SOOP Finnmaid is equipped with a variety of sensors to survey the surface water of the Baltic Sea between Lübeck–Travemünde in Germany and Helsinki in Finland (Fig. ). Parameters including SST, salinity, pCO2, and cCH4 are logged every minute. The data set used for this study refers to the time period from May to September and the regions defined in Table  and consists of 482 transects from 2010 to 2017.

The on-board trace gas measurement system consists of a Los Gatos Research CH4 and CO2 analyser coupled with an air–water equilibrator , which is described in detail in and , including details on the following calculations: the measured variables are the mole fractions xCO2 and xCH4 in parts per million, which are corrected to dry-air values using xH2O data from the same instrument. These mole fractions are converted into partial pressures using atmospheric pressure data and calculating saturation water vapour pressure following under the assumption of 100 % humidity in the equilibrator headspace. In literature, CO2 data are usually reported as partial pressure or fugacity, while CH4 data are converted into concentrations. Accordingly, we report pCO2 and cCH4; the latter was calculated from the partial pressure (pCH4) using Bunsen solubility coefficients determined by . Note that we can handle the concentration (of CH4 in nmolL-1) as a quasi-conservative parameter with respect to temperature changes in the discussion as the influence of temperature on water density is negligible in this case. In contrast, the partial pressure (of CO2) in equilibrium with the water phase is temperature-dependent (see also Sect. ). To compensate the effect of water warming from inlet to equilibrator, pCO2 is temperature-corrected following . The data set was not corrected for equilibrator response times, which especially affect CH4 measurements due to its poor solubility , for reasons detailed in Sect. .

We post-calibrated xCO2 and xCH4 using a single-point calibration to a standard gas at near-atmospheric mole fractions. These standard gas measurements were performed automatically when leaving the harbour to yield a drift correction between transects. The measurement system aboard SOOP Finnmaid also includes a LI-COR 6262 CO2 and H2O analyser with a separate equilibrator. Even though these additional CO2 data are not presented here, they provided cross-validation and quality control. Presenting both CO2 and CH4 measurements from the same instrument ensures the best consistency between the two trace gases. Therefore, minor deviations from the previously published CO2 data set in SOCAT Surface Ocean CO2 Atlas; https://www.socat.info, last access: 31 August 2020, exist, which is a combined product of both set-ups. In the study area and period, these differences in pCO2 have a median of 0.75 µatm and an interquartile range (IQR) of 2.1 µatm.

We further used monthly averaged atmospheric CO2 and CH4 data to calculate atmospheric-equilibrium conditions. For the closest distance to observations from SOOP Finnmaid, we utilised atmospheric data from Utö station (Finnish Meteorological Institute, Helsinki) starting in March 2012. Prior to that or to fill gaps in the Utö series, atmospheric data from Mace Head station (National University of Ireland, Galway) via the NOAA Earth System Research Laboratories (ESRL) carbon cycle cooperative global air sampling network were used, and both data sets were matched to those of Utö by linear regression (Fig.  for details). The atmospheric data are displayed as atmospheric partial pressure for CO2 or as equilibrium concentration calculated from SST and salinity for CH4. We also plotted relative CH4 saturation, which is the ratio of cCH4 to equilibrium concentration.

Wind-induced upwelling in summer results in decreasing SST. Thus, to attribute trace gas signals in the data set of SOOP Finnmaid to upwelling and to assess the spatial and temporal dimensions of upwelling events, we combined reanalysed wind and modelled SST data to locate upwelling events in space and time before starting the actual in situ data analysis. Using modelled SST data enabled us to also identify events that SOOP Finnmaid missed. We found that model-derived SST data were more suitable than remote-sensing-derived SST data, which are subject to, for example, cloud coverage.

We used the SST output of the numerical ocean model GETM (General Estuarine Transport Model) for the Baltic Sea. The model has a horizontal resolution of 1 nmi and 50 vertical terrain-following levels. The uppermost level has a maximum thickness of 50 cm to properly represent the SST and ocean–atmosphere fluxes. The model run covers the period from 1961 to 2019. For a detailed analysis of the model performance see and . For the present run, we restarted the model in 2003 but changed the atmospheric forcing to the operational reanalysis data set of the German Weather Service (DWD), with a spatial resolution of 7 km and a temporal resolution of 3 h . The same wind data – extracted for one location per upwelling region, respectively (Fig. ) – were used to identify upwelling events (Sect. ). To give an impression of the model performance, Fig.  and Animation S1 in the Supplement illustrate SST in the Baltic Sea during a strong upwelling event taken from both the model and a multi-sensor level 3 SST remote sensing product for the European seas . This comparison demonstrates both good agreement and the advantage of model data due to insensitivity to cloud coverage. Differences between modelled SST data along the track of SOOP Finnmaid and shipboard SST observations in the entire study area and period have a median of 0.04 ∘C and an IQR of 1.41 ∘C. Differences between model and observations partly result from different timescales, i.e. daily means (model data) vs. real time (in situ data).

Based on the statistical analysis of upwelling in the Baltic Sea by , we defined major upwelling areas that SOOP Finnmaid crosses (Fig.  and Table ). We excluded the Arkona Basin and the Mecklenburg Bight (areas west of 14∘ E) because strong wind may trigger vertical mixing through the entire water column in these shallower areas, thereby eliminating the usual decoupling between sediment and surface water and greatly enhancing surface trace gas concentrations . Thus, it is impossible to disentangle the influence of wind-induced upwelling in these areas by the method proposed here. We included an area in the open Gotland Sea, which should not be directly influenced by upwelling due to being far from the coast (>40 km; Table ), for comparison. Furthermore, we only considered data from May to September each year, when upwelling-induced SST signals can be observed , which is – together with a wind criterion – the basis of the detection method we used.

According to , we defined an upwelling event as upwelling-favourable wind, i.e. the wind component projected parallel to the coast (Fig. ) exceeding 3.5 ms-1 for 2 d, causing a temperature drop by more than 2 ∘C in the respective box. Both criteria (wind and ΔSST) were evaluated per day and box and visualised in yearly plots, which also display data coverage of SOOP Finnmaid (Fig. , , and ).

We calculated the wind criterion as a running mean of upwelling-favourable wind speeds of the last 48 h with a temporal resolution of 3 h. The criterion is considered to be “met” if at least four of the eight mean values per day exceed the threshold of 3.5 ms-1.

The ΔSST criterion was calculated as the difference between median and minimum model SST in the respective area since a local upwelling event will lower the minimum SST, while the median remains relatively stable. To achieve a more robust median, the boxes were selected to extend beyond the actual upwelling areas. This results in a pronounced increase in ΔSST during upwelling events, while the criterion is mostly below the 2 ∘C threshold otherwise. This calculation can be based first on the entire area inside the boxes (Fig. ) or second on just the sub-transects, i.e along the track of SOOP Finnmaid (Fig. ). We mainly used the latter for the purposes of this study, which is justified by a comparison of the capability of both approaches to match a daily ΔSST criterion calculated from SST observations aboard SOOP Finnmaid: the second approach based on sub-transects is less sensitive (hit rate: 0.57 vs. 0.94 for the first approach) but has a higher specificity (false alarm rate: 0.08 vs. 0.48) and better skill to forecast correctly (proportion correct: 0.88 vs. 0.57; critical success index: 0.36 vs. 0.21). These verification measures were calculated according to . The differences in number of events correctly identified depending on which subset of SST data is used are explained by the fact that upwelling events start near the coast and then propagate seawards, and thus SST drops along the sub-transect are delayed and often smaller. The first approach (using all SST data within the upwelling box) does not incorporate this lag but is usually better aligned with the wind criterion for the same reason. Therefore, the appropriate method choice depends on the desired use: including more spatial coverage of SST data would be appropriate to analyse the occurrence of upwelling in a certain region statistically. However, we chose to use only SST data along the SOOP route to amplify the agreement with the in situ SST and trace gas measurements. We provide a more detailed method assessment in Sect. .

Note that a large-scale upwelling event triggers a drop in median SST, but due to increased spatial variability during those events, the sensitivity of ΔSST is usually still sufficient to exceed the threshold of 2 ∘C in these cases (e.g. Figs.  and on ca. 10 August 2016).

To assess the prevalence of upwelling in the data set of SOOP Finnmaid, we identified the main upwelling periods and areas along the transect using the method of combining a ΔSST and a wind criterion (Sect. ). Here, we present a summary of the climatological mean number of days per month and box where the criteria were met (Fig. ). The ΔSST criterion was calculated based on sub-transects. We provide a full overview further distinguishing by year and selection of SST data (entire box vs. sub-transect) in the Appendix (Figs. , , and ). The wind criterion is usually met more frequently than the ΔSST criterion calculated along sub-transects. This reflects that not every occurrence of wind strong enough to induce upwelling leads to upwelled water masses actually reaching the track of SOOP Finnmaid. This is illustrated in Fig.  (June 2016) and Animation S1. Downwelling may also lead to quickly vanishing signals (Sect. ). In general, the ΔSST criterion is not very sensitive in May due to a less pronounced thermocline compared to summer. Similarly, only small upwelling-induced trace gas signals are observed in May, which become greater in late summer owing to longer decoupling of surface water and underlying sub-thermocline waters (Sect. ). Upwelling in autumn and winter either leads to a general deepening of the mixed-layer depth discussed in or plays no important role when the physical and biogeochemical differences between surface and upwelled waters have vanished in winter.

The ΔSST criterion based on the entire area is more sensitive than that calculated along sub-transects but less specific regarding the prediction of upwelling in dynamic areas like the GoF since it is essentially a measure for SST variability>2 ∘C within the box (Sect. ). It is triggered more frequently than the wind criterion, and due to the high sensitivity of ΔSST, the agreement with the wind criterion – thus both criteria being met – is high (Fig. ).

The Born, Ö-S, Ö-E, Go-SE, and GoF boxes follow similar patterns with respect to both criteria (Fig. ), which is not surprising given the fact that in all of these cases, upwelling is induced by the same south-westerly to westerly winds, and the minimum distances to the coast are rather similar. The upwelling-favourable wind direction is opposite in the Go-NW and Hiiu boxes. In the Hiiu box, however, both criteria are almost never met at the same time, which indicates that the distance between sub-transect and coast is too large to observe strong upwelling signals (minimum of 27 km, median of 43 km; Table ). Admittedly, the sub-transect in the Ö-S box is comparable to Hiiu in terms of distance to the coast, but the crucial difference seems to be the upwelling-favourable wind direction since strong westerly winds are more frequent and intense. This is supported by the fact that, even if we calculate ΔSST based on the entire area, the number of days where both criteria are met in the Ö-S box is higher than in the Hiiu box (Fig. ), clearly indicating that upwelling is more common in Ö-S. In contrast, the sub-transect in the Go-NW box is frequently influenced by upwelling, but yet, it is the only box where the ΔSST is met more often than the wind criterion (Fig. e). We attribute this to the small distance to the coast (minimum of 4 km, median of 10 km; Table ) leading to higher SST variability and thus more similarity to the ΔSST criterion that includes the entire area (Fig. e).

Based on this statistical analysis, we chose the Ö-S box as an example area for most of the following discussion since it features prominent upwelling signals concerning both frequency and magnitude. Additionally, data coverage in this area is high as it is crossed by SOOP Finnmaid on either of its routes (Fig. ).

In this section, we investigate upwelling events that were caused by strong winds across the entire study area in August 2016, leading to temperature and trace gas signals in almost all previously defined upwelling areas (Figs.  and ), which allows us to compare the observations in these regions and to assess the importance of upwelling for the observed trace gas dynamics. This case study exemplifies more general findings we gained during the analysis of the entire data set.

The entire month was characterised by strong westerly to south-westerly winds (Fig. ), leading to upwelling in the Born, Ö-S, Ö-E, Go-SE, and GoF boxes, interrupted by a week (15–22 August 2016) of more north-easterly winds, triggering upwelling in the Hiiu and Go-NW boxes. The resulting SST drops by up to 16 ∘C predominantly near all southern and eastern coasts propagated seawards and relaxed within several weeks (Animation S1). Coverage of data from SOOP Finnmaid in this period is very dense, with the majority of transects along the east side of Gotland (see ratio of black and grey dashes in Fig. ). We illustrate the temporal and spatial evolution of this event (Fig. ) taking the example of the Ö-S box.

Before the event, SST is at a typical summer value of 21 ∘C throughout the entire sub-transect. As expected, upwelling leads to SST decreases (displayed as peaks in Fig. a) with temperatures down to 9 ∘C. These minima move over time (see also Animation S1) and are subject to relaxation, which is further discussed in Sect. . The pre-upwelling temperature is usually not reached again during this time of the year, most probably due to an increased mixed-layer depth as an additional effect of stronger winds and weakened solar irradiation at the end of August.

The observed trace gas patterns are similar to the temperature distribution: the first sub-transect can be considered to be background conditions with typical late summer values of about 250 µatm for pCO2 and 3.2 nmolL-1 for cCH4 in this area. During the upwelling event, we observe elevated pCO2 and cCH4, with trace gas maxima correlated to minimum SST. For CO2, this results in a switch from undersaturation to supersaturation. CH4 is always supersaturated or in equilibrium with the atmosphere in the SOOP Finnmaid data set, and strong upwelling further increases this supersaturation and, eventually, CH4 outgassing. However, upwelling is not the only factor controlling increased CH4 supersaturation (Fig. d). Warming of upwelled waters increases pCH4 and, therefore, relative saturation. As with SST, the enhanced trace gas levels relax subsequentially.

To extend these findings to the different regions, we investigated the relationships between trace gas data and temperature over time (Fig. ). The example from the Ö-S box is representative of the majority of strong upwelling events affecting trace gases in the data set of SOOP Finnmaid, which are generally characterised by near-linear relationships between trace gases and SST. Maximum pCO2 and cCH4 values would not be reached without upwelling in summer (Fig. ). We observe the same behaviour in the Go-SE, Ö-E, and Go-NW boxes despite their reduced data coverage (Fig. ). The Ö-E box features the highest pCO2 in the data set of over 800 µatm. In the Go-NW box, the observable upwelling event began only at the end of trace gas data coverage on the western route due to a different favourable wind direction; hence, the more extreme values are missing in this example. However, the resulting pattern resembles the ones of the Ö-S, Ö-E, and Go-SE boxes, just with lower maximum pCO2 and cCH4.

The Born and GoF boxes show the same relationships as the previous boxes in their pCO2–SST diagram, with considerable dynamic range in the case of the GoF box (Fig. a and g). The respective cCH4–SST diagrams, however, only contain a small branch of increasing cCH4 with decreasing SST (Fig. i and o). These regions are dominated by temperature-independent CH4 variability, which indicates that other processes than upwelling might cause higher-than-usual cCH4: the Born box is situated between two basins (Arkona and Bornholm basins), which are interlinked via lateral transport and which both feature gassy sediments , from which CH4 may be released via pressure changes caused by strong winds ; cCH4 variability in the GoF box might be driven by the highly variable physical conditions, e.g. changes in the estuarine circulation up to full reversal or enhanced vertical transport by boundary wall shear . These effects would lead to a less distinct impact of upwelling compared to the Ö-S, Ö-E, Go-SE, and Go-NW boxes, where vertical decoupling is more stable.

The discussed phenomena can be contrasted with the behaviour of the sub-transect within the Hiiu box: although we find a clear correlation between decreasing SST and increasing pCO2 resembling that of the other boxes, we do not observe temperatures lower than 15 ∘C and pCO2 higher than 420 µatm, which is close to atmospheric equilibrium (Fig. f). This relationship is similar to that of the openGo box, the patterns in which we attribute to mixed-layer deepening and air–sea gas exchange caused by stronger winds instead of upwelling because of its distance to the coast (minimum of 40 km, median of 64 km; Table ). Since the route of SOOP Finnmaid within the Hiiu box is the farthest away from the coast of all boxes (minimum of 27 km; median of 43 km; Table ), and the observed pCO2–SST relationships are so similar to openGo, we infer that upwelling has only minor influence on the observed values in this region during this time period. This is consistent with maps of modelled SST (Fig.  and Animation S1; most pronounced around 18 August 2016), where no upwelled water masses reach out to the ship track, and confirms the same finding from the statistical identification of main upwelling areas presented in Sect. .

The cCH4–SST diagram of the Hiiu box (Fig. n) resembles, to some extent, that of the GoF box (Fig. o) without the upwelling branch and smaller maximum cCH4 and indicates considerable cCH4 variability compared to, for example, the Ö-S, Ö-E, Go-SE, and Go-NW boxes. In late July, for example, CH4 concentration drops from 4.8 to 3.3 nmolL-1 at more or less constant temperature (Fig. n), equating to a change in relative CH4 saturation from 1.9 to 1.3. In the adjacent region of openGo, no instances of increasing cCH4 at constant SST (vertical branches in Fig. n–p) were observed.

We summarise that upwelling affects observed SST, pCO2, and cCH4 drastically in the defined boxes in late summer of 2016. It typically causes near-linear relationships between surface trace gas signals and temperature with varying ranges and slopes between regions. For CO2, this can be observed in all regions (with limitations in the Hiiu box), while in the case of CH4, strong variability caused by other processes may mask the effects of upwelling, and closest-to-linear relationships are observed in the Ö-S, Ö-E, Go-SE, and Go-NW boxes.

The surface water properties of a region influenced by upwelling change over the course of the upwelling event. This can be seen in Fig. , where the evolution of the relationship over time between SST and pCO2 or cCH4 is indicated by colour, and in Fig. . Before an event, we observe high temperature and low trace gas levels, with low spatial variability within sub-transects. During strong upwelling, a larger variability in SST, pCO2, and cCH4 is observed concurrently as SOOP Finnmaid transects the respective region. Trace gas and SST data are usually related linearly after the upwelling event. After upwelling-favourable winds cease, the range of signals as well as their intensity is reduced through relaxation in a quasi-linear fashion (Fig. ). The final state after relaxation, when compared to the initial state, is shifted towards lower temperatures; higher pCO2; and slightly elevated cCH4, which equals a roughly comparable CH4 supersaturation at this decreased, final temperature. Depending on the time of the year, SST might re-increase due to subsequent warming or not recover completely (as in late summer).

In order to discuss the processes that are involved in the relaxation of upwelling signals, we calculated theoretical relaxation curves in trace gas–temperature diagrams (Fig. ). Assumed endmember characteristics, physical driving parameters, and process descriptions are summarised in Sect. . We focus on air–sea gas exchange, air–sea heat exchange, and mixing with a typical water mass with pre-upwelling conditions. CH4 oxidation in the upper, oxic water column should not play a major role on the short timescales considered here . Primary production (e.g. by nitrogen fixation) has the potential to decrease pCO2 distinctly but is difficult to constrain since it depends on meteorological conditions and nutrient availability with possible time lags of several weeks .

The relaxation of SST is mainly driven by mixing. We estimated a total surface heat flux of ca. 300 Jm-2s-1, which translates to a daily SST change of ca. 0.4 Kd-1 assuming a mixed-layer depth of 15 m, which is rather typical for windy conditions in summer (derived from model data, not shown). Therefore, air–sea heat exchange contributes only little to the observed warming of upwelled water masses on the order of 5–10 K, leaving mixing as the dominant process. Despite the excess of the surrounding water masses, mixing does not necessarily lead to pre-upwelling conditions since the endmember may change due to enhanced mixing in the open basins caused by stronger wind. SST might re-increase in the following weeks depending on meteorological conditions.

Mixing also shapes the typically observed cCH4–SST relationships (Figs. i–o and a), leading to near-linear mixing curves since concentration is a conservative parameter with respect to temperature changes (we neglect the influence on water density here). The upwelled water mass releases ca. 7700 nmolm-2d-1 of CH4 into the atmosphere. This results in a daily cCH4 loss of 0.51 nmolL-1d-1 in a 15 m mixed layer, which is an efficient sink considering the magnitude of observed concentrations. Therefore, air–sea gas exchange alters the slope of the cCH4–SST relationship. Note, however, that gas flux is highly dependent on wind speeds, which are biased in cCH4–SST diagrams presented here: pre-upwelling conditions involve low wind speeds, while the upwelling event is caused by stronger winds, which eventually weaken. Heat exchange has no influence on cCH4, but the relative CH4 saturation is determined by its partial pressure pCH4, which increases by the order of 2 %K-1 . This effect should not play a major role concerning relaxation given the low surface heat flux. However, as outlined above, SST might re-increase in the following weeks, thereby increasing pCH4, and thus potentially lead to enhanced fluxes into the atmosphere over a longer time period of weeks following the upwelling event. Likewise, mixing leads to elevated pCH4 and relative saturation compared to linear behaviour (Fig. b).

Similarly, the relaxation of pCO2 cannot be considered independently from SST relaxation due to its temperature dependence. Warming by air–sea heat exchange causes a pCO2 increase on the order of 4 %K-1 , which should not play a major role concerning relaxation given the low surface heat flux. As with pCH4, however, this effect could lead to increasing pCO2 and enhanced CO2 fluxes into the atmosphere (or reduced fluxes into the sea) in the following weeks.

The relaxation of upwelling-induced pCO2 signals (Fig. a–g) cannot be explained solely by mixing because the theoretical pCO2–SST mixing curve obtained from CO2 system calculations features a distinct curvature with lower pCO2 compared to linear behaviour (Fig. d). The observed near-linear relationship is likely caused by air–sea CO2 exchange: at a wind speed of 10 ms-1, the upwelled water mass in this example (Fig. d) releases ca. 0.074 molm-2d-1 of CO2 into the atmosphere, which translates into a daily CT (total dissolved inorganic carbon) loss of 4.8 µmolkg-1d-1 in a 15 m mixed layer. This CT decrease in CO2-oversaturated waters explains the deviation from the expected linear (conservative) mixing curve in CT estimated from pCO2 observations (Fig.  vs. Fig. c). Primary production triggered by upwelling has a similar (potentially even greater) influence on pCO2 but with different kinetics. One could argue that air–sea CO2 exchange should similarly increase CT in CO2-undersaturated waters, which is not observed (Fig. ). This can be explained with the aforementioned wind speed bias, resulting in very low fluxes under pre-upwelling conditions (see also Sect. ). The bent CT–SST curve translates into a near-linear pCO2–SST curve, which, in conclusion, can be interpreted as the combined result of mixing and decrease in the highest pCO2 values due to gas exchange and possibly primary production.

The importance of air–sea gas exchange as a relaxation process and the potential long-term effect of increasing supersaturation due to heat exchange imply that upwelling amplifies surface trace gas fluxes, especially for CH4, by circumventing the sink of CH4 oxidation in the water column. mentioned these upwelling-induced trace gas fluxes previously for the Baltic Sea but questioned the importance for the annual balance since the upper water column would be ventilated in autumn and winter anyhow, and CH4 turnover times in the upper, oxic water column are on the magnitude of years . Despite a more detailed analysis of the statistical prevalence of upwelling in this study, the question of the importance of upwelling in the annual trace gas balance of the Baltic Sea cannot be answered here based on the data available. Apart from the high variability within observed upwelling events, general statements on this matter are further complicated by little knowledge about fluxes in shallow areas , large heterogeneities between basins , and the unknown CO2 source and sink behaviour of the entire Baltic Sea . Answering this question in the future requires more knowledge of the Baltic Sea CO2 and CH4 balances in general and extended insight into limitations of upwelling-induced flux estimates in the Baltic Sea (discussed in Sect. ).

Another possible relaxation pathway is downwelling. Figure  provides an example of quickly vanishing upwelling signals after turning wind. There, we expect downwelling to quickly remove upwelled waters from the surface, thereby restoring the previous surface water mass that underwent only small changes in SST, pCO2, and cCH4. This limits enhanced trace gas fluxes to a short time period during the upwelling event. This example is rather unique because it requires upwelling- and downwelling-favourable wind conditions in quick succession and can only be observed in close proximity to the coast (the Go-NW box in this example), i.e. where the upwelled water mass is young and has not yet expanded towards the open sea. We can exclude lateral transport out of the box as a possible explanation for this effect based on maps of modelled SST (data not shown).

Since upwelling in the Baltic Sea is an episodic phenomenon based on wind conditions, it is subject to considerable interannual variability. In Fig. , we present seasonal plots (from May to September) of pCO2 and cCH4 versus SST in the Ö-S box. The coloured date scale allows the temporal evolution of signals to be followed throughout the season and also highlights larger data gaps (e.g. in 2012 and 2013).

Most years feature consistent patterns with respect to pCO2 (Fig. ), reflecting its yearly cycle see Introduction and: CO2 is already undersaturated with respect to the atmosphere in May due to primary production during the spring bloom. Over the following weeks, the change in pCO2 is usually rather small, but SST increases as a result of solar irradiation and often weaker winds (see also Fig. ). The resulting stabilisation of the surface thermocline and the accumulation of remineralised CO2 below combined with decreasing air–sea CO2 exchange and ongoing primary production lead to increasing pCO2 gradients between surface and sub-thermocline water (which are the cause of upwelling-induced pCO2 signals; Fig. ) and a permanent undersaturation of the surface water with respect to the atmosphere. The characteristic cCH4–SST conditions follow the CH4 equilibrium curve towards lower concentrations at higher temperatures most probably due to air–sea CH4 exchange, maintaining a persistent supersaturation. In most years, most notably in 2010, 2012, 2014, and 2016, strong upwelling around August overrides these typical summer conditions, resulting in characteristic pCO2–SST and cCH4–SST patterns. For these years, the ranges of SST, pCO2, and to a certain extent cCH4 are similar (but still not equal), with the notable exception of very dynamic cCH4 in 2010. For the other years, we observe a high degree of variability from these typical conditions: strong upwelling-favourable winds in June 2011 led to an early increase in pCO2 and lower SST overall. Later, at the end of July 2011, a pronounced, sharp increase in cCH4 at a rather constant temperature was observed, which clearly is not related to upwelling.

The year 2015 is particularly interesting because it demonstrates the influence of quasi-continuous upwelling-favourable winds over the course of several months, which overrides the typical summer trace gas situation. The year was dominated by upwelling-favourable, westerly winds until the beginning of August (Fig. ), effectively prohibiting strong thermal stratification of the surface water (Fig. a and low maximum temperature in Fig. f and n). This special case is problematic for the detection method because the observable ΔSST gradients become too small for every day to be counted as an “upwelling day” (Fig. ). As a result of weakened stratification, surface CO2 undersaturation is unusually weak compared to the typical summer situation (Fig. b and high minimum pCO2 in Fig. f). Furthermore, we observe reduced cCH4 variability as a result of continuous mixing and intensified air–sea exchange through increased turbulence so that cCH4 follows the equilibrium curve more closely than during most years (Fig. n). Elevated cCH4 (Fig. c) does not necessarily translate into elevated saturation (Fig. d) depending on SST; however, as pointed out in Sect. , the water mass will become supersaturated as a consequence of subsequent warming. In July 2015 (turquoise hues in Fig. f and n), near-linear trace gas–temperature curves are characteristic for strong upwelling (see Sect. ). Compared to, for example, August 2014 and 2016, however, where the upwelling SST, pCO2, and cCH4 signals stand out prominently from the rest of the values, their range concerning all three parameters is reduced in 2015 since decoupling of surface and underlying water was partly impeded.

It was not possible to identify trends in frequency or magnitude of enhanced pCO2 and cCH4 caused by upwelling events on the limited timescale of 8 years covered by our observations. The main reason for this is the high spatial and temporal variability in upwelling (and of several other processes with influence on dissolved trace gases) in the Baltic Sea, which led to the necessity to do parts of the analyses on a per-event basis and effectively impeded a universal approach. Moreover, the observed endmembers of minimum SST and maximum pCO2 and cCH4 are dependent on data coverage, which adds another layer of uncertainty to any trend analysis on the data set, especially in boxes around Gotland (two different ship routes) and during years with larger data gaps. Typical water residence times of 10–30 years imply that longer trace gas time series are needed to detect not only variability but also trends using the methods we presented here. In fact, managed to find a trend in surface pCO2 between 4.6 and 6.1 µatmyr-1 in the Baltic Sea from 2008 to 2015 but did so without a focus on upwelling events only and by filling data gaps through interpolation, which effectively yielded a considerably larger data basis compared to this study. We suppose that if, at some point, the extrapolation scheme proposed in Sect.  could be expanded to cover more than single events, a trend analysis based on the resulting pCO2 and cCH4 fields should be possible since these data would not be restricted by spatio-temporal coverage or event-specific features.

The observed near-linear relationships between pCO2 or cCH4 and SST can be used to spatially extrapolate trace gas observations from sub-transects based on modelled SST fields, assuming that these relationships are consistent for entire upwelling areas. This enables us to estimate air–sea CO2 and CH4 fluxes resulting from upwelling events (Fig. , Sect. ). Since we used linear regression (Fig. f and g), SST minima near the coast translate into pCO2 and cCH4 maxima, retaining the overall pattern and fine structure of the SST field (Fig. a–c).

The CO2 flux (FCO2; Fig. d) depends on the difference in pCO2 between sea and air, which determines the flux direction, and the transfer coefficient, which is parameterised mostly by wind speed. Therefore, pCO2 and FCO2 share the same spatial pattern, with positive and negative fluxes being present in the box at the same time. Both CO2 outgassing (0.13 molm-2d-1) and uptake (-0.046 molm-2d-1) peak on 9 August, when wind speeds are highest. CH4 fluxes (FCH4; Fig. e) into the atmosphere reach their maximum (5730 nmolm-2d-1) on the same day. However, the spatial distribution of FCH4 differs from that of cCH4 due to the temperature dependence of the CH4 equilibrium concentration: for instance, the lowest fluxes on 10 August occur close to the coast despite high concentrations in this area because supersaturation decreases with lower SST, indicating that the upwelled water mass has a lower CH4 supersaturation than the surrounding waters in this example. However, relative CH4 saturation is highly sensitive to changes in slope of the applied regression curve, which underestimates the observed maximum supersaturation in this example (Fig. g) and likely leads to this special spatial distribution. Even careful tweaking of the regression curve would result in a pattern much more similar to that of FCO2, and this similarity increases with increasing supersaturation of the upwelled water mass compared to pre-upwelling conditions. In other examples, the two flux patterns are more similar than here (data not shown). The discussed “tweaking” of the cCH4–SST regression, though impacting the derived pattern considerably, would have only a small impact on the areal flux. In any case, daily FCH4 peaks under intermediate conditions where the flux-increasing effects of rising cCH4 and rising SST combine. On many days in this example, including 10 August (Fig. e), this area of maximum daily FCH4 is in close proximity to the transect of SOOP Finnmaid, where it can be observed by in situ measurements, whereas areas of maximum daily FCO2 tend to be closer to the coast. It should be noted that the spatial variability in FCO2 is much higher than that in FCH4 (see maximum and minimum values in Fig. i and j).

The importance of wind is also reflected by the evolution of air–sea gas fluxes over time (Fig. i and j). Fluxes are weak under pre-upwelling conditions due to low wind speeds (Fig. h); increase distinctly with rising wind speeds; and reach a minimum (considering absolute values for FCO2) in the relaxation period after the upwelling event, when the wind calms down again. The sea is a permanent source of atmospheric CH4 with varying strength based mostly on wind speed in this example, which can be generalised to the entire data set. In contrast, FCO2 is negative (CO2 uptake from the atmosphere) under pre-upwelling conditions. CO2 outgassing starts with the onset of upwelling, but at this point, the area is still dominated by increasing CO2 uptake due to rising wind speeds. Both positive and negative CO2 fluxes intensify over the following days, but CO2 outgassing reaches higher absolute values as a result of high pCO2 due to upwelling. The area is a net source of CO2 for the atmosphere (mean FCO2>0) from 9 August, when wind speeds are maximal, to 19 August, when pCO2 gradients have sufficiently diminished due to relaxation. Note, however, that mean FCO2 depends on the (arbitrary) choice of box boundaries.

The presented flux estimates depend largely on the applicability of the observed near-linear trace gas–SST relationships for the entire area and period, including extrapolation to temperatures lower than the minimum temperature of the trace gas–SST regression (i.e. towards the core of the upwelled water mass; see SST axis in Fig. f and g). Verification of this assumption would require a dedicated research cruise involving trace gas measurements perpendicular to the track of SOOP Finnmaid with transects towards both the coast and open basin. Based on the presented findings, we assume that the extrapolation scheme proposed here leads to a conservative estimate of the actual fluxes since the applied regression is based on waters that have already been subject to air–sea gas exchange (see also Sect. ) as opposed to “young” upwelled waters, which are not observed by SOOP Finnmaid. Still, the presented method provides a means to constrain upwelling-induced trace gas fluxes based on SOOP and model (or, potentially, remote sensing) data on large spatial and temporal scales, which may also be used to study other upwelling areas than the Baltic Sea. We recommend using this approach on a per-event basis to properly calibrate the applied trace gas–SST relationships, which might differ between regions and events. In general, this extrapolation method should be applicable in every upwelling area worldwide where near-linear trace gas–SST relationships are observed and could, therefore, be a valuable tool to produce flux maps from (scarce) surface observations.