```After seeing the recent messages about various "Q-flux" methods, I'd
like to chip in with a description of how it is handled in the GENESIS
model at NCAR.  We have had to think about these issues in our
applications to Paleozoic geographies, with very different continental
distributions from the present.  We address both concerns raised by
Bob Gallimore and John Kutzbach, namely (i) keeping the heat
convergence (W/m2) constant and letting the net heat transport change
(PW) for differing continental distributions, and ii) adjusting the
heat convergence below sea ice *at each time step* to a low specified
value.

We first convert the present-day annual-mean net latitudinal heat
transport (PW) to a heat convergence by taking its gradient and
dividing by the area of ocean at each latitude bin. We "tweak" this
raw curve by making it tail to particular values at high latitudes to
represent the present-day under-sea-ice convergences (2 W m-2 in NH,
10 W m-2 in SH).  This convergence function vs. latitude is applied at
each ocean grid point of a new continental map, and a globally
constant shift is added or subtracted to restore the global integral
to zero. This forms a basic Q-flux input file that is read by the
model at the start of a run. These steps correspond to Bob and John's
suggestion (A) and Karl's reply (2), and of course the implicit
assumption (whether true or not) is that the transport *per unit
length of latitude circle* stays constant so the net transport is
larger for wider basins.

Then at each timestep of the model, the convergence at each grid point
is modified by the current predicted fraction of sea ice. The
convergence is
(1-f)*[basic value] + f*[sea-ice value]
where f is the sea-ice fractional cover at the grid point, "basic
value" is the convergence from the basic input file, and "sea-ice
value" is 2 W m-2 in the NH and 10 W m-2 in the SH. Then a global
constant is added at each time step to ensure the global integral is
zero.

This gets at Bob and John's concern (B). If the sea ice can advance at
all, there will be a positive feedback since the advancing ice edge
reduces the heat convergence under itself, and does not have to endure
open-ocean values (eg, 50 W m-2 at ~51 deg N mentioned by Bob and
John).

We have not yet done a Pleistocene glacial maximum simulation, so we
don't know how far the scheme would allow sea ice to advance. In our
paleo-simulations to date (Paleozoic, Mesozoic, Tertiary) the sea-ice
distributions have at least seemed well behaved.

Dave (pollard@ncar.ucar.edu, 303-497-1344).
```

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