Polar Amplification in CCSM4: Contributions from the Lapse Rate

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Polar Ampliﬁcation in CCSM4: Contributions from the Lapse Rate and Surface Albedo Feedbacks

RUNE G. GRAVERSEN Department of Meteorology, Stockholm University, Stockholm, Sweden

PETER L. LANGEN Danish Meteorological Institute, Copenhagen, Denmark

THORSTEN MAURITSEN Max Planck Institute, Hamburg, Germany

(Manuscript received 10 September 2013, in ﬁnal form 7 January 2014)

ABSTRACT

A vertically nonuniform warming of the troposphere yields a lapse rate feedback by altering the infrared irradiance to space relative to that of a vertically uniform tropospheric warming. The lapse rate feedback is negative at low latitudes, as a result of moist convective processes, and positive at high latitudes, due to stable stratification conditions that effectively trap warming near the surface. It is shown that this feedback pattern leads to polar amplification of the temperature response induced by a radiative forcing. The results are obtained by suppressing the lapse rate feedback in the Community Climate System Model, version 4 (CCSM4). The lapse rate feedback accounts for 15% of the Arctic amplification and 20% of the amplification in the Antarctic region. The fraction of the amplification that can be attributed to the surface albedo feedback, associated with melting of snow and ice, is 40% in the Arctic and 65% in Antarctica. It is further found that the surface albedo and lapse rate feedbacks interact considerably at high latitudes to the extent that they cannot be considered independent feedback mechanisms at the global scale.

1. Introduction (Serreze and Francis 2006; Graversen et al. 2008; Serreze and Barry 2011). The amplification may be due to the A forcing of the climate system due to a radiative forcing and feedback processes being stronger at high imbalance at the top of the atmosphere (TOA) results in latitudes. But it may also be a consequence of other a change of Earth’s surface temperatures. This temper- processes that redistribute energy within the climate ature response may activate feedback processes within system, and that are modified due to the forcing. For the climate system that either further enhance or dampen example, changes of the ocean and atmospheric energy the TOA imbalance, and hereby further increase or de- transport in response to a forcing induce warming at crease the temperature response. some latitudes and cooling at others (Graversen 2006). The temperature response will not be constant over Although such changes can have large local effects, they Earth’s surface but tends to be larger at higher than at constitute only weak global radiative feedbacks as they lower latitudes, which is referred to as polar temperature contribute little to the global-mean TOA imbalance. amplification (Manabe and Wetherald 1975; Hansen Many studies find that the meridional atmospheric en- et al. 2005; Holland and Bitz 2003). Observations reveal ergy transport does not contribute to polar amplification that the ongoing global warming is amplified in the Arctic but rather damps it (Hwang et al. 2011; Koenigk et al. 2013; Skific and Francis 2013), whereas other studies point in the opposite direction (Alexeev et al. 2005; Corresponding author address: Rune Grand Graversen, Department of Meteorology, Stockholm University, S - 106 91 Langen and Alexeev 2007; Graversen et al. 2008). In fact, Stockholm, Sweden. the sign of the energy transport is model dependent; E-mail: [email protected] models with weak Arctic warming tend to exhibit an

DOI: 10.1175/JCLI-D-13-00551.1

Ó 2014 American Meteorological Society Unauthenticated | Downloaded 09/28/21 06:24 AM UTC 4434 JOURNAL OF CLIMATE VOLUME 27 increased transport, and vice versa (Pithan and Mauritsen In the PRP approach, the radiation code is run in a 2014). standalone mode with fields associated with a given Forcings associated with a change of the atmospheric feedback changed to a perturbation level and all other content of CO2 or a change of the solar constant do not fields kept to a control level. For instance, the albedo directly contribute to polar temperature amplification, feedback can be estimated by running the radiation code since the induced radiative imbalance at TOA is larger with surface albedo from a 23CO2 climate and all other at lower than at high latitudes (Hansen et al. 2005). In fields from a 13CO2 climate. The kernel method is sim- contrast, some feedback processes are believed to con- ilar to the PRP approach, but here a unit perturbation of tribute to the amplification—for instance, the surface the fields associated with a given feedback is considered albedo feedback (Arrhenius 1896) and the lapse rate in order to obtain what is referred to as radiative kernels. feedback (Manabe and Wetherald 1975), both of which These kernels can be multiplied by the actual perturba- are examined here. The water vapor feedback, which tion of the fields in question, normalized by the temper- strongly enhances the global temperature response ature change at the surface, in order to obtain the (Arrhenius 1896; Held and Soden 2000), seems most feedback parameter. An advantage of the kernel method active at low latitudes (Langen et al. 2012), whereas is that the radiative kernels are to some extent in- the feedback associated with cloud changes is more dependent of models (Soden et al.2008); when the ker- uncertain. nels are already determined, it is straightforward and Although the tropospheric temperature will change in computationally inexpensive to calculate the feedback response to a forcing, the change may not be constant parameters. with height. The difference in temperature change with The online method wherein feedbacks are suppressed height gives rise to the lapse rate feedback. Because of in climate models has been applied earlier in order to the Clausius–Clapeyron relationship between tempera- study the surface albedo feedback (Hall 2004; Graversen ture and water vapor saturation pressure, the saturated and Wang 2009; Mauritsen et al. 2013), the water vapor mixing ratio of water vapor increases more at lower feedback (Schneider et al. 1999; Hall and Manabe 1999; than at upper levels in the troposphere when Earth is Langen et al. 2012; Mauritsen et al. 2013), and the cloud warming. In regions where strong convection is present, feedback (Vavrus 2004; Langen et al. 2012; Mauritsen such as at tropical latitudes, this leads to an increase of et al. 2013). In addition to studying the effect of the latent heat release and warming of the upper tropo- feedbacks, Langen et al. (2012) and Mauritsen et al. sphere (Hansen et al. 1984), which results in enhanced (2013) also tested the notion that the total temperature radiation back to space, and in a more efficient cooling change can be split into parts that can be attributed to of Earth. This contributes to a negative lapse rate feed- each of the feedbacks. Both studies concluded that this back. At the high latitudes, stable stratification conditions was indeed the case for the feedbacks considered. in the lower troposphere result in a larger warming of the In the present study we lock the lapse rate and the near-surface air than of the upper troposphere (Manabe surface albedo feedback. As far as the authors know, it is and Wetherald 1975), which contributes to a regionally the first time the lapse rate feedback has been sup- positive lapse rate feedback. Hence the lapse rate feed- pressed in a climate model. back is believed to be negative at low and positive at high latitudes, which leads to Arctic amplification (Pithan and 2. Model description Mauritsen 2014). In the present study the lapse rate and the surface The Community Climate System Model, version 4 albedo feedback are suppressed by locking the lapse rate (CCSM4; Gent et al. 2011), from the National Center for and the surface albedo one by one and in combination in Atmospheric Research (NCAR) is used. The model system a state-of-the-art climate model. Hereby the full effect includes submodels for the atmosphere, land surface pro- on the climate system due to each of the feedbacks is cesses, sea ice, and ocean. The atmosphere model has a fi- investigated. The contribution from these feedbacks to nite-volume dynamical core with 26 vertical layers and ;28 the polar amplification and the interactions between the horizontal resolution. It is run both in a slab-ocean mode feedbacks are studied. Feedback parameters that are (SOM) and a data-ocean mode (DOM), where in the latter assumed to be unique for each feedback (Hansen et al. theseasurfacetemperaturesandtheseaicearefixedto 1984) are estimated directly, as an alternative approach a climatology. In the SOM version, the ocean part includes to the indirect offline methods, such as the more com- an isothermal mixed layer only, which has a fixed horizontal monly used partial radiative perturbation (PRP) method transport of energy. The horizontal ocean energy transports (Wetherald and Manabe 1988) and the radiative kernel in the slab-ocean model, often referred to as the q fluxes, are method (Soden et al. 2008). determined from the climatology of an equilibrium run

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FIG. 1. Globally averaged, annual-mean (a) SAT and (b) sea ice extent as a function of model year for all slab- ocean experiments, the ocean–atmosphere coupled control run, and the data ocean control run with ﬁxed sea surface

temperatures and sea ice (SST/SI). The slab-ocean experiments are shown both for a 13CO2 and 23CO2 climate for the free experiment, the SAT-based locked LR, the TrMT-based locked LR, the locked SA, and the experiment with both SA and SAT-based LR locked. including a full dynamical ocean model (Bitz et al. 2012). feedback is suppressed. For each version the climate

The q fluxes are given as the climatological mean of the response to a CO2 doubling is estimated. Subsequently imbalance between the ocean mixed-layer energy change, the response is compared between versions with a feed- and the energy flux into the ocean across the atmosphere– back suppressed and versions where it is included, in ocean and ice–ocean interface and from river discharge. The order to investigate the feedback in question. q fluxes as well as the depth of the mixed layer were based on In Fig. 1 time series of the global-mean and annual- the climatology from the last 45 years of a 560-yr control run. mean SAT and sea ice extent are shown for all SOM For the DOM version, the sea surface temperatures (SSTs) experiments as well as for the coupled ocean model and and sea ice are taken from the same 45-yr coupled-model the DOM control runs. The 13CO2 experiments with climatology. Annual means of the globally averaged surface locked lapse rate feedback are initiated at year 20 from air temperature (SAT) and sea ice extent from the coupled corresponding experiments with the feedback active. In model and the DOM control runs are shown in Fig. 1 along the 23CO2 experiments, the CO2 is doubled instanta- with the results from all SOM experiments. neously at the beginning of the year 30. The 13CO2 The model is run in a 13CO2 and a 23CO2 configu- locked lapse rate experiments drift up to 1 K relative to ration with the atmospheric CO2 level set to 284.7 and the control run, whereas the locked surface albedo ex- 569.4 ppm, respectively, where the former represents periment shows negligible drift. Note that the climate the preindustrial conditions. In these two configura- response in a world with the lapse rate feedback sup- tions, experiments are undertaken with locked lapse pressed is estimated by comparing the 23CO2 and rate (LR), with locked surface albedo (SA), with both 13CO2 experiments that both have the lapse rate locked. locked, or with both free. The drift of the suppressed lapse rate experiments relative to the free experiments has no impact on the results as long as the drift is the same in both the 13CO and the 3. Experiments 2 23CO2 experiments, which is assumed in the present The surface albedo and the lapse rate feedbacks are study. The experiments are investigated based on 80-yr investigated by designing model versions where a given climatologies over the years 81–160.

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All experiments are repeated in a DOM configuration. other studies and the results can therefore be compared. These experiments are run for 70 years and 50-yr cli- Note that a fundamental difference between the ap- matologies are taken over the years 21–70. The 13CO2 proaches is that in the SAT-based suppression of the DOM control experiment is shown Fig. 1. The nomen- feedback, the tropospheric warming is locked to the clature of the experiments indicated in the legend of the warming at the surface, whereas in the TrMT approach figure is used throughout this paper. the troposphere may warm or cool freely relative to the surface, but in a vertically homogeneous manner. In the a. Locking of the lapse rate TrMT approach, the longwave flux to the surface is esti- The lapse rate feedback is suppressed by locking the mated from the locked lapse rate profiles, whereas in the tropospheric lapse rate in the longwave radiation code. SAT approach it is not. This is because the TrMT ap- In the present study, two ways of regarding the lapse rate proach is designed to suppress the feedback between the feedback are investigated, the tropospheric mean tem- surface and the atmosphere, while the SAT-based lapse perature (TrMT)-based feedback and the SAT-based rate feedback is regarded in a radiative feedback context; feedback. for that reason only the TOA fluxes are relevant. Variations in the vertical distribution of the tropospheric warming impact the atmospheric radiation to space and to 1) THE SAT-BASED FEEDBACK the surface. Hereby the tropospheric warming structure For the purpose of suppressing the lapse rate feedback influences the atmospheric cooling ability and the warming using the SAT-based method, longwave radiation to of the surface. In the polar regions stable stratification space is calculated from locked lapse rate temperature conditions often prevail. This hampers vertical mixing of profiles using the longwave radiation model code. In the troposphere and implies that a forcing-induced energy these profiles, the temperature changes at the tropo- input at the surface leads to an amplified warming of the spheric levels are set equal to the SAT changes, whereby near-surface troposphere relative to the upper tropo- the lapse rate in the troposphere is held fixed. The spheric levels. In comparison to a vertically homogeneous locked lapse rate is obtained by adding the SAT change warming, such an inhomogeneous warming structure to the climatological temperature profile: causes a different cooling ability of the atmosphere by 5 1 2 modifying the atmospheric radiation to the surface and Tlock(z) Tclim(z) (TS TSclim), (1) to space. In addition, in the polar regions the inhomogeneous warming structure contributes to surface where Tlock(z) is the temperature profile with a locked warming, since this structure compared to a vertically lapse rate, Tclim(z) and TSclim are 13CO2 climatologies homogeneous warming induces more radiation toward of the temperature profile and SAT, respectively, and the surface. Here we explore the feedback associated TS is the SAT simulated online by the model. All fields with the tropospheric warming being distributed inho- are functions of horizontal grid points and time, and mogeneously with height. We explore the feedback re- z indicates height. The climatological fields are from sponse in terms of atmospheric radiative cooling and a 70-yr climatology of a slab-ocean control run with all surface warming. This TrMT-based lapse rate feedback is feedbacks active and a 13CO2 climate. These have an suppressed online in the model by substituting the long- hourly resolution that corresponds to the frequency of wave radiation to space and at the surface with estimates the call to the radiation code. Hence Tclim(z) and TSclim based on temperature profiles, where the temperature include one year of data and are functions of the day of changes at all levels in the troposphere are equal to the the year, and the hour of the day. tropospheric mean change. In practice the longwave radiation code is run twice The SAT-based feedback is the traditional way of re- per radiation call; first in its original form using the free garding the feedback. Here we explore the feedback as- temperature profile simulated by the model T(z), and sociated with tropospheric temperature changes being second with T(z) substituted by Tlock(z). From the two different from the temperature change at the surface. The calls, the TOA longwave flux difference is determined. feedback is considered solely as a radiative feedback. This energy difference constitutes the effect on TOA Radiative feedbacks cause an alteration of the energy radiation associated with the locked lapse rate. The balance at TOA. Therefore, when suppressing the SAT- longwave flux to space is estimated by the model for based lapse rate feedback, only the longwave radiation to diagnostic purposes only. To take the energy difference space and not that to the surface is substituted. into account, and hereby suppressing the lapse rate These are two ways of regarding the lapse rate feed- feedback, an atmospheric warming rate, Q(z), is imple- back; many others may be defined. The definition of the mented between ps and ptr, the pressure at the surface SAT-based feedback applied here is consistent with and at the tropopause, respectively. The warming rate,

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FIG. 2. Zonal-mean and annual-mean climatologies of the tropopause height in the 13CO2 (red line) and the 23CO2 (white line) free experiment as a function of latitude. Also displayed is the climatology of the atmospheric temperatures from the 13CO2 climate (shading) as a function of latitude and pressure.

Q(z), is chosen to be constant over the tropospheric are active are shown in Fig. 2 for both the 13CO2 and levels, whereby, the dry-static stability of the troposphere 23CO2 case along with the temperature field from the is unaffected by Q(z). The vertical integral of Q(z)equals 13CO2 experiment. the TOA longwave radiation difference: In summary, in this design of suppressing the lapse ! rate feedback, the only online change to the model is ð 21 p s a shift of the energy with a constant amount over the hQ(z)i 5 dp/g (Lt 2 Lt ). lock tropospheric column. The point is that this energy shift ptr offsets the TOA energy flux associated with the lapse t t rate feedback. Note that the radiative warming/cooling Here L and Llock is longwave radiation up at TOA based on the free and locked temperature profiles, respectively, rates at each atmospheric level associated with the model and the brackets hi indicate the mass-weighted vertical temperature profiles are still used online in the model. In average over the troposphere: principle the lapse rate feedback may be suppressed by ! taking these warming/cooling rates from the locked lapse ð 21 ð ps ps rate profiles instead of implementing Q(z). However, this hX(z)i 5 dp/g X(z) dp/g. approach would likely have a large undesired effects on p p tr tr other variables important for the climate such as water vapor and clouds, which is not the intention. Again all fields are functions of horizontal grid points and time. 2) THE TRMT-BASED FEEDBACK For the tropopause height, a definition from the World The TrMT-based method is similar to that imposed Meteorological Organization (WMO) is applied (Reichler for the SAT-based feedback with three exceptions. First, et al. 2003): The tropopause is encountered at the lowest the locked lapse rate is obtained by adding the mass- 2 , 21 level where dT/dz 2Kkm , and where the average weighted mean change of the tropospheric temperatures lapse rate over the following 2 km does not exceed 2 to the climatological temperature profile: 2Kkm 1. In a few cases, especially over Antarctica, the 5 1 h 2 i tropopause cannot be determined using this definition. Tlock(z) Tclim(z) T(z) Tclim(z) . (2) The tropopause height is then taken from the 70-yr climatology from the slab-ocean control experiment men- Second, both the TOA upward and the surface down- tioned above. This backup tropopause climatology has ward longwave radiation from the atmosphere with the a monthly resolution. By implementing the tropopause locked temperature profile are taken into account. height this way it can vary in time and respond to an at- Hence the downward radiation is taken from the radi- mospheric CO2 doubling. Zonal averages of the tropopause ation call with the locked temperature profile and used height from the control experiment where all feedbacks online in the model. Third, the difference in surface

Unauthenticated | Downloaded 09/28/21 06:24 AM UTC 4438 JOURNAL OF CLIMATE VOLUME 27 longwave radiation between the two radiation calcula- calculated. Also a fraction of the incoming solar radiation tions is now also taken into account when estimating the passes through the snow and ice and is absorbed by the atmospheric warming rates, Q(z): ocean beneath. ! The locking of the surface albedo is implemented by ð 21 p scaling the absorption so that the albedo equals the cli- h i 5 s t 1 s 2 t 2 s Q(z) dp/g (L L Llock Llock), matological albedo. A scaling coefﬁcient c is obtained by p tr dividing S 5 Sal 1 Al with S 5 Saf 1 Af:

s where L is longwave radiation downward at the surface. Al 1 2 al Q z c 5 5 . (3) Again ( ) is chosen to be constant with height. Af 1 2 af b. Locking of the surface albedo Here S is downward shortwave radiation at the surface, The surface albedo feedback is suppressed by locking and Af and Al are the total surface shortwave absorption the surface albedo to the 70-yr climatology from a pre- associated with the modeled and locked surface albedo, industrial control experiment. This climatology was also af and al, respectively. The scaling coefficient can now used for locking of the lapse rate feedback. An hourly be applied to the absorption in each of the layers j, climatology of the surface albedo is used, which corre- l 5 f yielding Aj cAj , so that sponds to the frequency of the call to the shortwave radiation code. Locking of the surface albedo has been N N done previously (Hall 2004; Bitz 2008; Graversen and å f 5 å l 5 l cAj Aj A , Wang 2009; Mauritsen et al. 2013). j51 j51 The basic idea is that the albedo is kept fixed to a climatology even though the surface properties change in where N includes all snow and ice layers as well as the a way that would alter the albedo. For instance, if sea ice radiation fraction that is passed to the ocean beneath. appears in a certain grid point and time of the year, but Note that the scaling coefficient is estimated separately the climatology indicates no sea ice here, the locked for each of the 15 ice parts, and for each of the four al- surface albedo used in the model’s radiation calculations bedo types. will attain that of the ocean. In the land model, absorption is taken into account The albedo in CCSM4 distinguishes between short- both for the canopy and for the ground. The model in- wave radiation with wavelength larger and smaller cludes urban areas where absorption is encountered than 0.7 mm, and between direct and diffuse radiation, separately (e.g., roofs, roads, and house walls). A method which results in four albedo fields. In the atmospheric analog to that from the ice model, Eq. (3),isusedtoscale model component, the surface albedo is locked by the absorption in order to keep the albedo locked to the substituting in the shortwave radiation code the albedo climatology. For the ocean the modeled albedo is simply fields from the model with those from the climatology. substituted with the climatological albedo. This code estimates the shortwave heating rates as The effect on shortwave radiation due to locking of well as the shortwave fluxes at the top and bottom of the surface albedo is shown in Fig. 3. Here differences the atmosphere. However, the actual shortwave ab- between the 23CO2 and the 13CO2 climatology are sorption by the surface in the model is not taken from shown. In the free experiment, including the surface the atmosphere radiation code. Instead, this is estimated albedo feedback, the net shortwave radiation at TOA separately in each of the surface model components for increases considerably at the high latitudes in response land, sea ice, and ocean based on the downward short- to the albedo change associated with the retreat of snow wave fluxes at the surface and based on the surface and sea ice. The clear-sky fluxes indicate that this in- properties. crease at high latitudes would have been much stronger, In the sea ice model, the grid cells are separated into had it not been for the masking effect of clouds. five ice categories. Each ice category is further divided In the locked surface albedo experiment there is into bare ice, snow-covered ice, and ice with ponds. a small increase of net TOA radiation under clear-sky Hence the ice-covered part of the grid cell is constituted conditions, especially at high latitudes. This increase is by 15 minor parts in which shortwave absorption is es- due to the enhanced shortwave absorption by water timated separately. The absorption is estimated based vapor in the clear-sky atmosphere. The difference be- on the delta-Eddington method (Briegleb and Light 2007). tween the net clear-sky TOA radiation and the net clear- Each of the 15 minor parts includes a number of vertical sky surface radiation reflects the increase in absorption snow and ice layers in which shortwave absorption is by atmospheric gases due to the CO2 doubling. The

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small, this is the reason for the increase in net clear-sky shortwave radiation at TOA being larger at the polar latitudes than farther equatorward in the experiment with the surface albedo feedback suppressed.

4. Lapse rate feedback Proﬁles of atmospheric temperature changes due to

aCO2 doubling are shown in Fig. 4 for both types of locking of the lapse rate. Profiles are shown for the polar and equatorial regions separately. The changes of the locked lapse rate profiles, based on Eqs. (1) and (2), are indicated by dotted lines, while the changes of the free lapse rate profiles are shown by solid lines. For the SAT-based locking at the equatorial latitudes, the changes of the locked tropospheric temperatures are smaller than the changes of the free temperatures, while the opposite situation prevails at the polar latitudes. This is evident from a comparison of the thick solid and the dotted line in Figs. 4a–c. Since radiation to space is based on the locked profiles, the radiative cooling at TOA is reduced at low latitudes and increased at high. This is evident from Fig. 5a, where the difference in outgoing longwave radiation between the locked and the free temperature profiles are indicated by solid lines. The corresponding differences of longwave radiation at the surface are indicated by dashed lines. The differences are shown as a function of latitude. The thick solid line in Fig. 5a reveals that the lapse rate feedback induces an increase in radiation to space at low latitudes and a decrease at high latitudes. This is consistent with the temperature changes at upper tropospheric levels at the equatorial latitudes being smaller for the locked than for the free profiles, and vice versa at the polar latitudes (Fig. 4). In the upper troposphere, the TrMT-based locking of the lapse rate shows the same pattern of differences as FIG. 3. Doubling-of-CO2 change of net shortwave radiation for that of the SAT-based locking, although the differences all sky at TOA (solid line), for clear sky at TOA (thick dotted line), and for clear sky at surface (thin dotted line), for (a) the free ex- are smaller for the TrMT-based locking (Fig. 4). How- periment and (b) the locked SA experiment where the surface al- ever, in the lower troposphere the pattern is the opposite bedo feedback is suppressed. All fluxes are positive downward and between the two types of locking: At the equatorial 3 3 are estimated as the difference between the 2 CO2 and 1 CO2 latitudes the changes of the locked profiles are larger climatologies. than those of the free profiles for the TrMT-based feedback and vice versa for the SAT-based feedback, increase is most pronounced at lower latitudes consis- whereas the opposite situation prevails in the polar tent with the increase of water vapor being largest here. areas. These differences between the two types of The enhanced shortwave absorption by water vapor also locking are reflected in the impact on the radiation: A leads to a decrease of shortwave radiation reaching the comparison of the solid line in Figs. 5a and 5b indicates surface in the clear-sky atmosphere, which explains the that the effect on radiation to space by the lapse rate surface clear-sky net shortwave radiation change being feedback is much smaller for the TrMT-based than for negative. Under clear-sky conditions the absorption of the SAT-based feedback. A comparison of the dashed reflected solar radiation plays a larger role at the high lines shows that the effect on surface radiation is re- latitudes than at the low latitudes. Although the effect is versed between the two types. Hence the two types of

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FIG. 4. Area-mean and annual-mean profiles of atmospheric temperature changes due to a CO2 doubling. Shown are changes of the free temperature profiles in the free experiment with all feedbacks active (thin solid lines) and in the experiment with the lapse rate feedback suppressed (thick lines). Also shown are the changes of the locked temperature profiles used in the longwave radiation code in the experiment with the lapse rate feedback suppressed (dotted lines): (a)–(c) SAT-based locking of the temperature profile, and (d)–(f) TrMT-based locking. Hence (a)–(c) show results from the locked LR (SAT) and (d)–(f) from the locked LR (TrMT) experiment, while results from the free experiment are shown in all panels. Profiles are shown for (a),(d) the Arctic (north of 608N), (b),(e) the equatorial region (58S–58N), and (c),(f) the Antarctic region (south of 608S). In some panels, the thin solid line underlies the thick line. locking the feedback are rather different when it comes The SAT-based feedback leads to a reduction in its to the impact on radiation. However, as will be shown effect on TOA radiation as it becomes active (Fig. 5a). later, both feedbacks cause polar temperature amplifi- This is due to the cooling effect of the feedback at low cation by about the same magnitude. For the SAT-based latitudes, which is most efficient in the upper troposphere feedback, it is the increase in radiation to space at low (Fig. 4b). At high latitudes, in terms of TOA radiation latitudes, and the decrease at high latitudes that even- this feedback strengthens as it becomes active. This is tually lead to polar amplification. For the TrMT-based a result of the warming associated with the feedback feedback, polar amplification is mostly a result of the being larger at the surface than in the upper troposphere, enhanced radiation to the surface at high latitudes and which enhances the difference between the free and the the reduction at low latitudes. locked temperatures in the upper troposphere. The thin and the thick solid lines in Fig. 4 show the The TrMT-based feedback tends to amplify itself in change of tropospheric temperatures for experiments terms of radiation to the surface in the polar areas, since with the feedback active and suppressed, respectively. the radiation to the surface associated with this feed- Likewise thin and thick lines in Fig. 5 show radiation back is larger when the feedback is active than when it is responses due to the feedback for the active and sup- suppressed (Fig. 5b). This is because the radiation to the pressed feedback experiments. Note that for the free surface associated with this feedback causes polar sur- experiments, the locked profiles are not used online face warming, which enhances the difference between in the model but are estimated for diagnostic purposes the free and the locked temperature changes close to only. the surface.

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annual-mean SAT change due to a doubling of CO2 for different experiments as a function of latitude. For all experiments polar amplification is evident in all seasons except in the Arctic during boreal summer and around Antarctica during austral summer, when melting of sea ice hampers the surface warming (not shown). The differences between the free feedback experiment and each of the other experiments, where a feedback mechanism has been locked, are shown in Fig. 6b along with an estimate of the statistical significance of the differences (see appendix B for details concerning the estimation of the statistical significance). In general, the SAT-based lapse rate feedback (the dark green line) induces reduced warming at low but increased warming at high latitudes, hereby enhancing the polar amplification. This is consistent with the lapse rate feedback increasing the longwave radiation to space at low latitudes and decreasing it at high latitudes (Fig. 5). The global-mean surface air temperature change for the different experiments is given by Fig. 7a along with the Arctic and Antarctic changes. The SAT-based lapse rate feedback shows only negligible impact on the global-mean change. However, since the high-latitude warming is larger when the lapse rate feedback is included, part of the polar amplification (PA) can be attributed to this feedback, around 15% for the Arctic and around 30% for the Antarctic (Fig. 7b). This relative contribution of a given feedback is obtained by

PAfree 2 PAlocked PA 5 , PAfree 2 1

where PAfree and PAlocked are the polar ampliﬁcation in the experiment with active and suppressed feedback, respectively. The TrMT-based lapse rate feedback (light green line in Fig. 6) shows roughly the same ampliﬁcation pattern

FIG. 5. The lapse rate response in longwave radiation upward at as that based on SAT, although the cooling is smaller at the TOA (solid lines) and downward at the surface (dotted lines), low latitudes, and the warming larger at high latitudes. for the experiment where the lapse rate feedback is included (thin This pattern emerges despite the fact that the two ways lines) and where it is suppressed (thick lines). These responses are of regarding the feedback lead to rather different radi- estimated as the difference between the free lapse rate and locked ation patterns, both at the top and bottom of the at- lapse rate doubling-of-CO2 longwave radiation change upward at TOA and downward at the surface, respectively. The quantities are mosphere (Fig. 5). The TrMT-based feedback explains shown both for the (a) SAT-based and (b) TrMT-based lapse rate ;15% of the Arctic amplification and 20% of the am- feedback. Hence (a) shows results from the locked LR (SAT) and plification in the Antarctic region (Fig. 7b). (b) for the locked LR (TrMT) experiment, while results from the The surface albedo feedback enhances the warming free experiment are shown in all panels. In (b) the thin solid line is underlying the thick solid line. at all latitudes although the high latitudes are the most affected. The temperature response to the albedo feedback is clearly larger than that resulting from the lapse 5. Polar amplification rate feedback. As the albedo feedback becomes active,

Both the lapse rate and the surface albedo feed- the global-mean temperature response due to a CO2 backs induce polar ampliﬁcation associated with a CO2 doubling increases by ;1 K, while the response in the forcing, which is evident in Fig. 6a. This ﬁgure shows Arctic increases by ;3KandintheAntarcticregionby

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FIG. 6. Annual-mean and zonal-mean doubling-of-CO2 SAT response. (a) The response is shown for the free experiment including all feedbacks (red line), for the locked SAT-based lapse rate (dark green line), for the locked TrMT-based lapse rate (light green line), and for the locked surface albedo experiment (blue line). (b) The difference in responses between the free experiment and each of the locked experiments (free minus locked) is shown. Lines at the bottom at (b) indicate latitudes where the difference between the free and the locked experiments are signiﬁcant on the 95% level. See appendix B concerning the method used to estimate the signiﬁcances.

3.5 K. Hence in this CCSM4 slab-ocean model version, air temperature response DTeq is proportional to the the albedo feedback explains a large part of the polar forcing: ampliﬁcation, around 40% for the Arctic and 65% for DT 5 fF , (4) the Antarctic. However, although the albedo feedback eq appears important, approximately half of the polar where f is a climate sensitivity factor. A basic reasoning ampliﬁcation is still unexplained by this feedback as behind this assumption is that although Earth’s radiation given by the model employed here. to space is dependent on temperature to the power of 4, Even though the SAT-based lapse rate feedback small radiation perturbations of a few Watts per square contributes with little change of the global-mean tem- meter to a good approximation can be assumed to depend perature in the free-feedback experiment, it induces linearly on temperature. Also for small perturbations, a cooling of around 0.5 K when the surface albedo strong nonlinear feedback processes are less likely to feedback is not active. As will be discussed further in the be invoked. The size of f depends on feedback processes next section, in the polar areas the lapse rate feedback in the climate system that are activated by the climate becomes weaker when the surface albedo feedback is change induced by the forcing. The major feedback pro- suppressed. This is due to the surface warming at high cess is that associated with water vapor changes, which is latitudes being smaller when the surface albedo feed- believed to roughly double the global-mean temperature back is inactive. Hence globally, the lapse rate feedback response (e.g., Held and Soden 2000). Other important becomes stronger (more negative) as it becomes weaker feedbacks are those of clouds, surface albedo, and lapse at the high latitudes, where it is positive. rate, where the latter two are examined here. It may be further assumed that the total temperature D 6. Feedback parameters response ( Teq) can be divided into constant fractions that can be attributed to each of the feedbacks, i: Here the lapse rate and surface albedo feedbacks are N DT DT examined in the light of what is known as the feedback å i 5 i 5 D 1 and D constant. (5) parameters, which are assumed to be unique numbers i50 Teq Teq associated with each of the feedback processes. For a small forcing of the climate system F constituted by Then f is given as f 521/l (see appendix A), where the a radiative perturbation at the climate system bound- feedback parameter l consists of parts that are unique aries, it may be assumed that the equilibrium surface for each feedback:

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FIG. 7. Polar amplification of SAT associated with a CO2 doubling: (a) the global, Arctic (north of 608N), and Antarctic (south of 608S) temperature change, and (b) the Arctic and Antarctic amplification defined as the polar divided by the global change. Shown are the free experiment including all feedbacks (red), the locked SAT-based lapse rate (dark green), the TrMT-based locked lapse rate (light green), the locked surface albedo (dark blue), and the experiment with both surface albedo and SAT-based lapse rate locked (light blue).

N It may be shown that the assumption Eq. (5) is equiva- l 5 å l i , (6) lent to the constraint that feedbacks (i $ 1) induce a radi- 5 i 0 ation imbalance at the top of the atmosphere that is linearly dependent on the total temperature change, DT : whereby Eq. (4) can be expressed: eq F DR 5 l DT , (8) DT 52 . (7) i i eq eq l

This convention implies that a positive (negative) feed- where DRi is the feedback-induced TOA imbalance. back, enhancing (reducing) the temperature response, is Hence positive feedbacks increase the radiative imbal- associated with a positive (negative) li. Because of the ance at TOA induced by the forcing, whereas negative assumption given by Eq. (5), the feedback parameters feedbacks reduce it. are independent of each other (otherwise a fraction of Note that the feedbacks are invoked by the total the temperature change is attributed to more than one temperature change and that the magnitude of the feedback). A split of DTeq into parts was studied for the temperature response associated with a given feedback water vapor and cloud feedbacks by Langen et al. (2012) depends on the total temperature change (DTeq). Hence and for the water vapor, cloud, and surface albedo feed- the magnitude of the temperature response that a feedback by Mauritsen et al. (2013), and a good agreement back induces depends also on the contribution to DTeq with Eq. (5) was found. from the other feedbacks. In the experiments examined

Unauthenticated | Downloaded 09/28/21 06:24 AM UTC 4444 JOURNAL OF CLIMATE VOLUME 27 in this study, where feedbacks are suppressed, the as- where FL and FS are the longwave and shortwave com- sociated temperature changes also include contributions ponent of the forcing, respectively. from other feedbacks, since their temperature responses Table 1 provides forcings and feedback parameters are dependent on the temperature change from the sup- for five experiments where the lapse rate and the surface pressed feedbacks. In contrast the feedback parameters, albedo feedbacks are locked in different combinations. li, are invariant across the experiments given that the From these experiments, estimates of the lapse rate and assumptions mentioned above hold. Later in this section the surface albedo feedback parameters, llr and la, re- it will be shown this is not fully the case when it comes to spectively, are obtained from the lapse rate and surface albedo feedbacks. lL 5 l 1 lL and The forcing F can be estimated using a data-ocean all lr other version of the model following Hansen et al. (2005).In lS 5 l 1 lS all a other . (13) the DOM version the SSTs and the sea ice are fixed to a monthly climatology. The forcing can be found as For example, the lapse rate feedback parameter associ- 5 D 2D 2 lD ated with suppressing the feedback using the SAT-based F ( SD LD) TD , (9) method, llr(SAT), can be estimated by taking the differ- where DSD and DLD are the change in net incoming ence between the longwave feedback parameter in the lL shortwave radiation and outgoing longwave radiation, re- experiments including this feedback, all, and the exper- lL spectively, at TOA associated with a doubling of CO2 iment where it has been locked, other. If the difference is in the DOM version of the model, and DTD is the surface estimated on the basis of the free experiment and the air temperature change in that model. The temperature locked lapse rate (SAT based) experiment, it provides the change is small and due to the fixed SSTs and sea ice lapse rate feedback parameter in the free experiment. it appears mostly over land. The forcing defined this Likewise this lapse rate feedback parameter can be esti- way includes the radiative effect of the fast adjustments mated in the locked surface albedo experiment by com- (Hansen et al. 2005). These adjustments include cooling of paring this experiment with that named locked lapse rate the stratosphere and fast cloud changes, which are mostly (SAT based) and surface albedo. In a similar way the radiation-induced and mostly independent of the surface surface albedo feedback parameter can be achieved for air temperature response. Likewise for the slab-ocean the free and the locked lapse rate (SAT based) experi- version it can be taken into account that an equilibrium ments from shortwave feedback parameters. state has not been fully reached by modifying Eq. (7): In the free experiment the SAT-based lapse rate feed- 22 21 2 D 2D back is around 20.2 W m K and the surface albedo F ( S L) 2 2 DT 52 , (10) feedback around 0.6 W m 2 K 1. Bitz et al. (2012) found l 2 2 numbers of around 20.1 and 0.3 W m 2 K 1, respectively, so that the changes of downward shortwave and upward for the same model but with a 18 horizontal resolution and longwave radiation are encountered. Equations (9) and using the kernel method. The discrepancies may partly be l (10) can be solved for F and . associated with interactions between feedbacks in the Further, since the lapse rate and the surface albedo sense that Eq. (5) is not fulfilled. This means that a frac- feedbacks are examined here, and since these are assumed tion of the temperature response associated with one to separately impact the longwave and the shortwave ra- feedback is dependent on another feedback, which im- diation, it is convenient to divide the feedback parameter plies that the feedback parameters are dependent on one l 5 l 1 l into a longwave and a shortwave part ( L S), where another. Such interactions would be included in the esti- the lapse rate feedback is included in the former and the mates of our study but are not taken into account by the surface albedo feedback in the latter. Following Winton kernel method. The discrepancies of the results may also (2006),Eqs.(9) and (10) can simply be split into be related to uncertainties of the kernel method. In par- 52D 2 l D ticular, the surface albedo kernel has been shown to be FL LD L TD, dependent on the climate (Block and Mauritsen 2013). F 1DL D 52 L T l , (11) Interactions between the lapse rate and the surface L albedo feedback are evident: The SAT-based lapse rate 2 2 feedback parameter is around 20.2 W m 2 K 1 in the and 22 21 free experiment, but around 20.5 W m K in the model 5D 2 l D version without a surface albedo feedback. Further, the FS SD S TD, surface albedo feedback is weaker in the experiment where F 2DS D 52 S the lapse rate is locked. This indicates that the assump- T l , (12) S tion of feedbacks acting independently is questionable

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TABLE 1. Forcings and feedback parameters for experiments where the lapse rate and the surface albedo feedbacks are locked in different combinations. The total forcing is indicated by F, and its split into longwave and shortwave parts by FL and FS. The longwave and shortwave feedback parameters are given by lL and lS. The lapse rate feedback (SAT based), llr(SAT), is found from the difference between lL in experiments where this feedback is included and experiments where it is suppressed. A similar procedure is used to estimate l l lS lS lL lr(TrMT), a, lr(SAT), lr(TrMT), and a . The latter three indicate the change in the shortwave feedback parameter associated with the lapse rate feedback, and the change of the longwave feedback parameter associated with the surface albedo feedback. The forcings and the feedback parameters are estimated using Eqs. (11)–(13).

Locked Locked Locked Locked LR (SAT) and SA SA LR (SAT) LR (TrMT) Free Responses (K) DT 2.44 1.99 3.16 3.02 3.12 2 Forcings (W m 2) F 3.96 4.06 4.05 4.05 3.97 FL 3.12 3.16 3.16 3.23 3.16 FS 0.84 0.90 0.89 0.82 0.81 2 2 Longwave and shortwave feedback parameters (W m 2 K 1) lL 21.43 21.96 21.58 21.81 21.81 lS 20.19 20.09 0.30 0.47 0.53 2 2 Lapse rate and surface albedo feedback parameters (W m 2 K 1)

llr(SAT) — 20.53 — — 20.23 llr(TrMT) ————20.01 la — — 0.49 — 0.62 2 2 Additional effects of lapse rate and surface albedo feedbacks (W m 2 K 1) lS lr(SAT) — 0.11 — — 0.24 lS lr(TrMT) — — — — 0.07 lL 2 a ——0.15 — 0.15 when it comes to the lapse rate and surface albedo rate and surface albedo feedback parameters by solid feedbacks. Globally the lapse rate feedback is negative lines in Figs. 9c and 9d. The sections are based on zonal- and the surface albedo feedback is positive, but in the mean estimates of radiation changes and global-mean polar areas they are both positive, which leads to in- estimates of the surface air temperature change, and can teractions between the feedbacks. For instance, the sur- be derived from Eqs. (11) and (12): face albedo feedback induces large surface warming at DL~ (f) 2DL~(f) high latitudes, which enhances the lapse rate feedback in l~L(f) 5 D and DT 2DT this region, but has a smaller effect on the lower latitudes. D ~ ~ As a result the structure of the lapse rate feedback is to DS(f) 2DS (f) l~S f 5 D some extent dependent on the albedo feedback. ( ) D 2D , T TD Figure 8 shows profiles of temperature changes similar to those in Fig. 4, but for experiments with the surface where f is latitude and e indicates zonal estimates. By albedo feedback suppressed. A comparison with the decomposing the feedback parameters in this way, an profiles from the experiment including this feedback integration over all latitudes results in the global esti- (Figs. 4a–c) indicates that the difference between the mates presented in Table 1. locked and the free profiles in the polar areas is much The solid lines in Fig. 9c provide the SAT-based lapse smaller when the surface albedo is locked than when it is rate feedback as a function of latitude. The feedback is included. Hence the lapse rate feedback is more efficient positive at high but negative at low latitudes. Consistent at high latitudes when the surface albedo feedback is with the discussion above, the lapse rate feedback is active. In contrast, at the equatorial latitudes the profiles more positive at high latitudes when the surface albedo are only little affected by the surface albedo feedback. feedback is active than when it is suppressed. As a result, the lapse rate feedback is less negative when The surface albedo feedback (Fig. 9d, solid lines) is the surface albedo feedback is active since the surface strongest in areas where sea ice is vulnerable to melt as albedo feedback enhances the regionally positive lapse the global temperature rises. In addition, the surface rate feedback at high latitudes, while it has little effect at albedo feedback is stronger when the lapse rate feedback low latitudes. is active, especially in the Arctic. The lapse rate feedback Meridional sections of longwave and shortwave feed- induces warming at the high latitudes due to the pre- back parameters are shown in Figs. 9a and 9b and of lapse dominantly stable stratification conditions prevailing

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FIG.8.AsinFigs. 4a–c, but for the experiments with suppressed surface albedo feedback. Hence ‘‘free’’ refers here to the locked SA experiment with suppressed surface albedo feedback, and ‘‘locked’’ to the locked LR (SAT) and SA experiment with both surface albedo and lapse rate feedback suppressed. here, which hampers vertical mixing. This warming fur- than those where the feedback is active, which can be ther melts the ice, thereby amplifying the surface albedo seen from estimates of the 23CO2 changes of the cloud feedback. water path from each experiment (Fig. 9e). This dif- The surface albedo feedback has a relatively strong ference in cloud water path change indicates a cloud influence on the longwave part of the feedback param- shortwave warming effect associated with the SAT- eter, both for the free and for the locked lapse rate ex- based lapse rate feedback, which appears in the short- periment. Estimates of the effect on longwave radiation wave feedback parameter of this feedback. This is due of the albedo feedback, and on the shortwave radia- to the clouds reflecting less sunlight when the lapse rate tion of the lapse rate feedback, are given as additional feedback is active than when it is suppressed. effects in Table 1 and with dashed lines in Figs. 9c and As mentioned above, the longwave part of SAT-based 9d. Since the surface albedo feedback in itself affects lapse rate feedback is offset by the shortwave part in the only the shortwave feedback parameter, the impact on free experiment. This is consistent with the lapse rate the longwave part is associated with the surface albedo feedback providing only a negligible contribution to the feedback interacting with other feedbacks. As shown global temperature response (Fig. 7). The direct effect here, the longwave part of the surface albedo feedback is of the lapse rate feedback in terms of global cooling is 2 2 0.15 W m 2 K 1 when the lapse rate feedback is active, compensated by the impact of the lapse rate feedback on 2 2 but 20.15 W m 2 K 1 when it is suppressed. Again, the the surface albedo feedback and, presumably, on the cloud difference appears mostly at the high latitudes (Fig. 9c). feedback. When the effect on the surface albedo feedback This is due to the longwave cooling to space in these is suppressed, the lapse rate feedback leads to a global areas being more efficient when it is taken from the cooling, which can be seen from a comparison of the dark locked profiles than when it is based on the profiles es- and light blue columns for the global estimates in Fig. 7. timated by the model. The TrMT-based lapse rate feedback is near neutral The SAT-based lapse rate feedback has a shortwave (Table 1). With this design the feedback has little impact component of the same size as its longwave part (Table 1). on the longwave energy change at TOA (Fig. 5); rather, This is partly linked to the lapse rate feedback inter- this feedback redistributes energy between the atmo- acting with the surface albedo feedback, which can be sphere and the surface. seen from a comparison between the number taken from the free and the locked surface albedo experi- 7. Conclusions ments. The warming at high latitudes associated with the lapse rate feedback enhances the surface albedo Both the lapse rate and the surface albedo feedbacks feedback, which results in a positive contribution of induce polar temperature amplification. Around 40% of the shortwave part of the lapse rate feedback. However, the amplification in the Arctic and 65% of the Antarctic the surface albedo feedback does not alone account amplification can be attributed to the surface albedo for this shortwave part. Clouds may also play a role. In feedback, while the SAT-based lapse rate feedback ac- the tropics, the two experiments with suppressed SAT- counts for 15% of the Arctic and 30% of the Antarctic based lapse rate feedback show a larger cloud increase amplification.

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FIG. 9. Zonal mean of (a)–(d) feedback parameters and (e) cloud water path changes as a function of latitude. Longwave feedback parameters are displayed in (a), and those of shortwave in (b) for the free experiment with all feedbacks active, the SAT-based locked lapse rate (LR), the TrMT-based locked LR, the locked surface albedo (SA), and the experiment with both SA and SAT-based LR locked. The SAT-based lapse rate feedback parameter is displayed in (c) and the surface albedo feedback parameter in (d) by solid lines. See Table 1 for a detailed description of the feedback parameters shown in (c) and (d). Note that (c) and (d) include two estimates of either feedback. According to the linear theory the two estimates should be equal. Differences signiﬁcant on a 95% level between the estimates are indicated by solid red lines at the bottom of the frames. Corresponding longwave effects of the surface albedo feedback and shortwave effects of the SAT-based lapse rate feedback are shown by dotted lines in (c) and (d), respectively. Likewise, differences signiﬁcant on the 95% level between the estimates are indicated by dotted lines at the bottom of the frames. The cloud water path change shown in (e) includes liquid and frozen water.

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Stable stratification conditions at high latitudes, and snow and ice thicknesses and surface temperature. In an increase in upper tropospheric latent heat release at addition, the new version includes melt ponds, which low latitudes, induce differences in warming with height contribute to a positive albedo feedback (Holland et al. in the troposphere. This warming structure is associated 2012). A comparison to observations reveals that CCSM3 with more radiation to space at low and less radiation to as well as most of the other models included in the CMIP3 space at high latitudes, as compared to the radiation archive underestimate the decline of the Arctic sea from a height-independent warming in the troposphere ice extent during the last decades (Stroeve et al. 2007). that is equal to that at the surface (Fig. 5a). As a result, Furthermore, it has been pointed out that CCSM4 the SAT-based lapse rate feedback is negative at low better represents the twentieth-century Arctic climate latitudes but positive at high latitudes, which leads to than does CCSM3 (Jahn et al. 2012). All in all, based on polar amplification. In total, the feedback is negative the difference in sophistication and in performance, it 2 2 with a feedback parameter of ;20.2 W m 2 K 1. This is likely that the CCSM4 provides a more realistic number is less negative compared to estimates ob- picture of the surface albedo feedback than that obtained using the kernel method on model results from tained by CCSM3. phase 3 of the Coupled Model Intercomparison Project The lapse rate and the surface albedo feedbacks (CMIP3) used for the Intergovernmental Panel on Climate strongly interact with each other and violate the linear Change (IPCC) Fourth Assessment Report (AR4). The forcing response approximation, where feedbacks are kernel estimates from these models range from 20.3 assumed independent. The lapse rate feedback is consid- 2 2 to 21.3 W m 2 K 1 (Soden et al. 2008). However, our erably stronger (more negative) in a world without the number is more negative compared to a kernel method surface albedo feedback. This is due to the surface tem- 2 2 estimate of ;20.1 W m 2 K 1 based on the same model perature amplification being smaller when the surface version, CCSM4, as used here (Bitz et al. 2012). albedo feedback is not active, which reduces the positive In comparison with the SAT-based lapse rate feed- lapse rate feedback at high latitudes. Another example is back, the feedback based on TrMT is weak in terms of found in the experiment where all feedbacks are in- inducing radiative TOA imbalance (Fig. 5b). However, cluded. Here the global surface air temperature response when it comes to polar amplification the two ways of to the lapse rate feedback is small despite the fact that the 2 2 regarding the feedback lead to about the same results. feedback parameter is negative by ;20.2 W m 2 K 1 . For the SAT-based feedback, the polar amplification is This is due to the shortwave effect of the lapse rate due to TOA radiation changes characterized by radia- feedback offsetting the longwave part. The shortwave tive cooling to space at low and radiative warming at effect is partly a result of the high-latitude surface high latitudes, whereas for the TrMT-based feedback, it warming induced by the lapse rate feedback, which fur- is rather a redistribution of energy between the tropo- ther melts the sea ice whereby the surface albedo feed- sphere and the surface that induces the amplification. back is enhanced. Also a part of the shortwave effect of The surface albedo feedback parameter of the lapse rate feedback seems linked to cloud changes. A 2 2 ;0.6 W m 2 K 1 is at the upper end relative to estimates shortcoming of this study is that it is based on one climate based on the kernel method and the CMIP3 models, model only. A comparison with similar results from other 2 2 which range from 0.0 to 0.5 W m 2 K 1 (Soden et al. 2008). climate models would be interesting. The contribution of this feedback to the polar amplifica- The model with both the lapse rate and the surface tion of 40% for the Arctic and of 65% for Antarctica is in albedo feedback suppressed shows polar amplification, agreement with an earlier estimate by Hall (2004),but especially in the Arctic. Around 40% of the amplifi- around double the amounts relative to values found by cation in the Arctic appears to be unexplained by these Graversen and Wang (2009), using similar methods of two feedbacks. In the absence of the surface albedo online suppressing the feedback. feedback, the retreat of sea ice may still lead to en- TheestimatefromGraversen and Wang (2009) is based hanced warming at high latitudes (Hall 2004). For in- on an earlier version of the CCSM model, version 3 stance, in the dark seasons the sea ice insulates the (CCSM3). The sea ice model component has become warm ocean from the cold atmosphere and allows the more sophisticated in the CCSM4 relative to the earlier surface air temperature to become far below the freezing version, especially when it comes to shortwave absorption point. As sea ice retreats or thins, the temperature of the (Holland et al. 2012). In CCSM4 the absorption and hence surface air will increase and come closer to that of the the albedo is based on inherent optical properties of the ocean. different snow and ice layers (Briegleb and Light 2007), However, when it comes to revealing the causes of the whereas in the earlier model version the albedo is pa- amplification, attention should also be turned toward rameterized on the basis of bulk sea ice properties such as other processes such as cloud processes, changes of the

Unauthenticated | Downloaded 09/28/21 06:24 AM UTC 15 JUNE 2014 G R A V E R S E N E T A L . 4449 meridional energy transport, and the Planck tempera- radiative imbalance at the climate system boundary [Eq. ture feedback. (8)]. Hence, in that sense, the effect of the temperature change leading to a restoring of the energy balance at Acknowledgments. The authors would like to thank the boundary may itself be regarded as a negative three anonymous reviewers who provided very con- feedback, consistent with the negative sign of l as de- structive and helpful comments. The authors are grate- 0 fined by Eq. (A3). This feedback may be regarded as the ful for interesting and useful discussions with Rodrigo Planck feedback associated with a uniform, height- Caballero, Gunilla Svensson, Michael Tjernstrom,€ and independent temperature change in the troposphere. Jonas Nycander. All experiments were run at the Tri- olith supercomputer from the National Supercomputer € Centre (NSC), Linkoping, Sweden, as projects SNIC APPENDIX B 2013/1-101 and SNIC 2013/1-223 approved by the Swedish National Infrastructure for Computing (SNIC). The Statistical Significance CCSM4 model was obtained from NCAR, Boulder, Colorado, United States. This work is part of the pro- The statistical significance of differences in Figs. 6b, gram Advanced Simulations of Climate Change and 9c, and 9d is estimated based on a t test. The t test pro- Impacts on Northern Regions (ADSIMNOR) funded vides the statistical significance of the difference be- by the Swedish research council FORMAS. tween two means (e.g., Snedecor 1956, 85–101). The significance depends on the variances of the time series APPENDIX A on which the means are based. For the SOM experiments, the means are taken over 80 years and for the Feedback Parameters DOM experiments over 50 years. To estimate the variances the SOM time series are broken into four con- Following, for example, Hansen et al. (1984), it is here secutive 20-yr averages and the DOM time series into shown that the two assumption given by Eqs. (4) and (5) four 10-yr averages. The variances are taken over the lead to Eqs. (6) and (7). In a climate system without any four averages. It is here assumed that the consecutive 5 D feedback processes (N 0) the temperature change T0 averages are independent, which may not be entirely the eventually causes an offset of the radiation imbalance case. induced by the forcing. Let f0 be a climate sensitivity factor for such a system so that REFERENCES D 5 T0 f0F . (A1) Alexeev, V. A., P. L. Langen, and J. R. Bates, 2005: Polar ampli- Dividing DT by DT , using Eqs. (4), (5), and (A1) and fication of surface warming on an aquaplanet in ‘‘ghost forc- 0 eq ing’’ experiments without sea ice feedbacks. Climate Dyn., 24, a bit of algebra, yields 655–666, doi:10.1007/s00382-005-0018-3. f Arrhenius, S., 1896: On the influence of carbonic acid in the air f 5 0 . (A2) N DT upon the temperature of the ground. Philos. Mag., 41, 237– 2 å i 276, doi:10.1080/14786449608620846. 1 D i51 Teq Bitz, C. M., 2008: Some aspects of uncertainty in predicting sea ice thinning. Arctic Sea Ice Decline: Observations, Projections, Now define Mechanisms, and Implications, Geophys. Monogr., Vol. 180, 8 Amer. Geophys. Union, 63–76, doi:10.1029/180GM06. > 1 ——, K. M. Shell, P. R. Gent, D. A. Bailey, G. Danabasoglu, K. C. > 2 5 <> if i 0, Armour, M. M. Holland, and J. T. Kiehl, 2012: Climate sen- f0 sitivity of the Community Climate Model version 4. J. Climate, l 5 . (A3) i > DT 25, 3053–3070, doi:10.1175/JCLI-D-11-00290.1. > i Block, K., and T. Mauritsen, 2013: Forcing and feedback in the : D otherwise f0 Teq MPI-ESM-LR coupled model under abruptly quadrupled CO2. J. Adv. Model. Earth Syst., 5, 676–691, doi:10.1002/ Then Eq. (A2) can be written as jame.20041. Briegleb, B. P., and B. Light, 2007: A delta-Eddington multiple 1 scattering parameterization for solar radiation in the sea f 52 , N ice component of the Community Climate System model. l 1 å l NCAR Tech. Rep. NCAR/TN-4721STR, 100 pp, doi:10.5065/ 0 i i51 D6B27S71. Gent, P. R., and Coauthors, 2011: The Community Climate System which combined with Eq. (4) leads to Eq. (7). Positive Model version 4. J. Climate, 24, 4973–4991, doi:10.1175/ (negative) feedbacks tend to increase (decrease) the 2011JCLI4083.1.

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