The diurnal cycle of the p CO 2 in the coastal region of the Baltic Sea

. The direction and magnitude of carbon dioxide ﬂuxes between the atmosphere and the sea are regulated by the gradient in the partial pressure of carbon dioxide ( p CO 2 ) across the air–sea interface. Typically, observations of p CO 2 at the sea surface are carried out by using research vessels and Voluntary Observing Ships, which usually do not resolve the diurnal cycle of p CO 2 at a given location. This study evaluates the magnitude and driving processes of the diurnal cycle of p CO 2 in a coastal region of the Baltic Sea. We present p CO 2 data from July 2018 to June 2019 measured in the vicinity of the island of 5 Utö at the outer edge of the Archipelago Sea, and quantify the relevant physical, biological, and chemical processes controlling p CO 2 . The highest monthly median of diurnal p CO 2 variability (31 µ atm ) was observed in August and predominantly driven by biological processes. Biological ﬁxation and mineralisation of carbon generated sinusoidal diurnal p CO 2 variations, with maxima in the morning and a minima in the afternoon. Compared with the biological carbon transformations, the impact of air–sea ﬂuxes and temperature changes on p CO 2 were small, with their contributions to the monthly medians of diurnal p CO 2 10 variability being up to 12 and 5 µ atm , respectively. During upwelling events, short-term p CO 2 variability (up to 500 µ atm within a day) largely exceeded the usual diurnal cycle. If the net annual air–sea ﬂux of carbon dioxide at our study site and for the sampled period is calculated based on a data subset that consists of only one regular measurement per day, the bias in the net exchange depends on the sampling time and can amount up to ± 12%. This ﬁnding highlights the importance of continuous surface p CO 2 measurements at ﬁxed locations for the assessment of the short-term variability of the carbonate system and the 15 correct determination of air–sea CO 2 ﬂuxes.

In this contribution, we investigate the diurnal cycle of carbon dioxide system at a fixed station near the island of Utö, located in the transition zone between the northern Baltic Proper and the Archipelago Sea, representing a highly productive (euthrophied) coastal ecosystem. The aims of this study are (a) to investigate the diurnal cycle of pCO 2 during different seasons based on observations carried out at Utö and (b) to quantify the contributions of the main drivers and processes affecting the pCO 2 diurnal variations: air-sea flux, biological carbon uptake and release, and diurnal changes in temperature. 5 2 Materials and methods

Study site
The Utö Atmospheric and Marine Research Station is located on the island of Utö (Fig. 1) on the southern edge of the Archipelago Sea (59°46'55" N, 21°21'27" E). Utö is a small (0.81 km 2 ) rocky island with low vegetation.
As characteristic for the central Baltic Sea, our study site is affected by climate change induced increase of sea water 10 temperature . Besides the warming trend, also stratification has strengthened, affecting the connectivity between water layers separated by a seasonal thermocline and a permanent halocline (Liblik and Lips, 2019). Long-term trends of increasing alkalinity throughout the Baltic Sea have been shown to partly compensateacidification induced by rising atmospheric CO 2 . (Müller et al., 2016). Within our study region, phytoplankton blooms are a recurrent phenomenon due to eutrophication (Kraft et al., 2021). 15 The marine observations at the station focus on regional marine ecosystem functioning with a large number of biochemical and physical observations. The marine observations include, but are not limited to, CTD casts carried out northwest from the island, flow-through analyses at the Marine station and thermistor measurements in the vicinity of the seawater inlet (Fig 1). The measurements of the Utö Atmospheric and Marine Research Station belong to the Joint European Research Infrastructure for Coastal Observatories (http://www.jerico-ri.eu). Carbonate system dynamics is noted as one of the key sci-20 entific topics in coastal ocean studies (Farcy et al., 2019), and the study presented here, executed under the framework of the JERICO-RI, highlights the need for integrated and multidisciplinary observations. The atmospheric part of the station includes a wide range of meteorological, greenhouse gas and aerosol measurements. The micro-meteorological flux tower at the western shore, next to the Marine station, measures the CO 2 , sensible heat and latent heat fluxes between the sea and the atmosphere.  Kraft et al. (2021). Our study is based on one year's data gathered between July 2018 and July 2019. The timing of all data presented in this paper are given in UTC. Finland belongs to the UTC+2:00 timezone.

Flow-through sampling
The marine station, located on the western shore of the island (Fig. 1), is equipped with a flow-through system. A submersible pump located 250 m from the shore transports seawater from the inlet to the marine station, where seawater is analyzed automatically or manually on demand. The bottom-moored floating seawater inlet is at the approximate 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 5 location, there are no notable tides or tidal currents.
At the station, the transported water first enters a manifold. Any flow-through instrument can be attached to the manifold separately, enabling individual adjustment of the flow rate for each instrument. The time stamp of the flow-through data is shifted (5.6min 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.
All of the instruments attached to the flow-through system are automatically washed with cleaning fluid (hydrogen peroxide 5 or Triton X-100) daily. The data gathered during and immediately after the cleaning have been discarded.

Measurement of pCO 2
A SuperCO 2 instrument (Sunburst Sensors), which was connected to the flow-through system, was used to measure pCO 2 . In its two shower-head equilibrator chambers, the seawater CO 2 is equilibrated with the gas above according to Henry's law (Eq. B2). The equilibrated gas is analysed for its CO 2 molar fraction (xCO 2 ) by an infrared gas analyzer (LI-840A, LI-COR). The 10 logging interval was 10-15 s.
The sensor drift of the gas analyzer is taken into account by measuring four standard gases every fourth hour with differing CO 2 molar fractions (0. 00, 234.38, 396.69, and 993.45 ppm, ±2%) in order to form a correction equation for dry xCO 2 . FMI buys the reference gases from the Finnish branch of Linde-Gas (previously AGA). The gas concentrations are checked with instruments using cavity ring-down spectroscopy in the FMI's laboratory prior to measurements. These instruments are cali-15 brated using gases that are verified by the National Oceanic and Atmospheric Administration (USA). Aluminum gas containers have been used in order to minimize the concentration drift.
Drift-corrected dry xCO 2 is transformed into pCO 2 as described in Dickson et al. (2007), with a slight modification. Since the water trap attached to the sample gas line may slightly affect the water vapor content, the following calculation was used.
The dry CO 2 molar fraction was calculated using the H 2 O measured using the analyzer. The real water vapor content in the 20 equilibrium chambers was calculated using the temperature and salinity data assuming full saturation. This real water vapor content, together with the dry xCO 2 , was used when calculating the partial pressure of CO 2 .
During May-June 2019, the sampling and inlet tube system was tested by measuring pCO 2 with two SAMI 2 sensors (Sunburst Sensors) that were parallel to the SuperCO 2 system inside the measurement station on land (20-23 May 2019), followed by deployment of the SAMI 2 sensors next to the sampling inlet at sea (from 24 May to 7 June 2019). The parallel measurement 25 inside the station was used to correct the potential initial offset of the SAMI 2 sensors against the SuperCO 2 system. While the SAMI 2 sensors were positioned close to the inlet at sea, the in-situ concentrations for all three instruments closely followed each other: the root mean square difference between measurements at the sea inlet and the station was 4.1 µatm. We conclude that the pCO 2 analysis carried out in the station, despite the unusal long path of water from the inlet location to the lab, fully represent the conditions at the inlet.

Other flow-through measurements
The equilibrator temperature (together with salinity) was measured using a thermosalinograph (SBE45 MicroTSG, Sea-bird Scientific) next to the SuperCO 2 instrument. The thermosalinograph is cleaned 1-2 times a year. The accuracies for temperature and salinity given by the manufacturer are respectively 0.002°C and 0.005. The temperature drift is less than a few thousandths of a degree per year, whereas the stability of conductivity measurement depends mostly on the cleanliness of the measurement cell. The thermosalinograph logged data every 15 s. Oxygen was measured with an oxygen optode (Aanderaa 4330) with multipoint calibration. The optode has a preburned foil providing long term stability. The accuracy of the optode is 2 µM according to the manufacturer. For the work presented here, 5 we are mostly interested in hourly changes of oxygen, and thus the drift of the absolute value is not concern. Chlorophyll A was measured with a 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). Both instruments logged data every 15 s. The vertical temperature profiles were measured with temperature chains, supported with regular interval profiles of Conductivity-Temperature-Depth instrument (CTD), RBR XR-620. The CTD profiles were taken fortnightly by using a small boat during the productive period and with lower temporal resolution in winter (see Fig. 2). The CTD location is approximately 400 m west of the sampling inlet.

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The thermistor chain 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 heights of approximately 18 m, 13 m, 8 m, 1 m, and 0 m from the bottom (depths 3.3 m ± 0.5 m, 8.3 m ± 0.5 m, 13.3 m ± 0.5 m, 20.3 m ± 0.5 m, 21.3 m ± 0.5 m). In order to avoid instrument damages during rough weather conditions, there was no thermistors closer than 3 m to the surface. Pt-100 thermistors were calibrated prior to the deployment in FMI's laboratory, and the maximum error in temperature was found to 20 be less than 0.015°C. Thermistors logged data every 30 s.
The thermistor profiles were used to verify that the CTD casts, carried out at a slightly different location, were representative for the hydrographic conditions at the seawater inlet. More importantly, the 3 m thermistor measurement was used as insitu temperature at the inlet, and hence for correcting the pCO 2 for the temperature difference between in situ conditions and in the equilibration chamber.

Atmospheric CO 2 measurement
The atmospheric xCO 2 was measured at the Atmospheric ICOS site. The sample air was drawn from the tower (56 m) to the ground level where it was analyzed using using cavity ring-down spectroscopy (Picarro G2401). The data was logged as one minute average values. Three standard gases made by FMI were used for the reference measurement. Differences between the target and measured values of these gases were within -0.20 and 0.20 ppm. (Kilkki et al., 2015) 30 2.4 Calculated data 2.4.1 pCO 2 temperature correction To correct for the temperature difference between in situ and equilibrator temperature, we took the effect of the temperature change on pCO 2 into account by using the CO2SYS matlab program (van Heuven et al., 2011). This correction requires knowledge of another carbon system component, which is total alkalinity (from salinity) in our case. The widely used temperature 5 correction of pCO 2 suggested by Takahashi et al. (1993) is not applicable for the brackish conditions of the Baltic Sea (e.g. Schneider and Müller, 2018). The difference in temperature oscillates within ±2.0 • C.

Determination of the mixed layer depth
The mixed layer depth (z mix ) was determined from the vertical temperature profiles of the CTD casts. Even though the data by the thermistor chain has higher temporal resolution than the CTD castings, it is not applied for the assessment of the 10 mixed layer depth because it has significantly lower vertical spatial resolution. The water depth at the location of CTD casts is approximately 90 m, which is significantly deeper than the depth at the inlet location. If the mixed layer depth was deeper than the depth of 23 m at the inlet location, the water column at the inlet location was considered fully 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 thermocline depth was estimated. The thermocline depths with a questionably small (< 0.2 • C m −1 ) temperature gradient were 15 discarded.
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 the 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 20 of 3, 8, and 13 m were 0.42, 0.41, and 0.25 • C, respectively. The temperatures at 20 m, however, showed larger difference as the root mean square error (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 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 used in this study is based on two methods:

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(1) the eddy covariance method, using the data gathered using a micro-meteorological flux tower erected on the western shore of the island and (2) a wind speed-based flux parameterization. Due to strict quality control, the eddy covariance method was applicable for only 18% of time, and for the rest of the time, the parameterization was used.
Both methods have pros and cons, due to which they complement each other. The eddy covariance method considers the integrated flux within a large footprint area, whereas the parameterization is based on the pCO 2 measurement at a single 30 point at the depth of 4.5 m. The large footprint area may contain spatially heterogeneity in seawater pCO 2 . In some cases, the measurement at the depth of 4.5 m may not represent the surface conditions. Additionally, the parameterization of gas transfer velocity is based on the wind speed, which does not contain all the information about the surface turbulence used alone, in particular close to land masses.
The eddy covariance fluxes for the air-sea exchange of CO 2 were calculated at 30 min intervals. This flux measurement is based on the closed-path non-dispersive infrared gas analyzer (LI-7000, LI-COR). The sample air tubing has a 30 cm Nafion 5 drier (PD-100T-12-MKA, Perma Pure) in order to eliminate the water vapor interference of 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 fluxes were corrected for the high-frequency attenuation by using a transfer function that was calculated from the deviation of the normalized w-CO 2 cospectrum from the cospectrum 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 10 the atmosphere. Only westerly winds were considered (180-330 • ) here as the flux footprint during these cases originates from the sea. A small amount of flux data were excluded from the analysis because the reference gas pipeline for the CO 2 analyzer was leaking. More information about the flux system and its quality control can be found in Honkanen et al. (2018).
We used an air-sea exchange estimation based on the quadratic relationship created by Wanninkhof (2014) for the times without valid eddy flux measurements (82% of the time). Wind speed was measured with the micrometeorological flux tower 15 on the western 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 10 m, we corrected wind speed assuming a logarithmic wind profile and a constant surface roughness of 0.5 mm, an average value that is based on the data of Honkanen et al. (2018). More details about the compatibility of the parameterization for this specific site can be found in Appendix A1. 20 We use total alkalinity as a second carbon system variable in our calculations. The total alkalinity used here is calculated using the alkalinity-salinity relationship:

Alkalinity-salinity relationship
where salinity is unitless and total alkalinity has the unit of µmol kg −1 . This is based on the samples gathered from the flow-through system at Utö in summer 2017 (Lehto, 2019). Total alkalinity was determined from these samples by using 25 the potentiometric titration method (Metrohm Titrino 716). The samples were conserved with mercury chloride before the analysis in Finnish Environment Institute's research laboratory in Helsinki. The titrant and the rinsing water had the salinity of 7. Alkalinity was calculated from the titration curve based on the least squares method. More information on the alkalinitysalinity relationship, can be found in Appendix C.
2.4.5 The calculation of the pCO 2 changes generated by different processes

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The surface pCO 2 is affected by processes that change the concentrations of dissolved inorganic carbon (DIC) or total alkalinity (TA), or through changes in temperature, salinity, or pressure affecting the carbonate system balance (Takahashi et al., 1993).
In contrast to pCO 2 , DIC and TA behave conservative with respect to temperature changes and mixing of water masses, when expressed in concentration units of µmol kg −1 of seawater.
As DIC (see Appendix B) is introduced to or removed from the dissolved inorganic pool, its change is depicted by the so-called Revelle factor, Re (Sarmiento and Gruber, 2004): (2) 5 DIC in surface water is affected by the CO 2 exchange with the atmosphere, biological transformations, precipitation/dissolution of calcium carbonate, fresh water input, and the mixing of water masses. The processes controlling the freshwater balance include evaporation, precipitation and the formation and melting of sea ice. Precipitated water or melted sea ice may produce a layer of low saline water at the sea surface, which in most cases is likely to be eroded easily by turbulence.
Biological processes affecting pCO 2 include all transformations between the inorganic and organic carbon pools, i.e., pho-10 tosynthesis and respiration. The mixing processes include horizontal advection, vertical diffusion, and vertical entrainment.
TA (see Appendix C) is mainly altered by the formation and dissolution of calcium carbonate. A smaller contribution to TA originates from nitrogen transformations through biological processes, and the mixing processes. TA is not affected by the air-sea exchange of CO 2 . The effect of calcifying primary producers in the carbon pool can be neglected for the open Baltic Sea (Tyrrell et al., 2008). However, calcifiers may have an effect on the carbon cycle in the benthic zone.

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Temperature affects the dissociation constants and solubility of gases, which further alters the CO 2 partial pressure. For stable oceanic conditions, this change is well documented (Takahashi et al., 1993), but in estuary conditions, the temperature effect on pCO 2 varies significantly (Schneider and Müller, 2018). Based on the choice of the parameterization of dissociation constants, this value might show small variation as a function of temperature and salinity (Orr et al., 2015). Similarly to temperature, salinity and pressure also affect the dissociation constants. 20 In this study, we investigate the contribution of individual processes and drivers to the diurnal variation of pCO 2 . 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 biological transformations. There are multiple other processes that have the potential to affect the pCO 2 that are not included in the analysis. See Appendix C1 for more information on the omitted processes.

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Calculations of the carbon system were performed using the CO2SYS matlab program (van Heuven et al., 2011). Dissociation constants K 1 and K 2 were calculated based on the work of Millero (2010) and the sulfate contribution is based on the work of Dickson et al. (2007). We implemented the total boron parameterization of Kuliński et al. (2018), which is based on the empirical data of the Baltic Sea, in CO2SYS.
First, the carbon chemistry is calculated in CO2SYS for each hour based on the measured partial pressure of CO 2 , parame-30 terized total alkalinity (see above), temperature and salinity. This results in hourly data of DIC at the sea surface.
In the case of the hourly temperature-related pCO 2 change, we assume that DIC and TA do not change. Using the temperature of the next hour together with the previously known DIC and TA, we calculate the new pCO 2 in CO2SYS that is governed by solely the temperature change In the case of air-sea exchange and biological transformations, we calculate how much DIC has changed over one hour by these processes separately and add this DIC change, dDIC, to the original DIC content. Then, we calculated the carbon system using this new DIC and the unaltered 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. The DIC change due to the air-sea exchange of CO 2 is calculated as: where t is time, in our case one hour. The value of F as is calculated using either the eddy covariance method or the wind speed-based parameterization, with the former given priority when passing our rigorous quality control procedure (18% of the time considered in this study).
We inferred the biological effect on DIC indirectly from the oxygen measurements by assuming the Redfield ratio (Redfield 10 et al., 1963). As inorganic carbon is consumed (or released), a corresponding 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 on average oceanic conditions and may show variations in space and time. The last term in the equation takes the effect of air-sea exchange of oxygen into account. This flux, F O 2 , is calculated similarly to the carbon dioxide flux (Eq. A1) by 15 using the gas transfer velocity and the oxygen solubility, the measured oxygen concentration in seawater, and the oxygen concentration calculated for hypothetical equilibrium with the atmosphere. Oxygen solubility was calculated according to the salinity-temperature dependence fit of Garcia and Gordon (1992), which is originally based on the work of Benson and Krause (1980). The Schmidt number of oxygen and gas transfer velocity were calculated according to Wanninkhof (2014). Oxygen concentrations can also change due to mixing, the contribution of which remains unknown. 20 For each day, the cumulative sums of the hourly pCO 2 changes generated by a specific process (temperature, biological transformations or air-sea exchange of CO 2 ) were calculated for 00:00 -24:00, in order to know how the specific process alters the pCO 2 during a day. Finally, the mean of cumulative sum was removed from these values, because we are interested in the daily changes, not the absolute values. pCO 2,i is the cumulative pCO2 change between the i:th and the first hour: where i is the index of each hour and the 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 DIC that is altered by both the air-sea exchange of CO 2 and biological transformation, and additionally taking into account the temperature change. However, this pCO 2 change is only used for the verification of the method, and as base for the discussion 30 of the shortcomings and potential improvements. . Throughout the results, we use the range 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.
3 Results and discussion

Environmental conditions and seasonal pCO 2 variability
Our observations start in July 2018 during the so-called blue water period (Schneider and Müller, 2018), a phase in early 5 summer that is characterised by close-to-zero net community production between the spring and the mid-summer bloom events (Andersson et al., 2017). As it is typical for this period, chlorophyll A concentration was low, which is reflected in a low relative fluorescence unit (Fig. 2c). At the same time, surface pCO 2 was close to equilibrium with the atmosphere. In mid-July, a cyanobacteria bloom developed, as it is typical for the study area and time of the year (Kraft et al., 2021). The primary production activity lowered the pCO 2 below 200 µatm. This low pCO 2 level persisted for about one month (Fig. 3a). The measured oxygen concentration and calculated equilibrium concentration were close to equilibrium in the beginning of July, but due the cyanobacteria bloom, the oxygen concentrations diverged and for a week, the sea was strongly supersaturated. After the pCO 2 had increase to almost 600 µatm, another bloom occurred in early September and caused a second pCO 2 minimum.
After the another bloom, the measured oxygen stayed higher than the equilibrium concentration for a week. In late September 5 2018, pCO 2 peaked at 800 µatm. This is a result of the deepening of the mixed layer depth (Fig. 2a)  Proper (600 µatm). This could be due to the fact that the water depth at the sampling location is low and thus remineralised CO 2 from the sediment surface can directly be entrained into surface waters upon vertical mixing.
The thermocline was located at the depth of 20 m during most of the time in summer 2018. In autumn, the thermocline deepened and in winter the water column was considered to be completely mixed. The thermocline may have only been shallower than the inlet depth of the seawater supply occasionally, e.g., in spring 2019, when a shallow thermocline formed for 20 a short period. Therefore, most of the time our flow-through setup was supplied with water from the mixed layer. We did not observe surface freshwater layers or permanent ice coverage during the measurement period that would be of relevance for the interpretation of our findings. on that day, because the pCO 2 difference between the sea and atmosphere was close to zero. Including temperature as a driver 30 into our model of the surface pCO 2 variability slightly increases the deviation from the observed hourly changes. It is possible that this is due to a too low oxygen-derived biological component. In Sect. 3.2.5, we give evidence of a slightly too small biological component in September. The pCO 2 on December 20, 2018, was decreasing, almost linearly. This example shows that the oxygen-derived pCO 2 variation is higher than the observed pCO 2 variation in winter. The oxygen is primarily altered by mixing and air-sea exchange of oxygen. This issue is discussed in the chapter 3.2.5. Both the air-sea exchange of carbon and gradual cooling of the water contribute to the decrease of surface pCO 2 .

Examples
The largest daily pCO 2 range (503 µatm) was detected on July 22. This extreme case can be attributed to an upwelling event 5 as the water at the marine station, measured by the thermosalinograph, cooled by 5°C simultaneously. Most of the cooling effect did not reach the thermistor at 3 m, as the temperature at the thermistor chain cooled less than 2°C at 3 m depth. Observations made during this upwelling event were discarded from the following analysis of the diurnal pCO 2 variability. Another large pCO 2 change (452 µatm) occured on September 2, but the water temperature at the station changed approximately 1°C, and thus we did not exclude the data from this day from our analysis.

Observed diurnal pCO 2 variability
The observed diurnal variability of pCO 2 was lowest during the winter time (Fig. 5). On average, the monthly median range (maximum -minimum) in November-February was only 4 µatm. Within the winter months, February revealed the lowest monthly median range and the lowest range between the 10th and 90th percentiles: less than 11 µatm daily variation were observed for 80% of the time. In winter time, no clear diurnal pattern is visible, which goes along with varying times for the 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 09:00 UTC (12:00 local summer time), the pCO 2 is closest to the diurnal mean. The monthly median range of pCO 2 increased until August, which 10 had the highest monthly median range of 31 µatm. In the Baltic Proper, the highest diurnal pCO 2 variability (27 µatm) was observed in September (Lansø et al., 2017). However, this difference is likely due to the interannual variability as different years are compared. There is large variability in diurnal pCO 2 over the course of a single month during the productive season. During this time, a single day may deviate significantly from the monthly median value. According to the 10th and 90th percentiles, 80% of the days in September occur within a large range of 114 µatm.

Biology-related diurnal pCO 2 variability
The diurnal pCO 2 variability induced by biological activity and inferred from changes in the oxygen concentration, are closely similar to the observed pCO 2 dynamics (see Figs. 4, 5, and 6). In both cases, sinusoidal diurnal variability with the maximum 5 in the morning and the minimum in the afternoon during April-September is observed and the monthly median ranges are of similar strength. During nighttime, respiration (both heterotrophic and autotrophic) prevails, which increases DIC and thus also pCO 2 . Solar irradiance intensifies as the day progresses and the carbon fixation outweighs the respiration, causing DIC to decrease. For our shallow sampling location, it is further possible that benthic processes impact surface water carbon dynamics, especially when the water body is completely mixed.
In summer, the daytime increase in temperature partly counterbalances the pCO 2 reduction caused by primary production.
The temperature-driven diurnal pCO 2 maximum and the biologically controlled pCO 2 minimum occur at approximately the same time in the afternoon. However, the temperature effect is significantly smaller than the impact of primary production.
The largest observed and modeled biological pCO 2 diurnal variability occurs in August and is twice as large as the range observed during the spring bloom. On the one hand, the temperature is at its annual maximum during July-August, which 5 favors phytoplankton growth (Trombetta et al., 2019), but on the other hand, the solar irradiance is already decreasing from its annual maximum during June-July. During the spring bloom, chlorophyll A fluorescence was high compared with the one during August, when the highest pCO 2 variation is observed. However, microbial respiration tends to increase towards higher temperatures (Lopez-Urrutia et al., 2006), and thus the highest respiration rates are expected during July-August, contributing to the large amplitude of the diurnal cycle. It is possible that in spring, the daily pCO 2 range is lower than in autumn due to the 10 deeper mixed layer in spring (Fig. 2a) causing the production to be distributed across a larger water volume.
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 (especially mixing) can have a stronger impact, as Wesslander et al. (2011) have shown.
During winter, the diurnal pCO 2 pattern generated by the biological processes revealed a positive trend over the course of a 15 day, which could indicate the remineralization of organic matter. The fact that this directional trend is not seen in the observed pCO 2 , could be due to the CO 2 release to the atmosphere counterbalancing the biological effect. However, it is implausible that the remineralization occurs for the whole winter and is even strongest in February.

Temperature-related diurnal pCO 2 variability
The daily variation in seawater temperature follows the cycle of solar irradiation. The highest monthly average of daily tem-20 perature range (daily maximum temperature -daily minimum temperature) was in July with 1.6°C and the lowest in February with 0.2°C.
The diurnal pCO 2 variability driven by changes in temperature is generally small (Fig. 7). 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 reaches its annual maximum (Fig. 2e). Still, for 20% of the days in July, a temperature-related diurnal variability of 25 pCO 2 > 27 µatm was observed.
During months with high solar radiation, i.e. March-September (Fig. 2e), 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 temperaturerelated pCO 2 changes do not show a clear diurnal pattern nor directional trend.
The measurement depth of the temperature is 3 m. Directly at the sea surface, we would expect higher temperature-induced 30 pCO 2 variability since solar irradiance decreases with depth. shows the hour of the day. Range, r, and the time for the maximum and minimum pCO2 are also given.

Diurnal pCO 2 variability generated by the air-sea CO 2 flux
Diurnal pCO 2 fluctuations generated by the air-sea exchange of CO 2 exhibit a clear trend-like pattern (Fig. 8), due to the nature of the process. The direction of the air-sea CO 2 flux is controlled by the sign of the CO 2 partial pressure difference between the sea surface and the atmosphere. As the atmospheric pCO 2 is relatively stable compared to that of the sea, the flux direction is largely controlled by the seawater pCO 2 . The trend in the diurnal pattern of pCO 2 generated by air-sea exchange 5 thus represents the net carbon uptake of the Baltic Sea in summer when the sea surface pCO 2 is lower than atmospheric pCO 2 and vice versa in winter The magnitude of the air-sea fluxes is largest during September-October when a large partial pressure gradient and high wind speeds co-occur. In these months, the monthly median range was 10 µatm or higher. In contrast, the effect of air-sea exchange on diurnal pCO 2 variability is almost negligible (less than 2 µatm) when the sea and atmosphere were nearly balanced with 10 respect to pCO 2 , as during December-March, or when the wind speeds are low, as in the summer months.

Comparing observed and estimated pCO 2 variability
When comparing the observed hourly change in pCO 2 and the calculated change that takes into account the three processes airsea exchange, biology, and temperature ( Fig. 9), we found that the overall RM SE between all hourly modeled and observed pCO 2 changes was 10 µatm. RM SE was 9-14 µatm during July-October, while it was less than 3-6 µatm during the other seasons. The scatter in Fig. 9 is visibly highest during July-October. These months showed the highest observed diurnal pCO 2 5 variability, which may have a direct effect on the increased error. For each month, we divided the RM SE value with the average absolute change in hourly pCO 2 and found this ratio to be 1.26 on average during March-October, whereas during November-February it was 3.29 on average. Thus, the error introduced by the model during these winter months, though comparatively small in its absolute value, is large compared to the observed variability, which suggests that the estimates of the biological component during the winter time should be interpreted with care. This, however, does not have a significant effect Most of the variation in the modeled pCO 2 originates from the oxygen-derived biological processes, and thus we argue 5 that the different slopes in observations and modeled data are related to the parameterization of the biological processes.
To identify the reason for the mismatch between model and observations, we performed a similar analysis as in Fig. 9 but seperately disabled the oxygen flux between the atmosphere and sea (i.e. assuming all oxygen changes to originate from the biological transformations), , as well as temperature-induced pCO 2 changes and air-sea CO 2 flux, but these modifications of our pCO 2 model proved to only have a negligible effect on the slopes. Possible remaining sources of error thus include the air-sea flux, but that the flux at the surface is challenging to translate into the O 2 concentration changes at 5 m depth at one hour resolution. In summer, the oxygen flux is directed from the sea to atmosphere, and thus its effect on the biological component during daytime should be positive. If this process is not taken into account, we might end up with an underestimated biological component, i.e. low slopes in Fig. 9. In winter, vice versa would happen.
A bias in our estimation of the mixed layer depth may also introduce an error in the modelled pCO 2 change. It is possible that in spring, the vertical redistribution of surface O 2 fluxes may not extend to the mixed layer depth. This would cause the gas exchange term of oxygen to be underestimated in Eq. 4, leading to the biological pCO 2 component in the model to be too low. In autumn, the calculated mixed layer depth might be too shallow to fully capture the vertical mixing of surface O 2 fluxes. A major limitation in this regard is our definition of the mixed layer depth as the water depth at the sampling location 5 in cases when the true mixed layer depth at the CTD location was found deeper than the water depth in the inlet location. This limitation is critical, because it would not capture the loss of O 2 due to lateral mixing with deeper waters close to the sampling location. This would cause the gas exchange to be overestimated and the biological pCO 2 component to be too high.
The Redfield ratio for CO 2 -O 2 (-0.77) used in this study is based on an oceanic average (Redfield et al., 1963). To explain the slopes between the model and the observations (-0.3 to -2.1) would require a CO 2 -O 2 ratio of -0.37 in winter and as high 10 as -2.5 in some summer months. The CO 2 -O 2 ratio of respiration (the respiratory quotient) depends on the organic substrate in question, the degree of its oxidation, and the methabolic pathway used. This quotient may indeed vary between -0.13 and -4.00 (Robinson, 2019). In contrast, the required photosynthetic quotient of -2.5 in July appears very high compared with typical values (Laws, 1991). Wesslander et al. (2011) for example determined the CO 2 -O 2 ratio in April 2006 in the Baltic Proper to be -1.0, with some diurnal variation. We thus conclude that the changes in respiratory and photosynthetic quotients alone 15 cannot explain the seasonality in the slopes.

Effects on the air-sea exchange of CO 2
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 when the pCO 2 at the sea surface and in the atmosphere are close to equilibrium, as was observed on the July 22 and on September 2 (data not shown).

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The largest observed monthly median ranges in pCO 2 occurred during July-September (27-31 µatm). During this time the pCO 2 varied from slightly above 100 µatm to 800 µatm. In addition to the wind speed, the pCO 2 difference between the sea and the atmosphere controls the air-sea flux. The greatest relative effect on the daily flux occurs when the sea pCO 2 varies close to the atmospheric pCO 2 , 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 of CO 2 to the atmosphere at the study site. The diurnal pCO 2 variability 25 during these months are similar, with a maximum before noon and a minimum in the afternoon. However, in late July and early August, the pCO 2 difference between the sea and atmosphere is smallest before noon and largest in the afternoon, whereas in late August and September, the situation is reversed: the largest difference is before noon and the smallest is in the afternoon.
The discussion above only takes into account the diurnal variability of the air-sea pCO 2 gradient even though the flux also depends on the gas transfer velocity. This might also exhibit diurnal cyclicity, especially during clear skies in the coastal regions,  For the hypothetical case of a single sampling event per day, we calculated how the annual net exchange of carbon dioxide between the sea and atmosphere would vary depending on the sampling time (Fig. 10). The calculations were performed using the flux parameterization of Wanninkhof (2014). The reference net exchange (red line in Fig. 10, i.e. the "true" value) is calculated using the high-frequency one-hourly data, whereas the other fluxes are calculated using only one measurement at the daytime indicated on the x-axis. The closest match with the "true" net flux is achieved when sampling the seawater at 09:00, 5 17:00-18:00 or 24:00 UTC. In contrast, sampling between 00:00 and 09:00 UTC causes an overestimation of the net flux by up to 12%, whereas sampling between 09:00 and 18:00 UTC leads to an underestimation of up to -12%. The sinusoidal shape of the net flux bias as a function of the sampling time clearly originates from the biological component of surface pCO 2 , but the deviation from the sinusoid around 15:00-20:00 UTC must originate from the turbulence parameterization (wind speed) as such a shape is not observed in the pCO 2 .

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The diurnal variability of sea surface pCO 2 and the contributions of its drivers were studied at Utö station in the Archipelago Sea of the Baltic Sea. Multiple processes affecting the diurnal pCO 2 variability at Utö were distinguished and their interplay was found to depended on season, similarly as previously shown for the East of Gotland by Wesslander et al. (2011). At Utö, the largest variability was found during July-September, when the monthly median of the diurnal pCO 2 varied in the range of 27-5 31 µatm. This pCO 2 variability was mostly generated by the biological transformations (i.e. the production and respiration or organic matter). However, individual days showed significantly higher variations. Extreme pCO 2 variations exceeded 500 µatm a day and were attributed to upwelling of CO 2 -enriched water masses. Diurnal pCO 2 variability was less pronounced in winter time, which is comparable to the observations in the Baltic Proper (Lansø et al., 2017). Thus, on average, the magnitude and the timing of the diurnal pCO 2 variability at Utö are similar to the ones of the pelagic conditions in the Baltic Proper, except 10 for coastal upwelling at the study site.
Assessment of the annual air-sea flux based on the entire data set or individual one-hour sampling times revealed a potential bias caused by the time of sampling of up to 12%. This finding suggests that data from moving platforms which do not resolve the diurnal cycle, like research vessels or VOS lines, can lead to substantial biases in flux calculations or the estimation of natural variability.

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These findings emphasize the importance of continuous measurements at fixed locations providing a high temporal resolution, in order to complement VOS-based observations that achieve high spatial coverage. Our autonomous high-frequency measurements of the seawater carbonate system at fixed sites has proven to be valuable in the assessment of the short-term variability of the carbonate system. However, as European seas are spatially highly heterogeneous, our findings call for organized efforts to map the diurnal variability of the carbon system.

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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: The 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 = pCO 2 − pCO atm 2 ) between the surface seawater and atmosphere, or more precisely, the differences in fugacity, which refers 25 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 only differ 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:

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where K 0 is the solubility of CO 2 .
The effect of the kinematic viscosity of seawater and the diffusion efficiency of CO 2 on k are taken into account by including the ratio of momentum diffusivity in 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, a value of 660.
A wind speed measured at 10 m (U 10 ) is most commonly used to parameterize k 660 , and probably the most well-known parameterization is a quadratic relationship proposed by Wanninkhof (1992), which was revised by Wanninkhof (2014):

A1 The parameterization of gas transfer velocity
We patched the CO 2 air-sea flux time series using the U 10 based parameterization for k 660 proposed by Wanninkhof (2014).

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The applicability of this parameterization for the western marine region of Utö was assessed by calculating the absolute value of k 660 from the measured CO 2 air-sea flux (from eddy covariance), partial pressure difference, solubility (Weiss, 1974), and the Schmidt number (Wanninkhof, 1992). Only cases with southwestern (180-330 • ) winds and strong pCO 2 difference (>30 µatm) were considered. CO 2 flux outliers were discarded so that we only included the fluxes that are within two standard deviations from the median.

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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 than 30% from the 30 min flux. The fully stationary condition is purely a theoretical concept, and the threshold for the accepted deviation from this is a matter of choice.
The best quadratic fit (0.37 U 2 10 ) is somewhat larger than the parameterization proposed by Wanninkhof (2014), which might 20 indicate enhanced gas transfer due to the coastal characteristics of the study site. However, for the comparability, we stick with the common parameterization by Wanninkhof (2014). Low and medium wind speeds are well packed, whereas the 10th and 90th percentiles move further away from each other at high wind speeds. The parameterization of Wanninkhof (2014) 30 Figure A1. Measured gas transfer velocity as a function of wind speed.
Henry's law describes the relationship between the fugacity of gaseous CO 2 , which is in equilibrium with the underlying water, and the dissolved concentration of CO 2 : Carbonic acid dissociates to hydrogen carbonate (HCO − 3 , also known as bicarbonate), which further dissociates to carbonate (CO 2− 3 ) and hydrogen ions. The equilibrium states: Solubility and 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. If nutrients and photosynthetically active radiation are available, dissolved CO 2 is transformed into organic matter through the process of photosynthesis. When phytoplankton and other aquatic organisms respire, 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 the parameters of the carbonate system, one can only measure pCO 2 , DIC, TA, and pH (the negative logarithm of 5 hydrogen concentration). To gain the complete description of the carbonate system, one should know at least two of these variables in addition to the information on seawater temperature (T ), salinity (S), and pressure (P ). Ideally, the effect of dissolved organic matter on total alkalinity should also be known. From Henry's law (Eq. B2), we see that CO 2 fugacity depends on the solubility and dissolved CO 2 concentration. Both of these variables are functions of temperature, salinity, and pressure. The non-conservativity of [CO * 2 ] is due to the effect of the dissociation constants, K 1 and K 2 .
Borate alkalinity Self-dissociation of water component ± minor TA components.
Minor TA components include organic ions, which may have a large regional impact. In the case of the Baltic Sea, the bulk of dissolved organic matter has been shown to act as a proton acceptor (Kuliński et al., 2014 determinant effect on TA in the limestone-rich southern regions of the Baltic Sea (Müller et al., 2016).
We used the pair of the pCO 2 and the TA in our carbonate system calculations. The TA is parameterized using the salinity, because both of these variables are affected by the conservative mixing. The least squares fit of the relationship between the salinity and the directly measured total alkalinity (Fig. C1) had an R 2 value of 0.91. The RM SE between the measurements and the fit is 11.1 µmol kg −1 . The slope is almost identical to the dependence found for the Gulf of Bothnia by Müller et al. (2016), extrapolated for the year 2018.

C1 Processes controlling pCO 2 omitted in the analysis
In our analysis to distinguish the different processes that drive pCO 2 variability, we considered temperature changes, air-sea 5 exchange of carbon and biological transformations. Several processes were omitted.
The salinity changes are related to mixing, and thus the interpretation of the salinity effect is not straight-forward and is not dealt with in this paper. The salinity effect on 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 units during the whole year (see Fig. 2). We neglect the effect of pressure on pCO 2 , because we interpret surface water pCO 2 at one depth.

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Some of these unknown drivers, such as mixing processes and freshwater effects, are assumed to be temporally random in nature, and thus their effect on pCO 2 is considered to be negligible when inspecting average diurnal 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 a small effect on alkalinity that is not considered in In general, the tidal force is the most prominent process to generate a diurnal pattern on the mixing of the DIC. In this location of the Baltic Sea, the effect of the tidal currents on the water masses is very small and thus can be neglected. However, several other processes such as the upwelling can also generate mixing. The driving force of the upwelling (or downwelling) is steady wind over the sea, and at our study site, open sea which contains very small islands, sea-breeze cannot be completely neglected but is not expected to be strong. However, there is a possibility that the density driven mixing has a diurnal cycle due 5 to the diurnal heating/cooling of the surface waters.
The mixing component of the diurnal DIC variations can be large occasionally. For instance, there was clear indications of the mixing of water masses on July 22, 2018; the pCO 2 varied by 503 µatm while the water cooled by 8°C. However, there is not always that clear indicators suggesting the mixing events. In order to analyze the effect of the mixing on DIC precisely, one would need to know the 3D field of DIC and the water currents. This would require an array of carbonate system measurements.

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The analysis of the mixing of DIC is thus beyond the scope of this paper.
In the result and discussion section, we analyze the importance of individual drivers and the applicability of the method by comparing the calculated pCO 2 changes to the observations. Finnish Marine Research Infrastructure (FINMARI) is acknowledged for the funding of the marine research instrumentation. We thank Ismo and Brita Willström for the CTD castings and maintaining the stations, and we thank Anne-Mari Lehto for providing the total alkalinity measurements. Also, thanks are due to the Integrated Carbon Observation System (ICOS) for providing the atmospheric CO2 data at Utö. We acknowledge Theo Kurten for giving guidance in chemistry and Jani Särkkä for giving guidance in mathematical formulations. The CO2SYS program is acknowledged.

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We thank the referees for their insightful comments resulting in highly improved manuscript.