Low CO2 evasion rate from the mangrove-surrounding waters of the Sundarbans

Globally, water bodies adjacent to mangroves are considered significant sources of atmospheric CO2. We directly measured the partial pressure of CO2 in water [pCO2(water)] and related biogeochemical parameters with high temporal resolution, covering both diel and tidal cycles, in the mangrove-surrounding waters around the northern Bay of Bengal during the post-monsoon season. Mean pCO2(water) was marginally oversaturated in two creeks (470 ± 162 µatm, mean ± SD) and undersaturated in the adjoining estuarine stations (387 ± 58 µatm) compared to atmospheric pCO2, and was considerably lower than the global average. We further estimated the pCO2(water) and buffering capacity of all possible sources of the mangrove-surrounding waters and concluded that their character as a CO2 sink or weak source is due to the predominance of marine water from the Bay of Bengal with low pCO2 and high buffering capacity. Marine water with high buffering capacity suppresses the effect of pCO2 increase within the mangrove system and lowers the CO2 evasion even in creek stations. The δ13C of dissolved inorganic carbon (DIC) in the mangrove-surrounding waters indicated that the DIC sources were a mixture of mangrove plants, pore-water, and groundwater, in addition to marine water. Finally, we showed that the CO2 evasion rate from the estuaries of the Sundarbans is much lower than the recently estimated world average. Our results demonstrate that mangrove areas having such low emissions should be considered when up-scaling the global mangrove carbon budget from regional observations.

undersaturated in the adjoining estuarine stations (387 ± 58 latm) compared to atmospheric pCO 2 , and was considerably lower than the global average. We further estimated the pCO 2 (water) and buffering capacity of all possible sources of the mangrovesurrounding waters and concluded that their character as a CO 2 sink or weak source is due to the predominance of marine water from the Bay of Bengal with low pCO 2 and high buffering capacity. Marine water with high buffering capacity suppresses the effect of pCO 2 increase within the mangrove system and lowers the CO 2 evasion even in creek stations. The d 13 C of dissolved inorganic carbon (DIC) in the mangrovesurrounding waters indicated that the DIC sources were a mixture of mangrove plants, pore-water, and groundwater, in addition to marine water. Finally, we showed that the CO 2 evasion rate from the estuaries of the Sundarbans is much lower than the recently estimated world average. Our results demonstrate that mangrove areas having such low emissions should be considered when up-scaling the global mangrove carbon budget from regional observations.

Introduction
The carbon stocks within several coastal ecosystems (e.g. mangroves, tidal marshes and seagrass beds), collectively referred to as ''blue carbon'', have drawn attention in the context of global climate change (Donato et al. 2011;McLeod et al. 2011;Pendleton et al. 2012), and initiatives to characterize the functioning and long-term future of these blue-carbon ecosystems have also begun (Macreadie et al. 2019). These ecosystems are known to be carbon sinks; however, mangroves deserve special mention owing to their large soil organic carbon pool and for being a center for active deposition of both autochthonous and allochthonous organic matter (Breithaupt et al. 2012;Sanders et al. 2016aSanders et al. , 2016b. Mangroves, despite covering only 0.1% of the Earth's total land area (Jennerjahn and Ittekkot 2002), are one of the most productive ecosystems in the world, with high carbon-sequestration potential. The carbon (C) stock in mangroves per unit area (956 Mg-C ha -1 ) is much higher than that in other carbon-rich ecosystems such as salt marshes (593 Mg-C ha -1 ), seagrass beds (142 Mg-C ha -1 ), peatland (408 Mg-C ha -1 ), or even rain forests (241 Mg-C ha -1 ) (Alongi 2014;Donato et al. 2011;Twilley et al. 1992).
Although mangrove ecosystems as a whole are net sinks for atmospheric CO 2 , the waters adjacent to mangroves (as well as the associated sediments) emit substantial amounts of CO 2 because they have high organic carbon loading, which is mainly attributed to mangrove biomass, terrestrial detritus, the microphytobenthos, and phytoplankton (Borges et al. 2005(Borges et al. , 2018Borges and Abril 2011;Bouillon and Boschker 2006;Kristensen et al. 2008;Lekphet et al. 2005). In contrast to processes in other forests, tidal flow allows mangroves to exchange both inorganic and organic solutes and particulates with adjacent water bodies (Adame and Lovelock 2011). Several studies have attributed the high CO 2 emissions from mangrove-surrounding waters to the mixing of surface water with pore-water through tidal pumping, which leads to enrichment of the partial pressure of CO 2 in water [pCO 2 (water)] and dissolved inorganic carbon (DIC), as well as to metabolic activity in sediments (Bouillon et al. 2007b;Gleeson et al. 2013;Li et al. 2009;Maher et al. 2013;Robinson et al. 2007;Santos et al. 2012;Sippo et al. 2016).
The mineralization of dissolved and particulate organic carbon (DOC and POC, respectively) leads to additional DIC in water bodies adjacent to mangroves (Gattuso et al. 1998;Maher et al. 2013Maher et al. , 2015. The mineralization of organic carbon in mangrove sediments is facilitated through several pathways such as sulfate reduction, iron reduction, and aerobic respiration (Borges et al. 2003;Kristensen and Alongi 2006;Krumins et al. 2013). The diagenetic processes change the balance of exported DIC and total alkalinity (TAlk) from mangroves, which promotes carbonate buffering in the water bodies adjacent to mangroves (Sippo et al. 2016;Joesoef et al. 2017;Maher et al. 2018).
Although the mangrove-surrounding waters (or ''mangrove water'' or other similar terms) usually act as a source of CO 2 , there are still uncertainties with respect to the global budget of these emissions. Recent measurements in mangrove-surrounding waters showed negative fluxes in some regions and during certain times of the year (Akhand et al. 2013b(Akhand et al. , 2016Biswas et al. 2004). In this regard, Reiman and Xu (2019) reported significant underestimation of pCO 2 (water) and the air-water CO 2 flux due to the use of a single daily pCO 2 (water) value, compared to the diurnal dataset. Rosentreter et al. (2018) emphasized the importance of the temporal resolution of sampling, which can lead to considerable uncertainty. They argued that data acquisition at hourly or greater intervals often misses the tidal maxima and minima, and deducing the mean CO 2 flux from such data might lead to under-or overestimation of fluxes.
The Sundarbans is the world's largest mangrove forest and has a wide variety of mangrove flora and associated fauna. The Sundarbans mangroves encompass a complex network of channels, creeks and large estuaries. In the last decade, the air-water CO 2 flux has been well studied in the Indian section of the Sundarbans (hereafter, the Indian Sundarbans) in terms of spatial variability (Akhand et al. 2013b(Akhand et al. , 2016Dutta et al. 2019) and seasonal variability (Akhand et al. 2016;Biswas et al. 2004). Hence, in this study we do not emphasize these two aspects. Rather, we focus on a particular site previously reported as being a sink or reduced source of CO 2 during the post-monsoon season (Akhand et al. 2016;Biswas et al. 2004) in order to carry out a thorough and comprehensive investigation into the reasons for its being such a sink or weak source in that season.
The hydrology of the Indian Sundarbans is characterized mainly by marine water from the Bay of Bengal (BoB) and to some extent by monsoonal runoff (Cole and Vaidyaraman 1966;Mitra et al. 2009;Sarkar et al. 2004). At present, all rivers in the Indian Sundarbans, except for the Hooghly and its distributary the Muriganga, have lost their direct connections with the main flow of the River Ganga because of siltation in their upper reaches. However, these disconnected rivers receive reduced amounts of riverine freshwater from the Hooghly River through a large number of waterways such as the Hatania-Doania Canal (Ray et al. 2018a).
A unique quality of the BoB is that, despite being part of the open ocean, it has low salinity (Rao and Sivakumar 2003;Prasad 2004;Pant et al. 2015). The main reason for this low salinity is that several large perennial rivers (such as the Ganges, Brahmaputra, Meghna, Mahanadi, and others) discharge into the BoB (Sandeep et al. 2018). The BoB has low pCO 2 and is considered to be a sink for CO 2 (Akhand et al. 2013a;Goyet et al. 1999;Kumar et al. 1996). Hence, the tidally driven estuaries of the Indian Sundarbans are affected more by the low-pCO 2 water (nearly equal to or below atmospheric equilibrium) of the BoB than by high-pCO 2 riverine freshwater.
We hypothesized that despite being mangrovesurrounding waters, the CO 2 sink or weak source character of the Indian Sundarbans is mainly caused by the predominance of water with low-pCO 2 and high-buffering-capacity from the BoB, with higher TAlk than DIC (Goyet et al. 1999;Sabine et al. 2002). To examine this hypothesis, we obtained high-temporal-resolution data for pCO 2 (water) and other related biogeochemical parameters. In addition, we measured TAlk and DIC along with stable isotopic signatures of DIC to quantify and identify their sources in the surface water. Finally, we compared the estimated fluxes, considering the annual evasion rate over the entire estuary, with global average data. We used the Matla Estuary for comparison, as this estuary flows through the central part of the Indian Sundarbans as well as for a long distance covering almost the entire north-south extent. Moreover, the estuaries of the Sundarbans have been exhaustively studied in the recent past from the perspective of air-water CO 2 flux (Biswas et al. 2004;Akhand et al. 2013bAkhand et al. , 2016Dutta et al. 2019) as discussed previously. Our objectives were to reduce the uncertainty of flux estimation by direct and continuous measurement of pCO 2 (water) in order to confirm the previously observed low pCO 2 (water) of earlier studies and identify plausible reasons behind such low pCO 2 (water).

Study area
The Sundarbans is situated in the lower stretch of the Ganges-Brahmaputra-Meghna (GBM) Delta, extending into both India (40%) and Bangladesh (60%) and facing the BoB to the south. The present study was carried out in the Indian Sundarbans, which comprises an area of 10,200 km 2 out of which 4200 km 2 is demarcated as reserve forest (Ray et al. 2015). Sampling was conducted at six stations in a small north-south section of the estuary approximately 9 km long (width varying between 0.70 and 0.85 km) to the west of Dhanchi Island, and in two tributary creeks (&20 m wide) on the adjoining island ( Fig. 1). For details about the study area see Supplementary Material S1. Dhanchi Island covers an area of about 33 km 2 , and its southern tip ends at the BoB. To the east of the island flows the Thankuran Estuary (7 km wide).

Sample collection
We collected samples at a single station in each of two creeks (hereafter referred to as stations C1 and C2) on the western side of Dhanchi Island, and at six subtidal locations in the adjoining estuary (hereafter referred to as E1, E2, E3, E4, E5 and E6) (Fig. 1). The estuarine stations covered the north-to-south stretch of Dhanchi Island. The abbreviations ''C'' and ''E'' stand for ''creek'' and ''estuary'', respectively. Creek stations are more influenced by dense mangrove vegetation than estuarine stations.
Surface pCO 2 (water), salinity, water temperature, dissolved oxygen, and chlorophyll-a were monitored with sensors (for details see section Analytical Protocol). Data for a 24-h diurnal cycle for all of these parameters were acquired at 1-min intervals at each of the eight stations between 27 January and 6 February 2018. Surface water samples were collected at two peak low and high tides; i.e. four times from each station during a complete tidal and diurnal cycle for the analyses of the parameters TAlk, DIC, nutrients (PO 4 3and SiO 3 2-), and d 13 C DIC . In addition, surface water samples were collected from a station named Diamond Harbor (salinity 0.39, measured with the same salinity sensor used for diurnal sampling described later in section Analytical Protocol), which served as the riverine freshwater end-member. The samples were preserved as described in the next paragraph and sent to the laboratory for analysis.
Samples for TAlk and DIC were collected into 250-mL Duran bottles (SCHOTT AG, Mainz, Germany), filtered through glass-fiber filters (GF/F; Whatman, Maidstone, Kent, UK) and poisoned with mercuric chloride (200 lL saturated aqueous solution per bottle) to prevent changes in TAlk and DIC due to biological activity. Samples for nutrients analyses were collected for input parameters of CO 2 SYS software (Lewis and Wallace 1998). The samples were filtered through 0.2-lm polytetrafluoroethylene filters (DISMIC-25HP; Advantec, Durham, NC, USA) into acid-washed 50-mL polyethylene bottles and frozen at -20°C until analysis.

Analytical protocol
TAlk and DIC concentrations were determined using a batch-sample analyzer (ATT-05; Kimoto Electric Co., Ltd., Osaka, Japan) implementing the Gran Plot method (Dickson et al. 2007). The accuracy of TAlk and DIC was estimated to be ± 1 lmol kg -1 water and ± 2 lmol kg -1 water, respectively by triplicate measurements of the certified reference material (CRM) for TAlk and DIC (Kanso Company Ltd., Osaka, Japan).
The pCO 2 (water) was measured with a CO 2 analyzer (non-dispersive infrared sensor) through an equilibrator system (CO 2 -09, Kimoto Electric Co., Ltd.) Tokoro et al. 2014) using a gas-permeable membrane . The instrument was calibrated every day at the beginning of the measurements using certified reference gases [pure N 2 gas (0 ppm) and span gas (600 ppm CO 2 gas with a N 2 base; Chemtron Science Laboratories, Mumbai, India)]. The estimated accuracy and precision of the pCO 2 analyzer were ± 5 latm and ± 2 latm, respectively, which was in parity with the previous works (Saito et al. , 1999Kayanne et al. 2005) where the same pCO 2 measurement system was used.
Stable isotope signatures (d 13 C DIC ) were measured with an isotope-ratio mass spectrometer (Delta Plus Advantage; Thermo Electron, Bremen, Germany) coupled with an elemental analyzer (Flash EA 1112; Thermo Electron) following the method of Miyajima et al. (1995). Stable isotope ratios are expressed in d notation as the deviation from standards in parts per thousand (%) according to the following equation: where R is 13 C/ 12 C. Vienna Pee Dee Belemnite (VPDB) was used as the isotope standard for carbon. The analytical precision of the Delta Plus Advantage mass-spectrometer system, based on the standard deviation of the internal reference replicates, was \ 0.2% for d 13 C DIC . Salinity and temperature were measured with a CTsensor (INFINITY-CT; JFE Advantech CO., Ltd, Nishinomiya, Japan). Dissolved oxygen (DO) concentration was measured at hourly intervals with a portable DO meter (FiveGo Series; Mettler Toledo, Giessen, Germany). Chlorophyll-a concentration (Chl-a) and turbidity were measured in situ with a fluorometer (COMPACT-CLW, JFE Advantech CO., Ltd). The Chl-a fluorescence sensor was adjusted in a uranine solution by the manufacturer to yield a constant calibration factor. We have corrected the Chl-a data using the regression line between sensor data and 12 spectrophotometrically measured Chla data collected during sampling. Chl-a was measured following standard spectrophotometric procedures using Shimadzu UV-Visible 1600 double-beam spectrophotometer (Parsons et al. 1992). Nutrients concentrations (PO 4 3and SiO 3 2-) in sample filtrates were measured using an Auto Analyzer (QuAAtro; BL TEC K. K., Osaka, Japan; for nutrient data, see Table S1, Supplementary Material).

Estimation of air-water CO 2 flux
The air-water CO 2 flux (F CO 2 , lmol CO 2 m -2 h -1 ) was determined by the following equation: where k is the gas transfer velocity (cm h -1 ), K 0 denotes the solubility coefficient of CO 2 (mol m -3 atm -1 ), and DpCO 2 denotes the difference in fugacity (&partial pressure) of CO 2 between water and air [pCO 2 (water) -pCO 2 (air)]. K 0 is computed based on the equation given by Weiss (1974). The pCO 2 (air) was considered to be 408 latm, i.e. the global mean pCO 2 (air) observed during the study period (https://www.co2.earth/historical-co2datasets). The mole fraction of CO 2 was converted to partial pressure of CO 2 in air [pCO 2 (air)] by using the virial equation of state (Weiss 1974). A positive F CO 2 value indicates CO 2 efflux from the water to the atmosphere and vice versa. The parameter k was calculated by using three different empirical gas transfer velocity models based on wind speed: Liss and Merlivat (1986) (LM86), Raymond et al. (2000) (R00) and Ho et al. (2011) (H11). These formulae were selected for the present study because the estuarine channels in the Indian Sundarbans are very wide and there is no hindrance to the free-flowing wind, which makes the wind velocity the most important component regulating the CO 2 fluxes. The equations for the gas transfer velocity calculations are given below: where U 10 is the wind speed at 10-m height and a is a constant accounting for gas transfer from bottomshear-driven turbulence (assumed to be zero in the present study area, in accordance with Ho et al. [2011] and their study in the wide Hudson Bay, USA). Sc is the Schmidt number of CO 2 as given by Jähne et al. (1987). Only Eq. (3a) was used to compute the gas transfer velocity according to LM86, because the mean wind speed was always \ 3.6 m s -1 during the present study. Wind speed data were acquired by using a handheld anemometer (AM 4201; Lutron Inc., Singapore) and corrected for the 10-m measurement height (Kondo 2000).

Data analysis
The Hooghly River is the main ''artery'' (Ray et al. 2018a) and only possible source of riverine freshwater to the Indian Sundarbans. For this reason, the nearzero salinity region of the Hooghly River has been widely used in previous works (Dutta et al. 2019;Ray and Shahraki 2016;Ray et al. 2015Ray et al. , 2018a as the freshwater end-member for the Indian Sundarbans. In accordance with these previous studies, we defined the observed salinity at the Diamond Harbor station (salinity approx. 0) as a proxy for the riverine freshwater end-member. Figure 1 includes a schematic showing the pathway of riverine freshwater input to the study area through the Hatania-Doania Canal, which connects the Indian Sundarbans with the Hooghly River (Ray et al. 2018a).
To characterize the pathway of mineralization of organic matter in this study, we normalized both TAlk and DIC with respect to salinity. We analyzed the stoichiometric relationship (the slope) between salinity-normalized TAlk (nTAlk) and salinity-normalized DIC (nDIC). DIC was normalized according to the following equation (Friis et al. 2003): where DIC meas is the measured DIC, DIC s=0 is the DIC of the riverine freshwater end-member (i.e. where salinity = 0), S meas is the measured salinity, and S mean is the mean salinity, which is used for normalization (25.0 for this study). TAlk was also normalized using the same equation, replacing DIC meas and DIC s=0 with TAlk meas and TAlk s=0 , respectively.
Excess DIC for the creek and estuarine stations was calculated from the difference between the ''in situ DIC'' and the expected DIC in water when pCO 2 (water) is equal to pCO 2 (air) (Abril et al. 2000). The latter was determined by using CO 2 SYS software with the in situ salinity, temperature, measured alkalinity and an atmospheric pCO 2 of 408 latm as input parameters.
pH was estimated from the measured TAlk and DIC values (n = 31) using CO 2 SYS software (version 2.5) (Lewis and Wallace 1998). The uncertainty in pH estimation was 0.012 (estimated from the accuracy of the input parameters, TAlk and DIC, stated in section Analytical Protocol, by using the error computation tool of the CO 2 SYS software).
We estimated the pCO 2 (water) and Revelle factor of the sampled waters and all possible sources of the estuarine water-namely pore-water, groundwater, the riverine freshwater end-member, and offshore water of the northern BoB-by using CO 2 SYS software (Lewis and Wallace 1998). For the riverine freshwater end-member, we used the measured TAlk and DIC of the present study and data from previous studies (Akhand et al. 2016;Dutta et al. 2019) to calculate the Revelle factor. For groundwater, the pCO 2 (water) and Revelle factor were calculated by using measured TAlk and DIC (Akhand et al., unpublished data; see details of the sample collection in Table S2, Supplementary Material). We used the porewater pH data of Mandal et al. (2009) and pore-water DIC data of Dutta et al. (2019) (from samples collected from various sites in the Indian Sundarbans, depth reported as 30 cm below the water table) as input parameters in CO 2 SYS to compute the pCO 2 (water) and Revelle factor of pore-water. For the northern BoB, we used the measured pH and TAlk data of Akhand et al. (2012) and Sarma et al. (2012) [we used only the data from the station nearest to the Indian Sundarbans from Sarma et al. (2012)]. For waters farther offshore in the BoB (almost to latitude 10°N) we used the TAlk and DIC data of Goyet et al. (1999) to compute the Revelle factor. Unlike for the other possible sources, we could estimate only a single value of the Revelle factor and the pCO 2 (water) for pore-water and water from offshore in the BoB. We believe that as the data for pore-water is close to that of ground water and data from the far offshore BoB is close to the data from the northern BoB, these representative single data will not hamper any interpretation of the present study.
Oxygen saturation was calculated according to the solubility equation given by Benson and Krause (1984). Apparent oxygen utilization (AOU) was calculated according to the formula, AOU = C obs -C sat , where C obs is the observed DO concentration and C sat is the oxygen concentration at saturation.
Statistical analyses were done using SPSS software version 16.0 (SPSS Inc., Chicago, USA). We checked for normality of the biogeochemical parametersnamely salinity, water temperature, DO, pCO 2 (water), pH, TAlk, DIC, TAlk/DIC, d 13 C DIC and Chl-a-by applying the Shapiro-Wilk test. All of these parameters exhibited non-normal distributions. In order to test the significance of differences in these parameters between the creek and estuarine stations, we applied the non-parametric Mann-Whitney U test (also known as the Wilcoxon rank sum test).

Physicochemical setting
Salinity and water temperature were significantly higher in the creeks than in the estuary (salinity, p \ 0.001; water temperature, p \ 0.001; Mann-Whitney U test) but varied within very narrow ranges (Table 1). DO concentrations were significantly higher in the estuary than in the creeks (p \ 0.001, Table 1). Chl-a concentrations were significantly higher in the creeks than in the estuary (p \ 0.001, Table 1).
The Revelle factor varied over a wide range among the possible sources of the mangrove-surrounding waters in the estuary ( Table 2). The mean Revelle factors at the creek and estuarine stations were 12.8 ± 2.1 (range, 11.2-17.9) and 12.4 ± 1.4 (11.5-16.3), respectively. The Revelle factor of the riverine freshwater end-member was 26.7. The estimated Revelle factors of the northern BoB and the waters farther offshore in the BoB (almost to latitude 10°N) were 7.5-8.1 and 8.9, respectively, whereas those of pore-water and groundwater were 17.6 and 14.9, respectively. DIC showed significant negative correlations with d 13 C DIC both in the creeks (r = -0.990, p \ 0.001) and the estuary (r = -0.980, p \ 0.001) (Fig. 5a). There were significant negative correlations between TAlk/DIC and excess DIC both in the creeks (r = -0.995; p \ 0.001) and the estuary (r = -0.980; p \ 0.001) (Fig. 5b). nDIC and nTAlk were significantly correlated in the creeks (r = 0.995; p \ 0.001) and in the estuary (r = 0.992; p \ 0.001), with slopes of 0.84 and 0.81, respectively (Fig. 5c). There was no significant correlation between AOU and excess DIC (p \ 0.001, Fig. 5d).

Air-water CO 2 flux
Both the creek and estuarine stations exhibited diel and tidal variation in air-water CO 2 fluxes, and acted as both sinks and sources of atmospheric CO 2 at different times over the diel cycle (Fig. 5). The creeks acted as net sources of CO 2 with a mean flux of 13 ± 34 lmol m -2 h -1 , 107 ± 284 lmol m -2 h -1 and 69 ± 180 lmol m -2 h -1 according to Eqs. (3a), (4), and (5), respectively. In contrast, the estuary acted as a net sink for CO 2 with a mean flux of -4 ± 12 lmol m -2 h -1 , -37 ± 95 lmol m -2 h -1 and -23 ± 64 lmol m -2 h -1 according to Eqs. (3a), (4), and (5), respectively. 5.9 ± 0.2 (5.5 -6.2) n = 24 5.4 ± 0.2 (5.0 -5.9) n = 24 6.0 ± 0.2 (5.6 -6.2) n = 24 5.6 ± 0.2 (5.3 -6.0) n = 24 5.9 ± 0.1 (5.7 -6.3) n = 24 5.7 ± 0.3 (5.0-6.4) n = 144 Chlorophyll For tidal and diurnal variability of these variables see Fig. 3 and Supplementary Figure S1 Our results show that the estuary clearly acted as a net CO 2 sink and the mangrove creeks acted as a weak source of CO 2 . The uncertainty of the estimated pCO 2 (water) and air-water CO 2 flux was lower compared to previous studies in the Sundarbans because of the higher temporal resolution (cf. Rosentreter et al. 2018) and direct estimation of pCO 2 (water) (cf. David et al. 2018). We compared the pCO 2 (water) and air-water CO 2 flux with values from other studies around the world (Table 3), focusing on the recent studies that used high-temporal-resolution direct measurements of pCO 2 (water) or air-water CO 2 flux. It is evident that no previous study of mangrove-surrounding waters reported such a mean low pCO 2 (water) as that in the present study, although several previous studies reported values in the lower range of pCO 2 (water) from the mangrove creeks that were equal to or lower than the atmospheric CO 2 concentration (Call et al. 2015;Sippo et al. 2016;Rosentreter et al. 2018). The low pCO 2 (water) observed in the present study indicates that sometimes the mangrovesurrounding waters act as a sink or weak source of atmospheric CO 2 . Nevertheless, our high-temporalresolution and direct pCO 2 measurements can reduce the uncertainty in the data for the air-water CO 2 flux of mangrove-surrounding waters showing high spatiotemporal variability. The air-water CO 2 flux data for the mangrovesurrounding waters obtained by the present study and previous studies in the Sundarbans are markedly lower than the recently reported global average. Even the annual mean CO 2 flux for the entire Matla Estuary (approximately 6.3 ± 0.9 mmol m -2 d -1 ; Akhand et al.   Chlorophyll-a (mg m 3 -   (Fig. 6).
Predominance of marine water and low pCO 2 The waters around mangroves usually exhibit significant diel and tidal variability in terms of both pCO 2 (water) and air-water CO 2 flux, with higher pCO 2 (water) values during low tides and vice versa (Zablocki et al. 2011). However, the continuous high-temporal-resolution measurements in this study showed that these changes in pCO 2 (water) with the tide occurred only at the creek stations (Fig. 3) and not at the estuarine stations, except for station E1. The high pCO 2 (water) during low tide is generally attributed to pCO 2 -rich pore-water as well as groundwater, and the low pCO 2 (water) during flood tide results from the dilution of mangrovederived water (Akhand et al. 2016;Call et al. 2015;Maher et al. 2013). The absence of pCO 2 (water) maxima during low tide at our estuarine stations suggests that the pore-water, which seems to have a prominent effect in the creeks, did not play a significant role in regulating the diel variation of pCO 2 (water) at these estuarine stations. The most plausible reason behind this observation might be that the higher marine water volume in the estuarine stations and higher water residence time in the creek stations exceed the effect of pore-water in the estuarine stations even during the low tide period. The Revelle factor is the ratio of the relative change of pCO 2 (water) to the corresponding relative change of DIC in marine water; thus, it reflects the carbonate  buffering capacity of the water mass and is implicitly related to the TAlk/DIC ratio (Egleston et al. 2010). A low Revelle factor can indicate high carbonate buffering capacity and the potential for CO 2 uptake (Bates et al. 2012;Sabine et al. 2004). Among the possible sources of water in the mangrove-dominated estuary in this study, the riverine freshwater endmember, groundwater, and pore-water had both  Fig. 6 Schematic diagram of the underlying mechanism behind the low CO 2 evasion rate from the mangrove-surrounding waters of the Indian Sundarbans. The mean (± SE, standard error) air-water CO 2 flux data presented in this study (white arrows) are based on the gas transfer velocity k (cm h -1 ) from the model of Ho et al. (2011) (Eq. 5). The annual mean air-water CO 2 flux data for the Sundarbans and the global average data are adopted from Akhand et al. (2016) and Rosentreter et al. (2018), respectively. (Color figure online) Table 3 pCO 2 (water) and air-water CO 2 fluxes observed in this study (mean ± standard deviation), and in recent studies that directly measured pCO 2 (water) and/or air-water CO 2 flux of mangrove-surrounding waters. LM86, R00, and H11 indicate that the gas transfer velocities in the present study were calculated according to Eq. (3a) (Liss and Merlivat 1986), Eq. (4) (Raymond et al. 2000) or Eq. (5) (Ho et al. 2011 pCO 2 (water) values and Revelle factors higher than the observed values in the creeks and estuary (Table 2). In contrast, the waters from the northern BoB and farther offshore had pCO 2 (water) and an estimated Revelle factor lower than the waters at the study site (Table 2). These results indicate that the low-pCO 2 waters of the BoB have higher buffering capacity than all of the other possible sources of water in this estuary. Thus, we infer that the low pCO 2 (water) of the Sundarbans may be due mainly to the predominance of BoB water with low pCO 2 (water) (Akhand et al. 2012(Akhand et al. , 2013aGoyet et al. 1999;Sarma et al. 2012) and high buffering capacity. Another reason behind the low pCO 2 (water) of this study site, in addition to the predominance of low-pCO 2 water from the BoB, might be that the Indian Sundarbans receives comparatively less riverine freshwater input than other river-dominated estuaries (Chakrabarti 1998;Mitra et al. 2009). River-dominated estuaries having large riverine freshwater inputs have shown higher pCO 2 (water) than marine-dominated estuaries having less riverine freshwater inputs (Akhand et al. 2016;Jiang et al. 2008;Maher and Eyre 2012). The rapid export of material because of estuarine geometry and the meso-to macro-tidal nature of this estuary further enhance the low pCO 2 (water) character. Specifically, Ray et al. (2018a) and references therein have shown that the rapid transport of material from Sundarbans mangroves to the BoB is due to (i) the shorter water residence time, (ii) large tidal amplitudes, and (iii) the funnel-shaped geometry of the estuary, which tends to amplify the tide, in turn facilitating faster material transport.

Effects of mangroves on air-water CO 2 flux
The measured TAlk and DIC in the present study are in agreement with the reported ranges for TAlk and DIC for other mangrove-associated waters that act as net sources of CO 2 (David et al. 2018;Linto et al. 2014;Ray et al. 2018b;Zablocki et al. 2011) despite the sink and weak source behaviors of the Indian Sundarbans. Some high TAlk and DIC values at creek stations during ebb tide suggest that the TAlk and DIC were added from the mangrove ecosystem. The significant negative correlation between TAlk/DIC and excess DIC in both creeks and estuary suggests that higher TAlk/DIC suppressed excess DIC and contributed to the CO 2 sink or weak source character (Fig. 5b). Exports of higher TAlk-to-DIC ratios from mangroves to coastal waters, with a TAlk/DIC ratio of 1.2, led to an overall increase in pH and thus had a buffering effect (Sippo et al. 2016). The TAlk/DIC at our sites was 1.08 ± 0.06 (mol mol -1 ), indicating a relatively high buffering capacity in the mangrove-surrounding waters of the Sundarbans, but it was not markedly higher than that observed in other parts of the world (1.00-1.10; Sippo et al. 2016). Increased pH and under-saturation of pCO 2 in mangrove-surrounding waters can also occur as a result of the remnant TAlk after CO 2 outgassing and outwelling of mangrove TAlk, as discussed by Sippo et al. (2016).
Our results showed that diagenetic processes in this mangrove system reduced TAlk/DIC ratios, which increased pCO 2 in the mangrove-surrounding waters (Fig. 6). The diagenesis of organic carbon in mangroves sediments takes place through several anaerobic pathways that supply TAlk and DIC and change the pore-water TAlk/DIC (Borges et al. 2003;Bouillon et al. 2007b;Koné and Borges 2008). The relationships between nDIC and nTAlk in this study, with slopes of 0.84 (creeks) and 0.81 (estuary) (Fig. 5c), suggest denitrification, as observed in the waters around mangroves in the Mekong Delta, Vietnam (Alongi et al. 2000) and Gaji Bay, Kenya (Bouillon et al. 2007a). Denitrification has previously been reported in the mangrove sediment of the Indian (Das et al. 2013(Das et al. , 2020Ray et al. 2014) and Bangladesh (Neogi et al. 2016) Sundarbans. Das et al. (2020) reported a mean denitrification rate of 14.72 nmol N 2 O-N h -1 (g dry wt) -1 in the sediments of Lothian Island (Indian Sundarbans). The absence of a significant correlation between AOU and excess DIC (Fig. 5d) suggests that aerobic respiration was not the major diagenetic pathway for organic matter (OM) degradation in the present study. A primary assumption of the method of delineating the diagenetic pathway of OM mineralization using the nDIC:nTAlk ratio is that the C, N, and P of the OM follows the Redfield ratio (Krumins et al. 2013). However, the organic matter in the mangrove-surrounding waters might not always match the Redfield ratio, which implies an uncertainty in this stoichiometric analysis. Still, our principal purpose was to understand the nDIC:nTAlk ratio from the perspective of the carbonate buffering capacity, rather than determining the exact organic matter mineralization pathway. The nDIC:nTAlk ratios indicate that the diagenetic pathways at the study site provide a lower buffering capacity than the marine water, and increased excess DIC and pCO 2 (Fig. 5b and c). Marine water with high buffering capacity suppresses the effect of pCO 2 increase in the mangrove system and the lowers CO 2 evasion even in the creek stations (Fig. 5b).
The effect of mangroves on carbonate chemistry in coastal waters is variable depending on the biogeochemical processes in the mangrove systems. We found that the mean pH value at the more marineinfluenced estuarine stations was higher than that at the more mangrove-influenced creek stations (Table 1); however, the difference of pH was not found to be significant between creek and estuarine stations (p [ 0.05). pH values reported in the offshore waters of the BoB (8.13-8.46) were much higher (by 0.1-0.4 units; Akhand et al. 2012Akhand et al. , 2013aSarma et al. 2012) than the pH values observed in both the creek and the estuarine stations (Table 1). These results also support our suggestion that the low pCO 2 (water) of the mangrove-surrounding waters can be attributed to the effect of BoB water with low pCO 2 (Akhand et al. 2012(Akhand et al. , 2013aGoyet et al. 1999;Sarma et al. 2012;) and higher buffering capacity rather than to the effect of mangroves.
Biological uptake of DIC is also an important factor in explaining low pCO 2 (water) as well as the air-water CO 2 flux. Both buffering capacity and Revelle factor can be affected by biological factor(s) (Hauck and Volker, 2015;. In the present study, higher mean Chl-a concentrations (Table 1 and Supplementary Fig. S1) were associated with pCO 2 (water) above saturation at the creek stations and vice versa at the estuarine stations (Table 2). However, there was no significant negative relationship between Chl-a concentration and pCO 2 (water) at any of the stations, rather a significant positive correlation was found ( Fig. 4a and b). These results indicate that biological control of pCO 2 (water) was less important than physical mixing in this study. However, the negative excess DIC at several creek stations (Fig. 5b) might be related to higher phytoplankton production, which would contribute to reducing the CO 2 effluxes. The significant positive correlation between Chl-a and pCO 2 (water), along with significant positive correlation between turbidity and pCO 2 (water) (Fig. 4c and d), indicates that high Chl-a with turbidity led to a high organic matter degradation rate and high DIC input as observed in some previous studies (Abril et al. 2000;Fay and McKinley 2017;Tishchenko et al. 2018).
We found a significant negative correlation between DIC and d 13 C DIC (Fig. 5a), with higher DIC values and lower d 13 C DIC values in the creeks than in the estuary ( Fig. 2b and d). This suggests that the sources of DIC have lighter d 13 C values and were supplied from the mangroves. The most plausible explanation for the DIC sources is therefore a combination of mineralization of mangrove tissue (d 13 C TOC = -28.08% to -26.31%; Ray et al. 2015), POC in the water around mangroves (d 13 C POC = -23.3% to -22.3%; Dutta et al. 2019;Ray et al. 2015), and marine phytoplankton (-22.0% to -20.0%; Rosentreter et al. 2018). Groundwater DIC and pore-water DIC (-18.0%, pore-water DIC in Sundarbans, Dutta et al. 2019;-14.5% to -10.0 %, ground water/pore-water DIC, Maher et al. 2013) are also possible DIC sources. We assumed that air-water CO 2 fluxes had a negligible effect on isotopic fractionation, as the fluxes were at near-equilibrium. This type of mixed source for DIC has been reported in other mangrove environments (Maher et al. 2017;Rosentreter et al. 2018;Sea et al. 2018). Under such a scenario, the carbon dynamics in the mangrove-surrounding waters cannot be explained solely by mangrove-derived DIC loading, but must also be regulated by other allochthonous sources (Rosentreter et al. 2018).

Conclusion
The results of this study suggest that mangrovesurrounding waters can act as a sink or a weak source for atmospheric CO 2 , contrary to most previous studies. There have been previous studies of CO 2 dynamics in the Sundarbans, but the precision and temporal resolution of the data were too coarse to determine source/sink characteristics. The present study successfully overcame these problems and reduced the uncertainties by analyzing the diel variability of pCO 2 (water) at eight sites, covering tidal maxima and minima. Our findings further show that the CO 2 sink or weak source character of the Sundarbans' mangrove-surrounding waters was caused by predominance of the low-pCO 2 and high-buffering-capacity waters of the BoB. The TAlk export from the mangroves also buffers the increase in pCO 2 owing to the DIC addition. The marine water with high TAlk/DIC ratio buffers the effect of pCO 2 increase in the mangrove systems, lowering CO 2 evasion in the study site. Finally, we argue that areas with such low emissions should be included when the global mangrove carbon budget is estimated by scaling-up regional observations.