JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 91, NO. D2, PAGES 2709-2718, FEBRUARY 20, 1986 Effect of Ocean Mixing on the Transient Climate Response to a CO2 Increase' Analysis of Recent Model Results L. D. DANNY HARVEY 1 Department of Geo•7raphy, University of Toronto, Ontario, Canada National Center for Atmospheric Research, Boulder, Colorado Results of several recent reports on the role of ocean mixing in the transient response to a CO 2 doubling are analyzed and compared. WigIcy and Schlesinger (1985) obtained an analytical solution to a one-dimensional box-diffusion (BD) ocean model in which themixed layer e-folding time reOCfo2KAT• 2, where f0 is the planetary ocean fraction, K is the ocean diffusivity, and AT• is the equilibrium temper- ature response. The dependence of % obtained by WigIcy and Schlesinger is compared with that obtained using simple land-searesolved and box-advection-diffusion (BAD) models.For a BAD model the depen- dence of re on both K and AT• is significantly less than for a BD model. A comparison of the transient response of BD and BAD models using the same effective K indicates that the behavior of the BAD model cannot be captured using a BD model, except during the first few decades of the transient response. Schlesinger et al. (1985) estimated atmospheric and mixed layer valuesof % for their coupled atmosphere-ocean generalcirculation model (A/O GCM) by fitting a BD model to the first 16 years of their A/O GCM transient response and then integrating the BD model for 200 years.However, Schles- inger et al. appear to have overestimated values of Ze for their long-term A/O GCM by fitting their short-term A/O GCM transient response to a model in which the equilibrium globally averagedatmo- spheric and mixed layer temperature responses are equal, whereas this is apparently not true for their A/O GCM. Hansenet al. (1984) estimated % by modelingthree-dimensional oceanmixing as a series of isolated BD models, one below each horizontal grid point, and by using tritium-based diffusion coef- ficients, which probably are too large when applied to heat and probably lead to an overestimate of the actual Z e. 1. INTRODUCTION An issueof primary importance which has recently emerged in the context of the problem of climatic response to ongoing CO2 increase is the role of ocean mixing processes in delaying surfacetemperature response. Not only is this issuerelevant to determining the rates of probable climatic change and hence the rate at which human societies may have to adapt [Kellogg and Schware,1982], but it is also important for possibletran- sient climatic effects arising from geographical variations in the rate of climate response [Schneiderand Thompson, 1981] and has implications concerningthe empirical verification of climate model predictions [Hansen et al., 1984; Gilliland and Schneider, 1984]. Ideally, investigationof this problem should proceed using synchronously coupled, eddy-resolving atmosphere-oceangeneral circulation models (A/O GCMs). Current ocean GCMs, however, do not resolve eddies at the scale at which much of the oceanicheat transfer and mixing occurs (•-, 50 km) and sometimes fail to reproduce key features of the observed large-scale ocean temperature and density structure [i.e., Bryan et al., 1984], so that results obtained with thesemodels must still be regarded as very preliminary. Atmo- spheric GCMs, on the other hand, are considerablymore ex- pensive to integrate than ocean GCMs, so that in syn- chronously coupled A/O GCM experimentsthe length of inte- gration has been severelylimited [Bryan et al., 1982; Schles- inger et al., 1985]. To circumvent some of these problems, some workers have attempted to approximate the atmospheric forcing at the ocean-air interface rather than explicitly inte- grating the atmospheric component of a coupled A/O GCM and have adopted various simplified ocean models. Bryan et al. [1984] provided evidence indicating that three-dimensional •Now at Department of Geography, University of Toronto, On- tario, Canada. Copyright 1986 by the American Geophysical Union. Paper number 5D0804. 0148-0227/86/005D-0804505.00 oceanicmixing of heat, at least under some circumstances, can be modeled as one-dimensional vertical diffusion. Both Hansen et al. [1984] and Schlesinger et al. [1985] adopted this approach, and Wigley and Schlesinger [1985] present an ana- lytical approximation for a box-diffusion (BD) ocean model showing the dependence of the surface temperature e-folding time scale Ze on the ocean diffusion coefficient K, the ocean fraction fo,andthe model equilibrium sensitivity ATeq. An alternative one-dimensional ocean model is the box- advection-diffusion (BAD) model of Munk [1966], used re- cently by Hoffert et al. [1980], Siegenthaler and Oeschger [1984], and Harvey and Schneider [1985a, b]. Although nei- ther the BD nor the BAD model explicitly resolves such re- gional mixing processes as Ekman pumping or convection, it nevertheless seems justified to compare the dependence of % on K, fo, or AT• for bothmodels andto examine theextent to which the time dependentresponse of an advective-diffusive model can be capturedusinga purely diffusive model with an appropriate effective K. Furthermore, procedures usedto esti- mate values of K and the advection velocity w for modeling heat transfer need to be more critically examined. A third issue,relevant to the transient response of both diffusive and advective-diffusivemodels, is the role of the land response and land-ocean heat transport in accelerating the mixed layer tem- perature response. All three of theseissues are briefly analyzed in this paper, and recommendations for future research strate- gies are made. 2. COMPARISON OF BD AND BAD OCEAN MODEL TRANSIENT RESPONSE 2.1. Dependence on Ocean Fraction Wigley and Schlesinger[1985], subsequently referred to as WS, derived an analytical solution for a BD climate model consisting of a land box, land and ocean atmospheric boxes, and an oceanicmixed layer box, which in turn is coupled to a one-dimensional diffusive deeper ocean. The equations gov- erningthe mixedlayer and deepocean temperature changes in 2709