Constraining the concentration of the hydroxyl radical in a stratocumulus-topped marine boundary layer from seato-air eddy covariance flux measurements of dimethylsulfide

The hydroxyl radical (OH) is an important oxidant in the troposphere due to its high reactivity and relative abundance. Measuring the concentration of OH in situ, however, is technically challenging. Here we present a simple method of estimating an OH-equivalent oxidant concentration (“effective OH”) in the marine boundary layer (MBL) from the mass balance of dimethylsulfide (DMS). We use shipboard eddy covariance measurements of the sea-to-air DMS flux from the Vamos Ocean-Cloud-Atmosphere-Land Study Regional Experiment (VOCALS-REx) in October and November of 2008. The persistent stratocumulus cloudcover off the west coast of South America and the associated strong inversion between MBL and the free troposphere (FT) greatly simplify the dynamics in this region and make our budget estimate possible. From the observed diurnal cycle in DMS concentration, the nighttime entrainment velocity at the inversion is estimated to be 4 mm s −1. We calculate 1.4(±0.2)×106 OH molecules cm−3 from the DMS budget, which represents a monthly effective concentration and is well within the range of previous estimates. Furthermore, when linearly proportioned according to the intensity of solar flux, the resultant diel OH profile, together with DMS surface and entrainment fluxes, enables us to accurately replicate the observed diurnal cycle in DMS (correlation coefficient over 0.9). The nitrate radical (NO 3) is found to have little contribution to DMS oxidation during VOCALS-REx. An upper limit estimate of 1 pptv of bromine oxide radical (BrO) would account for 30% of DMS oxidation and lower the OH concentration to 1.0 ×106 OH molecules cm−3. Our effective OH estimate includes the oxidation of DMS by such radicals. Correspondence to: B. J. Huebert (huebert@hawaii.edu)


Introduction
While non-reactive towards the major constituents of the atmosphere, the hydroxyl radical (OH) is the principal oxidizing free radical in the troposphere for trace species (Levy, 1971).The primary source of OH is the reaction between water vapor and excited atomic oxygen (O( 1 D)); the latter is a product of the photo-dissociation of ozone (O 3 ) by photons between 290 and 320 nm.Reduction of the hydroperoxy radical (HO 2 ) by nitrogen oxide (NO), and to a lesser degree by O 3 , contributes to the recycling of OH (Donahue and Prinn, 1990).OH reacts readily with most trace gases and is often regenerated during the process, resulting in sustained OH concentrations on the order of 10 6 molecules cm −3 globally (Prinn et al., 1995;Spivakowsky et al., 2000).The radical is consumed primarily by reacting with carbon monoxide (CO), but it also reacts with sulfur dioxide (SO 2 ), nitrogen dioxide (NO 2 ), and a wide range of hydrocarbons.Models predict higher OH concentrations for the tropics and for the Southern Hemisphere.The former is attributed to higher humidity and solar fluxes that promote O 3 dissociation; the latter is presumably due to less CO south of the equator (a result of lower anthropogenic emissions; Seinfeld and Pandis, 2006).
Due to the transient nature of the radical, measuring OH in situ was not possible until the last two decades, when specialized instruments based on absorption, fluorescence, and mass spectroscopy were developed (e.g.Mount, 1992;Hard et al., 1984;Eisele and Tanner, 1991).However, direct observations of this radical cannot be made in all field experiments (such as during VOCALS-REx).Even when in situ OH measurements are available, they might not represent a temporal or regional average, which is of importance to large-scale models.
Published by Copernicus Publications on behalf of the European Geosciences Union.
M. Yang et al.: Constraining the concentration of the hydroxyl radical Alternatively, global and regional distributions of OH are often estimated by measuring chemicals with known lifetimes that are exclusively consumed by this radical, such as methyl chloroform (Prinn et al., 1992).Here we follow a similar approach and use a budget analysis of naturallyderived atmospheric dimethylsulfide (DMS) to constrain the equivalent OH concentration in a clean, stratocumuluscapped marine boundary layer.
Dimethylsulfide (CH 3 SCH 3 ) in the open ocean (DMS w ) is derived exclusively from phytoplankton.Due to photochemical destruction and rapid dilution, the atmospheric concentration of DMS is always orders of magnitude lower than the expected Henry's law equilibrium concentration with DMS w .Consequently, DMS gas always effluxes from the surface ocean and is the largest source of reduced sulfur to the atmosphere (Lovelock et al., 1972).The substantial magnitude of the flux and the lack of other sources make DMS an ideal gas with which to study air-sea exchange.In the atmosphere, DMS is principally oxidized by OH to form SO 2 , dimethylsulfoxide (DMSO) and methane sulfonic acid (MSA).SO 2 may be oxidized further to form sulfate, which contributes to aerosol growth and formation of cloud condensation nuclei (CCN).The coverage and lifetime of marine clouds formed from these CCN affect the earth's radiative balance and may in turn be linked to biological production in the ocean (Charlson et al., 1987;Kloster et al., 2006).
The oxidation of DMS by OH proceeds through two separate pathways: the hydrogen-atom abstraction at a methyl group that subsequently leads to mostly SO 2 : and the OH addition to the sulfur atom that can lead to a wider range of products, including DMSO and MSA: The abstraction pathway is favored under high temperatures; the Arrhenius form for this rate constant is k 1 = 1.1×10 −11 exp(−240/T ), equating to 4.9×10 −12 cm 3 molec −1 s −1 at 298 K.The addition pathway is favored under low temperatures; this oxygen (O 2 ) and temperature dependent rate constant is best represented by Sander et al., 2006).At 298 K, about 80% of the oxidation of DMS goes through the abstraction pathway; the two pathways are about equal at 285 K (Stickel et al., 1993;Wallington et al., 1993).
Other oxidants, including nitrate and halogen radicals, may also consume DMS.The nitrate radical (NO 3 ) is produced from the reaction between NO 2 and O 3 .The DMS-NO 3 reaction is several times slower than the DMS-OH reaction.Unlike OH, NO 3 can only have an appreciable concentration at night because it is photolyzed rapidly during the day.Studies from Equatorial Christmas Island showed that in the remote Pacific, the contribution to DMS loss from NO 3 is less than a few percent due to the low levels of NO x (NO + NO 2 ) away from anthropogenic activities (Davis et al., 1999;Chen et al., 2000).The same studies also suggested that the DMS-chlorine reaction, while still very poorly understood, accounts for no more than 5∼10% to the oxidation of DMS.Other authors (e.g.Sciare et al., 2000) have found OH and NO 3 to be inadequate in explaining their observed DMS losses, and speculated that the naturally derived bromine oxide (BrO) might be another significant DMS oxidant.
The aforementioned Christmas Island experiments demonstrated a clear diurnal cycle of DMS in the MBL (Bandy et al., 1996;Davis et al., 1999).While the supply of DMS to the boundary layer via air-sea exchange is continuous, destruction of DMS principally takes place during the sunlit hours, when OH is available.As a result, DMS starts to increase from its daily minimum just before sunset and builds up through the night until just after sunrise, at which time photolysis causes DMS to decrease until the next cycle.This diurnal cycle in DMS can be altered in a pollution-influenced marine environment where anthropogenically produced NO x level is higher, as nighttime oxidation of DMS by NO 3 can be comparable in magnitude to daytime oxidation by OH (Yvon et al., 1996).
The equivalent OH we estimate here from VOCALS-REx is an effective concentration, the concentration of OH that would cause the same rate of DMS loss as if OH were the only oxidant.In all likelihood, our effective OH is slightly higher than the actual OH concentration, since it includes minor contributions from the other oxidants.
The VOCALS-REx experiment took place in October and November of 2008 in the Southeast Pacific, off the west coast of Chile and Peru (http://www.eol.ucar.edu/projects/vocals/).The experiment aimed to address the interactions among the ocean, atmosphere, and clouds in this tightly coupled regional climate system.The Andes mountain range to the east forces strong winds parallel to the coast.Ekman transport results in coastal upwelling of cold, nutrient-rich waters, which leads to stability in the lower troposphere.The warm, dry air over the cool water surface, together with the largescale subsidence from the Hadley Cell, creates a widespread and persistent stratocumulus cloud deck (Bretherton et al., 2004).These thin, low-lying, and hence radiatively-cooling clouds form from CCN aerosols.While anthropogenic emissions dominate the coastal region, a significant fraction of CCN likely originates from DMS-derived sulfate in the clean marine environment offshore.From time to time, hundredkilometer sized openings (which can be observed from satellites) form in the stratocumulus cloud-deck and advect with the mean wind.These features have been coined "pockets of open cells" (POCs) and are hypothesized to be related to removal of CCN by drizzle from the air (Stevens et al., 2003).To further our understanding in this phenomenon, we need to look at the origin and fate of the CCN-precursors, including DMS and its oxidants.
A stratocumulus marine boundary layer is characterized by vigorous mixing due to the intense longwave radiative cooling at the cloud-top (Lilly, 1968).Air entrains down from the FT, which is balanced by a deepening of the MBL and wind divergence.The strong inversion in effect caps the MBL, confining surface-borne scalars like DMS.Therefore, a stratocumulus region such as the Southeast Pacific can be viewed as a natural analog to a box model, with clearly defined inputs and outputs.These simplified conditions enable us to estimate the effective OH concentration from mass balance.

Experimental and methods
The National Oceanographic and Atmospheric Administration (NOAA) ship Ronald H. Brown (RHB) was deployed in the Southeast Pacific from approximately 24 October to 30 November 2008.In addition to retrieving and maintaining the Woods Hole Oceanographic Institute's Stratus buoy at 85 • W and 20 • S, a number of E-W transects were made at latitudes between 18.5 • S and 21.5 • S to survey eddies and upwelling features.The edges of such eddies are often associated with higher levels of biological productivity, hence more DMS w (T. Bates and P. Matrai, unpublished data).In the same general time frame, multiple aircraft, including the National Science Foundation (NSF)/National Center for Atmospheric Research (NCAR) C-130, repeatedly flew westward from its base station in Arica, Chile to the stratocumulus region offshore.The anthropogenic influence was minimal away from the coast, with average CO, O 3 , and SO 2 concentrations of 65 ppbv, 30 ppbv, and 25 pptv, respectively, typical of a clean MBL.Most of the research flights were designed to survey the 20 • S cross-section and study the formation and development of POCs.
During the experiment, two nearly identical atmospheric pressure ionization mass spectrometers (APIMS) were used to measure DMS on board of RHB and the C-130, the distinction being that the instrument at sea was sampling at a high rate of 20 Hz to quantify the sea-to-air flux, whereas the one aloft was measuring concentration every 10 s.The measurement of DMS by the APIMS with isotopically labeled standard technique has been described previously (Bandy et al., 2002;Huebert et al., 2004;Blomquist et al., 2006).Most recently, Blomquist et al. (2009) discussed in great details about the instrument setup, flux processing, data refinement, and uncertainty estimates.
We estimate the OH-equivalent oxidant concentration from the budget analysis of DMS.The conservation equation for any chemical species, S, in the marine boundary layer is represented in Eq. (3) (with the overbar representing an average in time/space): The first term on the left represents the time rate of change in the concentration of S. The second term is the horizontal advection of S due to gradients along the mean wind (u).The third term is the flux divergence, the difference between vertical fluxes at the bottom and top of the box model.Local (chemical) production and loss of S are represented by P and L, respectively, on the right side of the conservation equation.
As described in the previous section, DMS fluxes upwards from the surface ocean to the stratocumulus-topped MBL, where it is oxidized (principally by OH), diluted by DMSfree air entrained from the FT, and transported horizontally.DMS is not produced chemically, so P = 0. Therefore the chemical loss due to oxidation can be calculated by closure if we know the DMS surface flux, entrainment flux, horizontal advection, and the time rate of change.

Surface flux of DMS
On the ship, the inlet of our mass spectrometer was located at 18 m above the water surface on the jackstaff, where flowdistortion due to the ship's superstructure is minimized.A precisely known amount of the triply-deuterated DMS standard was continuously injected at the inlet and combined with a high ambient air flow.The DMS concentration was determined from the ratio between the ambient and standard DMS mass spectrometer signals.Relative wind speeds, acceleration, and rotation in three axes were recorded at the same frequency as the DMS by a Gill Sonic anemometer and a Systron-Donner Motionpak accelerometer, respectively.Ship's motion was removed from relative winds to get true winds following Edson et al. (1998).To obtain surface flux (F 0 ) via eddy covariance, DMS concentration was correlated with the vertical wind velocity (w) in the form of F 0 = DMS w (primes here denote deviations from the means).Flux was initially computed in ten-minute segments that overlapped by 50%.To remove times when sampling conditions were unfavorable, any ten-minute segment with relative wind direction more than 90 degrees off the bow or gyro heading changing by over 10 degrees (ship maneuvering) was screened out.The remaining "good" segments were averaged to hourly values.
Time-series of 18-m DMS concentration and flux from the RHB are shown in Fig. 1, with campaign means (±standard deviations) of 57±(26) pptv and 3.4 (±1.9) µmoles m −2 day −1 , respectively.Also shown are true wind speed and direction from the sonic anemometer at the same height.The wind direction hardly varied, almost always coming from the South/Southeast (150 • ).We limit our averaging to offshore observations only (73 • W ∼86 • W and 18 • S ∼22 • S, hereinafter 'the VOCALS region').Nearshore data were not included in the averaging due to anthropogenic influence as well as heterogeneities in the atmospheric DMS field caused by spikes in DMS w on the edges of localized coastal eddies.Even with the ship steaming at up to 12 knots, the classic sinusoidal diurnal cycle in DMS is clearly visible on a number of days (Fig. 2).This observation implies a widespread horizontal homogeneity over the region with limited mesoscale variability.Continental influence, which is usually associated with high levels of NO x , and thus high NO 3 , was minimal.

Boundary layer structure
We determined the boundary layer structure during VOCALS-REx from shipboard radiosonde launches every six hours.Figure 3 shows a time series of temperature contours from the soundings, with the dark line indicating the inversion immediately above the stratocumulus cloud deck.Over the course of more than a month, the structure of the MBL was relatively constant, with an average temperature of 13 • C. In addition to radiosondes, a W-band radar (24 m range gate, 50 m pulse length) from the ship measured cloud top height continuously.On average, the stratocumulus cloud top varied from ∼1350 m near dawn to ∼1200 m near dusk, suggesting a greater entrainment rate in the nighttime.Inversion heights determined from radiosondes are nearly identical with the cloud top estimates from the W-band radar (S. de Szoeke, personal communication, 2009).
We used DMS concentration from the C-130 aircraft (DMS C130 ) to infer the distribution of the scalar within the MBL and exchange with the FT. Figure 4 shows a typical profile of the lower troposphere during VOCALS-REx.DMS C130 decreased gradually with altitude within the MBL and rapidly dropped to near-zero above the stratocumulus cloud-top in the FT.Across the thin inversion layer of only a few tens of meters, the changes in dew point and potential temperature were usually of the order of 20 and 10 K, respectively.
When the MBL is shallow and well mixed, scalars with long lifetimes are thought to be homogeneously distributed vertically.DMS in the boundary layer is emitted from the ocean surface and diluted by entrainment above; with a mixing time in the MBL (∼1 h) much shorter than its lifetime (1∼2 days, estimated later), DMS concentration at the top of the MBL is usually only a few pptv lower than at the surface (Faloona et al., 2005).However, this difference was more significant in the VOCALS region, where the average inversion height was 1.3 km. Figure 5 shows the mean profile from the C-130 during the campaign.Altitude was normalized to the inversion height (z i ).DMS C130 aloft was normalized to the concentration from the lowest leg at ∼30 m (DMS C130,0 ).On average, DMS C130 immediately below the inversion was ∼80% of the concentration near the surface, exhibiting a linear decrease with height.We linearly 2    regressed DMS C130 /DMS C130,0 against z/z i in the MBL (r 2 = 0.8).The fraction of DMS at height z relative to the surface value can then be parameterized as 1α (z/z i ), where α = 0.2 represents the "decoupling" parameter.This formulation of the MBL structure is similar to what is used in Wood and Bretherton (2004).

Advective flux of DMS
In VOCALS-REx, DMS concentration and flux measured from the ship show increasing trends away from the coast due to generally greater DMS w concentration and higher wind speeds offshore (Fig. 6).The ratio between DMS flux and concentration, however, was nearly constant with longitude.Bin-averaged inversion heights from radiosondes and 18-m  wind speeds within the latitude range of 20±2 • S are also plotted on the same figure.The boundary layer was deeper offshore (∼1.5 km at 85 • W) than at the coast (∼1.1 km), as is typical of this region.
We estimated the advective flux of DMS from the horizontal gradient computed from shipboard DMS concentration.Using multi-variate linear regression, DMS averaged to daily means (to remove diel variability) was regressed against Lat and Lon.The fitting coefficients were −2 pptv • Lon −1 and −1 pptv • Lat −1 , with higher DMS towards the West/Southwest (Fig. 7).For an average wind speed of 6 m s −1 from 150 • , multiplying the zonal and meridional winds (−3 and 5 m s −1 , respectively) by the DMS gradient gave an advection of 0.04 pptv h −1 .Integrating over the 1.3 km column led to an advective flux of only 0.05 µmoles m −2 day −1 , less than 1% of the DMS sea-to-air flux.Advection was small because the mean wind direction was largely orthogonal to the horizontal DMS gradient; we set it to zero hereafter.

Entrainment velocity
To calculate the entrainment flux of DMS, we need to know the entrainment velocity (ω e ) at the inversion.While ω e was not directly measured during VOCALS-REx, we can estimate it from the observed nighttime increase in shipboard DMS concentration.To account for the dilution effect from changing MBL depth, we integrate DMS concentration from the ship to the depth of MBL using the vertical gradient determined from Sect.2.2, resulting in column concentration, DMS , in units of µmoles m −2 .
The vertically integrated form of Eq. ( 3) is shown in Eq. ( 4), with the advection and production terms now dropped out.Now every term is in units of flux: The term on the left side of Eq. ( 4) is the time rate of change.The last term on the right represents the local loss of DMS, which has been expanded to the product of k PFO (a pseudo first order reaction rate constant) and DMS column concentration.We have separated flux divergence into the first and second terms on the right hand side of Eq. ( 4), representing the DMS fluxes at the ocean surface and inversion, respectively.The entrainment flux is formulated as the entrainment velocity, ω e , multiplied by the concentration jump across the inversion (Lilly, 1968), with subscripts z − i and z + i denoting just below and above z i .The concentration just below the inversion can be approximated from the 18-m concentration by the fraction (1α); the concentration above the inversion is taken to be zero.Equation (4) thus simplifies to: The nighttime build up of DMS column concentration appears to be linear with time (Fig. 8).The slope over these hours approximately represents the time rate of change in DMS , which includes the flux divergence plus any nocturnal chemical loss.There is no OH at night, and we assume the NO 3 reaction to be insignificant (this assumption  is validated in the last section); the loss term thus drops out.From hour 1 to 10:00 UTC (or 20:00 to 05:00 local time), we calculated a time rate of change in DMS of 2.6 µmoles m −2 day −1 .The mean nighttime surface flux obtained by eddy covariance was 3.2 µmoles m −2 day −1 .The nighttime entrainment flux thus needs to be 0.6 µmoles m −2 day −1 to balance the budget, requiring ω e = 4 mm s −1 .
The entrainment velocity derived above is only a nighttime value, and might not be representative of the climatological mean since there was possibly diurnal modulation of the inversion height.Shortwave heating of cloud top stabilizes the MBL and tends to reduce entrainment during the day, while longwave cooling at night may enhance entrainment.Off the coast of California, where stratocumulus clouds are also prevalent, eddy covariance flux measurements of three conserved scalars (DMS, O 3 , and total water) immediately above and below the inversion indicated a range of 1.2∼7.2mm sec −1 for ω e , with higher values at night (Faloona et al., 2005).Using a mixed-layer approach, Caldwell et al. ( 2005) found a 6-day average ω e of 4±1 mm s −1 during the East Pacific Investigation of Climate (EPIC) stratocumulus cruise in 2001.Combining satellite observations with National Centers for Environmental Prediction (NCEP) reanalysis, Wood and Bretherton (2004) determined an ω e of 2∼6 mm s −1 in the tropical and subtropical east Pacific, with a likely value of 4 mm s −1 in the VOCALS region.While our estimated nighttime ω e could theoretically be an overestimate of the diurnal average, 4 mm s −1 appears to be a reasonable value compared to previous results.We show later that our calculated effective OH concentration is not very sensitive to the choice of ω e , because reaction with OH represents a far greater removal term for DMS than dilution due to entrainment.At the limit of zero for α (i.e.no decoupling in DMS), ω e is lowered to 3 mm s −1 , still within the range of previous estimates.
M. Yang et al.: Constraining the concentration of the hydroxyl radical

Estimating effective OH
From the clear diurnal cycles and near-constant flux to concentration ratio in the project averages (Figs. 2 and 6), diurnally averaged DMS field in the MBL appears to be approximately constant in space and time over the duration of the project.We thus assume DMS to be in a steady-state on that scale.
For the purpose of this derivation we first assume that the oxidation of DMS is solely due to reactions with OH (Eqs. 1 and 2).The pseudo first-order rate constant k PFO in Eq. ( 5) is expressed as k OH , the total second order rate constant of the DMS-OH reaction (k OH = k 1 + k 2 ), multiplied by the concentration of OH.With an average MBL temperature of 13 • C during VOCALS-REx, we calculate k OH to be 7.9×10 −12 cm 3 molec −1 s −1 , with the abstraction pathway accounting for 60% of the total oxidation.
Rearranging and expanding Eq. ( 5) with no time rate of change leads to: Using ω e = 4 mm s −1 and α = 0.2, we find an effective OH concentration of 1.4×10 6 molec cm −3 for VOCALS-REx, somewhat higher than the estimated global average possibly due to high water content and solar radiation and low anthropogenic influence in this region.From PEM-Tropics A and B, which took place during September/October of 1996 and March/April of 1999, respectively, Olsen et al. (2001) showed that OH ranged from 1.4∼1.8×10 6molec cm −3 in the latitude range of 10S∼30S and in the lowest 2 km, with higher values in the austral spring.The PEM-Tropics experiments did not extend into the stratocumulus region, however, where solar flux is lowered by 10∼20% relative to the normal trade wind cumulus regime.An effective OH concentration of 1.4×10 6 molec cm −3 implies a lifetime of 1.1 days for DMS with respect to OH in the MBL, well within the range of previous estimates of 0.5∼2 days (e.g., Wine et al., 1981;Hynes et al., 1986).
Allowing for a substantial uncertainty of ±2 mm s −1 in the entrainment velocity (due to diel variability, for example), the relative error in the calculated OH concentration is only ∼12% because dilution due to entrainment is small compared to photochemical loss.The potential of ω e being biased high implies that our calculated OH might be an underestimate (though this could be partially compensated by the our assumption that OH is the only DMS oxidant).At a limit of α = 0, OH is lowered to 1.2×10 6 molec cm −3 .The uncertainties in the inversion heights from radiosoundes and the W-band were about 25 m (S. de Szoeke, personal communication, 2009).Assuming an absolute uncertainty of 2 mm s −1 for ω e and 0.1 for α, the propagated absolute uncertainty for the equivalent OH concentration is ∼0.2 molecules cm −3 , or 15%.One apparent benefit of estimating OH from the DMS flux and concentration is that both measurements are made by the same instrument; any calibration uncertainty in the instrument (such as flow rate or standard concentration) is thus negated, not affecting the final outcome.

Discussion
The above OH estimate is an average value over a month.In reality, OH is only produced during the day when photochemistry is possible; the radical is consumed completely when there is no light.The next logical step is to approximate the diel variation in OH, which has pronounced impacts on the cycling of sulfur species in the MBL, from DMS to SO 2 to sulfate.

Diel Variability in OH
To approximate the diel profile of OH, we need to know the sources and sinks of the HO x (OH + HO 2 ) system because the OH:HO 2 ratio is usually a steady-state constant (Faloona et al. 2000).To a first order, the availability solar flux, and hence the ozone photolysis frequency, J O( 1 D), limits OH production since the subsequent reaction between O( 1 D) and water vapor is rapid.OH can also be recycled from HO 2 by reaction with NO and O 3 .As for the sinks of HO x , both the self-reaction of HO 2 and OH + HO 2 (when NO x is low) represent quadratic loss in HO x .In a high NO x environment, the OH + NO 2 reaction is the major sink and a linear loss for HO x .
We can approximate the dependence of steady-state OH concentration on solar flux as JO( 1 D) b , with the exponent b being NO x -dependent.When NO x is high, OH relates linearly to JO( 1 D) because HO 2 becomes less important (e.g.Holland et al., 1998).When NO x is low, OH is formed by the reaction with water vapor as well as from recycling of HO 2 by O 3 (and NO, if any), while the loss of HO x is largely quadratic.Overall b likely takes on a value between 0.5 and 1. Berresheim et al. (2003) found that b = 0.68 off the coast of Crete in the Mediterranean, where the mean NO 2 mixing ratio was 0.4 ppbv.While there was no direct measurements of NO x during VOCALS-REx, in situ observations from 10S∼30S during PEM-Tropics A and B yielded 5∼10 pptv of NO x in the lowest 2 km (Olson et al., 2001).Schultz et al. (1999) showed that in the tropical South Pacific, the median NO x level was only 4 pptv in the lowest 2 km.Thus VOCALS likely falls in the low NO x regime and one may expect b to be less than 1.
We first binned solar flux measured by the shipboard radiometer in the VOCALS region to the time of day, which expectedly resulted in a smooth curve with peak insolation at ∼17:00 UTC.Not knowing the exact value of b, hourly hydroxyl concentrations (OH t ) were proportioned as linear and square root functions of the solar flux, with the diel average of the radical constrained by 1.4×10 6 molecules cm −3 .The Even a minuscule amount of NO 3 was found to degrade the fit between the implied and observed DMS.BrO cannot be distinguished from OH based on the DMS diurnal cycle.
For VOCALS-REx, the maximum DMS oxidation due to BrO was estimated to be 30%.radical peaked at ∼5×10 6 molecules cm −3 in the linear case and ∼4×10 6 molecules cm −3 in the square root case (with a broader distribution).While this method seems rather simplistic compared to photochemical models containing many photoactive species, the general shape of our derived diel OH profile agrees fairly well with previous direct observations in the tropical/subtropical Pacific basin (e.g.Davis et al., 2001;Mauldin et al., 2001).As another comparison to our effective OH estimate from DMS, we use photolysis rates of O 3 and hydrogen peroxide (H 2 O 2 ) predicted from the NCAR Tropospheric Ultraviolet and Visible (TUV) Radiation Model (http://cprm.acd.ucar.edu/Models/TUV/),reaction rate between O 3 and HO 2 , and destruction rate due to CO, methane, hydrogen gas, O 3 , H 2 O 2 , and HO 2 from Sander et al. (2006) to calculate the expected OH concentration.The TUV estimates photolysis rates based on time, latitude, longitude, and oxidant field, and accounts for clouds and aerosol scattering using climatological reflectivity from the Total Ozone Mapping Spectrometer (TOMS).The model yielded a noontime OH concentration of ∼6×10 6 molecules cm −3 , which is ∼20% higher than our daytime peak in the linear scenario but likely within the range of uncertainties.

Reproducing the diurnal cycle of DMS
The oxidation of DMS in the atmosphere has been modeled previously given an estimate of OH (Shon et al., 2001;Nowak et al., 2001).Using a similar approach and building upon Eq. 5, the surface DMS concentration at time t can be written as: For simplicity, we used the average ω e of 4 mm s −1 , neglecting any potential diel variation in the entrainment veloc-ity.The implied DMS diurnal variation is not very sensitive to the choice of ω e for the same reason as in Sect.2.5.
We first equated, k PFO,t , the pseudo first order reaction rate constant of DMS, simply to k OH OH t , with OH t being the time-dependent radical concentration calculated from Sect.3.1.Figure 9a shows the diel cycle of OH approximated as a linear function of solar flux, DMS column concentration calculated from Eq. ( 7), as well as the observation.Figure 9b shows the same calculation except OH was approximated as a square root function of solar flux.It is apparent that the calculated DMS agrees closer with the observation when the dependence on solar flux, and hence J O( 1 D), is linear.In the square root case, implied DMS does not decrease as rapidly as observed after sunrise because the OH distribution is too broad.The linear dependence might come as a surprise given the expectedly low level of NO x ; this might be due to chemistry that are not considered or well understood.In the next section we explore the importance of nitrate and bromine oxide radicals in DMS oxidation, and see whether we can further improve the fit to the observed diurnal cycle.

DMS Oxidation by NO 3 and BrO
The rate constant of the DMS-NO 3 reaction can be represented by k NO 3 = 1.9×10 −13 exp(500/T), giving 1.0×10 −12 cm 3 molec −1 s −1 at 298 K (Sander et al., 2006).Studies from Allan et al. (2000) in the relatively clean MBL at Mace Head suggested that the nocturnal level of the nitrate radical hovers on the order of a pptv, with reaction with DMS being its most important loss mechanism.Platt and Heintz (1994) estimated a globally averaged concentration of 3 pptv for NO 3 .
Uncertain about how much NO 3 was present in the Southeast Pacific, we apportioned the total oxidative loss of DMS to fractions due to NO 3 and OH (the prime denotes the "actual" OH concentration, assuming a linear dependence on www.atmos-chem-phys.net/9/9225/2009/solar flux).For example, if 10% of DMS oxidation was due to NO 3 , the ratio between diurnal averaged k NO 3 NO 3 and k OH OH should be 1:9.To crudely mimic the diel variation in NO 3 , we assume its nighttime level to be twice the diurnal average and the daytime concentration to be zero.In reality, NO 3 might not achieve steady-state through out the night (Allan et al., 2000).We arrived at the closest least-square fit between observed and calculated DMS (correlation coefficient exceeding 0.9) when 99% of DMS oxidation is due to OH, as any additional NO 3 would degrade the fit; this corresponds to less than 0.005 pptv of NO 3 .In all likelihood, low levels of NO x and O 3 were limiting the production of NO 3 during VOCALS-REx.
The rate constant of the DMS-BrO reaction can be represented by k BrO = 1.4×10 −14 exp(950/T), yielding 3.4×10 −13 cm 3 molec −1 s −1 at 298 K (Sander et al., 2006).Read et al. (2008) measured BrO with differential optical absorption spectroscopy (DOAS) at Cape Verde in the tropical Atlantic Ocean.They found an average BrO concentration over 2 pptv during the day and zero at night, with a diurnal profile resembling a "top hat" distribution.
During VOCALS-REx, with a similar DOAS technique, no significant BrO was detected, with ∼1 pptv being the upper limit daytime peak concentration (R. Volkamer, personal communication, 2009).The same instrument also detected ∼1 pptv of iodine oxide (IO), a level insignificant towards DMS oxidation due to its much lower reactivity.If we crudely approximate the diurnal profile of BrO with a square root dependence on solar flux, 1 pptv of daytime maximum BrO implies a diel average concentration just under 0.4 pptv.This upper limit concentration of BrO would account for ∼30% of total DMS oxidation; the OH concentration would then need to be reduced to 1.0×10 6 molecules cm −3 .The shape of implied DMS from Eq. ( 7) with this allocation of oxidants is not significantly different from what is shown in Fig. 9a.Therefore from the implied DMS diurnal cycle alone, it is difficult to assess whether 1 pptv of BrO is too high.Our OH-equivalent oxidant concentration may still include other DMS oxidants, such as NO 3 and BrO.

Conclusion
We have demonstrated that a month-long average OHequivalent oxidant concentration in a stratocumulus-capped marine boundary layer can be derived from the sea-to-air flux and concentration of DMS measured from a ship with a simple mass balance method.From aircraft profiles during VOCALS-REx, DMS concentration appeared to decrease linearly with altitude in the MBL due to decoupling.On average, DMS immediately below the inversion was ∼80% of the surface concentration.DMS concentration in the MBL displayed the classic sinusoidal diurnal cycle, in which daily maxima and minima were found to be just after sunrise and just before sunset, respectively, as a result of the continu-ous build up via air-sea exchange and daytime consumption by photochemistry.From the nighttime build up of DMS column concentration, we estimated an entrainment velocity of 4 mm s −1 from the difference between the time rate of change and the observed surface flux.The advective flux of DMS was found to be insignificant because the horizontal gradient in DMS was largely perpendicular to the mean wind direction.The calculated OH concentration of 1.4 (±0.2)×10 6 molecules cm −3 from the DMS budget equation agrees well with previous estimates, and represents a regional OH-equivalent oxidant concentration.Actual OH will be less by the extent that other DMS oxidants, such as nitrateand halogen-radicals, react with DMS.The applicability of this approach of estimating the equivalent-OH concentration hinged on the stationarity and horizontal homogeneity of the region over a long enough time scale.Areas with much greater mesoscale variability or additional source and sink terms will complicate the budget analysis.
We fitted the OH-equivalent oxidant concentration as both linear and square root functions of the observed solar flux averaged to the time of day.Using the resultant diel profiles in OH, the mean observed DMS surface flux, and an entrainment velocity of 4 mm s −1 , we were able to accurately replicate the observed diurnal cycle of DMS in the MBL.Despite the expected low NO x concentration, a linear relationship between OH and solar flux, and hence J O( 1 D), yielded a better fit between observed and implied diurnal cycles (correlation coefficient over 0.9) than a square root relationship.The nitrate radical was considered in the DMS oxidation and found to be unimportant in VOCALS-REx.We cannot rule out BrO as a possible oxidant, however.An upper limit estimate of 1 pptv of BrO (daytime peak) would account for 30% of total DMS oxidation, lowering our effective OH to 1.0×10 6 molecules cm −3 .

1Figure 1 .
Figure 1.Time-series of DMS concentration and surface flux (top), and true wind speed and direction (bottom) from the RHB during VOCALS-REx.Elevated DMS flux usually corresponded to spikes in DMS w on the edges of localized eddies and high winds.The wind was consistently from the S/SE.

Fig. 1 .
Fig. 1.Time-series of DMS concentration and surface flux (top), and true wind speed and direction (bottom) from the RHB during VOCALS-REx.Elevated DMS flux usually corresponded to spikes in DMS w on the edges of localized eddies and high winds.The wind was consistently from the S/SE.

Figure 2 .
Figure 2. Examples of diurnal cycles in DMS concentration observed from the RHB,

Fig. 2 .
Fig. 2. Examples of diurnal cycles in DMS concentration observed from the RHB, along with solar flux measured from a shipboard radiometer.Maxima and minima in DMS were usually observed just after sunrise and just before sunset, respectively, as a result of continuous build up of the gas via air-sea exchange and daytime photochemistry.

Figure 3 .
Figure 3. Time-series of temperature contours from the radiosondes from the RHB, with the dark line indicating the inversion.Over a ~monthly timescale, the trend in the depth of the MBL along the E-W transect was relatively constant, deeper offshore (e.g.Oct 26 th and Nov 20 th ) than near the coast (e.g.Nov 3 rd and Nov 10 th ).The average temperature was 13 ºC in the middle of the MBL.

Fig. 3 .
Fig. 3. Time-series of temperature contours from the radiosondes from the RHB, with the dark line indicating the inversion.Over a ∼monthly timescale, the trend in the depth of the MBL along the E-W transect was relatively constant, deeper offshore (e.g. 26 October and 20 November) than near the coast (e.g. 3 and 10 November).The average temperature was 13 • C in the middle of the MBL.

Figure 4 .
Figure 4.A typical profile of the lower troposphere determined from the C-130 (12:24~12:35 UTC on Oct 25 th during Research Flight No. 5).DMS C130 decreased linearly with altitude in the MBL (the lower ~1300 m in this profile) and dropped to zero in the FT.A strong inversion atop the stratocumulus cloud deck (indicated by high liquid water content) was defined by sharp gradients in dew point and potential temperature.

Fig. 4 .
Fig. 4. A typical profile of the lower troposphere determined from the C-130 (12:24∼12:35 UTC on Oct 25 th during Research Flight No. 5).DMS C130 decreased linearly with altitude in the MBL (the lower ∼1300 m in this profile) and dropped to zero in the FT.A strong inversion atop the stratocumulus cloud deck (indicated by high liquid water content) was defined by sharp gradients in dew point and potential temperature.

5Figure 5 .Fig. 5 .
Figure 5. Averaged profile from the C-130 with altitude normalized to the in height and DMS C130 normalized to concentration from the lowest leg.Conce height z is related to the near-surface concentration by the parameterization 1 with being the DMS "decoupling" parameter and on average equaling to 0 Fig. 5. Averaged profile from the C-130 with altitude normalized to the inversion height and DMS C130 normalized to concentration from the lowest leg.Concentration at height z is to the nearsurface concentration by the parameterization 1α (z/z i ), with α being the DMS "decoupling" parameter and on average equaling to 0.2.

Figure 6 .
Figure 6.VOCALS averages of atmospheric DMS concentration and surface flux from the RHB in the latitude range of 20±2°S, as well as wind speed and inversion height.The ratio between DMS flux to concentration was largely constant, suggesting minimal time rate of change in the DMS field on a monthly timescale.Both the boundary layer height and wind speed were greater offshore.

Fig. 6 .
Fig. 6.VOCALS averages of atmospheric DMS concentration and surface flux from the RHB in the latitude range of 20±2 • S, as well as wind speed and inversion height.The ratio between DMS flux to concentration was largely constant, suggesting minimal time rate of change in the DMS field on a monthly timescale.Both the boundary layer height and wind speed were greater offshore.

7Figure 7 .Fig. 7 .
Figure 7. Multi-regression of daily DMS concentration from the RHB (colored circles) vs. Lat and Lon.Contours from the regression analysis show a gradient in DMS concentration that is orthogonal to the mean wind vector.The advective flux was thus minimal.The box with dashed lines defines the "VOCALS region."Fig. 7. Multi-regression of daily DMS concentration from the RHB (colored circles) vs. Lat and Lon.Contours from the regression analysis show a gradient in DMS concentration that is orthogonal to the mean wind vector.The advective flux was thus minimal.The box with dashed lines defines the "VOCALS region."

8Figure 8 .
Figure 8. DMS surface flux, column concentration, shortwave radiation, and cloud top measured from the RHB in the VOCALS region averaged to the time of day.The nighttime increase in DMS column concentration was approximately linear, enabling us to estimate an entrainment velocity of 4 mm sec -1 .

Fig. 8 .
Fig. 8. DMS surface flux, column concentration, shortwave radiation, and cloud top measured from the RHB in the VOCALS region averaged to the time of day.The nighttime increase in DMS column concentration was approximately linear, enabling us to estimate an entrainment velocity of 4 mm s −1 .

9Figure 9 .
Figure 9. Observed and implied DMS diurnal cycle: a) with OH linearly proportional to the solar flux; b) with OH proportional to the square root of the solar flux.A linear relationship between OH and solar flux yielded a better fit to the DMS diurnal cycle, despite the expected low NO x concentration.To investigate the importance of other oxidants, the OH-equivalent oxidant concentration was apportioned to OH, NO 3 and BrO.

Fig. 9 .
Fig. 9. Observed and implied DMS diurnal cycle: (a) with OH linearly proportional to the solar flux; (b) with OH proportional to the square root of the solar flux.A linear relationship between OH and solar flux yielded a better fit to the DMS diurnal cycle, despite the expected low NO x concentration.To investigate the importance of other oxidants, the OH-equivalent oxidant concentration was apportioned to OH, NO 3 and BrO.Even a minuscule amount of NO 3 was found to degrade the fit between the implied and observed DMS.BrO cannot be distinguished from OH based on the DMS diurnal cycle.For VOCALS-REx, the maximum DMS oxidation due to BrO was estimated to be 30%.