Estimating Ocean Heat Uptake Using Boundary Green's Functions: A Perfect-Model Test of the Method

Ocean heat uptake is caused by "excess heat" being added to the ocean surface by air-sea fluxes and then carried to depths by ocean transports. One way to estimate excess heat in the ocean is to propagate observed sea surface temperature (SST) anomalies downward using a Green's function (GF) representation of ocean transports. Taking a "perfect-model" approach, we test this GF method using a historical simulation, in which the true excess heat is diagnosed. We derive GFs from two approaches: (a) simulating GFs using idealized tracers, and (b) inferring GFs from simulated CFCs and climatological tracers. In the model world, we find that combining simulated GFs with SST anomalies reconstructs the Indo-Pacific excess heat with a root-mean-square error of 26% for depth-integrated changes; the corresponding number is 34% for inferred GFs. Simulated GFs are inaccurate because they are coarse grained in space and time to reduce computational cost. Inferred GFs are inaccurate because observations are insufficient constraints. Both kinds of GFs neglect the slowdown of the North Atlantic heat uptake as the ocean warms up. SST boundary conditions contain redistributive cooling in the Southern Ocean, which causes an underestimate of heat uptake there. All these errors are of comparable magnitude, and tend to compensate each other partially. Inferred excess heat is not sensitive to: (a) small changes in the shape of prior GFs, or (b) additional constraints from SF₆ and bomb ¹⁴C.