PMIP qflux Newsletter (Taylor)


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Bob Gallimore and John Kutzbach have raised some complicating issues
concerning the Q-flux specified for 21 kyr. I have also thought a
little more about this issue (in response to the memo from Bob and
John), but we would like input from other groups before deciding how
to proceed.  Below are:

 1) Appendix 2 of PMIP newsletter #2 in which Tony suggested a method
 of adjusting the Q-Flux in response to a lowering of sea-level.

 2) The memo from Bob and John, which suggests a slightly different

 3) A few brief comments in response by me.

I am also sending by fax a figure that goes with the memo from Bob and

If you have already begun the simulations, please let us know what you
have done with the Q-flux.  What do you think the recommended
procedure should be?

TAYLOR Karl E.          Lawrence Livermore National Laboratory
                        P.O. Box 808, L-264
                        Livermore, CA 94550
                Tel.:   1 (510) 423-3623
                Fax.:   1 (510) 422-7675
                email:  taylor13 (NEW! Please check the PMIP 'Contacts' web page)


PMIP newsletter #2:

APPENDIX 2: About the "Q-flux" method

The purpose of this note is to share some ideas I have regarding the
use of a prescribed ocean heat flux (the so-called "Q-flux method") in
atmosphere-mixed layer ocean models when simulating the last glacial
maximum. The problem in the implementation of this technique arises due
to differences in the land-sea distribution due to lower sea level of
glacial times. As a result, some model gridpoints that are ocean in the
control climate simulation are land in the glacial climate simulation.
Thus it is not a simple matter to decide how to prescribe the same
ocean heat flux in both the control and glacial simulations.

My proposal assumes that the goal is to prescribe the same flux of heat
by the ocean across each latitude circle. While there is no reason to
believe that the ocean heat flux at the last glacial maximum was the
same as today, the assumption of no change in heat flux is commonly
made in simulations of greenhouse warming.One of the purposes of
performing LGM simulations with predicted sea surface temperatures is
to intercompare the sensitivity of various climate models. Thus the use
of prescribed ocean heat fluxes is essential to avoid the distortions
in sensitivity that can result from biases in the distribution of sea
ice. So while there are some uncertainties in implementing this
technique in LGM simulations, I believe it is preferable to the
alternative of having no prescribed ocean heat transport.

Ocean heat transport in atmosphere-mixed layer ocean models is mimicked
by prescribing a heating (or cooling) function at each ocean grid
point. If there were no change in the land-sea distribution, the same
heating function would be used at each grid point for both the control
and perturbation experiments.  Since this is not possible for LGM
simulation experiments, the objective is to provide the same net
heating (or cooling) integrated around each latitude circle. Thus my
suggestion is to take the net heating integrated over the pointsalong
each latitude circle that are ocean in the control but land in the LGM
experiment, and uniformly redistribute that heating over the points
that remain ocean in both experiments.


        If ocean in both experiments, then:

                qlgm(i,j) = qcontrol(i,j) + sum(qcontrol(i,j))/npoints(j)

        If land in the LGM, then:

                qlgm(i,j) = 0.0

        where   i is the longitude index,
                j is the latitude index,
                qcontrol(i,j) is the heating function at each grid point
                              from the control experiment,
                qlgm(i,j) is the heating function at each grid point for
                          the LGM experiment,
                sum() is a function that sums a quantity over the grid points
                      at each latitude circle that are ocean in the control
                      experiment but land in the LGM experiment,
                npoints(j) is the number of grid points along each latitude
                      circle that are ocean in both the control and the LGM

The above describes the computation for a latitude-longitude grid, or
any other grid where the grid boxes along each latitude circle are of
equal area.  Reformulation will be necessary for other types of grids.

This describes the methodology I plan to employ in the PMIP simulation.
I confess that I have not yet tested this method in a climate model
integration, but I plan to do so in the near future in preparation for
the PMIP experiment.  I will share my experiences with all of you.

                                                Anthony J. Broccoli


Memo from Bob Gallimore and John Kutzbach:


27 July 1993


TO:       A.J. Broccoli, Sylvie Joussaume, Karl Taylor

FROM:     Bob Gallimore and John Kutzbach

RE:       Concerning implementation of ocean heat flux correction for
              21 kyr bp experiment

Tony raised some important issues concerning the Q-flux method for 21
kyr given different land/sea distributions (Appendix 2: PMIP newsletter
#2).  In working with this scheme, we first encountered one specific
question and then began to consider a more general question. We discuss
both of these issues below.

A.  Land/Sea Distribution

We are currently in the process of implementing Broccoli's method for
our 21 kyr BP (PMIP) experiment using the NCAR CCM1 coupled to a
constant 50 meter depth mixed layer ocean (essentially the
Covey-Thompson model). For this CCM1 model a prescribed annual-average,
zonal-mean (no longitudinal variation) convergence of ocean heat
transport is incorporated in the calculation of ocean surface
temperature. For high latitude ocean areas (poleward of 60N) the
convergence of the heat transport is set at 2 W/m2 ostensibly
reflecting the heat convergence under sea ice. Other models may pick
slightly different values (4 W/m2, etc.) but we imagine that most
models keep this term small.

When we applied Broccoli's scheme to the CCM1 fluxes, based on the
CLIMAP reduction of high latitude ocean area for the glacial age
boundary conditions, we found the convergence of the heat flux (net
heat flux) at some grid points poleward of 60N increased to 4-5 W/m2.
If this increased net heat flux were applied to the sea ice it could
significantly (and artificially) influence (possibly reduce) simulated
sea ice for the glacial climate relative to modern.

As a modification to the Broccoli method we have therefore tested a
scheme whereby we require the net heat flux under sea ice (i.e.,
poleward of 60) to stay at 2 W/m2 for the glacial simulation. This
requirement necessitates adding +0.06 W/m2 to the net heat flux at all
ocean grid points equatorward of the sea ice boundary (60N) in order
that the global integral of net ocean heat flux be 0. This modification
of Broccoli's method slightly changes the longitudinally integrated
flux at particular latitudes (in contrast to Broccoli's method) but has
the desirable property of providing an invariant flux under sea-ice.

B. Proper O-flux for ``colder-than-control'' experiments

The first question raises another but related issue. Prescribing the
Q-flux will exert a strong control on where sea-ice can form. In
``global warming'' experiments, the model has the degree of freedom to
try to melt back the sea ice into the region of low ocean flux (2 W/m2)
and one could diagnose this tendency early in an experiment. However,
in ``global cooling'' experiments, it will be very difficult for the
model to grow ice equatorward of the control case sea-ice border where
most Q-flux methods impose ocean heat fluxes of 50-60 W/m2.

According to the CLIMAP data, sea ice extended equatorward to around 45
N over the North Atlantic in February and 48-56 over the Southern Ocean
in August at maximum glacial times. Associated with this equatorward
extension of sea ice in the North Atlantic is an apparent south and
eastward shift of the Gulf Stream.  In contrast, the modern net
(convergence of) ocean heat flux used in the CCM1 model increases from
2 W/m2 at 60 N to greater than 50 W/m2 at 51 N. This large heat flux
convergence would act to greatly limit sea ice formation in the region
45 N-60 N in a glacial simulation. To more realistically allow for
development of sea ice equatorward of control case sea ice limits in
the 21 kyr simulation, we propose to extend the domain of the
prescribed 2 W/m2 net heat flux (under sea ice) to 51 N and 51 S (2
grid points equatorward of the modern limit at 60). This modification
requires adding 2.8 W/m2 to the net heat flux at all ocean grid points
equatorward of 51.

We are raising these issues to stimulate discussion about what to do in
areas of sea ice. We feel different groups might make different
adjustments. The lack of a uniform strategy for sea ice areas could
lead to significant differences in model simulations. Without some
adjustment of the Q-flux to allow equatorward expansion of sea ice we
may end up with unrealistic results. For example, at around 50-60N,
cold continents could contrast with unrealistically warm oceans thereby
setting up perturbations in the planetary waves. On the other hand, the
proposed adjustment will have a strong influence on the results too.
However, if we've exaggerated the equatorward shift of the ice, the
model can attempt to move it back toward the poles. In this sense, we
constrain the model less by shifting the 2 W/m2 value ``too far'' than
if we don't shift it enough (or at all).

P.S. We are faxing a graph of our heat flux values for three cases:
control, modified Broccoli scheme, proposed 21 kyr scheme.

P.P.S. The version of CCM1 we use employs a longitudinally uniform
Q-flux. This means that in our proposed scheme we cannot incorporate
differences, say, between the N. Atlantic and the N. Pacific. A
longitudinally-varying Q-flux could be developed but that would further
constrain the model.


Comments from Karl Taylor to Bob and John:


1)  I agree that changes in the extent of sea ice may play a critical
role in determining regional climate change, so we must be careful to
allow for a realistic simulation of sea ice.  You have raised an
important issue that I had not previously considered and which may
require revision of Tony's suggested method of accounting for changes
in continental boundaries.

2)  Concerning the specific question, your solution seems quite
reasonable (given that only a .06 W/m**2 adjustment is required).
Alternatively, one could modify Tony's scheme such that the total ocean
heat flux across a given latitude when divided by the combined total
width of the ocean basins were required to remain the same as it is
today.  In this case the heat flux from below the mixed layer would
remain the same as it is today, but the total oceanic meridional heat
flux would be different.  A small adjustment would also have to be made
to force global conservation of energy, but if applied uniformly over
the globe,  I'm sure this would be small enough that it would not
affect sea ice formation significantly.

3)  Your more general concern about "colder-than-control" experiments
looks like it has a more important quantitative impacts.  If in fact
the the CLIMAP reconstructions are correct, then either the oceanic
heat flux into the regions just equatorward of the current sea ice
boundaries was much smaller than it is today (or perhaps today's
estimate of the heat flux are exaggerated), or else your sea ice model
is unrealistic and can't properly grow sea ice in the face of high heat
fluxes from the ocean below.  In either case we are in trouble.  I'm
not sure how I would proceed here, but I'm a little uncomfortable with
your approach and would like to give this some more thought.  I'll try
to send more comments later.


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