Phase-Locked Impact of the 11-Year Solar Cycle on Tropical Pacific Decadal Variability

Wenjuan Huo aGEOMAR Helmholtz Centre for Ocean Research Kiel, Kiel, Germany
bState Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

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Ziniu Xiao bState Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

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Liang Zhao bState Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

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Abstract

As an important external forcing, the effect of the 11-yr solar cycle on the tropical Pacific decadal variability is an interesting question. Here, we systematically investigate the phase-locking of the atmosphere and ocean covariations to the solar cycle in the tropical Pacific and propose a new mechanism to explain these decadal covariations. In both observation/reanalysis datasets and a solar cycle forced sensitivity experiment (named the SOL experiment), the ocean heat content anomalies (OHCa; 300 m) resemble a La Niña–like pattern in the solar cycle ascending phase, and the Walker circulation shifts westward. In the declining phase, the opposite is true. The accumulative solar irradiation directly contributes to this coherent decadal variability via changing the warm water volume and the solar-related heat is redistributed by the ocean dynamic processes. During the 11-yr solar cycle, the Pacific Walker circulation anomalies maintain the OHCa in the western equatorial Pacific and work as negative feedback for the eastern Pacific to help the OHCa phase transition. In addition, oceanic meridional heat transport via the subtropical cells and the propagation of off-equatorial Rossby waves also provide a lagged negative feedback to the OHCa phase transition according to the 11-yr solar cycle. The decadal coupled responses of the tropical Pacific climate system are 2 years more lag in the SOL experiment than in the observation/reanalysis.

Significance Statement

Here, we propose a new mechanism that the heating effect of the accumulative solar irradiation during the 11-yr solar cycle can be “integrated” into the tropical Pacific OHC and then provide a bottom-up effect on the atmosphere at decadal time scales. The strongly coupled processes in this region amplify the decadal phase-locking of the covariations to the 11-yr solar cycle. Our study demonstrates the role of the 11-yr solar cycle in the tropical Pacific decadal variability and provides a new explanation for the “bottom-up” mechanism of the solar cycle forcing. Our results update the understanding of the tropical Pacific decadal variability and may help to improve climate predictions at decadal time scales.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Wenjuan Huo, whuo@geomar.de

Abstract

As an important external forcing, the effect of the 11-yr solar cycle on the tropical Pacific decadal variability is an interesting question. Here, we systematically investigate the phase-locking of the atmosphere and ocean covariations to the solar cycle in the tropical Pacific and propose a new mechanism to explain these decadal covariations. In both observation/reanalysis datasets and a solar cycle forced sensitivity experiment (named the SOL experiment), the ocean heat content anomalies (OHCa; 300 m) resemble a La Niña–like pattern in the solar cycle ascending phase, and the Walker circulation shifts westward. In the declining phase, the opposite is true. The accumulative solar irradiation directly contributes to this coherent decadal variability via changing the warm water volume and the solar-related heat is redistributed by the ocean dynamic processes. During the 11-yr solar cycle, the Pacific Walker circulation anomalies maintain the OHCa in the western equatorial Pacific and work as negative feedback for the eastern Pacific to help the OHCa phase transition. In addition, oceanic meridional heat transport via the subtropical cells and the propagation of off-equatorial Rossby waves also provide a lagged negative feedback to the OHCa phase transition according to the 11-yr solar cycle. The decadal coupled responses of the tropical Pacific climate system are 2 years more lag in the SOL experiment than in the observation/reanalysis.

Significance Statement

Here, we propose a new mechanism that the heating effect of the accumulative solar irradiation during the 11-yr solar cycle can be “integrated” into the tropical Pacific OHC and then provide a bottom-up effect on the atmosphere at decadal time scales. The strongly coupled processes in this region amplify the decadal phase-locking of the covariations to the 11-yr solar cycle. Our study demonstrates the role of the 11-yr solar cycle in the tropical Pacific decadal variability and provides a new explanation for the “bottom-up” mechanism of the solar cycle forcing. Our results update the understanding of the tropical Pacific decadal variability and may help to improve climate predictions at decadal time scales.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Wenjuan Huo, whuo@geomar.de

1. Introduction

The excess energy from external forcings can be stored in the ocean in form of ocean heat content (OHC) and released into the climate system in the following years. Changes in OHC can be used for tracking the accumulation of excess external energy. Several studies have suggested that the global warming slowdown during 1998–2013 was closely tied to an acceleration of the ocean heat sink in the Pacific Ocean (England et al. 2014), Indian Ocean (Lee et al. 2015), Atlantic Ocean, and Southern Ocean (Chen and Tung 2014). In contrast to the Atlantic and Southern Oceans, where the heat was transported into deeper layers during this global warming hiatus period (Chen and Tung 2014), the changes in OHC in the Pacific Ocean occurred mainly within a shallow layer (above 300 m), resembling a La Niña–like pattern (Kosaka and Xie 2013; Chen and Tung 2014), which may be part of the Pacific decadal variability (Meehl et al. 2013; England et al. 2014; Nieves et al. 2015). The OHC anomalies (OHCa) in the tropical Pacific upper layers (above 300 m) not only have an impact on the variability and predictability of local phenomena but also contribute globally to ocean heat transport (Forget and Ferreira 2019) and surface warming on decadal time scales.

In most previous studies, the long-term ENSO-like pattern of upper-ocean OHCa in the tropical Pacific was taken as part of the interdecadal Pacific oscillation (IPO) of the whole Pacific, with a dominant periodicity of 20 years (Levitus et al. 2000; Hasegawa and Hanawa 2003; Meehl et al. 2013; Hu et al. 2020). Recently, Power et al. (2021) summarized the tropical Pacific decadal variability (TPDV) into the “internal” TPDV and “external” TPDV. The former can generate spontaneously without any change to external forcings and includes 8–40-yr variability. Tropical–extratropical “communications” via shallow meridional overturning circulations, or subtropical cells (STCs), were proposed as a key process for the TPDV (Nonaka et al. 2002; Capotondi et al. 2005; Lohmann and Latif 2005). STCs were first described by Liu (1994) and McCreary and Lu (1994) as linking the tropical and subtropical Pacific Oceans. The off-equatorial Ekman transport in the surface Ekman layer (above 50 m) brings surface water poleward and subducts in the subtropics owing to the existence of Ekman pumping/suction. The subducted water can return back to the equatorial subsurface along mean isopycnals in the ocean interior or reach the western boundary currents (McCreary and Lu 1994; Huang and Wang 2001) and rise to the surface or move eastward within the thermocline at the equator (Liu 1994; McCreary and Lu 1994; Huang and Wang 2001). Therefore, the mass exchanges between the subtropical and tropical Pacific can be characterized by these meridional transport convergences in the interior ocean pycnocline across 9°N and 9°S, as well as the equatorial upwelling and the poleward Ekman transport.

Besides, quasi-decadal (<20 years) sea surface temperature (SST) anomalies in the tropical Pacific can also be produced locally without involving extratropics. Several possible mechanisms have been proposed in this regard: 1) interactions between ENSO and the nonlinearity of the tropical ocean–atmosphere interaction on decadal and longer time scales (Timmermann and Jin 2002), 2) anomalous temperature propagation driven by the local wind stress curl (Luo and Yamagata 2001), and 3) the delayed action oscillator shared by the interannual and decadal oscillation (Knutson and Manabe 1998; White et al. 2003).

For the externally forced TPDV, Power et al. (2021) reviewed the tropical Pacific responses from both anthropogenic forcing and volcanic eruptions. However, the 11-yr solar cycle forcing, as a periodical external forcing, is presumed to have a smaller influence than other forcings and is almost ignored in most TPDV studies because of the small decadal changes in solar irradiation. Actually, the TPDV with a periodicity of 9–13 years fluctuates strongly in response to the 11-yr solar cycle (White and Liu 2008), and the impacts of the solar cycle could be amplified by the coupled atmosphere–ocean processes (Meehl et al. 2009). The response of the tropical Pacific to the solar cycle forcing is still under debate. A La Niña–like SST anomaly was found in the winter of solar-maximum years, which was followed by an El Niño–like anomaly after 1 or 2 years (Van Loon et al. 2007; Meehl et al. 2009; Meehl and Arblaster 2009). Meanwhile, Tung and Zhou (2010), as well as Roy and Haigh (2010), found that it is “neither El Niño nor La Niña” but rather weak warming in solar-maximum years. Huo and Xiao (2017b) found that the warming response appears first in the central Pacific in solar-maximum years and then extends into the eastern Pacific in the following years, resembling an El Niño Modoki. Although the response pattern is inconsistent among previous works, an interesting feature is that the 11-yr solar signals in the tropical Pacific are confined above the main pycnocline (White et al. 1997; Xiao et al. 2016; Wang et al. 2018; Huo et al. 2021) and distributed more in the east–west direction in the shallow layers rather than transported into deeper layers. This feature is different from the IPO-related OHCa whereby a Pacific-wide meridional distribution is found in the layers above 700 m. The IPO-related OHCa in the upper 100 m of the equatorial Pacific is opposite to those at depths of 100–300 m (Hu et al. 2018).

A “bottom-up” mechanism proposed by Meehl and Arblaster (2009) was used to explain the La Niña–like pattern in solar-maximum years (Van Loon et al. 2007; Meehl and Arblaster 2009; Meehl et al. 2009). More incoming solar irradiation in solar-maximum years produces a greater input of energy in the relatively cloud-free areas of the subtropics and enhances evaporation locally. More moisture is carried to the convergence zones by the trade winds, and the off-equatorial tropical precipitation and strength of the Hadley and Walker circulations are enhanced. Accordingly, the strength of the trade winds is increased, which can result in more upwelling of cold water in the equatorial eastern Pacific. This bottom-up mechanism suggests the coupled Pacific climate system can amplify the initial small solar signals and transport (or transform) the “extra” solar energy to produce a measurable response. In addition to this direct solar irradiation at the surface, the enhanced UV radiation in solar-maximum years strengthens the heating and production of ozone in the upper stratosphere. These solar signals can propagate downward through Rossby wave–mean flow interactions, thereby modulating the polar night jet and tropical tropospheric circulations (Kodera and Kuroda 2002; Gray et al. 2006, 2009; Matthes et al. 2006; Frame and Gray 2010).

Most previous studies have focused on the influences of peak solar forcing, with relatively few having investigated its phase-locked decadal covariations with the tropical Pacific OHCa based on statistical analysis (Wang et al. 2015; Huo and Xiao 2017a; Wang et al. 2020). Considering the 11-yr solar cycle as a periodic heating source of the climate system, its effects may be “memorized” by the ocean and amplified by the coupled processes. The role of the 11-yr solar cycle in the TPDV is worthy of careful examination. In addition, the responses of the tropospheric atmosphere to the 11-yr solar cycle [e.g., tropical convection (Xiao et al. 2016), the Walker cell (Misios et al. 2019), and the summer monsoon (Zhao and Wang 2014; Jin et al. 2019)] are closely tied to the tropical surface solar signals. Therefore, elucidating the mechanisms and physical processes involved in the impacts of the solar cycle on the tropical Pacific is crucial for the attribution of many observed changes. The tropical Pacific plays an important role in the climate system, and the possible connections between the 11-yr solar cycle forcing and the TPDV are important for improving the predictability of large-scale weather or climate events as well as decadal-scale climate changes.

In this study, we first investigate the phase-locking of the atmosphere–ocean covariations to the 11-yr solar cycle in the tropical Pacific by using observation/reanalysis datasets and comparing two sensitivity experiments (SOL and NOSOL), and then examine associated physical processes and discuss the possible mechanisms. The coupled covariations in the tropical Pacific phase-locked to the 11-yr solar cycle are presented in section 3. The physical processes associated with the decadal covariations and possible mechanisms are examined in sections 4 and 5. The major conclusions and some further discussion are presented in section 6.

2. Methods and data

a. Reanalysis data

The gridded ocean temperature and OHC datasets were obtained from the Institute of Atmosphere Physics ocean reanalysis (IAP-OHC; 1940–present), which is reconstructed based on all available observations from the World Ocean Database with newly introduced bias correction and reliability quantification (Cheng et al. 2017). The quality-controlled subsurface ocean temperature objective analyses dataset, EN.4.2.1 (1900–present), from the U.K. Met Office Hadley Centre (Good et al. 2013) is used to calculate warm water volume (WWV) and the depth of the 20°C isotherm. Oceanic meridional velocity and potential temperature from Simple Ocean Data Assimilation v2.2.4 (SODA; 1871–2008) (Carton and Giese 2008) are used to calculate the meridional ocean heat transport. The Extended Reconstructed SST dataset, version 5 (ERSST; 1854–present) provided by NOAA’s National Centers for Environmental Information, is also used in this study. Besides, the atmospheric vertical velocity, 3D wind, and surface heat fluxes (shortwave, longwave, sensible heat flux, and latent heat flux) obtained from the NOAA-CIRES Twentieth Century Reanalysis v2 (NOAA-20CR; 1871–2012) (Compo et al. 2011) are used to investigate the responses in the atmosphere, and these data were provided by the NOAA PSL at their website (https://psl.noaa.gov).

Considering the observational reliability of the data, all the observational/reanalysis variables from 1950 and afterward are used in this study (e.g., the IAP-OHC, ERSST, and EN4 reanalysis datasets are from 1950 to 2019; NOAA-20CR is from 1950 to 2012, and SODA spans 1950–2008). Please note that the composite results shown in this study can be confirmed by the reanalysis dataset in a shorter common period of 1950–2008 (figures are not shown). The annual mean is calculated from monthly data and detrended by the least squares quadratic at every grid point, and the anomaly is defined as the departure from the mean value over the whole analyzed period. As shown in Fig. A1 (see appendix), the total solar irradiation (TSI) from the reconstructed solar forcing datasets of CMIP6 is used as an index of observed solar forcing (black line). The TSI in our sensitivity experiments (SOL and NOSOL) is shown by the solid and dotted gray lines in Fig. A1, respectively.

b. Model description and sensitivity experiments

The Community Earth System Model (CESM 1.0) used here is a fully coupled climate model with a “high top” atmospheric component, known as the Whole Atmosphere Community Climate Model (WACCM 3.5) (Marsh et al. 2013). WACCM 3.5 has 66 vertical levels (up to 5.1 × 10−6 hPa; ∼145 km) and a horizontal resolution of 1.9° latitude × 2.5° longitude. It includes interactive chemistry and spectrally resolved solar variability from the Naval Research Laboratory model for spectral and total irradiance (NRLSSI; Wang et al. 2005). A realistic time-varying quasi-biennial oscillation is obtained by relaxing the equatorial stratospheric winds (4–86 hPa) toward observed winds (Matthes et al. 2010). The interactive ocean (POP) has 60 depth levels and a horizontal grid of 1° × 1°.

Two experiments (SOL and NOSOL) covering 145 years from 1955 to 2099 were conducted based on CESM-WACCM. The SOL experiment was forced by observed daily solar irradiance from 1955 to 2009 and by twice repeating the four last solar cycles from 2010 to 2099 (solid gray line in Fig. A1). The NOSOL experiment was forced by a fixed solar forcing, which was the averaged value from 1965 to 2008 (dotted gray line in Fig. A1). Greenhouse gases and ozone-depleting substances were fixed at 1960s levels for both SOL and NOSOL to exclude anthropogenic impacts. Time-evolving volcanic forcing over 1955–2000 was included in both experiments, the same as in the observations. Three large volcanic eruptions happened during our study period—namely, Mt. Agung (1963), El Chichón (1982), and Mt. Pinatubo (1991). Tropical volcanic eruptions can trigger El Niño within 2 years of the eruption (Khodri et al. 2017). To exclude its alignment with the solar activity, we removed the years of the three main eruptions and the following two years of each one before carrying out the composite analysis. For these two sensitivity experiments, the annual mean is calculated from monthly data and the anomaly is defined as the departure from the mean value over the whole data period (1955–2099).

c. Methods

As mentioned in the introduction, the 11-yr solar signal in the tropical Pacific only exists in the upper ocean layers (above 300 m). In this study, we used the OHC integral from the surface to a depth of 300 m to investigate the solar-related heat change for both the reanalysis and simulations (SOL and NOSOL). We defined the solar cycle phases as a function of TSI values in the 11-yr period. The TSI minimum is defined to be 0° (modulo 360°) and the maximum is 180°. Then, the ascending phase from minimum to maximum includes five parts (30°, 60°, 90°, 120°, 150°) with a center of 90°. Similarly, the declining phase from maximum to minimum has a center at 270° and also includes five parts (210°, 240°, 270°, 300°, and 330°). It is important to note here that we define the phases based on the mean values of the 11-yr solar cycle because we are investigating the averaged responses at the decadal time scale. The phase centers may shift a bit if applied to individual solar cycles, as the length can vary within 9–13 years. Phase transition (from 0° to 360°) in the 11-yr cycle is not a real “time” evolution, but a gradual change to the solar irradiance strength.

Cross-correlations are calculated to investigate the phase-locked relationship and the significance levels are assessed by the two-tailed Student’s t test with consideration of the effective degrees of freedom of the time series in correlation analysis. We followed the method used by Pyper and Peterman (1998) and simplified as only the autocorrelation coefficients at lag 1 are considered in this study:
1Ne1N+2N×(N1)N×ρxρy,
where Ne represents the effective number of degrees of freedom and N indicates the sample size of years in the time series; ρx and ρy represent the autocorrelation coefficients of each time series at a lag time of 1 year.

The composite mean difference (CMD) is used to deduce spatial patterns of responses to the solar cycle forcing (Camp and Tung 2007; Zhou and Tung 2012). For the lagged response, the patterns were obtained by shifting both the maximum and minimum at a lag of 1 (2, 3…) years at the same time. This method can reduce the influence of random internal variability to some extent when the dataset is long enough. The maximum and minimum of each solar cycle are shown in Fig. A1 (black circles and dots). The maximum OHC responses to the solar cycle appear at a lag of 2 years, and following the method proposed by Camp and Tung (2007), we projected the original detrended data onto this spatial pattern to obtain the associated time series. This CMD-P time series represents the temporal behavior of the response pattern in the original data. It includes the responses to the solar cycle forcing and internal variabilities that have a similar spatial pattern. Therefore, the higher-frequency variability with a different spatial pattern can be filtered out by this method, working as a spatial filter. The same CMD-P method was also applied to the OHCa of the SOL and NOSOL experiments. The 90% statistical significance of the CMD results compared to the whole dataset is estimated by a 1000-fold bootstrapping test with replacement (Diaconis and Efron 1983).

For comparison, we extracted the leading mode of the observed annual mean OHCa within the tropical Pacific region (30°S–30°N, 90°E–60°W) by EOF analysis to check the 11-yr solar signals in this dominant mode. The spectra of the time series were calculated via fast Fourier transform, and the confidence levels are indicated by the 90% and 95% confidence bounds of the Markov “red noise” spectrum. In addition, wavelet coherence and the cross-wavelet transform were calculated to reveal the covariance of two time series, their high common power, and relative phase shift (Grinsted et al. 2004).

The meridional heat transport (MHT) by the STCs is estimated according to
Q(t)=(1)ρoCpxwxehσϑ(x,z,t)θ(x,z,t)cosφdxdz,
where ρo is the ocean density (ρo = 1035.0 kg m−3); Cp is the specific heat (Cp = 3992.1 J kg−1 °C−1); ϑ(x, z, t) is the meridional velocity at latitude φ = 9°N/S as a function of longitude x, depth z, and time t; θ (x, z, t) is the potential temperature; and xe and xw are the eastern and western longitudes. To compute the total MHT across 9°N and 9°S, we integrated the meridional transport from 90°W to 145°E at 9°N and from 80°W to 165°E at 9°S, then vertically integrated from the base of the mixed layer (about 50 m) to the depth of the σ = 26 kg m−3 isopycnal surface (McPhaden and Zhang 2002). Please note that here the positive (negative) values at 9°N (9°S) indicate an equatorward heat transport.

3. Phase-locking of covariations to the 11-yr solar cycle in the tropical Pacific

a. Phase-locking of OHC decadal variations to the 11-yr solar cycle

We applied both the EOF and CMD methods to the observed tropical Pacific OHCa, as shown in Fig. 1a. Their spatial patterns (contours and shaded contours) are almost the same, with a spatial correlation coefficient of 0.996. Both patterns have very high spatial correlations with the TSI regression map in Fig. 1b (r ≈ 0.96). The same as the spatial pattern, the time series from the CMD projection (blue line) is similar to the PC1 (red line in Fig. 1c); their maximum correlation coefficients with the TSI are RCMD = 0.55 and RPC1 = 0.47 at a lag of 2 years. This implies that the lagged response to the 11-yr solar cycle forcing makes a large contribution to the leading mode of the OHCa.

Fig. 1.
Fig. 1.

Decadal covariation of the observed OHCa in the tropical Pacific with the 11-yr solar cycle. (a) Regression maps of the OHCa (1950–2019) onto the PC1 (shaded contours, with only those above the 90% significance level shown) and the CMD-P time series (contours, with hatching denoting regions above the 90% significance level). (b) TSI regressed onto the 2-yr lagged OHCa (black dotted regions are above the 90% significance level). (c) Time series of standardized TSI (black), 2-yr lagged PC1 (red), and CMD-P (blue), in which all the time series are smoothed with 3-yr running mean. Wavelet power spectra of (d) TSI and (e) the CMD-P time series. (f) XWT: Cross-wavelet spectrum of TSI and CMD-P time series. (g) WTC: Wavelet coherency spectrum of TSI and CMD-P time series. The black arrows indicate the phase lag of CMD-P time series with respect to TSI time series [pointing right: in-phase; left: antiphase; downward: TSI time series leads CMD-P by a quarter-cycle phase (2–3 years)]. The thick black lines indicate the 5% significance level against the red noise.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

The 11-yr solar cycle signal can be found in the spectra of both the CMD-P time series and PC1, the statistical significance of which exceeds the 95% confidence level, and with a doubled variance of the CMD-P compared to the PC1. Unfortunately, these two methods cannot effectively filter out the 2–7-yr ENSO signal because the response pattern resembles the ENSO pattern and the dataset (1950–2019) is not long enough to rule out the coincidence. However, a significant common power of around 11 years shows in the cross-wavelet spectrum of TSI and CMD-P time series with a 2–3-yr phase shift (Fig. 1f) and no common power in the 2–7-yr band. The TSI and CMD-P time series have an in-phase coherence during 1950–75 and significant coherence with a quarter-cycle phase shift (2–3 years) in the post-1980 period in the 9–13-yr band (Fig. 1g). The CMD spatial pattern is calculated based on the solar cycle and the CMD-P time series can indicate its temporal behavior in the original data. The decadal signal extracted by this method has a higher correlation with the 11-yr solar cycle and is easier to interpret than the EOF method. Therefore, we believe that the CMD (and CMD-P) method is more suitable than the EOF method when investigating the response to the solar cycle, and we therefore applied this method to the OHCa of the SOL and NOSOL experiments. Note that we used the same composite years in the NOSOL experiment as the SOL experiment to compare, even though no solar cycle forcing was included in the NOSOL experiment. Totally different CMD spatial patterns derived from SOL and NOSOL (not shown here) suggest that the OHCa in these composite years are changed by the solar forcing. Figures 2a and 2b show the wavelet power spectrum of the CMD-P time series of SOL and NOSOL, respectively. A clear decadal periodicity within 9–13 years appears in SOL (Fig. 2a), which is absent in NOSOL (Fig. 2b). A significant common power around of 11 years appears in the cross-wavelet spectrum of the TSI and CMD-P time series of OHCa in SOL, with a quarter-cycle phase shift (Fig. 2c). Their coherence is only significant during 2010–70 (Fig. 2d) when the 11-yr signal in SOL is strongest (Fig. 2b). The CMD-P time series in SOL has a significant positive correlation with the TSI, its maximum coefficient being 0.42 at a lag of 2 years. No correlation can be found between the time series of NOSOL and TSI. It is worth noticing that the decadal variability of OHCa and its coherence with the 11-yr solar cycle are significant and robust based on the reanalysis dataset. But for the SOL experiment, only the cross-wavelet spectrum of TSI and OHCa CMD-P time series shows a significant and robust common power at the 11-yr band (figures are not shown here).

Fig. 2.
Fig. 2.

Decadal covariation of the tropical Pacific OHCa in the SOL experiment with the 11-yr solar cycle. Wavelet power spectrum of the CMD-P time series in (a) SOL and (b) NOSOL. (c),(d) The cross-wavelet spectra and wavelet coherency spectra of TSI and the CMD-P time series in SOL. The black arrows indicate the phase lag of CMD-P with respect to TSI [pointing right: in phase; left: antiphase; downward: TSI leads CMD-P by a quarter-cycle phase (2–3 years)]. The thick black lines indicate the 5% significance level against the red noise.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

The above analysis implies that the 11-yr solar cycle may lead to a decadal covariation with the tropical Pacific OHCa, and the response pattern resembles the pattern of ENSO and internal TPDV. To further investigate the features of the covariation, we calculated a cross-correlation between the TSI and observed OHCa (1950–2019) averaged over 10°S–10°N (shaded contours in Fig. 3a). A positive correlation between the OHCa and TSI appears in the western Pacific, and a negative one in the eastern Pacific, when the OHC leads the TSI by 1–5 years and reverses at a lag of 0–5 years, with the largest correlations for both the positive and negative correlations appearing at a lag of 2 years. For the SST anomaly, its cross-correlation map with the TSI (contours in Fig. 3a) is slightly different from that of the OHCa. Negative correlations in the eastern Pacific extend into the central Pacific at around 160°E in the SST lead years [from lag −1 to −5 years] and turn into positive correlations in the SST lag years. The western Pacific SSTs appear to vary in phase with the TSI. The correlation in the western Pacific (west of 160°E) is weak, while significant positive (negative) correlations appear in the Maritime Continent at a lag of 0 (+5) years. The incoming solar irradiance absorbed by the upper ocean is attenuated exponentially with depth, but only 20–30 m in the open ocean. The different patterns of the solar signals in the OHCa and the SST anomalies suggest that the surface warm water is transported and redistributed in the subsurface by ocean dynamic processes.

Fig. 3.
Fig. 3.

Phase-locking of the equatorial Pacific OHCa to the solar cycle. (a) Cross-correlation of TSI with the observed OHCa (shaded contours, 1950–2019) and SST anomaly (contours) averaged over 10°S–10°N. (b) As in (a), but for the WWV anomaly. (c),(d) As in (a), but for OHCa in the SOL and NOSOL experiments (1955–2099), respectively. The black dotted regions and the hatched regions are above the 90% significance level based on a t test.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

Because the warm water in the tropical Pacific is produced by solar radiation and changes in warm water volume will impact the oceanic thermal structure, we calculated the cross-correlation between the TSI and the WWV anomaly, as shown in Fig. 3b. Here, the WWV is defined as the volume of water warmer than 20°C. There is no significant response of WWV anomalies in the central Pacific—only a positive correlation in the eastern Pacific (east of 150°W) in the WWV lag years (Fig. 3b), combined with a negative correlation in the western Pacific. Comparing Figs. 3a and 3b, the OHCa in the western Pacific are directly from the changes in local WWV, but they have different anomalous centers in the eastern Pacific. In the equatorial Pacific, the WWV depends on the depth of the 20°C isotherm and is sensitive to the surface wind stress. Therefore, the WWV anomaly also implies the “wind-driving” heat distribution in ocean layers. It is worth noting that WWV was taken as an index of OHC in some studies that focused on the relationship between ENSO and WWV (e.g., McPhaden 2003). The above opposing zonal OHCa responses are confirmed in the SOL experiment (Fig. 3c), but fewer regions are above the 90% significance level. Notably, the OHCa response pattern is opposite to the observations at a lag of 0 years, and the maximum OHC response appears at a lag of 4 years in the SOL experiment. These phase-locked responses are absent in the NOSOL experiment (Fig. 3d).

b. Phase-locking of the Walker circulation to the solar cycle

Considering the high degree of coupling in the tropical climate system, we also checked the possible phase-locking of the covariation in the atmospheric circulation to the solar cycle. Figure A2 shows dipole patterns in the zonal gradient of SST anomalies and the vertical velocity anomalies (downward is positive) at 300 hPa in a whole solar cycle. In the solar minimum and ascending phase (0°–120° in Fig. A2), the zonal SST gradient is stronger in the Maritime Continent and weaker in the western Pacific (Fig. A2a), corresponding to anomalous upwelling (negative in Fig. A2b) over the Maritime Continent and downwelling (positive in Fig. A2b) over the western Pacific. The signals reverse in the maximum and declining phase (120°–300° in Fig. A2). These dipole patterns suggest a thermally maintained circulation in the equatorial Pacific via a Bjerknes feedback (Bjerknes 1969), which is also phase-locked to the 11-yr solar cycle. As shown in Fig. A3, these dipole patterns have a common 11-yr period in their spectra—the same as the TSI index. These consistent features imply a coupled response of the tropical Pacific climate system to the 11-yr solar cycle forcing.

To further check the responses of the atmospheric circulation, we calculated the composite difference of divergent winds and velocity potential anomalies at 200 hPa between solar maximum and minimum based on reanalysis data and outputs of the SOL experiment, as shown in Fig. 4. Compared to the climatology (Figs. 4a,d), the ascending branch (divergence at 200 hPa) shifts westward from 150° to 120°E in the solar cycle ascending phase (Figs. 4b,e). Meanwhile, the descending branch (convergence at 200 hPa) appears in the central and eastern Pacific, with a maximum at around 150°W (Figs. 4b,e). Opposite signals appear in the solar cycle declining phase (Figs. 4c,f). The active center of the ascending (descending) branch is almost in the same location as the extreme positive (negative) OHCa (shaded contours in Figs. 3a,c). These phase-locked covariations are absent in the NOSOL experiment (Fig. A4). Compared to observations, the active centers are located more to the east in the SOL experiment during both the ascending and declining phases, which is consistent with the OHCa.

Fig. 4.
Fig. 4.

Phase-locked responses of the Pacific Walker cell to the solar cycle. (a) Divergent winds (vectors) and velocity potential (shaded contours) at 200 hPa in the observations for the climatology, and composite anomalies averaged in the (b) ascending phase (0°–180°) and (c) declining phase (180°–360°/0°). (d)–(f) As in (a)–(c), but for the SOL experiment. Negative (positive) shaded contours represent divergence and ascending (convergence and descending). White dotted regions are above the 90% significance level for velocity potential and only the zonal component of the divergent winds above the 90% significance level are shown, both tested by bootstrapping.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

Next, we discuss the possible mechanisms involved in the phase-locking of the covariation in the Walker circulation to the 11-yr solar cycle. One is the “bottom-up” effect from the solar-induced OHCa. Here, we calculated the static stability anomaly in the center of ascending (descending) branch based on the reanalysis data (Fig. A5) to investigate the thermal contribution to the Walker circulation responses. In the ascending phase, the significant negative static stability anomalies between 850 and 500 hPa (red line in Fig. A5a) indicate a stronger convectively unstable state at the center of the ascending branch (120°E). This may be due to the positive OHCa in the western Pacific that provides more energy to the overlying atmosphere. However, there are no significant anomalies in the vertical convection between 850 and 500 hPa in the solar cycle declining phase (black line in Fig. A5a) when the OHCa changes to negative. The negative static stability anomaly is larger in the levels above 300 hPa (Fig. A5a), suggesting that stronger vertical convections exist in the upper troposphere layers during the solar cycle ascending phase. Conversely, the vertical convections are significantly reduced above the 300-hPa level in the solar declining phase (black line in Fig. A5a).

In the eastern Pacific, the static stability anomaly at the center of the descending branch (150°W) is negative among almost all the levels below 300 hPa in the solar cycle ascending phase (red line in Fig. A5b). This indicates strengthened vertical convection that associates with the stronger ascending over the western Pacific. A similar feature but with the opposite sign can be found in the solar cycle declining phase (black line in Fig. A5b). In addition to the bottom-up influences, the latitudinal distribution of solar UV radiation in the solar-maximum years can increase the stability in the lower stratosphere and reduce the Brewer–Dobson circulation via a relative Eliassen–Palm flux divergence, leading to a weak equatorial upwelling in the troposphere, enhanced tropical precipitation, and broader Hadley cells (Crooks and Gray 2005; Rind et al. 2008). These “top-down” responses may modulate the Walker circulations (Meehl et al. 2009). Misios et al. (2019) found that the Pacific Walker circulation is weakened in the solar-maximum years by a muted hydrological cycle and Bjerknes feedback. Our results are consistent with the findings of Misios et al. (2019) insofar as the 11-yr solar cycle can affect the Pacific Walker circulation on decadal time scales.

Summarizing the above analysis, phase-locking of decadal covariations in the tropical Pacific climate system to the 11-yr solar cycle was found in both the observations and sensitivity experiment. To pinpoint the underlying mechanism of this decadal covariation, we first assess which processes contribute to the changes in OHCa during the solar cycle (section 4). Then, we investigate the accumulation of the heat from the solar radiation (section 5).

4. Possible processes responsible for the phase-locked covariations in the tropical Pacific

OHCa within a specific volume will be influenced by several processes, including surface heat flux, oceanic heat advection (horizontal and vertical), and subgrid mixing (Hu et al. 2020). To study which process contributes to the OHCa in the 11-yr solar cycle, we ignore the subgrid mixing and simply divide the possible processes into two groups. The first of these two groups is the surface net heat flux. This group indicates the ocean “communication” with the atmosphere in the tropical Pacific. The other group contains the ocean dynamic processes, the main focus of which here is the wind-driven surface zonal advection and the MHT. This group represents the zonal energy exchange and “communication” of the equatorial Pacific with the extra-equatorial regions and the subtropical Pacific.

a. Contributions of surface processes to the OHC–TSI phase-locked covariations

As shown in Fig. 5a (color-shaded contours), the positive OHCa in the western Pacific and negative OHCa in the eastern Pacific appear during the solar cycle ascending phase (0°–120°), and so we name this pattern the positive phase of OHC decadal oscillations. Therefore, its negative phase (negative in the west and positive in the east) appears in the solar cycle declining phase (180°–330°). The surface zonal wind anomalies (contours) converge around 130°E and diverge around 150°W in the solar cycle ascending phase (0°–150° in Fig. 5a), which reverse their signals in the solar maximum and declining phase (180°–300°). The anomalous easterly winds bring surface warm water into the western Pacific and the warm water accumulates into the subsurface layers, contributing to the positive OHCa in the western Pacific during the solar cycle ascending phase. Meanwhile, the upwelling of cold water in the far eastern Pacific (120°–90°W) is reduced by the anomalous westerly winds but increased in the zonal wind divergence region (around 150°W), leading to negative OHCa in the eastern Pacific with a maximum in 130°–160°W. All the signals of both OHC and zonal wind anomalies reverse in the solar declining phase (210°–330°). Therefore, the surface zonal wind anomalies make a positive contribution to the TSI–OHC phase-locked anomalies during the whole solar cycle.

Fig. 5.
Fig. 5.

Surface processes related to the phase-locked TSI–OHC decadal covariations in reanalysis data (1950–2012). Composite (a) OHCa (shaded contours; 1 × 108 J m−2) and zonal wind anomaly (contours; dashed is negative; m s−1), (b) surface net heat flux anomaly (W m−2; downward is positive) based on reanalysis data and averaged over 10°S–10°N. The black dotted regions are above the 90% significance level for (a) OHCa and (b) net heat flux anomalies based on bootstrapping. White scratches are the 90% significance level for zonal wind anomalies.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

As the above zonal wind anomalies are part of the Pacific Walker circulation, we further discuss the feedback of the Walker circulation to the OHCa. During the solar cycle ascending phase (0°–150°), a dipole pattern of cloud cover anomalies is collocated with the anomalous convections (Fig. A2b). The westward shift of the Pacific Walker circulation strengthens (weakens) the vertical convections over the western (central) Pacific and hence increases (decreases) the local high and medium cloud cover fraction (Fig. A6). As a result, negative (positive) net shortwave (longwave) flux anomalies appear in the western Pacific and positive (negative) anomalies in the central and eastern Pacific. These radiation fluxes, together with positive turbulent flux anomalies (figures are not shown here), could warm up the central and eastern equatorial Pacific in the minimum and earlier ascending phase (0°–60°) (Fig. 5b). There are no significant surface heat flux anomalies in the late-ascending phase (60°–150°) when the vertical velocity is weak (Fig. A2b), and hence the surface heat fluxes have less contribution to the OHCa. During the solar cycle declining phase (210°–300°), the opposite signals of the Walker circulation reverse the cloud cover anomalies as well as the surface net radiation flux anomalies. The negative surface heat flux anomalies in the solar cycle declining phase (Fig. 5b) provide negative feedback to the OHCa in the central and eastern Pacific. This is conducive to the OHC phase transition according to the solar cycle phases.

Note that we show some feedback in a coupled system, which cannot indicate the direction of air–sea interaction solely based on the physical consistency shown in Fig. 5. However, the ocean has a much larger heat capacity than the atmosphere, and the “extra” radiative heat from an active solar could be stored in the OHC and released later. Therefore, the solar-induced OHCa may serve as an energy source impacting the tropical atmospheric circulations, while the latter provide feedback to the ocean. The solar signals in the tropical Pacific are amplified by these coupled processes. Figure 6 shows the same analysis as Fig. 5 but with the output of the SOL. The lagged response of OHCa to the 11-yr solar cycle is 2 years more in the SOL experiment than in the reanalysis data (shaded contours in Figs. 6a and 5a). The positive OHCa in the western Pacific first appear in the center of the ascending phase (shaded contours, Fig. 6a, 90°) and then extend into the central Pacific in the late-ascending phase and solar maximum (Fig. 6a; 90°–210°). Meanwhile, negative OHCa exist in the eastern Pacific, and these OHCa are opposite in the declining phase and solar minimum (Fig. 6a, 240°–360°). Anomalous easterly (westerly) winds appear in the ascending phase and solar maximum (declining phase and solar minimum) (contours, Fig. 6a), which exceeds the 90% confidence level over the central Pacific. As in the observation, these zonal wind anomalies can provide positive feedback to the OHCa during the solar cycle. A bit different from the reanalysis, the surface heat flux anomaly has a negative contribution to the OHCa of the whole equatorial Pacific in the SOL experiment (Fig. 6b), but only a very few regions above the 90% significance level.

Fig. 6.
Fig. 6.

As in Fig. 5, but for the SOL experiment (1955–2099).

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

b. Contributions of ocean dynamic processes to the OHCa phase transition

As discussed above, the equatorial Pacific not only exchanges heat with the atmosphere and in the west–east direction, but it also “communicates” strongly with the extra-equatorial and subtropical regions. The surface warm water moves into extra-equatorial regions via the poleward Ekman transport, and can return back to the equator through off-equatorial Rossby waves and the Pacific shallow STCs. As we focused on decadal time scales, here we averaged the depth of the 20°C isotherm anomaly over latitude bands (10°–20°N/S) to show the propagations of the wind-driven off-equatorial Rossby waves during the 11-yr solar cycle (Fig. 7). We begin our description from 180° to show their contributions to the OHC phase transition after the solar maximum. During the solar maximum and declining phase (180°–300°), the strengthened trade winds (dashed contours in Fig. 5a) in the eastern Pacific drive a stronger poleward Ekman transport. More warm water is transported into the northern and southern off-equatorial Pacific, leading to positive Z20 (depth of the 20°C isotherm) anomalies (90°–140°W in Figs. 7a,c). The positive Z20 anomalies propagate westward with slower phase speeds than the theoretical Rossby waves, which take approximately three years from the eastern to the western boundary (Figs. 7a,c: 300° → 360°/0° → 30°). These Rossby waves are reflected at the western boundary and continue to travel equatorward along the boundary as coastal Kelvin waves and then eastward along the equator, taking around two to three years to arrive at the central and eastern equatorial Pacific (Fig. 7: 60° → 90° → 120°). Thus, these Rossby wave propagations from the off-equatorial Pacific to the equator provide a lagged negative feedback to the SST anomalies of the central and eastern equatorial Pacific (Fig. 7b or 7d: 150° → 180°), thereby contributing to the phase transition of the tropical Pacific decadal oscillation. Our results are consistent with the works of White et al. (2003) and White and Liu (2008), who found that the Pacific quasi-decadal oscillation with a 9–13-yr period is governed by a tropical delayed action oscillator, similar to ENSO but resonantly excited by the 11-yr solar signal.

Fig. 7.
Fig. 7.

Contribution of off-equatorial Rossby waves to the OHCa phase transition based on reanalysis data (m). Depth of the 20°C isotherm anomaly averaged over the (a) southern off-equatorial Pacific (10°–20°S) and (b) equatorial Pacific (10°S–10°N). (c),(d) As in (a) and (b), but for the northern off-equatorial Pacific (20°–10°N) and the equatorial Pacific. Black dotted regions are above the 90% significance level.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

The propagations of the oceanic Rossby waves partly indicate the adjustment of STCs to the extra-equatorial wind anomalies. Here, we calculated the oceanic MHT by STCs based on Eq. (2) with the SODA reanalysis dataset as well as the SOL and NOSOL experiments. Figure A7 shows the time series of the MHT by the interior STCs across 9°N and 9°S during the 11-yr solar cycle and the net equatorward heat transport based on the SODA reanalysis dataset. The positive net equatorward MHT around the solar minimum and early-ascending phase (red line in Fig. A7, 300°–360°/0°–60°) leads to fast warm water building up in the Pacific equator region. As a result, a positive OHCa develops in the western Pacific and the negative OHCa appears in the eastern Pacific (Fig. 5a). Oppositely, the negative net equatorward MHT (red line in Fig. A7, 60°–300°) and significant MHT divergence at 150° (positive at 9°S and negative at 9°N) suggest less warm water building up in the equator. The positive OHC anomaly in the western equatorial Pacific decreases and changes into negative in the declining phase (Fig. 5a). Therefore, the oceanic MHT by the STCs is in phase with the western equatorial Pacific OHCa and out of phase with the eastern Pacific OHCa. This feature is confirmed by the SOL experiment (Fig. 8) but with 90° (∼3 years) more lag than the reanalysis. The equatorward convergent heat transport (positive net MHT) during the late-ascending phase and the solar maximum (90°–210° in Fig. 8a) contributes to the positive OHCa in the western and central (Fig. 6a). An equatorward divergent heat transport around the solar minimum and early-ascending phase (Fig. 8a, 270°–0°–90°, negative at 9°S and positive at 9°N) reduces the equatorward transport of warm water, and hence less warm water accumulation in the equatorial Pacific during this stage. As a result, the positive OHCa in the western equatorial Pacific decreases and changes into negative. This phase-locked convergence (divergence) of heat transport at the decadal time scale is absent in the NOSOL experiment (Fig. 8b). The oceanic MHT by the STCs works as a lagged negative feedback to the equatorial eastern Pacific OHCa to favor to the phase transition according to the 11-yr solar cycle. It is important to notice that the decadal variability of MHT also can be internally generated in a coupled system (Solomon et al. 2003). Thus, Figs. A7 and 8 suggest the Pacific MHT is phase-locked to the 11-yr solar cycle in a solar cycle forced system, but the latter is not a necessary condition for the MHT decadal variability.

Fig. 8.
Fig. 8.

MHT by the Pacific STCs (PW; 1 PW = 1015W) in the (a) SOL and (b) NOSOL experiments. The black solid (dotted) lines indicate the total MHT by STCs across 9°N (9°S), southward is positive. The red lines indicate the net equatorward heat transport across 9°N and 9°S. The solid dots indicate above the 90% significance level based on bootstrapping.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

5. Accumulative solar irradiation in the tropical Pacific and its role in the decadal phase-locked covariations

The OHCa can be used to measure the heat accumulation in the ocean, but the cumulative process in upper ocean layers (300 m) is hard to show because of the frequent “communication” with the atmosphere and layers below. As solar radiation is the major external source producing warm water in the tropical climate system, we assume there is an “extra heat” from the solar radiation when it is more active than the mean state (e.g., peak years in an 11-yr solar cycle), enabling the production of “extra” warm water compared to the solar quiet state. This “extra” solar-related warm water will be redistributed by the oceanic dynamical processes and disturbs the local WWV. Therefore, we use the composite differences of WWV anomaly between solar maximum and minimum years to partly quantify the combined effect of direct solar heating effect and the associated oceanic dynamical feedback on WWV anomaly. The buildup and release of the WWV will change the state of the local OHCa. The solar radiation arriving at the surface is part of the surface net heat flux; thus, here we investigate the contribution of the accumulative surface fluxes (shortwave, longwave, sensible, and latent heat fluxes) to the WWV anomaly, as well as the OHCa, based on the observational/reanalysis data (Figs. 9a,b). Compared to the tropical eastern Pacific, more cloud cover exists in the western Pacific, leading to less incoming shortwave flux and trapping more longwave flux. In addition, the stronger vertical convection in the western Pacific is highly related to the local turbulent fluxes. Since the “heating source” for the western Pacific could be different from that for the eastern, we diagnosed these two regions separately.

Fig. 9.
Fig. 9.

(a) Direct effect of solar radiation in the eastern equatorial Pacific “cloud-free” region (150°–105°W, 15°S–5°N) during the solar cycle. (a1) Composite of cumulative sum of TSI anomaly, (a2) cumulative sum of surface heat fluxes anomalies [net shortwave (black), net longwave (green), sensible heat flux (red), and latent heat flux (blue), in which downward is positive], (a3) WWV anomaly, and (a4) OHCa averaged over 165°120°W, 10°S–10°N. (b) Indirect effect in the western equatorial Pacific “cloud-cover” region (120°–165°E, 10°S–10°N). (b1),(b2) As in (a2) and (a3), but averaged in the western equatorial Pacific. (b3) Composite surface zonal wind anomalies averaged in the central equatorial Pacific (165°E–165°W, 10°S–10°N). (b4) As in (a4), but for OHCa averaged in the western equatorial Pacific. (c1)–(c4),(d1)–(d4) As in (a1)–(a4) and (b1)–(b4), respectively, but for the SOL experiment. The solid dots indicate above the 90% significance level based on bootstrapping.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

As shown in Fig. 9a(1), the accumulative TSI increases from the center of the solar cycle ascending phase (90°) and reaches maximum at the center of the declining phase (240°), suggesting more energy input into the system. The accumulative shortwave anomaly varies along with the TSI and is above the 90% significance level at the TSI maximum [black line in Fig. 9a(2)]. The opposite feature of the accumulative longwave anomaly [green line in Fig. 9a(2)] suggests an impact of the cloud cover change in the radiation fluxes. The accumulative latent and sensible heat fluxes anomalies [blue and red lines in Fig. 9a(2)] are positive during the whole solar cycle, but the latent heat flux is much larger than the sensible flux and decreases in the solar cycle declining phase. The accumulative surface heat flux anomaly produces relatively more warm water (increased WWV) in the eastern Pacific [Fig. 9a(3)] and reduces gradually the negative OHCa [Fig. 9a(4)]. The OHCa changes into positive anomalies and reaches a maximum around the center of the solar cycle declining phase (270°). In the late-declining phase and solar minimum (270°–360°), the accumulative TSI decreases and the accumulation of surface heat flux also reach the minimum level [Fig. 9a(2)]. The positive WWV anomaly and OHCa reduce and change into negative around the solar minimum (330°). The surface heat flux anomaly explains approximately 39% of the OHCa in the eastern equatorial Pacific based on squaring their correlation coefficient. The net shortwave and latent heat flux anomalies are the major contributors to the surface heat flux anomalies.

For the western equatorial Pacific, the negative shortwave and latent heat fluxes anomalies [Fig. 9b(1)] produce less warm water [Fig. 9b(2)] during the solar cycle late-ascending phase and declining phase (90°–270°). This can help the OHCa changing from positive to negative [Fig. 9b(4)]. In addition, the WWV anomalies are also sensitive to the surface zonal wind anomalies over the central Pacific [Fig. 9b(3)]. The anomalous easterly winds weaken gradually during the solar late-ascending phase and change into westerly winds in the solar maximum and declining phase [Fig. 9b(3), 60°–270°]. These weakening zonal winds reduce the westward transport of surface warm water. As a result, less WWV builds up in the western Pacific [Fig. 9b(2)] and more warm water accumulates in the eastern Pacific [Fig. 9a(3)]. The warm water builds up quickly in the western Pacific around the solar minimum (0°–30°) when the warm water in the eastern Pacific is released by the anomalous easterly winds [Fig. 9b(3)], and this leads to a quick phase transition of the OHCa from negative to positive in the western Pacific [Fig. 9b(4)]. These features suggest that the accumulative solar irradiation works as a heating source, and its extra heating effect (compared to the TSI minimum) can be gradually accumulated in the OHCa of the eastern Pacific to be released quickly once this heat source disappears (back to the TSI minimum).

At this point, we applied the same analysis to the outputs of the SOL experiment (Figs. 9c,d). Noting that the maximum OHC responses in the SOL experiment have a 1/6 phase shift to the observations (∼2-yr lag than the observations), the negative (positive) OHCa in the eastern (western) equatorial Pacific first appears in the late-ascending phase and maintains for 5 years [Figs. 9c(4) and d(4), 90°–210°]. During this period, the negative WWV anomaly [Fig. 9c(3)] can be partly attributed to the negative accumulation of surface heat flux anomaly [Fig. 9c(2)]. The strength of the OHCa (negative in the east and positive in the west) decreases gradually and reverses its anomalous signals when the accumulative TSI reaches its maximum [black line in Fig. 9c(1)]. More warm water accumulation in the eastern Pacific reduces the local negative OHCa when the TSI is above the mean value and the accumulative TSI increases (120°–240°). However, different from the reanalysis, although the accumulative shortwave anomaly increases during the solar maximum and declining phase [black line in Fig. 9c(2)], it has much less contribution to the positive WWV anomaly than the latent heat flux anomaly [blue line in Fig. 9c(2)].

The changes in accumulative shortwave and longwave fluxes in the western Pacific [black and green lines in Fig. 9d(1)] in the SOL are opposite to those in the eastern Pacific during the ascending phase (0°–180°), and remain positive during the declining phase (180°–330°). They provide positive contributions to the WWV anomaly and OHCa in the western Pacific during the late-ascending phase and solar maximum (90°–210°). A weak surface heat flux accumulation during the solar minimum and earlier-ascending phase (330°–60°) has a negative contribution to the negative WWV (OHC) anomaly in the western equatorial Pacific [Figs. 9d(2),d(4)]. The accumulative shortwave flux in the SOL is quite different from the reanalysis dataset, which may be due to the cloud bias in both the reanalysis and model. Similar to the observation, the negative OHCa in the western Pacific changes into positive OHCa quickly when more surface warm water is transported west by the strengthened trade winds (330°–30°).

6. Conclusions and discussion

Using reanalysis datasets and two sensitivity experiments (SOL and NOSOL), we investigated the phase-locking of atmosphere and ocean covariations in the tropical Pacific to the 11-yr solar cycle and propose possible mechanisms. Both the reanalysis datasets and the SOL experiment showed a synchronization of the decadal oscillation of the tropical Pacific climate system to the 11-yr solar cycle with a phase shift [the maximum responses of OHCa lagged the TSI by ∼2 (∼4) years in the reanalysis (the SOL experiment). A La Niña–like pattern (positive anomalies in the west and negative in the east) appears in the solar cycle ascending phase, while an El Niño–like pattern appears in the declining phase. A convection dipole with negative anomalies over the Maritime Continent and positive anomalies over the western Pacific appears in the ascending phase, and vice versa in the declining phase. Meanwhile, the Pacific Walker circulation shifts westward (eastward) during the ascending (declining) phase of the solar cycle. Its ascending and descending branches are in the same locations as the extreme OHCa. These atmospheric responses closely coupled to the OHCa can result from the bottom-up effect. Meanwhile, top-down influences from the responses of the stratosphere to the UV radiation might also modulate the behavior of the Walker circulation, which should be further investigated in future studies.

The above coupled decadal covariations in the tropical Pacific phase-locked to the 11-yr solar cycle were confirmed by the solar-cycle-forced run (the SOL experiment) and were absent in the run without solar cycle forcing (NOSOL). However, the responses in the SOL experiment were smaller and with a 2-yr more phase shift than observed. The extrema of OHCa in the SOL experiment, as well as the ascending (descending) centers of the Pacific Walker circulation, were located more to the east than observed.

To elucidate the underlying mechanisms of the decadal covariations, we investigated the accumulation of heat from solar radiation in the tropical Pacific upper layers (300 m). Compared to the TSI minimum, the heating effect of the “extra” solar irradiation is gradually “integrated” into the OHC until the solar irradiation returns back to its lowest value (around the TSI minimum). During this period, the negative OHCa in the eastern Pacific (in the ascending phase) weaken and change into positive OHCa (in the declining phase). Once the “extra” solar irradiation disappears, the WWV in the eastern Pacific is quickly released and transported into the western Pacific by the strengthened trade winds. The WWV (and OHC) anomaly in the western Pacific is sensitive to the surface zonal wind anomaly. The phase-locked Pacific Walker cell anomaly provides a positive (negative) feedback to the OHCa in the western (eastern) equatorial Pacific. In addition, the oceanic MHT by the STCs and the wind-driven off-equatorial Rossby waves provide lagged negative feedbacks to help the OHCa phase transition.

Here, we should acknowledge that we only performed one pair of simulations (SOL and NOSOL) based on one model (CESM-WACCM) to check the observed responses, which cannot rule out model dependence or “contamination” by the internal variability. Therefore, more ensemble members and multimodel simulations are needed in future studies to isolate the decadal solar signals from those of others. Besides, the bias of cloud and surface fluxes in both reanalysis and model may increase the uncertainty of our results.

Acknowledgments.

We wish to thank Katja Matthes and Rémi Thiéblemon, who performed the two model simulations based on CESM-WACCM. This study is supported by a project from the Natural Science Foundation of China (42075040, 41790471), the National Key Research and Development Program of China (2018YFA0606203), and the State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences (Project No. LTO1916).

Data availability statement.

All observation/reanalysis data used in this study are publicly distributed and can be obtained from their corresponding providers, as described in section 2. The source code of the Community Earth System Model version 1.0 used in this study can be obtained at https://www.cesm.ucar.edu/models/cesm1.0/. The output of the two sensitivity experiments and codes to produce all figures are available from the corresponding author upon reasonable request.

APPENDIX

Supplemental Figures

Figure A1 shows the TSI time series used in CMIP6 and in our sensitivity experiments (SOL and NOSOL). Figure A2 shows that the anomalous convection over the western equatorial Pacific is controlled by the local zonal temperature gradient. Figure A3 indicates the dipole patterns of the anomalous convection and the zonal temperature gradient in the western equatorial Pacific have a common period as the 11-yr solar cycle. Figure A4 shows no phase-locked responses of the Pacific Walker cell to the 11-yr solar cycle in the NOSOL experiment when no solar forcings are included. Figure A5 shows the static stability anomalies at the centers of the ascending and descending branches. Figure A6 shows significant responses of the high and medium cloud cover anomalies in the western equatorial Pacific to the 11-yr solar cycle. Figure A7 shows the meridional heat transport (MHT) by the interior STCs based on the SODA reanalysis dataset.

Fig. A1.
Fig. A1.

TSI time series as an index of solar forcing in the CMIP6 (black line), SOL (solid gray line), and NOSOL (dotted gray line) experiments. The solar maximum (minimum) years are marked by the black circles (dots).

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

Fig. A2.
Fig. A2.

Anomalous convection over the western equatorial Pacific controlled by the local zonal temperature gradient. Composite difference between solar maximum and minimum of (a) SST zonal gradient SST/lon averaged in 10°S–10°N (°C per degree longitude) based on ERSST and (b) vertical velocities at 300 hPa averaged over 5°S–5°N (Pa s–1) by using NOAA-20CR. Black dotted regions are above the 90% significance level.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

Fig. A3.
Fig. A3.

(a) Spectrum of TSI (red) and SST/lon (black; ERSST) averaged in the western equatorial Pacific (white boxes in Fig. A2: 150°E–180°, 10°S–10°N). (b) As in (a), but for TSI and vertical velocities (NOAA-20CR) at 300 hPa. The thin dashed and solid lines are the 90% and 95% confidence bounds of the Markov “red noise” spectrum.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

Fig. A4.
Fig. A4.

Divergent winds (vectors) and velocity potential anomalies (shaded contours) at 200 and 850 hPa in the NOSOL experiment for (a),(d) the climatology, and composite results averaged in the (b),(e) ascending phase (0°–180°) and (c),(f) declining phase (180°–360°/0°).

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

Fig. A5.
Fig. A5.

Static stability at the (a) ascending center (120°E) and (b) descending center (150°W) averaged in the solar ascending (red lines) and declining (black lines) phases (based on air temperature data from NOAA-20CR). The solid dots indicate above the 90% significance level based on bootstrapping.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

Fig. A6.
Fig. A6.

Composite of cloud cover fraction anomaly based on solar cycle with NOAA-20CR for (a) high cloud cover, (b) medium cloud cover, and (c) low cloud cover. Black dotted regions are above the 90% significance level.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

Fig. A7.
Fig. A7.

MHT by the Pacific STCs (PW; 1 PW = 1015 W) in the SODA reanalysis dataset (1950–2008). The black solid (dotted) line indicates the total MHT by STCs across 9°N (9°S); southward is positive. The red line indicates the net equatorward heat transport across 9°N and 9°S. The solid dots indicate above the 90% significance level based on bootstrapping.

Citation: Journal of Climate 36, 2; 10.1175/JCLI-D-21-0595.1

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Save
  • Bjerknes, J., 1969: Atmospheric teleconnections from the equatorial Pacific. Mon. Wea. Rev., 97, 162172, https://doi.org/10.1175/1520-0493(1969)097<0163:ATFTEP>2.3.CO;2.

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    • Crossref
    • Search Google Scholar
    • Export Citation
  • Capotondi, A., M. A. Alexander, C. Deser, and M. J. McPhaden, 2005: Anatomy and decadal evolution of the Pacific subtropical–tropical cells (STCs). J. Climate, 18, 37393758, https://doi.org/10.1175/JCLI3496.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carton, J. A., and B. S. Giese, 2008: A reanalysis of ocean climate using simple ocean data assimilation (SODA). Mon. Wea. Rev., 136, 29993017, https://doi.org/10.1175/2007MWR1978.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, X., and K.-K. Tung, 2014: Varying planetary heat sink led to global‐warming slowdown and acceleration. Science, 345, 897903, https://doi.org/10.1126/science.1254937.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cheng, L. J., K. E. Trenberth, J. Fasullo, T. Boyer, J. Abraham, and J. Zhu, 2017: Improved estimates of ocean heat content from 1960 to 2015. Sci. Adv., 3, e1601545, https://doi.org/10.1126/sciadv.1601545.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Compo, G. P., and Coauthors, 2011: The Twentieth Century Reanalysis Project. Quart. J. Roy. Meteor. Soc., 137 (654), 128, https://doi.org/10.1002/qj.776.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Crooks, S. A., and L. J. Gray, 2005: Characterization of the 11-year solar signal using a multiple regression analysis of the ERA-40 dataset. J. Climate, 18, 9961015, https://doi.org/10.1175/JCLI-3308.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
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    • Crossref
    • Search Google Scholar
    • Export Citation
  • England, M. H., and Coauthors, 2014: Recent intensification of wind‐driven circulation in the Pacific and the ongoing warming hiatus. Nat. Climate Change, 4, 222227, https://doi.org/10.1038/nclimate2106.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Forget, G., and D. Ferreira, 2019: Global ocean heat transport dominated by heat export from the tropical Pacific. Nat. Geosci., 12, 351354, https://doi.org/10.1038/s41561-019-0333-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frame, T. H. A., and L. J. Gray, 2010: The 11-year solar cycle in ERA-40 data: An update to 2008. J. Climate, 23, 22132222, https://doi.org/10.1175/2009JCLI3150.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Good, S. A., M. J. Martin, and N. A. Rayner, 2013: EN4: Quality controlled ocean temperature and salinity profiles and monthly objective analyses with uncertainty estimates. J. Geophys. Res. Oceans, 118, 67046716, https://doi.org/10.1002/2013JC009067.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gray, L. J., S. A. Crooks, M. A. Palmer, C. L. Pascoe, and S. Sparrow, 2006: A possible transfer mechanism for the 11-year solar cycle to the lower stratosphere. Space Sci. Rev., 125, 357370, https://doi.org/10.1007/s11214-006-9069-y.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gray, L. J., S. T. Rumbold, and K. P. Shine, 2009: Stratospheric temperature and radiative forcing response to 11-year solar cycle changes in irradiance and ozone. J. Atmos. Sci., 66, 24022417, https://doi.org/10.1175/2009JAS2866.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grinsted, A., J. C. Moore, and S. Jevrejeva, 2004: Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes Geophys., 11, 561566, https://doi.org/10.5194/npg-11-561-2004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hasegawa, T., and K. Hanawa, 2003: Heat content variability related to ENSO events in the Pacific. J. Phys. Oceanogr., 33, 407421, https://doi.org/10.1175/1520-0485(2003)033<0407:HCVRTE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation