365
sidered it unlikely that the relatively short spin-up duration was responsible
for the drift, citing as evidence a later coupled run, which showed very similar drifts although it followed a 475-year spinup. He used as corroboration
that the drifts during the coupled stage were of opposite sign to the drifts
before the coupling.
Rahmstorf (1995a) has analyzed the drifts that occur when a global
ocean GeM, spun up under mixed boundary conditions, is coupled to a
diffusive energy balance model, the parameters of which are chosen such
that the resulting surface heat fluxes match those of the spinup exactly. In
the classification of the models of section 3, this corresponds to the shift
from model #2 to model #4, that is, to a different atmospheric transport
model. Normally, the different atmospheric model would lead to a different
model climate; insisting, as we do in section 3 and as Rahmstorf (1995a)
does, that the same ocean climate including surface fluxes be obtained,
is conceptually equivalent to flux adjustment (this will be made explicit
below). Rahmstorf (1995a) then shows that the drifts in his model occur because of a shift in convection patterns. Implied is an unconditional
instability of the convection patterns of the spinup; if the spinup is in mathematically exact steady-state, a change in the formulation of the boundary
conditions leaves the model in equilibrium, provided the new conditions are
exactly consistent. But even roundoff error can destroy this exact match.
This section investigates an alternative hypothesis for why coupled GeMs
might drift despite flux adjustments. The coupled box model is used to
show that a drift is likely when the switch from one atmospheric model to
another is made before the spinup is fully equilibrated. Strong motivation
comes from the paper that presented the first systematic introduction and
analysis of flux adjustments or 'flux correction' (Sausen et al., 1988), which
had an apparent predecessor in form of an MPI internal report (Sausen et
al., 1987). In this, two different spinup runs of an ocean GCM were described, before the GeM was coupled to a simple diagnostic atmospheric
model (but more complex than Rahmstorf's). If the spinup was run for
3000 years only, even the flux-adjusted coupled model showed drifts in
SST of 1°C and more, over widespread areas, within 100 years. If, however, the spinup was run for 20,000 years and a different convection scheme
used that reduced intermittence in convection, the residual drifts were very
small and, in their overall magnitude, independent of whether the model
was coupled, driven by Newtonian damping, or driven by fixed surface heat
flux (corresponding to models #4, #2, and #1, respectively).
sidered it unlikely that the relatively short spin-up duration was responsible
for the drift, citing as evidence a later coupled run, which showed very similar drifts although it followed a 475-year spinup. He used as corroboration
that the drifts during the coupled stage were of opposite sign to the drifts
before the coupling.
Rahmstorf (1995a) has analyzed the drifts that occur when a global
ocean GeM, spun up under mixed boundary conditions, is coupled to a
diffusive energy balance model, the parameters of which are chosen such
that the resulting surface heat fluxes match those of the spinup exactly. In
the classification of the models of section 3, this corresponds to the shift
from model #2 to model #4, that is, to a different atmospheric transport
model. Normally, the different atmospheric model would lead to a different
model climate; insisting, as we do in section 3 and as Rahmstorf (1995a)
does, that the same ocean climate including surface fluxes be obtained,
is conceptually equivalent to flux adjustment (this will be made explicit
below). Rahmstorf (1995a) then shows that the drifts in his model occur because of a shift in convection patterns. Implied is an unconditional
instability of the convection patterns of the spinup; if the spinup is in mathematically exact steady-state, a change in the formulation of the boundary
conditions leaves the model in equilibrium, provided the new conditions are
exactly consistent. But even roundoff error can destroy this exact match.
This section investigates an alternative hypothesis for why coupled GeMs
might drift despite flux adjustments. The coupled box model is used to
show that a drift is likely when the switch from one atmospheric model to
another is made before the spinup is fully equilibrated. Strong motivation
comes from the paper that presented the first systematic introduction and
analysis of flux adjustments or 'flux correction' (Sausen et al., 1988), which
had an apparent predecessor in form of an MPI internal report (Sausen et
al., 1987). In this, two different spinup runs of an ocean GCM were described, before the GeM was coupled to a simple diagnostic atmospheric
model (but more complex than Rahmstorf's). If the spinup was run for
3000 years only, even the flux-adjusted coupled model showed drifts in
SST of 1°C and more, over widespread areas, within 100 years. If, however, the spinup was run for 20,000 years and a different convection scheme
used that reduced intermittence in convection, the residual drifts were very
small and, in their overall magnitude, independent of whether the model
was coupled, driven by Newtonian damping, or driven by fixed surface heat
flux (corresponding to models #4, #2, and #1, respectively).