The patch experiments were conducted using the Community Earth System Model version 1.2.1 integrated with the Community Atmospheric Model version 5.3 (CESM1.2.1-CAM5.3; Neale et al., 2012), operating at a spatial resolution of 1.9° latitude by 2.5° longitude. The experimental setup included a control experiment and two sets of patch experiments – one with warm patches and another with cold patches. The control experiment spanned 41 years, maintaining the SST, sea ice, and climatic forcings at the constant present-day levels observed (in the year 2000). The global ocean was segmented into 80 overlapping rectangular areas, comprehensively covering the global ice-free ocean surface, as depicted in Fig. 1 of Zhou et al. (2020). In the warm patch experiments, a positive SST anomaly was introduced at the ocean surface within a designated patch, while the SST in other regions was the same as the control setup. Conversely, the cold patch experiments involved introducing a negative SST anomaly at the ocean surface within the respective patches. The SST anomalies in each patch were designed according to the equation proposed by Barsugli and Sardeshmukh (2002), which effectively mitigates nonlinearity due to unrealistic SST gradients, ensuring a more realistic simulation of oceanic temperature variations: 1ΔSSTP(lat,long)=Acos⁡2π2lat-latplatwπ2long-longplongw, where |lat-latp|<latw, |long-longp|<longw. The terms latp and longp are the latitude and longitude of the center point for a specific patch, respectively; latw and longw are the meridional and zonal half-width of the patch, respectively, with their values set to latw=10° and longw=40° in these experiments; and A is the amplitude of the SST anomaly, which is set to be +4 and -4 K in this study.

In this study, we analyzed the responses of polar TOA radiative fluxes (RTOA), polar surface fluxes (Rsfc), and heat fluxes resulting from atmospheric heat transport to the polar regions (RAHT). The equations for calculating these parameters are listed as follows: 2RTOA=FSNT-FLNT,3Rsfc=FSNS-FLNS-SH-LH,4RAHT=Rsfc-RTOA, where FSNT represents the net downward shortwave radiation at the TOA; FLNT denotes the net upward longwave radiation at the TOA; FSNS is the net downward shortwave radiation at the surface; FLNS represents the net upward longwave radiation at the surface; and SH and LH account for the sensible and latent heat fluxes, respectively. Additionally, both SH and LH are defined as positive upward.

To quantify the polar energy budget response to realistic SST anomaly patterns, we applied an empirical orthogonal function (EOF) analysis to historical SST data from 1980 to 2019, obtained from the Hadley Centre Sea Ice and Sea Surface Temperature dataset (HadISST; Rayner et al., 2003), and identified the first eight EOF modes. The first eight EOF modes explain approximately 55 % of the total variance in global SST anomalies, thereby representing the predominant variability patterns. We then conducted eight separate EOF-SST experiments, and the SST of each experiment was perturbed by a specific EOF mode relative to the control run. These experiments allow us to isolate and understand the impact of realistic SST anomaly patterns on the polar energy budget.

This study employs the radiative kernel approach (Soden et al., 2008; Huang et al., 2017) to decompose both surface and TOA radiation into the radiative effects of various meteorological variables, measured in watts per square meter (Wm-2). The core calculation involves multiplying the radiative kernels by the monthly anomalies of the corresponding climate fields as follows: 5ΔRX=KX⋅ΔX, where X denotes an arbitrary non-cloud climate variable; ΔRX represents the radiative effect at the surface or TOA associated with that variable; KX is the corresponding radiative kernel; and ΔX is the monthly anomaly of the climate variable, calculated as the deviation from the monthly climatological average. Positive values of ΔR indicate an increase in net incoming radiation, which corresponds to a warming effect on the Earth. The radiative kernels used in this analysis are derived from the ERA-Interim climatological fields and have been validated to perform well with the climate model surface outputs (Huang et al., 2017; Liu et al., 2024).

Cloud radiative effects are calculated following the methodology of Soden et al. (2008): 6ΔRcld=ΔCRF-∑X(KX-KX0)ΔX. In this equation, ΔRcld denotes the cloud-induced radiative anomalies, and CRF (cloud radiative forcing) is defined as the difference in surface net radiation fluxes between all-sky and clear-sky conditions. The superscript 0 means the clear-sky kernels.

Building upon this framework, the study further decomposes the TOA and surface radiative anomalies into specific feedback components to achieve a more detailed analysis of the factors influencing the Earth's radiation balance. ΔRTOA is partitioned into cloud-induced radiative anomalies (ΔRTOA,cld), albedo-induced radiative anomalies (ΔRTOA,alb), Planck-feedback-induced radiative anomalies (ΔRTOA,plk), and lapse-rate-feedback-induced radiative anomalies (ΔRTOA,LR). Similarly, ΔRsfc is broken down into cloud-induced surface radiative anomalies (ΔRsfc,cld), albedo-related surface radiative anomalies (ΔRsfc,alb), Planck-feedback-induced surface radiative anomalies (ΔRsfc,plk), lapse-rate-feedback-induced surface radiative anomalies (ΔRsfc,LR), LH anomalies (ΔLH), and SH anomalies (ΔSH).

The differences in the annual polar energy budget in conjugate SST warming patch experiments and SST cooling patch experiments are shown in Fig. 1. The location of each point denotes the center of the corresponding patch, and the colors of these points denote the differences in the polar energy budget between corresponding conjugate warming and cooling patch experiments. Additionally, t tests were conducted to assess their statistical significance. The difference between TOA radiation (Fig. 1a and d) and surface radiation (Fig. 1b and e) reflects atmospheric heat transport (Fig. 1c and f).

Figure 1a–c show the responses of the Arctic energy budgets to SST warmings in global oceanic regions. In response to western and central tropical Pacific SST warming, there is a significant increase in poleward energy transport toward the Arctic regions (Fig. 1c), as indicated by the positive poleward heat transport to the Arctic region (positive ΔRAHT). This enhanced energy transport warms the Arctic atmosphere, leading to an increase in surface radiation (positive ΔRsfc, Fig. 1b) due to higher surface and air temperatures. Simultaneously, the warmer atmosphere emits more longwave radiation into space, resulting in a decrease in TOA radiation (negative ΔRTOA, Fig. 1a). Conversely, warming in the tropical Indian Ocean reduces the poleward energy transport to the Arctic region (negative ΔRAHT), leading to cooler Arctic atmospheric temperatures, and there is a decrease in surface radiation (negative ΔRsfc, Fig. 1b) and an increase in TOA radiation (positive ΔRTOA, Fig. 1a). Sea surface warming in the mid-latitudes of the Northern Hemisphere increases Arctic surface radiation but has an insignificant impact on TOA radiation.

For the Antarctic energy budget, warming in the tropical Pacific and Indian oceans generally leads to increased poleward energy transport (positive ΔRAHT, Fig. 1f), which warms the Antarctic atmosphere and results in increased Antarctic surface radiation (positive ΔRsfc, Fig. 1e) and decreased Antarctic TOA radiation (negative ΔRTOA, Fig. 1d). However, the response of ΔRTOA to warmings in the tropical Atlantic is positive (Fig. 1d). Warming in the Southern Ocean also leads to an increase in Antarctic surface radiation and a decrease in Antarctic TOA radiation. The Antarctic energy budget is generally not sensitive to warmings in subtropical regions. Both ΔRTOA and ΔRsfc decrease in response to warmings in patches centered at 60° S, because patches centered at 60° S cover part of the Antarctic region (60 to 90° S in this study), and the surface emits more energy into space as the sea surface warms, leading to a cooling radiative effect.

The response of Arctic ΔRAHT to tropical warmings is generally greater than Antarctic ΔRAHT, indicating that more heat is transported to the Arctic region than to the Antarctic region when the tropics warm. This difference may partly contribute to faster Arctic warming than Antarctic warming under global warming.

The responses of the polar energy budget depend on the season. The spatial distribution of the Arctic polar energy budget response to regional SST in boreal winter (DJF) (Fig. 2a–c) is similar to the annual average values (Fig. 1a–c), but the magnitude of the DJF responses is greater than the annual responses. For the Antarctic region, the response of the DJF polar energy budget to tropical ocean warming aligns with the annual average values.

During boreal summer (JJA), the spatial distribution of the Arctic polar energy budget responses (Fig. 3a–c) differs from the annual average. Specifically, the responses of ΔRAHT to warmings in both the Indian Ocean and the western Pacific Ocean are positive. The responses of ΔRsfc and ΔRTOA in most patch experiments are statistically insignificant. Conversely, the Antarctic polar energy budget responses to tropical ocean warming in JJA are similar to the annual mean values.

The response of the polar energy budget to regional SST changes might be used to qualitatively explain how SST variations affect the polar energy budget.

The sensitivity of the polar energy budget to SST perturbations within a specific grid box, identified by index i, can be estimated using the following equation (Zhou et al., 2017): 7∂R∂SSTi=∑PΔSSTP∂R∂SSTPSiSP∑PΔSSTP, where R denotes a specific energy flux; SSTi denotes the SST in the ith grid box; Si and SP represent the ocean surface area of the specific grid point and the patch, respectively; and ΔSSTP is the SST anomaly of the ith grid in the pth patch. ∂R∂SSTP is the sensitivity of R to patch-averaged SST change, which is derived from experiments for the corresponding warming and cooling patch experiments. The sensitivity to grid boxes within a single patch corresponds to the average R change due to a 1 K warming within that specific grid box. The sensitivities of the polar energy budget to SST perturbation in each grid box are shown in Fig. 4.

Utilizing these sensitivities, we can reconstruct the polar energy budget response to arbitrary changes in SST through Green's function approach, represented as 8ΔR=Σi∂R∂SSTiΔSSTi+ε1, where ε1 is an error term which represents the contributions from nonlinearities and non-SST-induced factors.

Then we use Green's function approach to reconstruct the ΔRAHT in response to eight different SST patterns in the EOF-SST experiments (Fig. 5a–h). ΔRAHT reconstructed by Green's function is then compared to model-produced values in the EOF-SST experiments (Fig. 5i and j). The results show that the majority of the experimental simulations of ΔRAHT align closely with the ΔRAHT reconstructed by Green's function, lying near the y=x line. The biases of the values reconstructed by Green's function are partially induced by the SST change in the Arctic region, which is not captured by the Green's function reconstruction, and nonlinear terms also contribute to the bias. Therefore, Green's function approach can qualitatively explain how the SST perturbation patterns in Fig. 5a–h affect the polar energy budget.

To understand the mechanism of how the polar energy budget is affected by remote SST, we quantify the contributions of meteorological factors to the polar energy budget responses (Figs. 6 and 7) using radiative kernels (Huang et al., 2017).

Figure 6a shows that the contribution of cloud changes is relatively small compared to the Arctic ΔRTOA response. Pacific SST warming results in a negative Arctic ΔRTOA,cld, whereas Indian Ocean warming generates a positive Arctic ΔRTOA,cld. Albedo exhibits a positive response in both the tropical Indian Ocean and the Pacific Ocean (Fig. 6a). The impact of Arctic ΔRTOA,plk exhibits a positive response to SST increases in the tropical Indian Ocean and a negative response to the tropical western Pacific (Fig. 6c), indicating that the Planck feedback is the primary contributor to Arctic ΔRTOA. The sensitivity of Arctic ΔRTOA,LR to SST increases exhibits a negative response to warming in the tropical western Pacific, while showing a positive response in the Indian Ocean (Fig. 6d). The Planck feedback's response to SST warming is approximately twice that of the lapse-rate feedback.

For the Antarctic, the contribution of clouds to the ΔRTOA response is minimal (Fig. 6f), as is the contribution of albedo changes to the Antarctic ΔRTOA response (Fig. 6e). In contrast to the Arctic, the Antarctic ΔRTOA response to SST changes is jointly dominated by Planck and lapse-rate feedbacks. Warming in the Indian Ocean induces a stronger negative ΔRTOA,plk (Fig. 6g), whereas warming in the Pacific leads to a more pronounced negative ΔRTOA,LR (Fig. 6h). Additionally, warming in the tropical Atlantic triggers a notably strong positive ΔRTOA,LR (Fig. 6h).

Figure 7 shows the contributions of meteorological factors to the responses of Arctic and Antarctic ΔRsfc. For the Arctic, the spatial distribution of clouds' contribution to Arctic ΔRsfc is similar to that for Arctic ΔRTOA, but the values are significantly higher (Fig. 7b). The response of Arctic ΔRsfc,alb closely resembles that of ΔRTOA,alb, with similar magnitudes (Fig. 7a). Similar to the response of Arctic ΔRTOA,plk, the Arctic ΔRsfc,plk response is also strong (Fig. 7c), but the signs of ΔRsfc,plk responses are generally opposite to those of the ΔRTOA,plk response. The response of Arctic ΔRsfc,LR to tropical ocean warming also shows signs opposite to those of ΔRTOA,LR (Fig. 7d). Over the tropical Indian Ocean, Planck feedback is positive in the northern region and negative in the southern region, whereas lapse-rate feedback is consistently negative across the entire tropical Indian Ocean. Overall, Planck feedback remains dominant for Arctic ΔRsfc. The responses of Arctic ΔLH and Arctic ΔSH are negative in response to warmings in the tropical western Pacific and positive in response to warmings in the tropical Indian Ocean (Fig. 7e and f), although these factors have a minor impact on Arctic ΔRsfc. The negative responses of Arctic ΔLH and Arctic ΔSH in response to warmings in the tropical western Pacific indicate a suppression of upward turbulent heat fluxes at the Arctic surface, primarily due to enhanced energy transport from lower latitudes into the Arctic region. As warm air masses are advected poleward, the associated increase in downward longwave radiation warms the Arctic surface. This warming stabilizes the lower atmospheric boundary layer, thereby reducing the vertical turbulence necessary for effective heat exchange between the surface and the atmosphere.

Similar to the Arctic regions, the contribution of clouds to Antarctic ΔRsfc is small (Fig. 7h). Albedo has no significant impact on Antarctic ΔRsfc (Fig. 7g), because sea ice concentration is fixed in these patch experiments, and snow cover in Antarctica does not change significantly in these experiments. The Planck feedback dominates the contributions to Antarctic ΔRsfc, with Antarctic ΔRsfc,plk responding positively to tropical ocean warming (Fig. 7i). Similar to the Arctic, the lapse-rate feedback contributes less significantly to ΔRsfc (Fig. 7j). Antarctic ΔLH and Antarctic ΔSH show minimal responses, with opposite signs to ΔRsfc,plk (Fig. 7k and l). These results suggest that while temperature adjustments are notable in Antarctica, the responses of cloud cover and surface heat fluxes to remote SST warming have a small impact on Antarctic ΔRsfc.

According to Figs. 6 and 7, the Planck feedback, which is primarily driven by changes in temperature, is the primary contributor to the polar energy budget responses in these experiments. The sign of ΔRAHT is generally the same as ΔRsfc,plk and the opposite of ΔRTOA,plk. In addition, the difference between TOA and the surface energy budget reflects the contribution of changes in polar AHT. Therefore, AHT plays a critical role in determining the polar energy budget by changing the air temperature of polar regions. The responses of AHT to SST perturbations in the mid-latitudes are consistent with our intuition, but the opposite Arctic AHT responses to SST warming over the tropical Indian Ocean (TIO) and tropical Pacific Ocean (TPO) require further investigations.

To explore the underlying mechanisms of this phenomenon, we compare the climate responses to warmings in two illustrative patches within the TPO and TIO. The center of the illustrative TPO patch is 0° N, 180° E, and the center of the illustrative TIO is 0° N, 60° E.

Figure 8 presents the responses of surface temperature (ΔTs), 200 hPa geopotential height (ΔZ200), and 500 hPa geopotential height (ΔZ500) to warmings in these patches, providing background information to later AHT studies. Consistent with previous studies (Annamalai et al., 2007; Barsugli and Sardeshmukh, 2002; Ding et al., 2014), our experiments reveal that SST anomalies in different ocean basins induce contrasting atmospheric circulation patterns, primarily through Rossby wave responses affecting the Pacific–North American (PNA) pattern.

Specifically, warming in the TPO region leads to an increase in ΔTs over the Tibetan Plateau, eastern Europe, tropical Africa, northeastern North America, and most of the Antarctic regions. Concurrently, ΔZ200 exhibits a local increase over the TPO region, a decrease over the North Pacific, and an increase over northeastern North America and Antarctic regions. The ΔZ500 response mirrors the ΔZ200 pattern but with reduced intensity. In contrast, warming in the TIO region induces ΔTs increases over Antarctic regions and significant warming over the Indian subcontinent, while the Tibetan Plateau experiences cooling. Notably, the northwest of North America shows marked cooling under TIO warming. The ΔZ200 response to TIO warming displays a dipole pattern, characterized by increases in the tropical warming regions and decreases toward the poles, followed by subsequent increases. The ΔZ500 response follows a similar trend to ΔZ200, with weaker intensity.

To quantify the impacts of SST warming over the TPO and TIO on the Arctic AHT, we computed the AHT responses to the warming of the two patches separately. AHT can be calculated as the vertically integrated and zonally averaged transport of moist static energy (S). According to Neelin and Held (1987), S can be defined as follows: 9S=cpTa+LQ+gZ, where Ta represents atmospheric temperature, cp is the specific heat capacity of air at constant pressure, L denotes the latent heat of vaporization of water, Q is specific humidity, g is the acceleration due to gravity, and Z represents geopotential height. The components of S will be denoted below as ST, SQ, and SZ, respectively.

The poleward transport of moist static energy S can be decomposed into mean meridional circulation (MOC), stationary eddy (SE), transient eddy (TE), and transient overturning circulation (TOC) components, following the methodologies of Priestley (1948) and Lorenz (1955). According to Donohoe et al. (2020), for each latitude θ, atmospheric energy transport is 10AHT(θ)=2πacos(θ)∫0Ps[V‾][S‾]+[V∗S∗]‾+[V′∗S′∗‾]+[V]′[S]′‾dpg, where V represents the meridional velocity. Square brackets ([]) denote zonal averages, overbars denote time averages over each month of analysis, asterisks (∗) are departures from the zonal average, and primes (′) are departures from the time average. The first term signifies the MOC driven by the vertical gradient in S, taking into account mass conservation in MOC energy transport. The second term is SE, showing poleward transport in warm or moist sectors. These first two terms can be calculated from monthly mean data. The third term pertains to the transport associated with TE, primarily baroclinic synoptic eddies. The fourth term involves energy transport by the covariance between zonal-mean overturning circulation and vertical stratification, referred to as TOC, which is significantly smaller than the other components and thus is often excluded in AHT discussions.

Figure 9 shows the changes in AHT and its components in response to warmings in the TPO and TIO. AHT response to warmings in the TPO at 60° N is positive, and AHT response to warmings in the TIO at 60° N is negative. For both cases, AHT to the Arctic region is dominated by SE (Fig. 9b), and the opposite SE response to the TPO and TIO leads to opposite responses in AHT, which also causes different responses of TOA and surface energy budgets in the Arctic regions. Additionally, Fig. 9c and d further dissect the SE responses to warmings in the TPO and TIO, respectively. The results indicate that dry static energy predominantly drives the SE response to warmings in both the TPO and the TIO.

To better understand the opposite response of SE heat flux to warmings in the TPO and TIO, we analyzed the spatial distribution of SE heat fluxes. The vertically integrated SE heat flux (ϕ) can be computed through the following integral: 11ϕ=∫0PsV∗S∗dpg. In response to warmings in the TPO, the vertically integrated SE heat flux exhibits significant oscillatory characteristics over the Pacific Ocean. According to Fig. 10a, ϕ increases in the tropical western and northwestern Pacific, decreases over the central Pacific, and then increases again over the northeastern Pacific and Alaska. Over land, ϕ increases over northeastern Asia, the Tibetan Plateau, and Europe. This phenomenon is consistent with Goss et al. (2016), who found that warming in the low-latitude Pacific leads to increased ϕ in higher latitudes.

Combining Eqs. (9) and (11), we are able to further attribute ϕ to changes in dry static heat flux (ΔϕTa), latent heat flux (ΔϕQ), and potential energy (ΔϕZ), respectively. Among the three main contributing factors to Δϕ, ΔϕTa aligns closely with the overall Δϕ pattern, indicating it as the primary contributor (Fig. 10b). The spatial pattern of ΔϕTa can be explained by the change in ΔV∗ and ΔSTa∗ (Fig. 10c and d), which reflects the spatial pattern of stationary waves. In addition, ΔϕQ is large in the low latitudes but is small near the poles (Fig. 10e). Interestingly, ΔϕZ exhibits an opposite pattern to Δϕ in the Northern Hemisphere (Fig. 10f). Despite the changes in ΔSZ∗ that have a similar spatial distribution to ΔSTa∗ (Fig. 10h), ΔϕZ shows an opposite trend to ΔϕTa due to the differing correlation between ΔV∗ and ΔSZ∗. This indicates that while ΔSZ∗ increases in regions where ΔV∗ also increases, their combined effect on ΔϕZ leads to a negative contribution compared to Δϕ.

In response to warmings in the TIO, the spatial pattern of Δϕ oscillation is quite different from the TPO case. The transfer of SE heat flux encounters obstacles near the Tibetan Plateau, which might explain why the response of Δϕ is different in the Northern Hemisphere and the Southern Hemisphere. Globally, ΔϕTa remains the dominant contributor to Δϕ, while ΔϕQ's contribution remains relatively low. Notably, in the Tibetan Plateau region, ΔϕZ becomes the primary driver of Δϕ (Fig. 10i and n).

Based on these results, we are able to understand why the responses of AHT near 60° N to warmings in the TPO and TIO are different. The response of stationary waves to warmings in these two regions is different, so the poleward moist static energy transported by SE is also different, leading to opposite AHT responses. These findings support the research results of Goss et al. (2016) and the tropical excitation mechanism for Arctic warming outlined by Lee et al. (2011).