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  • View in gallery

    Geographical locations of q-flux perturbation patches (with 6 W m−2 isolines shown as contours). For each patch, q-flux perturbations are added to or subtracted from the control q-flux values.

  • View in gallery

    Zonal-mean (a) symmetric and (b) asymmetric surface temperature (TS) sensitivity (K PW−1) to q-flux perturbation at different latitudes. The abscissa (ordinate) is the location of q-flux forcing (TS response). Dashed lines show the latitudinal boundaries of the q-flux forcing. The TS sensitivity here is defined as the TS response normalized by the area integration of the q-flux anomalies over each patch. A spatial smoother derived from the inpainting algorithm (Garcia 2010) is employed here and in the following figures to ensure that only the statistically robust features are retained.

  • View in gallery

    (a) Same as Fig. 2b: zonal-mean asymmetric TS sensitivity (K PW−1) to q-flux perturbations at different latitudes; (b)–(g) decomposition of the asymmetric TS sensitivity into water vapor, lapse rate, albedo, and cloud radiative feedbacks, AHT convergence, and surface heat fluxes.

  • View in gallery

    (a) Leading EOF pattern of the asymmetric TS response (K PW−1) with the explained variance labeled; (c)–(h) the leading EOF patterns of the joint EOF analysis of the asymmetric TS response attributed to water vapor, lapse rate, albedo, and cloud radiative feedbacks, AHT convergence and surface heat fluxes and the sum of the leading joint EOFs; (b) the sum of (c)–(h).

  • View in gallery

    Leading EOF patterns of (a) the asymmetric sea ice area response (aice, in %PW−1) and (b) latent heat flux response (LHFLX in W m−2 PW−1; positive upward). Red contours in (a) demarcate the mean sea ice edge in the CTRL run, defined as where sea ice concentration drops to 15%. The right-side panels are the corresponding zonal-mean structures (red) and the zonal-mean climatology (black).

  • View in gallery

    Air temperature profiles at 70°S under control (black), and heating (red) and cooling (blue) experiments with q-flux perturbations placed at 55°S. The corresponding inversion strengths (IS) are labeled alongside each profile. IS is defined as the potential temperature difference between the surface and the level of the maximum temperature.

  • View in gallery

    Leading EOF patterns for the asymmetric TS response due to (a) SW cloud feedback and (b) LW cloud feedback, with their explained variance shown in parentheses. Unit is K PW−1.

  • View in gallery

    The annual cycle of zonal-mean TS asymmetric response (K) to q-flux perturbations at 55°S. (a) The total asymmetric TS response; (b)–(g) decomposition of the TS response into water vapor, albedo, and cloud radiative feedbacks, AHT convergence, and surface heat fluxes.

  • View in gallery

    Zonal-mean asymmetric TS response to q-flux forcings placed at 55°S: annual mean (black), September–February mean (red), and March–August mean (blue).

  • View in gallery

    (a) Symmetric component and (b) asymmetric component of the zonal-mean, annual-mean TS response to q-flux perturbations at 55°S in SOM55S (black), SOM55S-NS (blue), SOM55S-NI (green), and SOM55S-NI-NS (red) experiment sets. The latitude range at which the response is statistically significant at the 99% confidence level is highlighted with shaded edges. The significance test is against the null hypothesis that a 20-yr mean anomaly can randomly occur from internal variability, and the corresponding probability distribution is constructed from 5000 samples randomly picked from the control run of each experiment set.

  • View in gallery

    (a) Symmetric component and (b) asymmetric component of the zonal-mean, annual-mean TS response to q-flux perturbations at equator in SOMEQ (black) and SOMEQ-NS-NI (red) experiment sets. The shaded edges assume the same meaning as those in Fig. 10.

  • View in gallery

    (a) Symmetric component and (b) asymmetric component of the zonal-mean, annual-mean TS response to q-flux perturbations at 55°S in SOM55S (black) and SOM55S-4×CO2 (red). The shaded edges assume the same meaning as those in Fig. 10. Note that to prevent model from crash in a very warm climate, the magnitude of the q-flux perturbations in SOM55S-4×CO2 are 1/3 of those in SOM55S, thus the TS response here is scaled up by a factor of 3.

  • View in gallery

    Schematics depicting the key asymmetric processes in generating the asymmetric TS response due to (a) the presence of sea ice, and (b) the presence of seasonal cycle. In the presence of sea ice, evaporative cooling and effective heat capacity are the two major asymmetric factors; in cold season, the lapse rate feedback is the major source of asymmetry in response to cooling vs warming.

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Sensitivity of Surface Temperature to Oceanic Forcing via q-Flux Green’s Function Experiments. Part III: Asymmetric Response to Warming and Cooling

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  • 1 Key Laboratory of Physical Oceanography, Institute for Advanced Ocean Studies, Ocean University of China and Qingdao National Laboratory for Marine Science and Technology, Qingdao, China
  • | 2 Atmospheric Sciences and Global Change Division, Pacific Northwest National Laboratory, Richland, Washington
  • | 3 Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada
  • | 4 Atmospheric Sciences and Global Change Division, Pacific Northwest National Laboratory, Richland, Washington
  • | 5 Key Laboratory of Physical Oceanography, Institute for Advanced Ocean Studies, Ocean University of China and Qingdao National Laboratory for Marine Science and Technology, Qingdao, China
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Abstract

Climate response is often assumed to be linear in climate sensitivity studies. However, by examining the surface temperature (TS) response to pairs of oceanic forcings of equal amplitude but opposite sign in a large set of local q-flux perturbation experiments with CAM5 coupled to a slab, we find strong asymmetry in TS responses to the heating and cooling forcings, indicating a strong nonlinearity intrinsic to the climate system examined. Regardless of where the symmetric forcing is placed, the cooling response to the negative forcing always exceeds the warming to the positive forcing, implying an intrinsic inclination toward cooling of our current climate. Thus, the ongoing global warming induced by increasing greenhouse gases may have already been alleviated by the asymmetric component of the response. The common asymmetry in TS response peaks in high latitudes, especially along sea ice edges, with notable seasonal dependence. Decomposition into different radiative feedbacks through a radiative kernel indicates that the asymmetry in the TS response is realized largely through lapse rate and albedo feedbacks. Further process interference experiments disabling the seasonal cycle and/or sea ice reveal that the asymmetry originates ultimately from the presence of the sea ice component and is further amplified by the seasonal cycle. The fact that a pair of opposite tropical q-flux forcings can excite very similar asymmetric response as a pair placed at 55°S strongly suggests the asymmetric response is a manifestation of an internal mode of the climate model system.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jian Lu, jian.lu@pnnl.gov

Abstract

Climate response is often assumed to be linear in climate sensitivity studies. However, by examining the surface temperature (TS) response to pairs of oceanic forcings of equal amplitude but opposite sign in a large set of local q-flux perturbation experiments with CAM5 coupled to a slab, we find strong asymmetry in TS responses to the heating and cooling forcings, indicating a strong nonlinearity intrinsic to the climate system examined. Regardless of where the symmetric forcing is placed, the cooling response to the negative forcing always exceeds the warming to the positive forcing, implying an intrinsic inclination toward cooling of our current climate. Thus, the ongoing global warming induced by increasing greenhouse gases may have already been alleviated by the asymmetric component of the response. The common asymmetry in TS response peaks in high latitudes, especially along sea ice edges, with notable seasonal dependence. Decomposition into different radiative feedbacks through a radiative kernel indicates that the asymmetry in the TS response is realized largely through lapse rate and albedo feedbacks. Further process interference experiments disabling the seasonal cycle and/or sea ice reveal that the asymmetry originates ultimately from the presence of the sea ice component and is further amplified by the seasonal cycle. The fact that a pair of opposite tropical q-flux forcings can excite very similar asymmetric response as a pair placed at 55°S strongly suggests the asymmetric response is a manifestation of an internal mode of the climate model system.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jian Lu, jian.lu@pnnl.gov

1. Introduction

Linear approximation is widely assumed in understanding the climate sensitivity to the warming effect of anthropogenic greenhouse gases (e.g., Alexeev 2003; Watanabe and Jin 2004; Liu et al. 2008; Majda and Wang 2010). In general, if the climate forcing is sufficiently small, the nonlinear processes can be assumed small, and they can either be ignored or treated as a noise forcing. This simplification breaks down complex processes and helps quantify the first-order change in climate science (Knutti and Rugenstein 2015; Alexeev 2003; Huang 2013; Liu et al. 2018a). This way, the climate response can be determined by a constant feedback parameter (e.g., Hansen et al. 1984; Soden et al. 2008; Huang et al. 2017a; Liu et al. 2018b; Shell et al. 2008), and once the climate response to a certain forcing is known, the response to an arbitrary forcing can be estimated through this linear forcing-feedback framework. For example, once the warming response to a doubling of CO2 concentration is derived from a modeling experiment, one may determine the warming response to 0.5 × CO2 or 4 × CO2 by scaling the warming response to 2 × CO2 based on changes to the CO2 concentrations.

However, the dynamical system governing our climate is intrinsically nonlinear, and nonlinearity infiltrates every component of the complex climate system. For instance, El Niño–Southern Oscillation (ENSO), the dominant mode of interannual variability in the climate system, exhibits significant asymmetric behaviors associated with the opposite phase of ENSO (e.g., Hoerling et al. 1997; Eisenman et al. 2005; An 2008; Jin et al. 2003). Another example is the nonlinearity in ocean dynamics that gives rise to asymmetric SST responses in the equatorial Pacific under a pair of uniform surface energy flux perturbations of the same amplitude but opposite sign (Liu et al. 2017). Moreover, Feldl and Roe (2013) inferred the nonlinear term in climate feedbacks using a residual method and found it to be of comparable importance to the linear terms in affecting the top-of-atmosphere (TOA) energy balance. It has been well known that the Atlantic meridional overturning circulation can have multiple equilibrium states (Stommel 1961; Hawkins et al. 2011) and can undergo a hysteresis as the path of forcing is reversed (e.g., Rahmstorf et al. 2005; Jackson et al. 2017). Nonlinearities and asymmetric responses have also been found in sea ice–albedo feedback (Held et al. 1981; North 1984; Winton 2013; Eisenman and Wettlaufer 2009) and cloud and lapse rate feedbacks (Soden et al. 2008; Andrews et al. 2012; Colman 2001; Bony et al. 2006; Kim et al. 2018). The nonlinear behavior in various dynamic and thermodynamic processes, as well as their interactions, may lead to both local and global asymmetric climate response to even perfectly symmetric forcings.

While the linear and symmetric climate response has been investigated extensively in the literature, the investigation of nonlinear response has received relatively little attention. Given the lack of a priori knowledge as to how nonlinear the climate system is, one can only assess the nonlinearity by probing numerical climate models. Here, we study the asymmetric response—the consequence of dynamical system nonlinearity—in a set of slab ocean q-flux Green’s function experiments, which were originally conducted to understand the linear response relationship between global surface temperature and oceanic heat flux (Liu et al. 2018a, hereafter Part I) and the ocean heat uptake efficacy (Liu et al. 2018b, hereafter Part II). As the name implies, the q-flux Green’s function experiments are achieved by perturbing the q flux at a locality one at a time at all possible ocean locations (see Fig. 1) to retrieve a forcing–response relationship. For each location, twin experiments with a pair of opposite q-flux anomalies are performed, and a q-flux anomaly (denoted by q) can be considered to be a forcing to the ocean slab due to the oceanic heat divergence or convergence. If we express the surface temperature (TS) response–forcing relationship in a functional form T = f(q), the TS response to a pair of positive and negative q-flux perturbations can be parsed via Taylor expansion as follows:
{δT+=f(q)δq++12f(q)(δq+)2+16f(q)(δq+)3+δT=f(q)δq+12f(q)(δq)2+16f(q)(δq)3+,
where δq+ and δq denote the forcing pair and hence δq = − δq+; δT+ and δT denote the response to the heating and the cooling forcing, respectively. In the context of this study, we define δTs = (δT+δT)/2 and refer to it as the symmetric response, and δTa = (δT+δT)/2 as asymmetric response. One can see that the symmetric response results from all the odd power terms in (1), including the first order (linear), while the asymmetric response results from the even power terms. If function f is linear, the asymmetric response is identically zero as the higher-order terms are all equal to zero for a linear operator f. Therefore, the asymmetric response is a consequence of nonlinearity of the dynamical system described by f. As to be shown later, our results indicate that the asymmetric TS response has similar magnitude to the symmetric response, implicative of sizable nonlinearity intrinsic to the climate system examined, prompting further investigation of the origin and feedback processes responsible for the asymmetry.
Fig. 1.
Fig. 1.

Geographical locations of q-flux perturbation patches (with 6 W m−2 isolines shown as contours). For each patch, q-flux perturbations are added to or subtracted from the control q-flux values.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

We report the investigation into the source and mechanism of asymmetry of this slab-coupled climate system here as Part III of a three-part study series, and the remainder of the paper is structured as follows. Section 2 describes the AGCM model and the design of Green’s function experiments. Section 3 recapitulates the kernel decomposition of the surface temperature response, which serves as a crucial tool to dissect the roles of the radiative feedbacks in the formation of the full asymmetric response. Section 4 presents the asymmetric TS response and its mode behavior and diagnoses the related feedback processes using a kernel-based attribution method. Guided by the insights from kernel feedback decomposition, we investigate the origin of the asymmetry by disabling the key component and processes in the model deemed important for the asymmetry in section 5. Section 6 concludes the paper with a summary and discussion.

2. Green’s function experiments

The model we use is the slab ocean version of the Community Earth System Model, version 1.1 (CESM1.1-SOM), which is composed of the Community Atmosphere Model, version 5 (CAM5), the Community Land Model, version 4 (CLM4), the Community Ice Code (CICE), and a slab ocean model (SOM). For both atmosphere and land models, the horizontal resolution is 2.5° longitude × 1.9° latitude, with the atmospheric component having 30 vertical levels. For the sea ice model and SOM, the horizontal resolution is at a nominal 1°, telescoped meridionally to ~0.3° at the equator. In this model, the ocean and atmosphere are only thermodynamically coupled and SST is computed interactively from surface fluxes and q flux that accounts for the missing ocean dynamics.

A baseline simulation (CTRL) is obtained by running the CESM1.1-SOM to an equilibrium state with preindustrial forcing. Both the mixed layer depth and the q flux used in CTRL are diagnosed from a fully coupled CESM1.1 control simulation, the former varies in space but stays constant in time, while the latter has a repeating seasonal cycle. Branching out from 1 January of a year arbitrarily chosen from the equilibrated CTRL run, we perform 97 pairs of “warm patch” and “cold patch” simulations, in which an additional q-flux patch is added to or subtracted from the CTRL q flux. The locations of the 97 q-flux patches are illustrated as ovals in Fig. 1. Each q-flux patch is specified to be a localized hump:
{Qcos2(π2ϕϕkϕw)cos2(π2λλkλw),forϕwϕϕkϕwandλwλλkλw0,forϕϕkϕworϕϕkϕworλλkλworλλkλw,
where Q is the peak value of the q-flux patch and set to be ±12 W m−2 at the center of the rectangular patch (ϕk, λk). The half-widths of the rectangular patch in the zonal (λw) and meridional (ϕw) directions are 30° and 12°, respectively. The actual q-flux perturbations of an example patch are shown as shadings in Fig. 1. Each of the patch experiments is integrated for 40 years, and only the data of the last 20 years are used for estimating the forced response by subtracting the CTRL data therefrom. The CTRL data are constructed from a 150-yr average of a long control simulation. According to Eq. (1), the symmetric and asymmetric response of TS can be estimated as Ts = (δT+δT)/2 and Ta = (T+ + T)/2, respectively. For the sign convention, when the TS cooling in response to a negative q flux surpasses the TS warming to a positive q flux, we refer to the case as negative TS asymmetry, and vice versa. Further details documenting the Green’s function experiments can be found in Part I.

3. Kernel decomposition diagnostics

The radiative feedbacks associated with the asymmetric TS response are diagnosed using the radiative kernels developed by Huang et al. (2017a). These kernels are derived from the Rapid Radiative Transfer Model (RRTM) of Mlawer et al. (1997) based on 6-hourly atmospheric profiles from the ERA-Interim reanalysis dataset (Dee et al. 2011), as they have been demonstrated to be capable of accurately reproducing the radiation anomalies simulated by CESM (Huang et al. 2017a).

To examine the quantitative contribution from different feedbacks to the asymmetric TS response, we follow the radiative kernel-based attribution approach developed in Part II. The framework is built on the energy balance among (i) the sum of the TOA radiative feedback components (Ri), (ii) surface fluxes (Fs), and (iii) the divergence of the vertically integrated atmospheric heat transport (AHT; F): F=Ri+Fs, where the prime indicates deviation from the control. Ri is composed of the all-sky lapse rate, water vapor, cloud, albedo, and Planck radiative effects. Among these feedbacks, the Planck feedback from surface temperature is the major negative one, acting against all other terms to maintain the energy balance. If we denote the vertically integrated kernel of this Planck feedback as kP (note that kP < 0) and use it to divide the energy balance equation, we yield
Ts=kp1(Ri+FsF).
Now subscript i represents all TOA feedback except the vertically integrated Planck feedback. This constitutes an attribution framework for the TS response, whereby the total TS response can be decomposed into parts corresponding to the feedback processes represented by the right-hand terms in Eq. (3). For instance, for an energy gain G from certain feedback, the surface must warm by −G/kp to emit the same amount of energy to space to maintain the balance. The terms on the right-hand side therefore give the partial TS changes due to (i) water vapor feedback, (ii) lapse rate feedback, (iii) albedo feedback, (iv) cloud feedback, (v) the surface radiative and heat fluxes, and (vi) convergence of AHT. Note that the noncloud radiative effects are computed directly using the kernels and the cloud radiative feedback is obtained by subtracting the sum of noncloud feedback from the model-simulated total TOA radiation change, both the longwave (LW) and shortwave (SW) components of the cloud feedback are diagnosed this way. We have recomputed the cloud radiative feedback following the approach of Soden et al. (2008) to correct the cloud masking effect, and the result is almost unchanged compared to that calculated based on the residual method (not shown).

4. Asymmetric TS response to climate warming and cooling

a. Common asymmetric TS response in Green’s function experiments

The TS sensitivity is defined as the equilibrium TS response normalized by the area-integrated q-flux perturbation over each patch, representing the efficiency of the q-flux forcing of a given location in driving the global-mean TS response. Here, to examine the zonal-mean TS sensitivity to the latitudinal location of the q flux, we sum up the TS responses for the q-flux patches along the same latitudinal band. Thus, the abscissa of Fig. 2 is the location of q-flux forcing and the ordinate is the location of TS response. For example, the 1.4 K PW−1 symmetric TS response at (80°S, 0°) in Fig. 2a means a q-flux heating placed at the equator is able to induce a zonal-mean warming of 1.4 K along 80°S.

Fig. 2.
Fig. 2.

Zonal-mean (a) symmetric and (b) asymmetric surface temperature (TS) sensitivity (K PW−1) to q-flux perturbation at different latitudes. The abscissa (ordinate) is the location of q-flux forcing (TS response). Dashed lines show the latitudinal boundaries of the q-flux forcing. The TS sensitivity here is defined as the TS response normalized by the area integration of the q-flux anomalies over each patch. A spatial smoother derived from the inpainting algorithm (Garcia 2010) is employed here and in the following figures to ensure that only the statistically robust features are retained.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

To put things in perspective, we first recapitulate the key features of the symmetric response before getting to the asymmetric response. In Part II, we found that regardless of which latitude the q flux is applied to, it always tends to produce the largest symmetric response in the polar regions (see also Fig. 2a). In addition to this polar amplification tendency, we also found (i) that high-latitude oceanic forcing is several times more efficient than the low-latitude forcing, and (ii) forcing from the equatorial eastern Pacific is more efficient than the equatorial western Pacific and Indian Ocean in driving global TS warming, as measured by the ocean heat forcing efficacy. Overall, the symmetric component of TS response shows a substantial sensitivity to the location of the q-flux forcing, indicating a large spatial dependence of the ocean forcing efficacy.

Figures 2b and 3a show the asymmetric component of TS sensitivity to forcing at different latitudes. It is surprising to see that the asymmetric component in all forcing cases is characterized by a similar meridional structure, suggestive of a mode behavior; that is, a pattern of variability that is least damped in the system and hence most excitable when the system is perturbed. The asymmetric response is comparable in magnitude to the symmetric component, and is negative globally, demonstrating that the cooling response to a negative q-flux forcing is greater than the warming response to a positive q-flux forcing of the same magnitude. The asymmetric TS response is greatest in the polar regions (centered around 80°S and 80°N) regardless of the latitude of the forcing.

Fig. 3.
Fig. 3.

(a) Same as Fig. 2b: zonal-mean asymmetric TS sensitivity (K PW−1) to q-flux perturbations at different latitudes; (b)–(g) decomposition of the asymmetric TS sensitivity into water vapor, lapse rate, albedo, and cloud radiative feedbacks, AHT convergence, and surface heat fluxes.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

To extract the common asymmetric TS pattern, an empirical orthogonal function (EOF) analysis is performed on the asymmetric TS responses, treating each of the 97 patch cases as if it is a sample in time in a typical EOF analysis. The leading EOF explains 59% of the total variance and the dimensional EOF pattern is presented in Fig. 4a. As anticipated, it is characterized by a global cooling pattern with large loadings in high latitudes in both hemispheres, especially along the edges of sea ice (reference the red contour lines in Fig. 5a), implying that the strong asymmetry may be related to the sea ice, as to be elaborated later in section 4a. Note that global means are not removed from each forcing case for the EOF analysis, as the global-mean response is the key interest here.

Fig. 4.
Fig. 4.

(a) Leading EOF pattern of the asymmetric TS response (K PW−1) with the explained variance labeled; (c)–(h) the leading EOF patterns of the joint EOF analysis of the asymmetric TS response attributed to water vapor, lapse rate, albedo, and cloud radiative feedbacks, AHT convergence and surface heat fluxes and the sum of the leading joint EOFs; (b) the sum of (c)–(h).

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

Fig. 5.
Fig. 5.

Leading EOF patterns of (a) the asymmetric sea ice area response (aice, in %PW−1) and (b) latent heat flux response (LHFLX in W m−2 PW−1; positive upward). Red contours in (a) demarcate the mean sea ice edge in the CTRL run, defined as where sea ice concentration drops to 15%. The right-side panels are the corresponding zonal-mean structures (red) and the zonal-mean climatology (black).

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

b. Feedback analysis through kernel decomposition

Figures 3b–g show the decomposition of the zonal-mean asymmetric TS response into contributions from water vapor feedback, lapse rate feedback, albedo feedback, cloud feedback, convergence of AHT, and surface radiative and heat fluxes, as described in section 2. Figures 4b–h show the spatial patterns of the joint EOF of the TS response resulting from these feedback processes, to be explained later in this section. As far as the strong negative asymmetry in high latitudes is of concern, lapse rate and albedo feedbacks are clearly the two major contributors. Since lapse rate and albedo feedbacks are both positive feedbacks in the polar regions (e.g., Pithan and Mauritsen 2014; Part II), the negative asymmetry here actually means a more positive feedback in the cooling case than the warming case. The significant contribution of albedo feedback (Fig. 3d) appears to arise from the asymmetric behavior of sea ice (Fig. 5a). Specifically, a heating will cause ice to retreat near the edges and open up more ocean to be in contact with the atmosphere; without the insulation effect of sea ice, a temperature increase over an open water will lead to much larger evaporative cooling, keeping the initial warming in check. In contrast, in response to a cooling perturbation, newly formed sea ice along the edges will insulate the atmosphere from the ocean water, and the mechanism of evaporative cooling over open water is replaced by less efficient evaporation over ice. Both evaporative effects work as a negative feedback to the initial forcing, despite the sign of the forcing. The net asymmetric surface latent heat flux as a result of the average of the two forcing scenarios is dominated by the negative evaporative feedback to the warming case, and hence is negative (Fig. 5b). In addition, the heat capacity of the newly formed sea ice is much smaller than that of open water, as the latter is being determined by the deep mixed layer depth, which in the SOM is prescribed to be deep at high latitudes. Therefore, the temperature of open water is much harder to warm than the newly formed ice to cool. As a result, asymmetry would emerge in the surface response near the sea ice edge to a pair of forcings with the same magnitude but opposite sign. This mechanism has also been used to explain the reduction of seasonal cycle in surface temperature over the polar regions in Dwyer et al. (2012).

Lapse rate feedback, related to the vertical structure of atmosphere, has long been identified as a major positive feedback in polar regions (e.g., Pithan and Mauritsen 2014; Stuecker et al. 2018). Interestingly, the lapse rate feedback also contributes significantly to the cooling asymmetry along the sea ice edge, resembling the spatial pattern of albedo feedback (cf. Figs. 3c,d). The source of asymmetry in the lapse rate feedback there resides in the asymmetric changes in how the temperature inversion responds to heating versus cooling. In response to a heating, a surface confined warming will weaken the inversion strength, and in turn suppress the positive lapse rate feedback. In contrast, a bottom-confined cooling response increases the stability and enhances the temperature inversion, further compounding the positive lapse rate feedback (Fig. 6). Moreover, the cooling asymmetry associated with the lapse rate feedback leads to more sea ice, which in turn strengthens the temperature inversion and reinforces the asymmetry. This is the reason why the lapse rate feedback contribution to the asymmetric response appears to be the strongest near the sea ice edges.

Fig. 6.
Fig. 6.

Air temperature profiles at 70°S under control (black), and heating (red) and cooling (blue) experiments with q-flux perturbations placed at 55°S. The corresponding inversion strengths (IS) are labeled alongside each profile. IS is defined as the potential temperature difference between the surface and the level of the maximum temperature.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

The negative asymmetric cloud feedback mainly occurs over the stratocumulus regions in the Arctic and eastern side of the subtropical Pacific, and over the midlatitude oceans, particularly the Southern Ocean (Figs. 3e and 4f). For the subtropical cloud feedback, a prevailing view (e.g., Andrews et al. 2012; Andrews et al. 2015; Zhou et al. 2017; Ceppi and Gregory 2017) is that SST cooling in the stratocumulus regions increases lower-tropospheric stability, thereby increasing low cloud amount and reflected SW radiation. This notion appears to be consistent with the dominance of the SW cloud feedback over the LW cloud feedback shown in Fig. 7. The cloud feedbacks are computed for TOA radiative changes, so the longwave response over the low cloud regions of the Artic and subtropical Pacific is relatively weak. On the other hand, the change in cloud radiative feedback along 45°S may have something to do with the change in storminess. Given a positive q-flux perturbation, the meridional temperature gradient will decrease owing to the intrinsic polar-amplification tendency (Fig. 2a), leading to weakened storminess and suppressed cloudiness. The opposite is true for a negative perturbation, but to a much greater extent because of the greater TS cooling response over the polar regions. Taken together, the net cloud radiative effect on the asymmetric response is a cooling. The negative asymmetry in cloud radiative effect over the Arctic is arguably the result of local low cloud changes (Williams et al. 2008). Stronger TS cooling leads to more stratus cloud, which reflects more shortwave radiation back to space, eventually resulting in a negative asymmetry in SW cloud radiative feedback (Fig. 7a). However, climate models and even reanalysis data have shown large biases in simulating cloud properties over the Arctic (Zhao and Garrett 2015; Huang et al. 2017b), due to different choices and uncertainties of parameterization for clouds. Thus caution must be used in interpreting the cloud response in climate models and more research will be needed to build confidence in this aspect.

Fig. 7.
Fig. 7.

Leading EOF patterns for the asymmetric TS response due to (a) SW cloud feedback and (b) LW cloud feedback, with their explained variance shown in parentheses. Unit is K PW−1.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

It is interesting to note that the asymmetric AHT response tends to neutralize the asymmetric cloud feedback globally, except for the Southern Hemisphere (SH) polar region (Figs. 3f and 4g). Corresponding to poleward AHT transport in the Northern Hemisphere (NH) high latitudes, a convergence of AHT results in the Arctic region and a divergence of AHT in the subpolar region. Thus, the AHT term works to mediate the strong negative TS asymmetry north of 80°N, which itself is the response to the lapse rate, albedo, and cloud feedbacks. On the contrary, AHT in the SH high latitudes works to redistribute the cooling effects due to the different feedback processes from midlatitude-to-subpolar regions to Antarctica. Specifically, the largest asymmetric TS signal in the SH appears in sea ice covered regions, especially in the Ross Sea and Amundsen Sea (Fig. 4a). AHT works to compensate this excessive cooling due to the lapse rate and albedo feedbacks by drawing energy from the South Pole. As a result, Antarctica is cooled (Figs. 3f and 4g). It is also worth noting that the meridional dipole in the AHT convergence (Fig. 3f) bears a great resemblance to that associated with the positive phase of the southern annular mode (SAM) in observations (cf. Fig. 4 of Yamada and Pauluis 2015). Indeed, the asymmetric zonal wind response is also SAM-like (not shown).

Using the decomposed asymmetric TS response (into six components) through the radiative kernel approach above, we further conduct a joint EOF analysis on the concatenated matrix of the six TS components. In so doing, the resultant leading EOFs of the six components are additive to a total TS pattern (Fig. 4b), which can then be directly compared with the leading EOF of the full asymmetric TS response (Fig. 4a). It is important to note that the total TS pattern of the leading joint EOFs produces almost identically the leading EOF pattern of the actual asymmetric TS response (Fig. 4a). EOF analysis is also conducted separately with each feedback component and the resultant leading EOF patterns (not shown) are almost identical to the corresponding leading joint EOF patterns in Figs. 4c–h. These results suggest that the leading patterns do not emerge solely from the variance maximization, but also are dynamically organized and physically consistent. For example, it is not a coincidence that the AHT convergence over the eastern fringe of the Pacific co-occurs with the shortwave cloud radiative cooling (see Fig. 7). The column-integrated AHT convergence there is likely the result of increased upper-level convergence of high moist static energy (MSE) level and divergence of low MSE near the top of shallow stratocumulus cloud. The associated free-atmosphere downward motion provides favorable large-scale conditions for the formation of shallow cloud, which is an important agent for shortwave radiative cooling in the subtropical oceans. Near the edges of sea ice, the correspondence between the albedo and lapse rate feedbacks is feasibly related: ice formation (hence higher ice albedo) at the surface makes the planetary boundary easier to cool and facilitates the formation of temperature inversion (hence the stronger positive lapse rate feedback).

c. Seasonal cycle of the asymmetry

In view of the importance of the ice albedo and lapse rate feedbacks in the asymmetric TS response and the fact that they both have strong seasonal dependence, we next examine the seasonal cycle of asymmetric TS response as well as its attribution to different feedbacks. Since the structure of the zonal-mean asymmetric TS response exhibits weak dependence on the latitudes of the forcing (Fig. 3), we choose the 55°S case (denoted as SOM55S) to showcase the seasonality in the feedbacks. While the asymmetric TS response is much weaker in the tropics than the high latitude, it still exhibits some seasonal dependence with the negative TS signal tracing the seasonal evolution of the zonal-mean ITCZ. In the high latitude, asymmetry is present year around, but with large seasonal dependence (Fig. 8a). The analysis can be split into two extended seasons: an extended cold season of September–February (March–August) for the NH (SH), and an extended warm season of March–August (September–February) for the SH (NH). It can be seen that the asymmetric TS signal in the extended cold season is ~3 (1.75) times as large as the warm season in the NH (SH) (Fig. 9).

Fig. 8.
Fig. 8.

The annual cycle of zonal-mean TS asymmetric response (K) to q-flux perturbations at 55°S. (a) The total asymmetric TS response; (b)–(g) decomposition of the TS response into water vapor, albedo, and cloud radiative feedbacks, AHT convergence, and surface heat fluxes.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

Fig. 9.
Fig. 9.

Zonal-mean asymmetric TS response to q-flux forcings placed at 55°S: annual mean (black), September–February mean (red), and March–August mean (blue).

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

Figures 8b–g show the individual contribution from different feedback processes. In the above analysis, we have identified the lapse rate and albedo feedbacks to be the two most prominent contributors to the annual-mean asymmetry. Here we find that they make different contributions in different seasons. The seasonal cycle of the asymmetric lapse rate feedback exhibits a similar evolution to the total TS asymmetry (Fig. 8c). In particular, the strongest asymmetry in lapse rate feedback also occurs in the extended winter season, during which a strong temperature inversion exists due to the continuous emission of infrared radiation and the absence of solar radiation. This temperature inversion is weak or absent during the summer season, and consequently so is the asymmetry in lapse rate feedback.

The contribution of the albedo feedback (Fig. 8d) to the annual-mean TS asymmetry is comparable in magnitude to the lapse rate feedback (Figs. 3c,d and 4d,e). The albedo feedback, however, produces a large asymmetry in summer and negligible asymmetry in winter, which is out of phase with the seasonality in the total TS asymmetry. This is easy to understand: albedo feedback only operates when there is solar radiation, which is negligible in winter. Likewise, the negative cloud-induced temperature signal (Fig. 8e) also peaks in summer. Further breakdown of the cloud radiative feedback into shortwave and longwave components verifies this point (not shown).

While both surface albedo and cloud radiative feedback work to place the maximum asymmetric cooling in summer season in high latitudes, the surface heat fluxes (SHF; Fig. 8g) appears to counter the midsummer cooling and to shift the peak of the cooling to a later time of the year. The lapse rate feedback, as to be revealed in the next section via model experiments, mainly plays an amplification role on the seasonally dependent cooling asymmetry.

While the kernel decomposition does not tell causality for the large asymmetry in the TS response, clues may be learned from the major contributing terms. From the results shown in Fig. 8, we speculate that high-latitude processes, especially those related to the sea ice, might be responsible for the large asymmetry in this CESM1.1-SOM climate system.

5. The origin of the asymmetry

To test the hypothesis that it is the sea ice that instigates the large asymmetry of the global TS response, we modify the CESM1.1-SOM with three different configurations, in which the influence of sea ice or seasonal cycle are removed individually (denoted as NI and NS, respectively, meaning no ice and no season), or both factors are removed simultaneously (denoted as NI-NS). Specifically, we disable the sea ice processes in CESM1.1-SOM by letting seawater become supercooled so that ice cannot form (NI configuration). It should be noted that, as the sea ice is removed, the temperature in high latitudes becomes much higher in this set of experiments. To mitigate this problem, we modify the mean q-flux forcing with the Gaussian-shaped q-flux perturbations in Arctic and Southern Ocean, so that the mean state of the NI simulation agrees well with the control simulation with sea ice. The NS configuration is constructed by forcing CESM1.1-SOM with equinoctial radiation and a climatological q flux diagnosed from a long experiment with the fully coupled CESM1.1 under constant equinoctial solar forcing.

To extract the asymmetric response in each of the configurations, in addition to a 150-yr control simulation with the control q flux, a pair of perturbation experiments with q-flux anomalies prescribed along 55°S with a peak amplitude of 12 W m−2 is also performed (see Table 1). To facilitate the comparison with the local q-flux patch experiments, the meridional structure of the new q-flux perturbations is the same as that in Eq. (2) so that the total flux of the new experiments is the same as the sum of the fluxes of the patches along the corresponding latitude. With these experiments, we can qualitatively evaluate the role of seasonal cycle in producing asymmetry by comparing SOM55S against SOM55S-NS, and the role of sea ice by comparing SOM55 against SOM55S-NI. To further test the sensitivity of the asymmetric response to the location of the forcing, extra experiments with the NI-NS configuration are performed with a pair of q-flux forcings prescribed along the equator (experiment SOMEQ, SOMEA-NS-NI in Table 2). See Tables 1 and 2 for the specifics of these experiments.

Table 1.

High-latitude forcing (55°S) experiments.

Table 1.
Table 2.

Equatorial forcing (EQ) experiments.

Table 2.

Figures 10a and 10b show the zonal-mean symmetric and asymmetric TS response, respectively, in the experiments with different configurations. Considering the symmetric component, the removal of the seasonal cycle has limited influence (cf. the blue and black lines in Fig. 10a), except for an amplified warming effect at the South Pole. The removal of sea ice disables the positive albedo feedback and thus decreases the symmetric TS response (green line), yet the overall shape of the response agrees with that of SOM55S. In contrast, the asymmetric component exhibits substantial changes, in both pattern and magnitude. Contrasting SOM55S against SOM55S-NS in Fig. 10b gives the effect of the seasonal cycle on the asymmetry of the TS response. While the asymmetric cooling is still present in the absence of the seasonal cycle, the magnitude is reduced by an order of magnitude. Meanwhile, the large asymmetry south of 70°S in SOM55S largely disappears, seemingly related to the asymmetric AHT in the SH polar region (discussed in section 4b). When sea ice is disabled, the TS response becomes almost perfectly symmetric (see green and red lines in Fig. 10b), no matter the seasonal cycle is present or not. This points to sea ice and the related feedback processes as the originator for the asymmetry in the TS response.

Fig. 10.
Fig. 10.

(a) Symmetric component and (b) asymmetric component of the zonal-mean, annual-mean TS response to q-flux perturbations at 55°S in SOM55S (black), SOM55S-NS (blue), SOM55S-NI (green), and SOM55S-NI-NS (red) experiment sets. The latitude range at which the response is statistically significant at the 99% confidence level is highlighted with shaded edges. The significance test is against the null hypothesis that a 20-yr mean anomaly can randomly occur from internal variability, and the corresponding probability distribution is constructed from 5000 samples randomly picked from the control run of each experiment set.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

What is the source of the asymmetric TS response signal in low latitudes then? From the results above, we can only assert that the low-latitude asymmetric feature is the consequence of the high-latitude asymmetry, because the low-latitude asymmetry completely disappears once seasonal cycle and sea ice are removed. To further demonstrate that the tropical asymmetric signal is independent of the forcing location, we also compare the asymmetric TS features simulated by experiments SOMEQ and SOMEQ-NS-NI in Fig. 11. The asymmetric TS response in SOMEQ strongly resembles that in the SOM55S case, demonstrating that the large asymmetry at high latitudes shown in Fig. 10 is not a result of local forcing, but rooted in the nonlinear processes occurring at the high latitudes and the corresponding asymmetry with respect to warming or cooling. Once the influences of the seasonal cycle and sea ice are removed, the asymmetric component almost completely disappears while the symmetric component is only moderately affected. Despite being directly disturbed by the q-flux pair, the tropics exhibits no asymmetric response at all, implying that forcing placed at the equator cannot excite asymmetry directly through local cloud and water vapor feedbacks, those being induced rather indirectly. As shown in Fig. 11a, the tropical forcing first produces a large symmetric TS response in polar regions via polar amplification mechanisms; the large symmetric response in turn excites asymmetric feedbacks through the sea ice–related processes as detailed in section 4b; finally, the asymmetric signal spreads to the low latitudes via circulation and cloud and water vapor feedbacks. It appears that the atmospheric circulation plays an important role in organizing the pattern of the asymmetric response in the SH, noting the strong projection of the zonal wind and AHT divergence on the SAM.

Fig. 11.
Fig. 11.

(a) Symmetric component and (b) asymmetric component of the zonal-mean, annual-mean TS response to q-flux perturbations at equator in SOMEQ (black) and SOMEQ-NS-NI (red) experiment sets. The shaded edges assume the same meaning as those in Fig. 10.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

From the results above, one naturally conjectures that, in a warmer climate where sea ice has been largely melted, the cooling asymmetry should diminish accordingly. Indeed, when we repeat the q-flux twin perturbation experiments at 55°S with a climate wherein the CO2 concentration is quadrupled (SOM55S-4×CO2 set; Table 1) and the global sea ice area declines to be only ~1/8 that in SOM55S control, the negative asymmetry largely disappears in this warm climate, and merely exists at the southern high latitudes where some sea ice still exists (Fig. 12).

Fig. 12.
Fig. 12.

(a) Symmetric component and (b) asymmetric component of the zonal-mean, annual-mean TS response to q-flux perturbations at 55°S in SOM55S (black) and SOM55S-4×CO2 (red). The shaded edges assume the same meaning as those in Fig. 10. Note that to prevent model from crash in a very warm climate, the magnitude of the q-flux perturbations in SOM55S-4×CO2 are 1/3 of those in SOM55S, thus the TS response here is scaled up by a factor of 3.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

6. Summary and concluding remarks

A linear climate response assumption is widely adopted in studying climate response and sensitivity. However, through examining a large set of q-flux Green’s function experiments, we find strong asymmetry in the TS response to symmetric forcing, characterized by a common pattern that is insensitive to the location of oceanic forcing. The asymmetric TS response is negative across much of the globe, indicating that the climate tends to skew toward a cooler state. Considering that the magnitude of the asymmetric TS response is comparable to the symmetric component, it may serve as an important mediating factor in offsetting the anthropogenically forced global warming. The asymmetry pattern also features polar amplified cooling in both hemispheres, especially along the sea ice edges. Examination of the seasonal cycle shows that, though the asymmetric TS response in high latitudes exists all year long, it exhibits large seasonal variation, with larger asymmetry in the cold season than the warm season.

As for the physical mechanisms for the climate asymmetry, we have found compelling evidence that it is plausibly rooted in the switch between two coupling regimes: a two-way system between seawater and air and a three-way system among seawater, air, and sea ice. Comparing between the three-way system due to sea ice growth under cooling versus a two-way system due to melting under warming, several operating feedback processes are asymmetric: (i) the evaporative cooling is more efficient over a water surface than an ice one, (ii) the deep wintertime ocean mixed layer in high latitudes gives a much larger effective heat capacity to the temperature of open water than that of the newly formed sea ice, and (iii) the surface confinement of the temperature response in the presence of an inversion can enhance (weaken) the inversion and hence reduce (increase) the positive lapse rate feedback if it is cooled (warmed). Figure 13 presents a schematic characterization of these asymmetries. Moreover, these asymmetric processes can compound one another in maintaining the final, skewed equilibrium response. Further surgical numerical experiments will be needed to tease out the quantitative contribution from each of the processes surmised above.

Fig. 13.
Fig. 13.

Schematics depicting the key asymmetric processes in generating the asymmetric TS response due to (a) the presence of sea ice, and (b) the presence of seasonal cycle. In the presence of sea ice, evaporative cooling and effective heat capacity are the two major asymmetric factors; in cold season, the lapse rate feedback is the major source of asymmetry in response to cooling vs warming.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0131.1

Owing to the use of a slab-coupled AGCM here, the roles of active ocean dynamics in the global climate asymmetry are not addressed in this study. Including active ocean dynamics may bring significant changes to the asymmetry found in this study. Therefore, it is of great interest and importance to explore how interactive ocean heat convergence/divergence may alter the asymmetry in question, similar experiments with a fully coupled model configuration are warranted.

We cannot rule out the possibility that some of the above results are unique to the CESM1.1-SOM, and thus do not represent the asymmetry of the real climate. Intermodel comparison efforts would be needed to address the issue of model dependence with regard to the climate response asymmetry. Notwithstanding, the two major sources (sea ice and seasonal cycle) identified for generating the asymmetry are behaviors expected from fundamental physical principles not restrictive to the SOM framework, nor to any particular model, and the physical plausibility gives us some confidence in the discovered asymmetric response.

Acknowledgments

This study is supported by the National Natural Science Foundation of China (NSFC; 41906002 and 91858210), the National Key Research and Development Program of China (2018YFA0605702). It is also supported by the U.S. Department of Energy Office of Science Biological and Environmental Research (BER) as part of the Regional and Global Climate Modeling Program. The Pacific Northwest National Laboratory is operated for the Department of Energy by Battelle Memorial Institute under Contract DE-AC05-76RL01830. We acknowledge the use of computational resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231. The model data outputs are available upon request from the corresponding author.

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