high frequency. Intervals were rejected if (a) the cumulative sum at 0.004 Hz exceeded the total flux or was opposite in sign or (b) the difference between the cumulative flux at two consecutive frequencies exceeded 18 %. These criteria identified most intervals with obvious deviations in co-spectral shape from those defined in . Most of these intervals were caused by electronic noise on the sonic anemometer signal.

The field study was carried out from 6 to 27 April 2014. Time series of meteorological and oceanographic parameters and fluxes measured during this study are given in Fig. . Winds were generally light during the study, with a mean wind speed of 3.8±2.0 m s-1 and a range of 0–9.7 m s-1. Air temperatures were 16.2±1.3 ∘C with a range from 12.9 to 19.9 ∘C and the average relative humidity was 80 %. Sea surface temperatures averaged 16.5±0.9 ∘C with a range of 13.8–18.3 ∘C. The SO2 mixing ratio ranged from below detection to 560 pmol mol-1 with a mean of 100±114 pmol mol-1. Sharp spikes in SO2 were usually associated with military or commercial vessels passing upwind of the pier. Low SO2 levels were associated with the occurrence of morning fog. For the first few days of the study, a high-pressure region was located over the study site (DOY 97–100), during which winds were light and air temperatures were warm. Air mass back trajectories from this period indicate that marine air masses flowed from the north, passing inland over California before reaching the site. SO2 levels were relatively high during this time likely due to fossil fuel combustion. After the high-pressure system moved out of the region, airflow was from the northwest, arriving at the study site directly from the ocean, and SO2 levels were relatively low during this period. There was a notable increase in wind speed starting at DOY 106. On DOY 115 a low-pressure system passed over the region with higher wind speeds.

The Scripps Pier site experiences a consistent diurnal sea breeze, with offshore flow during the evening and extending to the early morning. Data from periods with offshore flow were excluded from the analysis in the quality control process. Due to the sea breeze locally and along the coast, there is likely advection of polluted air offshore, and the SO2 levels measured during onshore flow may be elevated compared to marine air from the open ocean. The average air–sea temperature differential during the study was 0.56±1.55 ∘C with a range from -3.5 to 2.7 ∘C, with positive values indicating a warmer ocean than atmosphere. Occasionally air–sea temperature differentials exhibited diurnal variability which reflected the changes in air temperatures. Starting on DOY 114, seawater temperatures warmed and were significantly warmer than air temperatures for the remaining 3 days of the study.

All the observed SO2 fluxes were from the atmosphere to the ocean surface (negative by convention) and ranged from 0 to -65 pmol m-2 s-1, with the largest fluxes observed at the beginning and end of the deployment associated with high SO2 levels and high wind speeds, respectively (Fig. ). All observed water vapor and sensible heat fluxes passing quality control were upward, which was consistent with the positive (from the ocean to the atmosphere) thermodynamic gradient for the duration of the study. The warm seawater temperatures combined with the high winds and cold temperatures on the last 2 days of the study resulted in large H2O and heat fluxes.

Frequency-weighted co-spectra of vertical wind and SO2 are shown in Fig. . Fluxes measured during DOY 114–117 were significantly larger than those measured during the rest of the campaign because of the strong winds and large air–sea temperature differences observed during that period (Fig. ). The co-spectra measured at Scripps Pier for all parameters were similar in shape to the characteristic boundary layer co-spectral shapes defined by .

The wind speed dependence of kmom observed in this study was significantly greater than predicted using the open ocean parameterization from the NOAA COARE (Fig. ). The relationship between wind speed and surface roughness can vary significantly between the open ocean and coastal environments because of bottom-generated turbulence, as well as other influences related to fetch, tidal currents, surfactants, and wave properties . Thus, the turbulent properties of the atmospheric surface layer in coastal environments are not well described by wind speed alone. To account for such effects, we examined the relationship between transfer velocities and both wind speed and friction velocity (u*) (Fig. ).

The transfer velocities measured for water vapor, sensible heat, and SO2 (kH2O, kSH, kSO2) were all positively correlated with friction velocity (Fig. , Table ). kmom was significantly higher than the scalar parameters and kSO2 was lower than kH2O and kSH. The regressions against friction velocity utilize slightly different data sets in each case because these regressions utilize flux measurement intervals that passed quality control for both the scalar parameter (water vapor, sensible heat, SO2) and for momentum flux. This means that the data sets used for the various parameters were not identical either in terms of the number of flux intervals or the physical conditions under which they were collected, i.e., temperature, wind speed, atmospheric stability, sea state, etc. Ideally, the comparison of transfer velocities would be carried out using intervals for which all four of the parameters passed quality control. However, given the limited data set, this constraint reduced the available data to an unacceptable degree. As an alternative, we also compared the gas transfer velocities to each other by computing two-way linear regressions between pairs of simultaneously measured transfer velocities (Fig. 5, Table ). This analysis was in general agreement with the k vs. u* analysis described earlier and showed kSO2<kH2O, kSO2<kSH and no significant difference between kSH and kH2O. Momentum transfer velocities were significantly larger than all the scalar transfer velocities. The comparison of transfer velocities from simultaneous intervals is a more robust approach to observing differences in transfer velocities.