Flux correction and the simulation of changing climate

A flaw is pointed out in the manner in which flux correction is currently applied to coupled atmosphere-ocean general circulation models. If a transient climate simulation were carried out using perfect initial data and a perfect model, then a perfect simulation would be made. However, if the model were flux corrected so that it is in equilibrium for current conditions, according to current practice, then errors in the simulation would grow initially to a finite amplitude and persist indefinitely. Larger errors would be produced by a simulation with the flux corrected model beginning from pre-industrial conditions than by a simulation beginning from current conditions. An example with a simple linear model is constructed to illustrate this point, and the relationship to the cold start problem is demonstrated. An optimal flux correction for the simple example is shown to be one which would eliminate the error in the current climate from a transient simulation begun sufficiently far in the past.