A global hybrid coupled model based on Atmosphere-SST feedbacks
Andrea A. Cimatoribus, Sybren S. Drijfhout, Henk A. Dijkstra
AA global hybrid coupled model based on Atmosphere–SSTfeedbacks
Andrea A. Cimatoribus ∗ and Sybren S. Drijfhout Royal Netherlands Meteorological Institute, De Bilt, The Netherlands
Henk A. Dijkstra
Institute for Marine and Atmospheric research Utrecht,Utrecht University, Utrecht, The Netherlands
Abstract
A global hybrid coupled model is developed, with the aim of studying the effects of ocean–atmosphere feedbacks on the stability of the Atlantic meridional overturning circulation. Themodel includes a global ocean general circulation model and a statistical atmosphere model. Thestatistical atmosphere model is based on linear regressions of data from a fully coupled climatemodel on sea surface temperature both locally and hemispherically averaged, being the footprintof Atlantic meridional overturning variability. It provides dynamic boundary conditions to theocean model for heat, freshwater and wind–stress. A basic but consistent representation of ocean–atmosphere feedbacks is captured in the hybrid coupled model and it is more than ten times fasterthan the fully coupled climate model. The hybrid coupled model reaches a steady state with aclimate close to the one of the fully coupled climate model, and the two models also have a similarresponse (collapse) of the Atlantic meridional overturning circulation to a freshwater hosing appliedin the northern North Atlantic. ∗ Electronic address: [email protected] a r X i v : . [ phy s i c s . a o - ph ] J a n . INTRODUCTION Since the pioneering work by [1] on a conceptual model of the thermohaline circulation,the problem of the stability of the Atlantic Meridional Overturning Circulation (AMOC)has become one of the main issues in climate research. A collapse of the AMOC is oftenused to explain abrupt changes in past climate records. In recent years, a possible AMOCcollapse in response to increased freshwater forcing in the northern North Atlantic, expectedas a consequence of global warming, has been identified as a low probability but high riskfuture climate event [2–4].An abrupt collapse of the AMOC, in response to a quasi–equilibrium increase in freshwa-ter forcing in the North Atlantic, has been reported in different ocean and climate modelsof intermediate complexity (EMICs) [5]. This implies a non–linear response of the ocean tothe freshwater forcing, with a sudden collapse of the overturning above a threshold valueof the freshwater forcing. The EMIC results are challenged by the model experiments of[6] and by IPCC–AR4 general circulation model (GCM) results, as analysed in [7]. In thelatter, it is found that the AMOC strength decreases approximately linearly in response toa CO increase according to the SRES–A1B scenario and there is no collapse. It must benoted that the simulations to detect possible multiple equilibria regimes of the AMOC inthese GCMs have not been done. The near–linear response to the gradual freshwater fluxperturbation as found in [7] does not rule out the possibility of a sudden collapse with astronger freshwater flux.However, from the GCM results it has been suggested that the existence of a multipleequilibria regime is an artifact of ocean–only models, and in particular of poor (or absent)representation of ocean–atmosphere interactions. In an ocean–only model, the salt advectionfeedback is the central feedback affecting the stability of the AMOC. When an atmosphereis coupled to the ocean model, other feedbacks, due to the ocean–atmosphere interaction,become relevant. The effect of these feedbacks may eventually overcome the effect of thesalt–advection feedback, and remove the multiple equilibria found in ocean–only models andEMICS.In some models, the response of the atmosphere to AMOC changes may indeed act tostabilise the present day AMOC [8, 9]. In particular, the southward shift of the intertropicalconvergence zone would enhance the surface salinity of the Atlantic north of the equator,2ncreasing the northward salinity transport by the northern hemispheric gyres [8, 10]. Thedecrease in the atmospheric temperature of the Northern Hemisphere (NH), as a consequenceof the AMOC collapse, may also play a role [9]. Lower atmospheric temperatures woulddetermine stronger heat extraction from the ocean and, consequently, higher densities ofsurface waters. This effect may be more than compensated by the insulating effect of aNH ice cover extending more to the south [8]. The potential impact of changes in thewind–stress, in particular zonal wind–stress, has recently been investigated in [11], but themagnitude of the changes induced by the wind–stress feedback remains unclear.The question that must be answered is: “Do the atmospheric feedbacks remove themultiple equilibria regime of AMOC, as found in ocean–only models and EMICs?” Thefirst step to try to answer this question is, in our view, to find a simple, but quantitative,description of these atmospheric feedbacks, extending that of box–model representations [12].Only when a quantitative description of the feedbacks is available, it is possible to assessthe impact of the ocean–atmosphere interaction on the stability properties of the AMOC.Studies to isolate the effect of the different feedbacks using a GCM are computationallyexpansive. Furthermore, the complexity of a full GCM can hinder the understanding of therelevant processes in the system. For these reasons, simpler atmospheric models are neededto provide dynamic boundary conditions to full ocean GCMs. Their design can benefit fromthe fact that the atmosphere, on the ocean time scales, can effectively be treated as a “fast”component that adjusts to the ocean anomalies. These coupled models are often referred toas “hybrid coupled models” (HCMs).Since the main known atmosphere–ocean coupled mode of variability is the El Ni˜noSouthern Oscillation (ENSO), HCMs have been developed mainly to study this phenomenon,focusing on the interaction between wind and sea surface temperature ( SST ) in the tropicaloceans. In this framework, the main atmosphere–ocean interaction to include in the model isthe change in the zonal winds over the equatorial Pacific in response to
SST anomalies [13].[14] used a statistical model of the wind–stress based on an empirical orthogonal functiondecomposition of real data, coupled to a regional GCM of the equatorial Pacific. They foundgood forecasting skill for ENSO variability prediction, and HCMs have been extensively usedfor ENSO forecasting since then [15]. Singular value decomposition of observational data hasbeen used in [16], to implement an anomaly model of wind–stress for the equatorial Pacific.The HCM including this model has been used to investigate the role of ENSO–like feedbacks3n seasonal variability. In [17], linear regressions on Ni˜no–3 and Ni˜no–4 indexes are used incombination with a red noise term to study the importance of local wind feedbacks in theTropical Pacific. Singular value decomposition in combination with a stochastic term hasbeen used also in [18]. In these studies, the wind–stress–
SST interaction is generally themain point of interest, but other feedbacks are active as well in the ocean–atmosphere system.Changes in wind speed affect evaporation and, as a consequence, surface temperature [19].Also the freshwater flux is correlated to
SST , through the triggering of convective events inthe atmosphere [20, 21].Our aim here is to develop a global HCM that includes all the main atmosphere–oceanfeedbacks relevant for the stability of the AMOC, in an approach that focuses on the quasi–steady state behaviour rather than on variability. As we want to follow an approach asgeneral as possible, we regress all the surface fluxes pointwise on
SST . Since the
SST variability has a typical extent ranging from regional to basin scale, the atmosphere–oceaninteraction is roughly captured by this local approach. In the HCM, two linear pertur-bation terms dependent on
SST are added to the climatology of the forcing fields of theocean model. A term depending on the local
SST anomaly represents the atmosphere–ocean feedbacks that are acting in a statistical steady state. The large–scale changes in thesurface fluxes due to the collapse of the AMOC can not be described by these local regres-sions alone, but are included through a second linear term that depends on the anomalousstrength of the overturning circulation itself, measured through the NH annual average
SST anomaly. Taken together, the local– and large–scale terms give a simple representation ofthe atmospheric feedbacks which play a role in the stability of the AMOC.As a demonstration of concept, our regressions are based on the output of an EMIC(described in section II). The linear atmospheric feedback representations are presented insection III with results in section IV. The performance of the HCM is compared to the one ofthe original EMIC in section V. With both local and large–scale regression terms, the HCMcaptures the changes in atmospheric fluxes in response to AMOC changes. The advantagesof the HCM over the EMIC are that (i) a more than ten fold decrease in computation timeis achieved and (ii) it gives the possibility to selectively investigate the effect of differentphysical processes on the stability of the AMOC separately.4
I. THE EMIC SPEEDO
The HCM is constructed from data of the EMIC SPEEDO [22], an intermediate com-plexity coupled atmosphere/land/ocean/sea–ice general circulation model. The choice foran EMIC is motivated by the fact that multi–thousand year runs are needed to constructthe HCM, which is at the moment not feasible with a GCM.The atmospheric component of SPEEDO is a modified version of Speedy [23–27], anatmospheric GCM, having a horizontal spectral resolution of T30 with a horizontal Gaussianlatitude–longitude grid (approximately 3 ◦ resolution) and 8 vertical density levels. Simpleparameterisation are included for large–scale condensation, convection, radiation, cloudsand vertical diffusion. A simple land model is included, with three soil layers and up to twosnow layers. The hydrological cycle is represented with the collection of precipitation in themain river basins and outflow in the ocean at specific positions. Freezing and melting of soilmoisture is included.The ocean model component of SPEEDO is the CLIO model [28]. It has approximatelya 3 ◦ × ◦ resolution in the horizontal, with 20 vertical layers ranging in resolution from10 m to 750 m from the surface to the bottom. The horizontal grid of the ocean modelis curvilinear, and deviates from a latitude–longitude one in the north Atlantic and Arcticbasins to avoid the singularity of the north pole. A convective adjustment scheme, increasingvertical diffusivity when the water column is unstably stratified, is used in the model. LIMsea–ice model is included in CLIO [20]. A coupler provides the boundary conditions to thecomponents, and performs the interpolations between the different ocean and atmospheremodel grids in a conservative way.Studies conducted both with an EMIC [29] and with a fully implicit ocean model [30]showed the fundamental role of the salinity budget at the southern boundary of the Atlanticocean in determining the response of the AMOC to freshwater anomalies [31]. The valueof the net freshwater transport by the overturning circulation at 35 ◦ S, shorthanded M ov ,is likely a control parameter that signals the coexistence of two stable equilibria of theAMOC. If M ov is positive, the AMOC is importing freshwater into the Atlantic basin andonly the present–day “ON” state of the overturning is stable. If M ov is negative, freshwateris exported out of the basin by the AMOC, and a second stable “OFF” state of the AMOCexists, with reversed or no overturning in the Atlantic ocean.5n the equilibrium solution of SPEEDO, the Atlantic basin integrated net evaporationis overestimated both with respect to most other models and to the few available obser-vations [31]. Furthermore, the zonal gradient of salinity in the south Atlantic is reversedtoo, with a maximum on the eastern side. The high evaporation over the basin, combinedwith the low freshwater import by the gyre due to the reversed zonal salinity profile, forcethe overturning circulation to import freshwater ( M ov = 0 .
29 Sv) in order to close the bud-get. For these reasons, a small freshwater flux correction is needed in the model for thepurpose of our study, since we are interested in the feedbacks connected with a permanentcollapse of the AMOC. Following the example of [29], a freshwater increase is applied overthe eastern Atlantic, from the southern boundary to the latitude of the Gibraltar strait,summing up to 0 . .
25 Sv[42]. All the corrections are performed asa virtual salt flux, keeping the global budget closed with an increased evaporation in thetropical Pacific and Indian oceans. As a consequence of these corrections, the net freshwatertransport of the AMOC at the southern boundary of the Atlantic basin becomes negative( M ov = − .
069 Sv). As proposed in [29] and [30], this situation may allow the coexistence ofmultiple equilibria of AMOC under the same boundary conditions. Even if the data neces-sary for the definition of the HCM comes from 300 years of simulations alone, in the testingphase of different freshwater corrections applied to reach the regime where the MOC canpermanently collapse, several tens of thousand years of integrations have been simulatedby the EMIC (i.e., changing fresh-water correction and going to equilibrium, testing fluxdiagnostics, testing whether the collapse of the AMOC is permanent), motivating the use ofa fast EMIC.The surface boundary conditions for the ocean are computed from the atmospheric modelas follows. Since the atmospheric boundary layer is represented by only one model layer, nearsurface values of temperature ( T sa ), wind ( (cid:126)U sa , the bold font indicating a vector quantity)and specific humidity ( Q sa ) are extrapolated from the values of the model lowest full layers.Furthermore, an effective wind velocity is defined to include the effect of unresolved windvariability as | V | = (cid:16) (cid:126)U sa · (cid:126)U sa + V gust (cid:17) , where V gust is a model parameter. The ocean modelprovides through the coupler the values of SST , from which also the saturation specifichumidity at the surface ( Q satsa ) is computed through the Clausius–Clapeyron equation. Withthese quantities, the surface boundary conditions for the ocean are computed. The sensible6Φ SQ ) and latent heat (Φ LQ ) fluxes into the ocean are obtained from the bulk formulas:Φ SQ = ρ sa c p C H | V | ( T sa − SST ) , Φ LQ = ρ sa L H C H | V | min (cid:2)(cid:0) Q sa − Q satsa (cid:1) , (cid:3) , (1)where ρ sa is the surface air density, c p and L H are the specific heat of air and the latentheat of evaporation, respectively, and C H is a heat exchange coefficient, a model parameterdepending on the stability properties of the boundary layer. The parameterisation of theradiative fluxes are more complex. For the short–wave (Φ SW ) and long–wave components(Φ LW ), two and four frequency bands are used, respectively. Transmittance is computed foreach band separately, taking into account air density, water content and cloud cover. Thetotal non–solar heat flux (Φ Q ) is just the sum of the different components:Φ Q = Φ SQ + Φ LQ + Φ LW . (2)Separate parameterisation are used for precipitation due to convection (Φ P cv ) and to large–scale condensation (Φ
P ls ). River runoff (Φ R ) is provided by the land model. The netevaporation (Φ E ) can then be computed as:Φ E = Φ LQ /L H − Φ P ls − Φ P cv − Φ R . (3)The wind–stress vector is computed as: (cid:126) Φ U = ρ sa C D | V | (cid:126)U sa , (4)where C D is a drag coefficient. III. LINEAR REGRESSIONS
Our aim is to capture the changes in the atmospheric forcing connected with the changesin the ocean state, that is the atmospheric response to a collapse of the AMOC. As moti-vated in the introduction, we assume that these atmospheric feedbacks can be expressed asfunctions of
SST alone. First, the feedbacks that keep the system in a statistical equilibriumstate are always present, and are expressed in our case as a function of local
SST . Theyare extracted from a 200 years long statistical steady state run (CLIM) of SPEEDO. Thedeparture from the steady state arises during an externally forced AMOC collapse, in asso-ciation with the large–scale
SST footprint of a AMOC decline. The feedbacks involved in7he collapse are different from the ones acting at the steady state. To study the large–scalefeedbacks, a 4000 year experiment was performed, starting from CLIM, with an additional0 . SST . This approach is clearly limited, but it is an approximation that gives a consistentrepresentation of the large–scale feedbacks. The results can be successfully used as boundaryconditions for the ocean–only model, as will be shown below.To force the ocean model, we need five surface fluxes: non–solar heat flux (that includeslong–wave radiation, latent and sensible heat fluxes), short–wave radiative heating, netevaporation, zonal and meridional wind–stresses. The incoming short–wave radiation isnot regressed, and only its average seasonal cycle is retained, since its response to SSTis completely mediated through a cloud cover response that is not well represented in theSpeedy model [22].Two linear models are used for regressing data from CLIM and PULSE. The CLIM datais fitted with: φ ( i, j ) − φ ( i, j ) = p ( i, j ) · (cid:16) SST ( i, j ) − SST ( i, j ) (cid:17) , (5)where φ ∈ (cid:110) Φ Q , Φ E , (cid:126) Φ U (cid:111) is a particular surface flux field to be regressed, p is the model8arameter field to be fitted, i ( j ) is the grid index in the east–west (north–south) directionand the overbar indicates a time average. Monthly data is used in the fit of CLIM data torepresent the seasonal cycle. Note that this formulation is a local regression, by which wemean a regression between quantities that belong to the same grid cell of the model.The natural variability signal caught by regressions from equation (5) is removed fromPULSE data. Only the first 100 years of PULSE are used, since we are interested in theresponse that can approximately be considered linear. The residual signal φ r ( i, j ) can thenbe regressed with a second linear model: φ r ( i, j ) = p ( i, j ) · (cid:16) (cid:104) SST (cid:105) NH − (cid:104) SST (cid:105) NH (cid:17) , (6)where the symbol (cid:104) (cid:105) NH denotes the average over the NH. In this case the regressor is,for all grid cells, the yearly average SST in the NH, a good indicator of the state of theAMOC [9], as figure 1 suggests (bottom panel, dashed line). Yearly mean data is used forthe fit of PULSE. It must be stressed that the last term of equation (6) is the average NH SST for the CLIM run, since we are interested in the deviation from the equilibrium state.Consequently, the intercept is set to zero, since the terms involving p need not to have aneffect when the climate is in a neighbourhood of CLIM.All the regressions are computed with the lm (linear model) function provided in the Rstatistical software, version 2.8.0 [32]. The regressions are computed through a least squaretechnique, and we require a statistical significance higher than the 95 percentile, discardingall the fits with a p–value (provided by lm itself) higher than 0 .
05. This equals to discardinga fit if the probability of having the same result using random data is higher than 5%.When this occurs the fit is considered unsuccessful, and only the climatological value ofCLIM ( φ ( i, j ) in equation (5)) is kept and both p ( i, j ) and p ( i, j ) are set to zero. Theoutput of the fitting procedure shows very weak sensitivity to the chosen significance level.The same regression procedure was applied also to the output of the uncorrected originalSPEEDO model. The results obtained from the two models, with or without freshwaterflux corrections, are consistent on both qualitative and quantitative grounds. A partialexception is the southern ocean and the Labrador sea, where the strength of the feedbacksis different. An analysis of these differences is beyond the scope of the present study, butmay be associated with changes in sea–ice cover in the two models.We now give the formulation of the boundary conditions for the ocean–only model to9e forced by our “climatology with feedbacks”. The surface heat flux into the ocean iscomputed as a combination of the regressions and a restoring term to the climatology:Φ Q ( i, j ) =Φ Q ( i, j ) + p Φ Q ( i, j ) · (cid:16) SST ( i, j ) − SST ( i, j ) (cid:17) + p Φ Q ( i, j ) · (cid:16) (cid:104) SST (cid:105) NH − (cid:104) SST (cid:105) NH (cid:17) +Φ SW ( i, j )+ ρ sa c p (cid:12)(cid:12)(cid:12) V ( i, j ) (cid:12)(cid:12)(cid:12) τ · (cid:0) SST ( i, j ) − SST ( i, j ) (cid:1) , (7)where p Φ Q and p Φ Q are the local and large–scale regression parameters for the heat flux, ρ sa and V ( i, j ) are fixed climatological values and the relaxation time τ is chosen to be 55 daysfor the ocean, consistently with the bulk formula of the coupled model of equation (1).The net evaporation flux is computed in three steps. First, the deviations from theclimatological values, δ Φ E , are computed at each grid cell: δ Φ E ( i, j ) = p Φ E ( i, j ) · (cid:16) SST ( i, j ) − SST ( i, j ) (cid:17) + p Φ E ( i, j ) · (cid:16) (cid:104) SST (cid:105) NH − (cid:104) SST (cid:105) NH (cid:17) , (8)where p Φ E and p Φ E are the regression parameters for the net evaporation flux. Then, theglobal integral of the deviations, ∆Φ E , is computed on the model grid and the budgetimbalance is set to zero. The total freshwater flux reads then:Φ E ( i, j ) = Φ E ( i, j ) + δ Φ E ( i, j ) − ∆Φ E / Σ , (9)where Σ is the ocean surface area.For the wind–stress vector, only the output of the regressions is used: (cid:126) Φ U ( i, j ) = (cid:126) Φ U ( i, j ) + (cid:126)p (cid:126) Φ U ( i, j ) · (cid:16) SST ( i, j ) − SST ( i, j ) (cid:17) + (cid:126)p (cid:126) Φ U ( i, j ) · (cid:16) (cid:104) SST (cid:105) NH − (cid:104) SST (cid:105) NH (cid:17) , (10)where (cid:126)p (cid:126) Φ U ( i, j ) and (cid:126)p (cid:126) Φ U ( i, j ) are the vectors of the regression parameters for local and large–scale regressions respectively, for the two components of the wind–stress. Over sea–ice, afixed climatology of air–ice fluxes is used. When sea–ice is present, weighting is applied bythe model to the surface fluxes multiplying by the fractional ocean area (1 − ε ( i, j )), where ε ( i, j ) is the fractional sea–ice cover of the cell.10he technique described returns the rate of change of the field with SST or (cid:104) SST (cid:105) NH only in those areas where a linear regression is statistically significant. Furthermore, settingthe regression parameters to zero still leaves a constant climatology that can be used asboundary condition for the ocean model. We thus have the complete control over whichfeedbacks are acting at the ocean–atmosphere interface, and we can selectively investigatetheir individual or collective effect. IV. RESULTSA. Local regressions
The fitting procedure for CLIM data is generally successful and the results of the regres-sions on CLIM data are reported in figures 2 and 3.In figure 2, the average value of the regressed fields is reported ( φ ( i, j ) in equation (5)).The total heat flux (including short–wave radiation) is shown in figure 2. The net evaporationincludes the river runoff. The values of the regression parameter p are shown in figure 3 forall the regressed fields. In both figures 2 and 3 the values are weighted by the fractional freeocean surface of the cell to compensate for the effects of average sea–ice cover. The effectof changes in sea–ice cover are not included into the regressions, as the effect of sea–ice istaken into account by CLIO model. As discussed below, the changes in sea–ice can stronglymodify the feedbacks (compare figures 3 and 6).For all the regressed fields, the contribution to the fluxes of the local regression terms canbe important compared to the average value, in particular at the western boundaries andoutside the equatorial and polar regions. This is clear when we consider the SST variabilityon a daily basis; the root of the variance is well above 1 ◦ C everywhere in the subtropicaland subpolar ocean, with peak values of about 7 ◦ C close to the NH western boundaries (notshown).The linear regressions only capture part of the natural variability of CLIM fluxes, butthe error is generally lower than 10% of the original field over a major part of the ocean (notshown).Apart from the standard damping on
SST that also operates in ocean–only models drivenby a prescribed atmosphere, the atmospheric control over the atmosphere–ocean heat flux11ounteracts this damping in many regions, in particular in the tropics and at high latitudes(positive values in figure 3 a). This means that the linear feedback for the heat flux isnot damping the
SST anomalies. Relevant exceptions are the equatorial ocean, the centralnorth Atlantic, the northern portion of the Southern Ocean and other smaller areas. Itshould be noted that in the polar areas, the sea–ice cover determines the effective feedbackin the heat flux, and often changes the sign of the feedback. The exact mechanism of thisfeedback is discussed in more detail in section IV B.To investigate the origin of the pattern of the local heat feedback outside the polar regions,the same regression procedure was applied to each component of the heat flux separately,namely sensible and latent heat fluxes and long–wave radiation (not shown). The changein the latent heat release is the most important component of the heat flux change. Thefeedback of sensible heat flux is slightly weaker in magnitude, and is positive with the onlyrelevant exceptions of the North Atlantic and the equatorial ocean. The long–wave radiationfeedback follows the same pattern, and is the weakest term. As first noted in [33], the signof the heat flux feedback from equation (1) depends to first order only on the relative changeof T sa and SST , if the wind is assumed constant. A positive feedback is possible only if thechange in T sa is larger than the one in SST . This is almost always true in our model inthe areas where the heat feedback is positive, as we find when T sa is regressed on SST (notshown).A plausible explanation of this positive heat feedback, at least at low and mid latitudes,is given by the convection–evaporation feedback mechanism as proposed by [21]. There isa strong resemblance between the patterns of increased convective precipitation and thoseof weaker latent heat loss at higher
SST . This suggests that, in the tropical and sub-tropical areas where a positive heat flux feedback is observed, a positive
SST anomaly isassociated with anomalous convergence of wet air that both contributes to the reductionof evaporation[43] and enhances precipitation if convection is triggered. Regression of sur-face pressure on
SST also supports this hypothesis, since higher
SST s correlate with lowersurface pressure in the tropical and subtropical areas. Regarding net evaporation (figure 3b), a weak increase is observed at higher
SST over most of the ocean. On the contrary, inmost of the tropical areas the increase in convective events leading to increased precipita-tion dominates the freshwater feedback (basically, the blue areas of figure 3 b), as discussedabove. 12n the case of wind–stress, a decreased magnitude is observed in connection with higher
SST (compare figure 3 c and d with the mean fields of figure 2). The term | V | of equation (1)is regressed on the local SST , confirming that over most of the ocean at low and midlatitudes lower than average winds are observed in association with higher than average
SST s (not shown), implying lower heat transfer through the interface. The correlationdecreases moving poleward and the mechanism involved is basically the wind–evaporationfeedback [19], that connects higher evaporation (lower
SST ) with stronger winds. The factthat we do not observe stronger winds where an increase of convective precipitation is foundis not surprising, since the parameterisation of convection does not affect the horizontal windfield [23]. A positive correlation between wind speed and
SST is observed only in the westernpart of the subtropical gyre of the Southern Hemisphere (SH) of the Atlantic ocean, south ofGreenland and in the Labrador sea, in the northeastern part of the subpolar gyre of Pacificocean, and in some other smaller regions. Even though the negative wind feedback is thoughtto be dominant, some evidence for a positive feedback has been found for the Kuroshioextension area, in the northeastern Pacific [34, 35]. The best known wind–
SST feedbackmechanism where the wind response to SST anomalies is central is the Bjerknes’ feedbackin the equatorial Pacific areas, in connection with the ENSO [13]. The fundamental coupledvariability of the equatorial ocean–atmosphere system is that of a decrease of the westernPacific trade winds in response to a positive anomaly of
SST in the eastern equatorialPacific. Even though the model has too low resolution to exhibit a realistic ENSO [22], aweakening of the trade winds in the western and central equatorial ocean is captured by thelinear regressions (figure 3 c) and is consistent with the anomaly patterns connected withENSO [36]. The stronger convective precipitation detected in the western Pacific at higher
SST s may be a sign of anomalous convergence of the low level atmospheric circulation,again in agreement with what shown by [36]. The origin of the dipole structure of themeridional wind feedback between NH and SH (figure 3 d) is basically a reflection of theweaker dominant winds at higher
SST . B. Large–scale regressions
Moving to the results of large–scale regressions, it must be kept in mind in the interpre-tation of the results that the fit is performed only on the residuals of local regressions, not13n the full data of PULSE and that the fit is performed on a decreasing quantity, the NHaverage
SST .The collapse of the AMOC causes a decrease in the NH average
SST of about 1 . ◦ C. Aweaker change of opposite sign is observed over the Southern Ocean (approximately 0 . ◦ C).This NH–SH temperature dipole is a robust feature of different models, and is connected withlower northward heat transport in the Atlantic ocean, as already found in [9]. The changesin the heat flux are mainly captured by the large–scale regression parameter alone. Thiscan be evinced comparing the large–scale heat flux parameter and the diagnosed changesin the flux from the coupled model, and is connected with the larger magnitude of thelarge–scale parameter. The main response of the heat flux after the overturning collapse,not considering changes in the sea–ice cover (figure 4 a), would be that of an increased heatextraction from the ocean in the NH (9 . W/ ( m ◦ C) on average). When the effect of achanging sea–ice cover is included in the computation of the heat feedback (figure 6 b), itssign changes in the high latitudes of the NH ( − . W/ ( m ◦ C) on average in the NH), whichmeans that heat released to the atmosphere decreases. This result is in contrast with whatthe regression parameter p suggests, but consistent with the sign of the effective regressionparameter. The difference is explained below. The net heat flux, weighted by the ice–freearea (1 − ε ), can be written as: φ Q = (1 − ε )( φ Q + ∂φ Q /∂SST + ∂φ Q /∂ (cid:104) SST (cid:105) NH ) . (11) p φ Q is simply ∂φ Q /∂ (cid:104) SST (cid:105) NH while the effective parameter is: p φ Q ,eff = ∂ ( φ Q · (1 − ε )) /∂ (cid:104) SST (cid:105) NH = (1 − ε ) ∂φ Q /∂ (cid:104) SST (cid:105) NH − φ Q ∂ε/∂ (cid:104) SST (cid:105) NH = (1 − ε ) p φ Q − φ Q ∂ε/∂ (cid:104) SST (cid:105) NH . (12)The second term on the right hand side of equation 12 describes the changes in sea–ice coverin response to SST changes. This term is larger than the first term over most of the NorthernNorth Atlantic. Sea–ice cover changes determine the sign change in the large–scale heatfeedback term. A similar reasoning holds for the local feedback. In general, the NH–SH heatflux dipole seen in figure 4 a is driven by the decrease of NH near–surface temperature, thatfollows a pattern similar to that of
SST (figure 5), but with stronger sensitivity to AMOCchanges everywhere except for the southern mid latitudes. This amplification of the
SST
SST and atmospheric temperature would tend to produce an increased upward heat fluxin the NH (figure 4 a). This increased heat loss is more than counteracted by the decreasein open ocean area; the increased ice cover effectively drives the cooling of amospherictemperatures above the North Atlantic. This can be seen from the changes in the heat fluxdiagnosed from the coupled model including the insulating effect of sea–ice (figure 6 c) andthis is confirmed by the large–scale regression parameter computed including the effect ofsea–ice (figure 6 b). This “effective” regression parameter is the result of the same fittingprocedure, applied in this case to the surface heat flux weighted by the actual sea–ice coverand not to the complete heat flux. The results for the local (large–scale) regression arethose shown in figure 6 a (b). As a consequence, this regression parameter gives a betterrepresentation of the feedbacks that the ocean effectively senses (including the effect of sea–ice). Note that the HCM only uses p and p , and not the effective response coefficients. Thechanges in sea–ice cover result from explicitly resolved ice dynamics and thermodynamics.At low and mid latitudes in the NH the changes are due to reduced evaporation inresponse to lower SST and, at low latitudes, to lower wind speed. The changes in thesurface long–wave radiation budget are smaller in magnitude, and amount to an increasednet emission of long–wave radiation almost everywhere in the NH except from the GIN seas.This effect has been observed in other model experiments and is connected with the reduceddownward long–wave radiation flux over compensating the decreased black body emissionat lower
SST s [37]. The decrease in the downward long–wave flux is an effect of a drieratmosphere, and partly balances the reduced latent heat flux. These changes in heat fluxamount to a positive feedback on an AMOC anomaly when the effect of sea–ice is included,favouring a decrease of the surface density in the deep water formation areas of the NorthAtlantic in connection with weaker overturning circulation.The patterns of the net evaporation change (figure 4 b) are consistent with the findingsof [9] (their figure 9 e, with opposite sign). The AMOC collapse causes a reduction of netevaporation over the tropical and subtropical NH and over the tropical SH, due to lower
SST s (figure 5). In the few areas where an increase in evaporation is observed (basicallythe north equatorial oceans), this is due to stronger winds. At low latitudes, a significantchange of the precipitation patterns also plays a role, with a dipole pattern centred around15he equator, and positive to the south. This southward shift of the intertropical convergencezone (ITCZ) produces the strongest precipitation increase over the Amazon river basin. Thisresponse of the Hadley cell is connected with the southward shift of the latitude of maximumheating, and has been observed consistently in different climate models [9, 10, 37] and inan idealised framework too [38]. A similar, though weaker, pattern of precipitation changeis observed in the Pacific and Indian oceans. The increased precipitation over the entiresouthern Atlantic more than compensates for the increased evaporation due to higher
SST in this part of the basin. A slow down of the hydrological cycle over Europe is detected as twonegative peaks off the coast of France and in the North sea. On a global scale, the regressionsof PULSE residuals determine an evaporation increase of 0 . mm/ ( day ◦ C). Therefore, ourlinear approach is not conserving the ocean water mass and needs a budget closure correctionwhen used as boundary condition for the ocean, as implemented in equation (9).In the case of wind–stress, the response of the atmosphere is somewhat less straightfor-ward to understand, and it deserves a longer discussion. For what concerns the meridionalwind–stress, the changes in the low and mid latitudes are driven by the response of the zon-ally averaged temperature profile to the AMOC collapse. The equator to pole temperaturedifference increases by approximately 4 ◦ C in the NH. In the SH, the opposite is true, witha smaller change. These changes are clearly mirrored in the zonally averaged wind–stress.Stronger southward wind blows on the ocean with a collapsed AMOC in the NH up to 50 ◦ N.The situation is similar in the SH, but with a weaker circulation down to 40 ◦ S, followingthe opposite change in the zonally averaged temperature. The zonal winds over the South-ern Ocean are also reduced. A more peculiar feature is observed in the north Atlantic. Apressure anomaly dipole between Greenland and northeastern Atlantic develops, with pos-itive sign to the east, in connection with the differential cooling between these two regions(stronger cooling over eastern Atlantic). This in turn determines an anomalous anticycloniccirculation centred north of Scotland, with impacts on both the meridional and zonal wind–stress. Referring to our regressions, the changes due to the AMOC collapse in the tropicalregions are already caught by the local regression parameter ( p , figure 3 c and d). This canbe understood considering that the change in SST due to the AMOC collapse (figure 5) isa dipole centred at the latitude of the southern tropic (at the equator in the Atlantic ocean)and positive to the south of it, with an amplitude of a few degrees. In fact, the changesdue to the overturning collapse are overestimated by the local regressions, and p (figure 416 and d) amounts to a correction opposite to p . The positive values of p for meridionalwind–stress in the intertropical regions (figure 4 d) signal the southward shift of the ITCZ,that is an anomalous southward wind with decreasing NH average SST , not representedby the local regressions. Also the anomalous anticyclonic circulation is reproduced in thelarge–scale regressions by the dipoles over northeastern Atlantic (positive to the south andto the east). The impact on AMOC stability of wind–stress feedbacks has been investigatedin the recent paper by [11], where a simple zonally averaged atmospheric model was used.Even though it is quite difficult to compare their results with the results from a GCM likeSPEEDO, the general picture is similar. The atmospheric circulation in the NH is strength-ened, while the opposite is true for the SH. The magnitude of the changes in SPEEDO isclose to their lowest estimates.
V. HCM TEST
The HCM consists of the ocean component of SPEEDO (i.e., CLIO) and the dynamicboundary conditions described in the previous section. It was tested by comparing its resultswith the original SPEEDO model. The first experiment (regCLIM) starts from the end stateof the ocean of the CLIM run. The model is forced only by the local regressions (values of p set to zero) for 3000 years. Next, all the large–scale regressions are also switched on, andthe model runs for 2000 years more.Results of the regCLIM run are shown in figure 7. On the top panel, the deviation fromCLIM mean value of the global average sea temperature (salinity) is reported in black (red).The area shaded in grey on the left margin of figure 7 marks the (200 years) data of theCLIM run. The light blue area marks the first 3000 years of the regCLIM of the ocean–onlymodel, with only local regressions active. To estimate the theoretical equilibrium state ofthe model, we fit the global average sea temperature and salinity from years 1201–5200 ofregCLIM with the function: f ( t ) = a sin (cid:18) t + a a (cid:19) exp (cid:20) − t + a a (cid:21) + B, (13)where t is time, a , . . . , a are the fit parameters, and B is a constant background thatrepresents the state of the system at infinite time. The theoretical equilibrium state com-puted from this procedure is 0 . ◦ C colder and 7 . · − psu fresher than the coupled CLIM17un. Little drift, but a substantial reduction of the variability due to the restoring term,is observed in the global average SST (figure 7, black line in the bottom panel). The NHaverage
SST increases by 0 . ◦ C (difference between last 200 years of regCLIM and CLIM).The maximum of the AMOC is, at the end of regCLIM, approximately 1 Sv weaker thanin the CLIM run (bottom panel of figure 7, in red). The AMOC, as the left bottom panelof figure 8 shows, is weaker and approximately 500m shallower in the HCM. The freshwatertransport by the AMOC at 30 ◦ S in the last 200 years of regCLIM (grey shaded area on theright of figure 7) is M ov = − .
06 Sv. To keep M ov <
0, the freshwater corrections describedin section II are 50% stronger than in the fully coupled model.To investigate the origin of the changes in the AMOC strength, we diagnose the surfacefluxes of density for the CLIM and regCLIM runs. The surface density flux Φ ρ can beestimated using the formula [39, 40]:Φ ρ = − αc p Φ H + ρ β Φ E · SSS − SSS · − , (14)where α = − /ρ ( ∂ρ/∂T ), β = 1 /ρ ( ∂ρ/∂S ), Φ H is the total surface heat flux into the ocean(Φ H = Φ Q + Φ SW ), ρ is the reference water density, SSS is the surface salinity measured inppt. The density flux into the ocean is shown in figure 9 in units of 10 − · kg/ ( m s ) for theCLIM run (top panel). The effect of sea–ice cover is taken into account in the computationof the density flux, and the model grid (distorted over north Atlantic and Arctic) is usedto avoid interpolation errors. The difference between the fluxes from the regressions in thelast 200 years of regCLIM and CLIM is reported in the bottom panel of figure 9. Evenif the changes are generally small (note the different colour scales in the figure), when thedifference is averaged over the GIN seas and the Arctic Mediterranean (taking as southernboundaries the Bering strait and the latitude of the southern tip of Greenland), we find thatthe density flux decreases by 2 · − kg/ ( m s ). This value represents a 10% decrease ofthe average density flux over the same area, that nicely fits the relative change in maximumoverturning strength.The definition of the HCM, that does not include any high frequency stochastic compo-nent, causes a strong reduction of variability, but low frequency variability of the systemseems to be preserved. To show this, a multi taper method (MTM) analysis [41] was per-formed on the time series of the maximum of overturning streamfunction of the Atlantic.The analysis is performed on the yearly data of CLIM (a longer control run is used, 100018ears long) and the last 1000 years of regCLIM (figure 10). At the lower end of the spec-trum, energy is concentrated at similar frequencies in the two models, below approximately0 .
02 year − . At higher frequencies, instead, the broad peaks found in the HCM between0 .
02 year − and 0 .
09 year − are not present in the original coupled model, while the peaksfound above 0 . − in CLIM are lost in the HCM. Also the first empirical orthogonalfunction of SST computed from the HCM resembles the one from CLIM only in the north-western Atlantic. This approach is thus limited when the internal variability of the ocean isof interest, but in the present work the focus is only on the quasi–equilibrium response. At-mospheric noise and lagged correlations are probably needed to better represent and excitethe modes of variability of the system.As a final test, a pulse experiment was performed in the HCM. In this test, that willbe shorthanded as regPULSE, we apply the same freshwater anomaly as in PULSE (seesection III), also increased by 50% as the corrections already applied in regCLIM. Theinitial conditions for regPULSE are provided by the final state of regCLIM: year 5200 offigure 7. In regPULSE, as in PULSE, the anomaly is applied for 1000 years, letting themodel reach a new equilibrium afterwards. We focus our analysis on the response of thesystem during the first hundred years of the run, where the regressions are expected to besignificant.The AMOC maximum for regPULSE is reported in figure 11 as a dashed line. Theresponse of the AMOC in regPULSE, when measured by this quantity, follows closely theone in PULSE. The only substantial differences are its lower initial condition and the weakervariability of the regPULSE signal. The weaker variability of regPULSE signal is no surprise,considering the fact that our regressions do not add any high frequency variability to thesystem, depending only on
SST .Looking at the entire overturning streamfunction of the Atlantic, the results are alsoencouraging. On the right hand side of figure 8, the overturning of the collapsed state thatis established after the first 100 years of the pulse experiment are compared in PULSEand regPULSE. In the top right panel of figure 8, the streamfunction of years 101–110of PULSE run is shown as a reference. The difference between regPULSE and PULSEduring the same years is reported below. The results of the HCM are in good agreementwith those of SPEEDO, showing a reversed cell only slightly weaker than in PULSE. Thelargest differences are at the southern border of the Atlantic basin, likely in connection19ith the general underestimation of the density flux over the southern ocean (figure 9).For what concerns the barotropic streamfunction during the pulse experiments, the onlysignificant differences are found in the southern ocean (not shown). Over the Pacific sectorof the Southern ocean, the underestimation of the barotropic streamfunction representsabout 20% of the transport predicted by PULSE. This discrepancy is probably connectedwith an overestimation of the decrease of the southern westerly winds in the regressed forcingin response to the collapse of the AMOC.
VI. SUMMARY AND CONCLUSIONS
In this paper we described a new technique for developing a global HCM that includesa basic representation of the feedbacks due to the ocean–atmosphere interaction, relevantfor the stability of the AMOC. The steady state feedbacks of the system were representedthrough linear regression terms depending on the local deviation of
SST from its meanvalue. The large–scale response of the atmosphere to an externally forced AMOC collapseis included with a regression on the NH hemisphere average temperature.The results of the regressions give a quantitative representation of the changes in thesurface fluxes that is consistent with other model experiments [9, 10, 37]. In particular,we can detect the changes in heat flux at the surface due to the cooling of the NH after aAMOC collapse. Significant changes are observed also in the freshwater flux, in connectionwith the response of the general circulation in the atmosphere to the changes in the equatorto pole temperature profile, that determine the response of the winds as well. The boundaryconditions computed in section III, were then successfully used as a dynamic forcing for anocean–only model.This ocean forced by a “minimal atmospheric model” guarantees a decrease of the com-putation time between ten and twenty times with respect to the original coupled model.The ocean model forced by the regressions which form the HCM reaches a steady state closeto the one of the original coupled model. Furthermore, an experiment is performed wherethe AMOC is collapsed in both the fully coupled model and in the ocean forced by theregressions. The two results are in good agreement. This enables us to proceed to furtheruse the HCM to investigate the impact of the atmospheric feedbacks on the stability of theAMOC. In particular, the formulation of the forcing shown in section III enables us to selec-20ively choose which fluxes are fixed to a climatological value, and which ones are computeddynamically as a function of
SST . We can thus investigate the impact of each feedbackseparately on quantitative grounds, and we can aim at a deeper understanding of the mainphysical processes involved in the collapse and recovery of the AMOC. It is also importantto analyse the response of the HCM to weaker freshwater anomalies. Reducing the anomalythat forces the AMOC collapse, the atmospheric feedbacks are likely to play an increasinglydominant role.The model can obviously be extended in many ways. Using higher order (nonlinear)models in the data fit is unlikely to be worth the effort. The study of the role of atmosphericnoise and of correlations lagged in space and time, and their inclusion in the HCM, mayinstead greatly improve the representation of atmosphere–ocean interaction with respect tothe variability of the AMOC.As a final remark, we want to stress that our technique to design the HCM is general.We do not rely on any ad–hoc assumption connected with the nature of the EMIC that wasused for this work. For this reason, this technique is potentially interesting for many otherproblems (apart from the stability of the AMOC) where a computationally efficient, simplerepresentation of the ocean–atmosphere interaction is desired. For instance, instead of usingdata from the atmospheric component of SPEEDO, the ocean component could be coupledto a statistical atmosphere derived from a state–of–the–art coupled climate model or fromreanalysis data, at least for the computation of local regressions.
Acknowledgments
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Sv . Sv y –axis). NH average SST in ◦ C (right y –axis) for PULSE (dashed black line). igure 2: Average value of the regressed fields from CLIM data ( φ ( i, j ) in equation (5)), weightedby the fractional ocean area (1 − ε ( i, j )). a) Total heat flux in W/m , positive downwards. b)Net evaporation in mm/day . c) and d) are the zonal and meridional components of wind–stressrespectively, in 10 − · N/m . igure 3: As in figure 2, but for the local regression parameter p . The units are the same offigure 2, divided by ◦ C. In panel a, only the non–solar heat flux is considered. igure 4: As in figure 2, but for the large–scale regression parameter p . The units are the sameof figure 2, divided by ◦ C In panel a, only the non–solar heat flux is considered. In panel b, thesignal of the freshwater pulse has been removed from the source data. igure 5: Difference in SST ( ◦ C) between the years 91–100 of PULSE experiment and the meanstate of CLIM. igure 6: Effective feedbacks for heat flux (short wave radiation excluded), when changes in sea–iceare considered (see text). Effective regression parameters for the heat flux, computed includingthe effect of changes in sea–ice ( p in panel a and p in panel b). Also the change in the heat flux,as directly diagnosed from the coupled model, is shown in panel c, computed as the difference inice–weighted heat flux from years 91-100 and 1-10 of PULSE. Note that a different color scale isused in the top panel. igure 7: Deviation from CLIM average in regCLIM of four quantities: global average sea temper-ature (top panel, black, left y –axis), global average salinity (top panel, red, right y –axis), globalaverage SST (bottom panel, black, left y -axis) and maximum AMOC (lower panel, red, right y –axis). igure 8: Overview of overturning streamfunction in the various models. In the top panels, AMOCfor the CLIM mean state (top left) and for years 101 to 110 of PULSE (top right) are shown. Theshaded contours are every 2 Sv, the red filling is for positive values, blue for negative. The thickline is the zero contour. In the left bottom panel, the difference of the overturning streamfunctionbetween the last 200 years of regCLIM and the CLIM mean state is shown. In the right bottompanel, the difference of the overturning streamfunction between years 101 to 110 of regPULSE andPULSE runs. The contours in the lower panels are every 1 Sv. igure 9: In the top panel, the surface density flux for CLIM is shown in 10 − · kg/ ( m s ). Inthe bottom panel, the difference of the same quantity between the last 200 years of regCLIM andCLIM. Different colour scales are used in the two panels. In the figure, the grid of the ocean modelis used (distorted in the north Atlantic and Arctic), to avoid interpolation errors. .001 0.01 0.1110 raw median 90% 95% 99% MTM Spectrum: CLIM0.001 0.01 0.10.0010.010.11 raw median 90% 95% 99% MTM Spectrum: regCLIM Figure 10: MTM spectra of the time series of the maximum AMOC (solid lines) for CLIM (toppanel) and regCLIM (bottom panel). The dashed smooth lines represent, from the lowest to thehighest, the estimated red noise background and the median, 90%, 95% and 99% significance levelsassociated with it. In both cases, the resolution is (5 years ) − and 7 tapers were used. Time seriesare 1000 years long. igure 11: Maximum AMOC for first 200 years of PULSE (full line) and regPULSE (dashed line)in Sv.igure 11: Maximum AMOC for first 200 years of PULSE (full line) and regPULSE (dashed line)in Sv.