Inﬂuence of the Nocturnal Effect on the Estimated Global CO 2 Flux

: We found that signiﬁcant errors occurred when diurnal data instead of diurnal–nocturnal data were used to calculate the daily sea-air CO 2 ﬂux ( F ). As the errors were mainly associated with the partial pressure of CO 2 in seawater ( pCO 2w ) and the sea surface temperature ( SST ) in the control experiment, pCO 2w and SST equations were established, which are called the nocturnal effect of the CO 2 ﬂux. The root-mean-square error between the real daily CO 2 ﬂux ( F real ) and the daily CO 2 ﬂux corrected for the nocturnal effect ( F com ) was 11.93 mmol m − 2 d − 1 , which was signiﬁcantly lower than that between the F real value and the diurnal CO 2 ﬂux ( F day ) (46.32 mmol m − 2 d − 1 ). Thus, the errors associated with using diurnal data to calculate the CO 2 ﬂux can be reduced by accounting for the nocturnal effect. The mean global daily CO 2 ﬂux estimated based on the nocturnal effect and the sub-regional pCO 2w algorithm ( cor_F com ) was − 6.86 mol m − 2 y − 1 (September 2020–August 2021), which was smaller by 0.75 mol m − 2 y − 1 than that based solely on the sub-regional pCO 2w algorithm ( day_F com ). That is, compared with day_F com , the global cor_F com value overestimated the CO 2 sink of the global ocean by 10.89%.


Introduction
Since the beginning of the Industrial Revolution, human activities such as fossil fuel combustion, cement production, and land-use change have released large amounts of carbon dioxide (CO 2 ) into the atmosphere, thus disrupting the global carbon cycle and causing global climate change [1]. As an important reservoir of carbon, the oceans currently absorb approximately 25% of anthropogenic CO 2 emissions [2]. Although this could reach 70-80% on a timescale of a few hundred years and 80-95% on a timescale of a few thousand years, these estimates remain uncertain [3]. Some studies have suggested that the estimated errors associated with the partial pressure of CO 2 (pCO 2 ) are mainly at the regional level, corresponding to a difference of >10% of the mean climatic pCO 2 , which is an order of magnitude greater than the uncertainty associated with the most advanced measurements. Yu (2014) found that a different CO 2 transfer velocity led to considerable uncertainty in the estimated global CO 2 flux [4]. Therefore, it is critical to reduce the uncertainty associated with the estimated oceanic CO 2 flux to improve our understanding of the potential processes that control the distribution of anthropogenic CO 2 between the atmosphere, land, and oceans in the present and future [5].
At present, the sea-air CO 2 flux can be measured directly using the eddy correlation method. Alternatively, the CO 2 flux is often calculated by the block method formula [4], as follows: sea-air CO 2 flux = sea-air gas transfer velocity × solubility of CO 2 in seawater × (pCO 2 in seawater-pCO 2 in air). These parameters are obtained by remote sensing. The algorithm for determining the pCO 2 of seawater based on remote sensing data mainly depends on the sea temperature (SST) and chlorophyll-a (Chl-a) concentration. Bai et al. (2015) used the relationship between these factors and the pCO 2 of seawater to establish the corresponding algorithm [6]. As SST and Chl-a data are mainly obtained using optical remote-sensing techniques, there are no nocturnal data; however, some researchers consider that the diurnal-nocturnal variations in SST and Chl-a are significant.
Stuart-Menteth et al. (2003) and Genemann et al. (2003) analysed SST data measured at mooring buoys and observed a significant daily variation in SST, which may have been due to the diurnal-nocturnal variation in solar radiation, wind stress, and cloud cover [7][8][9]. Lu (2007) observed a positive correlation between the daily variations in the pCO 2 of seawater and the SST [10]. Jeffery et al. (2007) found that the daily variation in the SST significantly affected the sea-air exchange of CO 2 , increasing the emission of air from the ocean and reducing the pCO 2 of seawater, especially at the equator. The SST affects the CO 2 flux by influencing the pCO 2 of seawater and the solubility of CO 2 at low wind speeds [9,11]. When the reference temperature is 20 • C, the effect of the SST on solubility accounts for 2.7% of the total variation in the CO 2 flux [12]. At high latitudes, as the solubility of CO 2 increases at low temperatures, the daily variation in salinity alters the ability of the oceans to absorb atmospheric CO 2 [13]. Marrec et al. (2014) and Borges et al. (1999) concluded that the tidal cycle affected the daily variation in phytoplankton abundance, and thus the daily variation in the pCO 2 of seawater [14,15]. Bates et al. (2001) argued that the extremely high productivity of organisms in coral reef ecosystems could also cause large daily variations in the pCO 2 of seawater [16]. Moreover, the daily variation in the pCO 2 of seawater is influenced by biological activity, whereby CO 2 is mainly consumed as a result of photosynthesis during the day and released due to respiration at night [17]. Marrec et al. (2014) estimated that the mean diurnal-nocturnal variation in the pCO 2 associated with the biological cycle accounted for 16% of the mean CO 2 sink [14].
In addition to SST and biological activity, Kuss et al. (2006) found that the water mass mixing process was one of the main factors controlling the variation in the pCO 2 of surface seawater, while the daily variation in the wind speed affected the water mass mixing process [18][19][20][21]. Jeffery et al. (2007) found that the diurnal-nocturnal variation in seawater convection also affected the sea-air CO 2 transfer velocity and the daily variation in the sea-air CO 2 flux [11,22,23]. Rousseau et al. (2020) observed that the daily variation in the atmospheric CO 2 concentration directly affected the pCO 2 of seawater [24]. Furthermore, the change in the pCO 2 of air affected the CO 2 flux. Figure 1 depicts the effects of these factors on the sea-air CO 2 flux. As there is a clear diurnal-nocturnal variation in the pCO2 of seawater, it is inaccurate to use solely diurnal data instead of diurnal-nocturnal data. One of the goals of this study was that the relationship between the diurnal pCO2 and nocturnal pCO2 was determined and used to revise the pCO2 calculated based on diurnal data only. In addition to this, it is As there is a clear diurnal-nocturnal variation in the pCO 2 of seawater, it is inaccurate to use solely diurnal data instead of diurnal-nocturnal data. One of the goals of this study was that the relationship between the diurnal pCO 2 and nocturnal pCO 2 was determined and used to revise the pCO 2 calculated based on diurnal data only. In addition to this, it is also our goal to determine the relationships between diurnal and nocturnal data for the other parameters involved in the CO 2 flux block method and to use the corresponding relationships to correct the diurnal data for each parameter. Ultimately improving the accuracy of the global CO 2 flux estimates by considering the diurnal variation of parameters.

Buoy Data
The pCO 2 , SST, and sea surface salinity (SSS) data used in this study were obtained from the global CO 2 time series and mooring project of the Ocean Carbon Data System (OCADS) (https://www.ncei.noaa.gov/access/ocean-carbon-data-system/oceans/ time_series_moorings.html, accessed on 8 May 2022). International organisations from 18 countries have installed sensors on moored buoys to provide high-resolution time series measurements of the pCO 2 of the atmospheric boundary layer and ocean surface. Time series and mooring projects on CO 2 are coordinated by the International Ocean Carbon Coordination Project (IOCCP) and OceanSITES. Figure 2 shows a map of the buoy stations, where data are taken at 00:00, 03:00, 06:00, 09:00, 12:00, 15:00, 18:00, and 21:00. In Figure 3, the period 2010 to 2020 has the largest number of buoy stations, so we chose this time range as the study time in our study.

Wind Data and Atmospheric Pressure Data
Wind and atmospheric pressure data from 2010 to 2020 were obtained from ERA5 (https:// cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels?tab=overview, accessed on 8 May 2022), which is the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis of global climate and weather over the past 4-7 years. We used the u and v components of the wind speed (m s −1 ) at a height of 10 m above the Earth's surface, with a time resolution of 1 h and a spatial resolution of 0.25 • × 0.25 • . To correspond to the pCO 2 , SST, and SSS data of the buoys, wind and atmospheric pressure data at 00:00, 03:00, 06:00, 09:00, 12:00, 15:00, 18:00, and 21:00 were selected.

Wind Data and Atmospheric Pressure Data
Wind and atmospheric pressure data from 2010 to 2020 were obtained from ERA5 (https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels?tab=overview, accessed on 8 May 2022), which is the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis of global climate and weather over the past 4-7 years. We used the u and v components of the wind speed (m s −1 ) at a height of 10 m above the Earth's surface, with a time resolution of 1 h and a spatial resolution of 0.25° × 0.25°. To correspond to the pCO2, SST, and SSS data of the buoys, wind and atmospheric pressure data at 00:00, 03:00, 06:00, 09:00, 12:00, 15:00, 18:00, and 21:00 were selected.

SST and Chl-a Data
The SST and Chl-a data used in this study were obtained from the Aqua MODIS global map 11-μm daytime SST and Chl-a data (version R2019.0, https://oceandata.sci.gsfc.nasa.gov/directdataaccess/Level-3%20Mapped/Aqua-MODIS, accessed on 8 May 2022) for the period June 2020 to May 2021 at a temporal resolution of 1 day and a spatial resolution of 4 km × 4 km.

SST and Chl-a Data
The SST and Chl-a data used in this study were obtained from the Aqua MODIS global map 11-µm daytime SST and Chl-a data (version R2019.0, https://oceandata.sci.gsfc.nasa. gov/directdataaccess/Level-3%20Mapped/Aqua-MODIS, accessed on 8 May 2022) for the period June 2020 to May 2021 at a temporal resolution of 1 day and a spatial resolution of 4 km × 4 km.

Carbon Dioxide and Water Vapour Data
The atmospheric CO 2 concentration and water vapour data were obtained from Aqua AIRS IR-only Level 3 climcaps (gridded daily V2 with integrated quality control), with two daily tracks divided into diurnal and nocturnal data with a spatial resolution of 1 • × 1 • (https://disc.gsfc.nasa.gov/datasets/SNDRAQIL3CDCCP_2/summary? keywords=CO2, accessed on 8 May 2022).

Calculation of the CO 2 Flux
The block formula of the sea-air CO 2 flux [25], F (mmol m −2 d −1 or mol m −2 s −1 ), is as follows: When the atmospheric CO 2 concentration is high, CO 2 moves from the atmosphere to the ocean; thus, F is negative. The direction of F is determined by the difference between the pCO 2 of seawater and air (i.e., ∆pCO 2 ) [26], which is usually expressed in units of µatm and is calculated using Equation (2): where pCO 2w is the pCO 2 of seawater (in Pa or µatm) and pCO 2a is the pCO 2 of air (in Pa or µatm). The sea-air gas transfer velocity, k (cm h −1 ), is expressed as follows [27]: where U 10 is the wind speed (m s −1 ) at a height of 10 m above sea level and Sc = A + Bt + Ct 2 + Dt 3 + Et 4 (t is the temperature in • C; A = 1923.6, B = −125.06, C = 4.3773, D = −0.085681, and E = 0.00070284). The solubility of CO 2 in seawater, L (mol L −1 atm −1 ), was calculated using Weiss' formula [28]: where SST is the absolute SST  Figure 4 shows that there was a significant diurnal-nocturnal variation in the sea-air CO 2 flux. As the sea-air CO 2 flux is usually estimated using diurnal remote sensing data, we studied the difference between the CO 2 flux calculated using (i) diurnal data (F day ) only and (ii) diurnal-nocturnal data (F real ). There was a significant difference between the F day and F real values ( Figure 5). The largest difference was observed at HogReef station (64 • W, 32 • N), where F real was 4.31 mmol m −2 d −1 lower than F day on average. In contrast, the smallest difference was observed at BOBOA station (90 • E, 15 • N), where F real was 0.01 mmol m −2 d −1 lower than F day . Of the stations where F real was larger than F day , CoastalMS (88 • W, 30 • N) had the largest F real − F day value of 2.64 mmol m −2 d −1 . Temporally, the largest difference was observed in 2018 (data for 2020 were sparse and not included in the comparison), whereas the smallest difference was observed in 2011. The largest difference was observed on 27 August 2018, when F real was 21.90 mmol m −2 d −1 lower than F day . The smallest difference was observed on 27 July 2011, when F real was 1.69 × 10 −5 mmol m −2 d −1 higher than F day . The average difference across the period from 2010 to 2020 was 0.16 mmol m −2 d −1 . Therefore, using diurnal data instead of diurnalnocturnal data to calculate the CO 2 flux will cause significant errors in the calculation of the daily CO 2 flux. Accordingly, this study attempts to eliminate such errors. Therefore, using diurnal data instead of diurnal-nocturnal data to calculate the CO2 flux will cause significant errors in the calculation of the daily CO2 flux. Accordingly, this study attempts to eliminate such errors.

Control Experiment on the Daily CO2 Flux
To understand the main factors controlling the difference between CO2 fluxes calculated using diurnal data and those calculated using diurnal-nocturnal data, a single-factor control experiment was conducted using buoy data from 2010 to 2020.
In the control experiment, the diurnal SST, SSS, wind speed, pCO2w, and pCO2a data were used to calculate the daily CO2 flux, thus obtaining SST F , SSS F , , respectively, where k660 is the gas transfer velocity k calculated using Sc of seawater at 20 °C (Sc = 660) and wind speed data. In each single-factor control experiment, the diurnal-nocturnal data were used to calculate the daily CO2 flux, but the selected influencing factor was excluded from the calculation. The results of the control experiment are shown in Figure 6. The maximum

Control Experiment on the Daily CO 2 Flux
To understand the main factors controlling the difference between CO 2 fluxes calculated using diurnal data and those calculated using diurnal-nocturnal data, a single-factor control experiment was conducted using buoy data from 2010 to 2020.
In the control experiment, the diurnal SST, SSS, wind speed, pCO 2w , and pCO 2a data were used to calculate the daily CO 2 flux, thus obtaining F SST , F SSS , F k 660 , F pCO 2w , and F pCO 2a , respectively, where k 660 is the gas transfer velocity k calculated using Sc of seawater at 20 • C (Sc = 660) and wind speed data. In each single-factor control experiment, the diurnalnocturnal data were used to calculate the daily CO 2 flux, but the selected influencing factor was excluded from the calculation. The results of the control experiment are shown in Figure 6. The maximum F pCO 2w − F real value from 2010 to 2020 was 1.21 mmol m −2 d −1 . The F k 660 − F real value, which indicated the influence of the daily variation in the second power of the wind speed on the calculation of the CO 2 flux, was also large, with a mean value of 0.312 mmol m −2 d −1 . Using only the diurnal data of pCO 2a to calculate the daily CO 2 flux also caused a considerable error of 0.157 mmol m −2 d −1 . The daily variation in SSS strongly affected the daily variation in L; however, this had little effect on the daily variation in the CO 2 flux. The influence of SST on L and Sc did not have a significant effect on the daily variation in the CO 2 flux ( Figure 6). However, SST strongly influenced the daily variation in pCO 2w , and in turn pCO 2w strongly influenced the daily variation in the CO 2 flux; therefore, SST significantly affected the diurnal variation in the CO 2 flux. CO2 flux also caused a considerable error of 0.157 mmol m −2 d −1 . The daily variation in SSS strongly affected the daily variation in L; however, this had little effect on the daily variation in the CO2 flux. The influence of SST on L and Sc did not have a significant effect on the daily variation in the CO2 flux ( Figure 6). However, SST strongly influenced the daily variation in pCO2w, and in turn pCO2w strongly influenced the daily variation in the CO2 flux; therefore, SST significantly affected the diurnal variation in the CO2 flux. (125 • W, 43 • N). These stations were selected to consider the influence of each single factor on the calculation of the daily CO 2 flux over time. As shown in Figure 7, data from HogReef station covered the period from August 2016 to July 2018. The maximum and minimum F pCO 2w − F real values were 21.77 mmol m −2 d −1 and 1.66 × 10 −2 mmol m −2 d −1 , respectively. The daily CO 2 flux that was calculated using the diurnal pCO 2w data only corresponded to an overall decrease (increase) in the CO 2 sink (source) of the ocean; thus, the correction of pCO 2w resulted in a larger oceanic CO 2 sink and smaller oceanic CO 2 source values. The F k 660 − F real value exhibited an obvious seasonal variation, being smaller during October-November and May-July, with a minimum value of −7.75 × 10 −4 mmol m −2 d −1 . Relatively large CO 2 fluxes were observed from December to April and from August to September, with a maximum of −26.71 mmol m −2 d −1 . Only diurnal wind data were used to calculate the daily CO 2 flux, which corresponded to increases in the CO 2 source and sink of the ocean. The sink value increased more than the source value. There were also significant differences between the Although the CO2 flux calculated using the diurnal data of each influencing factor was either larger or smaller than the daily CO2 flux, with an obvious seasonal variation, this difference was not observable at all stations. When the diurnal data of each influencing factor were used to calculate the CO2 flux, the calculated daily CO2 flux from June to September increased at some stations, whereas it decreased at other stations. This was also the case from October to December and from January to May. The daily variation in pCO2w had a considerable influence on the daily variation in the CO2 flux, and the SST value strongly influenced the daily variation in the CO2 flux by affecting pCO2w (when SSS was not considered). Although the daily variation in the wind speed also had a significant effect on the daily variation in the CO2 flux, wind speed was not considered when establishing the nocturnal effect relationship because 24 h wind data were generally available. Therefore, it is recommended to use diurnal-nocturnal wind data to calculate the daily mean wind speed, and not to use the daytime wind data instead. There were also significant differences between the F k 660 and F real values at stations CoastalMS (88 • W, 30 • N), GraysRf (81 • W, 31 • N), SoutheastAK (134 • W, 56 • N), and NH10 (124 • W, 44 • N). The results of the control experiment at SoutheastAK, where the difference between F k 660 and F real was large and the time series had the longest continuity, revealed that the influence of each factor on the error in the daily CO 2 flux calculation exhibited obvious seasonal differences. The F k 660 − F real values were lower from September to October and in March, with a minimum of −1.90 × 10 −3 mmol m −2 d −1 , whereas higher values were observed from April to August and from November to February, with a maximum of 97.70 mmol m −2 d −1 . Although the CO 2 flux calculated using the diurnal data of each influencing factor was either larger or smaller than the daily CO 2 flux, with an obvious seasonal variation, this difference was not observable at all stations. When the diurnal data of each influencing factor were used to calculate the CO 2 flux, the calculated daily CO 2 flux from June to September increased at some stations, whereas it decreased at other stations. This was also the case from October to December and from January to May.

Nocturnal Effect Relationship
The daily variation in pCO 2w had a considerable influence on the daily variation in the CO 2 flux, and the SST value strongly influenced the daily variation in the CO 2 flux by affecting pCO 2w (when SSS was not considered). Although the daily variation in the wind speed also had a significant effect on the daily variation in the CO 2 flux, wind speed was not considered when establishing the nocturnal effect relationship because 24 h wind data were generally available. Therefore, it is recommended to use diurnal-nocturnal wind data to calculate the daily mean wind speed, and not to use the daytime wind data instead.

Nocturnal Effect Relationship
To eliminate the error caused by using diurnal data instead of diurnal-nocturnal data to calculate the CO 2 flux, we studied the relationship between diurnal and nocturnal CO 2 fluxes. The relationship between diurnal and nocturnal pCO 2w values is termed the nocturnal effect of pCO 2w , and the relationship between diurnal and nocturnal SST value is termed the nocturnal effect of SST. The nocturnal effects of pCO 2w and SST are collectively termed the nocturnal effect of the CO 2 flux. Diurnal and nocturnal CO 2 fluxes were calculated using diurnal and nocturnal data from various stations worldwide. The correlation coefficients between the calculated diurnal and nocturnal CO 2 fluxes were determined using a 99.9% significance test. As shown in Figure 8, the diurnal and nocturnal CO 2 fluxes were significantly correlated, with a correlation coefficient of 0.998 at station TAO155W (155 • W, 0 • N) in the Pacific Ocean. The weakest correlation (0.953) was observed at station NH10 (124 • W, 44 • N) in the Pacific Ocean. No obvious regional characteristics were observed between the location of stations in the global ocean ( Figure 8) and the correlation coefficients between their diurnal-nocturnal mean CO 2 fluxes. Moreover, the correlation coefficients differed between proximate stations.   The nocturnal effect on the pCO 2w value was obtained from the fitting results in Figure 9a: where pCO 2wn is the nocturnal pCO 2 of seawater (µatm), pCO 2wd is the diurnal pCO 2 of seawater (µatm), Y 1 = 0.9898, and Y 2 = 3.0999.

• Nocturnal effect of SST
The nocturnal effect on the SST value was obtained from the fitting results in Figure 9b: where SST n is the nocturnal SST ( • C), SST d is the diurnal SST ( • C), Z 1 = 1.0012, and Z 2 = 0.0753.

Nocturnal effect of SST
The nocturnal effect on the SST value was obtained from the fitting results in Figure  9b: Figure 9. Fitting results of (a) nocturnal pCO 2w (pCO 2wn ) and diurnal pCO 2w (pCO 2wd ), and (b) nocturnal SST (SST n ) and diurnal SST (SST d ), whereby fitting results of using 75% of the data from 2010 to 2020.

• Daily variation in Chl-a
The Chl-a data from the Kiyomoto Yoko experiment (2003) are scarce and have little temporal continuity, and we chose the data with the longest temporal continuity to plot Figure 10. As no diurnal-nocturnal rule in Chl-a was observed (Figure 10), the nocturnal effect of Chl-a was not considered in this study. The Chl-a data is limited, so the conclusions may not be representative, and more Chl-a diurnal-nocturnal data is needed to support this conclusion. We couldn't obtain the nocturnal effect formula of Chl-a similar to SST (Equation (6)). So, we directly considered the nocturnal effects of pCO 2w . There were two obvious changes in the curve, which probably related to the change in the sampling station during the Chl-a experiment.

Daily variation in Chl-a
The Chl-a data from the Kiyomoto Yoko experiment (2003) are scarce and have little temporal continuity, and we chose the data with the longest temporal continuity to plot Figure 10. As no diurnal-nocturnal rule in Chl-a was observed (Figure 10), the nocturnal effect of Chl-a was not considered in this study. The Chl-a data is limited, so the conclusions may not be representative, and more Chl-a diurnal-nocturnal data is needed to support this conclusion. We couldn't obtain the nocturnal effect formula of Chl-a similar to SST (Equation (6)). So, we directly considered the nocturnal effects of pCO2w. There were two obvious changes in the curve, which probably related to the change in the sampling station during the Chl-a experiment.

Comparison of Calculated and Real Daily CO2 Fluxes
Equation (5)  pCO , and the diurnal-nocturnal data of SSS, wind speed, pCO2a, and were used to calculate the diurnal-nocturnal CO2 flux (Fcomp). In addition, Equation (6) and were used to calculate , and the diurnal-nocturnal data of SSS, wind speed, pCO2a, and 2 wd pCO were used to calculate the diurnal-nocturnal CO2 flux (Fcomt). By using Equations (5) and (6), and

Comparison of Calculated and Real Daily CO 2 Fluxes
Equation (5) and pCO 2wd were used to calculate pCO 2wn , and the diurnal-nocturnal data of SSS, wind speed, pCO 2a , and SST d were used to calculate the diurnal-nocturnal CO 2 flux (F comp ). In addition, Equation (6) and SST d were used to calculate SST n , and the diurnal-nocturnal data of SSS, wind speed, pCO 2a , and pCO 2wd were used to calculate the diurnal-nocturnal CO 2 flux (F comt ). By using Equations (5) and (6), SST n and pCO 2wn were calculated based on SST d and pCO 2wd , respectively, and the daily CO 2 flux was calculated by combining the diurnal-nocturnal data of SSS, wind speed, and pCO 2a (F com ). The F com , F comp , and F comt values were compared with the F real data using the root-mean-square error (RMSE): where comF is F comt , F comp , or F com ; F real is the real daily CO 2 flux; and n is the number of data observations. The results are shown in Figure 11, where F comp is overlapped by F com because the difference between F comp and F com was very small. The RMSE values between F real and F comt , F comp , F com , and F day were 12.58 mmol m −2 d −1 , 11.94 mmol m −2 d −1 , 11.93 mmol m −2 d −1 , and 46.32 mmol m −2 d −1 , respectively. Thus, compared with F day , the values of F comt , F comp , and F com were more accurate and closer to F real . The similar RMSE of F comt , F comp , and F com indicate that there was a coincidence between the nocturnal effects of pCO 2w and SST. As SST is the most important influencing factor of pCO 2w , it is an important parameter for establishing the algorithm of pCO 2w .
Remote Sens. 2022, 14, 3192 11 of 19 Figure 11. Results of using 25% of the data from 2010 to 2020 verify the calculated nocturnal effect.

Estimated Global CO2 Flux
where SSTd is the absolute daily SST (°C) and Chl-a is the Chl-a concentration (mg m −3 ) at the sea surface. According to the fitting results in Figure 12a

pCO 2 Remote Sensing Inversion Algorithm
As the remote sensing data of the SST and Chl-a parameters that correspond to the algorithm are solely diurnal, pCO 2wd and SST d were used to develop a global pCO 2w algorithm as follows: where SST d is the absolute daily SST ( • C) and Chl-a is the Chl-a concentration (mg m −3 ) at the sea surface. According to the fitting results in Figure 12a, W 1 = 3.40 in the pCO 2wd calculation model. The influence of SST on pCO 2wd was removed to obtain npCO 2wd . According to the fitting results in Figure 12b, W 2 = −4.44 and W 3 = 325.11 in the pCO 2wd calculation model.  Using all the buoy data, a pCO 2wd calculation model was established. The correlation coefficient between pCO 2wd and SST d was 0.327 and passed the 99.9% significance test. The correlation coefficient between npCO 2wd and Chl-a was 0.238 and also passed the 99.9% significance test. As the fitting effect was poor, the Pacific Ocean, Atlantic Ocean, and Indian Ocean sub-regions were selected to establish the calculation model.
According to the results in Figure 13, W 1 = 3.67, W 2 = 8.58, and W 3 = 346.94 in the pCO 2wd model of the Pacific Ocean sub-region. The correlation coefficient between pCO 2wd and SST d was 0.369, while that between npCO 2wd and Chl-a was −0.143. Both passed the 99.9% significance test. For the pCO 2wd model of the Atlantic Ocean sub-region, W 1 = 6.28, W 2 = −11.48, and W 3 = 231.98. The correlation coefficient between pCO 2wd and SST d was 0.413, whereas that between npCO 2wd and Chl-a was −0.392. Both passed the 99.9% significance test. For the pCO 2wd model of the Indian Ocean sub-region, W 1 = 12.96, W 2 = 0, and W 3 = 12.54. The correlation coefficient between pCO 2wd and SST d was 0.826 and passed the 99.9% significant test; however, pCO 2wd was not correlated with Chl-a. Although the pCO 2wd model performed well for the Indian Ocean sub-region, the Pacific and Atlantic Ocean sub-regions had the strongest influence on the global pCO 2wd model.

Estimation of the CO 2 Flux Using the Nocturnal Effect
Remote sensing data of SST d and Chl-a were used to calculate the pCO 2wd (com_pCO 2wd ) for the pCO 2wd sub-region calculation model. In addition, com_pCO 2wd was combined with the remote sensing data of SST d and the diurnal data of SSS, pCO 2a and wind speed data were used to calculate the diurnal CO 2 flux (day_F com ). The corresponding (com_pCO 2wn ) was calculated using Equation (5) and com_pCO 2wd , whereas the corresponding SST n was calculated using Equation (6) and SST d . Combining com_pCO 2wd , com_pCO 2wn , SST d , and SST n with the diurnal-nocturnal data of SSS, pCO 2a , and wind speed, the CO 2 flux considering the nocturnal effect and pCO 2wd calculation model (cor_F com ) was calculated. The distribution of cor_F com − day_F com is shown in Figure 14. The cor_F com value was smaller than the day_F com value at low latitudes, whereas it was greater at high latitudes. The cor_F com − day_F com value also varied considerably with latitude, being smaller and greater at low and high latitudes, respectively.    Figures 14. The cor_Fcom value was smaller than the day_Fcom value at low latitudes, whereas it was greater at high latitudes. The cor_Fcom−day_Fcom value also varied considerably with latitude, being smaller and greater at low and high latitudes, respectively.
As shown in Figure 14, the source and sink areas of CO2 in the ocean were at low and high latitudes, respectively. The mean daily, monthly, and annual global CO2 fluxes were −4.80 × 10 −3 mmol m −2 d −1 , −23.36 mmol m −2 month −1 , and −6.86 mol m −2 y −1 , respectively, indicating that the global ocean acted as an overall sink of atmospheric CO2 from September 2020 to August 2021.  As shown in Figure 14, the source and sink areas of CO 2 in the ocean were at low and high latitudes, respectively. The mean daily, monthly, and annual global CO 2 fluxes were −4.80 × 10 −3 mmol m −2 d −1 , −23.36 mmol m −2 month −1 , and −6.86 mol m −2 y −1 , respectively, indicating that the global ocean acted as an overall sink of atmospheric CO 2 from September 2020 to August 2021.
As shown in Figures 14 and 15, compared with the use of day_F com , the use of cor_F com decreased the source and sink amounts of oceanic CO 2 . Specifically, compared with day_F com , the global cor_F com value increased by 4.90 × 10 −4 mmol m −2 d −1 , thereby overestimating the oceanic CO 2 sink by 10.21%. The mean monthly increase was 2.50 mmol m −2 month −1 , thus overestimating the mean oceanic CO 2 sink by 10.68%. The mean annual increase was 0.75 mol m −2 y −1 , thereby overestimating the mean oceanic CO 2 sink by 10.89%. As shown in Figures 14 and 15, compared with the use of day_Fcom, the use of cor_Fcom decreased the source and sink amounts of oceanic CO2. Specifically, compared with day_Fcom, the global cor_Fcom value increased by 4.90 × 10 −4 mmol m −2 d −1 , thereby overestimating the oceanic CO2 sink by 10.21%. The mean monthly increase was 2.50 mmol m −2 month −1 , thus overestimating the mean oceanic CO2 sink by 10.68%. The mean annual increase was 0.75 mol m −2 y −1 , thereby overestimating the mean oceanic CO2 sink by 10.89%. For the convenience of understanding, we drew the flow diagram of the nocturnal effect establishment-checking-application, which is shown in Figure 16. There are many For the convenience of understanding, we drew the flow diagram of the nocturnal effect establishment-checking-application, which is shown in Figure 16. There are many variable symbols in this paper, so we describe each of these in the accompanying Table A1. variable symbols in this paper, so we describe each of these in the accompanying Table  A1.

Conclusions
Calculating the daily CO2 flux based on solely diurnal data of SST, SSS, wind speed, pCO2w, and pCO2a instead of the corresponding diurnal-nocturnal data can lead to significant errors. In this study, the mean Fday−Freal value calculated based on buoy data from 2010 to 2020 was 0.0751 mmol m −2 d −1 . The corresponding CO2 flux calculated using solely the diurnal data of SST, SSS, wind speed, pCO2w, and pCO2a increased or decreased the

Conclusions
Calculating the daily CO 2 flux based on solely diurnal data of SST, SSS, wind speed, pCO 2w , and pCO 2a instead of the corresponding diurnal-nocturnal data can lead to significant errors. In this study, the mean F day − F real value calculated based on buoy data from 2010 to 2020 was 0.0751 mmol m −2 d −1 . The corresponding CO 2 flux calculated using solely the diurnal data of SST, SSS, wind speed, pCO 2w , and pCO 2a increased or decreased the F real value and exhibited obvious seasonal variations. The results of a control experiment showed that the daily variation in pCO 2w had the greatest influence on the daily variation in the CO 2 flux; therefore, the SST value, which influences the daily variation in pCO 2w , also significantly affected the daily variation in the CO 2 flux.
We found that the diurnal and nocturnal CO 2 fluxes were significantly correlated, with correlation coefficients of >0.950 based on a 99.9% significance test. In addition, the strength of the correlation was independent of the station location. To eliminate errors associated with using diurnal data instead of diurnal-nocturnal data to calculate the CO 2 flux, 75% of the randomly selected buoy data from 2010 to 2020 were used and the relationship between the nocturnal effects of SST and pCO 2w was established (Equations (5) and (6)). The nocturnal effect of the CO 2 flux was verified based on the remaining buoy data (i.e., 25%), and the RMSE values between F real and F comt , F comp , F com , and F day were 12.58 mmol m −2 d −1 , 11.94 mmol m −2 d −1 , 11.93 mmol m −2 d −1 , and 46.32 mmol m −2 d −1 , respectively. Thus, F com provided a more accurate estimation of F real than did F day . The results indicate that the error associated with using diurnal data instead of diurnal-nocturnal data to calculate the CO 2 flux can be reduced by accounting for the nocturnal effect.
As the SST value was the most important factor influencing pCO 2w , the nocturnal effects of these parameters partially coincided. In contrast, no obvious diurnal-nocturnal relationship was observed for Chl-a; thus, the nocturnal effect of Chl-a was not considered in this study. Although the daily variation in the wind speed significantly affected the daily variation in the CO 2 flux, this parameter was not considered when we established the relationship of the nocturnal effect because 24 h wind data can usually be obtained.
The fitting effect of using the complete set of buoy data to build the pCO 2wd model was poor; therefore, we chose to build the pCO 2wd models based on data for the Pacific Ocean, Atlantic Ocean, and Indian Ocean, respectively. The Pacific and Atlantic Ocean sub-regions played major roles in the regional algorithmic model. The pCO 2wd of the Indian Ocean was only related to SST d , and the fitting results between pCO 2wd and SST d were good. However, the algorithm for the Indian Ocean was only based on one station (BOBOA) from 2013 to 2017 because there was insufficient data for stations in the Indian Ocean. In the future, we hope to obtain more relevant data for the Indian Ocean to further improve the algorithmic modelling of this region.
The global CO 2 flux was calculated using the pCO 2wd model and the established nocturnal effect. The source and sink areas of CO 2 in the global ocean were at low and high latitudes, respectively. The mean daily, monthly, and annual global CO 2 fluxes were −4.80 × 10 −3 mmol m −2 d −1 , −23.36 mmol m −2 month −1 , and −6.86 mol m −2 y −1 , respectively, indicating that the global ocean was an overall sink for atmospheric CO 2 from September 2020 to August 2021. During this period, the oceanic sources and sinks of CO 2 determined based on cor_F com were smaller than those based on day_F com . Compared with day_F com , the global cor_F com value was greater by 4.90 × 10 −4 mmol m −2 d −1 , thereby overestimating the oceanic CO 2 sink by 10.21%. The mean monthly increase was 2.50 mmol m −2 month −1 , thus overestimating the mean oceanic CO 2 sink by 10.68%. The mean annual increase was 0.75 mol m −2 y −1 , thus overestimating the mean oceanic CO 2 sink by 10.89%.
In the current studies, the pCO 2W algorithms were frequently built using data from small regions, and few algorithms were built from large areas. However, in order to estimate the global CO 2 flux using satellite data, a large-scale algorithm was used, which was not so accurate as the small-scale regional algorithms. We will improve the accuracy of the global-scale pCO 2W algorithm to further refine the process of estimating global daily CO 2 fluxes in future studies. The equation for calculating the k used to determine the CO 2 flux is one of the many parameterised formulas that have been developed for establishing the relationship between the k of CO 2 and wind speed. Different k equations will yield different CO 2 fluxes. Although such differences were not considered in this study, we hope to address them in future studies.  . generation European Centre for Medium-Range Weather Forecasts (ECMWF) for providing the wind and atmospheric pressure data (https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels?tab=overview), Copernicus Marine Service for providing the SSS data (https: //marine.copernicus.eu), and Earthdata for providing the atmospheric CO 2 and water vapour data (https://disc.gsfc.nasa.gov/datasets/SNDRAQIL3CDCCP_2/summary?keywords=CO2); accessed date: 8 May 2022.

Conflicts of Interest:
The authors declare no conflict of interest. Partial pressure of CO 2 in air F day The CO 2 flux calculated using diurnal buoy data F real The CO 2 flux calculated using diurnal-nocturnal buoy data F SST The daily CO 2 flux calculated using diurnal SST buoy data only, and other parameters except SST were diurnal-nocturnal buoy data F SSS The daily CO 2 flux calculated using diurnal SSS buoy data only, and other parameters except SSS were diurnal-nocturnal buoy data F k 660 The daily CO 2 flux calculated using diurnal wind speed buoy data only, and other parameters except wind speed were diurnal-nocturnal buoy data

Appendix A
The daily CO 2 flux calculated using diurnal pCO 2w buoy data only, and other parameters except pCO 2w were diurnal-nocturnal buoy data The daily CO 2 flux calculated using diurnal pCO 2a buoy data only, and other parameters except pCO 2a were diurnal-nocturnal buoy data pCO 2wn The nocturnal pCO 2w . This variable was used to establish the nocturnal relationship using buoy data The diurnal-nocturnal CO 2 flux calculated combining com_pCO 2wd , com_pCO 2wn , SST d , and SST n with the diurnal-nocturnal remote sensing data of SSS, pCO 2a , and wind speed, considering the nocturnal effect