Diurnal cycle of the CO2 system in the coastal region of the Baltic Sea

The direction and magnitude of carbon dioxide exchange between the atmosphere and the sea is regulated by their difference in partial pressure of carbon dioxide (pCO2). Typically, observations of pCO2 are carried out by using research vessels and voluntary observing ships which cannot easily detect the diurnal cycle of pCO2 at a given location. This study evaluates the magnitude and driving processes of the diurnal cycle of pCO2 in a coastal region of the Baltic Sea during the different seasons. We present pCO2 data from July 2018 – June 2019 carried out in the vicinity of the island of Utö 5 in the Archipelago Sea and quantify the relevant physical, biological and chemical processes affecting pCO2. The highest monthly median diurnal pCO2 peak-to-peak amplitude (31 μatm) was observed in August. This high diurnal variation was found to be related predominantly to biological processes. The biological transformations of carbon generated a sinusoidal diurnal pCO2 variation, with a maximum in the morning and a minimum in the afternoon. Compared to the biological carbon transformations, the effect of air-sea excange of carbon dioxide and the effect of temperature changes on pCO2 are smaller, with 10 their monthly median peak-to-peak amplitudes were up to 12 and 5 μatm, respectively. Single diurnal peak-to-peak amplitudes can be significantly larger (up to 500 μatm), during upwelling. If the net exchange of carbon dioxide between the sea and atmosphere on our study site and sampling period is calculated based on a data set that consists of only one measurement per day, the error in the budget depends on the sampling time and can be up to ±12%.

2 Controls on the partial pressure of CO 2 The surface pCO 2 can be altered by processes that alter dissolved inorganic carbon (DIC) or total alkalinity (T A) or affect the chemistry of the carbonate system through changes in temperature, salinity or pressure (Takahashi et al., 1993).

Carbon control of pCO 2
As dissolved inorganic carbon (see Appendix B) is introduced to or removed from the dissolved inorganic pool, the change of 5 dissolved CO 2 concentration is depicted by the so-called Revelle factor, Re (Sarmiento and Gruber, 2004): DIC in surface water can be altered by the CO 2 exchange with the atmosphere, biological transformations, precipitation/dissolution of calcium carbonate, fresh water input and mixing of water masses. The freshwater input includes evaporation, precipitation and the formation and melting of sea ice. Fresh water effect is likely negligible in diurnal time scale for the mixed layer deep 10 enough. Biological processes affecting pCO 2 include all transformations between the inorganic and organic carbon pools, i.e.
photosynthesis and respiration. The mixing processes include horizontal advection, vertical diffusion and vertical entrainment.
Arguably, mixing processes are random in nature and do not show diurnal cyclicity and thus do not affect our analysis.
2.2 Alkalinity control of pCO 2 T A (see Appendix C) is altered mainly by the formation and dissolution of calcium carbonate. Smaller contribution to T A 15 originates from nitrogen transformations through biological processes, fresh water balance and the mixing processes. T A is not affected by the air-sea exchange of CO 2 . The effect of calcifying primary producers on the carbon pool in the Baltic Sea can be neglected for open sea (Tyrrell et al., 2008). However, calcifyers may have an effect on carbon cycle in benthic zone.

Physical control of pCO 2
Temperature affects the dissociation constants and solubility, which further alters the CO 2 partial pressure. For the stable 20 oceanic conditions, this change is well documented (Takahashi et al., 1993), but in estuary conditions, the value varies significantly (Schneider and Müller, 2018). Based on the choice of the parametrization of dissociation constants, this value might show small variation as a function of temperature and salinity (Orr et al., 2015).
Similarly to temperature, also salinity affects the dissociation constants. However, salinity changes are related to mixing, and thus the interpretation of salinity effect is not straight-forward and is not dealt with in this paper. The salinity effect on 25 pCO 2 is generally small: in oceanic conditions, a salinity change of 1 would generate a 9 µatm change in pCO 2 (Sarmiento and Gruber, 2004). At Utö, the salinity varies less than 1.5 PSU during the whole year (see Fig. 1).
We neglect the effect of pressure on pCO 2 , because we are dealing with surface water pCO 2 at one depth.

Included processes controlling pCO 2
In this study, we are considering the pCO 2 changes that are generated by the changes in DIC or by temperature fluctuations. DIC changes are further divided into the changes that are caused by the air-sea exchange of CO 2 or by the biological transformations. There are multiple processes affecting the pCO 2 that are not included in the analysis.
Some of these unknown drivers, such as mixing processes and fresh water effects, are assumed to be temporally random in 5 nature and thus their effect on pCO 2 is considered to be negligible when inspecting average cycles. Some of the processes, e.g.
alkalinity related variations affecting pCO 2 are unknown and may involve diurnal cyclicity. A salinity-alkalinity relationship used in the analysis takes into account the conservative variation of these variables due to the mixing and freshwater input.
Nitrogen transformations during primary production can have small effect on alkalinity that is not considered in the salinityalkalinity relationship.

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In the results, we analyze applicability of the method by comparing the calculated pCO 2 changes to the observed changes.

Materials and methods
The Utö Atmospheric and Marine Research Station is located on the small island of Utö in the southern edge of the Archipelago Sea (59°46'55" N, 21°21'27" E). The marine observations ("marine station") at the station focus on regional marine ecosystem functioning with a large number of biochemical and physical observations. The atmospheric part of the station include a 15 wide range of meteorological, trace and greenhouse gas and aerosol measurements. Greenhouse gas and some meteorological measurements are part of ICOS (Integrated Carbon Observation System) atmospheric station network. Marine measurements of Utö Atmospheric and Marine Research Station belong to Joint European Research Infrastructure for Coastal Observatories (JERICO-RI, www.jerico-ri.eu). Carbonate system dynamics is noted as one of the key scientific topics in the coastal ocean (Farcy et al., 2019) and the current study, done under framework of JERICO-RI, highlights the need for integrated and multi-20 disciplinary observations. For detailed list of observations, site bathymetry and other information about the station, please see Laakso et al. (2018).
Our study is based on one year of data gathered between July 2018 and 2019. All data presented in this paper is given in the UTC time. Finland belongs to the UTC+2:00 timezone.
3.1 Flow-through sampling 25 The marine station is equipped with a flow-through pumping system that transports water from 250 m from the shore to the station, where seawater is analyzed automatically and manually on demand. The bottom-moored floating seawater inlet is approximately at the depth of 4.5 m ± 0.5 m. The mean depth at this location is 23 m and the sea level at Utö varies ± 0.5 m relative to theoretical mean sea level.
At the station, the transported water first enters a manifold. Any flow-through instrument can be attached to the manifold 30 separately, enabling arbitrary adjustment of the flowrate for each instrument.
All of the instruments attached to the flow-through system are automatically washed with cleaning fluid (Hydrogen peroxide or Triton X-100) daily. The data gathered during and immediately after the cleaning have been discarded.
Most of the instruments that analyze seawater logged data every 15 s. These data are shifted (5.6 min on average) according to the concurrent flow rate (54-68 LPM) to match the time of sampling at the intake, based on the known volume of the pipe system. 3.2 Measurement of pCO 2 and CO 2 pCO 2 was measured using a SuperCO 2 instrument (Sunburst Sensors), which was connected to the flow-through system. In its two shower-head equilibrator chambers, the seawater CO 2 is equilibrated with the gas above according to Henry's law (Eq. B2 is transformed into pCO 2 according to Dickson and Goyet (1994). One hour median values are used in the final analysis of pCO 2 changes.
Since the sample water temperature decrease (in summer) during the transport due the colder bottom water temperatures 15 passed by the water line, we took the effect of temperature change on pCO 2 into account using the CO2SYS matlab program.
This correction requires that knowledge of another carbon system component, which is total alkalinity (from salinity) in our case. The equilibrator temperature (together with salinity) was measured using a thermosalinograph (SBE45 MicroTSG, Seabird Scientific) next to the SuperCO 2 instrument. The in situ temperature was measured using a PT-100 thermometer at the depth of 3 m at the upper level of the thermistor chain near the inlet. On average, seawater cooled when transported, 0.4±2.0 • C.

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In May-June 2019, the sampling and inlet tube system was tested by measuring CO 2 concentrations with two SAMI 2 sensors (Sunburst Sensors) parallel to the SuperCO 2 system inside the measurement station (20-23 May 2019), after which the SAMI 2 's were deployed next to the sampling inlet in the sea (24 May -7 June 2019). The parallel measurement inside the station was used to correct the potential initial offset of the SAMI sensors, against the SuperCO 2 system. When the SAMI 2 sensors were in the sea, the in-situ concentrations for all three instruments closely followed each other and no impact on pCO 2 25 observed by SuperCO 2 was found: the root mean square difference between the between the sea inlet and the station was 4.1 µatm. The difference, or the absolute values, do not influence the analysis of diurnal cycle.
Atmospheric CO 2 molar fractions were measured at the Atmospheric ICOS site using cavity ring-down spectroscopy (Kilkki et al., 2015). Wetlabs FLNTU fluorometer, as a proxy of chlorophyll concentration, using factory calibration. Both were connected to the flow-through system. Chlorophyll A measurement was offline in winter (January-March).

Hydrographic measurements and determination of mixed layer depth
The vertical temperature profiles were measured with temperature chains, supported with regular interval CTD (Conductivitytemperature-depth) profiles. In this paper, we use the the measurements of a chain that was deployed 150 m northeast from the seawater inlet in July 2018: this chain was moored at the depth of 21.3 m ± 0.5 m, and its Pt-100 thermistors were placed at The mixed layer depth (z mix ) was determined from the temperature vertical profiles which were measured using a CTD (RBR XR-620) approximately 400 m west of the sampling inlet. CTD profiles were taken by local Ismo Willström by using a small boat, fortnightly during the productive period and with lower temporal resolution in winter (see Fig. 1). Eventhough 10 the data by the thermistor chain has higher temporal resolution than the CTD castings it is not applied for the assessment of the mixed layer depth, because it has significantly lower vertical spatial resolution. The water depth at the location of CTD castings is approximately 90 m, which is significantly deeper than the depth at the inlet location. If the mixed layer depth was larger than the depth of 23m at the inlet location, the water column at the inlet location was considered mixed. The thermocline depth, i.e. the depth of the strongest temperature gradient in the profile, was considered to represent z mix . For each CTD cast, a 15 thermocline depth was estimated. Due to the marked horizontal distance between the inlet and CTD profiling, the applicability was assessed by comparing these CTD measurements to the Pt-100 thermistor chain measurements near the inlet, which confirmed relatively good match of the measurements with the root mean square difference of 0.6 • C. The CTD measurements reproduced well the hydrography of the upper water column at the inlet location, as the root mean square differences between the sites for the depths of 3, 8 and 13 m were 0.42, 0.41 and 0.25 • C, respectively. The temperatures at 20,m, however, showed 20 larger difference, as the RMSE was 1.08 • C for this depth. This implies that the mixed layer depths were well reproduced using the CTD castings unless the thermocline was be located close to the bottom of the inlet location.

Estimation of F as
The estimation of the air-sea exchange of CO 2 between the sea and atmosphere is based on two methods: 1) on the the eddy covariance method from the data gathered using a micro-meteorological flux tower erected on the western shore of the island 25 and 2) on the wind speed based flux parametrisation. Due to strict quality control, the eddy covariance method was applicable for only 18% of time, and for the rest of the time, the parametrisation was used.
Both methods have pros and cons, due to which they complement each other. The eddy covariance method considers the integrated flux within large footprint area, whereas the parametrization is based on the pCO 2 measurement at single point at the depth of 5 m. The large footprint area may contain spatially heterogeneity in seawater pCO 2 . In some cases, the measurement 30 at the depth of 5 m may not represent the surface conditions. Additionally, the parametrization of gas transfer velocity is based on the wind speed, which solely does not contain all the information about the surface turbulence.

Eddy covariance method
The eddy covariance fluxes for air-sea exchange of CO 2 were calculated for 30 min intervals. This flux measurement is based on the closed-path non-dispersive infrared gas analyzer (LI-7000, LI-COR), of which sample air tubing has a 30 cm Nafion drier (PD-100T-12-MKA, Perma Pure) in order to eliminate the water vapor interference on CO 2 fluxes. The covariance of 10 Hz vertical wind velocity (w) and CO 2 molar fraction (xCO 2 ) data was calculated for each 30 min averaging period. These 5 fluxes were corrected for the high-frequency attenuation by using a transfer function which was calculated from the deviation of the normalized w-CO 2 cospectrum from the one of sensible heat flux. Only stationary CO 2 flux conditions were included, because during non-stationary conditions, the measured fluxes do not represent the exchange between the surface and the atmosphere. Only western winds were considered (180-330 • ) here as the flux footprint during these cases originates from the sea. Small amount of flux data were excluded from the analysis because the reference gas pipeline for the CO 2 analyzer was 10 leaking. More information about the flux system and its quality control can be found in Honkanen et al. (2018).

Flux parametrisation
We used an air-sea exchange estimation based on the quadratic relationship by Wanninkhof (2014) for the times without valid eddy flux measurements (82%). Wind speed was measured with the micrometeorological flux tower on the westenr shore, and data were converted to wind speed at the height of 10 m, U 10 . As the wind speed is not precisely measured at the height of 15 10 m, we corrected wind speed assuming a logarithmic wind profile and a constant surface roughness of 0.5 mm, a value which is based on the data of Honkanen et al. (2018). More details about the compatibility of the parametrization for this specific site can be found in the Appendix D.

Calculation of pCO 2 changes generated by different processes
Calculations were performed using the CO2SYS matlab program. Dissociation constants K 1 and K 2 were calculated based on 20 Millero (2010) and the sulfate contribution is based on Dickson (1990). We implemented the total boron parametrisation by Kuliński et al. (2018), which is based on the empirical data of the Baltic Sea, in CO2SYS.
We use total alkalinity as a second carbon system variable in our calculations. The total alkalinity used here is based on alkalinity-salinity relationship, which was determined by using the titration measurements carried out at Utö in summer 2017 (Lehto, 2019): The slope is almost identical to the dependence found for the Gulf of Bothnia by Müller et al. (2016) extrapolated for year 2017. See Appendix C for more information.
First, the carbon chemistry is calculated for each hour based on the measured partial pressure of CO 2 and parameterised total alkalinity. This way, we know the DIC at every starting step. Hourly mean values are used thorough this analysis. The effect on temperature fluctuations on the diurnal cycle of pCO 2 was calculated in CO2SYS using the T A and previously calculated DIC with the temperature of the next hour. The effect of temperature changes on pCO 2 is then quantified as the difference between this pCO 2 , that is affected only by the temperature change, and the original pCO 2 .
In the case of air-sea exchange and biological transformations, we calculated how much DIC changed over one hour and add this d DIC to the original content. We assume that total alkalinity does not change in the process, and calculated the carbon 5 system using this new DIC and the total alkalinity in order to get the new pCO 2 .
We assume that the new inorganic carbon (d DIC A ) derived from the air-sea exchange of carbon dioxide is evenly distributed within the mixed layer. DIC change due to the air-sea exchange of CO 2 is calculated as: where t is time, i.e. one hour. The value of F as is calculated using either the eddy covariance method or the wind speed based 10 parametrization depending on the concurrent wind direction and the flux stationarity.
We inferred the biological effect on DIC indirectly from the oxygen measurements by assuming the Redfield ratio (Redfield et al., 1963). As inorganic carbon is consumed (or released), a relative amount of oxygen is released (or consumed), The ratio of 106 C : -138 O refers to the Redfield ratio of carbon to oxygen (Redfield et al., 1963). However, this ratio is based 15 on average oceanic conditions and may show variations in space and time. The last term in the equation takes the effect of airsea exchange of oxygen into account. This flux, F O 2 , is calculated similarly to the carbon dioxide flux (Eq. A1) by using the gas transfer velocity, (oxygen) solubility and (oxygen) concentration gradient. Oxygen solubility was calculated according to the salinity-temperature dependence fit by Garcia and Gordon (1992) which is originally based on Benson and Krause (1980).
The Schmidt number of oxygen and gas transfer velocity were calculated according to Wanninkhof (2014). Oxygen can also 20 change due to the mixing, whose contribution remains unknown.
We examined the diurnal fluctuations of pCO 2 by examining each day at a time. For each day, the cumulative sums of the pCO 2 changes generated by different processes were calculated, and finally the mean of cumulative sum was removed from these values: 25 where i is the index of each hour and angle brackets denote the averaging.
In addition to the pCO 2 evolution generated by the air-sea exchange of CO 2 , biological transformations and temperature alone, we also examined the pCO 2 evolution generated by these three processes simultaneously. This is calculated using the new DIC that is altered by both air-sea exchange of CO 2 and biological transformations and additionally taking into account the temperature change. However, this pCO 2 change is only used for the verification of the method. Throughout the results, we use the range, r, to describe the diurnal pCO 2 variability. The range, or the peak-to-peak amplitude, is defined as a difference between the diurnal pCO 2 maximum and minimum: 4 Results and discussion 4.1 Environmental conditions 5 The measuring period started in July 2018, during phytoplankton summer minimum in the Baltic Sea (Andersson et al., 2017).
Chlorophyll A concentration was low, reflected as a low relative fluorescence unit (Fig. 1c). In mid-July, the summer cyanobacteria bloom developed, as typical for the study area (Kraft et al., 2020), which lowered the pCO 2 below 200 µatm for ca month (Fig. 2a). Another small bloom occurred in early September. In late September 2018, pCO 2 peaked at 800 µatm, which is likely a result of mixing with the sub-thermocline water masses that have high DIC due to the remineralization of organic 10 matter, which is supported by the deepening of the mixed layer depth (Fig 1a). In winter, the pCO 2 slowly equilibrated with  and (c) wind speed (gray dots) and direction (black arrows).
The thermocline was predominantly at the depth of 20 m during the summer of 2018. In autumn, the thermocline deepened and in mid-winter the water column was considered to be thoroughly mixed. Only in few cases, the thermocline may have been shallower than the inlet depth, e.g. in spring 2019, when the shallow thermocline formed quickly. Therefore, in most of the time our flow-through setup was sampling the water from the mixed layer. This supports the assumption that there were no 10 fresh water lenses or they were so short-lived that they do not play any role on the analysis. There was no permanent ice cover during the measurement period.

Examples of diurnal pCO 2 variability
Examples of pCO 2 diurnal variability in the beginning of September 2018 are given in Fig. 3. On the 2nd of September 2018, the pCO 2 showed much larger variation (452 µatm), but generally, the sinusoidal shape of 10 the diurnal variation was closely similar to the one on the 3rd day. On both days, pCO 2 had the highest change rate at 9 UTC.
The diurnal evolution supports the theory that even this large pCO 2 variation at this location could be generated by biological transformations. Again, we notice that the oxygen-derived biological component gives lower variability than observed.
The Largest (503 µatm) pCO 2 range was detected in 22nd of July, but this rare case was clearly generated by an upwelling event, as the water cooled 8 C simultaneously. This particular case is discarded from the following pCO 2 diurnal analysis.

Observed diurnal pCO 2 variability
The observed diurnal variability of pCO 2 was lowest during the winter time (Fig. 4): the monthly median range (maximumminimum) in November-February was only 4 µatm. In February the monthly median range and the range between the 10th and 90th percentiles are lowest: less than 11 µatm daily variation is expected for 80% of the time. In winter time, no clear diurnal pattern is visible, which is also indicated by the varying times for the daily minimum and maximum pCO 2 . The absence of  percentiles. The y-axis has the pCO2 deviation in µatm and the x-axis is the hour of the day. Range, r, and the time for the maximum and minimum pCO2 are also given.
In April, the observed diurnal pCO 2 variability starts to show a sinusoidal form, which remains until October. The diurnal pCO 2 minimum occurs during the afternoon and the maximum in early morning. At approximately 9 o'clock UTC (12 o'clock local summer time), the pCO 2 is closest to the diurnal mean. The monthly median range of pCO 2 increased until August, which had the highest monthly median range of 31 µatm. In the Baltic Proper, the highest diurnal pCO 2 variability (27 µatm) is met 10 one month later, in September (Lansø et al., 2017). The difference between these two datasets might be due to the interannual 12 https://doi.org/10.5194/os-2020-115 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License.
variability, as different years are compared, or it might indicate the effect of slightly longer growing season for the Baltic Proper, or the benthic production/respiration may have larger role in our shallow station than it has in pelagic Baltic Proper.
There is large variability in diurnal pCO 2 over the course of a single month during the productive season: a single day may deviate significantly from the monthly median value as, based on the 10th and 90th percentiles, 80% of the days in September have the range less than 114 µatm. The diurnal pCO 2 variability generated by temperature is generally small (Fig. 5). Apart from June, July and August, the monthly median range was 3 µatm or less. The largest monthly median range occured in July (5 µatm), when the solar irradiance has its annual maximum (Fig. 1e). Still, for 20% of the days in July, a temperature-related diurnal variability of pCO 2 > 27 µatm was observed.

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During months with high solar radiation, March-September (Fig. 1e), the maximum of the temperature-related diurnal pCO 2 cycle occurs at noon and the minimum in the middle of the night or in the early morning. In winter, the temperature-related pCO 2 does not show clear variation. We would expect a decline of the temperature-related pCO 2 in winter time, but the effect is probably small.
The measurement depth of the temperature is 3 m. For the surface conditions we would expect higher temperature-related 15 pCO 2 variability since the solar irradiance penetrating the water column decreases with the depth.

Diurnal pCO 2 variability generated by air-sea CO 2 flux
The pCO 2 diurnal fluctuations generated by air-sea exchange of CO 2 exhibits a clear trend-like pattern (Fig. 6), due to the nature of the process. This exchange drives to balance the CO 2 pools between the sea and atmosphere.
The effect is largest in September-October when the partial pressure difference and the wind induced mixing are largest. In 20 September, the monthly median range was 10 µatm. When the sea and atmosphere were nearly balanced with respect to pCO 2 as in December-March, or when the wind speeds are low as in summer months, the effect of air-sea exchange on diurnal pCO 2 variability is almost negligible (less than 2 µatm).
The mixed layer depth has an effect on this pCO 2 diurnal variability. However, the turbulent mixing that drives the CO 2 exchange between the sea and atmosphere, also deepens the mixed layer.

Biology related diurnal pCO 2 variability
The diurnal pCO 2 signals calculated from the oxygen data are closely similar to the observed ones (Figs. 3, 4 and 7). Sinusoidal diurnal variability with the maximum in the morning and the minimum in the afternoon during April-September is observed in both cases and the monthly median ranges are of same order. During the nighttime respiration (both heterotrophic and autotrophic) prevails and pCO 2 increases. Solar irradiance intensifies as the day progresses and the carbon fixation outweighs  the respiration. For our shallow measurement location, it is possible that the benthic processes may have an effect on the carbon system, especially when the water body is completely mixed.
In summer, the increasing temperature partly counterbalances the biological effect. The temperature generated diurnal pCO 2 maximum occurs approximately at the same time in the afternoon with the production generated the daily pCO 2 minimum.
However, this temperature effect is significantly smaller than the production effect.

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The largest observed and modeled biological pCO 2 diurnal variability occurs in August, and is twice as large as the one observed one during the spring bloom. On one hand, the temperature is at its annual maximum in July-August, which favors phytoplankton growth, but on the other hand, the solar irradiance is already decreasing from its annual maximum in June-July. During the spring bloom, Chlorophyll A fluorescence was high compared to the one during August, when highest pCO 2 variation is observed. The microbial part of the respiration is highly governed by the temperature, and thus the highest microbial  spring, the daily pCO 2 signal is less pronounced than in autumn due to the deeper mixed layer in spring (Fig. 1a) causing the production to be more diluted than in the case of shallower mixed layer.
Our data set suggests that on average the biological component controls pCO 2 diurnal variability, but on specific days during the biological season, other components can have greater effect as have Wesslander et al. (2011) shown.
During winter, the diurnal pCO 2 pattern generated by the biological processes is an increasing trend, which could indicate 5 mineralisation of organic matter. This kind of trend is, however, not seen in observed pCO 2 . This could be due the CO 2 release to the atmosphere counterbalancing the biological effect. This could be the case for the November, but as it is unplausible that the mineralisation would occur effectively for the whole winter. Range, r, and the time for the maximum and minimum pCO2 are also given.

Comparing observed and estimated pCO 2 variability
When comparing the observed hourly change in pCO 2 and the calculated change that takes into account all three processes (airsea exchange, biology and temperature), we found a reasonable correlation. The correlation coefficient was 0.51 (p < 0.001), which lends credibility to our approach. The correlation coefficient shows monthly variation (Fig. 8). In April, the highest correlation is found with the value of 0.89 (p < 0.001), and the lowest one in July (R 2 = 0.55, p < 0.001).

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The root mean square error (RM SE) between all hourly modeled and observed pCO 2 changes was 10 µatm. RM SE was 9-14 µatm in July-October, while it was less 3-6 µatm during the other seasons. The scatter in Fig. 8 is visibly highest in July-October. These months showed the highest diurnal pCO 2 variability (see next chapters), which may have a direct effect on the increased error. We divided the monthly RM SE values with the monthly means of the absolute hourly pCO 2 changes to find out this sensitivity variable to be 1.26 on average in March-October, whereas in November-February it was 3.29 on is large compared to the observed variability, which suggests that the estimates of the biological component during the winter time should be treated with cautious. This, however, does not have a significant effect on the analysis, since the biological activity in winter is negligible (see Fig. 1c). The fitted slope between the modeled and observed hourly pCO 2 changes appears to vary during the seasons. During the early winter months (November-January), the modeled pCO 2 changes are twice as large as the observations (slope of 2.1). and also all other processes (temperature and air-sea CO 2 flux), but these changes proved to have only negligible effect on the slopes. The crude assumption of evenly distributed DIC within the mixed layer does not take into account that large vertical gradients in DIC can be present in the water column. Photosynthesis is most pronounced in the immediate surface promoting the decrease of DIC whereas in the deeper water the mineralisation of organic carbon prevails generating larger DIC. Thus, in some cases this assumption can lead to too high presentations of DIC in the surface.
Possible error sources include the carbon-oxygen ratio in Eq. 4. The Redfield ratio for CO 2 -O 2 (-0.77) used in this paper is based on the average oceanic conditions (Redfield et al., 1963). (-0.13) and methane (-0.50). In summer time, photosynthesis takes place. The photosynthetic quotient (here, ratio of carbon dioxide assimilated to oxygen released, CO 2 -O 2 ) could be as high as -2.5 in July, which is very high compared to typical values (Laws, 1991). The diurnal pCO 2 variability can have a significant effect on the instantaneous air-sea CO 2 fluxes. The sign of the integrated daily air-sea CO 2 flux can even change, as was observed on the 22nd of July and on 2nd of September (data not shown).
Largest observed monthly median ranges in pCO 2 occurred in July-September (27-31 µatm). During this time the pCO 2 varied from slightly above 100 µatm to 800 µatm. In addition to the surface turbulence, the CO 2 partial pressure difference 20 between the sea and the atmosphere dictates the air-sea flux. The atmospheric CO 2 partial pressure is approximately constant when compared to the to the variability in the surface water. The greatest relative effect on the daily flux occurs when the sea pCO 2 varies close to the atmospheric one, i.e. at approximately 400 µatm. In late July and early August 2018, the sea was a sink and in late August and September, the sea was a source at the study site. The diurnal pCO 2 variability during these months are similar, with a maximum before noon and minimum in the afternoon. Thus, in late July and early August, the 25 pCO 2 difference between the sea and atmosphere is smallest before noon and largest afternoon. In late August and September, the situation is vise versa: largest difference before noon and smallest afternoon.
The discussion above takes into account only the diurnal pCO 2 variation even though the flux also depends on the gas transfer velocity. This might also contain diurnal cyclicity, especially during clear skies on the coastal regions, where spatially uneven heating of the ground generates pressure gradients and thus winds. The most popular parametrisation for gas transfer 30 velocity, i.e. the one by Wanninkhof (1992), is a quadratic function of the wind speed and thus even small changes in wind speed have large impact on the flux.
We calculated how the annual net exchange of carbon dioxide between the sea and atmosphere would vary depending on the sampling time (Fig. 9). The calculations were performed using the flux parametrisation of Wanninkhof (2014). The reference net exchange (red line in Fig. 9) is calculated using high frequency one hour data, whereas the other fluxes are calculated using only one measurement per day. The closest match with the high frequency net exchange is captured when sampling the seawater at 9, 17-18 or 24 h UTC. Sampling between 0 and nine o'clock generates an overestimation of the net exchange by up to 12%, whereas sampling between 9 and 18 h leads to an underestimation of up to -12%. The sinusoidal shape of the net exchange as a function of the sampling time clearly originates from the biological component, but the deviation from the 5 sinusoid around 15-20 h must originate from the turbulence parametrisation (wind speed) as such shape is not observed in the pCO 2 .

Conclusions
The diurnal variability of the CO 2 partial pressure and the contributions of its drivers were studied at Utö station in the Archipelago Sea, the Baltic Sea. At this location, the largest variability was found to take place during July-September, when 10 19 https://doi.org/10.5194/os-2020-115 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License.
the monthly median of the diurnal pCO 2 varied in the range of 27-31 µatm. This pCO 2 variability was mostly generated by the biological transformations (production and respiration). However, individual days may show higher variation: pCO 2 varying within 500 µatm a day was attributed to the mixing of water masses.
Assessment of the annual air-sea flux based on the entire data set or individual one hour sampling times, respectively, revealed a potential bias caused by the time of sampling of up to 12%. This finding suggests that data from moving platforms 5 like recearch vessels or voluntary observing ships can have a substantial bias depending on the time of sampling, which might lead to biases in flux calculations or estimation of natural variability.
These findings emphasize the importance of continuous measurements at fixed locations providing temporal coverage on processes, in addition to VOS-lines providing spatial coverage. Autonomous high frequency measurements of carbonate system at fixed sites have proved to be valuable in the assessment of short-term variability of carbonate system (Gac et al., 2020). As

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European seas are spatially highly heterogeneous, we need organized efforts to map the diurnal variability of the carbon system.

Data availability. TEXT
The data used in this paper can be found in the Zenodo repository (https://doi.org/10.5281/zenodo.4292384).
Appendix A: Air-sea exchange of CO 2 The CO 2 exchange between the atmosphere and the sea, F as , is driven by the difference in CO 2 partial pressure (∆pCO 2 = 15 pCO 2 − pCO atm 2 ) between the surface seawater and atmosphere, or more precisely the differences in fugacity, which refers to the effective partial pressure of CO 2 that takes into account the non-ideal gas behaviour of CO 2 . CO 2 partial pressure and fugacity differ only slightly and for this reason, only partial pressure is used from now on. The efficiency of the exchange through the diffusive boundary layers of the gas and liquid fluids is defined by the gas transfer velocity, k. Thus, F as may be written as: where K 0 is the solubility constant of CO 2 .
The effect of kinematic viscosity of seawater and the diffusion efficiency of CO 2 on k are taken into account by including the ratio of momentum diffusivity to mass diffusivity, the Schmidt number (Sc), in k: Since the Schmidt number is a function of temperature, it is normalized with the Sc of seawater at 20 • C, value of 660.
k 660 is most commonly parameterized by using a wind speed measured at 10 m (U 10 ), and probably the most well known parametrization is a quadratic relationship proposed by Wanninkhof (1992), which was revised by Wanninkhof (2014): k 660 = 0.251U 10 and the dissolved concentration of CO 2 , Carbonic acid dissociates to hydrogen carbonate (HCO − 3 , also known as bicarbonate) which further dissociates to carbonate ion (CO 2− 3 ). The equilibrium states: Solubility constant and the dissociation constants (K 1 and K 2 ) depend on the free energy of the reaction and thus are functions of temperature and pressure. As these stoichiometric constants are defined using concentrations instead of ion activities, they are also a function of salinity.
Dissolved carbon dioxide, carbonic acid, bicarbonate and carbonate ions form the pool of total dissolved inorganic carbon 15 (DIC): DIC is a conservative quantity, i.e. it does not vary as temperature or pressure change. The concentrations of different DIC species change but the sum of these concentrations remains the same if no carbon is added to or removed from the system.
If nutrients and photosynthetically active radiation are available, dissolved CO 2 is transformed into organic matter through 20 the process of photosynthesis. When phytoplankton and other aquatic organisms respirates, the opposite occurs and CO 2 is released. Through microbial degradation in water or in sediments, dissolved organic matter is transformed again into inorganic carbon.
Of all parameters of carbonate system, one can measure only pCO 2 , DIC, T A and pH (negative logarithm of hydrogen concentration). To gain the complete description of the carbonate system, one should know at least two of these variables in 25 addition to the information of seawater temperature (T ), salinity (S) and pressure (P ). Ideally, the effect of dissolved organic matter on total alkalinity should be also known. From Henry's law (Eq. B2), we see that CO 2 fugacity depends on the solubility constant and dissolved CO 2 concentration. Both of these variables are functions of temperature, salinity and pressure. The nonconservativity of [CO * 2 ] is due to the effect of dissociation constants, K 1 and K 2 . Minor T A components include organic ions, which may have a large regional impact. In case of the Baltic Sea, the bulk dissolved organic matter has been shown to act as proton acceptor (Kuliński et al., 2014). Similarly to DIC, T A is a conservative 10 quantity.
Calcium carbonate (CaCO 3 ) is formed in a slow precipitation process by specific calcifying organisms. The precipitation and dissolution of CaCO 3 affect both DIC and T A. However, in the case of the Baltic Sea, there exists calcifying phytoplankton only in the areas next to the North Sea (Tyrrell et al., 2008), and thus, the formation of CaCO 3 can be excluded in calculations for most parts of the pelagic Baltic Sea, including our study site. On the other hand, the weathering of fluvial CaCO 3 has a 15 determinant effect on T A in the limestone-rich southern regions of the Baltic Sea (Müller et al., 2016).

C1 Salinity relationship
For the carbonate system calculations, we used the pair of T A and pCO 2 . Whereas pCO 2 was measured, T A was calculated from salinity using an empirical relationship, which was determined based on the direct total alkalinity measurements carried out at Utö in 2017 (Lehto, 2019). The least squares fit of the relationship between the salinity and the directly measured total 20 alkalinity (Fig. C1) had a R 2 value of 0.91.
T A = 123.3 + 221.8 · S, where salinity is unitless and total alkalinity has the unit of µmol kg −1 . The root mean square error between the measurements and the fit is 11.1µmol kg −1 . The slope of this fit is very similar to the parametrisation of T A − S relationship for the Gulf of Bothnia by Müller et al. (2016) extrapolated for year 2017 (220.9 µmol kg −1 PSU −1 ).
25 Figure C1. Measured total alkalinity (black dots) as a function of salinity in Utö in 2017 (Lehto, 2019). Solid red line shows the T A-S relationship for Gulf of Bothnia given by Müller et al. (2016). Black dashed line is the best fit, and gray dashed lines show the same line with the limits of root mean square errors.

Appendix D: Gas transfer velocity
We patched the CO 2 air-sea flux time series using a U 10 based parametrization for k 660 proposed by Wanninkhof (2014). The applicability of this parametrization for the western marine region of Utö was assessed by calculating k 660 from the measured CO 2 air-sea flux (from eddy covariance), partial pressure difference, solubility (Weiss, 1974) and Schmidt number (Wanninkhof, 1992). Only cases with southwestern (180-330 • ) winds and strong pCO 2 difference (>30 µatm) were considered.

5
CO 2 flux outliers were discarded so that we included only the fluxes that are within the two standard deviations from the median.
Non-stationarity is one of the determinant factors for the quality of direct flux measurement, and thus, non-stationary fluxes are discarded. Here, this means that the mean of 5 min fluxes can deviate less 30% from the 30 min flux. Fully stationary condition is purely theoretical concept, and the threshold for the accepted deviation from this is a matter of choice.

10
The best quadratic fit (0.31U 2 10 ) is only slightly larger than the parametrization proposed by Wanninkhof (2014), and thus we stick with the common parametrization. Low and medium windspeeds are well packed, whereas the 10th and 90th percentiles move further away from each other at high wind speeds. The parametrization of Wanninkhof (2014) shows the highest deviation from the binned median values at highest wind speeds. The binned median at the highest wind speeds is low compared to the Wanninkhof (2014), which may indicate fetch-limitation. More observations at high wind speeds is thus required for the in-