Lagged Responses of the Tropical Pacific to the 11-yr Solar Cycle Forcing and Possible Mechanisms

Solar irradiance is one of the main drivers of the earth’s climate. The total solar irradiance (TSI), with a mean value of 1360 ± 1 W m⁻², changes over the 11-yr solar cycle; its variance between the solar minimum and maximum is approximately 0.1% (Kopp and Lean, 2011). Although the globally averaged sea surface temperature (SST) response to this small solar irradiance variation is only 0.04 ± 0.01 K on decadal scales (White et al., 1997), more significant and detectable solar influences are found on regional scales (Kodera et al., 2016), especially in the tropical Pacific (Meehl et al., 2008, 2009; Meehl and Arblaster, 2009; Misios and Schmidt, 2012; Huo and Xiao, 2017a, b; Misios et al., 2019). The tropical Pacific variability significantly affects the global weather and climate from annual to interdecadal timescales. The El Niño Southern–Oscillation (ENSO) in this region has a direct association with extreme weather (Gershunov and Barnett, 1998; Ward et al., 2014), precipitation (Dai and Wigley, 2000), and climate anomalies across the world (Brönnimann, 2007; Zhou et al., 2014). The ENSO-like tropical Pacific decadal variability (Zhang et al., 1997) acts as part of the Interdecadal Pacific Oscillation (IPO) and is related to the global mean surface temperature change (Kosaka and Xie, 2013). Therefore, identifying the role of the solar cycle in this region will improve our understanding of the possible origins of tropical Pacific decadal variability and nature of solar influences on surface climate.

Previous observational studies have shown some SST responses in the tropical Pacific to solar cycle forcing but with inconsistent features. van Loon et al. (2007) found a La Niña-like SST anomaly pattern in the Northern Hemisphere (NH) winter during the solar maximum, which was followed by an El Niño-like pattern after 1 or 2 yr (Meehl and Arblaster, 2009). Tung and Zhou (2010) as well as Roy and Haigh (2010) found a weak warming response in the tropical Pacific to the solar irradiative heating during the solar maximum, which was “neither El Niño nor La Niña.” Huo and Xiao (2017b) found that the delayed warming response to the 11-yr solar cycle seems stronger in the central tropical Pacific than the eastern Pacific, resembling the El Niño Modoki pattern. There are several possible reasons for these discrepancies, such as the different solar maximum years defined by the sunspot number (SSN) and TSI (Roy and Haigh, 2010), or the solar maximum years coinciding with the ENSO cycle during a short period given that both the 11-yr solar cycle and the 2–7-yr ENSO phenomena are quasi-periodic (Haam and Tung, 2012; Roy and Haigh, 2012). However, this coincidence was ruled out when using the much longer Quinn El Niño index (1525–1987) and the SSN series back to 1750, which implies that the responses to the solar cycle and ENSO are independent phenomena (Haam and Tung, 2012).

Although reliable instrumental records are limited, sensitivity experiments based on state-of-the-art climate models can provide a possible way to investigate the influence of the 11-yr solar cycle in the tropical Pacific. White and Liu (2008) found that adding an 11-yr-period cosine signal of amplitude ~2.0 W m⁻² to the solar constant in the Fast Ocean–Atmosphere Model enabled the model to simulate both ENSO and a Pacific quasi-decadal oscillation (QDO), with the warm phase of the QDO lagging the peak solar forcing by ~1–3 yr, which was absent in the solar constant simulation. Using an ensemble of simulations with atmosphere–ocean coupled general circulation models, Misios and Schmidt (2012) also found that the tropical Pacific SST decadal oscillation is almost in-phase with the 11-yr solar cycle. Specifically, a basin-wide warming is simulated when the sun is more active, and the region of deep convection shifts eastward in the western Pacific. This weakened and eastwards displacement of the ascending branch of the Walker circulation during the solar maximum has been confirmed in recent publications (Xiao et al., 2016; Misios et al., 2019). However, in the Coupled Model Intercomparison Project Phase 5 (CMIP5) historical simulations, a lagged multimodel mean warming is found only in the west and central equatorial Pacific Ocean 1–2 yr after the solar maximum (Misios et al., 2016).

Therefore, the response of the tropical Pacific SST to solar cycle forcing is still uncertain. A warming response seems to appear in this region at the time of the solar maximum or in the following years, but with various features; for instance, warming in the western Pacific (La Niña-like), in the eastern Pacific (El Niño-like), or basin-wide. However, due to the strong “ENSO-like” internal variabilities (e.g., ENSO and IPO), the responses of the tropical Pacific to the 11-yr solar cycle forcing may be veiled by the internal modes, which is worthy of further investigation by separating it from the internal variability (e.g., ENSO and IPO) and other external forcings (e.g., greenhouse gases).

Given the possible mechanisms of the solar cycle’s influence on surface climate, together with an indirect “top-down” mechanism that involves a stratospheric response to the enhanced ultraviolet radiation and ozone production (Kodera and Kuroda, 2002), direct solar radiation forcing in the tropical Pacific as a “bottom-up” mechanism has been proposed. A higher energy input into the tropical cloud-free regions at the solar maximum leads to more evaporation in the subtropical Pacific and more moisture carried to convergence zones by the trade winds, resulting in the intensified precipitation and strengthened surface trade winds that then lead to a “La Niña-like” pattern in the eastern Pacific (Meehl et al., 2008). This “La Niña-like” pattern transforms into an “El Niño-like” pattern at a lag of 1–2 yr owing to the wind-forced oceanic Rossby waves in the equatorial Pacific (Meehl and Arblaster, 2009). However, the eastward shift of the central location of the deep convection in the western Pacific can be found in both the coupled and uncoupled simulations, which reduces the surface easterlies and drives the tropical Pacific response in the coupled system (Misios and Schmid, 2012). Cai and Tung (2012), based on an idealized experiment forced by a 2% increased solar constant in a simple general circulation model, proposed that the “evaporative” and convective feedbacks play a role in reducing the tropical surface warming response but favoring upper-tropospheric warming. Furthermore, a damped-resonant excitation of the tropical delayed action oscillator mechanism with the 11-yr solar cycle was proposed to explain the in-phase fluctuation of the QDO and solar cycle (White and Liu, 2008). In a recent study, Misios et al. (2019) proposed that a muted hydrological response to the 11-yr solar cycle and Bjerknes ocean–atmosphere feedback induces a relaxed east–west SST gradient and a weaker Pacific Walker circulation during the solar maximum. Although the above possible mechanisms depend to a certain extent on the response patterns, all of them imply that the initial solar signal in this region will be redistributed through the strong atmosphere–ocean coupling processes.

As most previous studies have found a warming response in some regions of the tropical Pacific [the western Pacific (Misios et al., 2016), eastern Pacific (Roy and Haigh, 2010), mid-to-eastern Pacific (Tung and Zhou, 2010), central Pacific (Huo and Xiao, 2017b), and the whole tropical Pacific (Misios and Schmid, 2012)], in this study, we further investigate the warm response of the tropical Pacific to the solar cycle forcing and possible mechanisms based on observational/reanalysis datasets as well as a subset of the CMIP5 historical-Nat simulations and pi-Control simulations. Due to the historical-Nat simulations including a full solar cycle forcing but excluding anthropogenic forcings, we selected those climate models from CMIP5 that can simulate the tropical Pacific warming response in the historical-Nat simulations and compared them with the solar fixed pi-Control simulations to investigate the role of the solar cycle forcing in this region. We try to identify the major contributor to the response patterns through a simple ocean mixed-layer heat budget diagnosis and discuss the possible mechanism. Figuring out the role of solar cycle forcing in the tropical Pacific air–sea system may provide a potential source of decadal-scale prediction skill.

The remainder of this paper is organized as follows. The observational/reanalysis data, model experiments, and methods used in this study are described in Section 2. Section 3 presents the solar signals and responses in the tropical Pacific from both observational/reanalysis data and the CMIP5 multimodel ensemble (MME) mean. The mixed-layer heat budget analysis and possible mechanisms are presented in Section 4. Further discussion and concluding remarks are provided in Section 5.

The observed SSN is often used to characterize the solar cycle forcing and can be obtained from the Sunspot Index and Long-term Solar Observations (SILSO) website of the World Data Center (WDC) at the Royal Observatory of Belgium, Brussels (http://www.sidc.be/silso/datafiles). The TSI in the CMIP5 historical-Nat simulations is prescribed by the reconstruction work of Wang et al. (2005) covering 1850 to 2008. As shown in Fig. 1, both of these two solar indices present the dominant 11-yr solar cycle, and their contemporaneous correlation coefficient is 0.94, meaning that these two indices should obtain consistent results for correlation or regression with the climate variables. However, when performing composite analysis based on the solar maximum and mini-mum, the discrepancy of the solar cycle peaks (or valleys) between the annual mean SSN (dotted gray line at the bottom of Fig. 1) and TSI (solid gray line in Fig. 1) could be a possible reason for inconsistency (Roy and Haigh, 2010). Since the TSI directly indicates the solar radiation arriving at the top of the earth’s atmosphere and is used as solar forcing data in CMIP5, we identified the central year of the broad solar maximum (minimum) in each cycle based on the 3-yr running mean TSI (solid black line in Fig. 1), which almost has common peaks (valleys) with the 3-yr running mean SSN (dotted black line). Each solar maximum (black dots in Fig. 1) and minimum (black circles) is defined by the central year and two surrounding years following the composite method in the work of Thiéblemont et al. (2015).

Figure 1.  The reconstructed TSI (solid gray line at top) used in the CMIP5 historical-Nat simulations and its 3-yr running mean (solid black line at top), as well as the observed annual mean SSN (dotted gray line at bottom) and 3-yr running mean SSN (dotted black line at bottom). The black dots (circles) indicate the solar maximum (minimum) years used for composite analysis in this study.

The ocean temperature data used in this study include the monthly SST of the NOAA Extended Reconstructed SST dataset v5 (1854–present) available at https://www.esrl.noaa.gov/psd/data/gridded/data.noaa.ersst.v5.html and the subsurface temperature of the Met Office Hadley Centre quality-controlled objective analysis dataset, EN.4.2.1, from 1900 to present (Good et al., 2013) obtained from http://www.metoffice.gov.uk/hadobs/en4/download.html. Besides, three-dimensional wind vectors from the NCEP/NCAR Reanalysis 1 dataset (https://www.esrl.noaa.gov/psd/data) covering the period 1948–2018 are also used in this study.

Outputs of the historical-Nat simulations and pi-Control simulations from seven CMIP5 models (see Table 1) are used in this study. A model was selected if it could simulate a similar lagged solar-associated SST pattern as the observation. We firstly regressed the TSI time series on to the observed SST anomaly and obtained the maximum regression map at a lag of 2 yr. Secondly, we performed the same regression analysis of the TSI and the ensemble mean SST anomaly for each model, and then calculated the pattern correlation between the regression maps of the observation and simulation for each model. We selected a model if its pattern correlation coefficient was positive and above the 95% confidence level (see Table 1). Here, the effective number of spatial degrees of freedom (ESDOF) of the tropical Pacific SST was calculated by the total number of the leading empirical orthogonal functions (EOFs) that explained 95% of the overall variance. More details on calculating the ESDOF can be found in Bretherton et al. (1999).

Here, four of the models (CanESM2, CSIRO-Mk3.6.0, FGOALS-g2, GFDL-ESM2M, and HadGEM2-ES) prescribe the ozone time series provided by Cionni et al. (2011), whereas GFDL-CM3 and MIROC-ESM-CHEN calculate the ozone changes interactively. Before analysis, all of the modeling data were gridded onto a 1.0° × 1.0° regular grid, and the MME mean was the averaged response of all models with the same weight applied to each model, regardless of its ensemble size. A common period of the seven models from 1861 to 2005 was analyzed for the historical-Nat simulations, and 255 modeling years were analyzed for the pi-Control simulations. For both the simulation and observational data, we calculated the annual mean from monthly data and defined an anomaly as the departure from the mean value over the whole period. The linear local trend in observational/reanalysis data was subtracted by the least-squares quadratic at every grid point before the analysis. Considering the data observationally reliable, all the observational/reanalysis variables in a common period from 1950 to 2018 were analyzed in this study.

We extracted the leading modes of the annual mean SST anomaly within the tropical Pacific region (30°S–30°N, 100°E–60°W) using an EOF analysis, and calculated the spectrum of the first principal component (PC1) in the CMIP5 historical-Nat and pi-Control simulations via Fast Fourier Transform to find the sensitivity of the leading mode to the solar cycle forcing. The confidence levels in the spectral analysis were indicated by the 90% and 95% confidence bounds of the Markov “red noise” spectrum. A lagged cross-correlation and consecutive lagged composite differences between the solar maximum and minimum were used to investigate the mean response patterns in the tropical Pacific to the 11-yr solar cycle forcing. The lagged composite difference was obtained by shifting all indices by a chosen lag year. It is worth noting that volcanic eruptions are also included in the historical-Nat simulations and observations, and some of the volcanic eruptions occurred just after the solar maximum and tropical volcanic eruptions can trigger El Niño by cooling tropical Africa (Khodri et al., 2017). To exclude the alignment of volcanic eruptions with periods of high solar activity, we removed the years of the five main eruptions in the study period (as shown in Table 2) and their following three years before the composite analysis.

A two-tailed Student’s t-test was used to test the null hypothesis that the two variables in the linear correlation (Pearson’s r) were independent. Effective degrees of freedom for the time series were calculated following the method used by Pyper and Peterman (1998):

where ${N_{\rm{e}}}$ represents the effective number of degrees of freedom and $N$ indicates the sample size of years in the time series; ${\rho _x}$ and ${\rho _y}$ represent the autocorrelation coefficients of each time series at a lag time of $j$ years.

A controlling false discovery rate (FDR) method was used to achieve the field significance through collecting and assessing every grid point hypothesis test result. More details of this method can be found in Wilks (2016). The significance level of composites was assessed by using the bootstrap method (Diaconis and Efron, 1983), whereby the mean difference between the composite data and all data was tested by repeating 1000 times with replacement.

A simplified ocean mixed-layer heat budget analysis was used to diagnose the “solar-induced” SST anomalies in the tropical Pacific and try to identify the contributors to the response patterns. Assuming that the ocean temperature in the mixed layer is always effectively mixed and the SST is equal to the mixed-layer mean temperature, as well as the excess heat from solar radiation can presumably be balanced there by the ocean heat transport effect and the surface heat exchange with the overlying atmosphere, we then integrated the ocean temperature equation from the surface to the bottom of the mixed layer. The SST equation related to the heat budget anomaly of the mixed layer can be expressed as:

where $T'$ is the SST change; $C = c_{p}^{\rm{o}}{\rho _{\rm{o}}}H$ is the heat capacity of the mixed layer; $c_{p}^{\rm{o}}$ and ${\rho _{\rm{o}}}$ are the specific heat at a constant pressure and density of seawater, respectively; H is the depth of the mixed layer; ${D_{\rm{o}}}$ represents the total ocean heat transport effect caused by diffusion and entrainment; and ${Q_{{\rm{net}}}}$ is the change in the net surface heat flux into the ocean (positive downwards for all of the heat flux hereafter).

Due to the SST change over decadal and longer timescales being one order of magnitude smaller than the surface heat flux and ocean heat transport (Xie et al., 2010; Schneider and Fan, 2012), Eq. (2) can be simplified to the first order, as shown in Eq. (3), wherein the total ocean heat transport effect can be balanced by the net surface heat flux:

In this study, we used this convenient diagnostic relationship to infer the total ocean heat transport effect without explicitly calculating all of the ocean transport terms.

The atmospheric heat fluxes ${Q_{\rm{a}}}$ include four physical components: the net shortwave radiation flux ${Q_{\rm{S}}}$ (solar radiation), the net longwave radiation flux ${Q_{\rm{L}}}$, the sensible heat net flux ${Q_{\rm{H}}}$, and the latent heat net flux ${Q_{\rm{E}}}$. Due to the existence of the wind–evaporation–SST adjustment, in studying SST variations, the effect of surface latent heat net flux ${Q_{\rm{E}}}$ should be treated as a mixture of atmospheric forcing ($Q_{\rm{E}}^{\rm{a}}$) and an ocean Newtonian cooling response ($Q_{\rm{E}}^{\rm{o}}$; de Szoeke et al., 2007; Du and Xie, 2008; Xie et al., 2010), as shown in Eq. (4),

in which the ocean Newtonian cooling represents the ocean’s ability to limit SST warming by evaporation, which can be calculated through the following equation:

Therefore, the changes in the net surface heat flux $ {Q}_{\rm{net}} $, including the radiative and turbulent fluxes should be written as:

According to Eq. (2), ${Q_{{\rm{net}}}}$ in Eq. (6) can be replaced by $ - {D_{\rm{o}}}$, and $Q_{\rm{E}}^{\rm{o}}$ replaced by the right-hand side of Eq. (5). Then, the SST changes $T'$ can be obtained from the following equation:

where $\overline {{Q}}_{\rm{E}} $ is the climatological latent heat flux, $\alpha = LR_{\rm{v}} ^{ - 1}{T^{ - 2}}$ is a coefficient, in which L is the latent heat of evaporation, ${R_{\rm{v}} }$ is the gas constant for water vapor, and T is the SST in degrees Kelvin. According to the Clausius–Clapeyron equation, $\alpha $ is about $ {0\rm{.}\rm{06 }\;K}^{-1} $, as defined by Xie et al. (2010).

Previous research has found a significantly positive anomaly of the ocean heat content in the central and eastern tropical Pacific that lags the solar cycle by 1–2 yr (Huo and Xiao, 2017a). A similar time lag is also evident here in the correlation coefficients between TSI and the observed SST anomaly (left-hand column of Fig. 2). When the SST anomaly lags TSI by 1 and 2 yr, significant positive correlation coefficients occur over the central equatorial Pacific and the northeastern Pacific along the west coast of North America, while negative correlation coefficients appear over the western Pacific. The lagged positive correlation maps of the historical-Nat MME SST and TSI show some different features (right-hand column of Fig. 2) in that the negative correlation in the western equatorial Pacific is absent and the positive correlation extends far into the western Pacific. Both correlation maps show a larger positive correlation over the central equatorial Pacific (above the 95% confidence level) than the eastern Pacific at lagged 0–1 yr, and the correlation in the eastern Pacific increases during the lagged years.

Figure 2.  (a–d) Lagged correlation maps between TSI and the observational annual SST anomaly (ERSST; only 1950–2018 is used here). (e–h) As in (a–d), but between TSI and the MME SST anomaly from CMIP5 historical-Nat simulations (1861–2005). The dotted (solid) lines indicate a negative (positive) correlation. Black dots indicate the 95% confidence level (two-tailed Student’s t-test and controlling FDR method).

To further check whether the solar signal does exist in the tropical Pacific or if it is just an alias of the ENSO signal, we extracted the leading mode of the MME SST anomaly over the tropical Pacific for both historical-Nat and pi-Control simulations, as shown in Fig. 3. The leading EOF mode (EOF1) of the historical-Nat MME SST is a basin-wide warming that explains about 46.4% of the total variance (Fig. 3a). The second mode is the residual ENSO-cycle mode left in the ensemble mean SST with 12.5% explained variance and a period of 3–7 yr (not shown here), while the ENSO-cycle mode exists in the EOF1 of the pi-Control MME SST with 35.2% explained variance (Fig. 3d). A common period of 11 yr shows in the spectra of TSI and PC1 of the historical-Nat MME SST, which is above the 90% confidence level and is absent in PC2 as well as the pi-Control simulation (Figs. 3c, f). The correlation coefficient between the TSI and PC1 of the historical-Nat MME SST is 0.32 at a lag of 2 yr, which is above the 99% confidence level (two-tailed Student’s t-test, N_e = 107, and the critical value is 0.246 for the 99% confidence level) and no significant correlation with PC2 (r = 0.12). The same correlation analysis was also applied to the TSI and pi-Control PC1 in the same 145-yr window as the historical-Nat, and no significant correlation could be found among the total 111 windows. As the solar cycle forcing is fixed in the pi-Control simulations and the MME SST is obtained from the same model-set as the historical-Nat, the above results suggest that the 11-yr solar cycle has a footprint in the EOF1 of the tropical Pacific SST when adding the solar cycle forcing to the climate system; plus, it is independent of the internally generated ENSO cycle and less aliased by the ENSO signal in the historical-Nat MME SST.

Figure 3.  (a) The spatial pattern of the EOF1 of the annual mean MME SST anomaly over the tropical Pacific region in the historical-Nat simulations, (b) the corresponding PC1, and (c) the spectrum of PC1 (black thick solid line). The black thin (dotted) lines represent the 90% (95%) confidence level of the Markov “red noise” spectrum, and the red lines are the same as the black ones but for the spectrum of TSI. (d–f) As in (a–c), but for the pi-Control simulations.

The observed annual mean SST anomalies (shaded contours) and wind anomalies (vectors) are shown in Fig. 4. The positive observational SST anomaly above the 90% confidence level firstly appears in the central equatorial Pacific at a lag of 0 yr (shaded contours in Fig. 4a), which intensifies and extends into the eastern Pacific at lagged 1–3 yr (shaded contours in Figs. 4b–d). Associated with the SST anomaly, a significant westerly wind anomaly firstly appears over the central Pacific around the dateline at a lag of 0 yr (vectors in Fig. 4a), and then increases in the western and central Pacific at lagged 1–3 yr (vectors in Figs. 4b–d).

Figure 4.  Composite differences of the annual mean SST anomaly (ERSST; shaded; only values above the 90% confidence level are shown) and wind anomaly at 850 hPa (NCEP/NCAR Reanalysis 1; vector) between the (a) solar maximum and minimum years and (b–d) lagged 3 yr for 1950–2018. Green vectors indicate that it is above the 90% confidence level for zonal wind (bootstrapping difference).

In the historical-Nat MME SST and wind anomalies (Fig. 5), the significant positive SST anomaly and westerly wind anomaly firstly appear in the off-equator and western equatorial Pacific at a lag of 0 yr (Fig. 5a) and extend into the eastern Pacific at lagged 1–3 yr (Figs. 5b–d). Compared to the composite observational SST and wind anomalies (Fig. 4), the historical-Nat simulated responses are approximately three times smaller than the observations, and the anomalous warming and westerly winds (at lag 0 yr) are located farther west. Possible reasons for these different features are that the observations include all the external forcings and inter-nal variability, especially the strong ENSO-like behavior during the latter half of the 20th century (1956–1997), which might superimpose on the responses to the solar cycle (Roy and Haigh, 2012). Besides, the “strong cold tongue” bias among CMIP5 models (Li and Xie, 2014) may be responsible for the western extension of the initial signals in the simulations. More discussion on the differences between model results and observations is provided later in the paper, in Section 5. Note that the SST response pattern in the solar maximum years (lag 0 yr; Figs. 4a, 5a) is a warming in the western and central Pacific rather than a “La Niña-like” or basin-wide warming, since there is no cooling in the eastern Pacific but a weaker warming below the 90% confidence level.

Figure 5.  As in Fig. 4, but for the annual mean MME SST anomaly (shaded and only values above the 90% confidence level are shown) and MME wind anomaly at 850 hPa (vector) from the CMIP5 historical-Nat simulations.

As revealed in previous work, an anomalous updraft appears over the central equatorial Pacific after the solar peak years in the reanalysis data [see Fig. 6 of Huo and Xiao (2017b)]. This can also be found in the CMIP5 historical-Nat simulations that an anomalous updraft appears over the western equatorial Pacific at a lag of 1 yr (Fig. 6b) and extends eastward at lagged 2–3 yr (Figs. 6c, d), and meanwhile an anomalous downdraft develops over the Maritime Continent and far eastern Pacific. These circulation anomalies are consistent with previous work in which the center position of deep convection was found to shift eastward at lagged 1–2 yr in observations (Misios et al., 2016; Xiao et al., 2016). Previous work has also demonstrated a slowdown in Pacific Walker circulation in the solar maximum years (Misios et al., 2019); however, this slowdown of the Walker circulation seems more significant in the following 1–3 yr after the solar maximum in our results.

Figure 6.  Composite differences of the annual mean MME vertical velocity anomaly averaged over the equatorial Pacific (5°S–5°N) in the CMIP5 historical-Nat simulations for (a) solar maximum minus minimum years and (b–d) lagged 3 yr. Black dots indicate the 95% confidence level (bootstrapping difference). Downward is positive (solid lines).

A statistically significant positive temperature anomaly appears in the upper-ocean layers of the central equatorial Pacific in observations (Fig. 7), which increases and migrates eastward along the thermocline (black line in Fig. 7) at lagged 1–3 yr, and meanwhile a negative anomaly develops in the subsurface of the western Pacific in the lagged years. These features are consistent with previous work by using another set of ocean reanalysis data (ECMWF ORAS4; Wang et al., 2019), and can also be found in the CMIP5 historical-Nat simulations, as shown in Fig. 8. The positive anomaly is confined above the main thermocline (thick black line in Fig. 8) and the negative anomaly appears in the subsurface of the western Pacific below the depth of 100 m and extends into the eastern Pacific along the thermocline at lagged 2–3 yr.

Figure 7.  As in Fig. 6, but for the annual mean subsurface temperature anomaly from the objective analyses EN4 dataset (1950–2018). Black dots indicate the 95% confidence level (bootstrapping difference) and the thick black line represents the 20°C-isotherm depth (m).

Figure 8.  As in Fig. 7, but for the annual mean MME subsurface temperature anomaly in CMIP5 historical-Nat simulations.

The ocean temperature anomalies suggest a reduced ocean dynamical transport of the surface warm water and a relaxed east–west thermocline tilt in the lagged 1–3 yr due to the weakening of the westward trade winds (Philander, 1981). This reduced ocean dynamical transport contributes to the warm water accumulation in the eastern Pacific upper layers, and meanwhile reduces the warm water in the western Pacific. As a result, the negative anomaly firstly appears in the western Pacific subsurface at a lag of 1 yr (Fig. 8b), and then replaces the positive anomaly in the subsurface layers of the central and eastern Pacific along the thermocline after the lag of 2 yr (Figs. 8c, d), which may work as a negative feedback to the maintenance of the positive anomaly in the eastern Pacific upper layers (above 150 m).

The warming response of ~0.13 K in the mixed layer in the historical-Nat MME is one order weaker than in the observations but consistent with previous work that found anomalous warming of ~0.14 K in the western equatorial Pacific in a subset of CMIP5 historical simulations (Misios et al., 2016). However, here, we analyzed the historical-Nat simulations rather than the historical simulations and included different models. More comparison with the work of Misios et al. (2016) can be found below in the discussion (Section 5). The differences between Figs. 7 and 8 suggest that the observations involve more dynamical processes into the thermocline to amplify the initial small solar signal than the historical-Nat simulations used in this study. More details about this are also discussed below in Section 5.

Although the simulated responses in the historical-Nat MME are weaker than in the observations, both the present similar lagged warming responses in the upper-ocean layers above the thermocline of the equatorial Pacific to the 11-yr solar cycle forcing, combined with anomalous westerly winds at the surface and anomalous updrafts shifting eastward during the lagged years. A good part of the historical-Nat MME is that the effect of greenhouse gases is excluded and there is less contamination of internally generated modes (e.g., ENSO-like mode) than in the observation after averaging the 27 ensemble members. Therefore, only the analyzed results based on the historical-Nat simulations are shown in the following heat budget diagnosis.

As shown above, the warming responses to the solar cycle forcing appear in the upper layers above the thermocline. We diagnosed the mixed-layer heat budget following the method described in Section 2.3 to identify the contributors to the SST anomaly patterns. Based on Eq. (6), the SST anomaly in the tropical Pacific arises from the effects of atmospheric forcing ${Q_{\rm{a}}}$, the ocean heat transport effect ${D_{\rm{o}}}$ including all advection and diffusion in the mixed layer, and the Newtonian cooling coefficient $\alpha \; {{{\bar Q}_{\rm{E}}}} $ that represents the ability of the ocean to limit SST increasing by evaporation. Consecutive lagged composite anomalies for the ocean and atmosphere terms in Eq. (6) along longitudes averaged over 10°S–10°N are shown in Fig. 9, and the four components of atmospheric forcing are shown in Fig. 10.

Figure 9.  Lagged composite solar maximum minus minimum differences for the (a) annual mean SST change and associated (b) atmospheric forcing (${Q_{\rm{a}}}$), and (c) ocean transport effect (${D_{\rm{o}}}$) of the histori-cal-Nat simulations, in which all variables are averaged over 10°S–10°N. Black dots in (a) indicate exceedance of the 95% confidence level (bootstrapping difference test).

Figure 10.  Lagged composite solar maximum minus minimum differences (W m⁻²) for the (a–d) surface net shortwave radiation (${Q_{\rm{S}}}$), (e–h) surface net longwave radiation (${Q_{\rm{L}}}$), (e–h) net sensible heat flux (${Q_{\rm{H}}}$), and (m–p) latent heat flux from atmospheric forcing ($Q_{\rm{E}}^{\rm{a}}$) after subtracting the ocean Newtonian cooling response. Downward is positive. Black dots indicate exceedance of the 95% confidence level (bootstrapping difference test).

The ocean heat transport effect (${D_{\rm{o}}}$; Fig. 9c) is responsible for the significant positive SST anomaly (Fig. 9a) over the western equatorial Pacific while the contribution of atmospheric forcing (${Q_{\rm{a}}}$; Fig. 9a) is negative, but the atmospheric forcing is positive over the eastern Pacific at lagged 0–1 yr. The climatological “cloud-free” condition allows more solar radiation to reach the surface in the solar maximum years (${Q_{\rm{S}}}$; Figs. 10a, b), and the surface warm water is transported into the western Pacific by the trade winds and accumulates in the subsurface (Figs. 8a, b). The positive SST anomaly in the central and eastern Pacific is partly contributed by the positive atmospheric forcing during lags of 0–2 yr, and taken over by the reduced ocean heat transport effect after the lag of 2 yr (${D_{\rm{o}}}$; positive in Fig. 9c). Even though the meridional variation in the mean latent heat flux ($\overline {{Q}}_{\rm{E}} $) is a strong pattern formation mechanism for SST (Xie et al., 2010), here we only diagnosed the heat budget averaged over 10°S–10°N, where the changes of the climatological latent heat flux during the lagged years can be ignored.

However, the radiative fluxes (${Q_{\rm{S}}}$ and ${Q_{\rm{L}}}$) of the atmospheric forcing are dominantly controlled by the cloud cover, and an intensification of precipitation in the convergence zones plays an important role in amplifying the initial small solar signal in the previous “bottom-up” mechanism (Meehl et al., 2008). To assess the atmospheric forcing in more detail, we decomposed it into four parts (as shown in Fig. 10): the net shortwave radiation flux ${Q_{\rm{S}}}$, net longwave radiation flux ${Q_{\rm{L}}}$, sensible heat net flux ${Q_{\rm{H}}}$, and latent heat net flux from the atmosphere $Q_{\rm{E}}^{\rm{a}}$ from which the ocean Newtonian cooling response $Q_{\rm{E}}^{\rm{o}}$ is subtracted. Positive shortwave radiation anomalies appear in the eastern Pacific (Figs. 10a, b) but decay during the lagged years (Figs. 10c, d), which suggests some responses of the cloud cover to the solar cycle forcing. As shown in Fig. 11, the total cloud fraction anomaly is positive over the western Pacific and negative over the eastern Pacific at a lag of 0 yr. This is consistent with previous work revealing that the greater energy input in the solar maximum years to the cloud-free region leads to anomalous subsidence over the equatorial eastern Pacific (also apparent from Fig. 6a), which produces fewer clouds there (Fig. 11a), and this allows even more solar radiation to reach the surface and produce the positive feedback to the cloud cover (Meehl et al., 2008).

Figure 11.  Lagged composite solar maximum minus minimum differences of the annual mean MME total cloud fraction anomaly in historical-Nat simulations (color shading). Black dots indicate exceedance of the 95% confidence level (bootstrapping difference test) and the white contours in (a) are the climatological total cloud fraction averaged over 1861–2005.

However, we found that this positive cloud fraction anomaly increases and shifts eastward (Figs. 11b–d) along with the eastward displacement of the anomalous updraft shown in Figs. 6b–d. This implies that the solar cycle forcing mainly influences the cloud cover through the anomalous updraft over the deep convection regions. Dima and Voiculescu (2016) identified that the solar influence on high-cloud cover has maximum amplitudes over the Pacific basin, that the warmer SST affects the high-cloud cover through deep convection, and that more high-cloud cover may in turn amplify the warming through the positive feedback of longwave fluxes. However, this positive feedback of the longwave flux does not show in Figs. 10e, h, in that the contribution of the longwave radiation (${Q_{\rm{L}}}$) to the anomalous SST pattern is approximately one order of magnitude less than the solar radiation (${Q_{\rm{S}}}$; Figs. 10a–d). The eastward displacement of the positive cloud fraction anomaly during the lagged years (Figs. 11b–d) leads to eastward movement of the negative shortwave anomaly in the equatorial Pacific (Figs. 10b–d) and hence a negative contribution of the atmospheric forcing to the warm SST anomaly during the lagged years (Fig. 9b). After subtracting the ocean Newtonian cooling effect, the net latent heat flux of atmospheric forcing makes a positive contribution to the warming response in the central subtropical Pacific and western equatorial Pacific at lagged 0–2 yr and decays in the lag of 3 yr (Figs. 10m–p). However, due to the ocean Newtonian cooling effect increasing along with the positive SST anomalies, the net contribution of the latent heat flux, including both the atmospheric and oceanic components (${Q_{\rm{E}}} = Q_{\rm{E}}^{\rm{a}} + Q_{\rm{E}}^{\rm{o}}$), is small in the subtropical Pacific and negative in the central and eastern Pacific during the lags of 1–3 yr (figure not shown here).

Based on the above analysis, we propose a possible mechanism to explain these lagged response patterns in the tropical Pacific to the solar cycle forcing (shown in Section 3.2). In the solar maximum years (at the lag of 0–1 yr), the influence of the solar cycle forcing is similar to the “bottom-up” mechanism (Meehl et al., 2008) in that the atmospheric forcing, especially the enhanced solar radiation (${Q_{\rm{S}}}$; Fig. 10a), warms up the eastern tropical Pacific in the “cloud-free” regions, and the warmer surface water is transported westward by the trade winds and sinks into the subsurface layers (Figs. 5a, 8a). Meanwhile, the downwelling over the eastern equatorial Pacific maintains the negative cloud cover anomalies (Fig. 6a). However, the trade wind anomaly over the eastern equatorial Pacific is not strong enough to lead to a La Niña-like response, and a westerly wind appears over the western and central equatorial Pacific because the local west–east temperature gradient is reduced by the anomalous warm water accumulation. This anomalous westerly wind weakens the surface warm water westward transport, and more warm water accumulates in the subsurface (Figs. 8a–c), providing the positive feedback to the westerly wind anomaly. Therefore, the anomalous westerly winds combined with the positive SST anomaly increase over the equatorial Pacific in the following years (Figs. 5c, d), and meanwhile the anomalous updraft over the western Pacific extends into the central Pacific (Figs. 6c, d). Due to the anomalous ascending motion that brings more water vapor into the upper troposphere, positive cloud fraction anomalies increase in these anomalous deep convection regions (Fig. 11), which reduce the surface net shortwave radiation (Figs. 10a–d). Therefore, the positive atmospheric forcing decays in the eastern equatorial Pacific during the lagged 2–4 yr (Fig. 9b) and the reduced wind-driven ocean dynamical transport effect is the major contributor to the eastward shifting of the positive SST anomalies after the lag of 2 yr (Figs. 9a, c).

The 11-yr solar cycle is an important external natural forcing for the earth’s climate system, the signals of which have been found in the tropical Pacific. This quasi-decadal external forcing may modulate the Pacific decadal variability and increase the potential predictability at decadal timescales, and thus the response of the tropical Pacific to solar cycle forcing has received considerable attention in recent years. However, the response pattern and mechanism are still under debate, because of the small solar irradiation forcing and the strong internal variability in this region.

In this study, the lagged warming responses of the tropical Pacific to 11-yr solar cycle forcing are investigated by using two subsets of CMIP5 historical-Nat simulations and the corresponding pi-Control simulations, as well as observational/reanalysis datasets. We selected seven models that can produce a similar lagged positive SST response in the tropical Pacific to the solar cycle forcing as the observations. By comparing the solar-related pattern with the internally generated ENSO-like mode of the pi-Control simulations, a robust 11-yr solar signal is found in the time series of the leading EOF mode (PC1) of the tropical Pacific SST of the historical-Nat MME, but is absent in the corresponding pi-Control MME with a fixed solar forcing. As PC1 is highly spatially filtered through EOF decomposition, to rule out this influence and check the solar signal in “raw SST data,” we calculated the spectrum of the SST anomaly averaged over the central equatorial Pacific (10°S–10°N, 160°E–150°W), where the largest SST response is found. A common solar period of 11 yr is found in both the historical-Nat MME SST and the observation (ERSST), while it is absent in the pi-Control MME (figures not shown). Therefore, the 11-yr solar signal in the tropical Pacific SST is independent of the internally generated ENSO cycle in the historical-Nat MME, albeit the patterns are similar to some extent. Initial warming responses firstly show in the central equatorial Pacific in observations and more in the western Pacific in the CMIP5 historical-Nat simulations, both of which are confined in the upper-ocean layers above the thermocline and extend into the eastern Pacific in lags of 1–3 yr. Combined with the ocean temperature anomaly, anomalous westerly winds appear over the equatorial Pacific, and an anomalous updraft arises over the western equatorial Pacific and shifts eastward during the lagged years in both observations and simulations.

Both the ocean temperature and wind responses of the historical-Nat MME are smaller than in the observations. Possible reasons for this difference are discussed as follows: First, contamination of the ENSO signal and the responses to other external forcings (e.g., greenhouse gases) is hard to rule out in the observational data, which may lead to a “fake” large response to the solar cycle forcing, while this contamination is largely reduced in the historical-Nat MME. Second, considering the data observationally reliable, we only analyzed the observational/reanalysis data from 1950 to 2018, which is a shorter period than the historical-Nat MME (1861–2005). We repeated the composite analysis of the historical-Nat MME SST as in Fig. 5 but based on the later period of 1950–2005, and found that the warming response is a little bit larger than for the whole period (1861–2005) but still weaker than the observed (figure not shown). Third, the “top-down” influence of the solar cycle forcing in observations involves the solar heating due to the solar ultraviolet radiation and ozone formation in the stratosphere, and the solar signal can propagate down to the surface through atmospheric dynamical processes (Kodera and Kuroda, 2002; Gray et al., 2006, 2009; Matthes et al., 2006; Frame and Gray, 2010), which might also modulate the atmosphere–ocean coupling at the surface. However, most of the models used in this study have poorly resolved stratospheres and 11-yr ozone variations, so may be unable to simulate the dynamical “top-down” propagation of the solar effect as in observations. The responses revealed in the historical-Nat simulations are likely attributable to the direct influence of the TSI changes.

The warming response with a magnitude of ~0.13 K in the western equatorial Pacific in the historical-Nat simulations is close to that of a previous study using the CMIP5 historical simulations (Misios et al., 2016). However, here, we analyzed the output of a subset of the historical-Nat simulations rather than the historical simulations to exclude the effect of anthropogenic forcings and compare with the solar fixed pi-Control simulations. Besides, we selected the seven models by a statistically significant positive pattern correlation with the observations and focused on the tropical Pacific. The work of Misios et al. (2016) included 16 models showing significant positive anomalies either over the globe or at the equator.

Based on a simple mixed-layer heat budget diagnosis of the historical-Nat MME SST, we found that the atmospheric forcing, especially the increase in net shortwave radiation (solar radiation flux), is the major contributor to the initial warming in the solar maximum years, and this warm response is amplified by the air–sea interaction during the lagged years. The ocean heat transport effect is responsible for the eastward displacement of the positive SST anomaly at lags of 2–3 yr. Meanwhile, anomalous cloud cover patterns provide the positive feedback in the solar maximum years to amplify the initial solar signal but a negative contribution during the lagged years. The cloud cover fraction anomalies associated with the anomalous updraft suggest a “bottom-up” influence of the solar cycle forcing on the tropical atmospheric circulations and complicated feedback of the cloud cover.

Acknowledgments. The authors thank all of the CMIP-5 modeling groups listed in Table 1 for allowing the use of their data. We acknowledge Prof. Katja Matthes and all the three reviewers for their very helpful suggestions and comments.