We begin by comparing the climate responses to the three forcing locations in the zonal-mean context. In the slab ocean setting, the zonally averaged surface temperature and precipitation responses are largely independent of forcing location (solid lines in Fig. 1). The zonal-mean precipitation responses for the SOM experiments are correlated at 0.99 between 30°S and 30°N. By contrast, in the presence of a dynamic ocean, the zonal-mean climate responses are spatially distinct depending on the extratropical forcing location. The zonal mean tropical precipitation responses are only weakly correlated among the DOM experiments, ranging from 0.33 to 0.58. In this section, we invoke the energetics framework to understand the sensitivity of zonally averaged tropical precipitation response to the forcing location.
The zonal-mean tropical precipitation response is linked to the cross-equatorial atmospheric energy transport response ΔAHT0 (e.g., Kang, 2020), with a southward tropical precipitation shift corresponding to a northward ΔAHT0 (Fig. 2). The atmospheric energy budget in a quasi-equilibrium state, in which the energy tendency in the atmospheric column can be neglected, gives:
$${\Delta }{\text{A}\text{H}\text{T}}_{0}=⟨{\Delta }{R}_{\text{T}\text{O}\text{A}}⟩-⟨{\Delta }\text{O}\text{H}\text{U}⟩$$
1
where \({R}_{\text{T}\text{O}\text{A}}\) is the net downward top-of-atmosphere (TOA) radiation and OHU the ocean heat uptake, calculated as net downward surface heat flux. Brackets denote the spatial integral in the Southern Hemisphere minus that in the Northern Hemisphere divided by 2, indicative of a cross-equatorial flux in the unit of PW. The net TOA radiation response Δ\({R}_{\text{T}\text{O}\text{A}}\) includes the prescribed solar flux perturbation \({\Delta }{S}^{\downarrow }\), only a fraction of which is felt by the climate system due to the planetary albedo. We may define the prescribed forcing as \({R}_{\text{S}}=\left(1-\alpha \right){\Delta }{S}^{\downarrow }\) where α is the planetary albedo averaged between the control and perturbed experiments. Defining \({\Delta }{R}_{\text{T}\text{O}\text{A}-\text{S}}\) as the difference between the net downward TOA radiation response \({\Delta }{R}_{\text{T}\text{O}\text{A}}\) and the prescribed forcing \({R}_{\text{S}}\) allows us to rearrange Eq. (1) as:
$$1=\frac{{\Delta }{\text{A}\text{H}\text{T}}_{0}}{⟨{R}_{\text{S}}⟩}+\frac{⟨-{\Delta }{R}_{\text{T}\text{O}\text{A}-\text{S}}⟩}{⟨{R}_{\text{S}}⟩}+\frac{⟨{\Delta }\text{O}\text{H}\text{U}⟩ }{⟨{R}_{\text{S}}⟩}$$
where the terms on the right-hand-side represent the atmospheric compensation \({C}_{\text{A}\text{T}\text{M}}\), TOA compensation \({C}_{\text{T}\text{O}\text{A}}\), and oceanic compensation \({C}_{\text{O}\text{C}\text{N}}\), respectively (Kang et al., 2019).
Figure 3 compares the fractional compensation by each component in all experiments. In SOM with no ocean dynamics (Fig. 3a), the forcing is mostly compensated by the atmospheric energy transport (\({C}_{\text{A}\text{T}\text{M}}\) = 93.2 ± 5.7 %) ith some contribution from the TOA radiation (\({C}_{\text{T}\text{O}\text{A}}\)= 12.7 ± 5.4 %). Theoceanic compensation \({C}_{\text{O}\text{C}\text{N}}\) is negligible in the slab ocean setting but non-zero due to surface heat flux change on the ice edges. While the relative contribution of each component in balancing the forcing is fairly insensitive to the forcing location, SOM-NAMER exhibits a larger \({C}_{\text{A}\text{T}\text{M}}\) associated with a smaller \({C}_{\text{T}\text{O}\text{A}}\)relative to other cases. With active ocean dynamics (Fig. 3b), the TOA compensation \({C}_{\text{T}\text{O}\text{A}}\) stays similar to that in the SOM while the oceanic compensation \({C}_{\text{O}\text{C}\text{N}}\) takes over a considerable fraction of the atmospheric compensation \({C}_{\text{A}\text{T}\text{M}}\), effectively dampening the zonal-mean tropical precipitation shift in DOM (Fig. 2). Next, we examine the TOA radiation response and the ocean heat budget in more detail.
3.1. TOA radiation response
In order to examine what sets the TOA compensation, we divide \({C}_{\text{T}\text{O}\text{A}}\) into the contributions from the extratropics (i.e., \(⟨-{\Delta }{R}_{\text{T}\text{O}\text{A}-\text{S}}⟩\)poleward of 30°S/N; Fig. 4a) and the tropics (i.e., \(⟨-{\Delta }{R}_{\text{T}\text{O}\text{A}-\text{S}}⟩\) equatorward of 30°S/N; Fig. 4b). We further attribute the regional \({C}_{\text{T}\text{O}\text{A}}\) to the clear-sky longwave radiation response (\({\Delta }{L}_{\text{c}\text{l}\text{r}}\)), longwave cloud radiative effect response (\({\Delta }{L}_{\text{c}\text{r}\text{e}}\); the TOA longwave flux in all-sky minus clear-sky), and shortwave radiation response due to changes in cloud (\({\Delta }{S}_{\text{c}\text{l}\text{d}}\)), non-cloud atmospheric constituents (\({\Delta }{S}_{\text{n}\text{c}\text{l}\text{d}}\)), and surface albedo (\({\Delta }{S}_{\text{a}\text{l}\text{b}}\)). The shortwave terms are separated by the Approximate Partial Radiative Perturbation (APRP) method (Taylor et al., 2007; Kim et al. 2022). The \({C}_{\text{T}\text{O}\text{A}}\) decomposition results for the SOM experiments are shown in Fig. 4. The positive values indicate a compensating effect (i.e., negative feedback) and the negative values indicate an amplifying effect (i.e., positive feedback).
On average, the TOA radiation response in the extratropics offsets the forcing by 38.6% while that in the tropics acts to amplify the forcing by 25.9%, giving the net \({C}_{\text{T}\text{O}\text{A}}\) of 12.7 %. n the extratropics, the compensating effect results from the reduction in clear-sky outgoing longwave radiation associated with the northern extratropical cooling, about half of which is cancelled by the positive feedback from the shortwave radiation (Fig. 4a). The shortwave-induced positive feedback arises from the increase in low cloud amount (\({\Delta }{S}_{\text{c}\text{l}\text{d}}\)), reduction in shortwave absorption by water vapor (\({\Delta }{S}_{\text{n}\text{c}\text{l}\text{d}}\)), and increase in surface albedo (\({\Delta }{S}_{\text{a}\text{l}\text{b}}\)). Positive feedback from the shortwave component in the extratropics is slightly larger in SOM-NAMER (Fig. 4a), leading to a relatively weaker \({C}_{\text{T}\text{O}\text{A}}\) than other cases (Fig. 3a). The SOM-EURO exhibits comparably large shortwave-induced positive feedback, but larger negative feedback from \({\Delta }{L}_{\text{c}\text{l}\text{r}}\) (Fig. 4a) associated with a stronger Arctic cooling (Fig. 1a) results in a larger \({C}_{\text{T}\text{O}\text{A}}\) than SOM-NAMER (Fig. 3a). In the tropics, the positive TOA feedback results from the increase in clear-sky outgoing longwave radiation in the northern tropics as the ITCZ shifts southward (Clark et al. 2018) whereas the cloud radiative effects feature little hemispheric asymmetry due to the cancellation between the longwave and shortwave components (Fig. 4b).
With interactive ocean dynamics, the negative TOA feedback in the extratropics is damped (cross symbols in Fig. 4a) as a consequence of weaker temperature responses and the positive TOA feedback in the tropics (cross symbols in Fig. 4b) is also damped associated with a muted ITCZ shift. As a result, the TOA compensation is nearly independent of the degree of atmosphere-ocean coupling (Fig. 3).
3.2. Oceanic compensation
The zonally- and vertically-integrated oceanic heat budget indicates that the ocean heat uptake \(\text{O}\text{H}\text{U}\) consists of the ocean heat storage \(\text{O}\text{H}\text{S}\) and ocean heat transport divergence \(\nabla \bullet \text{O}\text{H}\text{T}\):
$$\text{O}\text{H}\text{U}=\text{O}\text{H}\text{S}+\nabla \bullet \text{O}\text{H}\text{T}$$
with \(\text{O}\text{H}\text{T}={\int }_{-H}^{0}{\rho }_{o}{C}_{p}v\theta \text{d}\text{z}\) and \(\text{O}\text{H}\text{S}=\frac{\partial }{\partial t}{\int }_{-H}^{0}{\rho }_{o}{C}_{p}\theta \text{d}\text{z}\) (i.e., the ocean heat content tendency), where \(v\) is the velocity, \({\rho }_{o}\) is the seawater density, \({C}_{p}\) is the specific heat of seawater, \(\theta\) is the potential temperature, and \(-H\) denotes the ocean depth. We calculate OHS by the linear trend of ocean heat content over the 70-year period at each grid point. We use the direct model output of Eulerian-mean ocean heat transport \({\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}}={\int }_{-H}^{0}{\rho }_{o}{C}_{p}\stackrel{-}{v}\stackrel{-}{\theta }\text{d}\text{z}\) where the overbar denotes the time average, and consider the residual \({\nabla \bullet \text{O}\text{H}\text{T}}_{\text{r}\text{e}\text{s}}=\text{O}\text{H}\text{U}-\text{O}\text{H}\text{S}-\nabla \bullet {\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}}\) as the ocean heat transport divergence by eddies and diffusion. Hence, the oceanic compensation \({C}_{\text{O}\text{C}\text{N}}\) (i.e., \(⟨{\Delta }\text{O}\text{H}\text{U}⟩/⟨{R}_{\text{S}}⟩\)) can be induced by changes in ocean heat storage \(⟨{\Delta }\text{O}\text{H}\text{S}⟩\), cross-equatorial ocean heat transport by Eulerian-mean flow \({{\Delta }\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}\), and the residual, as compared in Fig. 5 for the DOM experiments.
The oceanic compensation can be largely attributed to the anomalously northward Eulerian-mean ocean heat transport across the equator \({{\Delta }\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}\) with relatively small contributions from anomalous ocean heat storage and residual. That is, \({{\Delta }\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}\) is responsible for the sensitivity in oceanic compensation to the forcing location. We further decompose \({{\Delta }\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}\) into contributions from each basin. The DOM-NASIA and DOM-EURO cases induce a substantial \({{\Delta }\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}\) over both Indo-Pacific and Atlantic basins while the DOM-NAMER case is primarily balanced from the Atlantic with a negligible contribution from the Indo-Pacific basin. The contrasting \({{\Delta }\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}\) by basin can be understood from the distinct response of the ocean meridional overturning circulation (Fig. 6). The AMOC strengthens regardless of the forcing location as the air temperature response is effectively homogenized by atmospheric eddies and mean westerlies, making the surface ocean density over the Labrador Sea denser, thereby enhancing the deep water formation. However, the extent to which the AMOC strengthens is weakest in DOM-NASIA (Fig. 6, left), presumably due to the distance between the forcing region and the Atlantic basin, corresponding to the smallest \({{\Delta }\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}\) in the Atlantic basin (i.e., \({\Delta }{\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}^{\text{A}\text{t}\text{l}}\) in Fig. 5).
The Indo-Pacific \({{\Delta }\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}\) changes in proportion to the North Pacific subtropical cell response, which in turn is anchored to the North Pacific Subtropical High. That is, the North Pacific subtropical cell strengthens in association with the amplified North Pacific Subtropical High and vice versa. The sea level pressure response is characterized by a surface high east of the forcing domain and a surface low west of the forcing domain in order to balance the prescribed extratropical cooling by meridional warm advection (Hoskins and Karoly 1981). Consequently, the North Pacific Subtropical High strengthens in response to NASIA forcing (Fig. 7a,d) while weakening in response to NAMER forcing (Fig. 7b,e). The EURO forcing gives rise to a weak strengthening of the North Pacific Subtropical High (Fig. 7c,f). As a result, the North Pacific subtropical cell most effectively strengthens in DOM-NASIA (Fig. 6d), giving rise to the largest \({{\Delta }\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}\) in the Indo-Pacific basin (i.e., \({\Delta }{\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}^{\text{I}\text{n}\text{d}-\text{P}\text{a}\text{c}}\) in Fig. 5). A modest strengthening of North Pacific subtropical cell in DOM-EURO (Fig. 6f) results in a smaller \({\Delta }{\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}^{\text{I}\text{n}\text{d}-\text{P}\text{a}\text{c}}\) than in DOM-NASIA (Fig. 5). In DOM-NAMER, anomalous low pressure in the North Pacific extends to the western basin of the tropical Pacific whereas the eastern basin exhibits weak anomalous high pressure as the Atlantic cold SST anomaly reaches the northeastern tropical Pacific across the Central American Isthmus (Fig. 7b,e). As a result, the NAMER forcing has little impact on the North Pacific subtropical cell (Fig. 6e), causing negligible \({\Delta }{\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}^{\text{I}\text{n}\text{d}-\text{P}\text{a}\text{c}}\) (Fig. 5). Consequently, the oceanic compensation \({C}_{\text{O}\text{C}\text{N}}\) is smallest in DOM-NAMER, leading to the largest atmospheric compensation \({C}_{\text{A}\text{T}\text{M}}\) (Fig. 3b) and thereby the strongest zonal-mean ITCZ shift (Fig. 2).
It is worth noting that the sea level pressure anomaly pattern is broadly insensitive to ocean dynamical adjustment (contrast left and right columns to Fig. 7). Hence, the effectiveness of oceanic compensation in the Indo-Pacific basin \({\Delta }{\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}^{\text{I}\text{n}\text{d}-\text{P}\text{a}\text{c}}\) can be crudely predicted from the corresponding SOM experiments. Considering the large area of the Indo-Pacific basin, \({\Delta }{\text{O}\text{H}\text{T}}_{\text{E}\text{u}\text{l}0}^{\text{I}\text{n}\text{d}-\text{P}\text{a}\text{c}}\) is an important fraction of overall oceanic damping effect, which ultimately determines the extent to which zonal-mean tropical precipitation shifts are muted by a dynamic ocean.