Quantifying the feedback between ocean heating and CO 2 solubility as an equivalent carbon emission

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1 GEOPHYSIL ESEACH LETTES, VOL. 36, L15609, doi: /2009gl039247, 2009 Quantifying the feedback between ocean heating and CO 2 solubility as an equivalent carbon emission Philip Goodwin 1 and Timothy M. Lenton 1 eceived 19 May 2009; revised 23 June 2009; accepted 7 July 2009; published 7 August [1] There are inherent difficulties in quantifying carbon cycle-climate feedbacks over the 21st century because the system is in a transient state. The conventional approach of deriving gain factors only strictly applies at equilibrium, and they differ with scenario and with respect to different climate variables (e.g., CO 2, radiative forcing, and temperature) which have different time lags. Here we show that the positive feedback whereby ocean heating reduces the solubility of CO 2 can be quantified in a scenario-independent way, directly from ocean heat content changes, by expressing it as an equivalent carbon emission. On annual to centennial timescales, the feedback has the same impact on atmospheric CO 2 as an equivalent emission flux of fossil fuel carbon. From ocean heat-content data we quantify the ocean heating-co 2 solubility positive feedback, which increased in average strength from an equivalent emission of 0.08 PgC yr 1 over to 0.19 PgC yr 1 during Citation: Goodwin, P., and T. M. Lenton (2009), Quantifying the feedback between ocean heating and CO 2 solubility as an equivalent carbon emission, Geophys. es. Lett., 36, L15609, doi: /2009gl Introduction [2] The conventional gain factor approach for analysing climate feedbacks has inherent problems when considering transient climate changes, because it is defined at equilibrium (after infinite propagation of a perturbation around a feedback loop) [Aires and ossow, 2003]. In spite of the transient nature of the system, carbon-climate feedback predictions for the 21st century are conventionally quantified using gain factors [Friedlingstein et al., 2006] (for detailed discussion, see Gregory et al. [2009]). However, the resulting gain factors will differ between scenarios. [3] Here, we consider the feedback between ocean heating and the solubility of CO 2 (hereafter termed CO 2 solubility feedback ) and ask: How can this feedback be quantified from ocean data during transient climate changes, in a way that is not scenario specific? At steady state, a process driven view of ocean carbon storage [Ito and Follows, 2005] can be used to analytically relate carbon cycle changes to atmospheric CO 2 [Goodwin et al., 2008]. Here, we develop this approach to investigate the transient response of atmospheric CO 2 to ocean heating. We outline a 1 School of Environmental Sciences, University of East Anglia, Norwich, UK. Copyright 2009 by the American Geophysical Union /09/2009GL method to quantify the CO 2 solubility feedback as an equivalent carbon emission (PgC yr 1 ). This equivalent carbon emission induces the same impact on atmospheric partial pressure of CO 2, C A (matm), as an identical increase in fossil fuel emissions. This method of quantification is applicable to a transient state, and depends upon current warming of the ocean and the ambient atmospheric CO 2 concentration, the method is independent of the emission scenario used to reach these values. 2. Theory [4] Consider carbon partitioning in an atmosphere-ocean system (Figure 1). The atmosphere contains CO 2 at partial pressure C A (matm), which is assumed spatially uniform over annual and longer timescales. The ocean contains dissolved inorganic carbon (DIC) with spatially varying concentration C DIC (gc m 3 ). In the surface mixed layer this DIC concentration can be split into two contributions from different processes [Ito and Follows, 2005]: a saturation concentration, C sat, which a water parcel would have if brought into equilibrium with the present overlying atmospheric C A, and a disequilibrium concentration, C dis reflecting the difference between the saturation concentration and the actual concentration (Figure 1). Outside the mixed layer, there are also contributions to local C DIC from the dissolution of biological material at depth, C bio, and the dissolution of marine CaCO 3 at depth, C CaCO3 [Ito and Follows, 2005]. [5] This study focuses on the CO 2 solubility feedback, other carbon-climate feedbacks are not considered here, such as changes in terrestrial ecosystems, ocean circulation or biological cycling. To isolate the CO 2 solubility feedback, consider the air-sea system in the abiotic limit, with C bio = C CaCO3 = 0 throughout the ocean. For the atmosphere-mixed layer system in this abiotic limit, the rate of change in atmospheric CO 2 plus the rate of change in mixed layer DIC is equal to the rate of emissions plus the DIC flux across the mixed layer-deeper ocean boundary (Figure 1): M dc A d ðc sat C dis ÞdV ¼ de C DIC v:da; ð1þ where dc A / is the rate of change of atmospheric CO 2 partial pressure, and M (gc matm 1 ) converts this into atmospheric mass of CO 2, is the (assumed constant) volume of the mixed layer (m 3 ), de/ is the carbon emission rate (gc s 1 ), v is the velocity of a water parcel (m s 1 ), da is an area pseudo-vector element (m 2 ), and is the surface area separating the mixed layer and deeper ocean (m 2 ). Vectors pointing into the mixed layer are treated as positive. L of5

2 Figure 1. Schematic of the atmosphere-ocean mixed layer deeper ocean system with an abiotic ocean. As carbon emissions, de/, enter the atmosphere, the partial pressure of CO 2, C A, increases. There is then a global net transfer of CO 2 from the atmosphere into the ocean since the mixed layer is under-saturated with respect to the increased C A. The DIC concentration of the mixed layer then exceeds that of the deeper ocean, and so there is a net transport of DIC into the deeper ocean: C DIC v.da, where C DIC is the spatially varying DIC concentration, is the surface separating the mixed layer deeper ocean boundary, v is the velocity of water as it crosses and A is a pseudovector area element where up is positive. [6] To simplify (1), we assume that the global average mixed layer disequilibrium concentration does not vary over annual timescales or longer, dc dis dv ¼ 0; because globally, the mixed layer is brought into equilibrium with an overlying atmosphere on an annual timescale [IPCC, 2007], although significant local disequilibrium exists at steady state. In the present situation, in which C A is continually rising, (2) is equivalent to assuming that there is a constant lag between the increase in C A and the mixed layer carbon uptake from one year to the next. [7] To analyse the CO 2 solubility feedback, we take the critical step of separating the change in mixed layer saturated carbon concentration, C sat, in (1) into a component from increasing atmospheric C A, and a component from increasing mixed layer temperatures T, dc sat ðdc A ; dt Þ dc A dt: It should be noted that C sat is also a function of titration alkalinity and salinity, which can also be altered by climate changes leading to additional feedbacks. However, these quantities are not directly affected by the CO 2 solubility feedback, and so are outside the scope of this study. ð2þ ð3þ [8] Consider local values of C DIC, C sat and C dis throughout the ocean when atmospheric C A undergoes an annual increase: C sat of the whole ocean instantaneously increases since it is defined here according to the present atmospheric C A (3). In the ocean mixed layer C DIC increases as carbon is exchanged between the atmosphere and ocean, and C dis remains unchanged (2). However, since the deep ocean undergoes little increase in C DIC on an annual timescale, deep ocean C dis must become more negative to compensate. This definition of C sat and C dis forms an important departure from the standard terminology when considering ocean carbon uptake, where a direct contribution to local C DIC from anthropogenic emissions is defined [Gruber et al., 1996; Sabine et al., 2004]. The departure arises because here we do not wish to distinguish between the impact of fossil fuel emissions and equivalent emissions from ocean heating. [9] Substituting (2) and (3) into (1) yields an expression which states that the rate of change in atmospheric C A plus the rate of change of mixed layer C sat (due to changes in C A and T), is equal to the carbon emission rate plus the DIC flux across the mixed layer/deeper ocean boundary: M dc A ¼ de dc dv dt dv C DIC v:da: ð4þ We now consider the effects of anthropogenic ocean heating, which have been isolated in (4), by considering the causes of temperature changes in the mixed layer. The change in C sat from temperature changes in the mixed layer is equal to a contribution from the net anthropogenic heating plus a contribution from exchanges of water of different temperatures across the mixed layer-deep ocean boundary: dt dv dq f c Tv:dA; where dq/ is the net anthropogenic heating of the ocean, f is the fraction of this heating that induces ocean warming (as opposed to, say, changes in latent heat transport [Sutton et al., 2007]) and c is the specific heat capacity of seawater. The net heating of the ocean surface can be considered as an average, dq/, in (5), rather than having to integrate the total heating across the ocean surface, because C sat changes approximately linearly with T at fixed C A (Figure 2a). The CO 2 solubility feedback is positive because is negative (i.e., increasing temperature reduces the saturation concentration of carbon). As C A increases, dq/ increases which tends to strengthen the feedback, however, also becomes less negative (i.e., comes closer to 0), which tends to weaken the feedback (Figure 2b). [10] The fluxes of C DIC and temperature induced C sat differences (3) across the mixed layer-deeper ocean bound- ð5þ 2of5

3 2.1. Equivalence of Ocean Heating and Emissions With Constant Ocean Circulation [12] If ocean circulation is held constant, the atmosphereocean system responds to emissions and/or ocean heating with only one parameter with the freedom to vary, the time evolution of atmospheric CO 2, dc A /. Thus, for identical values of forcing, dc A / must be identical regardless of the balance between emissions and ocean heating. The effect of ocean heating upon the time evolution of atmospheric CO 2 is therefore identical to an increase in fossil fuel usage by an equivalent emission : Figure 2. The variation of DIC saturation concentration (C sat ) with water temperature, calculated using an explicit solution of the carbonate chemistry system [Follows et al., 2006] (black dots) using salinity 34.7 psu, titration alkalinity 2.33 mol m 3, and then linearly approximated (grey dashed lines). (a) C sat against temperature, T, fora water parcel saturated to C A = 280 matm and (b) / against the logarithm of C A /280 matm. ary can be combined and expressed as the flux of disequilibrium carbon, C dis =C DIC -C sat, C dis v:da ¼ ¼ ðc DIC C sat Þv:dA C DIC T v:da; using Xv.dA DXv.dA for constant (requiring annual timescales), where X is any arbitrary conserved tracer and DX is the difference between X and an arbitrary constant. Note that there is no C A component to the C sat exchange in (6) since here we define C sat of the whole ocean with respect to the same, present, atmospheric C A (3). [11] Substituting (5) and (6) into (4) reveals a relationship of the form atmospheric response plus ocean response is equal to the forcing from emissions and ocean heating, 2 3 M dc A 6 dc A 7 4 dv C dis v:da5 ocean " ¼ # sat dq f : ð7þ c forcing Thus, the atmosphere-ocean system responds to emissions and/or ocean heating with two terms that depend on the time evolutions of C A, dc A /, and one term representing the flux of disequilibrium carbon across the mixed layer-deeper ocean boundary, (6). This last term on the left hand side in (7) depends on the time evolution of ocean circulation as well as that of atmospheric CO 2. The preceding terms are independent of ocean circulation. ð6þ Equivalent emission ¼ dq f PgC yr 1 : c This provides a method independent of emission scenario with which to quantify the CO 2 solubility feedback effect on atmospheric CO 2, simply by knowing the rate of anthropogenic heating Feedback From Ocean Circulation Changes [13] Ocean heating changes ocean circulation by altering local seawater density, both directly (increasing temperature decreases density) and indirectly by altering fresh water transport. We now consider how the time evolution of atmospheric CO 2 might be affected if ocean circulation changes. [14] In the present situation, in which atmospheric CO 2 is increasing over time, the deep ocean carbon is in a greater state of disequilibrium (i.e., is more negative) than the surface ocean, making the net flux of disequilibrium carbon into the mixed layer negative, C dis v.da < 0. This is because deep ocean DIC concentrations increase more slowly than surface ocean DIC in response to the rising atmospheric CO 2, so there is a net negative flux of C dis into the mixed layer. If the exchange of water between the mixed layer and deep ocean decreases, say due to a slowdown of the meridional overturning circulation (MOC), the transport of C dis into the mixed layer, C dis v.da, will weaken, becoming less negative. If this happens, the impact on atmospheric CO 2 can be illustrated by assuming that the forcing from emissions and ocean heating remains unchanged. Theory (7) then predicts that atmospheric CO 2 will increase more quickly to compensate. This change in the rate of increase of atmospheric CO 2 represents the ocean heating-ocean circulation feedback, which works in addition to the CO 2 solubility feedback. 3. Illustrating the Theory With a Box Model [15] A simple numerical model (auxiliary material) containing a well mixed atmosphere, surface mixed layer and deep ocean boxes, is used with a constant exchange of 100 Sv between the mixed layer and deeper ocean. 1 When ocean heating is allowed, the surface ocean is warmed directly by the radiative forcing affect of elevated 1 Auxiliary materials are available in the HTML. doi: / 2009GL ð8þ 3of5

4 Figure 3. Box model response to carbon emissions starting at 0 PgC yr 1 and increasing by 0.06 PgC yr 2 : without heating (grey dashed), with heating (black dashed) and without heating but with extra effective emissions to mimic the effect of heating (grey solid). (a) dc A / against time and (b) C dis v.da against time. CO 2, and the warmed surface water is then exchanged with the deep ocean. The constant ocean circulation means that the CO 2 solubility feedback is represented, but the ocean heating-ocean circulation feedback is not. [16] As the emission rate and/or ocean heating increases, so atmospheric CO 2 also increases (Figure 3a), and there is a net negative flux of disequilibrium carbon into the surface mixed layer (Figure 3b). As predicted from theory, model integrations with the same total forcing, (7) (see auxiliary material), follow the same atmospheric CO 2 and disequilibrium flux paths (Figure 3, grey solid and black dashed lines), despite different balances of heating and emissions. Where there is a lower overall forcing (due to an absence of ocean heating), there is a slower rise in dc A / (Figure 3, grey dashed line) and a less negative disequilibrium flux into the mixed layer. This is despite having identical emissions to the with heating scenario. 4. Testing the Theory in an Earth System Model [17] Now we test the theory against a model with interactive representations of ocean circulation and the surface energy balance of the ocean. We expect the theory to predict the effect of the CO 2 solubility feedback, but not the additional ocean heating-ocean circulation feedback. [18] The GENIE-1 Earth System model was configured after idgwell et al. [2007, and references therein] with a 3D 8-level reduced physics (frictional-geostrophic) ocean, a 2D energy-moisture balance atmosphere and dynamicthermodynamic sea ice representation, and forced with non-seasonal climatology. An abiotic ocean carbon cycle is imposed, with no organic or CaCO 3 marine production, and the system is spun up with pre-industrial atmospheric CO 2 of 278 matm. There is no representation of terrestrial carbon storage. [19] First an atmospheric CO 2 time series was generated by integrating the model, including heating from elevated CO 2, with historic C A up to year 2001 followed by SES A2 emissions into the future. Two integrations were then performed with the generated time series of C A (Figure 4a): (1) heating, in which the system is interactively forced by the radiative forcing from increased CO 2 above 278 matm, and (2) no heating, in which the increased CO 2 does not exert a radiative forcing on the system and no warming occurs. Ocean circulation and temperatures are constant in the no heating case and vary in the heating case. [20] The difference in the required annual carbon emissions to meet the same C A time series between heating (configuration 1) and no heating (configuration 2) configurations is equal to the sum of the equivalent emissions from both the CO 2 solubility and ocean heating-ocean circulation feedbacks. We then compare this with the theoretical prediction for the CO 2 solubility feedback (8). [21] The fraction of incident radiative forcing since 1750 that has warmed the ocean in configuration 1 stays at 0.6 between 1900 and 2100 (Figure 4b). Therefore we use f = 0.6 in the theory calculating equivalent emissions from the CO 2 solubility feedback (8) (Figure 4c, black solid line). From 1750 to the present day, the extra carbon added into the no heating case 2 is accurately predicted from theory (8) (Figure 4c), with both theoretical and modelled equivalent emissions from ocean heating reaching 0.3 PgC yr 1 in present day. Equivalent emissions from all climate-carbon Figure 4. The response of the GENIE-1 model to carbon emissions with and without climate feedbacks. (a) Atmospheric C A increases over time. (b) The total fraction of radiative forcing since 1750 that causes the ocean to warm, analysed from 1900 to 2100 (grey line), when heating is allowed. (c) Equivalent emissions from ocean heating predicted from (8) using f = 0.6 (black solid), using f =1.0 (black dashed) and from GENIE-1 model output (grey). (d) Maximum North Atlantic overturning streamfunction over time for no heating (black) and heating (grey) integrations. 4of5

5 feedbacks in the GENIE-1 model rise to 2 PgC yr 1 by 2100, well exceeding the prediction for the CO 2 -solubility feedback after Total equivalent emissions even exceed that that predicted if all incident radiative forcing warmed the ocean (Figure 4c). [22] This underestimation by theory after 2020 represents the effect of the ocean heating-ocean circulation feedback, as indicated by the decrease in maximum North Atlantic overturning streamfunction when heating is allowed (Figure 4d). This change in ocean circulation reduces the amount of disequilibrium carbon exchanged between the mixed layer and deeper ocean, making C dis v.da less negative in (7). 5. Calculating the CO 2 -Solubility Feedback From Ocean Heat Content Changes [23] A framework has been provided to calculate the ocean heating-co 2 solubility feedback from ocean heat content considerations alone, with no carbon cycle information required (8). Data-based reconstructions of ocean temperature changes [IPCC, 2007; Levitus et al., 2005] indicate that global ocean heat content rose by (14.2 ± 2.4) J between 1961 and 2003, with (8.11 ± 0.74) Jof this warming occurring in the last decade. These heat content changes imply the average equivalent emissions from the CO 2 solubility feedback were 0.08 ± 0.01 PgC yr 1 between 1961 and 2003, but rose to 0.19 ± 0.02 PgC yr 1 for the last decade of this period (8). These values include uncertainty in dq/ and f but ignore uncertainty in the specific heat capacity of seawater, c, and the dependence of C sat on T. Any changes in ocean circulation would lead to additional equivalent emissions. This method can also be used to quantify the CO 2 solubility feedback in non-carbon cycle GCMs. The present day equivalent emissions from the CO 2 solubility feedback are comparable to the decrease in ocean sink from 1981 to 2004 ascribed to wind changes by Le Quéré et al. [2007] and are circa 3% of current anthropogenic emissions [IPCC, 2007]. eferences Aires, F., and W. B. ossow (2003), Inferring instantaneous, multivariate and nonlinear sensitivities for the analysis of feedback processes in a dynamical system: Lorenz model case-study, Q. J.. Meteorol. Soc., 129, , doi: /qj Follows, M. J., S. Dutkiewicz, and T. Ito (2006), On the solution of the carbonate system in ocean biogeochemistry models, Ocean Modell., 12, , doi: /j.ocemod Friedlingstein, P., et al. (2006), Climate carbon cycle feedback analysis: esults from the C4MIP model intercomparison, J. Clim., 19, , doi: /jcli Goodwin, P., M. J. Follows, and. G. Williams (2008), Analytical relationships between atmospheric carbon dioxide, carbon emissions, and ocean processes, Global Biogeochem. Cycles, 22, GB3030, doi: / 2008GB Gregory, J. M., C. D. Jones, P. Cadule, and P. Friedlingstein (2009), Quantifying carbon-cycle feedbacks, J. Clim., doi: /2009jcli2949.1, in press. Gruber, N., J. Sarmiento, and T. Stocker (1996), An improved method for detecting anthropogenic CO 2 in the oceans, Global Biogeochem. Cycles, 10, , doi: /96gb Intergovernmental Panel on Climate Change (IPCC) (2007), Climate Change 2007: The Physical Science Basis: Contribution of Working Group I to the Fourth Assessment eport of the Intergovernmental Panel on Climate Change, edited by S. Solomon et al., Cambridge University Press, New York. Ito, T., and M. J. Follows (2005), Preformed phosphate, soft tissue pump and atmospheric CO 2, J. Mar. es., 63, , doi: / Le Quéré, C., et al. (2007), Saturation of the Southern Ocean CO 2 sink due to recent climate change, Science, 316, , doi: / science Levitus, S., J. I. Antonov, and T. P. Boyer (2005), Warming of the world ocean, , Geophys. es. Lett., 32, L02604, doi: / 2004GL idgwell, A., J. Hargreaves, N. Edwards, J. Annan, T. Lenton,. Marsh, A. Yool, and A. Watson (2007), Marine geochemical data assimilation in an efficient Earth System Model of global biogeochemical cycling, Biogeosciences, 4, Sabine, C. L., et al. (2004), The oceanic sink for anthropogenic CO 2, Science, 305, , doi: /science Sutton,. T., B. Dong, and J. M. Gregory (2007), Land/sea warming ratio in response to climate change: IPCC A4 model results and comparison with observations, Geophys. es. Lett., 34, L02701, doi: / 2006GL P. Goodwin and T. M. Lenton, School of Environmental Sciences, University of East Anglia, Norwich N4 7TJ, UK. (p.goodwin@uea.ac.uk) [24] Acknowledgment. This work was supported by the UK Natural Environment esearch Council through the QUEST feedbacks project NE/ F001657/1. 5of5