In this study we use a simple steady-state model for surface ocean isoprene consisting of a mass balance between biological production, chemical and biological losses, and emission to the atmosphere (Palmer and Shaw, 2005): P-CW∑kCHEM,iCXi+kBIOL+kASMLD-LMIX=0, where biological production (P) is balanced by all loss processes, CW is the seawater concentration of isoprene, kCHEM is the chemical rate constant for all possible loss pathways (i) with all reactants (X) (X = OH and O2), kBIOL is the biological loss rate constant, which takes into account the biodegradation of isoprene, kAS is the air–sea gas transfer coefficient that considers the loss processes due to air–sea gas exchange scaled with the depth of the ocean mixed layer (MLD), and LMIX is the loss due to physical mixing (Table 1). The model equation was rearranged to solve for CW (Eq. 2) as follows: CW=P-LMIX∑kCHEM,iCXi+kBIOL+kASMLD. The air–sea flux of isoprene (F) was calculated using the equation F=kASCW-CA/KH=∼kASCW, where CA is the air-side concentration of isoprene and KH is the dimensionless form of the Henry's law constant (equilibrium ratio of CA and CW). CA is assumed to be negligible compared to CW as noted above (Eq. 3). As a result, the air–sea isoprene gradient is assumed equal to the surface ocean isoprene level, and emissions are assumed to be first order in CW. This assumption is justified over the open ocean because of the short atmospheric lifetime of isoprene. In coastal regions downwind of strong isoprene sources, this assumption may not be valid. The air–sea exchange transfer coefficient (kAS) is computed using the Wanninkhof (1992) wind-speed-based (U10) parameterization and the Schmidt number SC of isoprene (Palmer and Shaw, 2005): kAS=0.31U102SC660-0.5. Further details about the rate constants and input parameters are described in Table 1. Monthly mean wind speed (U10) and sea surface temperature (SST) were obtained from the Quick Scatterometer (QuickSCAT) satellite and the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument on board the Aqua satellite, respectively, and from in situ shipboard measurements. MLDs were obtained from climatological monthly means (de Boyer Montégut et al., 2004) and compared to those calculated by in situ conductivity, temperature, and depth (CTD) profile measurements during each cruise. MLD was defined as the depth at which temperature is at least 0.2 ∘C higher or lower than the temperature at 10 m depth (de Boyer Montégut et al., 2004). Chlorophyll a (chl a) concentrations were obtained either from the MODIS instrument on board the Terra satellite or from in situ shipboard measurements (here chl a is defined as the sum of monovinyl chl a, divinyl chl a, and chlorophyllide a). Model calculations were carried out using MATLAB (Mathworks).

The steady-state model assumption is justified by the relatively short lifetime of isoprene in seawater as air–sea exchange is the dominant loss term over all latitudes and seasons (lifetime: 7–14 days) followed by kBIOL and kCHEM (Palmer and Shaw, 2005). In this study, model runs were carried out using three different sets of model parameters (Table 1).

ISOPS05: the original configuration used by Palmer and Shaw (2005). In this configuration, the production of isoprene is parameterized as the product of the bulk chl a concentration and a chl a normalized isoprene production rate (Pchloro) inferred from laboratory phytoplankton monocultures of several cyanobacteria, eukaryotes, and coccolithophores (Shaw et al., 2003). This approach inherently assumes that all phytoplankton have the same isoprene production characteristics. Palmer and Shaw (2005) also assumed that biological degradation of isoprene occurs in the water column, based on indirect evidence of a biological sink for isoprene (Moore and Wang, 2006), but no isoprene loss rate constants have been published to date. They assumed a global average lifetime of ∼ 17 days (kBIOL=0.06 day-1) based on the biological degradation rates of different data sets of methyl bromide (Tokarczyk et al., 2003; Yvon-Lewis et al., 2002).

Isoprene was measured in the surface seawater during three separate cruises: the ANT-XXV/1 in the eastern Atlantic Ocean, the SPACES/OASIS cruises in the Indian Ocean, and the ASTRA-OMZ cruise in the eastern Pacific Ocean. ANT-XXV/1 took place in November 2008 on board the R/V Polarstern from Bremerhaven, Germany, to Cape Town, South Africa (Fig. 1; for details about isoprene and ancillary data see also Zindler et al., 2014). The SPACES/OASIS cruises took place in June–July 2014 on board the R/V Sonne from Durban, South Africa, via Port Louis, Mauritius, to Malé, Maldives, and the ASTRA-OMZ cruise took place in October 2015 on board the R/V Sonne from Guayaquil, Ecuador, to Antofagasta, Chile (Fig. 1). Air mass backward trajectories (12 h; starting altitude: 50 m) from the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT; http://www.arl.noaa.gov/HYSPLIT.php) model were calculated for the sampling sites. The trajectories, in combination with atmospheric measurements, suggest that the air masses encountered on these cruises were from over the ocean for more than 12 h prior to sampling and are therefore unlikely to contain significant isoprene derived from terrestrial sources (Fig. 1).

The shipboard isoprene measurements from the ANT-XXV/1 cruise ranged from 2 to 157 pmol L-1, with the highest levels in the subtropics of the Southern Hemisphere and lower levels in the tropics (Fig. 2). Model simulations were carried out along the cruise track using monthly mean satellite data from November 2008 for chl a, surface winds, SST, and MLD as input parameters. The simulations underestimated the measured isoprene concentrations significantly, by as much as a factor of 20 over most of the cruise track (mean error of 19.1 pmol L-1). Simulations were also carried out using in situ shipboard measurements (chl a, wind speed, SST, MLD) as the input parameters. In both cases, the model simulations show a peak in the calculated isoprene levels at 13–17∘ N which is not present in the observations, whereas the peak, using in situ data as input parameter, is much smaller. This peak corresponds to elevated chl a concentrations, suggesting that while there may have been high biological activity in this region, isoprene-producing species were not abundant (Figs. 3, 4). These results demonstrate that a single isoprene production factor and bulk chl a concentration do not adequately describe the variability in isoprene production. When isoprene-producing PFTs are dominant, however, the modeled isoprene values follow the observed isoprene values (increasing isoprene concentration north of 33∘ N; Figs. 2, 5). The elevated isoprene concentrations in the subtropics of the Southern Hemisphere are not represented by the model.

Monthly mean satellite data cannot resolve rapid changes like short phytoplankton blooms or wind events. We compared the satellite data to the ship's in situ measurements of SST, wind speed, calculated MLD, and in situ measured chl a concentration as input parameters for the model (Fig. 3) in order to determine if the resolution of the satellite data does resolve important features. The modeled isoprene concentrations closely follow the variability in chl a, demonstrating that chl a has the strongest influence of the four input parameters to the model. The differences between modeled isoprene concentrations using in situ data vs. satellite data are due primarily to the differences in chl a (in situ data are in general 2 times higher than satellite data) with the largest differences in the regions from 10–25 to 40–45∘ N. As the discrepancies between in situ and satellite data are significant, in situ measured data of chl a are used from now on for further calculations with the ISOPS05 model. Using monthly mean satellite data for wind speed, SST, and climatological values for MLD does not bias the model results significantly relative to the in situ data. Eight-day mean chl a and weekly wind speed satellite data (not shown) are also available and could lower the discrepancies to the in situ data. For this study, 8-day values were not useful for this region and time due to cloud coverage (loss of 46 % of data points). A compromise between the two would be to average the 8-day values over a larger area grid to increase the amount of satellite-derived data, but this would lower the resolution and therefore the accurate comparison with the cruise track.

Palmer and Shaw (2005) used a universal Pchloro value of 1.8 ± 0.7 µmoles (g chl a)-1 day-1 based on laboratory phytoplankton monoculture experiments with several cyanobacteria, eukaryotes, and coccolithophores (Table 1; Shaw et al., 2003). Subsequent laboratory experiments with monocultures of different phytoplankton species have shown generally higher isoprene production rates with large variations between PFTs (Arnold et al., 2009; Bonsang et al., 2010; Colomb et al., 2008; Exton et al., 2013). In addition, Tran et al. (2013) observed that isoprene concentrations in the field are highly PFT dependent.

We averaged the Pchloro values of different PFTs (Table 2) and multiplied these values by the amount of the corresponding PFT. Using PFTs instead of total biomass of phytoplankton (chl a) in the model run results in higher isoprene model concentrations (orange, Fig. 4), which match the overall isoprene concentration levels measured north of 10∘ N quite well. However, there are also regions where the model still cannot reproduce the measured isoprene concentrations. Between 10∘ N and 25∘ S, the calculated isoprene concentrations are quite stable with only small variations between 6 and 23 pmol L-1. Measured concentrations are slightly higher between 10∘ N and 12∘ S (15–30 pmol L-1) and sharply increase to 40–60 pmol L-1 south of 12∘ S with a maximum concentration of 150 pmol L-1 (16∘ S). As there were no significant differences in wind speed, SST, or MLD in these two regions during the cruise, there must be at least one additional source which is not captured in the model. In contrast, at 15∘ N and at 22∘ N the model overestimates the isoprene concentration (Fig. 4). Chl a concentrations are 10–20 times higher in these two areas than elsewhere on the cruise (Fig. 3) and dominated by diatoms. However, the calculated isoprene is not 10–20 times higher, since diatoms have a relatively low Pchloro value (2.54 µmol (g chl a)-1 day-1) and, therefore, using their respective PFT value modulates the influence of the increased chl a on isoprene concentrations (Fig. 5).

Excluding the two bloom areas, the main PFTs contributing to the modeled isoprene concentrations were prokaryotic phytoplankton (cyanobacteria and Prochlorococcus) and haptophytes (Fig. 5, see also Taylor et al., 2011a). It should be noted that the PFTs considered in our study are only part of the full phytoplankton community. In addition, these values can be easily over- or underestimated due to a high variability in the Pchloro values within one group of PFTs (e.g., haptophytes: 1–15.36 µmol isoprene (g chl a)-1 day-1; Table 2). Using the ISOPFT-kBIO model approach, the isoprene concentrations increase by a factor of 1.35, resulting in better agreement with the observations (Fig. 4). Overall for the conditions of this cruise, the ISOPFT-kBIO model simulation yields 12-fold higher isoprene levels than ISOPS05 (mean error of 11.8 pmol L-1).

It is obvious that even after implementing these changes the model does not reproduce all the measured isoprene values or their distribution pattern. One particular problem is that marine isoprene emissions are very low in comparison to terrestrial isoprene emissions. Coastal emissions have to be calculated and interpreted carefully due to this terrestrial influence. We assume no terrestrial influence in the open ocean, since the atmospheric lifetime of isoprene is short. Despite the terrestrial influence on atmospheric isoprene values over the ocean, calculating surface ocean isoprene concentrations, other assumptions in the model should be scrutinized in order to understand the discrepancies between measured and calculated values:

The model assumes well-mixed isoprene concentrations through the MLD, which is, in fact, not the case. Measurements of depth profiles show a vertical gradient with a maximum of isoprene at the depth of the chl a maximum slightly below the MLD (Bonsang et al., 1992; Milne et al., 1995; Moore and Wang, 2006), which was also measured during our three campaigns (data not shown). Gantt et al. (2009) tried to solve this problem using a light-dependent isoprene production rate, but this resulted in high fluxes in the tropics that are questionable when compared to field measurements.

Isoprene concentrations calculated with the original (ISOPS05) and revised (ISOPFT-kBIO) model are compared to measured isoprene in the surface ocean at two additional campaigns in two widely differing ocean basins (Indian Ocean, SPACES/OASIS, 2014; eastern Pacific Ocean, ASTRA-OMZ, 2015). The original model ISOPS05 predicts on average 19 ± 12 times lower isoprene concentrations compared with measured values for the additional two ship campaigns (circles, Fig. 6), which confirms the results obtained for ANT-XXV/1. With the newly determined (lower) value for kBIOL and PFT-dependent Pchloro values, the ISOPFT-kBIO model predicts concentrations that are 10 times higher than the original model ISOPS05 output (crosses, Fig. 6). This leads to a mean underestimation of 1.7 ± 1.2 between modeled and measured isoprene concentrations. The main cause of the better agreement between measured and modeled isoprene concentrations is the isoprene production rate related to the production input parameter (color coding, Fig. 6). The mean isoprene production rate using chl a as an input parameter multiplied by a factor of 1.8 µmol (g chl a)-1 day-1 is less than 0.5 pmol L-1 day-1, which is insufficient to explain the measured concentrations in all three campaigns. Using Pchloro values multiplied with the concentration of the related PFT yields in an isoprene production rate of 1–2 pmol L-1 day-1 in non-bloom areas and even higher rates during phytoplankton blooms, resulting in isoprene concentrations that are comparable to the measured ones. The opposite can also occur, as seen on DOY 322 (Fig. 6), when PFT specific production rates are smaller than those using chl a only, due to the dominance of a low isoprene-producing PFT. Even though the improved model is tested in three widely different ocean basins, there are still different regions where the model should be tested with direct isoprene measurements to verify the model output.