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 procedure. 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 John. 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? Cheers, Karl TAYLOR Karl E. Lawrence Livermore National Laboratory P.O. Box 808, L-264 Livermore, CA 94550 USA 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. Symbolically: 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 experiments. 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 MEMORANDUM 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.