Abstract

Unforced global mean surface air temperature () is stable in the long term primarily because warm anomalies are associated with enhanced outgoing longwave radiation () to space and thus a negative net radiative energy flux (, positive downward) at the top of the atmosphere (TOA). However, it is shown here that, with the exception of high latitudinal and specific continental regions, warm unforced surface air temperature anomalies at the local spatial scale [T(θ, ϕ), where (θ, ϕ) = (latitude, longitude)] tend to be associated with anomalously positive N(θ, ϕ). It is revealed that this occurs mainly because warm T(θ, ϕ) anomalies are accompanied by anomalously low surface albedo near sea ice margins and over high altitudes, low cloud albedo over much of the middle and low latitudes, and a large water vapor greenhouse effect over the deep Indo-Pacific.

It is shown here that the negative versus relationship arises because warm anomalies are associated with large divergence of atmospheric energy transport over the tropical Pacific [where the N(θ, ϕ) versus T(θ, ϕ) relationship tends to be positive] and convergence of atmospheric energy transport at high latitudes [where the N(θ, ϕ) versus T(θ, ϕ) relationship tends to be negative]. Additionally, the characteristic surface temperature pattern contains anomalously cool regions where a positive local N(θ, ϕ) versus T(θ, ϕ) relationship helps induce negative . Finally, large-scale atmospheric circulation changes play a critical role in the production of the negative versus relationship as they drive cloud reduction and atmospheric drying over large portions of the tropics and subtropics, which allows for greatly enhanced .

1. Introduction

Changes in surface air temperature (T) can be caused by external radiative forcings that impose a net radiative energy flux (N, positive down) at the top of the atmosphere (TOA):

 
formula

where SW represents shortwave (solar) radiation at the TOA, LW represents longwave (terrestrial) radiation at the TOA, and the arrows represent the direction of the flux. Additionally, T experiences unforced variability that originates from the internal dynamics of the climate system (Brown et al. 2014a; Hasselmann 1976; Hawkins and Sutton 2009; Palmer and McNeall 2014). Unforced variability in global mean T () has generated great scientific and public interest as it has the ability to either enhance or obscure externally forced signals such as the long-term warming due to increased greenhouse gas concentrations (Brown et al. 2015). Much work on the causes of unforced variability has focused on changes in the net heat flux between the ocean and atmosphere (Chen and Tung 2014; Drijfhout et al. 2014; England et al. 2014; Meehl et al. 2013). However, it is also recognized that unforced variability in N, due to changes in clouds in particular, can enhance the magnitude and persistence of unforced T variability locally (Bellomo et al. 2014, 2015; Evan et al. 2013; Trzaska et al. 2007). Therefore, there has been substantial interest in the relationship between and in the context of unperturbed climate variability (Allan et al. 2014; Brown et al. 2014a; Kato 2009; Loeb et al. 2012; Palmer and McNeall 2014; Smith et al. 2015; Trenberth et al. 2014) as this relationship may have implications for the magnitude and persistence of unforced variability.

When the climate system is unperturbed by external radiative forcings, it is expected that would be stable on long time scales predominantly because of the Planck response, or the direct blackbody radiative response to a uniform temperature change of the surface and the atmosphere (Bony et al. 2006; Dessler 2013; Hallberg and Inamdar 1993; Ingram 2013). In the global mean sense, the Planck response suggests that positive anomalies tend to be associated with enhanced , which would cause negative , and thus an eventual return of to its equilibrium value (Brown et al. 2014a; Dessler 2013; Koumoutsaris 2013; Trenberth et al. 2015). Indeed, both satellite observations and atmosphere–ocean general circulation models (AOGCMs) show this negative versus global mean relationship for interannual variability (Fig. 1a).

Fig. 1.

Sign difference between the global mean vs and the local N(θ, ϕ) vs T(θ, ϕ) relationship. (a) Linear least squares relationship between annual mean and annual mean pooled across 27 CMIP5 AOGCMs (black), and in CERES/ERA-I observations from 2001–14 (red). (b) Map of the multimodel means of the linear least squares regression coefficients between annual anomalous N(θ, ϕ) and annual anomalous T(θ, ϕ). The zero isopleth is contoured in blue and stippling represents where at least 90% of the models agree on the sign of the regression coefficient. (c) As in (b), but for CERES/ERA-I observations from 2001–14. (d) Zonal mean of (b) and (c) with gray shading representing the across-AOGCM standard deviation of the zonal mean of the regression values.

Fig. 1.

Sign difference between the global mean vs and the local N(θ, ϕ) vs T(θ, ϕ) relationship. (a) Linear least squares relationship between annual mean and annual mean pooled across 27 CMIP5 AOGCMs (black), and in CERES/ERA-I observations from 2001–14 (red). (b) Map of the multimodel means of the linear least squares regression coefficients between annual anomalous N(θ, ϕ) and annual anomalous T(θ, ϕ). The zero isopleth is contoured in blue and stippling represents where at least 90% of the models agree on the sign of the regression coefficient. (c) As in (b), but for CERES/ERA-I observations from 2001–14. (d) Zonal mean of (b) and (c) with gray shading representing the across-AOGCM standard deviation of the zonal mean of the regression values.

It may be tempting to suppose that this negative versus global relationship should hold at the local spatial scale as well, but it was recently pointed out that the N(θ, ϕ) versus T(θ, ϕ) relationship [where (θ, ϕ) = (latitude, longitude)] is in fact positive in observations over much of Earth (Trenberth et al. 2015). Indeed, the same observations and AOGCMs that demonstrate the negative versus relationship (Fig. 1a) indicate that the N(θ, ϕ) versus T(θ, ϕ) relationship tends to be positive over most of the surface of the planet (Figs. 1b–d). The underlying reasons for the spatial distribution of the N(θ, ϕ) versus T(θ, ϕ) relationship as well as the cause of the relationship’s sign reversal at the global scale are the primary topics of investigation in this study. Elucidating these relationships will improve our physical understanding of unforced T variability and may improve efforts to model climate variability on both local and global scales.

2. Data, preprocessing, and definitions

a. AOGCM data

We focus on the relationship between unforced anomalous annual mean T and unforced anomalous annual mean energy fluxes in 27 AOGCMs that participated in phase 5 of the Coupled Model Intercomparison Project (CMIP5; Taylor et al. 2012). Details on the AOGCMs used in this study can be found in Table S1 in the supplementary material. We utilized unforced preindustrial control runs, which included no external radiative forcings, and thus all variability emerged spontaneously from the internal dynamics of the modeled climate system. We used the first 200 years of each AOGCM’s preindustrial control run and linearly detrended all analyzed variables so that our analysis was not contaminated by possibly unphysical model drift (Fig. 2).

Fig. 2.

Global mean temperature (K) and net TOA radiation (W m−2) for the 27 AOGCM preindustrial control runs used in this this study. Time series of are black and time series of are blue.

Fig. 2.

Global mean temperature (K) and net TOA radiation (W m−2) for the 27 AOGCM preindustrial control runs used in this this study. Time series of are black and time series of are blue.

We focus our analysis on multimodel mean values (e.g., the mean of the AOGCMs’ N vs T linear regression coefficients) in order to highlight the most robust relationships across the ensemble. However, the AOGCM spread about these mean values is shown where appropriate (e.g., Figs. 1d and 10; see also Fig. S6 in the supplementary material) and we indicate model agreement with stippling that denotes where more than 90% of AOGCMs agree on the sign of the regression coefficients (e.g., Figs. 1b, 3a–k, and 6a–k).

Fig. 3.

Maps of variables defined locally, α(θ, ϕ) regressed against anomalous local temperature, T(θ, ϕ) [Eq. (11)]. Multimodel mean of the annual linear least squares regression coefficients of (a) N(θ, ϕ), (b) ClearSW(θ, ϕ), (c) CRESW(θ, ϕ), (d) T(θ, ϕ), (e) ClearLW(θ, ϕ), (f) CRELW(θ, ϕ), (g) SLP(θ, ϕ), (h) S(θ, ϕ), (i) CRE(θ, ϕ), (j) , and (k) cloud fraction at (θ, ϕ), all regressed against T(θ, ϕ). The spatially weighed global mean value is displayed above each panel. The zero isopleth is contoured black in each panel. All fluxes are positive into the atmospheric column. Stippling in (a)–(k) represents where over 90% of the AOGCMs agreed on the sign of the regression coefficient. (l)–(v) As in (a)–(k), but for observations. Note that (a) and (l) are the same as Figs. 1b and 1c respectively but are reproduced here for convenience.

Fig. 3.

Maps of variables defined locally, α(θ, ϕ) regressed against anomalous local temperature, T(θ, ϕ) [Eq. (11)]. Multimodel mean of the annual linear least squares regression coefficients of (a) N(θ, ϕ), (b) ClearSW(θ, ϕ), (c) CRESW(θ, ϕ), (d) T(θ, ϕ), (e) ClearLW(θ, ϕ), (f) CRELW(θ, ϕ), (g) SLP(θ, ϕ), (h) S(θ, ϕ), (i) CRE(θ, ϕ), (j) , and (k) cloud fraction at (θ, ϕ), all regressed against T(θ, ϕ). The spatially weighed global mean value is displayed above each panel. The zero isopleth is contoured black in each panel. All fluxes are positive into the atmospheric column. Stippling in (a)–(k) represents where over 90% of the AOGCMs agreed on the sign of the regression coefficient. (l)–(v) As in (a)–(k), but for observations. Note that (a) and (l) are the same as Figs. 1b and 1c respectively but are reproduced here for convenience.

b. Observational data

We supplement the AOGCM analysis with TOA radiation measurements from the Clouds and Earth’s Radiant Energy System (CERES; Wielicki et al. 1996) Energy Balanced and Filled (EBAF, version 2.8) product and cloud area fraction from the CERES–MODIS product (Minnis et al. 2011). Additionally, we use the European Center for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim, hereinafter ERA-I; Dee et al. 2011) to provide historical estimates of T, sea level pressure (SLP), and surface heat flux (S). We use annual mean values for these datasets over the 14-yr period in which they overlap (2001–14). For simplicity we refer to both ERA-I and CERES data as observations even though ERA-I output represents observations assimilated into a weather forecast model. We linearly detrend all of the observations prior to further analysis. It should be noted that the historical record contains a combination of both forced and unforced variability; these are difficult to disentangle but over the relatively short time period of investigation (2001–14) unforced variability accounts for a substantial majority of the observed variation (Dessler 2010; Trenberth et al. 2010).

The purpose of this manuscript is to use both AOGCMs and observations to gain physical insight on the covariability between N and T. Therefore, it is not our intent to rigorously compare AOGCMs to observations in order to assess model performance. Nevertheless, AOGCMs are known to struggle with the simulation of clouds, and thus it is useful to keep in mind that there are some large differences between AOGCM-modeled and observed cloud climatologies (Fig. S1 in the supplementary material). See also Dolinar et al. (2015) for further discussion.

c. Definitions

1) Local and global spatial scale

We bilinearly interpolate all variables (α) from both AOGCM and observational datasets to a common 2.5° × 2.5° latitude–longitude [(θ, ϕ)] grid. Global mean values, denoted by an overbar, are calculated as

 
formula

where the i subscript indicates the ith value of a total of M, which is weighed by the grid box area ai and normalized by the total Earth surface area A.

2) Components of N

To gain insight into the underlying physics governing N variability, we follow previous studies (Ramanathan et al. 1989) to decompose N into four linearly additive components:

 
formula
 
formula
 
formula
 
formula

where ClearSW, ClearLW, CRESW, and CRELW represent the anomalous clear-sky shortwave, anomalous clear-sky longwave, anomalous cloud radiative effect (CRE) shortwave, and CRE longwave components, respectively, at the TOA (all positive downward). We also investigate the net impact of clouds using

 
formula

The CRE is a measure of the impact of cloud radiative properties and cloud fraction on the TOA radiation budget relative to a cloudless atmosphere (Ramanathan et al. 1989). Thus, a change in the CRE with T is not a pure measure of cloud feedback since a change in the CRE can occur because of a change in clouds or a change in the clear-sky radiation budget (Soden et al. 2004). This makes it difficult to isolate the effect of clouds on N over regions with large changes in the clear-sky energy budget. Nevertheless, decomposing N using Eqs. (3)(7) provides some physical insight that would not be available otherwise. In future work it may be valuable to investigate the components of N using different methods such as the partial radiative perturbation technique (Donohoe and Battisti 2011).

3) Surface and atmospheric energy fluxes

The net anomalous upward surface heat flux (S) is

 
formula

where LE is the anomalous latent heat flux, SH is the anomalous sensible heat flux, SWS is the anomalous shortwave radiation flux, and LWS is the anomalous longwave radiation flux all defined at Earth’s surface under all-sky conditions.

We follow (Trenberth et al. 2002a,b) to define an estimate of the convergence of the vertically integrated atmospheric energy transport (AET):

 
formula

For observations, both S(θ, ϕ) and N(θ, ϕ) in Eq. (9) came from ERA-I [rather than using N(θ, ϕ) from CERES] so that potentially disparate datasets were not mixed. This approximation ignores any atmospheric storage of heat, which was assumed to be small.

4) Linear regression relationships

In the sections below we will make use of the following notation to denote a variety of different linear least squares regression relationships between climatic variables (α) and T both on the local [T(θ, ϕ)] and global [] scales.

The regression coefficient between any global mean variable and is denoted as

 
formula

The corresponding regression coefficient at the local spatial scale is denoted as

 
formula

Note that the global mean of the regression coefficients calculated on the local scale [] is not the same quantity as the regression coefficient calculated on global means [] as Fig. 1 demonstrates.

Finally, the linear relationship between a variable defined at the local spatial scale and is denoted as

 
formula

5) Feedbacks

We follow convention by referring to the linear relationship between a TOA radiative flux anomaly and a T anomaly as a “feedback” (Bellomo et al. 2015; Colman and Power 2010; Dessler 2013; Koumoutsaris 2013; Trenberth et al. 2015). This language can give the impression that we know the change in T is the cause and the change in TOA flux is the effect. It is safe to assume this direction of causality when an external forcing is obviously responsible for the T change but the direction of causality is more ambiguous in the unforced climate state where all variability is spontaneously generated by the system itself. Undoubtedly there are instances where changes in the TOA flux (e.g., atmospheric circulation induced changes in clouds over land) lead to the T anomaly (Trenberth and Shea 2005). Therefore, we caution that we use the term feedback to be consistent with other contemporary work on this subject but we do not wish to convey that the direction of causality is necessarily known in all cases.

3. The geographic distribution of the γN(θ, ϕ) relationship

We first investigate the local relationships between N and T [γN(θ, ϕ); Eq. (11)] with the intent of uncovering the physical processes underlying these relationships as well as how these physical processes differ by geographic location. Figure 3 maps γα(θ, ϕ) for a number of variables in both AOGCMs (Figs. 3a–k) and observations (Fig. 3l–v). Note that (Figs. 3e,p) is affected by the lapse rate feedback, the water vapor feedback, and the Planck response (Colman and Power 2010; Crook et al. 2011), but over most of Earth’s surface the Planck response dominates this component and there is enhanced to space during elevated T(θ, ϕ). [Note that via the Planck response is more heavily influenced by tropospheric mean temperature than by T itself but that T and tropospheric mean temperature are positively correlated on these time scales (Trenberth et al. 2015).] In the AOGCMs, the primary exception to this enhanced with warm T(θ, ϕ) is over the Indo-Pacific warm pool where higher climatological surface temperatures allow for a water vapor response that is strong enough to overwhelm the Planck response (Allan et al. 1999; Inamdar and Ramanathan 1994; Larson and Hartmann 2003; Pierrehumbert 1995; Ramanathan and Collins 1991; Su et al. 2006). In this region, anomalous warmth is also associated with enhanced convection and cloud fraction (Fig. 3k) but since the shortwave (Fig. 3c) and longwave (Fig. 3f) CRE components mostly cancel (Fig. 3i) (Kiehl 1994), it is the water vapor feedback (Fig. 3e) that is primarily responsible for the positive γN(θ, ϕ) relationship there. Note that the strength of the water vapor response also depends on enhanced convection as moistening of the middle and upper troposphere is crucial for its large magnitude in this region (Hallberg and Inamdar 1993).

Observations tell a similar story except that is negative over the central portion of the Indo-Pacific warm pool (Fig. 3p). This disagreement may be because satellites are only able to sample ClearLW(θ, ϕ) in regions that are actually cloud-free [unlike AOGCMs which calculate ClearLW(θ, ϕ) at all grid points and at every time step regardless of the simulated cloud cover]. A consequence of this is that the ClearLW(θ, ϕ) measurement from satellites will disproportionately represent the cloudless areas with less humidity and less of a water vapor greenhouse effect.

Over most of the remainder of the surface, with the exception of the subpolar latitudes, the positive γN(θ, ϕ) relationship is due mostly to the component (Figs. 3c,n) associated with a reduction in cloud fraction (Figs. 3k,v) and an overall positive (Figs. 3i,t). This is consistent with the shortwave cloud feedback that has been noted in regions characterized by high-albedo, low-level stratiform clouds in particular (Evan et al. 2013; Park et al. 2005). In these regions, elevated T(θ, ϕ) is associated with increased convection and destabilization of the boundary layer (Bellenger et al. 2014) as well as a lack of sufficient increase in evaporation to maintain the boundary layer cloudiness (Webb and Lock 2013). The surface albedo component also plays an important role in the positive γN(θ, ϕ) relationship over the Southern Ocean, near the Arctic sea ice margin, and over the high altitude Rockies and Himalayan mountain ranges (Figs. 3b,m) where warm years are associated with less snow or sea ice.

The γN(θ, ϕ) relationship (Figs. 3a,i) tends to be negative near both poles and over some specific continental regions (e.g., equatorial South America, equatorial Africa, Australia, and northern Eurasia). In these areas, the (Figs. 3b,m) and (Figs. 3i,t) components of γN(θ, ϕ) are near zero. Since atmospheric water vapor in these locations is limited compared to the tropical ocean, the Planck response [embedded within the component; Figs. 3e,p] is able to emerge as the dominant influence on γN(θ, ϕ).

Figure 3 also maps the γS(θ, ϕ) relationship (Figs. 3h,s), which tends to be positive over the equatorial ocean where natural variability in the thermocline heat budget can cause persistent, large-magnitude T(θ, ϕ) anomalies (Deser et al. 2010). In this part of the globe, γS(θ, ϕ) is much larger than γN(θ, ϕ), indicating that it dominates the local energy budget. Furthermore, both the γS(θ, ϕ) and the γN(θ, ϕ) relationships are positive over much of the equatorial ocean (see Figs. 3a,h and 3l,s), indicating that T(θ, ϕ) anomalies in these location cannot be damped locally and tend to be associated with anomalous atmospheric energy transport, which communicates local anomalous S(θ, ϕ) to higher latitudes (Kosaka and Xie 2013). The relationship (Figs. 3j,u) shows that warm T(θ, ϕ) anomalies over the equatorial ocean and portions of the subtropics are associated with net anomalous horizontal export of energy while warm T(θ, ϕ) anomalies over many continental and high-latitude regions are associated with the net anomalous horizontal import of energy from other locations.

4. Dependency of the γN(θ, ϕ) relationship on climatological T(θ, ϕ)

The geographic distribution apparent in Fig. 3 suggests that the physics of the γN(, ϕ) relationship may depend fundamentally on the climatological value of T(θ, ϕ) [T(θ, ϕ)Clim] as well as whether the location is over land or ocean. Figures 4 and 5 illustrate how the variables shown in Fig. 3 vary as a function of T(θ, ϕ)Clim and anomalous T(θ, ϕ) over land (Fig. 4) and ocean (Fig. 5) grid points. The bins and the number of data points underlying each average value are shown in Fig. S2 of the supplementary material. Figures 4a, 4l, 5a, and 5l label four regimes [regime I with T(θ, ϕ)Clim values below 255 K; regime II with T(θ, ϕ)Clim values from 255 to 273 K; regime III with T(θ, ϕ)Clim values from 273 to 300 K; and regime IV with T(θ, ϕ)Clim values above 300 K] that were chosen to highlight noteworthy shifts in the underlying physical mechanisms of the N(θ, ϕ) versus T(θ, ϕ) relationship.

Fig. 4.

Dependency of relationships on local climatological temperature, T(θ, ϕ)Clim. Bivariate plots over land grid points for the same variables from Fig. 3 plotted as a function of climatological T(θ, ϕ) [T(θ, ϕ)Clim] and T(θ, ϕ) anomaly. Regimes discusses in the text are labeled in (a) and (l) and are delineated in the plots with vertical dashed lines. Figure S3 in the supplementary material contours the mean geographical extent of the regimes. These panels are produced by sampling every grid point and every year, pooling the data into two-dimensional histograms, and averaging over the pooled values to produce the number displayed (in the observations and AOGCMs separately). The bins and the number of data points underlying each average value are shown in Fig. S2. White areas had no values to calculate an average.

Fig. 4.

Dependency of relationships on local climatological temperature, T(θ, ϕ)Clim. Bivariate plots over land grid points for the same variables from Fig. 3 plotted as a function of climatological T(θ, ϕ) [T(θ, ϕ)Clim] and T(θ, ϕ) anomaly. Regimes discusses in the text are labeled in (a) and (l) and are delineated in the plots with vertical dashed lines. Figure S3 in the supplementary material contours the mean geographical extent of the regimes. These panels are produced by sampling every grid point and every year, pooling the data into two-dimensional histograms, and averaging over the pooled values to produce the number displayed (in the observations and AOGCMs separately). The bins and the number of data points underlying each average value are shown in Fig. S2. White areas had no values to calculate an average.

Fig. 5.

As in Fig. 4, but over ocean grid points.

Fig. 5.

As in Fig. 4, but over ocean grid points.

All four regimes indicate that over land, elevated T(θ, ϕ) anomalies are associated with a negative ClearLW(θ, ϕ) contribution to N(θ, ϕ) (Figs. 4e,p) via the Planck response. Over the ocean, however, the strong water vapor feedback overwhelms the Planck response near 300 K in the AOGCMs (Fig. 5e), but this feature is not present in observations (Fig. 5p) as was discussed in section 3. Since there is no water vapor runaway greenhouse effect over land, the anomalous N(θ, ϕ) versus T(θ, ϕ) relationship (Figs. 4a,l) is governed by the ability of the surface albedo (Figs. 4b,m) and CRE(θ, ϕ) components (Figs. 4i,t) to overwhelm the ClearLW(θ, ϕ) component.

Over regime I, cold climatological T(θ, ϕ) values, which are well below the freezing point of water, produce semipermanent ice that is not prone to variation. Consequently, there is little shortwave variability in this regime over land or ocean from either ClearSW(θ, ϕ) (Figs. 4b,m and 5b,m) or CRESW(θ, ϕ) (Figs. 4c,n and 5c,n). Additionally, the shortwave components of variability make less of an impact in this regime because these locations are at high latitudes and experience less annually averaged incoming solar radiation than the rest of the planet. Anomalous warmth in regime I is associated with increased cloud fraction (Figs. 4k,v and 5k,v) and a positive CRELW(θ, ϕ) and CRE(θ, ϕ) anomaly (Figs. 4i,t and 5i,t); however, this effect is not large enough to overwhelm the ClearLW(θ, ϕ) response (Figs. 4e,p and 5e,p). This implies that anomalous warmth over Antarctica and the polar Arctic Ocean (likely caused by anomalous convergence of AET; Figs. 4j,u and 5j,u) will tend to be strongly damped by the Planck response.

Unlike regime I, regime II experiences anomalously positive N(θ, ϕ) during positive T(θ, ϕ) anomalies. Regime II is characterized by T(θ, ϕ)Clim values near the freezing point of water so positive T(θ, ϕ) anomalies are associated with significant reductions in surface albedo over land and ocean (Figs. 4b,m and 5b,m). These reductions in surface albedo are larger than the negative ClearLW(θ, ϕ) response (Figs. 4e and 5e,p), except in observations over land where the ClearLW(θ, ϕ) mostly overwhelms the ClearSW(θ, ϕ) component (Fig. 4l) but this may be an artifact of a limited number of observations (Fig. S2b).

Regime III also tends to experience anomalously positive N(θ, ϕ) during positive T(θ, ϕ) anomalies. Regime III, is generally above the freezing point of water and thus it is the CRESW(θ, ϕ) component that is primarily responsible (Figs. 4c,n and 5c,n) for the positive N(θ, ϕ) versus T(θ, ϕ) relationship. In this regime, anomalous warmth is associated with a reduction in cloud fraction (Figs. 4k,v and 5k,v) that causes a larger reduction in cloud albedo (Figs. 4c,n and 5c,n) than cloud greenhouse effect (Figs. 4f,q and 5f,q). The direction of causality is particularly ambiguous in this regime since reduced cloudiness leads to warmth (Trenberth and Shea 2005).

Over land, where the water vapor supply is limited, T(θ, ϕ) warmth in regime IV is associated with anomalously negative N(θ, ϕ) (Figs. 4a,l). In this regime, anomalous warmth is associated with decreased precipitation (Trenberth and Shea 2005) and cloud fraction (Figs. 4k,v); however, because of longwave and shortwave cancellation, the CRE(θ, ϕ) response is relatively small (Figs. 4i,t). Also, since the T(θ, ϕ)clim value is well above the freezing point of water, the ClearSW(θ, ϕ) response is near zero. These factors allow the Planck response (embedded in Figs. 4e and 4p) to dominate the total response (Figs. 4a,l). Like regime I, regime IV over land tends to be an area of AET convergence during anomalous T(θ, ϕ) warmth (Figs. 4j,u).

5. The negative relationship

Having established some of the underlying physics governing the geographic distribution of the local N(θ, ϕ) versus T(θ, ϕ) relationship, we now turn our attention to the problem of reconciling the mostly positive local N(θ, ϕ) versus T(θ, ϕ) relationship (Figs. 1b–d and 3a,l) with the negative versus () relationship (Fig. 1a). One possible way to square these seemingly paradoxical results would be through the specific spatial pattern of T(θ, ϕ) anomalies associated with changes in [i.e., ζT(θ, ϕ); Eq. (12)]. Specifically, we showed in sections 3 and 4 that certain locations on the surface of the planet are better able to damp T(θ, ϕ) anomalies to space than others. For example, anomalous warmth over Antarctica and the polar Arctic Ocean will tend to be effectively damped by the Planck response (Figs. 1b–d and 3a,l). Therefore, if ζT(θ, ϕ) was distributed such that most of the anomalous warmth was in high-latitude regions characterized by a negative γN(θ, ϕ) relationship, then the apparent contradiction of Fig. 1a and Figs. 1b–d might be resolved.

Figure 6 displays the ζT(θ, ϕ) pattern (Figs. 6d,o) as well as the corresponding, ζα(θ, ϕ) for all the other variables shown in Figs. 35. On the interannual time scale, variability in is dominated by El Niño–Southern Oscillation (ENSO; Wigley 2000), which has a distinct ζT(θ, ϕ) pattern (Brown et al. 2014b). Importantly, the ζT(θ, ϕ) pattern does include large positive values at high latitudes where γN(θ, ϕ) tends to be negative and the ζT(θ, ϕ) pattern includes negative values over some locations with a locally positive γN(θ, ϕ) relationship (cf. Figs. 6d,o and 3a,l). The high-latitude amplification in the characteristic ζT(θ, ϕ) pattern is partly a result of a large surface energy flux [ζS(θ, ϕ); Figs. 6h,s] from the tropical Pacific that is transferred to high latitudes by the atmosphere where horizontal convergence occurs (Figs. 6j,u). The negative ζT(θ, ϕ) values in the North Pacific (Figs. 6d,o) occur due to an atmospheric circulation response to enhanced convection at the equator during El Niño (Trenberth et al. 1998), which strengthens the Aleutian low (Figs. 6g,r). The deeper Aleutian low implies anomalous northerly (southerly) winds over the northwestern (northeastern) Pacific and thus anomalously negative (positive) ζT(θ, ϕ) (Alexander et al. 2002; Emery and Hamilton 1985; Lau and Nath 1994). There is also an anomalously cool region in the South Pacific off the coast of Australia that arises primarily due to a shift in the South Pacific convergence zone (SPCZ) during El Niño (Folland et al. 2002).

Fig. 6.

As in Fig. 3, but local variables are regressed against global mean temperature, [Eq. (12)], rather than local temperature, T(θ, ϕ). Note that the magnitude of the response for observations is larger than that for AOGCMs and that this is partially because differences in the location of sharp gradients in the AOGCMs will result in smaller absolute values when the average is taken. [The global mean of each map is the L = 0 value in Fig. 9 and the global mean of (a) and (l) is represented in Fig. 1a.]

Fig. 6.

As in Fig. 3, but local variables are regressed against global mean temperature, [Eq. (12)], rather than local temperature, T(θ, ϕ). Note that the magnitude of the response for observations is larger than that for AOGCMs and that this is partially because differences in the location of sharp gradients in the AOGCMs will result in smaller absolute values when the average is taken. [The global mean of each map is the L = 0 value in Fig. 9 and the global mean of (a) and (l) is represented in Fig. 1a.]

These surface temperature features play a role in the production of the negative versus relationship. In AOGCMs, −0.4 W m−2 K−1 of the −0.8 W m−2 K−1 originates from locations with that are warm when the global mean is warm and have a negative local feedback [i.e., positive and negative ] like Antarctica (Fig. 7). Also, −0.5 W m−2 K−1 of the −0.8 W m−2 K−1 originates from locations that are cool when the global mean is warm but have a positive local feedback [i.e., negative and positive ] like the northwestern Pacific (Fig. 7). Similarly, in observations −1.2 W m−2 K−1 of the −2.4 W m−2 K−1 originates from locations with positive and negative while −1.3 W m−2 K−1 originates from locations with negative and positive (Fig. 7). This is consistent with the finding that AOGCMs with more Arctic amplification in their subdecadal pattern have less variable (Brown et al. 2014b) due to more of the weighting being in regions where energy can be easily damped to space. However, the ζN(θ, ϕ) spatial pattern (Figs. 6a,l) has other unique characteristics (Dessler 2013; Koumoutsaris 2013; Trenberth et al. 2010) that are not explained by the superposition of ζT(θ, ϕ) (Figs. 6d,o) and γN(θ, ϕ) (Figs. 3a,l).

Fig. 7.

Values of [Eq. (12); Figs. 6a,l] averaged over locations with the indicated properties of [Eq. (12); Figs. 6d,o] and [Eq. (11); Figs. 3a,l]. Units for all values are W m−2 K−1. Colors give an indication of relative magnitude with reds representing positive values and blues representing negative values.

Fig. 7.

Values of [Eq. (12); Figs. 6a,l] averaged over locations with the indicated properties of [Eq. (12); Figs. 6d,o] and [Eq. (11); Figs. 3a,l]. Units for all values are W m−2 K−1. Colors give an indication of relative magnitude with reds representing positive values and blues representing negative values.

To quantify the component of ζN(θ, ϕ) that is not explained by the surface temperature pattern associated with variability, we follow a procedure similar to Armour et al. (2013) where we multiply the local feedback relationships γα(θ, ϕ) (Fig. 3) by the characteristic surface temperature pattern associated with variability, ζT(θ, ϕ) (Figs. 6d,o):

 
formula

This calculation, shown in Fig. 8, illustrates what ζα(θ, ϕ) would be if local T(θ, ϕ) explained 100% of the variance in local α(θ, ϕ). For AOGCMs the κN(θ, ϕ) pattern is qualitatively similar to the ζN(θ, ϕ) pattern (cf. Figs. 6a and 8a). In particular, both ζN(θ, ϕ) and κN(θ, ϕ) have strong positive values over the tropical Pacific and more negative values over the anomalously cool subtropical Pacific, continents, and high latitudes. However, the surface temperature pattern by itself significantly underpredicts the damping of anomalies. In particular, = −1.1 W m−2 (Fig. 8e) is less negative than = −1.9 W m−2 (Fig. 6e), and = 1.7 W m−2 (Fig. 8f) is far more positive than = 0.2 W m−2 (Fig. 6f). For observations, there is less qualitative similarity between the κN(θ, ϕ) and ζN(θ, ϕ) patterns (cf. Figs. 6l and 8l). It is not surprising that the patterns in the observations contain less coherent structure than the corresponding patterns in the AOGCMs given that the observed regression coefficients are based on 14 years while the AOGCM regression coefficients are based on 5400 years (200 years each for 27 AOGCMs). Nevertheless, observations also show that the surface temperature pattern times the local feedback underestimates the damping of anomalies. This results from = −1.5 W m−2 (Fig. 8p) being less negative than = −2.6 W m−2 (Fig. 6p).

Fig. 8.

The portion of the ζα(θ, ϕ) pattern (Fig. 6) due to the characteristic surface temperature pattern associated with variability [ζT(θ, ϕ); Figs. 6d,o] multiplied by the local feedback pattern [γα(θ, ϕ); Fig. 3]; see Eq. (13).

Fig. 8.

The portion of the ζα(θ, ϕ) pattern (Fig. 6) due to the characteristic surface temperature pattern associated with variability [ζT(θ, ϕ); Figs. 6d,o] multiplied by the local feedback pattern [γα(θ, ϕ); Fig. 3]; see Eq. (13).

For both AOGCMs and observations, is positive [1.1 W m−2 (Fig. 8a) and 0.9 W m−2 (Fig. 8l)], indicating that the superposition of the characteristic surface temperature pattern associated with variability and the local feedback would, by itself, produce a positive and would be indicative of an unstable climate system. This implies that the mechanisms other than the characteristic surface temperature pattern associated with variability must be crucial for stabilizing to internal perturbations. To highlight the contribution from these other mechanisms we subtract (Fig. 8) from the directly simulated or observed relationship ζα(θ, ϕ) (Fig. 6),

 
formula

and plot these values in Fig. 9.

Fig. 9.

The portion of the ζα(θ, ϕ) pattern (Fig. 6) that is not due to the characteristic surface temperature pattern associated with variability [ζT(θ, ϕ); Figs. 6d,o] multiplied by the local feedback pattern [γα(θ, ϕ); Fig. 3]; see Eq. (14).

Fig. 9.

The portion of the ζα(θ, ϕ) pattern (Fig. 6) that is not due to the characteristic surface temperature pattern associated with variability [ζT(θ, ϕ); Figs. 6d,o] multiplied by the local feedback pattern [γα(θ, ϕ); Fig. 3]; see Eq. (14).

This calculation reveals that greatly underpredicts the magnitude of negative N values over much of the surface of the planet, particularly over the Pacific tropics and subtropics (Figs. 9a,l). It is well known that positive (and thus positive ENSO) is associated with a great amount of heat flux from the Pacific Ocean to the atmosphere (Trenberth et al. 2002a; see Figs. 6h,s herein). This anomalous heat flux causes a large reorganization of the atmospheric circulation that leads to a strengthening of the Hadley cell over the Pacific and alters the Walker circulation leading to anomalous subsidence over Indonesia (Klein et al. 1999). Figure 9 indicates that these ENSO-specific atmospheric features are not heavily tied to the characteristic T(θ, ϕ) pattern. In particular, the patterns of ζS(θ, ϕ) (Figs. 6h,s) and ζSLP(θ, ϕ) (Figs. 6g,r) are very similar to their corresponding patterns of ωS(θ, ϕ) (Figs. 9h,s) and ωSLP(θ, ϕ) (Figs. 9g,r).

These ENSO-caused shifts in S and large-scale atmospheric circulation have a profound impact on the ωN(θ, ϕ) pattern (Figs. 9a,l). In particular, the large negative ωN(θ, ϕ) values over Indonesia and the equatorial Atlantic are associated with anomalously high ωSLP(θ, ϕ) (Figs. 9g,r), indicating that these are regions of anomalous subsidence during positive that are not caused by the local T(θ, ϕ) anomaly. This subsidence is associated with reduced cloud fraction (Figs. 9k,v) and a negative ωCRE(θ, ϕ) response (Figs. 9i,t), due mostly to a negative response (Figs. 9f,q). The negative values in these regions may also be influenced by reduced cloud height (Allan et al. 2002; Cess et al. 2001). Additionally, there is a circulation-induced negative response in these regions (Figs. 9e,p) associated with drying of the of the middle to upper troposphere during ENSO events (Colman and Power 2010; Dessler 2013; Koumoutsaris 2013; Nilsson and Emanuel 1999; Pierrehumbert 1995). The decoupling of TOA net radiation from the surface temperature pattern in this region is consistent with previous findings showing that in the tropics is controlled much more by middle and upper tropospheric water vapor than by local surface temperature (Allan et al. 1999).

The analysis above demonstrates that at the peak of an unforced anomaly, the negative versus relationship results largely from mechanisms other than the spatial distribution of the characteristic surface temperature pattern associated with the anomaly (Figs. 9a,l). However, the above analysis has not indicated when, over the course of an unforced anomaly, the decoupling between the actual TOA radiation response (i.e., ) and that expected from the characteristic surface temperature pattern [i.e., ] takes place. We investigate this question by calculating regressions of global mean variables, , against at time lags of L years,

 
formula

and comparing these with the corresponding values that would be expected if the local feedback, γα(θ, ϕ), and the characteristic surface temperature pattern, ζT(θ, ϕ), explained 100% of the variability:

 
formula

The comparison of Eqs. (15) and (16) is shown in Fig. 10. Many years are required to perform robust cross-regressions so we omit the observational data from this portion of the analysis. Figure 10 shows that from 3 years to 1 year prior to a typical maximum, a positive net TOA energy imbalance [] develops, reaching a maximum of 0.87 W m−2 K−1 the year before the maximum (Fig. 10b). The development of this positive anomaly is largely due to the characteristic surface temperature pattern [ζT(θ, ϕ, L)] itself since nearly matches from L = −3 to L = −1 (Fig. 10b). The positive net TOA energy imbalance [] is associated with a negative net surface heat flux imbalance [] at L = −1, indicating that the ocean tends to be absorbing net energy from space in the year leading up to the maximum in (Fig. 10c).

Fig. 10.

Cross regression between global mean values and , as well as the cross regression that would be expected if the ζT(θ, ϕ) pattern and the local γα(θ, ϕ) feedback explained 100% of the variability ; see Eq. (16). This analysis was conducted for AOGCMs only. Shading represents the across-AOGCM standard deviation of the regression values.

Fig. 10.

Cross regression between global mean values and , as well as the cross regression that would be expected if the ζT(θ, ϕ) pattern and the local γα(θ, ϕ) feedback explained 100% of the variability ; see Eq. (16). This analysis was conducted for AOGCMs only. Shading represents the across-AOGCM standard deviation of the regression values.

The positive progression of the net TOA energy imbalance [] from L = −3 to L = −1 is largely due to the cloud radiative effect component [], which ascends in accord with expectations based on the characteristic surface temperature pattern [ζT(θ, ϕ, L); Fig. 10g]. Since ENSO variability leads variability in time (Trenberth et al. 2002a), it is likely that the positive and at L = −1 represent positive cloud feedbacks operating in conjunction with local ENSO activity in the Pacific (Radley et al. 2014).

Between L = −1 and L = 0, the net surface heat flux imbalance [] switches sign from negative to positive, indicating a large release of energy from the ocean to the atmosphere (Trenberth et al. 2014). It is over this period that the ζT(θ, ϕ, L) pattern predicts an increase in the net TOA energy imbalance [; i.e., an increase in ] but AOGCMs actually simulate a drop in from positive to negative (Figs. 10b, 6a, and 1a). The ζT(θ, ϕ, L) pattern nearly perfectly predicts the ice albedo component (Figs. 10f and 9b) but it underestimates the magnitude of the negative component (Figs. 10e and 9e) and greatly overestimates the positive component. The implication is that during the peak of a positive anomaly (i.e., an El Niño event), there is a great amount of heat flux from the ocean to the atmosphere where it can more easily be emitted to space in the form of . Additionally ENSO dynamics cause a large-scale rearrangement of atmospheric circulation that causes more efficient (Figs. 10e,h) due to drying and reduced cloud fraction over large portions of Indo-Pacific tropics and subtropics. Overall, this causes the net TOA energy imbalance [] to reduce to a negative value at L = 0 despite continuing in its positive ascent (Fig. 10b).

A year after the maximum in , remains positive (Fig. 10f) but a negative (Fig. 10e) and a negative (Fig. 10h) help remain negative despite the tendency of the characteristic surface temperature pattern [ζT(θ, ϕ, L)] to induce a positive TOA net radiation imbalance [; Fig. 10b]. This negative TOA net radiation imbalance acts as a restoring force, causing the anomaly to return to its equilibrium value.

6. Summary

In order for the unforced climate system to be stable in the long run, it is expected that the global mean TOA net radiation imbalance, , will exhibit a negative relationship with unforced global mean surface temperature anomalies, . We show that this negative relationship exists in both contemporary observations as well as in state-of-the-art AOGCMs. However, we also show that, at the local spatial scale, the simultaneous relationship between N(θ, ϕ) and T(θ, ϕ) tends to be positive over most of the surface of the planet. The reasons for the positive relationship differ by geographic location and have a strong dependence on the climatological mean T(θ, ϕ). The locally positive relationship is mostly due to the surface shortwave component (i.e., ice albedo feedback) for regions with T(θ, ϕ)clim values near the freezing point of water, mostly due to the shortwave cloud radiative effect component over regions with intermediate to high T(θ, ϕ)clim values (from ~273 to ~300 K), and mostly due to the longwave water vapor feedback over oceanic regions with the highest T(θ, ϕ)clim values.

The mostly positive N(θ, ϕ) versus T(θ, ϕ) relationship at the local spatial scale can be reconciled with the globally negative versus relationship when anomalous atmospheric energy transport, the characteristic surface temperature pattern, and adjustments in the large-scale atmospheric circulation are considered. In particular, positive anomalies are associated with El Niño events in which there is large anomalous heat flux from the Pacific Ocean into the atmosphere where the local N(θ, ϕ) versus T(θ, ϕ) relationship is positive. This leads to significant horizontal divergence of atmospheric energy transport over the tropical Pacific, and convergence of atmospheric energy transport at high latitudes and specific continental regions. This redistribution of energy helps create a characteristic T(θ, ϕ) versus pattern with a substantial amount of warmth at high latitudes [characterized by a locally negative N(θ, ϕ) versus T(θ, ϕ) relationship where the temperature anomaly can be more easily damped to space]. Additionally, the characteristic T(θ, ϕ) versus pattern contains anomalously cool T(θ, ϕ) regions where a locally positive N(θ, ϕ) versus T(θ, ϕ) relationship promotes a locally negative N(θ, ϕ).

However, the characteristic T(θ, ϕ) versus pattern by itself cannot explain the negative versus relationship because a multiplication of the local N(θ, ϕ) versus T(θ, ϕ) map by the T(θ, ϕ) versus map produces a positive estimate of the versus relationship. This indicates that atmospheric circulation changes associated with unforced interannual variability are crucial in the explanation of the negative versus relationship. In particular, a maximum is preceded, a year prior, by a positive that is consistent with expectations based on the T(θ, ϕ) versus pattern. However, simultaneous to the peak, a great rearrangement of large-scale atmospheric circulation causes reduced cloud cover and subsidence-induced drying in broad regions of the tropical and subtropical Indo-Pacific. This circulation change allows for much more efficient release of energy than would otherwise be expected from the T(θ, ϕ) versus pattern alone. Because the short time scale relationship between and is heavily influenced by large-scale atmospheric circulation changes (opposed to local feedbacks), this study supports the notion that there may be very little relationship between the climate feedback parameter (i.e., γN) diagnosed from annual or subannual time scale variability and 2 × CO2 equilibrium climate sensitivity.

Acknowledgments

We thank Dr. Drew Shindell for helpful discussions on this topic. We acknowledge Dr. Aaron Donohoe and two anonymous reviewers whose comments greatly enhanced the manuscript. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups for producing and making available their model output. For CMIP the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. This work was partially supported by NSF Grant AGS-1147608. We also acknowledge the support from NASA ROSES13-NDOA, ROSES12-MAP, and ROSES-NEWS programs. This research was partially conducted at the Jet Propulsion Laboratory, California Institute of Technology, sponsored by NASA.

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Footnotes

*

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JCLI-D-15-0384.s1.

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