## 1. Introduction

[2] Controversy over the magnitude of the oceanic sink for bomb radiocarbon remains an important unresolved issue [*Broecker et al.*, 1985; *Sarmiento and Sundquist*, 1992; *Siegenthaler and Sarmiento*, 1993; *Hesshaimer et al.*, 1994; *Joos*, 1994; *Broecker et al.*, 1995; *Hesshaimer and Levin*, 2000; *Nydal*, 2000]. On the apparent discrepancy between ocean-based and atmosphere-based approaches to estimating the magnitude of the ocean bomb radiocarbon sink, *Hesshaimer et al.* [1994] stated, “This problem needs to be resolved,” to which *Broecker et al.* [1995] responded, “We see no way by which this estimate [295–305 × 10^{26} atoms] could be reduced to the 225 × 10^{26} atom value suggested by Hesshaimer et al.”

[3] Assuming a production rate of 1.05 × 10^{26} radiocarbon atoms per megaton of TNT, and utilizing measurements of bomb-radiocarbon in the troposphere and stratosphere, *Hesshaimer et al.* [1994] argued that the *Broecker et al.* [1995] estimate of ocean bomb radiocarbon uptake for the mid-1970s [*Broecker et al.*, 1985, 1995] led to a global budget which was seriously out of balance. On the basis of a simple global carbon cycle model, they argued that either a missing source of bomb radiocarbon equaling some 80×10^{26} atoms must be invoked, or that existing estimates of the ocean sink must be overestimated by this amount.

[4] The *Broecker et al.* [1995] (hereinafter referred to as B95) estimate of 305 ± 30 × 10^{26} atoms ocean uptake of bomb radiocarbon in 1975 (or, 295 × 10^{26} atoms on 1 January 1974, corresponding to the date adopted in the *Hesshaimer et al.* [1994] study) is based on an observed correlation between natural radiocarbon and dissolved silicate in waters assumed to be free of bomb-derived tracers. Extrapolation of this correlation to thermocline waters led these authors to an estimate of the natural (pre-bomb) radiocarbon distribution in the upper ocean at specific locations for which there existed both radiocarbon and silicate measurements. The bomb radiocarbon at each hydrographic station was then estimated as the difference between observed and natural radiocarbon profiles. If the B95 natural radiocarbon estimate at each station is correct, then the estimate of bomb radiocarbon at each station must, by definition, also be correct.

[5] However, the *Broecker et al.* [1995] approach has a number of sources of hard-to-quantify error. The first global ocean survey (Geochemical Sections, “GEOSECS,” mid-1970s) sampled radiocarbon only at a number of discrete locations, and coverage was far from uniform (the black dots in Figure 9 (in section 2.4) represent the GEOSECS station locations at which radiocarbon was measured). Therefore, in order to obtain a global inventory estimate, *Broecker et al.* [1995] chose to divide each ocean into 10-degree-wide latitude bands, and to assume the bomb radiocarbon estimates at stations falling within each band represented the mean for the entire band. It is likely, however, that tracer distributions are in places strongly non-uniform across a line of constant latitude. A second source of error in the B95 approach is in the estimation of the natural radiocarbon field. The average least squares error of the silicate-natural radiocarbon correlation is just over 13‰, which introduces an error to the predicted natural radiocarbon field which is of order 10%. Furthermore, the linear silicate-Δ^{14}C relation that holds in most of the ocean was observed to break down at the few high-latitude Southern Ocean GEOSECS stations, leading to a higher error in Southern Ocean bomb radiocarbon inventories.

[6] The error in the estimation of the natural radiocarbon field can be expressed as an error bar on the final inventory estimate, and this was done by B95. However, the error arising from the non-uniform station distribution, and the extrapolation over 10 latitude bands of station-based bomb radiocarbon estimates, is harder to quantify. This problem is addressed by two separate approaches in this paper.

[7] The first part of the paper is concerned with better constraining the ocean bomb radiocarbon inventory in the mid-1970s. Two separate approaches are taken. One method relies on an ocean model to separate bomb and natural radiocarbon in the ocean. Once waters have been sorted into bomb-contaminated and bomb-free, a multiple tracer correlation-based extrapolation method is used to infer the total (natural + bomb) radiocarbon concentrations throughout the ocean. A slight variation on the B95 silicate method is used to infer the natural radiocarbon distribution. Global gridded 1° fields are estimated for natural and total radiocarbon, and the global bomb radiocarbon field is then simply the difference between natural and total. The main error in this approach is the large scatter in the tracer-tracer correlations in the thermocline. The second method relies on using an ocean model to correct for the extrapolation error in the B95 method. In the second part of the paper, an estimate of the ocean bomb-radiocarbon distribution is made for the mid-1990s based on the recently collected World Ocean Circulation Experiment (WOCE) data-set.