Influence of the Nocturnal Effect on the Estimated Global CO₂ Flux

Abstract

We found that significant errors occurred when diurnal data instead of diurnal–nocturnal data were used to calculate the daily sea-air CO₂ flux (F). As the errors were mainly associated with the partial pressure of CO₂ 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 CO₂ flux. The root-mean-square error between the real daily CO₂ flux (F_real) and the daily CO₂ 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 CO₂ flux (F_day) (46.32 mmol m⁻² d⁻¹). Thus, the errors associated with using diurnal data to calculate the CO₂ flux can be reduced by accounting for the nocturnal effect. The mean global daily CO₂ 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 greater by 0.75 mol m⁻² y⁻¹ than that based solely on the sub-regional pCO_2w algorithm (day_F_com = −7.61 mol m⁻² y⁻¹). That is, compared with cor_F_com, the global day_F_com value overestimated the CO₂ sink of the global ocean by 10.89%.

1. 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 (CO₂) 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 CO₂ 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 CO₂ (pCO₂) are mainly at the regional level, corresponding to a difference of >10% of the mean climatic pCO₂, which is an order of magnitude greater than the uncertainty associated with the most advanced measurements. Yu (2014) found that a different CO₂ transfer velocity led to considerable uncertainty in the estimated global CO₂ flux [4]. Therefore, it is critical to reduce the uncertainty associated with the estimated oceanic CO₂ flux to improve our understanding of the potential processes that control the distribution of anthropogenic CO₂ between the atmosphere, land, and oceans in the present and future [5].

At present, the sea–air CO₂ flux can be measured directly using the eddy correlation method. Alternatively, the CO₂ flux is often calculated by the block method formula [4], as follows: sea–air CO₂ flux = sea–air gas transfer velocity × solubility of CO₂ in seawater × (pCO₂ in seawater–pCO₂ in air). If the CO₂ flux is positive, it means that CO₂ enters the atmosphere from the ocean, i.e., the ocean is the source of CO₂. If the CO₂ flux is negative, it means that CO₂ enters the ocean from the atmosphere, i.e., the ocean is the sink of CO₂. These parameters are obtained by remote sensing.

The algorithm for determining the pCO₂ 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 pCO₂ 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 pCO₂ 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 CO₂, increasing the emission of air from the ocean and reducing the pCO₂ of seawater, especially at the equator. The SST affects the CO₂ flux by influencing the pCO₂ of seawater and the solubility of CO₂ 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 CO₂ flux [12]. At high latitudes, as the solubility of CO₂ increases at low temperatures, the daily variation in salinity alters the ability of the oceans to absorb atmospheric CO₂ [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 pCO₂ 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 pCO₂ of seawater [16]. Moreover, the daily variation in the pCO₂ of seawater is influenced by biological activity, whereby CO₂ 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 pCO₂ associated with the biological cycle accounted for 16% of the mean CO₂ 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 pCO₂ 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 CO₂ transfer velocity and the daily variation in the sea–air CO₂ flux [11,22,23]. Rousseau et al. (2020) observed that the daily variation in the atmospheric CO₂ concentration directly affected the pCO₂ of seawater [24]. Furthermore, the change in the pCO₂ of air affected the CO₂ flux. Figure 1 depicts the effects of these factors on the sea–air CO₂ 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 also our goal to determine the relationships between diurnal and nocturnal data for the other parameters involved in the CO₂ flux block method and to use the corresponding relationships to correct the diurnal data for each parameter. Ultimately improving the accuracy of the global CO₂ flux estimates by considering the diurnal variation of parameters.

2. Data and Methods

2.1. Buoy Data

The pCO₂, SST, and sea surface salinity (SSS) data used in this study were obtained from the global CO₂ 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 pCO₂ of the atmospheric boundary layer and ocean surface. Time series and mooring projects on CO₂ 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.

2.2. Satellite Remote Sensing Data

2.2.1. 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.

2.2.2. 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.

2.2.3. SSS Data

The SSS data were obtained from the 10-day 3D global ocean forecast data (spatial resolution of 0.083° × 0.083°), which are updated daily at 00:00, 06:00, 12:00, and 18:00 by the global ocean analysis and prediction system (https://resources.marine.copernicus.eu/product-detail/GLOBAL_ANALYSIS_FORECAST_PHY_001_024/INFORMATION, accessed on 8 May 2022).

2.2.4. Carbon Dioxide and Water Vapour Data

The atmospheric CO₂ 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).

2.3. Calculation of the CO₂ Flux

The block formula of the sea–air CO₂ flux [25], F (mmol m⁻² d⁻¹ or mol m⁻² s⁻¹), is as follows:

$$F=kL\Delta pC{O}_2$$

(1)

When the atmospheric CO₂ concentration is high, CO₂ moves from the atmosphere to the ocean; thus, F is negative. The direction of F is determined by the difference between the pCO₂ of seawater and air (i.e., $\Delta pC{O}_2$) [26], which is usually expressed in units of μatm and is calculated using Equation (2):

$$\Delta pC{O}_2=pC{O}_{2\mathrm{w}}-pC{O}_{2\mathrm{a}}$$

(2)

where pCO_2w is the pCO₂ of seawater (in Pa or μatm) and pCO_2a is the pCO₂ of air (in Pa or μatm).

The sea–air gas transfer velocity, k (cm h⁻¹), is expressed as follows [27]:

$$k=0.251U_{10}^2{(Sc/660)}^{-0.5}$$

(3)

where $U_{10}$ is the wind speed (m s⁻¹) at a height of 10 m above sea level and Sc = A + Bt + Ct² + Dt³ + Et⁴ (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 CO₂ in seawater, L (mol L⁻¹ atm⁻¹), was calculated using Weiss’ formula [28]:

$$\begin{array}{l}\ln L=A_1+A_2(100/SST)+A_3\ln (SST/100)+\\ SSS{‰[B}_1{+B}_2(SST/100)+B_3{(SST/100)}^2]\end{array}$$

(4)

where SST is the absolute SST (in K) (absolute SST = t (°C) + 273.15), SSS is the surface seawater salinity, A₁ = −58.0931, A₂ = 90.5069, A₃ = 22.294, B₁ = 0.027766, B₂ = −0.025888, and B₃ = 0.0050578.

3. Results and Discussion

3.1. Estimated Daily Variation in the CO₂ Flux

Figure 4 shows that there was a significant diurnal–nocturnal variation in the sea–air CO₂ flux. As the sea–air CO₂ flux is usually estimated using diurnal remote sensing data, we studied the difference between the CO₂ 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 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.

3.2. 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, pCO_2w, and pCO_2a data were used to calculate the daily CO₂ flux, thus obtaining $F_{SST}$, $F_{SSS}$, $F_{k_{660}}$, $F_{pC{O}_{2w}}$, and $F_{pC{O}_{2a}}$, 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 $F_{pC{O}_{2w}}$ − 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 CO₂ 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 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 pCO_2w, and in turn pCO_2w strongly influenced the daily variation in the CO₂ flux; therefore, SST significantly affected the diurnal variation in the CO₂ flux.

As shown in Figure 6, there were clear differences between the $F_{pC{O}_{2w}}$ and F_real values at stations CCE2 (121°W, 34°N), Cheeca (80°W, 25°N), HogReef (64°W, 32°N), and CE-06 (125°W, 43°N). These stations were selected to consider the influence of each single factor on the calculation of the daily CO₂ 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 $F_{pC{O}_{2w}}$ − F_real values were 21.77 mmol m⁻² d⁻¹ and 1.66 × 10⁻² mmol m⁻² d⁻¹, respectively. The daily CO₂ flux that was calculated using the diurnal pCO_2w data only corresponded to an overall decrease (increase) in the CO₂ sink (source) of the ocean; thus, the correction of pCO_2w resulted in a larger oceanic CO₂ sink and smaller oceanic CO₂ 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 CO₂ 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 CO₂ flux, which corresponded to increases in the CO₂ source and sink of the ocean. The sink value increased more than the source value.

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 CO₂ 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 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 pCO_2w 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 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 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.

3.3. Nocturnal Effect Relationship

To eliminate the error caused by using diurnal data instead of diurnal–nocturnal data to calculate the CO₂ flux, we studied the relationship between diurnal and nocturnal CO₂ 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 CO₂ flux. Diurnal and nocturnal CO₂ fluxes were calculated using diurnal and nocturnal data from various stations worldwide. The correlation coefficients between the calculated diurnal and nocturnal CO₂ fluxes were determined using a 99.9% significance test. As shown in Figure 8, the diurnal and nocturnal CO₂ 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 CO₂ fluxes. Moreover, the correlation coefficients differed between proximate stations.

• Nocturnal effect of the pCO₂ of seawater

The nocturnal effect on the pCO_2w value was obtained from the fitting results in Figure 9a:

$$pC{O}_{2\mathrm{wn}}=Y_1\times pC{O}_{2\mathrm{wd}}+Y_2$$

(5)

where pCO_2wn is the nocturnal pCO₂ of seawater (μatm), pCO_2wd is the diurnal pCO₂ of seawater (μatm), Y₁ = 0.9898, and Y₂ = 3.0999.

• Nocturnal effect of SST

The nocturnal effect on the SST value was obtained from the fitting results in Figure 9b:

$$SS{T}_n=Z_1\times SS{T}_d+Z_2$$

(6)

where $SS{T}_n$ is the nocturnal SST (°C), $SS{T}_d$ is the diurnal SST (°C), Z₁ = 1.0012, and Z₂ = 0.0753.

• 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.

3.4. Comparison of Calculated and Real Daily CO₂ Fluxes

Equation (5) and $pC{O}_{2\mathrm{wd}}$ were used to calculate $pC{O}_{2\mathrm{wn}}$, and the diurnal–nocturnal data of SSS, wind speed, pCO_2a, and $SS{T}_d$ were used to calculate the diurnal–nocturnal CO₂ flux (F_comp). In addition, Equation (6) and $SS{T}_d$ were used to calculate $SS{T}_n$, and the diurnal–nocturnal data of SSS, wind speed, pCO_2a, and $pC{O}_{2\mathrm{wd}}$ were used to calculate the diurnal–nocturnal CO₂ flux (F_comt). By using Equations (5) and (6), $SS{T}_n$ and $pC{O}_{2\mathrm{wn}}$ were calculated based on $SS{T}_d$ and $pC{O}_{2\mathrm{wd}}$, respectively, and the daily CO₂ 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):

$$RMSE=\sqrt{\frac{{\displaystyle {\sum }_{\mathrm{i}=1}^n{\left[\mathit{comF}-F_{\mathrm{real}}\right]}^2}}{n}}$$

(7)

where comF is F_comt, F_comp, or F_com; F_real is the real daily CO₂ 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.

3.5. Estimated Global CO₂ Flux

3.5.1. pCO₂ Remote Sensing Inversion Algorithm

As the remote sensing data of the SST and Chl-a parameters that correspond to the algorithm are solely diurnal, $pC{O}_{2\mathrm{wd}}$ and SST_d were used to develop a global $pC{O}_{2\mathrm{w}}$ algorithm as follows:

$$pC{O}_{2\mathrm{wd}}=W_1\times SS{T}_d+W_2\times ln\left(Chl-\mathrm{a}\right)+W_3$$

(8)

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, W₁ = 3.40 in the $pC{O}_{2\mathrm{wd}}$ calculation model. The influence of SST on $pC{O}_{2\mathrm{wd}}$ was removed to obtain $\mathrm{n}pC{O}_{2\mathrm{wd}}$. According to the fitting results in Figure 12b, W₂ = −4.44 and W₃ = 325.11 in the $pC{O}_{2\mathrm{wd}}$ calculation model.

Using all the buoy data, a $pC{O}_{2\mathrm{wd}}$ calculation model was established. The correlation coefficient between $pC{O}_{2\mathrm{wd}}$ and SST_d was 0.327 and passed the 99.9% significance test. The correlation coefficient between $\mathrm{n}pC{O}_{2\mathrm{wd}}$ 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, W₁ = 3.67, W₂ = 8.58, and W₃ = 346.94 in the $pC{O}_{2\mathrm{wd}}$ model of the Pacific Ocean sub-region. The correlation coefficient between $pC{O}_{2\mathrm{wd}}$ and SST_d was 0.369, while that between $\mathrm{n}pC{O}_{2\mathrm{wd}}$ and Chl-a was −0.143. Both passed the 99.9% significance test. For the $pC{O}_{2\mathrm{wd}}$ model of the Atlantic Ocean sub-region, W₁ = 6.28, W₂ = −11.48, and W₃ = 231.98. The correlation coefficient between $pC{O}_{2\mathrm{wd}}$ and SST_d was 0.413, whereas that between $\mathrm{n}pC{O}_{2\mathrm{wd}}$ and Chl-a was −0.392. Both passed the 99.9% significance test. For the $pC{O}_{2\mathrm{wd}}$ model of the Indian Ocean sub-region, W₁ = 12.96, W₂ = 0, and W₃ = 12.54. The correlation coefficient between $pC{O}_{2\mathrm{wd}}$ and SST_d was 0.826 and passed the 99.9% significant test; however, $pC{O}_{2\mathrm{wd}}$ was not correlated with Chl-a. Although the $pC{O}_{2\mathrm{wd}}$ model performed well for the Indian Ocean sub-region, the Pacific and Atlantic Ocean sub-regions had the strongest influence on the global $pC{O}_{2\mathrm{wd}}$ model.

3.5.2. Estimation of the CO₂ Flux Using the Nocturnal Effect

Remote sensing data of SST_d and Chl-a were used to calculate the $pC{O}_{2\mathrm{wd}}$($com\_pC{O}_{2\mathrm{wd}}$) for the $pC{O}_{2\mathrm{wd}}$ sub-region calculation model. In addition, $com\_pC{O}_{2\mathrm{wd}}$ was combined with the remote sensing data of SST_d and the diurnal data of SSS, $pC{O}_{2\mathrm{a}}$ and wind speed data were used to calculate the diurnal CO₂ flux (day_F_com). The corresponding ($com\_pC{O}_{2\mathrm{wn}}$) was calculated using Equation (5) and $com\_pC{O}_{2\mathrm{wd}}$, whereas the corresponding SST_n was calculated using Equation (6) and SST_d. Combining $com\_pC{O}_{2\mathrm{wd}}$, $com\_pC{O}_{2\mathrm{wn}}$, SST_d, and SST_n with the diurnal–nocturnal data of SSS, $pC{O}_{2\mathrm{a}}$, and wind speed, the CO₂ flux considering the nocturnal effect and $pC{O}_{2\mathrm{wd}}$ 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.

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 and Figure 15, compared with the use of day_F_com, the use of cor_F_com decreased the source and sink amounts of oceanic CO₂. Specifically, compared with day_F_com, the global cor_F_com value increased by 0.18 mmol m⁻² d⁻¹, thereby day_F_com overestimating the oceanic CO₂ sink by 10.21%. The mean monthly increase was 2.50 mmol m⁻² month⁻¹, thus day_F_com overestimating the mean oceanic CO₂ sink by 10.68%. The mean annual increase was 0.75 mol m⁻² y⁻¹, thereby day_F_com 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 variable symbols in this paper, so we describe each of these in the accompanying

Table A1. Variable symbols in this article defined in the corresponding table.

Quantity	Meaning
pCO2w	Partial pressure of CO2 in seawater
pCO2a	Partial pressure of CO2 in air
Fday	The CO2 flux calculated using diurnal buoy data
Freal	The CO2 flux calculated using diurnal–nocturnal buoy data
$F_{SST}$	The daily CO2 flux calculated using diurnal SST buoy data only, and other parameters except SST were diurnal–nocturnal buoy data
$F_{SSS}$	The daily CO2 flux calculated using diurnal SSS buoy data only, and other parameters except SSS were diurnal–nocturnal buoy data
$F_{k_{660}}$	The daily CO2 flux calculated using diurnal wind speed buoy data only, and other parameters except wind speed were diurnal–nocturnal buoy data
$F_{pC{O}_{2w}}$	The daily CO2 flux calculated using diurnal pCO2w buoy data only, and other parameters except pCO2w were diurnal–nocturnal buoy data
$F_{pC{O}_{2a}}$	The daily CO2 flux calculated using diurnal pCO2a buoy data only, and other parameters except pCO2a were diurnal–nocturnal buoy data
pCO2wn	The nocturnal pCO2w. This variable was used to establish the nocturnal relationship using buoy data
pCO2wd	The diurnal pCO2w. This variable was used to establish the nocturnal relationship using buoy data
$SS{T}_n$	The nocturnal SST. This variable was used to establish the nocturnal relationship using buoy data
$SS{T}_d$	The diurnal SST. This variable was used to establish the nocturnal relationship using buoy data
Fcomp	The CO2 flux calculated using only the nocturnal effect for pCO2w and satellite data for each parameter
Fcomt	The CO2 flux calculated using only the nocturnal effect for SST and satellite data for each parameter
Fcom	The CO2 flux calculated using only the nocturnal effect for pCO2w and SST and satellite data for each parameter
$com\_pC{O}_{2\mathrm{wd}}$	$pC{O}_{2\mathrm{wd}}$ calculated using remote sensing data of SSTd and Chl-a
$com\_pC{O}_{2\mathrm{wn}}$	The $pC{O}_{2\mathrm{wn}}$ calculated using the nocturnal effect for pCO2w and $com\_pC{O}_{2\mathrm{wd}}$
day_Fcom	The diurnal CO2 flux calculated using diurnal remote sensing data of SSS, $pC{O}_{2\mathrm{a}}$ and wind speed and remote sensing data of SSTd and $com\_pC{O}_{2\mathrm{wd}}$
cor_Fcom	The diurnal–nocturnal CO2 flux calculated combining $com\_pC{O}_{2\mathrm{wd}}$, $com\_pC{O}_{2\mathrm{wn}}$, SSTd, and SSTn with the diurnal–nocturnal remote sensing data of SSS, $pC{O}_{2\mathrm{a}}$, and wind speed, considering the nocturnal effect

.

4. Conclusions

Calculating the daily CO₂ 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 CO₂ 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 CO₂ flux; therefore, the SST value, which influences the daily variation in pCO_2w, also significantly affected the daily variation in the CO₂ flux.

We found that the diurnal and nocturnal CO₂ 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 CO₂ 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 CO₂ 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 CO₂ 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 CO₂ 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 CO₂ flux was calculated using the $pC{O}_{2\mathrm{wd}}$ model and the established nocturnal effect. The source and sink areas of CO₂ in the global 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 was an overall sink for atmospheric CO₂ from September 2020 to August 2021. During this period, the oceanic sources and sinks of CO₂ 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 0.18 mmol m⁻² d⁻¹, thereby day_F_com overestimating the oceanic CO₂ sink by 10.21%. The mean monthly increase of cor_F_com was 2.50 mmol m⁻² month⁻¹, thus day_F_com overestimating the mean oceanic CO₂ sink by 10.68%. The mean annual increase of cor_F_com was 0.75 mol m⁻² y⁻¹, thus day_F_com overestimating the mean oceanic CO₂ 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 CO₂ 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 CO₂ fluxes in future studies. The equation for calculating the k used to determine the CO₂ flux is one of the many parameterised formulas that have been developed for establishing the relationship between the k of CO₂ and wind speed. Different k equations will yield different CO₂ fluxes. Although such differences were not considered in this study, we hope to address them in future studies.