In 2023, we conducted a series of lab experiments to assess the trace gas loss during glass plate sampling: (A) preliminary test (B) glass plate sampling without surfactants (C) glass plate sampling with and without an artificial surfactant. SML samples in experiment A were taken with the mesh screen (Garrett, 1965). All other SML samples were taken with the glass plate technique (Harvey and Burzell, 1972). The preliminary test from experiment A is described in Sect. S1 of the Supplement, while we exclusively address experiments B and C further on. To exclude biological and chemical consumption or production of gases as potential sources or sinks affecting the measured concentrations, we used isotopically labelled gases in fresh water (FW) and artificial seawater (AS): deuterated DMS (DMS-d3), deuterated isoprene (isoprene-d5) and ¹³CS₂ as representatives for DMS, isoprene and CS₂, respectively. Trace gas concentration, water temperature, salinity, and surfactants were varied in the ULW to assess their effect on sampling efficiency, whereas surfactants in the SML, sampling duration for SML, sample volume of SML samples, number of glass plate dips, pH in ULW, air temperature and person who sampled SML were recorded to accompany our measurements. To exclude sampling bias with glass plate sampling, only one person was sampling SML samples (with exceptions in experiment B). The experiments were performed with different media to address two research objectives:

Pure sampling efficiency was determined using ultrapure water (as FW) and AS with varying temperatures, salinities and trace gas concentration, as those parameters affect the solubility and diffusivity of gases.

Table 1 summarizes the experiments, which took place in two different locations in Germany: (1) under the roof of the SURF facility at ICBM, Wilhelmshaven and (2) in the laboratories at GEOMAR Helmholtz Centre for Ocean Research Kiel. Two different tanks were used: (1) aquarium made of glass (2) ”AZ crate” (Polypropylene, Schoeller Allibert, Schwerin, Germany).

Before each sampling, we mixed the water body carefully for 1 min to homogenize any gradients that had formed towards the air side due to the oversaturation and waited for 2 min for the turbulent motion to subside. We sampled the SML, ULW (10–13 cm) and surface (1–6.5 cm). All samples were collected in amber borosilicate glass bottles (20 mL). SML samples were taken with the glass plate technique (Harvey and Burzell, 1972). Following the recommendation by Cunliffe and Wurl (2014) and examples from recent studies (e.g., Adenaya et al., 2021), we reduced the speed of extracting the glass plate to 5 cm s⁻¹. The glass plate (borosilicate glass, 30 cm × 25 cm × 0.5 cm in experiment B, 40 cm × 30 cm × 0.5 cm in experiment C) was immersed to a depth of about 20 or 25 cm. Both sides of the glass plate were wiped with a regular silicone or rubber wiper and the run-off was collected into a sample bottle with a plastic funnel. A single dip provided between 1.8–4.0 mL of medium when no surfactants were present, and 3.4–6.3 mL when an artificial surfactant was added. To collect sufficient sample volume for analysis, two to five dips were required for analysis with gas chromatography–mass spectrometer (GC–MS) and voltammetry samples. The thickness of the sampled layer is determined by Eq. (1) (Cunliffe and Wurl, 2014). 1hSML≈hsampled=VsamplendipsA where hSML is the true thickness of the SML, hsampled is the thickness that was actually sampled in cm, Vsample is the total volume of the glass plate sample in mL, A is the wetted surface area of the glass plate in cm² and ndips is the number of dips that were needed to collect Vsample.

Each SML sample is always associated with a reference ULW sample and sometimes with additional ULW or surface samples. All samples taken together after the same mixing event are referred to as a sample set. The reference ULW sample was taken immediately after the first dip of the SML sample was collected, interrupting the SML sampling for less than a minute (overall SML sampling took 90–235 s). All additional ULW or surface samples were taken after the SML sample had been finished (exception from this order is 19 April in experiment B). ULW samples were taken with a pipette (5 and 10 mL, Eppendorf SE, Hamburg, Germany) set to the required sample volume by inserting the tip of the pipette vertically and carefully into the water. For sample volumes of 15 mL, a pipette was immersed twice in the same location. ULW samples were taken from a water depth below surface of ∼10 cm in experiment B and ∼13 cm in experiment C. Surface samples were sampled the same way as ULW samples, with the only difference that we were aiming for a depth below surface of less than 1 cm in experiment B and ∼4.5 cm in experiment C (with exception of 31 August: ∼6.5 cm). Additional ULW and surface samples were collected once or twice daily to confirm that the tank was well mixed. These tests were necessary, as the concentration difference between the oversaturated water and the near-zero air is large and might re-establish gradients in the SML quickly. Before each sample set was obtained, all of the equipment was rinsed with ultrapure water.

Samples were taken for trace gas analysis and voltammetry (surfactants). Trace gases were analysed during all of the experiments, whereas voltammetry was only performed in selected cases (Table 1). The targeted sample volume for trace gas analysis was 10 mL. SML samples were filled to at least the targeted sample volume and later on weighed to calculate the sample volume based on the density of the medium. In the treatment with surfactants, a larger sample volume was required for voltammetry measurements to permit a subsequent 10 mL subsample. Given the limited SML volume in the tank and the presence of surfactants, collecting two true replicate SML samples was not feasible. Consequently, the target sample volume was increased to 15 mL for GC–MS analysis, and the purged sample from GC–MS analysis was subsequently reused for surfactant analysis. No effect on final concentrations from the GC–MS measurements was found between 10 and 15 mL samples, as gases are stripped completely out of the medium within the purge time. Sample bottles used for the voltammetry measurements were additionally acid-rinsed (10 % HCl) and pre-combusted at 500 °C before sampling.

The system used to measure the trace gases DMS-d3, isoprene-d5, and ¹³CS₂ is a purge and trap GC–MS (Zavarsky et al., 2018). It consists of a self-constructed purge and trap system, a type 7890A GC, and a 5975C MS (Agilent, Waldbronn, Germany). The GC uses a capillary column (Supel-Q-PLOT, 30 m × 0.32 mm, Merck KGaA, Darmstadt, Germany). The MS is equipped with electrical ionisation, a quadrupole mass filter and a triple-axis electron multiplier detector. All three compounds are measured from the same sample. As samples cannot be preserved, no replicates could be taken for GC–MS analysis. Samples were stored at room temperature in the dark and measured within less than one hour after sampling. Samples (both 10 and 15 mL) are purged with helium (99.999 %, Air Liquide, Düsseldorf, Germany) at a flow rate of 80 mL min⁻¹ for 10 min. The sample gas stream is dried with a Nafion^® membrane dryer (Perma Pure, Lakewood, United States) and trapped with liquid nitrogen in a Sulfinert^® stainless steel tube (Restek GmbH, Bad Homburg, Germany). Injection into the GC is semi-automated with a 6-port valve that channels the carrier gas flow through the trap while it is heated with hot water (70–100 °C) to release the sample. The MS is operated in single-ion mode. The raw peak areas (PA_raw) in the spectra were integrated manually with MSD Productivity ChemStation (version E.02.02.1431, Agilent, Waldbronn, Germany). The unit of PA_raw is arbitrary and, therefore, is not used throughout the manuscript. Qualification and quantification of DMS-d3, isoprene-d5, and ¹³CS₂ was done using m/z ratios of 64 and 65, 72 and 73, and 77 and 79, respectively. The limit of detection (LOD, i.e., minimum PA_raw detectable) was defined as 7 times the root mean square error of the baseline noise and was determined for each compound individually from one representative chromatogram for each experiment. This yielded LODs for DMS-d3 of 209 and 90, for isoprene-d5 of 300 and 309, and for ¹³CS₂ of 258 and 181 respectively for experiment B and C. To extract only isotope signals, all PA_raw were corrected for spectral fragmentation, which causes overlap in the mass spectra of natural and isotopically labelled compounds. A calibration was deemed not necessary, as we are only interested in ratios of SML trace gas content over ULW trace gas content, each sampled directly one after another. The calibration usually used with this setup translates PA_raw linearly into concentrations, which means that the ratio of two PA_raw equals the ratio of concentrations, thus the ratio of two PA_raw is sufficient. It takes less than 1 h to measure all samples from one set, therefore also the drift of the GC–MS is negligible for one sample set. By skipping the calibration, the number of measured SML–ULW pairs for each day was increased. Example calibration curves are shown in Sect. S2. Each PA_raw was normalized by the sample volume to allow for comparability, further referred to as PA. Associated uncertainty of GC–MS measurements is 10 %. An additional step in quality control (QC) was added to identify measurements with poor quality. Peaks of mass 91 at retention time ∼8.10 min were integrated for all SML, ULW and surface samples and normalized by sample volume (PA₉₁). Mass 91 is associated with toluene. There is a stable toluene contamination in the purge system, therefore, the variability in PA₉₁ is indicative of poor-quality measurements (see Sect. S3).

Surface activity (SA) of surfactants was measured only for samples when Triton X-100 (TX-100, with molecular weight 625 g mol⁻¹, Merck, Darmstadt, Germany) was added to the tank (experiment C, see Table 1). Of those samples, only a subset was measured, which was a representative ULW triplicate at the beginning and end of the day, as well as each SML (singlets) sample. SA was quantified using phase-sensitive alternating current voltammetry with a hanging mercury drop electrode 797 VA (Computrace, Metrohm, Switzerland), following the method established by Ćosović and Vojvodić (1982, 1998). This electrochemical technique exploits the adsorption behaviour of surfactants at the interface between the mercury electrode and electrolyte, altering the capacitive current (Scholz, 2015). Samples were stored at -20 °C until analysis. Prior to measurement, all samples were brought to room temperature and adjusted to a uniform ionic strength corresponding to a SP of 35.0 (0.55 mol L⁻¹ NaCl) to ensure comparability across measurements. Depending on the TX-100 concentration added to the tank, measurements were performed with a deposition time ranging between 10–60 s and a voltage sweep between -0.6 and -1.0 V. Additionally, high TX-100 concentration samples required dilution before measuring (dilutions from 0.7–0.97). For evaluation, the initial current response at -0.6 V was used, and the difference in capacity current between sample and blank was calculated with ΔI=Iblank-Isample. Three scans were recorded per replicate and the mean of the three scans was used for final analysis. Calibration was performed using TX-100 across a concentration range of 0.01–1.3 mg L⁻¹. Only the linear portion of the response curve was used for quantification. Analytical precision was assessed using daily standards and blanks, yielding an average precision of 6 %, with all values remaining below 10 %.

For each triplicate of ULW surfactants samples the standard error (SE) of mean was calculated with Eq. (2). Only a few representative ULW samples were taken per day and then were averaged over the day. Errors were propagated with Eq. (3) to show the precision of the daily mean accounting for replicate uncertainty. 2SE=SDn3SEday=1m∑i=1mSEi2 where SE and SE_i are the standard error of the triplicate, SD is standard deviation of the triplicate, n the number of samples per triplicate, SE_day is standard error of the mean of triplicates per day and m is number of triplicates per day.

Spread of triplicate means is calculated as SD of the mean values with Eq. (4). 4SDday=1m-1∑i=1mx‾i-x‾day2 where SD_day is standard deviation for the daily mean, m the number of triplicates, x‾i the mean of the triplicate and x‾day the daily mean.

Sampling efficiency is calculated as ratio of trace gas content per volume in the SML over content per volume in ULW (Eq. 5). Units should be a concentration (e.g., mol L⁻¹) or linearly proportional to the resulting concentration (e.g., PA, which is given per millilitre of sample). Sampling efficiency E is given as a dimensionless fraction. The complement of this fraction represents the sampling losses (Eq. 6). Note, that this resembles the EF commonly computed to determine enrichment in the SML in field samples, e.g., EF = xSML/xULW, where x is a measured property. 5E=PASMLPAULW∝CSMLCULW6L=1-E7CSML,true=CSMLE where E is sampling efficiency (unitless), PA is the peak area per millilitre of sample, C is a concentration in, e.g., mol L⁻¹, taken from the SML or ULW, as indicated by the subscripts and L is the sampling loss.

Sampling efficiency corresponds to the integrated error introduced by sampling with the glass plate, used in Eq. (7) for correction. This is based on a multiplicative error model, where the error (i.e., sampling efficiency) scales linearly with the quantity needing correction (i.e., measured concentration in glass plate samples), without an offset.

In experiment B, air and water temperature were measured occasionally with common thermometers. In experiment C, additional parameters were measured for each sample set. Practical salinity and temperature of the water were measured with a Cond 330i with a TetraCon 325 (WTW, Weilheim, Germany) at a depth of about 2 cm below surface. The pH of water was measured at about 1.5 cm below surface with a digital pH meter PH-100 ATC (Voltcraft, Hirschau, Germany), calibrated every morning with buffer solutions with pH of 7.0 and 4.0 (Scharlab, Barcelona, Spain). Air temperature was measured with a common digital thermometer (about 46 cm above water surface) and a liquid expansion thermometer (about 15 cm above water surface, low precision of ΔT= 0.5 °C). The number of dips, sample volume in mL (or sample weight in gram) and the person who was sampling were recorded in both experiments. In experiment C, the duration of glass plate sampling in seconds was recorded as well.

Data processing, visualization and statistical analysis was performed in Python version 3.11.11 (Python Software Foundation, 2025). The libraries used for data processing and visualization were pandas version 2.3.2 (McKinney, 2010; The pandas development team, 2025), NumPy version 2.3.3 (Harris et al., 2020), seaborn version 0.13.2 (Waskom, 2021) and matplotlib version 3.10.0 (Hunter, 2007; The Matplotlib Development Team, 2024). For statistical analysis, SciPy version 1.16.2 (Virtanen et al., 2020) and statsmodels version 0.14.5 (Seabold and Perktold, 2010) were used. The main function for each statistical calculation is given below. Parameters of the function call are only mentioned if they were changed from default. Observations with missing values were only excluded if the variable concerned was used in the respective statistical analysis. Outliers were included in descriptive statistics and statistical tests, as large variation was expected and removing outliers would potentially remove true values. In boxplots, however, outliers are shown with the common 1.5 times interquartile range (IQR) in order to present all of the data and to highlight the skewedness. Pair-wise differences between means of treatments and experiments for each trace gas were assessed with Welch's t-test (SciPy, ttest_ind(…,equal_var=False)), as for a few cases the heteroscedasticity could not be safely assumed (minimum and maximum variances were off by a factor of more than 3). No multiple testing correction was applied. One-way ANOVA was used to determine if purging of surfactants samples had an effect on the measurements and to identify (categorical) factors (without order) driving well-mixed ratios in Fig. 3 (SciPy, f_oneway()). The null hypothesis was rejected at p<0.05, and statistical significance assumed accordingly. Where applicable, p-value levels of <0.05, <0.01 and <0.001 are indicated by ^*, ^** and ^*** respectively. Levene's test was used to assess similarity of variances for treatments and experiments, since sample sizes per group were small (n≤11) and, consequently, non-normality had to be assumed. Linear regression was calculated with ordinary least-squares (SciPy, linregress()) using Eq. (8). Coefficient of determination R2 was calculated as squared Pearson correlation coefficient. Exponential fit was fitted using Eq. (9) (SciPy, curve_fit(…,p0=(max(y),0.1,min(y))). Multiple linear regression (MLR, statsmodels, smf.ols(…).fit(cov_type='HC3')) was used to asses which independent variables drive sampling efficiency. Data was standardized using z-scores before applying MLR with ordinary least-squares (Eq. 10). 8y=mx+y09y=aebx+c where y is the dependent quantity, x is the independent quantity, m is the slope and y0 is the intercept at x= 0 of the linear function, a is the amplitude, b is the exponential rate constant, and c is the asymptote of the exponential function. 10Y=β0+β1X1+β2X2+…+βnXn+ε where Y is the response variable, β0 is the intercept, βi (i≥1) are the coefficients determined by the MLR, Xi are the independent variables and ε is the error term. Reported are R2 and adjusted R2, which accounts for the number of predictors vs samples size, and p-value for F-statistics. Heteroscedasticity was not assumed.

Our experiments are based on the premise that SML and ULW have the same trace gas concentration, achieved by mixing the tank before each sampling. In order to test our assumption, a reference ULW sample (PA_ref) was taken and compared to samples from other depths and locations in the tank (Fig. 3). PA was either taken at reference depth, but at a different location, or at the surface. Almost all ratios (PA / PA_ref) lie within the range of uncertainty of the measurements (grey shaded area) for all three trace gases. Four sample sets outside that range (i.e., not well mixed, indicated as grey points) were removed manually from further calculations (i.e., sampling efficiency), as the additional QC did not indicate poor quality, nor were there deviations from the general sampling procedure noted in the protocols. Four points for isoprene-d5 and three for ¹³CS₂ from 20 April and 8 August were outside the uncertainty range, but were not removed from the data set. Mean values of the ratios (excluding grey points) are 1.00 ± 0.05, 1.01 ± 0.10, and 1.01 ± 0.08 for DMS-d3, isoprene-d5, and ¹³CS₂ respectively. Standard deviations vary between trace gases, with the largest variation for isoprene-d5. Ratios are independent of sampling location, depths, day or experiment (one-way ANOVA failed to reject null hypothesis in all cases).

Figure 4 shows measured PA from treatments FW, AS and AS with surfactants, plotted as SML against ULW, for DMS-d3, isoprene-d5, and ¹³CS₂. The SML value is always much lower than the ULW value. The order of magnitude for PA varies between trace gases due to different amounts of trace gas in the spike and different trapping and ionisation efficiencies. Therefore, while comparisons of PA within the same trace gas are valid, direct intercomparisons across trace gases are not possible due to the skipped calibration. DMS-d3 is in the order of 10⁴, isoprene-d5 at 10³, and ¹³CS₂ up to 10⁵. ¹³CS₂ shows two distinct clusters of points, as the two spikes used were significantly different in the amount of ¹³CS₂, whereas the amounts for DMS-d3 and isoprene-d5 were similar. For all three gases, a clear linear, positive correlation is visible between SML and ULW. R2 of the linear fit (SciPy, linregress()) for DMS-d3 and isoprene-d5 are both 0.77 for FW, 0.79 and 0.75 for AS, and much lower at 0.55 and 0.50 for AS with surfactants respectively. R2 for ¹³CS₂ is 0.93 for FW and 0.95 for AS, and much lower than for the other trace gases for AS with surfactants at 0.37. Note, that the latter data points all fall exclusively into one cluster only, indicating a bad fit without the influence of the large spread present for FW and AS. These values, together with slope and intercept as well as mean PA with standard deviation are reported in Table 3. Mean values and standard deviation visualize the order of magnitude, as within each treatment the amount of spike added differed slightly, causing high standard deviation. This is especially visible for ¹³CS₂, where standard deviation is close to the mean value for FW and AS (includes both clusters), but standard deviation is much lower than the mean for AS with surfactants (only lower value cluster). Slopes differ slightly between gases and treatments. Slopes for DMS-d3 are 0.17 (FW), 0.21 (AS) and 0.14 (AS with surfactants). Slopes for isoprene-d5 are similar, with 0.17 (FW), 0.20 (AS) and 0.12 (AS with surfactants). Slopes for ¹³CS₂ are lower, with 0.09 (FW and AS) and 0.10 (AS with surfactants). Intercepts are not zero, but all are much smaller than the respective mean PA_ULW and therefore considered negligible. Correlation of all data points without distinguishing treatments yields R2 of 0.80 (DMS-d3), 0.76 (isoprene-d5) and 0.96 (¹³CS₂).

The sampling efficiency of the trace gases is calculated using the ratio of measured PA in SML over measured PA in ULW (Eq. 5). Due to mixing in the tank the theoretical maximum value for the sampling efficiency is, thus, 1.0 (or 100 %), i.e., when PASML= PA_ULW.

Figure 5 shows sampling efficiency for the studied trace gases in FW and AS treatment, separated by experiment. Overall the three trace gases exhibit similar trends in E, but there are significant differences between the experiments (fails to reject null hypothesis with p < 0.001, Table 5). In experiment B sampling efficiency is lower than in C. For all three trace gases, sampling efficiency decreases in experiment B with the addition of salt, whereas, this reverses for experiment C and sampling efficiency increases with the addition of salt.

Mean sampling efficiency for DMS-d3 in experiment B is 0.105 ± 0.018 (n= 11) in FW, decreasing to 0.090 ± 0.020 (n= 6) in AS, though the difference is not significant (p= 0.15, outliers in Fig. 5 included). In experiment C, the mean sampling efficiency for DMS-d3 in both treatments is higher than in experiment B, with 0.144 ± 0.034 (n= 6) in FW increasing to 0.164 ± 0.033 (n= 7) in AS. The difference between FW and AS within experiment C is not significant (p= 0.32). This overall picture repeats for isoprene-d5 and ¹³CS₂. In experiment B, mean sampling efficiency for isoprene-d5 is 0.112 ± 0.025 (n= 10) in FW, reducing to 0.079 ± 0.018 (n= 6) in AS, whereas in experiment C sampling efficiency is overall higher, with 0.143 ± 0.035 (n= 6) in FW and then further increasing to 0.158 ± 0.036 (n= 7) in AS. For ¹³CS₂, sampling efficiency in experiment B averages to 0.101 ± 0.025 (n= 11) in FW and lowers to 0.079 ± 0.019 (n= 6) in AS, whereas it is overall higher in experiment C with 0.131 ± 0.032 (n= 6) in FW and rising to 0.158 ± 0.031 (n= 7) in AS. Similar to DMS-d3, the differences within both experiments between treatments are not significant (Table 5), except for isoprene-d5 in experiment B (p= 0.009).

Standard deviations of sampling efficiency are slightly larger in experiment C than in B for all three trace gases and differ significantly between treatments FW and AS (Levene's test for equal variances failed to reject null hypothesis with p 0.045, 0.0497 and 0.033 for DMS-d3, isoprene-d5, and ¹³CS₂, SciPy, levene(…,centre='mean')). Standard errors are almost two times larger in experiment C than in B. Standard error (SE) in FW and AS for DMS-d3 is 0.0074 and 0.013, for isoprene-d5 is 0.0080 and 0.014 and for ¹³CS₂ is 0.0073 and 0.013. SE overall (n= 30) are 0.0070, 0.0074 and 0.007 for DMS-d3, isoprene-d5, and ¹³CS₂.

There is no significant difference between FW in experiment B and C for any of the three trace gases (except for DMS-d3, p= 0.038), but in AS the differences are significant for all three trace gases (p < 0.001), see Table 5. The medium used in FW was ultrapure water, from different devices, but same models. The media used for AS, on the other hand, were different in the composition of the salts and other substances added, though also SP slightly varied.

Sampling efficiency as a function of water temperature, salinity, spike volume per litre added (i.e., proportional to trace gas concentration) and number of dips was investigated using MLR models (n= 19 complete observations of 30). Note, that 10 of 11 data points in experiment B treatment FW were excluded, because of missing temperature measurements, and one of seven in experiment C treatment AS, because of unrecorded number of dips. The MLR models were significant for all three trace gases (F(4,14) > 5.6, p < 0.01) and explain about 60 % of the variance observed in sampling efficiency (adjusted R2 is 0.63, 0.60 and 0.65 for DMS-d3, isoprene-d5, and ¹³CS₂ respectively). The models predicted average (±SE) sampling efficiency of 0.129 ± 0.007, 0.127 ± 0.008 and 0.120 ± 0.007 for DMS-d3, isoprene-d5, and ¹³CS₂, when all predictors were at their mean values (p < 0.001). Spike volume per litre is a significant, positive predictor for sampling efficiency for all three trace gases (p < 0.01, β is 0.0342, 0.0404 and 0.0353 for DMS-d3, isoprene-d5, and ¹³CS₂, sspike= 1.4 µL L⁻¹). For DMS-d3 and ¹³CS₂ also water temperature is a significant, but negative predictor (p < 0.05, β is -0.0223 and -0.0219, sTw= 1.8 °C), whereas, for isoprene-d5 the number of dips is a significant, positive predictor (p= 0.018, β= 0.0213, sdips= 0.6). Salinity was not a significant predictor for any of the trace gases (p between 0.448 and 0.608). See Sect. S5 for details of MLR, linear regression results and additional plots.

Since surfactants are often present in natural surface waters, the experiments were extended to include a treatment of AS with surfactants.

When an artificial surfactant (TX-100) was added to AS (Fig. 6), the mean sampling efficiency for all of the three trace gases reduced even below the FW treatment, DMS-d3 to 0.130, isoprene-d5 to 0.127 and ¹³CS₂ to 0.121 (Table 4). Standard deviations are also smaller than in FW and AS treatment (0.025 for DMS-d3, 0.024 for isoprene-d5 and ¹³CS₂). The range (difference from minimum to maximum) is still similar to the range observed in FW and AS for each of the three trace gases.

Sampling efficiency decreases with increasing SA_SML (Fig. 7). It decreases fast from SA = 0 until about SA = 3.0. Above SA = 3.0 the values seem to arrange around a constant value of sampling efficiency. Linear fit is weak (R2 between 0.26 and 0.28 for all three trace gases). The slope is negative and small with about -0.005 per mg L⁻¹ TX-100 equiv. and intercepts are between 0.146 to 0.154 for the three trace gases (Table 6). Though small, the slope is significantly different from no slope (p < 0.05 for all three trace gases). An exponential fit was only possible for DMS-d3 and ¹³CS₂, for which it explains slightly more variability than the linear fit (R2 between 0.42 and 0.44). When treatment FW was included an exponential fit was only possible for DMS-d3 (not shown). The exponential fit approaches 0.12 and 0.11 for DMS-d3 and ¹³CS₂ with a small amplitude of 0.05 for both at a decay rate of -0.68 and -0.88. The exponential fit is added for visualization in Fig. 7.

Sampling efficiency in response to water temperature, salinity, spike volume per litre added (i.e., proportional to trace gas concentration), number of dips and SA in the SML was investigated using MLR models for each trace gas (n= 27 complete observations of 29). The MLR models were not significant for any of the three trace gases (F(5,21) > 1.9, p > 0.09) and explained less than 25 % of the variance observed in sampling efficiency (adjusted R2 is 0.25, 0.22 and 0.23 for DMS-d3, isoprene-d5, and ¹³CS₂ respectively). The model predicted average (±SE) sampling efficiency of 0.139 ± 0.006, 0.137 ± 0.006 and 0.131 ± 0.006 for DMS-d3, isoprene-d5, and ¹³CS₂, when all predictors were at their mean values (p < 0.001). Spike volume per litre is a significant, positive predictor for sampling efficiency only for DMS-d3 (p= 0.029, β = 0.0213, sspike= 0.94 µL L⁻¹). Water temperature is a significant, negative predictor for all three trace gases (p < 0.05, β is -0.0324, -0.0309 and -0.0321 for DMS-d3, isoprene-d5, and ¹³CS₂, sTw= 1.4 °C). SA in the SML was a significant, negative predictor for ¹³CS₂ only (p= 0.041, β= -0.0137, sSA,SML= 2.91 mg L⁻¹ TX-100 equiv.), though DMS-d3 is on the limit (p= 0.05), and isoprene-d5 is non-significant (p= 0.07). Neither number of dips (p > 0.8), nor salinity (p is 0.247 and 0.206 for DMS-d3 and isoprene-d5, but much lower at 0.066 for ¹³CS₂) were a significant predictor for any of the trace gases. See Sect. S6 for details of MLR, linear regression results and additional plots.

Water temperature in this study covered a modest range of ΔT= 5.9 °C. Sea surface temperature in the field encompasses a wider range. At the time-series station Boknis Eck (Western Baltic Sea), for example, the range studied here is only observed during the summer season (Laß et al., 2013). In our treatments, intermediate salinity was excluded, focussing on fresh water and seawater. We do not expect to see any improvement in our results by including intermediate salinity, as salinity was a non-significant predictor for sampling efficiency. Additionally, we did not expect that the type of salt (Tropic Marin^® Pro-Reef Sea Salt vs. ordinary aquarium salt) would have an effect. Differences in the FW treatments between experiments were not statistically significant, while for the AS treatment they were (Table 5). We do not attribute this to the composition of the salt (affecting the solubility differently than ordinary aquarium salt, e.g., Weisenberger and Schumpe (1996)), other substances, or the alkalinity of the water (see Table 1 for details of the salts), as neither are known to affect the isotopically labelled trace gases used in this study. Additionally, they are not expected to alter the physicochemical properties enough to affect sampling efficiency as they are dosed in natural concentrations. As the three trace gases exhibit a similar effect, something more general appeared to change between the AS experiments. It is, therefore, more likely that the differences are attributable to the combined effect of changes in (environmental) parameters between experiments, which were not ideally overlapping across all treatments (see Fig. S6), e.g., changes in number of dips, water temperature, different glass plate size and wiper, mixing in of the trace gases, degree of oversaturation. In that respect, the differences between B and C might also be explained by a smoother sampling routine in C due to the practice gained in B.

The increase in targeted sample volume from 10 mL (FW, AS) to 15 mL (AS with surfactants) did not affect PA_ULW. However, we could not assess whether PA_SML differed between 10 and 15 mL. The increase in volume is achieved by dipping the glass plate more often, potentially affecting the sampling efficiency. Since the number of dips was a non-significant predictor for sampling efficiency in the MLR, the effect on PA_SML and consequently on sampling efficiency, is considered negligible. Finally, a range of saturation states was not investigated. We only performed experiments with oversaturated conditions in the water, but we expect that the concentration gradient (magnitude and direction) has an effect on sampling efficiency.

Each experiment was conducted at a different location (and time of year, Table 1). The tanks were placed indoors (the roof at ICBM in experiment B closes all around), to make sure that results are independent of location (and time of year), and consequently comparable between experiments. Air properties (e.g., temperature, humidity) likely varied (though not measured), but due to the strong concentration gradient we deem their effect negligible. The material of the tanks was either glass or plastic (Table 1). Contamination was ruled out, since we were using isotopically labelled trace gases. Neither of the materials used is known to react with the studied isotopically labelled trace gases or the added artificial surfactant. Adsorption to the surfaces likely differs between glass and plastic, as well as the exchange of heat across the material. These effects are accounted for by measuring water temperature and surface activity.

The above noted differences in setup between experiment B and C make the interpretation of our results more difficult, given that no clear factor driving the differences between the experiments could be identified. The effect of the differences does not seem to overrule the overall trends (as seen in the combined data set of B and C in Fig. S6). Throughout this manuscript we kept information about the source experiment visible (except for Table 7).

Yang (1999) and Yang et al. (2001) used the glass plate to sample DMS from the SML in the field. The enrichment factors range from 1.21–3.08 and 0.41–1.18 respectively, highlighting that measurements are possible, and not all DMS is lost in the process of sampling. But whether those values and their variations are meaningful or mainly driven randomly has yet to be investigated. To accompany their field data interpretation. Yang et al. (2001) investigate what drives differences in CSML in the lab, but they do not derive a sampling efficiency. Our results show evidence – against the accepted notion that glass plate sampling is not meaningful for volatile compounds (Engel et al., 2017) – that the glass plate is a reliable sampling method for trace gases, yet associated with high losses (i.e., low sampling efficiency).

Our results for FW and AS are more consistent than expected across the parameter space we investigated. Additionally, sampling efficiency does not vary significantly between the tested trace gases. However, the variance cannot be explained fully by the recorded parameters, therefore, any correction approach of CSML should be qualitative and not quantitative, i.e., Eq. (7) cannot be used at this state of research. The consistency of the results is less surprising in view of the limited parameter space (i.e., water temperature and trace gas concentration in the ULW always oversaturated) we achieved in this study. For example, Table 2 in Yang et al. (2001) showed in a lab setup that an enrichment of DMS correlates negatively with water temperature (0–28 °C), starting from an enrichment factor of 0.58 and reducing to 0.11. It is, therefore, likely that the effect water temperature would have on sampling efficiency is simply not visible in our study.

There are more parameters, that will affect sampling efficiency, that have not been covered in this study. Wind influence on the glass plate will likely decrease sampling efficiency for the short-lived trace gases with increasing wind speed, until a wind speed U10,max, when all trace gas content is removed towards the near-zero atmosphere (i.e., E= 0). During 5 weeks of glass plate sampling in the Jade Bay (Southern North Sea, May/June 2023) we found that one of the SML samples was completely stripped of DMS. Personal communication with Theresa Barthelmeß, who had taken the sample, revealed that operation of the glass plate had been at the limit due to the wind pushing the glass plate around. This indicates that the U10,max might coincide with the limits of glass plate operation. Furthermore, local wind variations in space and time on the scale of the glass plate size and on the order of the sampling duration will likely increase the variability of sampling efficiency.

Extending the study to long-lived trace gases with a non-zero atmospheric background will yield different sampling efficiency, as well. While for short-lived, highly reactive trace gases, as studied here, the sampling efficiency is relatively low, it is probably much higher for long-lived, less reactive trace gases, like N₂O. A small, test data set (data not shown) of N₂O glass plate and ULW samples (12 SML–ULW pairs) that we collected using AS (SP= 30.2, Twater= 22.9 ± 0.7 °C) in a tank (equilibrated with lab air over more than 24 h), showed mean sampling efficiency of 0.97 ± 0.12, indicating that the ΔC and the corresponding equilibration behaviour of the trace gas play a major role.

The aim of this study was to capture pure sampling error (as sampling efficiency), for which we introduced the premise of a fully homogenized water body (i.e., CSML= CULW). The verification of the premise worked well, but in the absence of alternatives lacked the ability to account for gradients in the SML. In the 2 min waiting time after mixing and during sampling, gradients could have formed due to turbulent or diffusive fluxes through the air-water interface, both enhanced by the strong oversaturation present. As all experiments were performed indoors wind was not present, therefore the only potentially significant source for turbulent fluxes was the sampling itself, which we consider as part of the sampling efficiency. Diffusive losses were negligible. These two aspects are discussed in more detail in Sect. 4.1.2 and 4.1.3. Despite the discussed low contribution of the turbulent and diffusive fluxes, sampling efficiency as determined here remains a combination of pure sampling error and other on-going air-water exchange processes, to which the latter might even contribute as much as the uncertainty (Table 7) associated with sampling efficiency.

Sampling efficiency in general is driven by turbulence effects, the equilibration between water on the glass plate and the surrounding air, potential adsorption effects (Walker et al., 2016) and photochemical processes (Zemmelink et al., 2005). Note, that chemical and biological reactions are excluded from this study and not considered to be factors for driving sampling efficiency here. The dilution of SML samples by ULW water due to varying sampling thicknesses, is also excluded from our concept of sampling efficiency, because CSML= CULW. Turbulence effects and equilibration can both reduce and increase sampling efficiency, depending on the concentration gradient from the glass plate towards the surrounding air. All trace gases studied here were always oversaturated, i.e. outgassing prevailed. Photochemical processes heavily depend on the trace gas, light intensity and duration of exposure. Sampling efficiency will decrease with degradation and increase with production processes, however, the increase would be artificial (i.e., not due to sampling effects). All experiments were performed indoors and UV light, therefore, was filtered out. Adsorption to the glass plate, the wiper and the funnel always reduces sampling efficiency by removing molecules from the sample, though, the effective amount is hard to quantify. Adsorption losses are deemed negligible in our setup, because of the regular cleaning of all used materials. Furthermore, each trace gas likely would be adsorbed to different degrees. Consequently, sampling efficiency between trace gases would look more dissimilar than actually observed. Turbulence increases the effect of equilibration many times and we kept this at a minimum by omitting wind influence. The presence of substances other than trace gases, e.g., surfactants, can have an enhancing, reversing, or neutral effect on turbulence and equilibration. In this study the concentration gradients were always going towards the near-zero atmosphere concentration, therefore, we hypothesize that the turbulence introduced by the sample handling during glass plate sampling decreases sampling efficiency. Additionally, the sampling efficiency is expected to further decrease, due to fast paced equilibration along the high concentration gradient (from oversaturated water to near-zero atmosphere) and the short-lived, highly reactive species with low solubility that we used.

The MLR (explains about 60 % variance) identifies spike volume per litre (positive) and water temperature (negative) as significant predictors for DMS-d3 and ¹³CS₂ sampling efficiency in FW and AS without surfactants. For isoprene-d5 it is spike volume per litre (positive) and the number of dips (positive). This changes with the addition of an artificial surfactant (MLR explains less than 25 % of variance). Spike volume per litre (positive) and water temperature (negative) are still significant predictors for DMS-d3 sampling efficiency in FW and AS without and with surfactants. SA_SML is almost a significant predictor (negative). The only significant predictor for isoprene-d5 sampling efficiency is water temperature (negative), while spike volume per litre and the number of dips are no longer significant. Water temperature (negative) remains a significant predictor for ¹³CS₂ sampling efficiency, together with SA_SML, while spike volume per litre is no longer significant.

It is reasonable that the spike volume per litre is correlated with sampling efficiency, as it is proportional to the concentration of the trace gases in the tank, which in turn is proportional to the ΔC (as Cair= constant ≈ 0). The identified, negative relationship of sampling efficiency and water temperature matches the expectations and the findings by Yang et al. (2001). Most likely this effect relates to the negative relationship of solubility and water temperature, highlighting that the solubility is a potential candidate to be used to predict sampling efficiency. Furthermore, water temperature increases the speed of molecular diffusion, which in turn would also further reduce sampling efficiency. Although, the trend is captured there is only a weak effect of water temperature on sampling efficiency, despite the statistical significance in the MLR, due to the modest range of water temperature covered in this study. Salinity is not significant for any of the trace gases. Although, salinity has an effect on solubility (Weisenberger and Schumpe, 1996), it is much lower than the effect of temperature.

The differences in water composition in AS without surfactants between B and C might lead to the variability (grey shaded area) depicted in Fig. S6, but are unlikely to explain the differences in sampling efficiency. Clear trends for temperature and spike volume per litre (Fig. S6, statistically significant in MLR) indicate that the differences are more likely contributed to the differences in parameter range covered in experiment B and C, e.g., experiment B (FW ≤ 20.9 °C, AS 21.5 °C) was overall warmer than experiment C (FW 17.6 °C, AS 19.5 °C).

Surprisingly the number of dips was only significant in one case, with a predicted positive relationship, which would imply a larger sampling efficiency with more dips. This is counter to the hypothesis, that the sampling duration (which is a multiple of the number of dips) decreases sampling efficiency, and this result is therefore deemed a mathematical artifact. Although each dip has its individual sampling efficiency, it is to be expected that the number of dips affects the overall variability of our sampling efficiency estimate, but not the mean sampling efficiency. However, the number of dips is closely linked to sampling duration. The sampling duration affects how long the vial is left open, potentially resulting in a change of the mean sampling efficiency. Nonetheless, our lab experience has shown that leaving the vial open has a negligible effect and non-significant results for the number of dips from the MLR supports this.

SA_SML was included in MLR as the factor driving sampling efficiency, though SA_ULW seemed to have an effect on PA as well. We expected a positive relationship with sampling efficiency, since field studies show a decrease in gas exchange for increased SA_SML, i.e., more retained in SML. Instead, the model and linear regressions (see Sect. S6) show negative correlations. Most recent gas exchange reduction publications look into wind-driven effects, which is why those are not directly applicable here, but Schmidt and Schneider (2011) show a decrease in gas exchange for stirring samples with surfactants only, highlighting that a positive correlation is still more likely. The observed negative correlation might be related to the differing sampling thickness (less dips required with an artificial surfactant, i.e., larger thickness sampled), though with the mixing we should have achieved a homogeneous concentration throughout the tank (Fig. 3). Even if there had been a negative gradient towards the SML (e.g., DBL, due to outgassing to the near-zero atmosphere), the increased sampling thickness would have put proportionally more ULW into the sample, i.e., increasing CSML and causing an (artificial) increase in sampling efficiency (i.e., positive correlation). However, Adenaya et al. (2021) show that the thickness of the DBL increases with the addition of artificial surfactants (as opposed to natural surfactants), which would counteract the effect of the sampling thickness. The final assessment, though, is difficult, as the increase of the DBL cannot be quantified in our setup. Though SA_SML was much higher than natural values, it was still very far from the critical micelle concentration of TX-100, which is why the negative correlation can also not be explained by micelle formation. It is possible that the surfactants affect the homogeneous mixing of the trace gases. If surfactants decrease the trace gas concentration with increasing SA, this would explain the negative correlation and the decrease in mean sampling efficiency. The trace gases would mix less into the SML than in the ULW (as SA_SML > SA_ULW), decreasing sampling efficiency. Furthermore, SA is a good choice to understand how likely (mixes of) substances are to accumulate at the surface, yet, it overlooks other physicochemical processes potentially affecting sampling efficiency, like ionic/non-ionic characteristics. In view of the relatively low effect on sampling efficiency, this highlights that a single and artificial surfactant, though considered a good model surfactant, might not have been enough to represent the complexity of natural (mixed) surfactant pools. Finally, the data is relatively scattered and the linear correlation is weak, which might be an indication that we are not capturing a single, physical relationship, but a net effect of entangled factors.

SML samples from the field retain short-lived trace gases, but lack any correction so far, though volatility usually is addressed as an uncertainty source in respective publications. In order to obtain meaningful (i.e., interpretable) results from SML field studies, a measure of sampling efficiency is required and presented in this study. In view of the experimental constraints, quantitative correction is not advisable using the sampling efficiency derived here. A qualitative approach to account for sampling efficiency is better suited with the current state of research, while due care should be taken, when applying the sampling efficiency in cases where the environmental parameters deviate much from the settings in this experiment. The two major differences encountered in the field for short-lived trace gases are the presence of wind and natural surfactant pools. As in the field we want to sample existing gradients (unlike the experimental premise of this study) it is merely the effect of increased losses on the glass plate due to wind during sampling that matters as compared to this study. It decreases sampling efficiency, though the work boat deployed for glass plate sampling usually operates in low winds, weakening this restriction in practice. In this study we find that the addition of an artificial surfactant decreases sampling efficiency, likely due to a larger surface area of the medium on the glass plate, though this remains speculative. The decrease might also relate to specific physicochemical properties of TX-100 (e.g., non-ionic, soluble) and the usage of a different surfactant might alter the effect on sampling efficiency. Therefore, some uncertainty with respect to the behaviour in the field is expected, though it looks like the presence of surfactants would reduce sampling efficiency. The effect was not very pronounced in this study even though the SA exceeded natural values by far, indicating that the effect on sampling efficiency might also be low even with natural surfactant pools. The studied gases here are usually oversaturated in the oceans. For oversaturated cases, therefore, the sampling efficiency determined here should fit. Yet, when equilibrium is approached sampling efficiency might increase, as the exchange process driven by the concentration gradient slows down. In oversaturated cases (looking at CULW) the sampling efficiency E presented here can be used as a threshold to compare with EF. For EF > E then follows that CSML > CULW, though how much is more difficult to obtain, as wind and surfactants might have lowered the actual sampling efficiency in relation to the experimentally determined one. Any samples with EF < E remain inconclusive with the data from this study. The same holds for cases closer to equilibrium, though we can assume that the closer to equilibrium the closer E will be to 1 (i.e., no losses). Thus, EF > 1 would still indicate an enrichment (i.e., CSML > CULW), though how much is difficult to say. For undersaturated cases (Cair > Cwater) the presented sampling efficiency cannot be used, as the medium on the glass plate would attain more trace gas, yielding a sampling efficiency above 1.