Ozone deposition to a coastal sea: comparison of eddy covariance observations with reactive air–sea exchange models

Abstract. A fast-response (10 Hz) chemiluminescence detector for
ozone (O3) was used to determine O3 fluxes using the eddy covariance
technique at the Penlee Point Atmospheric Observatory (PPAO) on the south
coast of the UK during April and May 2018. The median O3 flux was −0.132 mg m−2 h−1 (0.018 ppbv m s−1),
corresponding to a deposition velocity of 0.037 cm s−1
(interquartile range 0.017–0.065 cm s−1) – similar to the
higher values previously reported for open-ocean flux measurements but not
as high as some other coastal results. We demonstrate that a typical single
flux observation was above the 2σ limit of detection but had
considerable uncertainty. The median 2σ uncertainty of deposition
velocity was 0.031 cm s−1 for each 20 min period, which
reduces with the square root of the sample size. Eddy covariance footprint
analysis of the site indicates that the flux footprint was predominantly
over water (> 96 %), varying with atmospheric stability and, to
a lesser extent, with the tide. At very low wind speeds when the atmosphere
was typically unstable, the observed ozone deposition velocity was elevated,
most likely because the footprint contracted to include a greater land
contribution in these conditions. At moderate to high wind speeds when
atmospheric stability was near-neutral, the ozone deposition velocity
increased with wind speed and showed a linear dependence with friction
velocity. This observed dependence on friction velocity (and therefore also
wind speed) is consistent with the predictions from the one-layer model of
Fairall et al. (2007), which parameterises
the oceanic deposition of ozone from the fundamental conservation equation,
accounting for both ocean turbulence and near-surface chemical destruction,
while assuming that chemical O3 destruction by iodide is distributed over
depth. In contrast to our observations, the deposition velocity predicted by
the recently developed two-layer model of Luhar et al. (2018) (which
considers iodide reactivity in both layers but with molecular diffusivity
dominating over turbulent diffusivity in the first layer) shows no major
dependence of deposition velocity on wind speed and underestimates the
measured deposition velocities. These results call for further investigation
into the mechanisms and control of oceanic O3 deposition.



Abstract.
A fast-response (10 Hz) chemiluminescence detector for ozone (O 3 ) was used to determine O 3 fluxes using the eddy covariance technique at the Penlee Point Atmospheric Observatory (PPAO) on the south coast of the UK during April and May 2018. The median O 3 flux was −0.132 mg m −2 h −1 (0.018 ppbv m s −1 ), corresponding to a deposition velocity of 0.037 cm s −1 (interquartile range 0.017-0.065 cm s −1 ) -similar to the higher values previously reported for open-ocean flux measurements but not as high as some other coastal results. We demonstrate that a typical single flux observation was above the 2σ limit of detection but had considerable uncertainty. The median 2σ uncertainty of deposition velocity was 0.031 cm s −1 for each 20 min period, which reduces with the square root of the sample size. Eddy covariance footprint analysis of the site indicates that the flux footprint was predominantly over water (> 96 %), varying with atmospheric stability and, to a lesser extent, with the tide. At very low wind speeds when the atmosphere was typically unstable, the observed ozone deposition velocity was elevated, most likely because the footprint contracted to include a greater land contribution in these conditions. At moderate to high wind speeds when atmospheric stability was near-neutral, the ozone deposition velocity increased with wind speed and showed a linear dependence with friction velocity. This observed dependence on friction velocity (and therefore also wind speed) is consis-tent with the predictions from the one-layer model of Fairall et al. (2007), which parameterises the oceanic deposition of ozone from the fundamental conservation equation, accounting for both ocean turbulence and near-surface chemical destruction, while assuming that chemical O 3 destruction by iodide is distributed over depth. In contrast to our observations, the deposition velocity predicted by the recently developed two-layer model of Luhar et al. (2018) (which considers iodide reactivity in both layers but with molecular diffusivity dominating over turbulent diffusivity in the first layer) shows no major dependence of deposition velocity on wind speed and underestimates the measured deposition velocities. These results call for further investigation into the mechanisms and control of oceanic O 3 deposition.

Introduction
Tropospheric ozone is important due to its considerable effects on human health (Medina-Ramón et al., 2006), agricultural yields (Heck et al., 1982), and global warming (Stevenson et al., 2013). Dry deposition is a major sink of tropospheric ozone, comprising as much as 25 % of total loss from the troposphere (Ganzeveld et al., 2009;Lelieveld and Dentener, 2000;Pound et al., 2020). Deposition to the sea surface is the greatest source of uncertainty in global estimates Published by Copernicus Publications on behalf of the European Geosciences Union. 6916 D. C. Loades et al.: Ozone deposition to a coastal sea of total ozone dry deposition (Hardacre et al., 2015) due to deposition occurring at a slow and highly uncertain rate but over a vast area.
Ozone deposition flux is commonly parameterised according to Eq. (1) (Pacyna, 2008): where F is the flux in mol cm −2 s −1 , v d is the deposition velocity in cm s −1 , and [O 3 ] is the ozone concentration in mol cm −3 . In models, the deposition velocity is commonly calculated using a series of resistance terms, each defining barriers to deposition in separate layers (Wesely and Hicks, 2000): R a is the aerodynamic resistance, independent of the species being considered. R b represents the resistance through the quasi-laminar thin layer of air in contact with a surface -this varies with the species' diffusivity. Lastly R c is the surface resistance, which is typically the largest barrier to deposition for insoluble gases -roughly 95 % of total resistance in the case of ozone (Chang et al., 2004;Lenschow et al., 1982). There are few reported observations of ozone deposition to the sea surface. Early work to determine oceanic O 3 deposition velocity was either laboratory-based (Garland et al., 1980;McKay et al., 1992) or used box enclosure loss rate experiments in the field (Aldaz, 1969;Galbally and Roy, 1980). Such experiments are valuable in determining surface resistance (describing the affinity of a surface for absorbing a given gas) for ozone deposition. However, these experiments are limited in their ability to represent real-world physical processes such as turbulence at the air-sea interface. More recent flux measurements have been made with the eddy covariance method, which is the best way of observing fluxes in the atmospheric surface layer without perturbing it. Eddy covariance measurements have been made from coastal towers (Gallagher et al., 2001;Whitehead et al., 2009;McVeigh et al., 2010), aircraft (Lenschow et al., 1982;Kawa and Pearson, 1989), and ships (Bariteau et al., 2010;Helmig et al., 2012). The deposition velocities reported in the few eddy covariance studies over saltwater vary greatly: 0.01-0.15 cm s −1 , with wind speed dependencies evident in some measurements and not in others.
The reported eddy covariance measurements use two different techniques to measure ozone at high frequency, both utilising chemiluminescent reactions of ozone. In the instruments used for tower-based measurements (Gallagher et al., 2001;McVeigh et al., 2010;Whitehead et al., 2009), ozone is reacted with a coumarin-based dye on the surface of a silica gel disk. Aircraft (Kawa and Pearson, 1989;Lenschow et al., 1982) and ship-borne (Bariteau et al., 2010;Helmig et al., 2012) instruments have instead utilised the reaction between ozone and gas-phase nitric oxide.
Ozone deposition to the ocean depends both upon physical exchange, facilitated by diffusion and turbulence, and chemical reaction at the water surface (Chang et al., 2004;Fairall et al., 2007;Luhar et al., 2018). Iodide in seawater has been identified as a key reactant (Garland et al., 1980). There has been considerable recent progress in understanding the global distribution of oceanic surface iodide Macdonald et al., 2014;Sherwen et al., 2019). However, there has only been one report of the dependence of the iodide-ozone rate constant with temperature (Magi et al., 1997), and this remains a considerable uncertainty in global models. Dissolved organic material (DOM) has been suggested to be of similar importance for ozone deposition as iodide (Martino et al., 2012;Shaw and Carpenter, 2013), especially given its enrichment in the sea-surface microlayer (SML) (Zhou and Mopper, 1997). The complex and variable composition of DOM makes assessing its global reactivity with ozone a challenge.
Early work by Garland et al. (1980) formulated a description of ozone loss to seawater based on surface properties: where a is the reactivity of iodide with ozone, D is the diffusivity of ozone in water, and v dw is the waterside deposition velocity, related to surface resistance (R c ) by where α is the dimensionless solubility (liquid/gas) of ozone in water. This interpretation incorporates the chemical properties of the reaction but neglects turbulent diffusion and underestimates the deposition velocity in cold water.  allowed deposition velocity to vary with oceanic turbulence by considering the O 3 -iodide reaction beyond the molecular sublayer, obtaining the dependence K 0 and K 1 are modified Bessel functions of the second kind, of order 0 and 1 respectively, and where κ is the von Kármán constant (∼ 0.4), and u * w is the waterside friction velocity. This is sometimes referred to as a one-layer model, due to the assumption that reactivity is uniform with depth. This one-layer approach has been reported to match observations better than a using a fixed-surface resistance term but overestimates deposition velocity by a factor of 2-3 in colder waters, where the rate of reaction between ozone and iodide is slower. An alternative, two-layer scheme is explored by  and expanded upon by Luhar et al. (2017). The authors consider an enhancement in reactivity in a very thin layer (reaction-diffusion sublayer) at the surface, while the water beneath has only very minor background reactivity. In a revision of the two-layer scheme, Luhar et al. (2018) assumed turbulent transfer to be negligible compared with chemical removal of ozone within the reaction-diffusion sublayer but with both turbulence and chemistry accounted for in the layer beneath, defining the waterside deposition velocity: The terms ψ, ξ δ , and λ in Eq. (7) all vary according to the reaction-diffusion sublayer depth, δ m : Equations (7)-(10) describe the two-layer scheme that will be discussed in this work. The method of assigning a value to δ m is discussed by Luhar et al. (2018), who found that a fixed depth of 3 µm was a good fit to the data of Helmig et al. (2012). When a variable reaction-diffusion sublayer depth was considered as being proportional to the reactiondiffusion length scale (l m = √ D/a), Luhar et al. (2018) found it necessary to multiply l m by a factor of 0.7 to obtain a δ m value that fitted reasonably with observations. Pound et al. (2020) were however able to obtain a good fit to observational data without this factor by using the oceanic iodide parameterisation of Sherwen et al. (2019) in place of that of Macdonald et al. (2014). Pound et al. (2020) define the reaction-diffusion layer depth according to Eq. (11).
The dependence of deposition velocity with wind speed (or friction velocity, u * , which scales linearly with wind speed over the ocean) within the Fairall et al. (2007) and Luhar et al. (2018) models is markedly different, and it is not clear which is a better fit to existing observations. The deposition velocity estimated by the one-layer model of Fairall et al. (2007) increases linearly with friction velocity and compares favourably with the TexAQS06 and GOMECC07 cruises (Helmig et al., 2012). However, observations made during other cruises discussed by Helmig et al. (2012) show no dependence on friction velocity. The two-layer model of Luhar et al. (2018) predicts almost no influence of friction velocity on deposition velocity, except at very low (< 2 m s −1 ) wind speeds. Better characterisation of the effects of wind speed and the chemical composition of the surface water on ozone deposition velocity to the sea surface would significantly improve our understanding of the global tropospheric O 3 budget (Ganzeveld et al., 2009;Pound et al., 2020). Here we present coastal ozone flux measurements made at Penlee Point Atmospheric Observatory (PPAO; https:// www.westernchannelobservatory.org.uk/penlee/, last access: 10 December 2020) on the south-west coast of the UK using a fast-response gas-phase chemiluminescence detector (CLD). Factors affecting the variation and uncertainty in the observed deposition velocity are discussed, including the effects of changing relative contributions from sea and land within the flux footprint.
2 Materials and methods

Measurement location
The PPAO is situated on a headland just south-west of Plymouth, UK (50 • 19.08 ′ N, 4 • 11.35 ′ W). The observatory is located 11 m a.m.s.l., with an extendable mast on the roof. It lies 30-60 m away from the sea, depending on the tide, with the intervening land predominantly bare rock with some grass immediately surrounding the tower. For the work presented here, the top of the tower was extended to 19 m a.m.s.l. The dominant wind directions are from the south-west, followed by the north-east (Fig. 1). The focus of this work is the south-west (180-240 • ) wind sector, which brings in air from the Atlantic Ocean and English Channel to the site (Yang et al., 2016).

Experimental set-up
The ozone chemiluminescence detector was adapted from an Eco Physics ® CLD 886 NO x detector, working on the same principle as the instrument used by Helmig et al. (2012). A supply of excess NO is introduced to the sample, which reacts with O 3 to generate NO 2 in an excited state. The relaxation process leads to emission of a photon that is amplified and detected using a photomultiplier tube (PMT). In order to maintain a low number of dark counts, the PMT is cooled to −5 • C by a Peltier cooler. Clean dry air is continuously pumped over the PMT to avoid the build-up of water (Fig. 2).
Sample air was drawn from the top of the tower through ∼ 10 m of 3/8 ′′ PFA tubing by a vacuum pump at 13.5 SLPM. This maintained a turbulent flow in the main sampling line (Reynolds number ∼ 3000). A flow of 300 mL min −1 was drawn from this sample line through 1/8 ′′ PFA tubing and into the analyser using an internal vacuum pump (Fig. 2), limited by a critical orifice. Before entering the analyser, the sample air was first passed through a dryer consisting of 60 cm of Nafion™ tubing coiled in a container of desiccant (indicating Drierite) to reduce humidity. A threeway solenoid valve allowed for a sample of indoor air passed through a charcoal filter to remove O 3 to record an instrument zero. A 50 mL min −1 flow of 2 % NO in N 2 was supplied separately to the analyser at a pressure of 4 bar through approximately 1.5 m of 1/8 ′′ PFA tubing. The NO and O 3  were then mixed immediately before the reaction chamber (at ∼ 26 mbar pressure) and the resulting chemiluminescence detected by the PMT.
The CLD counts were logged at 10 Hz and converted into ozone mixing ratios using the signal from a colocated, recently calibrated 2B Model 205 Dual Beam Ozone Monitor. The CLD sensitivity was determined to be 240 counts s −1 ppbv −1 and showed no obvious dependence on ambient humidity (Fig. S1 in the Supplement), providing evidence for the efficacy of the dryer. Instrument dark counts were 480 ± 40 count s −1 , leading to a 10 Hz signal-to-noise ratio of 33 for the average 46 ppbv O 3 measured during this work.
Three-dimensional wind data were obtained from a Gill WindMaster Pro 3D sonic anemometer at 10 Hz. Humidity, air pressure, and temperature data were logged at 0.25 Hz from a Gill MetPak Pro. Vertical wind data were adjusted by +16.6 % and +28.9 % in magnitude for positive and negative values, respectively, in line with the corrections recommended for a reported firmware bug in the Gill WindMaster instruments (http://gillinstruments.com/data/ manuals/KN1509_WindMaster_WBug_info.pdf, last access: 10 December 2020).

Pre-flux processing
The eddy covariance method (EC) relies on the simultaneous measurement of vertical wind speed (w) and the relevant scalar (in this case, ozone dry mixing ratio). These values were determined at 10 Hz in order to resolve the full range of eddies responsible for vertical ozone transport. It is necessary to calculate eddy covariance fluxes over a suitable averaging interval to reduce random noise and capture transport from large eddies whilst avoiding too long a period such that non-turbulent transport and non-stationarity become more important. An averaging time of around 30 min is often recommended (Foken, 2008). Previous measurements of O 3 flux have used averaging intervals from 10 min (Helmig et al., 2012) to 1 h (Gallagher et al., 2001), and a 20 min pe-riod was chosen for this work. Prior to the flux calculation, data were despiked using a median filter despiking method (Brock, 1986;Starkenburg et al., 2016) using an order of N = 4 (9 points in a window). This involves binning the differences from the normalised data into exponentially more bins until bins exist within the range of the histogram that have zero values. Difference values beyond these empty bins are then identified as spikes and removed. For the flux calculation, data were linearly detrended to determine deviation from the mean within the averaging interval. A double rotation was applied to the wind data in each averaging interval to align the u axis with the mean wind and remove any tilt in the wind vector, resulting in a mean vertical wind of zero. A planar fit method (Wilczak et al., 2001) was considered as an alternative to double rotation, but a single set of planar fit coordinates was found to be inappropriate for the Penlee site. Instead, an approach defining separate planar fit coefficients for each 10 • sector (e.g. Mammarella et al., 2007;Yuan et al., 2011) was used, resulting in a median 7 % increase in flux compared with the double rotation method. This sector-wise approach does, however, introduce discontinuous adjustments at the boundaries of the somewhat arbitrarily chosen sectors. A possible solution is to define the tilt angle as a continuous function of the wind direction (Ross and Grant, 2015), but given the minor difference between the fluxes resulting from the sector planar fit and double rotation methods, the latter was chosen for this work.
Due to the Nafion™ dryer and the fixed temperature and pressure of the reaction chamber, density corrections known as WPL (Webb-Pearman-Leuning) corrections (Webb et al., 1980) were unnecessary for determining an accurate ozone mixing ratio. However, the presence of water vapour was taken into account for the determination of ancillary parameters such as the Obukhov length used in footprint modelling. It should be noted that in addition to its effect on mixing ratio, water vapour also quenches the chemiluminescence of the reaction of NO with O 3 . This can be dealt with either by determining the instrument sensitivity over a range of water vapour conditions (at the cost of some sensitivity) and applying a correction or by sufficiently drying the sample air. The latter approach was taken here. Despite a range of humidity (2.8 × 10 −5 -1.8 × 10 −2 mol mol −1 ; Fig. S1) over the 42 d observation period, the two instruments compare well when using a fixed sensitivity for the CLD. The sensitivity value of 240 ppbv s −1 also compares favourably to 213 ppbv s −1 , which was estimated using a supply of known ozone in the absence of water vapour (supplied from a calibrated Thermo model 49i-PS ozone primary standard) during lab tests prior to deployment. These results suggest that the dryer removed any major water vapour effect on the detection of ozone concentration and flux.
The sample air must travel to the detector through the inlet tubing, which introduces a time lag relative to the instantaneously measured wind data. The two datasets must therefore be realigned in order to calculate the covariance. A cross- Figure 3. Example cross correlation function (CCF) for ozone and vertical wind on 10 April. The negative peak minimum indicates that ozone data lag 3.9 s behind the wind data. Dashed blue lines denote the 95 % significance threshold. correlation function (CCF) was calculated at different time lags, with a high-pass Butterworth filter applied to the input values. The presence of a negative peak in the resulting CCF spectrum indicated a strong anticorrelation between ozone concentration and vertical wind, characteristic of deposition. Individual CCF plots were noisy and gave scattered lag values, with a high density around 4 s. Daily average CCF plots indicated clear peaks in all but one case and drifted from 3.9 to 4.1 s over the course of the experiment (e.g. Fig. 3). This is likely a consequence of slight particulate build-up in the sample line filters over the course of the measurements. Individual 20 min flux interval lags were accepted if they fell between 3.5 and 4.5 s to allow for some variability in conditions (e.g. atmospheric pressure), vacuum pump strength, etc. Lags that fell outside of these boundaries were then set to a value determined by a linear fit of the accepted data (Fig. S2). Simply setting the lag to 4 s in all instances was found to decrease the flux by 5 % relative to the method used here (CCF lag determination maximises the flux magnitude). The expected lag was also estimated from the inlet set-up: a 13.5 L min −1 flow rate through 10 m of 3/8 ′′ tubing plus a 300 mL min −1 sample flow through 2 m of 1/8 ′′ tubing yields a calculated lag of 4.2 s, similar to the CCF-determined values.
Following these steps, the ozone flux was calculated on a 20 min basis using eddy4R , with a workflow customised for our measurements. Flux values were then used to determine the deposition velocity according to Eq. (1). The molar flux was calculated using the instantaneous vertical wind, ozone mixing ratio, and density of dry air. Similarly, the ozone concentration used in Eq. (1) was calculated for dry air using the mean ozone mixing ratio for the averaging interval to avoid introducing a dependence on water vapour to the deposition velocity.

Data selection
A series of selection criteria were applied to the calculated 20 min flux data. Firstly, periods with more than 10 % missing data were excluded. Missing data were most commonly caused by periods of maintenance or when heavy rain disrupted the sonic anemometer readings. Data were also selected by wind direction -only data between the true wind direction of 180 and 240 • were accepted to avoid observing deposition on the headland to the north-west.
A selection criterion based on ozone variation, as used by Bariteau et al. (2010), was introduced to avoid periods of non-stationarity i.e. significantly different conditions within an averaging interval (such as a sudden change in the air mass passing by the sensor or a change in wind direction). Data were excluded if the ozone concentration drifted significantly (> 6 ppbv in 20 min) or if the standard deviation in ozone was above 2 ppbv. Data with a standard deviation in wind direction of > 10 • were also removed to avoid nonstationarity of wind, as performed by Yang et al. (2016) for the same site.
Flux footprint analysis was used to investigate the potential for land influence within the footprint area. Land influence may increase as the footprint contracts during the unstable conditions coinciding most frequently with low wind speeds. Using the flux footprint parameterisation of Kljun et al. (2015), footprints were calculated for each averaging interval. These were defined using tide-adjusted measurement height, roughness length, friction velocity, wind speed (and direction), crosswind variability, and stability conditions, then aggregated into 1 m s −1 wind speed bins. Using these aggregated footprints, the percentage of land area contribution in the footprint area was estimated to increase from 1 %-2 % at high wind speeds, when atmospheric stability was predominantly neutral, to 15 % at winds below 2 m s −1 , when the atmosphere was generally unstable (Fig. 4). It should be noted that the footprint model is designed for flat homogeneous terrain -not a heterogeneous coastal site. This will therefore introduce some additional uncertainty to footprint extent and land coverage, beyond that inherent to the parameterisation.
where z 0 is the roughness length in m, z is the measurement height in m, κ is the von Kármán constant, U is the wind speed in m s −1 , u * is the friction velocity in m s −1 (determined directly from the covariance of the fluctuations of horizontal and vertical wind components), and m z L is the integral of the universal function (with dimensionless Obukhov stability z/L calculated from observed heat flux and u * ), de- fined as (Businger et al., 1971;Högström, 1988) where Roughness lengths at high wind speeds are scattered approximately around 0.0002 m, which is expected for an open sea fetch (World Meteorological Organisation, 2008), but a large increase can be seen at wind speeds < 3 m s −1 (Fig. 5). Roughness length can be slightly higher during very low wind speed, low u * conditions (Vickers and Mahrt, 2006). However the scale of the increase at the PPAO is indicative of a surface with more roughness elements, such as the rocks and grass found on the headland. Greater inaccuracies in the double rotation method at low wind speeds can mean that the removal of horizontal wind from the rotated vertical component is incomplete, further contributing to the elevated surface roughness values. Additionally, higher deposition velocities were observed during periods of very low winds, contrasting with the trend of increasing deposition velocity with wind speed proposed by Chang et al. (2004) and observed during open-ocean cruises by Helmig et al. (2012). Yang et al. (2016Yang et al. ( , 2019a) observed a similar enhancement in CO 2 transfer at low wind speeds and chose to filter out low wind speed data. The above discussion indicates the need for a filter to exclude land-influenced flux data. A wind speed filter of > 3 m s −1 was used in this work, whereby median fluxes and deposition velocities are reported for the whole dataset  (or model work), though filters on the basis of z 0 could also be used to a similar effect. Previous eddy covariance work on CO 2 flux over land has applied filters on the basis of friction velocity (e.g. Barr et al., 2013) to avoid underestimation of flux during periods of poorly developed turbulence, especially at night (Aubinet, 2008). However past measurements of oceanic ozone deposition velocity have not reported using such a filter (Gallagher et al., 2001;Helmig et al., 2012;McVeigh et al., 2010) because very low wind speeds and u * are uncommon over the ocean. For our data, removing data with u * < 0.1 cm s −1 in addition to the criteria in Table 1 made no difference to the observed median deposition velocity. Therefore, given that a wind speed filter was already applied, no additional friction velocity filter was included.
Longer averaging intervals than 20 min were also considered, but 60 min averaging caused a large loss of data to the selection criteria. Missing data, as well as the nonstationarity of wind and ozone, contributed to an overall 23 % reduction in total data accepted when using 60 min averaging compared with 20 min averaging. This shorter averaging time was therefore retained.

Flux uncertainty
Flux uncertainty can be estimated in a number of ways, and in this work we make use of an empirical method (Langford et al., 2015;based on Wienhold, 1995) and a theoretical method (Fairall et al., 2000). In the method of Langford et al. (2015), cross-correlation functions (discussed in Sect. 2.3) are calculated at a series of improbable lag times (150-180 s) for each averaging interval, and the root mean squared deviation of these values is taken to be representative of the random error of the flux measurement. Alternatively, the theoretical estimation of flux uncertainty of Fairall et al. (2000) can be made according to the expression where F X is the flux uncertainty, w' is the instantaneous vertical wind velocity fluctuation, X' is the instantaneous ozone fluctuation, σ w is the standard deviation in vertical wind velocity, σ X is the standard deviation in ozone concentration, T is the length of the averaging interval in seconds, and τ wca is the integral timescale for the instantaneous covariance time series w ′ X ′ . A factor with a value of 1-2 is sometimes also included in the numerator of Eq. (16) to reflect uncertainty in this relationship (Blomquist et al., 2010). A factor of 1 is used in this work. The integral timescale τ wca can either be determined from a flux co-spectrum peak frequency, or empirically according to where z is the measurement height in metres, U is the mean wind speed, and b is a value that varies with atmospheric stability. The value of b has been reported variably as 0.3-3 for near-neutral conditions (Blomquist et al., 2010;Lenschow and Kristensen, 1985) and on the order of 10-12 for convective or unstable conditions (Blomquist et al., 2010;Fairall, 1984). The application of these methods to our data is discussed further in Sect. 3.5.  (Figs. 6 and 7). The resulting distribution of v d values was compared to that obtained with the lag time set to 180 s and was significantly different from the results of the disjoined data (Kolmogorov-Smirnov test, p < 0.001; Fig. S3), rejecting the null hypothesis that the two sets of values could be taken by chance from the same distribution. This confirms that the experimental set-up used here has a sufficiently low limit of detection to discern the flux from noise over the whole duration of the measurements. The 2σ flux uncertainty was determined for each 20 min period (see Sect  (Gallagher et al., 2001). These measurements were carried out at Mace Head (west Ireland), Weybourne (east UK), and Roscoff (north-west France) respectively. Our median v d of 0.037 cm s −1 is towards the upper end of previous work, though much lower than Gallagher et al. (2001).

Wind speed dependence
Reports on the dependence of v d on wind speed and friction velocity (u * ) have varied considerably; the cruise observations discussed by Helmig et al. (2012) 2010) reported a similar trend, fitting an exponential curve to their data. Lastly, deposition velocity during two of the five cruises reported by Helmig et al. (2012) increased with increasing wind speeds. The dependence observed in our data is discussed further in Sect. 4.2.

Land influence
Aggregate flux footprint analysis of the PPAO site (as discussed in Sect. 2.4) shown in Fig. 9 suggests that the spatial contribution of land surfaces to our observed deposition velocity is approximately 3.9 %. However, deposition velocity to land is typically greater than to the ocean, amplifying the potential influence of land deposition on our data. If our observations were adjusted for 3.9 % spatial contribution of grassland (v d ≈ 0.25 cm s −1 , median land deposition value from datasets analysed by Hardacre et al., 2015), then our calculated median coastal water v d would be 0.028 cm s −1 (23 % lower than we measured). In reality the terrain is a mixture of grassland and rocky shoreline, varying in extent with the tide, so the land v d discussed above may be an overestimate. It should also be noted that the grassland deposition velocity value used here is itself prone to considerable uncertainty due to the variability of the datasets used in the model. Although there are insufficient data over the land to the north-west to reliably determine a v d value to the land around the PPAO, an estimate can be made by obtaining a least-squares solution using the land cover determined in Fig. 4 and the observed v d values in Fig. 8. Data from wind speeds > 14 m s −1 were not used (only four data points). Using all data from 2-13 m s −1 yielded values of 0.167 ± 0.080 and 0.034 ± 0.016 cm s −1 for land and sea respectively, suggesting a lesser effect from land than using the fixed value from Hardacre et al. (2015). Given that the land contribution in Fig. 4 does not stabilise until 9 m s −1 , it is possible that constant v d between 4 and 10 m s −1 wind speeds (Fig. 8) may be a consequence of land influence and wind speed enhancement counteracting one another. Estimated water-only v d values, calculated by subtracting the product of the land fraction and the land v d value from the measured v d , are shown in Fig. 10.
It is worth reiterating that the Kljun footprint model is designed for use in homogenous environments, which is not the case for our site. Furthermore, the double rotation applied to the wind data will result in varying pitch angles relative to the water surface, introducing a dependence of the footprint extent on this pitch angle. These limitations may be important for work relying on direct interpretations of the flux footprint, such as comparisons to emissions inventories (Squires et al., 2020;Vaughan et al., 2017). In contrast to an inventory comparison, we only use the flux footprint model to develop a strategy for robust data selection and generate an aggregate footprint from several individual footprints. This approach follows the works of Amiro (1998), Göckede et al. (2006Göckede et al. ( , 2008, Kirby et al. (2008), Metzger (2018, and Xu et al. (2018), who have demonstrated the utility of aggregation for deriving robust footprint-based metrics in heterogeneous environments.

Tidal influence
The PPAO site flux footprint also experiences periodic variations associated with the tide, which alters the effective measurement height and changes the land type in the footprint when the shoreline is exposed. Whitehead et al. (2009) provide an extreme example of this, reporting v d increasing from 0.030 cm s −1 at high tide to 0.21 cm s −1 at low tide during the day. This large variation in their work was a consequence of a 9 m tidal range exposing the sea floor up to 3 km from the shore. At Penlee, the tide also causes periodic movement of the river plume around the headland, altering the salinity and composition of the surface water (Yang et al., 2016). This altered composition could affect the reactivity of ozone at the sea surface. Such effects will be examined in future work. Tower height above the water was determined for all flux calculations using tidal data from the British Oceanographic Data Centre (BODC), measured approximately 6 km upstream. Periodograms were also used to look for periodic variation in deposition velocity from exposed shoreline or riverine water, but none could be identified above the variability in the data. We note that previous measurements of air-sea exchange of momentum (Yang et al., 2016), CO 2 (Yang et al., 2019a), and sea spray (Yang et al., 2019b) at the PPAO were also unable to identify tidal cycles in the data. Gallagher et al. (2001) report a tentative (though statistically insignificant) diurnal cycle for coastal water during observations made at Weybourne in East Anglia, UK. However, no diurnal variability was observed in the PPAO O 3 flux data (as might be expected due to deposition to land), again implying minimal land influence in our filtered observations.

Measurement uncertainty
To understand the variability in our v d observations, a flux limit of detection was obtained empirically according to the method of Langford et al. (2015) (Sect. 2.5). Limits of detection were calculated for each averaging interval due to its dependence on wind speed and atmospheric stability, giving a median 2σ flux limit of detection of 0.113 mg m −2 h −1 . At the average ozone concentration of 48 ppbv, this equates to a deposition velocity of 0.031 cm s −1 , with 305 of the 491 averaging intervals exceeding their individually determined 2σ limit of detection.
To determine a theoretical uncertainty using Eq. (16), the peak frequency of the co-spectrum shown in Fig. 11 (0.07 Hz) was used to determine τ wca as approximately 2.2 s during near-neutral conditions and wind speeds of 12.1 m s −1 . Using Eqs. (17) and (18), this corresponds to a value for b of 1.5, similar to the literature values for nearneutral conditions (Blomquist et al., 2010;Lenschow and     . Average ozone flux co-spectrum for the 17 April, normalised to area = 1, shown in blue with a smoothed local regression (LOESS, dashed line) and 95 % confidence interval (blue shading). Wind speeds were 10.3-12.3 m s −1 , and dimensionless Obukhov lengths were 0.14-0.17, representing near-neutral, slightly stable conditions. Expected co-spectral shape predicted by Kaimal et al. (1972) shown in black. Kristensen, 1985). Since individual 20 min co-spectra were too noisy, this b value was used with Eq. (18) to determine τ wca for each 20 min period. It should be noted that the value of b is stability-dependent. However, since stability was nearneutral for most periods (z/L = −0.39 to 0.15, 20th-80th percentile), the effects of varying stability on b are expected to be small.
Using these integral timescales, a theoretical flux uncertainty can be calculated for each averaging interval using Eq. (16). The theoretical values obtained were much higher than those found empirically -the median theoretical 2σ limit of detection was 0.241 mg m −2 h −1 compared with the empirical value of 0.113 mg m −2 h −1 . We note however that this is an approximation, derived from the work of Lenschow and Kristensen (1985), who multiplied the right-hand side of Eq. (16) by 2 to derive an upper limit on flux uncertainty.
Equation (16) demonstrates how the variability of ozone and of vertical wind within averaging intervals are directly related to uncertainty in the measured flux. White noise in the wind measurement is expected to be very small, whereas random noise in the ozone instrument likely represents a significant contribution to the total variance of ozone observed at 10 Hz. Given the relatively low sensitivity of the instrument used in this work (240 counts ppbv −1 s −1 compared to 2800 counts ppbv −1 s −1 reported by Helmig et al., 2012), autocovariances were calculated for each averaging interval using the 10 Hz ozone data to examine the extent to which variance in ozone concentration is caused by instrument white noise. White noise only correlates with itself at zero lag time, so it can be estimated from the difference between the first and second points in an autocovariance plot (Blomquist et al., 2010). Instrument white noise derived using this approach was found to contribute 45 %-98 % to the total ozone variance (10th-90th percentile), with a median σ noise of 1.4 ppbv. A more sensitive ozone instrument could therefore significantly improve the flux uncertainty at a 20 min averaging interval.
Besides the random uncertainty discussed above, systematic errors are also worthy of some consideration, specifically, whether the highest and lowest frequencies of turbulence have been adequately observed. High-frequency information can be lost if measurements are made too infrequently or if the sample is attenuated significantly in the sample tubing. Measurements at 10 Hz, as performed here, are widely considered sufficient to observe this high-frequency structure. Sensor separation was minimised by locating the sample inlet directly beneath the sonic anemometer (∼ 20 cm below). Laminar flow was also avoided through the length of the sample line (Reynolds number = 3000). As a result, the co-spectrum in Fig. 11 shows no major loss of highfrequency information compared to theory. Since fluxes were calculated over 20 min averaging intervals using linear detrending, there is also a chance that low-frequency information may not be fully observed. Firstly, using a simple block average in place of linear detrending had little effect on the median flux observed (+1.7 %), implying that linear detrending is not causing much low-frequency information loss. Using an averaging interval of 1 h instead of 20 min gave a slightly larger magnitude flux (+4.1 %) as well. However, the longer period led to much greater data loss (22 %) to the selection criteria in Sect. 2.4; hence the 20 min average was used for this work. This suggests that any low-frequency loss is approximately 5 % of the total flux -a small amount relative to the calculated 2σ random uncertainty (85 %).

Model comparison
For the average meteorological conditions observed during this work, the one-layer model of Fairall et al. (2007) predicts a deposition velocity of 0.037 cm s −1 , assuming reaction of ozone with iodide only. Here, one layer refers to considering the water column to have uniform reactivity to ozone with depth. This is not the same as considering the chemical reaction only in the reaction-diffusion sublayer and both chemical reaction and turbulent transfer in the layer beneath (the two-layer model). By contrast, the revised two-layer model of Luhar et al. (2018) predicts a deposition velocity of 0.018 cm −1 for the same conditions using a reaction-diffusion sublayer (δ m ) of 4.2 µm, parameterised using Eq. (11). An iodide concentration of ∼ 600 nmol dm −3 would be necessary to yield the observed deposition velocity -much higher than a typical oceanic value of ∼ 80 nmol dm −3 . However, DOM (Shaw and Carpenter, 2013), chlorophyll (Clifford et al., 2008), andsurfactants (McKay et al., 1992) have also been shown to increase ozone deposition velocity. Therefore the effective pseudo-first-order rate constant for the reaction of ozone with water, a, is likely to be higher than accounted for by iodide alone. Chang et al. (2004) defined this total reactivity as where a is the effective pseudo-first-order rate constant for the reaction of ozone with water, and k i and C i are the second-order rate constant and concentration of species i, respectively. We include an estimate of the effects of DOM reactivity using a typical oceanic DOM concentration of 52 µmol dm −3 (Massicotte et al., 2017) and a rate constant of 3.7 × 10 −6 dm 3 mol −1 s −1 (average of the values reported by Sarwar et al., 2016, andColeman et al., 2010). Doing so increases a from 544 to 737 s −1 and leads to average deposition velocities for our field campaign of 0.048 and 0.028 cm s −1 for the models of Fairall and Luhar, respectively. The magnitude of the effect of DOM on O 3 deposition velocity remains highly uncertain due to the uncertainties in how O 3 interacts with DOM and surfactants, variability in the sea-surface microlayer (SML) composition, and the effect of temperature. The coastal waters near the PPAO experience large phytoplankton growth during the spring bloom (Cushing, 1959;Smayda, 1998), and the organic content and composition of the SML could be very different compared to the open ocean. The seasonal and spatial variations in these O 3reactive substances could in turn drive differences in ozone deposition velocity. For example, Bariteau et al. (2010) reported v d increasing from 0.034 to 0.065 cm s −1 as the waters changed from open ocean to coastal during the TexAQS-2006 cruise. It is unclear how much of the observed gradi-ent is a result of SML composition or of terrestrial influence. Similarly, the model of Ganzeveld et al. (2009) underestimated coastal ozone deposition velocities when DOM reactivity was omitted, suggesting that this may be a particularly important factor in coastal environments. While the model of Fairall et al. (2007) appears to match our observed v d well, it is possible that this is a consequence of some missing reactivity. Inclusion of DOM causes the one-layer model to overestimate v d , as reported by Luhar et al. (2018).

Wind speed dependence
In their discussion on wind speed dependence, Helmig et al. (2012) found that their data fit reasonably well with the parameterisation of Fairall et al. (2007): where α is the dimensionless solubility of ozone in water, a is the effective rate constant for the reaction of ozone with molecules in the surface water in s −1 , D c is the molecular diffusion coefficient of ozone in water in m 2 s −1 , κ is the von Kármán constant (0.4), and u * w is the waterside friction velocity in m s −1 . The fit shown in blue in Fig. 12 was determined using parameter values relevant to the experiment at the PPAO, with u * w derived from u * , assuming atmospheric surface stress to be equal to the waterside surface stress (Luhar et al., 2017): where ρ air and ρ water are the densities of air and water respectively. α, a, and D c were determined empirically according to Eq. (22) (Morris, 1988), Eq. (23) (Magi et al., 1997), and Eq. (24) where T s is the sea-surface temperature (in K), and [I − ] is the aqueous iodide concentration in mol dm −3 . We note that Eq. (23) only accounts for the reactivity of ozone with iodide in the sea surface. Other species present in the SML have also been shown to react with ozone (Martino et al., 2009;Shaw and Carpenter, 2013), but given the uncertainty surrounding their reactivity and any temperature dependence, they have been omitted here. Fixed T s (284 K) and [I − ] (85 nmol dm −3 ) values from April-May 2018 and representative of the footprint of PPAO  were used to determine α, a, and D c and thus v d (cm s −1 ) using Eq. (20) (dashed blue line in Fig. 12). This can be simplified to In comparison, the linear fit (dashed red line in Fig. 12) of our experimental 20 min v d values against u * (with standard errors) is v d measured = (0.02017 ± 0.00570) + (0.07537 ± 0.01953)u * .
Our results therefore show comparable but slightly lower dependence on friction velocity (and therefore also wind speed) than predicted by the parameterisation of Fairall et al. (2007). Comparison of our data to this parameterisation yielded a root mean square error (RMSE) of 0.0522 cm −1 and a mean bias of 0.0020 cm s −1 (a positive bias here denoting observations greater than the model). Given the assumptions of the simplified model (Eq. 20) and the uncertainties in various parameters, not least the rate constant for the reaction of O 3 with I − (e.g. Moreno and Baeza-Romero, 2019), this agreement is perhaps surprising. The two-layer model of Luhar et al. (2018) for the same data is shown in black in Fig. 12. Considering only iodide reactivity (i.e. omitting any enhancement in the reaction rate due to the presence of organic material in both models), this model appears to under-predict deposition velocity compared with the one-layer model of Fairall et al. (2007) and lacks any major dependence on wind speed except during very calm conditions. Comparison of our data to the two-layer model gave a higher RMSE and mean bias (0.0584 and 0.0247 cm s −1 respectively).
The two-layer model is set up to account for ozone reactions with chemical species other than iodide. Inclusion of these additional reactions would increase the predicted deposition velocity to be more similar to our observations. However, the two-layer model also predicts that v d does not strongly depend upon variations in wind speed, which is in contrast with our observations.

Summary and conclusions
An ozone chemiluminescence detector adapted from an Eco Physics ® CLD 886 NO x detector was used to measure the ozone deposition velocity to the sea surface at a coastal site near Plymouth, on the south-west coast of the UK. The median observed deposition velocity was 0.037 cm s −1 , comparable with previous values from tower-based measurements of 0.025 cm s −1 (McVeigh et al., 2010) and 0.030 cm s −1 (Whitehead et al., 2009). Furthermore, our data are at the upper end of the values obtained by Helmig et al. (2012) during ship-based, open-ocean measurements (0.009-0.034 cm −1 ). Cross-covariance was used to empirically determine a 2σ limit of detection for the O 3 flux for each averaging interval. This limit of detection had a median value of 0.113 mg m −2 h −1 and was exceeded in 305 out of 491 flux intervals. Autocovariance of high-frequency ozone data indicated that instrument noise was a significant component in the observed ozone variability (45 %-98 %), and lowering the noise level would reduce the flux uncertainty.
In moderate to high winds, the observed deposition velocity showed a linear dependence on friction velocity in the mean. This is comparable to that predicted by the one-layer model of Fairall et al. (2007) considering only ozone-iodide reaction. However, including estimated (but unverified) contributions from ozone-DOM reactions causes the one-layer model to overpredict the observations.
For the conditions encountered during the campaign, the two-layer model of Luhar et al. (2018) yields a v d of 0.018 cm s −1 with iodide reaction only and 0.026 cm s −1 with reactions of both iodide and contributions from DOM. While the latter value is close to our median observation, the two-layer model does not reproduce the observed wind speed dependence in v d .
Elevated deposition velocities were observed at low wind speeds, contrary to predictions (Chang et al., 2004) and to previous observations (Helmig et al., 2012). We attribute this observation to a contribution to v d from land within the footprint during periods of low wind. Periods with wind speeds > 3 m s −1 (corresponding to approximately < 10 % land cover in the footprint) were used to evaluate v d . However, the possibility of land influence could not be completely removed, with our oceanic v d estimates potentially overestimated by 8 %, even after wind speed filtering. The potential for tidal effects on v d (exposing shoreline and input of river water with different chemical composition) was also examined, though no clear periodicity could be observed, either at the tidal frequency or on a diurnal timescale.
Future work will link the properties of the sea-surface microlayer in the footprint area to observed O 3 fluxes. A longer time series with more observations of microlayer chemical composition may help to elucidate the influence of biogeochemical parameters, seasonal variation, and wind speed dependence, which have not been definitively characterised to date.
Author contributions. Experimental work was carried out by DCL, TGB, and MY. DCL also conducted the formal analysis and visualisation of the results, with relevant supervision from TGB and MY. SM developed the eddy4R codebase, with ARV providing modification for its use here. RJP provided software for instrumentation and validation of model applications to the data. JDL and LJC supervised the interpretation of the results. The work was proposed by LJC, who also acquired the necessary funding. DCL prepared the paper, with all authors contributing to the editing process.
Competing interests. The authors declare that they have no conflict of interest.
Disclaimer. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
Acknowledgements. Lucy J. Carpenter and David C. Loades acknowledge funding from the Natural Environment Research Council (NERC), UK, through the grant "Iodide in the ocean: distribution and impact on iodine flux and ozone loss" (NE/N009983/1). David C. Loades also thanks NERC for the funding of his PhD project (NERC SPHERES DTP NE/L002574/1). Lucy J. Carpenter acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 programme (project O 3 -SML; grant agreement no. 833290). The National Ecological Observatory Network is a project sponsored by the National Science Foundation and managed under co-operative agreement by Battelle. This material is based upon work supported by the National Science Foundation (grant DBI-0752017). Trinity House (https://www.trinityhouse.co.uk/, last access: 10 December 2020) owns the Penlee Point Atmospheric Observatory (PPAO) site, who allows Plymouth Marine Laboratory (PML) to use the building to house instrumentation. Access to the site is arranged thanks to Mount Edgcumbe Estate (https://www.mountedgcumbe.gov.uk/, last access: 10 December 2020). PPAO research (including the contributions of Thomas G. Bell and Mingxi Yang to this paper) is supported by NERC via the national capability ACSIS project (grant no. NE/N018044/1). We thank Frances Hopkins (PML), Daniel Philips (University of East Anglia), and Oban Jones (PML) for assistance at the field site. This work is contribution number 8 from the PPAO.
Financial support. This research has been supported by the Natural Environment Research Council (grant no. NE/L002574/1), Natural Environment Research Council (grant "Iodide in the ocean: distribution and impact on iodine flux and ozone loss", grant no. NE/N009983/1), Natural Environment Research Council (AC-SIS project, grant no. NE/N018044/1), and the European Research Council (ERC) under the European Union's Horizon 2020 programme (project O 3 -SML; grant agreement no. 833290).
Review statement. This paper was edited by Christof Ammann and reviewed by Christopher Fairall, Ivan Mammarella, and one anonymous referee.