In this study, sea surface pCO2 is used as the primary in situ data for model validation. Whereas models favor DIC and TA , shipboard pCO2 can be measured underway, and hence there are more observations available. Additionally, since model pCO2 is calculated from DIC and TA (see Sect. 2.2), pCO2 measurements act as an independent dataset. Here, pCO2 validation stems from in situ un-gridded data merged from SOCAT v. 2019 (downloaded from https://www.socat.info/index.php/version-2019/, last access: 3 September 2019) and the Lamont–Doherty Earth Observatory (LDEO) surface pCO2 database . Both databases aggregate all available in situ surface pCO2 data, including JGOFS. SOCAT and LDEO contain > 180 000 and ∼ 90 000 data points on the AS, respectively. SOCAT has more data because it includes multiple methodologies. As a result, SOCAT data are preferred, and LDEO observations are included for the years 1980–81 when SOCAT data are unreported. SOCAT fugacity (fCO2) values are converted to pCO2 and mole fraction (xCO2) using reported SST and SSS data included in the products using routines from the CO2SYS software package . The anthropogenic effect of increasing surface pCO2 is removed by calculating a fit linear trend of 2 µatm yr-1, slightly higher than ≈ 1.5 seen in . The pCO2 values are calibrated to the year 2005, the representative year used for the model's atmospheric xCO2. The year 2005 is chosen for the model's xCO2 concentration because it is the end of the historical period for the Intergovernmental Panel of Climate Change (IPCC) models used in its fifth report published 2014. The earliest SOCAT data comes from 1962, and different databases used in this study stem from similarly different time spans. As a result, we assume there is a baseline seasonal cycle of pCO2 and air–sea CO2 flux which has held stable over the past decades.

Alternative pCO2 products are used for comparison purposes. A complete list of these datasets and their characteristics is provided in Table 1. For all the comparison datasets, air–sea CO2 flux is calculated from monthly values. The ΔpCO2 values are calculated using Keeling curve data (downloaded from https://gml.noaa.gov/ccgg/trends/gl_data.html, downloaded 1 February 2022) of atmospheric xCO2 for the respective calibrated year of each dataset. The same climatological winds as used in the model (Sect. 2.2) are applied to the pCO2 products. The gridded product TK09 is chosen because previous modeling studies in the AS use it as validation (see “Introduction”). The L15 climatology, while based upon the same in situ data mentioned above, represents different processing methodologies and, as a high-resolution, global pCO2 dataset, also serves to provide independent context to the model validation. pCO2 is also calculated from DIC and TA provided by the statistical fits to JGOFS data by and to the gridded GLODAP climatological product. The statistical fits of are used twice, first using model SST, SSS, and chl a, and second with World Ocean Atlas (WOA) 2009 SST and SSS with SeaWiFS chl a. GLODAP-derived pCO2 also uses WOA 2009 SST and SSS applied to the annual DIC and TA values. Calculations of pCO2 are performed using the CO2SYS software package . Since all calculations are conducted at the near surface, differences between this software suite and are minimal. Furthermore, for air–sea CO2 flux intercomparison purposes, all pCO2 values except for TK09 are interpolated to the same 1∘ × 1∘ grid already shared by GLODAP, WOA, and L15. Due to the model's higher resolution, the re-gridding process reduces the area covered, consequently lowering the total model CO2 flux quoted in later sections of this study.

The model we use is the Regional Ocean Modeling System Adaptive Grid Refinement In Fortran (ROMS-AGRIF) version 3.1.1. . Previously used in the AS by , the model is a free-surface primitive equation model, with a sigma and curvilinear grid for the vertical and horizontal dimensions, respectively. ROMS implements a forward–backward time-stepping algorithm with split baroclinic and barotropic modes. The advection of tracers uses a rotated-split third-order upstream biased algorithm to reduce spurious mixing . The K-profile parameterization KPP; for vertical mixing is used. The model domain spans from 5.3∘ S to 30.5∘ N and from 33 to 78.1∘ E (Fig. 1). For the sake of comparison with , we will present the region north of the Equator and exclude the Red Sea and Arabian Gulf. The model's horizontal resolution is 1/24∘, resulting in ∼ 5 km horizontal grid spacing.

Coupled to the hydrodynamic model is a nitrogen-based biogeochemical model with two components for nutrients, nitrate and ammonium, with one phytoplankton, one zooplankton, and two detrital pools . Biological parameters for the model are the same as those used in . A carbon module is also applied to the model with the state variables of DIC, TA, and calcium carbonate (CaCO3) . In addition to the usual physical transport and mixing, CaCO3 is allowed to vertically sink at 20 md-1. The chosen sinking rate is a simplification in that it does not include the faster rates observed for foraminifera shells , which as a biological group are not resolved by the biological model due to numerical constraints. Organic carbon is linked to organic nitrogen through the Redfield ratio 106:16. DIC is altered by air–sea CO2 flux, primary production, respiration, remineralization, and dissolution/precipitation of CaCO3. TA changes with the removal and creation of nitrate (NO3), including nitrification and denitrification, as well as dissolution/precipitation of CaCO3. The amount of CaCO3 precipitation is linked to primary production through a constant ratio of 0.07, meaning 0.07 moles of CaCO3 are produced for each mole of organic carbon. The dissolution rate is a constant 0.0057 d-1 in the water column and 0.002 d-1 in the sediments. Surface fluxes of DIC and TA due to evaporation, precipitation, and river input are included as virtual fluxes proportional to SSS forcing. Inside the module, surface carbon chemistry is calculated using routines from the Ocean Carbon-Cycle Model Intercomparison Project (OCMIP) carbonate chemistry routines (http://ocmip5.ipsl.jussieu.fr/OCMIP/phase3/simulations/, last access: 1 February 2022). Carbon chemistry coefficients used here include K1 and K2 CO2 dissociation from and original data from which was refit by . A summary of the biological parameters used in the biogeochemical model is provided in Table 2.

The model is run with 360 d years and interpolated, climatologically averaged monthly forcing. The different climatological products derive from datasets spanning slightly different periods, and so here we assume that the dynamics represented within them have not changed in the time since. Heat flux, evaporation and precipitation, and restoring SSS are provided by the Comprehensive Ocean-Atmosphere Data Set COADS;. SST forcing is provided by a monthly climatology of Pathfinder data from 1985 to 1997 . Wind stress is produced using the QuikSCAT/SCOW monthly climatology from 1999 to 2009 . Tracer values for the initial conditions and the boundaries are given by WOA 2009 for temperature, salinity, NO3, and oxygen. Horizontal velocities u,v for initial and boundary conditions derive from the Simple Ocean Data Assimilation (SODA) analysis . Initial and boundary conditions for DIC and TA come from GLODAP from 300 m down to the bottom. Surface TA was calculated using the relations from , and the corresponding DIC was calculated using WOA phosphate, silicate, T, and S values along with L15 pCO2. DIC and TA values between the surface and 300 m are calculated using density weighting. The model is spun up for 30 years, with 5 additional years for analysis. Atmospheric xCO2 values are set to 380 ppm, equivalent to 2005 levels, with an annual sinusoidal perturbation of 2.9 ppm.

In this study we focus on six distinct regions (Fig. 1). The first, the entire analysis domain, is the AS north of the Equator. The upwelling regions of the Omani and Somalian coasts are included separately to focus on the summer monsoon impact of enhanced DIC but also enhanced biological productivity . The Omani region begins at the coast and extends 300 km outward. The Somalian region begins near 3.8∘ N and extends north to the tip of the Horn of Africa, with an eastern extension to 58.6∘ E so as to encompass the region known as the Great Whirl , shown to be important for air–sea exchange in previous studies . The north region is defined by a rectangle from 21∘ N, 59.4∘ E to 26.5∘ N, 69.5∘ E, encompassing the northern part of the AS where the winter monsoon's primary productivity is most intense . An oligotrophic region representing the central AS, which has less productivity and chlorophyll a on average (Fig. 1), is defined by a rectangle from 3.3∘ N, 61.31∘ E to 17∘ N, 70.8∘ E. The last region, covering the western coast of India, extends from the coastline 100 km offshore.

The implementation of ROMS-AGRIF presented here has been used in previous studies of the AS . Model output of net primary productivity (NPP) captures the summer monsoon highs near the upwelling regions of Oman and Somalia (model > 400 vs. data > 500 gCm-2yr-1), with enhanced NPP in the north during the winter monsoon (model ∼ 300 vs. data > 400 gCm-2yr-1) (Fig. 1). The model also captures the vertical distributions of temperature and salinity (Figs. S1 and S2 in the Supplement) with deviations from WOA around 1 oC and 0.2 psu. Depth profiles of nitrate, oxygen, DIC, and TA are similarly conserved (Figs. S3–S6 in the Supplement). Nitrate, DIC, and TA all show their usual nutrient-like profiles, while oxygen is its minimum within the OMZ. The deviations seen between in situ data and model output are greatest at depths less than 500 m. Deviations in near-surface NO3 (Fig. S3) can be large for intermediate values (5–20 µM) but overall do not show a systematic bias. DIC (Fig. S5) also has large deviations (∼ 50 µM) in the top 500 m and with a slight positive bias. It is in TA (Fig. S6) that deviations, while similarly ∼ 50 µMeq, show a consistent near-surface underestimation. The surface currents in the model also demonstrate the monsoonal shifts and reversals seen in the AS (Fig. S7 in the Supplement).

Regarding pCO2, in situ data from the merged SOCAT–LDEO database show that ∼ 90 % of ΔpCO2 values in the AS are positive (Fig. 2a, inset), indicating a positive flux to the atmosphere that is applicable geographically (Fig. 2a). Sampling dates for pCO2 (Fig. 2b) show that ∼ 70 % are from the summer monsoon months (June–September, JJAS). Most observations similarly date from the 1990s, with 1995 and 1997 alone accounting for 96 %.

Seasonal pCO2 distributions from both data and the model are shown in Fig. 3. During the winter monsoon, pCO2 values are at their lowest (range: 348–455 µatm; Fig. 3a). The spring intermonsoon (Fig. 3d) finds pCO2 values similar to the winter (range: 354–451 µatm), with data coverage improving in the western AS. The summer monsoon, with the best data coverage (Fig. 3g), has pCO2 peaking at 773 µatm. In contrast, the fall intermonsoon (Fig. 3j) has very little data coverage, with pCO2 ranging from 311 to 485 µatm. Similar to the data, model pCO2 (Fig. 3b) is at its lowest during the winter. However, in the spring (Fig. 3e) open-ocean pCO2 finds its peak with a domain average of 439 µatm, which is not reflected in the in situ dataset (Fig. 3d and e). Maximum model pCO2 is found in the summer monsoon near upwelling regions (Fig. 3h), with values attaining > 800 µatm in Oman. Fall model pCO2 (Fig. 3k) still has elevated values averaging 427 µatm but less than the summer period. Certain regions in the model show persistent maxima in pCO2, such as the Gulf of Oman and the Strait of Hormuz, which are not reflected in the few data collected there. Model pCO2 values in the Gulf of Aden increase during spring and then peak during the summer, a pattern which is unclear from the data. Annual and seasonal pCO2 means, with standard deviations in parentheses, are displayed in Table 3 for both the data and model. Differences from interpolated model output and in situ data are shown on the right column of Fig. 3 (Fig. 3c, f, i, and l). Most differences show that model output is higher in value than the data, averaging 24.6, 48.4, and 33.7 µatm higher for the winter, spring, and fall seasons, respectively.

A Taylor diagram comparing in situ pCO2 data with model output shows the model's relative performance (Fig. 4). The distance from the origin is model variability normalized by standard deviation of the in situ data. The angle created from the y axis is the Pearson correlation coefficient between the model and in situ data. If the model were to perfectly reproduce the data, it would appear at the position (1,0), equivalent to a normalized standard deviation of 1 and correlation coefficient of 1. For the entire dataset, as well as for the spring and summer seasons, the model's correlation with data is ∼ 0.5. Winter and fall have lower values at 0.2 and 0.06, respectively. Variability expressed as normalized standard deviation shows that overall, and during spring and summer periods, the model underestimates data variability (∼ 0.5 µatm). During the winter and fall, however, the model overestimates variability (1.1 and 1.6, respectively). For all periods apart from summer, model pCO2 has a positive bias (9.1, 24.6, 48.4, and 33.7 µatm for the annual, winter, spring, and fall, respectively). During the summer, the model has a negative bias of -3.1 µatm.

The source of bias in pCO2 is linked to the four state variables SST, SSS, DIC, and TA. Comparisons with the model are made with SST and SSS from the merged SOCAT–LDEO database, while DIC and TA come from the ungridded GLODAP product (Fig. S8 in the Supplement). In this case, model SST and SSS (Fig. S8a and b) largely overlap with a 1:1 relationship but with slight positive biases of ∼ 0.4 oC and 0.3 psu. Removing these biases from the model results in a pCO2 shift of -6.8 and -3.5 µatm for SST and SSS, respectively. These deviations are close in magnitude to the best-case measurement error of ∼ 2 µatm. Taylor diagrams for SST and SSS (Fig. S9 in the Supplement) further show the seasonal performance of these two variables. The model performs best for SST (Fig. S9a) during the winter, with a correlation of 0.93 and a normalized standard deviation of 0.97. The other seasons have lower correlations (0.74–0.81) and reduced standard deviations (0.63–0.8) except for the fall with a standard deviation of 1. SSS (Fig. S9b) has lower correlations and standard deviations than SST, with all seasons demonstrating a positive bias (0.02–0.39 psu). Correlation is best in the winter at 0.89 and worst in the fall at 0.46. Model variability in SSS is also less than the data, with standard deviations ranging from 0.33 to 0.72. Lower variability is most likely due to the raw nature of the in situ data used here, in opposition to the monthly averaged climatological forcing and initial conditions of the model.

Ungridded DIC and TA data from GLODAP, though more sparse (n=334 data points with both DIC and TA at depths ≤ 50 m), show more deviation from the 1:1 line (Fig. S8c and d) with overall negative biases of -15.8 µmolkg-1 and -30.0 µmoleqkg-1 for DIC and TA. These biases result in pCO2 perturbations of -33.8 and +45.7 µatm, respectively, when accounted for individually. Since the buffering capacity of seawater is related to the ratio of TA and DIC, when both biases are considered, average pCO2 shifts +16.7 µatm. As a result, while the DIC model bias lowers pCO2, the stronger bias in TA is the most likely cause for the model's overall positive pCO2 bias, which may in part be due to the unresolved fast sinking rates of foraminifera in the model.

Direct comparisons between the in situ and model output demonstrate the positive bias and middling correlations of the model with respect to the data, as well as the model's tendency to underrepresent variability. As a result, it is necessary to investigate how these shortcomings compare with alternative pCO2 estimates in the AS. Figure 5 shows monthly comparisons of the pCO2 probability distribution functions from in situ data, model output, and L15. For most of the year, the data (Fig. 5a) stays within a relatively narrow range (375–425 µatm) except for the summer monsoon when values can exceed 500 µatm and the median value has its peak. In the model (Fig. 5b), pCO2 is almost entirely above 400 µatm, with the median value increasing during the spring intermonsoon and peaking in June (453 µatm). Similar to the data, the upper-bound variability in pCO2 peaks in August. L15 (Fig. 5c), by contrast, has a tighter envelope of variability, with 5–95 percentile values never going beyond the range of 368–434 µatm. Median pCO2 in L15 peaks in the summer like the data at 402 µatm, but there is no large increase in upper-bound variability, with the 95 % upper bound in L15 reaching 434 µatm in September.

In summary, the survey of available data and comparing it to the model output produces a few distinct features: (1) available in situ data show that the majority of observations are skewed towards the summer monsoon during the years 1995 and 1997; (2) most in situ data show CO2 out-gassing in the AS; (3) the model has a net positive bias in surface pCO2, driven by a joint DIC-TA bias which is slightly stronger in TA; and (4) the model captures the high summer monsoon pCO2 values better than the alternative L15 climatology.

Modeled annual mean atmospheric flux of CO2 (Fig. 6a) shows outgassing (positive, red) throughout the entire domain, producing an average annual CO2 flux density rate of 1.9 molCm-2yr-1 and a total of 162.6 Tg C yr-1. Similar to pCO2, several hotspots appear in the geographic distribution. Near the coast of Oman, the average flux density is 2.7, with 3.2 in Somalia and 2.4 along the coast of India, producing a flux of 11.4, 32.9, and 4.9 Tg C yr-1, respectively. The other regions, the north AS and oligotrophic central AS, have average densities of 2.0 and 1.5 molCm-2yr-1, with total fluxes of 10.5 and 28.6 Tg C yr-1. The seasonal air–sea flux (Fig. 6b–e) has minima during fall and winter, with an increase in spring and a strong maximum during the summer monsoon. Omani and Somalian flux densities during the summer monsoon are 5.8 and 5.9 molCm-2yr-1, respectively. The distribution of enhanced summer air–sea CO2 flux coincides with the southwest monsoon winds (Fig. S10 in the Supplement), as well as the band of cooler temperatures impacting spatial pCO2 anomalies (see Sect. 3.3.1). The entire domain fluxes of 32.0, 26.6, 90.9, and 13.1 Tg C yr-1 for the winter, spring, summer, and fall periods, respectively, each contribute 19.7, 16.3, 55.9, and 8.1 % of the annual total.

The variability in air–sea CO2 flux can be attributed to the contributions of winds, ΔpCO2, and interacting cross-terms, as described in Eq. (2). The temporal anomalies for the summer monsoon, the period with the strongest CO2 flux signal, are presented in Fig. 7. Most of the domain has positive but variable strength anomalies in air–sea flux (Fig. 7a), averaging 1.3 molCm-2yr-1 with a standard deviation of 1.35. The wind contribution to flux variability, κα (Fig. 7b), is also positive in most of the domain except the Gulf of Aden and the southeastern corner of the domain. The wind anomaly's magnitude and distribution closely match the total anomaly in Fig. 7a, with a mean flux anomaly of 1.18 molCm-2yr-1 and 0.96 standard deviation. The ΔpCO2 contribution to seasonal flux anomaly (Fig. 7c) has a lower-magnitude effect overall (mean flux anomaly 0.1, deviation 0.5, maximum 6.2 molCm-2yr-1), with positive values north of 10∘ N and slightly negative to the south. The maxima approaching 6.2 molCm-2yr-1 are in the upwelling centers of Oman, Somalia, and the Indian coast. Second-order cross-term values (Fig. 7d) are almost all positive, with maxima also occurring near upwelling centers similar to the ΔpCO2 term but weaker in magnitude with an average of 0.04 molCm-2yr-1.

The seasonal flux anomalies for all regions are displayed in Fig. 8. The summer monsoon flux is so strong that it makes the anomalies (black lines) for all the other seasons negative except for May in the spring. During the winter months (DJFM), both wind and pCO2 terms produce negative flux anomalies (ranging to -0.78 and -0.38 in the domain for wind and pCO2, respectively; Fig. 8a), indicating the relative lack of winds and minimum pCO2 values. In winter, while the negative wind term is universally strongest, within the upwelling regions the pCO2 term is 58 % (Fig. 8b) of the wind term's magnitude, and 49 % for the entire domain. The spring intermonsoon, where many regions such as Somalia and the central oligotrophic AS (Fig. 8d and e) experience their pCO2 maximum, shows a positive pCO2 effect on flux anomaly that is as large as or larger than the negative wind effect (Somalian May pCO2 anomaly of 1.1 molCm-2yr-1, wind anomaly of 0.1). Summer monsoon winds represent the majority contribution to CO2 flux variability, with a minimum 64.7 % contribution relative to the total anomaly in India, a maximum of 112.8 % in the oligotrophic AS, and 90.8 % for the whole domain. By contrast, summer pCO2 and cross-terms contribute 6.0 % and 3.1 % to the domain's anomaly, respectively. Fall intermonsoon months resemble the winter monsoon, with negative wind anomalies contributing most with small or negative pCO2 contributions. In most scenarios, pCO2 contributes in the same direction as the winds or little at all, with the notable exceptions of Oman, oligotrophic AS, Somalia, and the domain during spring intermonsoon.

While strong monsoon winds dominate the timing of air–sea CO2 flux, and the AS is always a source of CO2 due to positive ΔpCO2, differences in pCO2 between independent sources can still result in a wide range of overall magnitudes. In the AS, CO2 outgassing estimates vary from 7 TgCyr-1 to > 90 TgCyr-1 and everything in between , with each study using their own pCO2 data and wind parameterizations. Considering the important seasonal role of winds, the best way to investigate the role of pCO2 variability is to keep winds (and their flux parameterization) constant. Towards this end, we use multiple pCO2 products to calculate CO2 flux with the same wind and parameterization as the model (Fig. 9). As summarized in Table 1, pCO2 from TK09, L15, GLODAP data, and , interpolated to the WOA 1∘ × 1∘ grid, is used in these calculations (except for TK09 in which the coarse resolution reduced coverage). The original applicability of the model is north of 10∘ N, and so flux is calculated for this region, as well.

All calculations have their peak CO2 flux sometime in the summer, confirming the role of winds in CO2 flux timing. This study's model consistently produces one of the higher estimates with 120 TgCyr-1 (reduced from 162.6 due to re-gridding) and 57 TgCyr-1 north of 10∘ N. The only estimate higher than the model is GLODAP data in the region north of 10∘ N with 65 TgCyr-1 possibly driven by summer monsoon sampling bias. The high model estimate is perhaps unsurprising, considering the pCO2 bias. The range in estimates of total CO2 flux is 57–120 TgCyr-1, resulting in a ratio of 2.1× variability. In the reduced domain of the AS north of 10∘ N, estimates range from 12.3 to 65.6, resulting in 5.3× variability. The 5.3× ratio is quite high and is in part driven by the low estimates from the model, which are 12.3 and 17.6 using tracer data from WOA and ROMS, respectively. Indeed, the model estimates have negative CO2 flux for some months, which is not observed in the original publication, and the total fluxes are quite smaller than the 70 TgCyr-1 reported. If the two lower estimates are removed, the range in air–sea CO2 flux in the domain north of 10∘ N is 41–65 TgCyr-1, providing a ratio of 1.6 similar to 2.1 for the whole domain. Even considering the model's pCO2 bias, as previously mentioned the GLODAP estimate supersedes it in the region north of 10∘ N, as does the original estimate of 70 TgCyr-1. Thus, while we may think the model overestimates flux, it is still within the range of previous studies in the AS.

SST's effect on pCO2 reflects physical processes like surface heating and cooling, mixing, and advection. DIC, by contrast, reflects both physical and biological processes because in addition it is also impacted by photosynthesis, CaCO3 shell formation and dissolution, zooplankton respiration, detritus remineralization (bacterial respiration), and air–sea exchange. Budgets of DIC fluxes in the upper 20 m (Fig. 12; see Fig. S11 in the Supplement for a volume-specific DIC flux) show that two major processes dominate: vertical circulation (light blue lines) and net biological processes (magenta lines). In the entire domain and all subregions, and for all months, vertical circulation (advection and mixing) acts as a source of DIC, with the sum of all biological processes acting as a sink (NB the top 20 m does not constitute the entire euphotic zone, so respiration and remineralization at depth is not included). Maximum magnitudes of both vertical circulation and biological flux occur during the summer monsoon for all regions except for the north AS where they occur during the winter monsoon bloom (Fig. 12c). The maximum DIC flux in the domain due to vertical circulation is 1.76 PgCyr-1, whereas biological flux peaks at -1.0 PgCyr-1. Biological fluxes are nearly phase-matched with vertical circulation, though peaks in summer biological flux lag vertical circulation by a month (Fig. 12d, e, and f). Comparing the two flux terms, after normalizing biological flux by vertical circulation flux, the relative strength of biological processes vs. vertical sources of DIC becomes apparent. In the whole domain, biological flux ranges from -90 % to -34.5 % of vertical flux, similar to . As a result, biological fixation of carbon is generally weaker than physical vertical delivery of DIC.

Air–sea flux (red lines) is always negative due to the high pCO2 values, peaking during the summer monsoon. DIC flux due to atmospheric escape, while reaching its maximum magnitude of ∼ 0.32 PgCyr-1 in June and July for the whole domain (Fig. 12a), only surpasses biological flux in May, when 0.23 PgCyr-1 is released to the atmosphere compared to 0.15 PgCyr-1 in biological processes. Evaporation and precipitation (brown lines) result in higher DIC for most of the year in the entire domain and upwelling regions (i.e., net evaporation, averaging 0.07 PgCyr-1 in the domain) except India where it is negative (net precipitation, averaging -4.8 × 10-3 PgCyr-1). The oligotrophic region's evaporation and precipitation flux (Fig. 12d) oscillates from being either positive or negative four times during the year, with magnitudes rivaling air–sea flux at times (5 × 10-2 PgCyr-1). Horizontal advection (dark blue lines) is negative on average for the whole domain (-0.2 PgCyr-1), denoting net export (Fig. 12a). The same pattern occurs for all subregions except India with net horizontal import of surface DIC (Fig. 12f; 2.9 × 10-3 PgCyr-1). The Omani upwelling region and the oligotrophic region experience positive peaks of horizontal import during the summer monsoon (27 and 56 TgCyr-1 for Omani and oligotrophic regions, respectively), though for Somalia this period is the maximum DIC export, peaking at 220 TgCyr-1 in July.

The pCO2 output from the model has a positive bias with respect to the in situ data, as is clear from Figs. 3 to 5. The question becomes whether the model bias precludes its use in acquiring a reasonable air–sea CO2 flux estimate. Regarding the direction of CO2 flux (positive outgassing or negative uptake), since most in situ ΔpCO2 data are already positive (Fig. 2), an additional positive bias will not impact flux direction, reaffirming the previous findings of and subsequent work demonstrating that the AS is a source of CO2 to the atmosphere. A positive model bias in pCO2 has been noted in previous modeling studies. For instance, in the global data assimilation study of , they found an overall positive bias in the northern Indian Ocean, ∼ +5–15 µatm above TK09 (compared to our -3.1 to +48.4 µatm with respect to in situ data). Additionally, that study found a similar underestimate near the upwelling regions (summer negative bias in the model) of the AS and overestimate elsewhere (their Figs. 3 and 4). In , ROMS resulted in a systematic positive pCO2 bias, whereas the offline Ocean Transport Tracer Model (OTTM) produced negative bias in pCO2 in comparison to TK09.

The search for the model bias source is hindered by the lack of in situ data in the region. As already noted, GLODAP has 334 locations with DIC and TA in the top 50 m. The few available in situ data that do exist in the AS have a number of deficiencies for the purpose of validating model output. First, the data available are both old and concentrated around the years 1995 and 1997. While the JGOFS studies were quintessential in diagnosing the seasonal cycle of pCO2, they preclude being able to decipher the secular trend in surface pCO2 due to increasing atmospheric CO2 concentrations. In our analysis, we estimated a +2 µatm yr-1 trend, close to that of , though finding an interannual linear trend requires more data at regular intervals. Second, due to the nature of strong upwelling in the AS, previous cruise sampling also biases not only the summer months (≈70 % of data) but also places in the vicinity of the Omani coast (Fig. 3g). As a result, it is difficult to determine to what extent the data are representative of the entire AS. Consider that in the model, flux intensities are lower in the central, oligotrophic region (Fig. 6), but due to its surface area the total flux (28.6 TgCyr-1) was close to that of Somalia (32.9 TgCyr-1), an observation also made by . Determining to what extent the model over- or underestimates CO2 flux due to pCO2 bias would require more in situ sampling, which would need to be designed around solving the problems of areal coverage (outside of Oman and upwelling zones) and temporal coverage (off-summer months and recurrent over multiple years).

The distribution of model pCO2 is both similar to and different from previous data-based and modeling studies. Apart from the aforementioned bias leading to heightened absolute values (though , have > 400 µatm for large parts of the AS), the relatively enhanced pCO2 values near Oman, along the west coast of India, and in the Gulf of Aden have already been observed . These same studies, however, note a minimum of pCO2 outside of the summer monsoon near the southwest coast of India due to freshwater influx, which is not replicated well in the model. Additionally, elevated pCO2 near the Equator is not observed , although it can appear in other models . The model's seasonal pCO2 minimum during the winter monsoon is also not reflective of results found elsewhere (; though many studies highlight the north AS, where minimum model pCO2 occurs during the spring). Instead, these papers state pCO2 is minimal during the fall intermonsoon. Likewise, the large-scale spring maximum of pCO2 seen in the model is not found in these studies, except for in , though this result is somewhat anomalous since that study showed a pCO2 minimum during the summer monsoon. Thus, while the model agrees with previous work insofar as the coastal regions impacted by upwelling show enhanced pCO2, mismatches do appear in the seasonal timing of maxima and minima, especially within certain subregions.

Despite the model's limitations, its advantages are also clear. Beyond the obvious increase in spatiotemporal coverage, capturing the monsoon's strong seasonal dynamics helps the model where other approaches fall short. This is especially illustrated in Fig. 5. Since upwelling regions are limited in geographic extent near the coast, capturing their high pCO2 values can be difficult for other approaches, such as TK09 with its coarse grid. Even the L15 product, with its finer grid, is unable to produce the higher pCO2 values seen during the summer. Judging from these comparisons, the trade-off appears to be that the model currently may produce less accurate pCO2 values outside of summer, but the explicit resolving of upwelling allows for enhanced pCO2 values during the summer monsoon, the peak of CO2 flux.

The model results both affirm the conclusions of previous studies in terms of CO2 flux direction and seasonality and yet find difference in magnitudes. As previously stated, the AS is an atmospheric CO2 source, with most flux occurring (56 %) during the summer monsoon (Fig. 6). In our results, however, there is no region during any of the seasons where CO2 uptake takes place. While somewhat expected, this is still in disagreement with some of the other pCO2 datasets previously considered, such as in , in which negative ΔpCO2 values appear, such as during the winter monsoon near the south coast of India. The model's positive pCO2 bias may be to blame for this, making it so that no negative ΔpCO2 appears. Despite the positive pCO2 bias, a few other patterns are clear in comparison to other CO2 flux estimates. and both find the maximum flux occurring during the summer monsoon centered around the upwelling regions, which is also quite visible in the model results (Fig. 6d). However, found that a secondary maximum of flux occurs during the winter monsoon, though due to the color scale in their Fig. 6 it is difficult to ascertain much beyond CO2 outgassing from the AS during all months of the year. Their secondary max in flux may be partly attributable to higher wintertime pCO2, as well.

The spatial decomposition of factors influencing pCO2 (Fig. 10) highlights how geographically DIC can be the strongest factor, with SST and TA taking secondary roles and SSS being a weak contributor. Since DIC and TA can co-vary with salinity, when they are not normalized, their distribution in the AS mirrors the north–south salinity gradient (see Figs. 2 and 3 in ). Once corrected for salinity, it is clear that the upwelling region of Oman still has elevated DIC, whereas the central, oligotrophic AS shows a DIC deficit. By contrast, the onshore–offshore gradient in TA is weaker. Differences between coastal and offshore normalized DIC and TA in the AS have been previously observed , but the stronger relative absence of DIC in the central AS and its role in affecting pCO2 has not been emphasized. A similar analysis in the California Current upwelling system indicates near-compensation of DIC and temperature in opposing directions, nearly overlapping each other. In that scenario, DIC overpowers temperature at the coast, with TA and SSS being secondary. For the AS, while the upwelling regions of Oman and Somalia show temperature and DIC working against each other, they are not as well compensated for. Furthermore, the gradients of positive/negative pCO2 contributions from temperature and DIC do not overlap, leading to the curious scenario in which temperature and DIC both contribute positively to the pCO2 anomaly along the Indian coast. The positioning of these gradients and the surprising negative influence of DIC away from upwelling regions perhaps underscores how the AS is rather unique, where strong seasonal upwelling winds mingle with strong tropical heating and there is the influence of outflows from marginal seas .