Past exam of the physics of atmospheres and oceans course of the University of Oxford / 2015 / 2 / d / Solution

Interpret a uniform increase of $0.3\%$ per year from the present value as a constant slope, $F(t)=F_0(1+0.003t)$ with $t$ in years. Under quasistatic tracking of the stable branch, the time to its fold isIf instead the phrase means a compounded fractional increase, $F=F_0{e}^{0.003t}$, the corresponding time is $\ln (F_c/F_0)/0.003=51.3$ yr. These are two different forcing prescriptions, not two different critical freshwater fluxes.

The branch does not remain exactly at $15$ Sv until that date. Differentiating its quadratic giveswhich is $-24.71$ at the present state. The initial decrease is about $0.0371$ Sv per year under the linear ramp. At the fold the flow is only $10.887$ Sv, about 27 percent below its present intensity. Thus maintained close has no unique duration without a tolerance: for example, a ten-percent decrease to $13.5$ Sv occurs atA five-percent criterion gives about $18.4$ yr. The 55-year value estimates persistence of the positive equilibrium branch, not a perfectly flat present-day circulation.

These times are model extrapolations, not forecasts. The reservoirs' finite adjustment times are unspecified; near a fold, weakening restoring rates can invalidate quasistatic tracking and produce a delayed transition. Real ocean temperatures, reference salinity, winds, mixing, ice, geometry, regional freshwater pathways and the density-to-transport relation do not stay fixed. The imposed freshwater trend and the two-box reduction need independent justification before an actual transition time can be inferred.

A strong weakening of northward Atlantic heat transport could cool the North Atlantic and northern Europe relative to a climate with stronger overturning, altering atmospheric circulation and precipitation. It does not imply that all wind-driven transport vanishes or that greenhouse forcing ceases. The defensible implication is sensitivity of regional climate to ocean heat-transport changes, while the toy model supplies a transparent example of feedback and a threshold rather than a reliable dated prediction.