The inventories of bomb-14C are calculated following the procedures of Broecker et al. . The area (A) between the measured Δ14C depth profile and the reconstructed pre-nuclear Δ14C depth profile (Δ14C0) is calculated as
Here, z0 is the depth at which the difference between Δ14C and Δ14C0 becomes negligible (<1‰). The mean penetration depth (Z) of bomb-14C is obtained as
Here, ΔΔ14C = (Δ14C − Δ14C0)surface is the measured excess of surface water Δ14C from its pre-nuclear value. The total column-inventory of bomb-14C is given by
Here ΣCO2is the mean DIC of the water column up to which bomb-14C has penetrated. The proportionality constant ‘k’ takes into account density of seawater (average ∼1025 kg m−3), Avogadro's number (6.023 × 1023 atoms mol−1), and the 14C/12C atom ratio of the NBS Oxalic Acid-I standard (1.176 × 1012 [Karlen et al., 1968]). The inventory of bomb-14C is expressed in units of atoms of 14C per square unit area of the seawater column. Following this procedure, the estimate uncertainty of the calculated inventory is about ±10% [Peng et al., 1998]. To compute the bomb-14C inventories, the measured depth profiles of Δ14C, silicate and ΣCO2values were interpolated to every 1 m. Pre-nuclear Δ14C profiles (Δ14C0) were then reconstructed from the measured values of silicate, using the empirical relationship of Broecker et al. , Δ14C0 (‰) = −70 − silicate (μmol kg−1). The reconstructed pre-nuclear Δ14C of surface was forced to match with the values obtained from pre-bomb shells. The excess (measured Δ14C − Δ14C0) are then integrated until the difference becomes negligible and the inventory of bomb-14C is obtained using (B1) and (B3).
 The air-sea CO2 exchange rates were calculated following the procedure outlined by Stuiver The total amount of bomb-14C penetrated in ocean is proportional to the air-sea exchange rate of CO2 and the time integrated gradient of Δ14C between the atmosphere (Δ14Catm) and the ocean surface mixed layer (Δ14Cmix). Assuming the mean steady state difference in Δ14C values between atmosphere and oceanic mixed layer is −60‰ for the northern Indian Ocean, the total amount of bomb-14C (Q14), transferred per unit of ocean surface over time t(in years) is related to the air-sea exchange rate of CO2 (F12) as
The constant term on the right hand side of (B4), takes into account the isotopic fractionation factors for ocean-atmosphere transfer and normalization of14C activity to δ13C value of −25‰ [Stuiver, 1980]. Here Q14 is expressed in mol m−2 and F12 in mol m−2 yr−1. For the onset of input of bomb-14C to the oceans, 1954 is taken as the initial year (t = 0). The values of the integrals for Δ14Catm and Δ14Cmix are obtained from Δ14C measurements in the atmosphere and in corals. The tropospheric Δ14C from 1954 and 1968 has been adopted from the reported measurements from the tropical regions [Nydal and Lövseth, 1996; Hua and Barbetti, 2004; Chakraborty et al., 2008], with peak Δ14C of 700‰ in the year 1965. From 1968 onward, an exponentially decreasing atmospheric Δ14C trend with e-folding time of 17 years has been adopted, fixing the Δ14C for the years 1980 and 1999 at 265‰ and 88‰ respectively. There are too few coral Δ14C measurements in the open northern Indian Ocean, to reconstruct the mixed layer Δ14C history for different regions. Between the years 1954 and 1973, the value of the integral of Δ14Cmix is taken as 1400 [Stuiver, 1980]. From 1973 onward, a linear decrease of surface ocean Δ14C has been assumed, from a value of 140‰ in 1973 to 50‰ in 2000, to match with the observed values from the GEOSECS measurements during 1977–1978 [Stuiver and Östlund, 1983] and during late 1990s [Dutta et al., 2006]. Q14 are calculated from the bomb 14C inventories for different stations, to determine the air-sea CO2 exchange rates (F12) using (B4). Based on the uncertainty in bomb-14C inventory (15%) and the integral of the atmosphere-ocean Δ14C gradient (5%), the uncertainty of 14C-based exchange rates estimated to ∼20%.Druffel and Griffin  showed that for surface samples, the total uncertainty of a DIC Δ14C value at a given site over a several week period is approximately two times the reported uncertainty (∼7‰). Thus, depending on the application, post-bomb Δ14C data should consider this short-term variability of surface ocean Δ14C values and factor this into their analysis as it might affect the estimates of air-sea CO2 exchange rates.
 Once the rate of air-sea CO2 exchange (F12) is known, the net transfer rate (F) of atmospheric CO2 across the ocean surface can be determined from the difference of the partial pressure of CO2 (ΔpCO2) in the surface ocean and that in the atmosphere [Wanninkhof, 1992]. The net transfer rate of CO2 (F) is given by
In this case, the sign of F (or direction of flux) is positive upwards. Thus the net flux of CO2 will be from sea to air, in regions where ΔpCO2 is positive. This condition is common in most tropical oceanic areas due to equatorial upwelling, which brings deeper CO2rich waters to the surface. The exchange rates calculated from bomb-14C inventories are the long-term averaged values. Thus, if average ocean-atmospherepCO2 gradient (ΔpCO2) over a given oceanic region is known, it is possible to compute the net transfer rate of CO2 from the exchange rates. Based on the uncertainties in the 14C-based exchange rates (20%) and in the estimates of ΔpCO2 (10%) the maximum uncertainty on F is expected to be within 30%.