Understanding the Formation of the Reduced Warming Pattern in the Pacific Sector of the Southern Ocean

Abstract

Sea surface temperature (SST) warming patterns exhibit a reduced warming band in the Pacific Sector of the Southern Ocean (PSSO) in response to global warming, known as the Southern Ocean reduced (SOR) warming pattern. This study utilizes data from 30 climate models participating in the Coupled Model Intercomparison Project Phase 6 (CMIP6), under the 1% CO2 increase per year (1pctCO2) scenario. Through factor decomposition, we identify the radiation forcing, wind cooling in evaporation, and oceanic heat flux as the essential contributors to multi-model ensemble (MME) mean distribution and inter-model uncertainty of the SOR pattern. It is crucial to highlight that the significant impact of the intensified westerlies on the formation of the SOR pattern involves both the wind cooling effect and the wind-driven oceanic dynamics, in both the MME mean distribution and inter-model uncertainty aspects. Our findings suggest that improving the simulation skills of the westerly winds could lead to more precise projection of Southern Ocean warming.

1. Introduction

In the context of global warming, the rise in concentrations of greenhouse gases (GHGs) induces an increase in sea surface temperature (SST), exhibiting distinct warming patterns despite a nearly uniform increase in GHGs [1]. These SST warming patterns play a crucial role in projecting regional and global climate change [1,2,3,4,5,6,7]. For instance, SST warming patterns dominate tropical precipitation change by inducing changes in atmospheric circulations [1,3,4,5,7]. This results in increased rainfall in regions where the sea surface warming exceeds the tropical mean warming and decreased rainfall in regions where the sea surface warming is less than the tropical mean warming [1,3,5,7]. SST warming patterns also contribute to changes observed in tropical cyclone activity [4,8,9,10] and can exert remote influences through atmospheric teleconnection [4,6,11]. However, substantial discrepancy exists in SST patterns projected by models from Phases 3 and 5 of the World Climate Research Programme’s (WCRP’s) Coupled Model Intercomparison Project (CMIP) [12,13,14]. The large inter-model uncertainty in SST patterns is a crucial source for uncertainties in future projections of precipitation, atmospheric circulations, and global water vapor plus lapse rate feedback [2,4,14,15,16,17].

As the most prominent region, extensive research has focused on SST patterns in the tropical Pacific, particularly the zonal El Niño-like warming pattern observed in Tropical Pacific SST warming (TPSW). The weakened Walker circulation decreases the zonal SST gradient, contributing to the formation of the El Niño-like pattern [18,19,20]. Additionally, the asymmetry in evaporative cooling between the western and eastern Pacific favors the El Niño-like pattern [21], while the ocean dynamical thermostat and the Bjerknes feedback tends to enlarge the zonal SST gradient [20,22]. Ying and Huang [23,24] suggested that cloud-radiation feedback is the largest source of inter-model TPSW uncertainty, while ocean advection plays a secondary role.

Another distinguishing characteristic of TPSW is inter-hemispheric asymmetry, with larger warming in the northern tropics than the southern tropics [1,25]. Xie et al. [1] argued that warming asymmetry is associated with changes in trade winds, with intensified trade winds in the southern tropics and weakened trade winds in the northern tropics. Geng et al. [25] pointed out that the source of the inter-model spread in tropical asymmetry can be traced to surface heat flux changes in the mid-to-high latitudes, prompting us to pay attention to the Southern Ocean (SO).

The SO serves as an essential sink for excess heat as well as anthropogenic CO₂ under global warming [26,27,28]. Model simulations suggest that both stratospheric ozone depletion and the rise in GHGs are important drivers of SO warming [29,30]. The projected SO warming shows substantial inter-model variability influenced by factors such as model climate sensitivity, El Niño-Southern Oscillation, ozone recovery, and mesoscale eddy activity [27,31,32]. Sea ice–albedo feedback introduces additional variability, with larger sea ice decline associated with more significant SO warming [25]. Sea ice decline in the Antarctic is also strongly influenced by climatological sea ice [25,33,34]. However, Simmonds and Li [35] documented an increase in Antarctic sea ice extent during 1979–2015, contrary to the consistent decrease in CMIP6 simulations [25,33,34,35]. Model simulation produces great inter-model spread in SO warming when the meltwater from the Antarctic ice sheet is included [30,36]. Previous studies demonstrate that SO warming has climate impacts on the melt of Antarctic ice [30], sea level rise [37], and precipitation [38]. Moreover, SO warming can have far-reaching effects on oceanic and atmospheric circulations, influencing tropical climate [39,40]. Hence, understanding the drivers and impacts of SO warming is essential for projecting the evolution of the global climate system.

The strengthening midlatitude westerly winds have been documented in previous studies [41,42], linked to the poleward expansion of the South Pacific Subtropical High (SPSH) [43], stratospheric ozone depletion [44], and changes in sea ice area [45]. As an important pattern of circulation variability in the high latitudes, the Southern Annular Mode (SAM) has undergone a positive trend in the last three decades, especially in austral summer and autumn [46]. The Positive SAM index is associated with the intensification of the midlatitude westerlies [47,48]. Despite these findings, the contribution of the intensified westerlies to SO warming has not been fully understood.

Given the constraints of limited observational data in both time and space, climate models become valuable tools in climate change research [25,27,33,49]. In the present study, we analyzed ocean mixed-layer heat budget based on outputs from 30 CMIP6 models to evaluate the formation of SO warming and examine the effect of the intensified westerlies. The structure of the remaining sections of the paper is as follows: Section 2 provides details on the data and analysis methods used in the paper. The results are presented in Section 3, and Section 4 gives the conclusions and discussions.

2. Data and Methods

2.1. Model Data

In this paper, we used monthly mean data from 30 climate models participating in CMIP6.

Table 1. 30 CMIP6 models utilized in this investigation.

Model Name	Institute	Unavailable Outputs
ACCESS-CM2	CSIRO-ARCCSS, Australia
AWI-CM-1-1-MR	AWI, Germany
CAMS-CSM1-0	CAMS, China
CESM2	NCAR, USA	uas, vas
CESM2-FV2	NCAR, USA	uas, vas
CESM2-WACCM	NCAR, USA	uas, vas
CESM2-WACCM-FV2	NCAR, USA	uas, vas
CMCC-CM2-SR5	CMCC, Italy
CNRM-CM6-1	CNRM-CERFACS, France
CNRM-CM6-1-HR	CNRM-CERFACS, France
CNRM-ESM2-1	CNRM-CERFACS, France
E3SM-1-0	E3SM-Project LLNL, USA	uas, vas
E3SM-2-0	E3SM-Project LLNL, USA	uas, vas
E3SM-2-0-NARRM	E3SM-Project LLNL, USA	uas, vas
FGOALS-f3-L	CAS, China
FIO-ESM-2-0	FIO, China
GISS-E2-2-G	NASA-GISS, USA
HadGEM3-GC31-LL	MOHC NERC, UK
HadGEM3-GC31-MM	MOHC NERC, UK
INM-CM5-0	INM, Russia
KACE-1-0-G	NIMS-KMA, Republic of Korea
MIROC6	MIROC, Japan
MIROC-ES2L	MIROC, Japan
MPI-ESM-LR	MPI-M, Germany
MPI-ESM-MR	MPI-M, Germany
MPI-ESM-1-2-HAM	MPI-M, Germany
MRI-ESM2-0	MRI, Japan
NorESM2-LM	NCC, Norway	uas, vas
SAM0-UNICON	SNU, Republic of Korea	uas, vas
UKESM1-0-LL	MOHC NERC NIMS-KMA NIWA, UK

provides the names of these models along with their respective institutes, and specifies the unavailable outputs. The outputs were derived from fully coupled 1pctCO2 simulations, wherein atmospheric CO₂ concentration gradually increases at a rate of 1% per year from the preindustrial state until quadrupling. The 1pctCO2 experiment is often employed to investigate the response of the global climate system to the sustained growth of CO₂ concentrations, offering insights into trends and potential impacts of climate change.

The key variables used in this work are listed in

Table 2. Key variables used in this investigation.

Long Name	Output Variable Name	Unit
Surface Temperature	ts	K
Eastward Near-Surface Wind	uas	m s−1
Northward Near-Surface Wind	vas	m s−1
Near-Surface Wind Speed	sfcWind	m s−1
Surface Upward Latent Heat Flux	hfls	W m−2
Surface Upward Sensible Heat Flux	hfss	W m−2
Surface Downwelling Longwave Radiation	rlds	W m−2
Surface Upwelling Longwave Radiation	rlus	W m−2
Surface Downwelling Shortwave Radiation	rsds	W m−2
Surface Upwelling Shortwave Radiation	rsus	W m−2

, along with necessary information. Note that uas and vas are unavailable in some models as specified in Table 1.

2.2. Definition of Changes and Patterns

To ensure coherence in our analysis, all model outputs were interpolated onto a uniform 2° × 2° grid at first. The 1pctCO2 experiment began in the year 1850 and typically spanned 150 years up to 1999 in CMIP6. The long-term mean of the most recent 20 years (1980–1999) represents the mean state during the current warming period (CWP), while the long-term mean of the earliest 20 years (1850–1869) reflects the mean state in the pre-industrial era (PIE). Hence, the changes in each model under global warming are consistently defined as the difference between the CWP and the PIE,

$$\mathsf{\Delta }V={\overline{V}}_{\mathrm{CWP}}-{\overline{V}}_{\mathrm{PIE}}$$

(1)

where $\mathsf{\Delta }$ denotes the change under global warming, $V$ can be any variable, the over bar represents the temporal mean, ${\overline{V}}_{\mathrm{CWP}}$ is the temporal mean of $V$ during the CWP, and ${\overline{V}}_{\mathrm{PIE}}$ is the temporal mean of $V$ over the PIE. Changes are then normalized by their respective tropical mean (0°–360° E, 40° S–40° N) SST change,

$$\mathsf{\Delta }{V}_N=\frac{\mathsf{\Delta }V}{\overline{\mathrm{T}}\mathrm{r}\mathrm{o}(\mathsf{\Delta }\mathrm{SST})}$$

(2)

where $\mathsf{\Delta }{V}_N$ is the normalized change in $V$, and $\overline{\mathrm{T}}\mathrm{r}\mathrm{o}(\mathsf{\Delta }\mathrm{SST})$ is the tropical mean SST change. The tropical mean SST change is just a scalar, utilized as an indicator to assess the simulated magnitude of global warming in a given model. Normalization is performed to eliminate the impact of inter-model difference in the magnitude of global warming. While the absolute changes in variables vary from model to model, the normalized changes are comparable across different models because they signify the changes when the tropical mean SST warms by 1 K in each model [1,20,23,24,50]. For example, the normalized SST change is derived from

$$\mathsf{\Delta }{\mathrm{SST}}_N=\frac{\mathsf{\Delta }\mathrm{SST}}{\overline{\mathrm{T}}\mathrm{r}\mathrm{o}(\mathsf{\Delta }\mathrm{SST})}$$

(3)

where the unit of $\mathsf{\Delta }{\mathrm{SST}}_N$ is K K⁻¹ to indicate that it has been normalized by the tropical mean SST warming. Subsequently, patterns are obtained by subtracting the tropical mean (a scalar) from the normalized changes, thus emphasizing the relative changes [1,20,23,24,50],

$$\mathsf{\Delta }{V}^{\prime }=\mathsf{\Delta }{V}_N-\overline{\mathrm{T}}\mathrm{r}\mathrm{o}(\mathsf{\Delta }{V}_N)$$

(4)

where $\overline{\mathrm{T}}\mathrm{r}\mathrm{o}(\mathsf{\Delta }{V}_N)$ is the tropical mean of $\mathsf{\Delta }{V}_N$, the prime denotes the pattern, and $\mathsf{\Delta }{V}^{\prime }$ is the pattern of $V$. For instance, SST patterns are computed using

$$\mathsf{\Delta }{\mathrm{SST}}^{\prime }=\mathsf{\Delta }{\mathrm{SST}}_N-\overline{\mathrm{T}}\mathrm{r}\mathrm{o}(\mathsf{\Delta }{\mathrm{SST}}_N)$$

(5)

where $\overline{\mathrm{T}}\mathrm{r}\mathrm{o}(\mathsf{\Delta }{\mathrm{SST}}_N)$ is the tropical mean of $\mathsf{\Delta }{\mathrm{SST}}_N$, and $\mathsf{\Delta }{\mathrm{SST}}^{\prime }$ is the SST pattern. Positive (negative) values of SST patterns indicate stronger (weaker) warming compared to the tropical mean SST warming. All changes and patterns are calculated prior to computing the multi-model ensemble (MME) mean. In climate science, ‘climatology’ generally refers to the average conditions over a long period. However, in the context of this research, it specifically corresponds to the long-term mean over the PIE (1850–1869).

2.3. Heat Budget Analysis and SST Change Decomposition

To investigate the formation mechanism of the SOR pattern, we analyzed the ocean mixed layer heat budget equation for each model in the following manner [1,20,23,24,50]:

$$\mathsf{\Delta }{Q}_{\mathrm{LWD}}-\mathsf{\Delta }{Q}_{\mathrm{LWU}}+\mathsf{\Delta }{Q}_{\mathrm{SWD}}-\mathsf{\Delta }{Q}_{\mathrm{SWU}}-\mathsf{\Delta }{Q}_E-\mathsf{\Delta }{Q}_H+\mathsf{\Delta }{Q}_O=0$$

(6)

where $\mathsf{\Delta }$ denotes the change, and $\mathsf{\Delta }{\mathrm{Q}}_{\mathrm{LWD}}$, $\mathsf{\Delta }{\mathrm{Q}}_{\mathrm{LWU}}$, $\mathsf{\Delta }{\mathrm{Q}}_{\mathrm{SWD}}$, $\mathsf{\Delta }{\mathrm{Q}}_{\mathrm{SWU}}$, $\mathsf{\Delta }{\mathrm{Q}}_E$, $\mathsf{\Delta }{\mathrm{Q}}_H$ and $\mathsf{\Delta }{\mathrm{Q}}_O$ represent changes in downward longwave radiation, upward longwave radiation, downward shortwave radiation, upward shortwave radiation, latent heat flux, sensible heat flux, and oceanic heat flux (including all of the advection, mixing, and lateral entrainment terms), respectively. The term of heat content change is an order of magnitude smaller than the terms in the left side of Equation (6), so it is ignored following previous studies [1,20,23,24,50].

Following previous studies [1,20,24,50,51], the change in latent heat flux can be further decomposed into three parts,

$$\mathsf{\Delta }{Q}_E=\mathsf{\Delta }{Q}_E^O+\mathsf{\Delta }{Q}_E^W+\mathsf{\Delta }{Q}_E^R$$

(7)

where $\mathsf{\Delta }{Q}_E^O$ is the Newtonian cooling effect, $\mathsf{\Delta }{Q}_E^W$ is the wind cooling effect, and $\mathsf{\Delta }{Q}_E^R$ is the residual term of latent heat. Specifically, they are calculated as

$$\mathsf{\Delta }{Q}_E^O=(L/R_v{T}^2)\overline{Q_E}\mathsf{\Delta }T$$

(8)

and

$$\mathsf{\Delta }{Q}_E^{\mathrm{W}}=(\overline{Q_E}/\overline{W})\mathsf{\Delta }W$$

(9)

where $L$ is the latent heat of evaporation, $R_v$ is the gas constant for water vapor, $T$ is SST, $\overline{Q_E}$ is the climatology of latent heat flux, $W$ is the wind speed, and $\overline{W}$ is the climatology of wind speed. The Newtonian cooling effect $\mathsf{\Delta }{Q}_E^O$ is governed by the SST change, serving as a response to SST warming. The wind cooling effect $\mathsf{\Delta }{Q}_E^W$ accounts for the contribution of wind speed change to the overall latent heat, while the residual term $\mathsf{\Delta }{Q}_E^R$ encapsulates the combined effects of changes in relative humidity and surface stability.

The upward longwave radiation adheres to the Stefan–Boltzmann law, subject to the surface temperature as follows

$$Q_{\mathrm{LWU}}=\sigma T^4$$

(10)

where $\sigma$ is the Stefan–Boltzmann constant and $T$ is SST. Based on Equation (10), the change in upward longwave radiation can be expressed as

$$\mathsf{\Delta }{Q}_{\mathrm{LWU}}=4\sigma {\overline{T}}^3\mathsf{\Delta }T$$

(11)

where $\overline{T}$ is the climatology of SST. Thus, the change in upward longwave radiation also acts as a response to SST warming.

Moreover, the upward shortwave radiation is exclusively regulated by the surface albedo. Then, we categorized the sum of changes in upward shortwave, downward shortwave, and downward longwave radiation as the total radiation forcing for surface ocean warming. By substituting Equations (7)–(9) and (11) into Equation (6), we can decompose the total SST change into components attributed to different factors [49],

$$\mathsf{\Delta }{Q}_{\mathrm{LWD}}+\mathsf{\Delta }{Q}_{\mathrm{SWD}}-\mathsf{\Delta }{Q}_{\mathrm{SWU}}-\mathsf{\Delta }{Q}_E^W-\mathsf{\Delta }{Q}_E^R-\mathsf{\Delta }{Q}_H+\mathsf{\Delta }{Q}_O=4\sigma {\overline{T}}^3\mathsf{\Delta }T+(L/R_v{T}^2)\overline{Q_E}\mathsf{\Delta }T$$

(12)

which can be further simplified to

$$\begin{array}{l}\mathsf{\Delta }T=\frac{\mathsf{\Delta }{Q}_{\mathrm{LWD}}+\mathsf{\Delta }{Q}_{\mathrm{SWD}}-\mathsf{\Delta }{Q}_{\mathrm{SWU}}-\mathsf{\Delta }{Q}_E^W-\mathsf{\Delta }{Q}_E^R-\mathsf{\Delta }{Q}_H+\mathsf{\Delta }{Q}_O}{4\sigma {\overline{T}}^3+(L/R_v{T}^2)\overline{Q_E}}\\ \hspace{1em}\hspace{0.25em}=\frac{(\mathsf{\Delta }{Q}_{\mathrm{LWD}}+\mathsf{\Delta }{Q}_{\mathrm{SWD}}-\mathsf{\Delta }{Q}_{\mathrm{SWU}})+(-\mathsf{\Delta }{Q}_E^W)+(\mathsf{\Delta }{Q}_O)+(-\mathsf{\Delta }{Q}_E^R-\mathsf{\Delta }{Q}_H)}{4\sigma {\overline{T}}^3+(L/R_v{T}^2)\overline{Q_E}}\\ \hspace{1em}\hspace{0.25em}=\mathsf{\Delta }{T}_{\mathrm{RAD}}+\mathsf{\Delta }{T}_{\mathrm{WC}}+\mathsf{\Delta }{T}_O+\mathsf{\Delta }{T}_R\end{array}$$

(13)

where $\mathsf{\Delta }T$, $\mathsf{\Delta }{T}_{\mathrm{RAD}}$, $\mathsf{\Delta }{T}_{\mathrm{WC}}$, $\mathsf{\Delta }{T}_O$, and $\mathsf{\Delta }{T}_R$ are the total SST change and SST change induced by the radiation forcing $(\mathsf{\Delta }{Q}_{\mathrm{LWD}}+\mathsf{\Delta }{Q}_{\mathrm{SWD}}-\mathsf{\Delta }{Q}_{\mathrm{SWU}})$, wind cooling effect $(-\mathsf{\Delta }{Q}_E^W)$, oceanic flux $(\mathsf{\Delta }{Q}_O)$ and atmospheric residual term $(-\mathsf{\Delta }{Q}_E^R-\mathsf{\Delta }{Q}_H)$, which consists of the latent heat residual and the sensible heat. The pivotal function of Equation (13) is to convert the heat fluxes, measured in units of W m⁻² into their corresponding contributions to SST change, denoted in units of K, thus rendering the analysis more intuitively clear.

Note that, for each model, if we replace every term in Equation (13) with its respective pattern following the definition in Section 2.2, the equation still holds. For the purpose of studying the formation of SST patterns in PSSO (i.e., the SOR pattern), rather than the SST changes, we need to transform the terms in Equation (13) into their respective patterns,

$$\mathsf{\Delta }{T}^{\prime }=\mathsf{\Delta }{T^{\prime }}_{\mathrm{RAD}}+\mathsf{\Delta }{T^{\prime }}_{\mathrm{WC}}+\mathsf{\Delta }{T^{\prime }}_O+\mathsf{\Delta }{T^{\prime }}_R$$

(14)

where $\mathsf{\Delta }{T}^{\prime }$, $\mathsf{\Delta }{T^{\prime }}_{\mathrm{RAD}}$, $\mathsf{\Delta }{T^{\prime }}_{\mathrm{WC}}$, $\mathsf{\Delta }{T^{\prime }}_O$, and $\mathsf{\Delta }{T^{\prime }}_R$ represent the total SST pattern and SST pattern contributed by radiation forcing, wind cooling effect, oceanic flux, and atmospheric residual, respectively.

3. Results

Analysis of the MME mean involving 30 CMIP6 climate models revealed a distinctive band-like reduced warming pattern, termed the Southern Ocean reduced (SOR) pattern, in the Pacific Sector of the Southern Ocean (PSSO, 170° E–80° W, 60°–45° S), delineated by the green box in Figure 1. According to the definition of SST patterns in Section 2.2, the regional mean of the SOR pattern is −0.32 K K⁻¹. This implies that the regional mean SST increase in the PSSO is 32% smaller than the tropical mean SST increase in model simulations. Notably, the SOR pattern corresponds with the intensified midlatitude westerlies (Figure 1a). The spatial correlation within the PSSO between the MME mean of wind speed changes and SST patterns is −0.67 (Figure 1b), underscoring the crucial role of the intensified westerlies in forming the SOR pattern. Subsequently, a systematic factor decomposition using Equation (14) is conducted to elucidate the formation mechanism of the SOR pattern and to understand how the westerly wind forcing influences the surface ocean warming. It is important to note that the regional means and spatial correlations discussed in the following are conducted within the PSSO.

The outcomes of the factor decomposition are depicted in Figure 2, revealing contributions from various heat fluxes to the SST patterns. The theoretical total SST responses closely mirrored the actual SST patterns (Figure 3a), showing an extremely high spatial correlation (r = 1), thereby affirming the applicability of the decomposition described in Equation (14). The radiation forcing components exhibited robust and extensive negative patterns (Figure 3b), displaying a strong correlation with the SST patterns (r = 0.82). In contrast, the wind cooling components portrayed relatively weak negative patterns (Figure 3c), correlating with the SST patterns at 0.62. Moreover, the oceanic flux component manifested as a broad negative band (Figure 3d), similar to the SOR pattern (r = 0.80). Consequently, the radiation forcing, wind cooling, and oceanic flux components all displayed positive correlations with the SST patterns, supporting the presence of the SOR pattern. It is noteworthy that the oceanic flux components showed a significant minimum at the SST minimum in the western part of the PSSO (Figure 3d), indicating the primary contribution to the corresponding extremely low warming.

Regional mean values of various components in the MME mean are compared in

Table 3. Regional means within the PSSO of various components (K K⁻¹) in the MME mean.

Factors	SST	$\mathit{\Delta }{\mathit{T}}^{\prime }$	$\mathit{\Delta }{{\mathit{T}}^{\prime }}_{\mathit{R}\mathit{A}\mathit{D}}$	$\mathit{\Delta }{{\mathit{T}}^{\prime }}_{\mathit{W}\mathit{C}}$	$\mathit{\Delta }{{\mathit{T}}^{\prime }}_{\mathit{O}}$	$\mathit{\Delta }{{\mathit{T}}^{\prime }}_{\mathit{R}}$	$\mathit{\Delta }{{\mathit{T}}^{\prime }}_{\mathit{W}\mathit{C}}+\mathit{\Delta }{{\mathit{T}}^{\prime }}_{\mathit{O}}$
Regional means	−0.32	−0.32	−0.16	−0.12	−0.35	0.30	−0.47

, demonstrating that the regional mean of the theoretical total responses exactly matched that of the actual SST patterns; both were −0.32 K K⁻¹. The radiation forcing and wind cooling components together contributed about −0.28 K K⁻¹ to the SOR pattern, while the oceanic flux component alone contributed −0.35 K K⁻¹, suggesting the predominant role of the oceanic flux in the formation of the SOR pattern.

Furthermore, in the MME mean, wind speed changes exhibited a spatial correlation (r = −0.53) with the oceanic flux components (Figure 3a). The oceanic flux components were also strongly correlated with the SST patterns at 0.80 (Figure 3b). In conjunction with Figure 1b, a spatial correlation chain among the wind speed changes, oceanic flux components, and SST patterns could be established. It can be concluded that, on the one hand, the intensified westerlies drive oceanic dynamic processes, potentially including vertical mixing, equatorward Ekman transport, and upwelling, drawing up cold subsurface water to suppress surface ocean warming [27,30]. This represents an indirect process of the intensified westerlies influencing the SST patterns. On the other hand, westerly wind forcing also directly contributes to the SOR pattern through the wind cooling effect. The combined effect of these processes is demonstrated by the robust correlation between wind speed changes and the SST patterns (r = −0.67; Figure 1b).

The combined contributions of wind cooling and oceanic flux are illustrated in Figure 4a with a regional mean of −0.47 K K⁻¹ (Table 3), exhibiting a strong spatial correlation with the SST patterns (r = 0.84). Considering the correlation between the wind speed changes and the SST patterns is -0.67, the regional mean contribution of the westerly wind forcing can be roughly estimated as −0.31 K K⁻¹. Additionally, it was observed that the atmospheric residual components displayed evident positive patterns in the PSSO (Figure 4b), acting as a counteractive factor to the formation of the SOR pattern (r = −0.81), especially at the SST minimum in the western part of the PSSO.

Climate projections in the PSSO vary substantially across the CMIP6 models (Figure 5a–d). The inter-model uncertainty in the theoretical total responses correlated perfectly with the inter-model uncertainty in SST patterns (r = 1; Figure 5a), reaffirming the correctness of the decomposition in Equation (14) from an inter-model perspective. The radiation forcing components also exhibited a strong inter-model correlation (r = 0.91) with the SST patterns (Figure 6b), serving as an essential source of the inter-model uncertainty in SST patterns. Moreover, the wind cooling (Figure 5c) and oceanic flux components (Figure 5d) both exhibited high inter-model correlations with the SST patterns (r = 0.75, 0.72, respectively). Nevertheless, the atmospheric residual components showed a low inter-model correlation (r = −0.3; not shown) with the SST patterns. Therefore, radiation forcing, wind cooling, and oceanic flux are the primary direct contributors to the inter-model uncertainty in SST patterns.

The wind speed changes showed strong inter-model correlations with the oceanic flux components (r = −0.63; Figure 6a) and SST patterns (r = −0.83; Figure 6b). Drawing insights from Figure 5d and Figure 6, the pronounced inter-model correlations among the wind speed changes, oceanic flux components, and SST patterns reveal a distinct inter-model correlation chain that aligns with the previously highlighted spatial correlations. Consequently, the intensified westerlies exert a significant impact on the inter-model uncertainty in SST patterns through the wind cooling effect and wind-driven oceanic dynamics.

4. Conclusions

We undertook a comprehensive investigation into the formation mechanism of the SOR warming pattern in the PSSO, utilizing outputs from 30 CMIP6 models under the 1pctCO2 scenario. Initially, a robust spatial correlation between the MME mean of the SST patterns and the intensified westerlies was observed, implying the influence of the westerly wind forcing on surface ocean warming. Subsequently, we performed a factor decomposition based on the ocean mixed-layer heat budget to precisely isolate the distinct effects of various heat fluxes on the SST patterns. The decomposition proved applicable to our analysis, allowing for the perfect reconstruction of the MME mean distribution and inter-model uncertainty of the actual SST patterns. In the MME mean distribution, the results indicate that the radiation forcing, wind cooling, and oceanic flux components all favor the formation of the SOR pattern, while the atmospheric residual components act to suppress its formation. The conducive effect of radiation components is associated with increased cloud cover due to the poleward shift of storm tracks [30,52]. The oceanic flux involves complicated processes in the SO, including equatorward Ekman transport, upwelling, mixing, and mesoscale eddies [27,30]. The warming effect of the atmospheric residual components is related to the increased rainfall weakening the evaporation and faster warming of the atmosphere than the ocean [30,52].

In terms of strength, the oceanic flux components (−0.35 K K⁻¹) emerged as the primary contributors to shaping the SOR pattern, while the atmospheric residual components exhibited a strong counter-effect (0.30 K K⁻¹) that nearly offset the oceanic flux influence. According to Equation (9), the relatively modest effect of wind cooling (−0.12 K K⁻¹) is subject to low climatological evaporation and high climatological wind speed in high latitudes. It is noteworthy that the oceanic flux components play a vital role in forming the SST warming minimum in the western part of the PSSO. This low SST warming potentially amplifies the warming contrast between the atmosphere and ocean, prompting the atmosphere to warm the ocean [30]. Hence, the atmospheric residual components displayed a strong warming effect on the ocean in that region. Additionally, a correlation chain among the wind speed changes, oceanic flux components, and SST patterns was observed. We concluded that the intensified westerlies drive a portion of the oceanic flux, thereby influencing the SST patterns. Therefore, the impact of westerly wind forcing on the formation of the SOR pattern involved both the wind cooling effect in evaporation and wind-driven oceanic dynamics.

An in-depth exploration of the sources of the uncertainty in the SOR pattern revealed the pivotal contributions of the radiation forcing, wind cooling effect, and oceanic flux. In contrast, the atmospheric residual made a relatively minor contribution to the SOR pattern (r = −0.35). Moreover, a robust inter-model correlation chain appeared among the wind speed changes, oceanic flux components, and SST patterns. In conclusion, for the formation of the SOR pattern, the significant contributions of the wind cooling effect, radiation forcing, and oceanic flux were consistent both in the MME mean distribution and the inter-model uncertainty. Furthermore, we found that the intensified westerlies exerted impact on the formation of the SOR pattern through both the wind cooling effect and the wind-driven oceanic dynamics, in both the MME mean distribution and inter-model uncertainty.

Please be aware the intensified westerlies contributed only to a portion of the oceanic flux. The spatial correlation between the MME mean of wind speed changes and oceanic flux components was relatively low (r = −0.38) in the region of minimum SST warming (160°–130° W, 60°–50° S). This suggests that westerly wind forcing drove only a minor part of the oceanic dynamics in that specific area.

Clarifying the formation mechanisms of SST warming patterns and reducing their inter-model uncertainties are of significant importance for the projection of climate change. This study offers valuable insights into the formation of the SOR pattern in the PSSO and suggests that improving the modeling skill of the westerly winds can help reduce the uncertainty in projecting SO warming. However, the CMIP6 models feature a relatively coarse resolution, potentially overlooking certain sub-grid processes. Advancements in high-resolution modeling are necessary to facilitate more comprehensive research into SO warming.