Relaxation-type models have good skill at reproducing glacial-interglacial transitions in climatic variables. Here we propose a simple two-box and two-state relaxation-type model for the upper ocean (surface and permanent thermocline layers) where dissolved inorganic carbon/nutrients are supplied by the deep ocean and through remineralization within the upper ocean. The model is tuned using genetic algorithms to simulate the atmospheric CO_2 time series for the last four glacial-interglacial cycles. The fit to the data is very good, with correlations above 0.8, as the upper ocean responds to shifts in (1) the intensity of the meridional overturning circulation, from off to on during the glacial-interglacial transition,and (2) the size and sign of net primary production, with respiration greatly exceeding primary production during interglacial periods and production larger than respiration during the glacial phase. The glacial-interglacial transitions are interpreted as shifts between two distinct metabolic states of the Earth system, with high/low supply of dissolved inorganic carbon and nutrients to the productive upper ocean during interglacial/glacial periods.
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