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While biogeochemical and physical processes in the Southern Ocean are thought to be central to atmospheric CO2 rise during the last deglaciation, the role of the equatorial Pacific, where the largest CO2 source exists at present, remains largely unconstrained. Here we present seawater pH and pCO2 variations from fossil Porites corals in the mid equatorial Pacific offshore Tahiti based on a newly calibrated boron isotope paleo-pH proxy. Our new data, together with recalibrated existing data, indicate that a significant pCO2 increase (pH decrease), accompanied by anomalously large marine 14C reservoir ages, occurred following not only the Younger Dryas, but also Heinrich Stadial 1. These findings indicate an expanded zone of equatorial upwelling and resultant CO2 emission, which may be derived from higher subsurface dissolved inorganic carbon concentration.

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Abstract. We consider an optimization reformulation approach for the generalized Nash equilibrium problem (GNEP) that uses the regularized gap function of a quasi-variational inequality (QVI). The regularized gap function for QVI is in general not differentiable, but only directionally differentiable. Moreover, a simple condition has yet to be established, under which any stationary point of the regularized gap function solves the QVI. We tackle these issues for the GNEP in which the shared constraints are given by linear equalities, while the individual constraints are given by convex inequalities. First, we formulate the minimization problem involving the regularized gap function, and show the equivalence to GNEP. Next, we establish the differentiability of the regularized gap function and show that any stationary point of the minimization problem solves the original GNEP under some suitable assumptions. Then, by using a barrier technique, we propose an algorithm that sequentially solves minimization problems obtained from GNEPs with the shared equality constraints only. Further, we discuss the case of shared inequality constraints and present an algorithm that utilizes the transformation of the inequality constraints to equality constraints by means of slack variables. We present some results of numerical experiments to illustrate the proposed approach.

The excess radiocarbon produced by nuclear bomb testing in the atmosphere in the 1950s–1960s (bomb‐14C) is used as a tracer in the surface ocean, extending our understanding of geophysics and biogeochemical cycles. However, there is no bomb‐14C record for the high‐latitude western North Pacific Ocean because of the paucity of long‐lived marine calcifying organisms equivalent to reef‐building corals. The shells of Stimpson's hard clam, Mercenaria stimpsoni, potentially provide such a record because the clam's lifespan is very long (>100 years). We analyzed 14C in six live‐caught M. stimpsoni shells from the western North Pacific (39.4°N, 142°E) and report, for the first time, the bomb‐14C record with robust calendar ages based on annual growth increments. The value was constant in 1934–1952 (Δ14C = −66‰), with a sudden increase in 1959, a peak in 1974 (107‰), which was 60‰ lower than that of the Kuroshio Current, a gradual decline after 1974, and a current value of 16–18‰, which is ∼10‰ higher than the atmospheric value. The bomb‐14C values are between the Kuroshio Current (the northwestern subtropical gyre) and Oyashio Current (the Western Subarctic Gyre) values, suggesting that the Tsugaru Current, downstream from the Kuroshio Current, mixes with the Oyashio Current after passing through Tsugaru Strait.