Editorial Type:
Article
Article Type:
Research Article

Precessional Forced Zonal Triple-Pole Anomalies in the Tropical Pacific Annual Cycle

Yue Wang State Key Laboratory of Marine Geology, Tongji University, Shanghai, China

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ZhiMin Jian State Key Laboratory of Marine Geology, Tongji University, Shanghai, China

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Ping Zhao State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China

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Kang Xu State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China

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Haowen Dang State Key Laboratory of Marine Geology, Tongji University, Shanghai, China

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ZhongFang Liu State Key Laboratory of Marine Geology, Tongji University, Shanghai, China

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Dong Xiao Chinese Academy of Meteorological Sciences, Beijing, China

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JunMing Chen Chinese Academy of Meteorological Sciences, Beijing, China

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Print Publication:
01 Nov 2019
DOI:
https://doi.org/10.1175/JCLI-D-18-0668.1
Page(s):
7369–7402
Open access

Abstract

Based on a transient simulation of the Community Earth System Model, we identified two anomalous “zonal triple-pole type” annual cycles in the equatorial Pacific sea surface temperature (SST), which were induced by precessional evolution of the summer-minus-winter insolation difference and the autumn-minus-spring insolation difference, respectively. For example, due to the increased summer–winter insolation contrast, a zonal positive–negative–positive pattern of equatorial SST anomalies was detected after subtracting basin-scale summer SST warming. The positive SST anomalies were associated with anomalous upward air flows over the western Pacific and eastern Pacific, whereas the negative SST anomalies in the central Pacific were coupled with anomalous downward air flows, oceanic upwelling, and thermocline cooling. These central Pacific anomalies were due to multiple air–sea interactions, particularly zonal advection feedback and Bjerknes feedback. This anomalous annual cycle also included winter equatorial air–sea coupled anomalies with similar spatial patterns but opposite signs. The annual mean equatorial rainfall was significantly increased west of 135°E but decreased between 135°E and 160°W in response to the moderately intensified Walker circulation west of 160°W. The autumn–spring insolation contrast induced similar seasonal reversed anomalies during autumn and spring, but the annual means were only weakly enhanced for the Walker circulation and the rainfall anomalies had smaller magnitudes east of 160°E. These distinct responses of the annual mean climate indicated different seasonal biases in terms of the equatorial SST and associated Walker circulation anomalies due to forcing by the two seasonal insolation contrasts, and these findings had meaningful implications for paleoceanographic studies.

Denotes content that is immediately available upon publication as open access.

© 2019 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: Yue Wang, 163wangyue@tongji.edu.cn

Abstract

Based on a transient simulation of the Community Earth System Model, we identified two anomalous “zonal triple-pole type” annual cycles in the equatorial Pacific sea surface temperature (SST), which were induced by precessional evolution of the summer-minus-winter insolation difference and the autumn-minus-spring insolation difference, respectively. For example, due to the increased summer–winter insolation contrast, a zonal positive–negative–positive pattern of equatorial SST anomalies was detected after subtracting basin-scale summer SST warming. The positive SST anomalies were associated with anomalous upward air flows over the western Pacific and eastern Pacific, whereas the negative SST anomalies in the central Pacific were coupled with anomalous downward air flows, oceanic upwelling, and thermocline cooling. These central Pacific anomalies were due to multiple air–sea interactions, particularly zonal advection feedback and Bjerknes feedback. This anomalous annual cycle also included winter equatorial air–sea coupled anomalies with similar spatial patterns but opposite signs. The annual mean equatorial rainfall was significantly increased west of 135°E but decreased between 135°E and 160°W in response to the moderately intensified Walker circulation west of 160°W. The autumn–spring insolation contrast induced similar seasonal reversed anomalies during autumn and spring, but the annual means were only weakly enhanced for the Walker circulation and the rainfall anomalies had smaller magnitudes east of 160°E. These distinct responses of the annual mean climate indicated different seasonal biases in terms of the equatorial SST and associated Walker circulation anomalies due to forcing by the two seasonal insolation contrasts, and these findings had meaningful implications for paleoceanographic studies.

Denotes content that is immediately available upon publication as open access.

© 2019 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: Yue Wang, 163wangyue@tongji.edu.cn
Keywords: Paleoclimate

1. Introduction

Precession (or ϖ) is one of Earth’s orbital parameters and it significantly modulates the annual solar radiation cycles at the top of the atmosphere (Berger 1978), where the difference in the time series of daily mean equatorial insolation between the two solstices (21 June minus 21 December) has the same magnitude as that between the two equinoxes (22 September minus 20 March), although with a phase shift of 90° at the precessional band (for details, see Fig. A1 in the appendix). These two orthogonal seasonal insolation contrast modes can fully describe the precessional-related modulation of the annual equatorial insolation cycle, and they are referred to as the solstice mode and equinox mode (Figs. 1a,b). Each mode is indispensable for fully understanding past climate changes, especially El Niño–Southern Oscillation (ENSO) variability, which is phase-locked to the annual cycle of the eastern equatorial Pacific (EEP) sea surface temperature (SST) (Qian et al. 2011).

Fig. 1.
Fig. 1.

(a) EOF1-PCs for the SSTavg (blue line) and SSTresidual (black line) in the tropical Pacific (30°S–30°N, 105°E–80°W) from the CESMtransient experiment are shown along with the time series of the solstice insolation mode (red line; W m−2). (b) As in (a), but for EOF2-PCs and the equinox insolation mode (purple line; W m−2). (c) The first two EOFs for the SSTavg (K). (d) Composite differences of the SSTavg (K) between experiments CESMslab_11ka and CESMslab_0ka (blue line), and between experiments CESM11ka and CESM0ka (red line). In (a) and (b), the contribution of each EOF-PC to the total variance is shown as a percent, and R denotes its correlation coefficient with the solstice or equinox insolation mode. Here the solstice or equinox insolation mode is defined as the time series of daily mean equatorial insolation difference between the two solstices (21 Jun minus 21 Dec) or equinoxes (22 Sep minus 20 Mar). Asymmetry in (d) is defined as the difference between absolute values of the minima and maxima for each time series.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

For example, paleoceanographic proxies indicate two different Holocene evolution patterns in terms of the interannual paleo-ENSO variability, where one pattern exhibits a minimum during the Early Holocene from 10 to 11 thousand years ago (10–11 ka; “ka” is used similarly hereafter) (Moy et al. 2002; Conroy et al. 2008; Driscoll et al. 2014) and the other has a minimum during the Mid-Holocene at 5–6 ka (Koutavas and Joanides 2012; Z. Zhang et al. 2014; Chen et al. 2016), corresponding to the latest maxima of the solstice and equinox modes, respectively. Timmermann et al. (2007) suggested that the precessional forced interannual ENSO variability was negatively correlated with the EEP SST annual cycle amplitude, as in the modern climate (An and Choi 2013). However, recent paleoclimate simulations determined a smaller amplitude for the EEP SST annual cycle during the Mid-Holocene or Early Holocene relative to 0 ka (Chiang et al. 2009; Ashkenazy et al. 2010; Braconnot et al. 2012; Luan et al. 2012; Salau et al. 2012; Erb et al. 2015; Lu et al. 2017). In addition, An and Choi (2014) argued that the weakened annual cycle over the EEP during the Mid-Holocene can still lead to intensification of the interannual ENSO variability, but the latter is dominated by the effects of air–sea interactions associated with a basinwide cooling of the tropical Pacific mean state (Clement et al. 1999, 2000; Liu et al. 2003).

Moreover, there are still many uncertainties regarding the background climate state due to the different appearances of the tropical Pacific annual cycle in paleoclimate modeling (Emile-Geay et al. 2016). The annual mean EEP SST follows the spring insolation in the Zebiak–Cane model with a fixed annual cycle (Clement et al. 1999, 2000), whereas it is in phase with winter insolation in the CCSM3 model with a variable annual cycle (Liu et al. 2014; Lu et al. 2017). However, little is known about the anomalous spatial patterns of the precession-modulated annual cycle across the entire equatorial Pacific, which may be essential for understanding why there seem to be more central Pacific (CP)–type [rather than eastern Pacific (EP)–type] interannual El Niño events under anomalous global warming backgrounds, such as the present or Mid-Holocene (Ashok et al. 2007; Kao and Yu 2009; Yeh et al. 2009; Karamperidou et al. 2015). In the present study, we analyzed the outputs from a fully coupled general circulation model under transient orbital insolation forcing since 300 ka (Wang et al. 2015) and identified two anomalous “zonal triple pole or central Pacific–type” annual patterns in the tropical Pacific SST, which are associated with solstice and equinox insolation changes at the precessional band. We then assessed the different contributions of multiple types of air–sea feedback to these two anomalous “zonal triple pole” SST annual cycle responses, particularly oceanic advection feedback and Bjerknes feedback in the central equatorial Pacific. Finally, we determined the different effects of the solstice insolation contrast and equinox insolation contrast on the anomalous annual mean states of the tropical Pacific climate.

2. Model, experiments, and data processing

We used the Community Earth System Model 1.0.4 (CESM) with resolution at T31_gx3 (Shields et al. 2012), which employs an atmospheric horizontal grid with nominal 3.75° and 26 vertical levels, and an oceanic horizontal grid with nominal 3° and 60 vertical levels. This coarse-resolution model can reproduce the modern variability in the tropical ENSO, including its two different spatial types (EP-type and CP-type), in a realistic manner due to its improved convection scheme (Shields et al. 2012; Vega-Westhoff and Sriver 2017). It was reasonable to select this model for our analysis because previous studies have demonstrated the successful application of coarse-resolution models of the paleoclimate, that is, paleo-ENSO changes under orbital forcing (Liu et al. 2014; Lu et al. 2017). After a spinup experiment for 200 model years under fixed orbital parameters at 300 ka (Berger 1978), CESM was further integrated for another 3000 model years under transient insolation forcing from 300 to 0 ka (experiment CESMtransient), where the orbital parameters were advanced by 100 calendar years at the end of each model year (acceleration factor = 100) (Wang et al. 2015). Except for insolation forcing, all of the other boundary conditions in CESM were kept at their modern values. The monthly mean outputs for the last 2500 model years in the CESMtransient experiment were analyzed after correcting the “calendar effect” (Chen et al. 2011).

According to Wang et al. (2015), the ocean temperature was averaged between 0 and 20 m as a four-dimensional SST dataset (model year, month, latitude, and longitude), where the 12 months for each model year were extracted and treated as a spatial dimension similar to longitude. To separate the zonal SST gradient variability from the basin-scale uniform SST changes, we first calculated the regional averaged SST (called SSTavg) over the tropical Pacific (30°S–30°N, 105°E–80°W), which comprised a two-dimensional dataset (y axis = month and x axis = model year) or 12 time series (each with a length of 2500 model years). A residual SST term (SSTresidual, with the same dimensions as SST) was then defined as the deviation of the SST from its regional means (SSTavg). After linear detrending and nine-point smoothing on the model year dimension, unrotated empirical orthogonal function (EOF) analysis was conducted based on the tropical Pacific SSTresidual and SSTavg to extract their principal components (EOF-PCs in 2500 model years). The associated EOF mode for each EOF-PC was determined as the regression coefficients against the standardized EOF-PC time series, which comprised a dataset with three dimensions (latitude, longitude, and months) for the SSTresidual or a one-dimensional dataset (months) for the SSTavg. The month dimension was treated as a spatial dimension similar to the longitude, so each EOF of the SSTavg was represented as a seasonal curve.

To elucidate the contributions of different types of air–sea coupled feedback to the SST anomalies, we conducted mixed layer heat budget analysis as described by Xu et al. (2017). The mixed layer temperature budget can be described by the following equation:
∂T′∂t=−u′∂T¯∂x−u¯ ∂T′∂x−u′∂T′∂x−υ′∂T¯∂y−υ¯ ∂T′∂y−υ′∂T′∂y−w′∂T¯∂z−w¯ ∂T′∂z−w′∂T′∂z+QnetρcpH+Qresidual,
where the bars and primes represent the climatological mean variables and the anomaly departure from the climatological mean, respectively. The variables T, u, υ, and w are the oceanic temperature, and the zonal, meridional, and vertical velocities averaged above the mixed layer depth H, respectively; H is defined as the shallowest depth where the local buoyancy gradient reaches its maximum and T above depth H is assumed to be “well mixed” and the same as the SST. Also, Qnet is the net downward heat flux at the sea surface, ρ is the seawater mean density, and cp is the heat capacity of seawater under constant pressure. The first nine budget terms on the right-hand side of the equation denote the oceanic heat advection in the zonal, meridional, and vertical directions (summed as QAdv), where −u′⁡(∂T¯/∂x)=QZA (referred to as the zonal advection feedback term), −υ′⁡(∂T¯/∂y)−υ¯⁡(∂T′/∂y)−υ′⁡(∂T′/∂y)=QTMA (or total meridional advection term), −w′⁡(∂T¯/∂z)=QBJ (wind–upwelling–SST feedback or Bjerknes feedback term), and −w¯⁡(∂T′/∂z)=QTH (thermocline–SST feedback term). The other three terms [−u¯⁡(∂T′/∂x), −u′(∂T′/∂x), and −w′(∂T′/∂z)] are small, and they were not considered in this study. In addition, Qnet/ρcpH = QTD is called the thermal damping feedback term, and Qresidual represents the residual heating term (or the difference between the terms ∂T′/∂t and QTD + QAdv).

Several meridional averaged variables were calculated along the equator between 5°S and 5°N, including the SSTeq, rainfalleq, mixed layer heat budget terms, ocean temperature Teq and currents (zonal and vertical velocities) above the 200-m depth, and atmospheric circulation (zonal wind u and vertical p velocity). Linear regression was performed against the standardized time series for each insolation mode on these equatorial variables, where the SSTeq and heat budget terms were three-dimensional datasets (model year, month, and longitude) whereas the others were four-dimensional datasets (model year, month, vertical level, and longitude). Statistical significance in this paper was assessed by the 95% confidence level by a t test unless stated otherwise.

To quantify the impact of the acceleration method, we also conducted four time slice experiments with the CESM under its default present-day configuration (or component set B_2000, including the initial files and boundary conditions) but with different precessional angles (ϖ = 102.89°, 282.89°, 180°, and 0° for 0, 11, 17, and 6 ka, respectively), which we designated as experiments CESM0ka, CESM11ka, CESM17ka, and CESM6ka. In general, these four experiments represented the latest minimum and maximum of the solstice insolation mode (Fig. 1a), and the latest minimum and maximum of the equinox insolation mode, respectively (Fig. 1b). However, they were not real simulations of 0, 11, 17, and 6 ka because the obliquity and eccentricity were still kept at their modern values (as shown in Fig. A2a) in order to isolate the effect of the precessional angle. The CESM model was run for 200 model years in each experiment and only the outputs for the last 100 model years were used to calculate the climatological mean values. In addition, another four time slice experiments were performed with the same configurations described above but the dynamical ocean component of the CESM was replaced by a mixed layer ocean or slab ocean component (CESMslab) in experiments CESMslab_0ka, CESMslab_11ka, CESMslab_17ka, and CESMslab_6ka. The CESMslab model was run for 100 model years in each experiment and only the last 50 model years were analyzed.

In these eight CESM slice experiments, the mixed layer ocean should have reached equilibrium after spinup for 100 or 50 model years because the time series of the global annual mean SST (Figs. A2b–e) exhibited no common climate drift (i.e., the slopes of their linear trends were smaller than 0.0008 K per model year), and their standard deviations were constrained within 0.05 K. Similar features were also found in the ocean temperature at water depths of 60–80 m (Figs. A2b–e). A deeper ocean requires more time to equilibrate but it was acceptable to conduct these slice experiments to test whether the upper ocean changes in the CESMtransient experiment were biased by the acceleration method. We calculated the monthly mean climatology during each time slice based on the outputs for the nearest 10 model years from the CESMtransient experiment (indicated by vertical gray bars in Fig. A2a), and the associated climatological differences between various time slices were compared with those obtained from the CESM slice experiments.

3. Results and discussion

a. Zonal triple-pole anomalies in the tropical Pacific SST annual cycle

According to their comparable contributions (51.3% and 41.6%) to the total variance, the first two EOF-PCs of the SSTavg both exhibited significant precessional fluctuations (blue lines in Figs. 1a and 1b) and they matched well with the time series for the solstice and equinox insolation modes. The correlation coefficient R between EOF1-PC and the solstice mode reached 0.95, and it was significant at the 99% confidence level with 22 degrees of freedom. Similarly, the value of R between EOF2-PC and the equinox mode reached 0.96. The first two EOF-PCs for the SSTresidual (black lines in Figs. 1a and 1b) made contributions of 44.5% and 28.9%, and they showed that the similar precessional fluctuations were nearly in phase with the EOF-PCs for the SSTavg. Therefore, at the precessional band, we indeed detected two orthogonal modes of the tropical Pacific SST annual cycles for the changes in the basin-scale uniform SST (SSTavg) and also in the zonal gradient (SSTresidual).

It should be noted that EOF1 for SSTavg (red line in Fig. 1c) was induced by the solstice insolation mode and it represented an anomalous annual cycle with warming of 0.4 K in August and cooling of −0.9 K in February. EOF2 for SSTavg (purple line in Fig. 1c) was induced by the equinox insolation mode and it exhibited more symmetric magnitudes, with warming of 0.7 K in November and cooling of −0.6 K in May. The solstice insolation mode was nearly symmetric in winter and summer (gray line in Fig. A1b), but it induced larger magnitudes for the tropical Pacific SST anomalies during boreal winter than boreal summer, which is consistent with previous studies (Lorenz et al. 2006; Laepple and Lohmann 2009). Laepple and Lohmann (2009) attributed this asymmetry to the higher nonlinearity of the ocean feedbacks, but our time slice simulations of 11 and 0 ka suggested another explanation. In response to the solstice insolation mode, the composite difference in the SSTavg between experiments CESMslab_11ka and CESMslab_0ka indicated a larger degree of asymmetry (0.40 K) compared with the composite difference (0.11 K) between experiments CESM11ka and CESM0ka (Fig. 1d). The SSTavg asymmetry was 0.09 or 0.03 K for the composite difference between experiments CESMslab_6ka and CESMslab_17ka or between experiments CESM6ka and CESM17ka, respectively. Thus, the feedback processes between the atmosphere and mixed layer ocean are essential for the seasonal asymmetry, and the subsurface oceanic feedback in the fully coupled CESM will suppress the asymmetry.

We then focused on the zonal inhomogeneity in the longitudinal–latitudinal distributions of the SSTresidual EOF1 and EOF2 (Fig. 2). In general, the SSTresidual EOF1 exhibited an anomalous zonal triple-pole pattern during February–April (FMA; Figs. 2a–c), which resembles the CP-type El Niño pattern (also called Modoki El Niño) in the modern climate (Ashok et al. 2007; Ashok and Yamagata 2009; Kao and Yu 2009; Yu et al. 2011). This CP El Niño pattern formed an anomalous annual cycle for the SSTresidual together with the CP La Niña pattern during July–September (JAS; Figs. 2d–f). In particular, positive SSTresidual anomalies occurred in the central equatorial Pacific between 160°E and 160°W, and negative SSTresidual anomalies in the western equatorial Pacific (WEP) and EEP (Figs. 2a–c). As shown in Figs. 2d–f, negative central Pacific anomalies were accompanied with positive anomalies in the WEP and EEP. Similar zonal triple-pole patterns (CP El Niño plus CP La Niña) were also identified based on the EOF2 for SSTresidual (Figs. 2g–l), although they were concentrated in different months (or shifted by 2–3 months relative to those for EOF1). For example, a positive–negative–positive pattern appeared during October–December (OND; Figs. 2j–l) and a negative–positive–negative pattern during April–June (AMJ; Figs. 2g–i).

Fig. 2.
Fig. 2.

(a)–(l) The regressed monthly spatial pattern of the tropical Pacific SSTresidual (K) against its standardized EOF1-PC and EOF2-PC from the CESMtransient experiment, in which white shaded areas are not significant at the 95% confidence level. Note that only those months with clear zonal triple-pole anomalies are shown.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

The positive or negative SSTresidual anomalies in the central equatorial Pacific at 180° were still significant in the SST EOF results, although with a smaller spatial scale (Fig. 3). This is because the basin-scale SST cooling or warming anomalies (i.e., red lines in Fig. 1c) were added to the SSTresidual anomalies (Figs. 2a–f) during FMA or JAS. A notable feature was that the negative SST anomalies during JAS in the EOF1 mode still occupied the central equatorial Pacific between 160°E and 160°W (Figs. 3d–f). This also reflected the asymmetric SST response to the solstice insolation mode, and it differed from the SST EOF2 response (Figs. 3g–l) to the equinox insolation mode. For example, the negative central equatorial Pacific anomalies in the SST EOF2 occupied only a small region near 180° (Figs. 3j–l), and they were seasonally symmetric with respect to the positive central Pacific SST anomalies shown in Figs. 3g–i. In Figs. 2 and 3, only the seasons dominated by the zonal triple-pole pattern are illustrated for clarity, whereas other transitional seasons are omitted to avoid redundancy (the full versions are shown in Figs. A3–A6). These findings were independent of the acceleration method used in the CESMtransient experiment because the zonal triple-pole patterns for SSTresidual EOFs illustrated in Fig. 2 (or the SST EOFs in Fig. 3) were generally captured by the climatological differences between the time slices for 11 and 0 ka shown in Fig. A7 (or Fig. A8) and between the time slices for 6 and 17 ka in Fig. A9 (or Fig. A10). Because of the differences in the obliquity and eccentricity configurations (Fig. A2a), the two versions of the climatological differences in Figs. A7–A10 (first columns vs second columns) exhibited moderate discrepancies (illustrated in the third columns in Figs. A7–A10), but they were outside the scope of this study.

Fig. 3.
Fig. 3.

(a)–(l) The regressed monthly spatial pattern of the tropical Pacific SST (K) against its standardized EOF1-PC and EOF2-PC from the CESMtransient experiment, in which white shaded areas are not significant at the 95% confidence level. Potential source areas of the equatorial subsurface cooling or warming anomalies are marked by the yellow contours of −0.6 K in (c) or the yellow contours of 0.6 K in (e).

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Overall, precession induced two anomalous zonal triple-pole annual cycles in the tropical Pacific SST, which significantly modulated the climatological equatorial SST (SSTeq) seasonality (Fig. 4a), that is, the semiannual cycle in the WEP and the annual cycle in the EEP (An and Choi 2013). The regression coefficients for the SSTeq against the standardized solstice and equinox insolation modes (Figs. 4b,c) exhibited similar zonal triple-pole patterns after applying a shift of 3 months to the equinox-induced SSTeq anomalies. The solstice insolation mode itself also shifted by 3 months relative to the equinox insolation mode (black lines in Figs. 4b and 4c), thereby indicating that there was a common and robust zonal triple-pole response of the equatorial SST to either of these two precessional insolation modes. This feature was also confirmed by the climatological differences between the time slices of 11 and 0 ka (or 6 and 17 ka) (Fig. A11). Similar zonal triple-pole patterns with comparable magnitudes were reproduced by both the CESMtransient experiment (Figs. A11a,e) and CESM slice experiments (Figs. A11b,f). The relatively larger SSTeq discrepancies east of 150°W (shaded contours in Figs. A11c and A11g) were a secondary influence and they can be attributed to the insolation discrepancies induced by the obliquity and eccentricity between the CESMtransient experiment and CESM slice experiments (black lines in Figs. A11c and A11g).

Fig. 4.
Fig. 4.

(a) The longitude–month profile of the climatological annual cycle of the SSTeq (with annual means removed; K) along the latitudes 5°S–5°N from the CESMtransient experiment. (b),(c) As in (a), but for the regression coefficients (K) against the standardized time series of the solstice and equinox insolation modes respectively. Black lines in (b) and (c) show the regression coefficients of the equatorial insolation (W m−2) against the standardized time series of the solstice and equinox insolation modes, respectively.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

The two anomalous SSTeq annual cycles at the precession band can provide a better explanation of the anomalous annual cycles for the EEP SST in previous time slice simulations of the Holocene (Ashkenazy et al. 2010; Luan et al. 2012; Salau et al. 2012; An and Choi 2014; Erb et al. 2015). For example, compared with the situation at 0 ka (Fig. 4a), the weakened EEP SST annual cycle in the Early Holocene can be fully attributed to the solstice-induced SSTeq anomalies during JAS and FMA (Fig. 4b), whereas the weakened EEP SST annual cycle in the Mid-Holocene was affected jointly by the solstice-induced SSTeq anomalies and the equinox-induced SSTeq anomalies (Fig. 4c). However, when we treated the climatological annual cycle at 17 ka as a reference, the EEP SSTeq annual cycle in the Mid-Holocene was fully damped by the equinox-induced anomalies, and the effects of the solstice-induced anomalies could be neglected. Therefore, we obtained a simpler explanation by selecting a different reference time.

b. Mechanism responsible for zonal triple-pole anomalies in the equatorial SST seasonality

Previous simulation studies (Luan et al. 2012; Erb et al. 2015) suggested that although the WEP SST warming responds in a linear manner to increases in local insolation with a time lag of two months, the EEP SST warming leads the WEP due to the eastward propagation of positive subsurface water temperature anomalies along the thermocline. This was confirmed by our simulation, which showed that positive EEP SSTeq anomalies occurred two months before positive WEP anomalies (Figs. 4b,c) and they were nearly synchronous with the local insolation (black lines in Figs. 4b and 4c). The regression coefficients for the equatorial upper ocean temperature Teq above a depth of 200 m (Fig. 5) against the standardized solstice insolation mode also showed that the positive anomalies at 150°E between depths of 60 and 150 m in July (Fig. 5g) propagated eastward during the following 10 months, thereby explaining the positive EEP SST anomalies in May (Fig. 5e). Similarly, the negative subsurface Teq anomalies at 150°W also propagated eastward during the next 4 months and contributed to the negative EEP SST anomalies during November (Fig. 5k) through thermocline feedback and zonal advection feedback (see the heat budget analysis results in the following). Therefore, the earlier warming or cooling of the EEP SST relative to the WEP SST can actually be traced back to the subsurface ocean dynamics. The eastward advections of Teq anomalies in the subsurface ocean have been attributed to a Kelvin wave excited by westerly wind anomalies in the WEP (Luan et al. 2012; Erb et al. 2015; Karamperidou et al. 2015).

Fig. 5.
Fig. 5.

(a)–(l) The longitude–depth cross sections of the regressed monthly ocean temperature Teq (shaded; K) and currents (vectors; horizontal velocity: cm s−1; vertical velocity: 3.33 × 10−5 cm s−1) along the latitudes 5°S–5°N against the standardized time series of the solstice insolation mode from the CESMtransient experiment. White shaded areas are not significant at the 95% confidence level for the ocean temperature.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Similar zonal advection of the thermocline Teq anomalies was determined for the equinox-induced Teq anomalies (Fig. 6), where all of the eastward propagations of the positive anomalies at 150°E and negative anomalies at 150°W occurred after October. Before the appearance of these eastward propagations, the equinox insolation mode induced negative anomalies at 150°E during JAS (Figs. 6g–i), whereas the solstice insolation mode induced negative anomalies at 130°E during AMJ (Figs. 5d–f). This difference will be investigated in our future research because the present study focused on the common mechanism responsible for anomalous SSTeq annual cycles. The detailed mechanisms responsible for the subsurface Teq anomalies are discussed in the following.

Fig. 6.
Fig. 6.

(a)–(l) The longitude–depth cross sections of the regressed monthly ocean temperature Teq (shaded; K) and currents (vectors; horizontal velocity: cm s−1; vertical velocity: 3.33 × 10−5 cm s−1) along the latitudes 5°S–5°N against the standardized time series of the equinox insolation mode from the CESMtransient experiment. White shaded areas are not significant at the 95% confidence level for the ocean temperature.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

In both the solstice and equinox situations, negative SSTeq anomalies appeared at 180° two months before the negative EEP SST anomalies (Figs. 4b,c), and they were related to the subsurface Teq anomalies at 150°W (especially for JAS in Figs. 5g–i). This feature has not been detected in previous simulations, which suggests that the central Pacific may be a key region for zonal triple-pole SST annual cycle anomalies (Fig. 2), as also confirmed by comparing the climatological Teq differences between the time slices of 11 and 0 ka shown in Fig. A12 (or between 6 and 17 ka in Fig. A13). In the central Pacific, anomalously enhanced oceanic upwelling prevailed from June to October (Figs. 5f–j), which favored the expansion of negative thermocline Teq anomalies to the surface. If no subsurface ocean changes occurred, there would have been no SSTeq cooling anomalies according to the climatological SSTeq differences in the CESM slice experiments with slab ocean (Figs. A11d,h). By contrast, precursory positive SSTeq anomalies appeared in the central Pacific during FMA (Fig. 4b), which were associated with oceanic downwelling and subsurface Teq warming (Figs. 5b–d). The central Pacific changes indicated major roles for local air–sea feedbacks (Bjerknes feedback, thermocline-SST feedback, and zonal advection feedback), which have been used to explain different types of ENSO (CP-type and EP-type) in modern and paleoclimate simulations (Kao and Yu 2009; Yu et al. 2011; Capotondi 2013; Liu et al. 2014; Karamperidou et al. 2015).

The relative contributions of different types of air–sea feedbacks were resolved by comparing the regression coefficients for multiple mixed layer heat budget terms (Fig. 7). Under the solstice insolation forcing, the zonal triple-pole SSTeq anomalies (Fig. 4b) were explained well by the anomalous zonal triple pattern of the mixed layer temperature tendency 3 months before (Fig. 7a), which shared many similarities with the sum of the thermal damping feedback and oceanic heat advections east of 140°E (shown by the budget term QTD+Adv, Fig. 7b). In the central Pacific, the Qresidual term exhibited much smaller magnitudes between 160°E and 160°W (Fig. 7c), which indicates that the temperature tendencies reflected the balance between the QTD term (Fig. 7d) and the four main oceanic advection terms (Figs. 7e–h). The central Pacific heating anomalies were large in the QZA term, moderate in the QBJ term, and small in the QTH term, thereby highlighting the relative importance of zonal advection feedback, Bjerknes feedback, and thermocline–SST feedback, respectively. The Qresidual term had larger values in the regions west of 160°E and east of 160°W, which reflected the effects of nonlinear processes not included in the heat budget calculations (e.g., mixing, diffusion, parameterized eddies, and submonthly scale currents). Apart from the Qresidual term, most of the temperature tendency anomalies west of 160°E (Fig. 7a) could be explained by the QTD term, QZA term, and QTMA term (Figs. 7d,e,h), whereas the temperature tendency anomalies east of 160°W were attributed to the QTH term and QBJ term. These air–sea feedbacks were consistent with the heat budget results obtained from the CESM slice experiments (Fig. A14). Similar mechanisms can apply to the equinox-induced SSTeq anomalies (Fig. A15).

Fig. 7.
Fig. 7.

Results of the mixed layer heat budget analysis are shown as the regression coefficients (K month−1) against the standardized time series of the solstice insolation mode from the CESMtransient experiment. (a) Longitude–month profile of the mixed layer temperature tendency along the latitudes 5°S–5°N. The remaining panels are as in (a), but for the (b) QTD+Adv, (c) Qresidual, (d) QTD, (e) QZA, (f) QBJ, (g) QTH, and (h) QTMA terms.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

It should be noted that the meridional oceanic heat advection (or the QTMA term) also exhibited large anomalies west of 150°E and moderate anomalies in regions east of 130°W (Fig. 7h), which greatly compensated for the QZA and QBJ anomalies in the western and eastern Pacific, respectively (Figs. 7e,f). The QTMA anomalies were mainly attributed to the −υ′⁡(∂T¯/∂y) term (not shown), and they represented the negative feedback associated with off-equatorial regions. Previous studies indicated the effects of solstice-induced subtropical responses, namely anomalous anticyclones in the South Pacific changing the local SST seasonality (yellow contours in Figs. 3c and 3e) (Liu et al. 2003; Erb et al. 2015; Lu et al. 2017), where the latter then propagate toward the equator via the wind–evaporation–SST feedback in the South Pacific meridional mode (H. Zhang et al. 2014). In addition, the extratropical North Pacific changes during boreal winter–spring (Chiang et al. 2009; Wang et al. 2014) lead to a “seasonal footprint” in the subtropical eastern Pacific SST (shown by the yellow contours in Fig. 3c), which expand westward via a Rossby wave (Yeh et al. 2014). Moreover, off-equatorial processes can also cause significant subsurface ocean temperature anomalies in the equatorial Pacific via local late-winter subduction of surface water anomalies from the subtropics in both hemispheres (Liu et al. 2003, 2014; Anderson et al. 2013).

To illustrate the interactions between the equatorial and off-equatorial regions, Fig. 8 shows the EOF1 for the subsurface water temperature at depths of 60–80 m, which contributed 57.8% of the total variance. It should be noted that this water depth was selected based on Fig. 5 in order to capture the eastward and upward movements of thermocline anomalies from a depth of 150 m to the EEP surface. In this EOF1, the solstice insolation mode induced perennial subsurface cooling in the equatorial Pacific between 110° and 135°E (Fig. 8), which came mainly from the subtropical northwest anomalies between January and June (shown by the yellow areas in Figs. 8a–g). The equatorial cooling anomalies east of 180° during JAS were contributed by cooling anomalies from the subtropical northeast Pacific (shown by the yellow areas in Figs. 8g–i). The equatorial warming anomalies between 135°E and 180° were mainly attributed to the northwestward propagation of southwest Pacific warming anomalies from July to November (shown by the yellow contours in Figs. 8g–k). The subtropical surface source areas associated with the thermocline cooling or warming anomalies are shown by the yellow lines in Fig. 3c or Fig. 3e. The intensification of the positive subsurface temperature anomalies at the equator (Figs. 8f–i and 5f–i) was a source of the positive QZA anomalies from June to September around 145°E (Fig. 7e), which required negative QTMA anomalies (Fig. 7h) to balance them. In addition, from January to April, the negative subsurface temperature anomalies (Figs. 8a–d and 5a–d) were related to the negative QZA anomalies (Fig. 7e) and positive QTMA anomalies (Fig. 7h) around 145°E.

Fig. 8.
Fig. 8.

(a)–(l) EOF1 for the monthly subsurface ocean temperature at depths of 60–80 m (K) from the CESMtransient experiment, in which white shaded areas are not significant at the 95% confidence level. The white rectangular box in each panel marks the latitudes 5°S–5°N. Yellow shaded areas (with values between −0.6 and −0.8 K) in (a)–(i) indicate the movement of cooling anomalies from the northwest Pacific and northeast Pacific, whereas yellow contours of 0.6 K in (g)–(l) indicate the propagation of warming anomalies from the southwest Pacific.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

EOF1 for the subsurface temperature not only featured eastward propagation of warming anomalies along the equator (Figs. 8a–e), but also exhibited westward propagation of warming anomalies along 10°N and 10°S (Figs. 8f–h). From July to September, the off-equatorial warming anomalies moved toward the equator and further enhanced the Teq warming anomalies between 150°E and 180° (Figs. 8g–i). The EOF1 for the sea surface height (Fig. 9) can be used to indicate the effect of oceanic Rossby or Kelvin waves (Wu et al. 2000). In association with the subsurface warming anomalies shown in Fig. 8, positive height anomalies occurred along the equator east of 160°E, where their magnitudes increased from January to May (Figs. 9a–e), thereby indicating the eastward movement of a Kelvin wave. From June to September, off-equatorial (westward) Rossby waves were also identified based on the positive height anomalies in the North Pacific between 5° and 10°N, and in the South Pacific between 5° and 15°S (Figs. 9f–i). In association with the subsurface Teq cooling anomalies shown in Figs. 8f–h, negative height anomalies occurred where their centers moved from 150°E to 150°W along the equator (Figs. 9f–h), thereby indicating an eastward Kelvin wave from the WEP.

Fig. 9.
Fig. 9.

(a)–(l) EOF1 for the monthly sea surface height (cm) from the CESMtransient experiment, in which white shaded areas are not significant at the 95% confidence level. This EOF1 contributes 57.7% to the total variance, whereas the EOF2 (not shown) only contributes 17.4%. The white rectangular box in each panel marks the latitudes 5°S–5°N.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

As an improvement compared with previous studies that focused only Kelvin waves (Luan et al. 2012; Erb et al. 2015; Karamperidou et al. 2015), our results suggested that bidirectional advections of the subsurface temperature anomalies were associated with a westward off-equatorial Rossby wave and eastward equatorial Kelvin wave. These two types of advection are important for the solstice-induced zonal triple-pole SST mode at the precessional band. It should be noted that thermocline adjustment and the associated equatorial oceanic waves have relatively short time scales, which range from several months (Cane and Sarachik 1981; McCreary and Anderson 1984; An 2005) to 2–5 years (Wu et al. 2000), but the longest time scale is only 10–15 years for basin-scale waves transmitted from middle or high latitudes to the equator (Liu 2002). After multiplying by an acceleration factor of 100, the actual thermocline response time was determined as several hundred years or 1000–1500 years, which is much shorter than the time scale for external insolation forcing (23 000 years). Therefore, it is reasonable to treat the subsurface water anomalies in our CESMtransient experiment as quasi-equilibrium responses at the precessional band. After comparing the climatological differences between the time slices of 11 and 0 ka (Fig. A16), we consider that the bidirectional advections of the subsurface temperature anomalies were not qualitatively affected by the acceleration method.

c. Distinct effects of two anomalous annual cycles on annual mean state

In the modern climate, CP-type or Modoki-type El Niño events always occur with atmospheric ascendant anomalies over the central equatorial Pacific and downward air flows over the WEP and EEP, which form an anticlockwise zonal–vertical circulation west of 180° (weakened Walker circulation) and a clockwise circulation east of 180° (enhanced Walker circulation) (Ashok et al. 2007; Ashok and Yamagata 2009). It should be noted that all of the atmospheric circulations considered in this study were viewed from south to north unless stated otherwise. We also analyzed the changes in the atmospheric Walker circulation associated with two anomalous zonal triple-pole SST annual cycles, and assessed their relative importance for the changes in the annual mean climate at the precessional band.

Based on the regression coefficients for the zonal wind and vertical p velocity against the standardized time series for the solstice insolation mode, we identified a clockwise zonal–vertical circulation over the western-central equatorial Pacific and anomalous upward motions over the EEP during JAS, as shown in Fig. 10a, which indicated stronger western and weaker eastern Walker circulation anomalies. Similar Walker circulation anomalies appeared during FMA but with opposite signs (Fig. 10b). These seasonal reversed atmospheric circulation anomalies matched well with the CP La Niña and CP El Niño patterns of the SSTresidual anomalies along the equator (Figs. 10d,e), where the positive SSTresidual anomalies over the equatorial Pacific corresponded to anomalous upward motions in the troposphere and vice versa. According to the annual means, both SSTresidual and SST featured negative anomalies (with an average of −0.2 K) along the equator (Figs. 10f,i), and the moderately enhanced clockwise zonal–vertical circulation west of 160°W (Fig. 10c) was dominated by changes in JAS (Fig. 10a).

Fig. 10.
Fig. 10.

Regression coefficients for (top) atmospheric circulation, (middle) SSTresidual, and (bottom) SST from the CESMtransient experiment against the standardized time series of the solstice insolation mode: (a) the longitude–height map of JAS mean vertical p velocity (shaded; 0.005 Pa s−1) and zonal–vertical circulation (vectors; u: m s−1; vertical p velocity: 0.005 Pa s−1) along the latitudes 5°S–5°N; (b),(c) as in (a), but for FMA and annual means; (d)–(f) JAS, FMA, and annual mean SSTresidual; and (g)–(i) JAS, FMA, and annual mean SST. White areas in (a)–(c), (d)–(f), and (g)–(i) are not significant at the 95% confidence level for vertical p velocity, SSTresidual, and SST, respectively.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Due to induction by the equinox insolation mode, stronger western and weaker eastern Walker circulation anomalies prevailed over the equatorial Pacific during OND (Fig. 11a), which coupled with the zonal positive–negative–positive anomalies in the equatorial SSTresidual (Fig. 11d) under the basin-scale SST warming background (Fig. 11g). The AMJ anomalies (Figs. 11b,e,h) had opposite signs and symmetric magnitudes relative to the OND anomalies (Figs. 11a,d,g). These seasonal anomalies canceled each other out, so the annual mean state only comprised a weak clockwise zonal–vertical circulation east of 160°E (Fig. 11c) and a slight SST warming with an average of 0.1 K along the equator (Fig. 11i). Therefore, in contrast to the solstice mode, the equinox mode had less influence on the changes in the annual mean climate over the equatorial Pacific.

Fig. 11.
Fig. 11.

As in Fig. 10, but for the (left) OND, (center) AMJ, and (right) annual mean distributions of (a)–(c) the regressed equatorial Pacific atmospheric circulation, (d)–(f) the tropical Pacific SSTresidual, and (g)–(i) SST against the standardized time series of the equinox insolation mode.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Previous paleoceanographic studies always assumed that a warmer SST is accompanied by upward air flows, enhanced convective activities, and more rainfall in the tropical Pacific. By contrast, our simulation determined a mismatch between the annual mean SST and rainfall (Fig. 12a). The solstice insolation mode induced positive rainfall anomalies of 0.83 mm day−1 west of 135°E and negative anomalies of −0.38 mm day−1 between 135°E and 165°W, but few changes east of 160°W (solid red line in Fig. 12a), which is difficult to explain based on the general SST cooling pattern (dashed red line in Fig. 12a). The equinox-induced SST warming (dashed purple line in Fig. 12a) did not explain the positive rainfall anomalies (0.15 mm day−1) between 170°E and 160°W or the negative rainfall anomalies (−0.24 mm day−1) east of 160°W (solid purple line in Fig. 12a). These results highlighted the seasonal bias in the annual mean climate in the equatorial Pacific under precessional insolation forcing. For example, the solstice-induced annual mean rainfall seesaw west of 160°W was largely biased toward rainfall changes from July to November (Fig. 12b), and the equinox-induced annual mean drier conditions east of 160°W were biased toward negative anomalies from January to May (Fig. 12c). The seasonal rainfall biases were different from those in the SSTeq but similar to those in the atmospheric Walker circulation (Figs. 10a–c and 11a–c), so we suggest that the changes in equatorial rainfall were linked more strongly to the anomalous vertical motions of the Walker circulation.

Fig. 12.
Fig. 12.

(a) Regression coefficients for annual mean SSTeq (dashed lines; K) and rainfalleq (solid lines; mm day−1) against the standardized time series of two insolation modes (red color for the solstice mode and purple color for the equinox mode). (b),(c) Regression coefficients of monthly mean rainfalleq (mm day−1) against the standardized time series of the solstice and equinox insolation modes, respectively. Note that the month axis in (c) is shifted by two months for better comparison with (b).

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

4. Conclusions and final remarks

Given that the difference in equatorial insolation between summer and winter solstices is orthogonal to that between autumn and spring equinoxes at the precessional band, in the present study we aimed to clarify the effects of modulation of these seasonal insolation changes on the seasonality and annual mean state of the tropical Pacific based on a transient simulation of the CESM. Our main conclusions can be summarized as follows.

  1. We identified two anomalous orthogonal modes of the tropical Pacific SST annual cycle, which are induced by the contrasts in solstice and equinox insolation at the precessional band. The solstice-induced response is seasonal asymmetric with basin-scale cooling anomalies during February–April, which have larger magnitudes than the warming anomalies during July–September. The equinox-induced response is nearly seasonal symmetric with basin-scale SST warming anomalies during October–December and cooling anomalies during April–June. The two anomalous SST annual cycles along the equator were determined as highly similar after we applied a shift of 3 months to the equinox-induced anomalies, and they both exhibited an anomalous zonal triple-pole spatial pattern, which included a CP La Niña stage with basin-scale SST warming and a CP El Niño stage with basin-scale SST cooling.

  2. For the CP La Niña stage of each anomalous annual cycle, negative central Pacific SST anomalies always occurred after anomalously enhanced thermocline water cooling and upwelling around 150°W, and the associated atmospheric zonal–vertical circulation anomalies along the equator were characterized by a clockwise cell west of 180° and an anticlockwise cell east of 180°. During the CP El Niño stage, similar atmospheric Walker circulation anomalies and subsurface ocean anomalies appear in the equatorial Pacific but with opposite signs. The annual mean climate along the equatorial Pacific featured an anomalous clockwise atmospheric circulation west of 160°W and a general SST cooling pattern due to the solstice insolation forcing, but it exhibited a weak clockwise zonal–vertical circulation east of 160°E and a slight SST warming pattern due to the equinox insolation forcing.

  3. The zonal triple-pole spatial patterns of the equatorial SST anomalies were due to the balance of multiple types of air–sea feedbacks according to mixed layer heating budget analysis. In terms of the thermal damping feedback, zonal advection feedback and meridional advection feedback dominated in the WEP west of 160E°, whereas the SST anomalies east of 160°W could be attributed mainly to two types of vertical advection feedbacks (thermocline–SST feedback and Bjerknes feedback). The central Pacific heating anomalies comprised the center of the zonal triple-pole pattern and they were caused mainly by zonal advection feedback and Bjerknes feedback. In addition, bidirectional subsurface oceanic heat advections due to equatorial Kelvin and off-equatorial Rossby waves were important for the zonal triple-pole anomalies in the CESM.

In addition to the mismatch between the annual mean SST and rainfall due to seasonal bias, our results have meaningful implications for paleoceanographic studies. First, distinct spatiotemporal patterns in the annual mean climate were associated with two anomalous zonal triple-pole type SST annual cycles, which helped to explain the different phase relationships in multiple paleo-proxies of the SST and rainfall (Carolin et al. 2013; Sadekov et al. 2013; Dang et al. 2015), or the synchronous Holocene evolution of the interannual variability and annual cycle amplitude of Niño-3 SST (Timmermann et al. 2014). Second, our results suggested that the annual averaged Niño-3 SST and the WEP-minus-EEP SST gradient were not sufficient to effectively indicate changes in the atmospheric Walker circulation and rainfall for the paleo-ENSO at the precessional band. Thus, it is better to develop new proxies for the seasonal paleoclimate conditions across the entire tropical Pacific. In addition, our simulated zonal triple-pole type annual cycle anomalies only represented an idealized sensitive response to orbital insolation forcing alone, whereas the existing paleoceanographic reconstructions mostly reflected climatic changes induced by multiple forcing factors (not precession alone), and these proxies are now scarce in the central equatorial Pacific. This would require the incorporation of more thorough simulations and paleo-proxies; for example, our results should be validated further based on higher-resolution models that include the effects of other boundary conditions (changes in the greenhouse gas concentrations, ice sheets, and sea level), which are beyond the scope of the present study.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grants 41606045, 41630965, 91428310, 41405078, 41606049, and 41776023), Rising Star Foundation of the South China Sea Institute of Oceanology (NHXX2018WL0201), and the Fundamental Research Funds for the Central Universities (10120172016KJ005). Our CESM experiment was conducted on the supercomputer MagicCube (DAWN5000A) of the Shanghai Supercomputer Center under the framework of the Laboratoire International Associé MONOCL (Monsoon, Ocean and Climate). We thank Chen Guangshan for providing source codes of “calendar effect” correction, and thank three reviewers for their constructive comments. And we thank International Science Editing (http://www.internationalscienceediting.com) for editing this manuscript.

APPENDIX

Precessional Modulated Equatorial Insolation and Its Decomposition

The daily mean equatorial insolation W is determined by the following equation (Berger 1978): W = 86.4 × S0 × [1 − sin(ε)2 × sin(λ)2]1/2 × [1 + e × cos(λ − ϖ)]2/[π × (1 − e2)2], where S0, e, ε, ϖ, and λ are the solar constant, eccentricity, obliquity, precessional angle (or longitude of perihelion), and true longitude of Earth at the ecliptic, respectively. The terms λ and ϖ are both angles in degrees (0°–360°) measured anticlockwise from the vernal equinox, where the former has an annual cycle (circles the sun every year), the latter varies at the precessional band of 23 kyr, and each ϖ value determines a certain annual cycle of W via the term e × cos(λ − ϖ) or climatic precession. This precessional-modulated annual cycle can be described as two-dimensional trigonometric function anomalies that propagate along the λ and ϖ directions, respectively. Because cos(λ − ϖ) = cos(λ) × cos(ϖ) − sin(λ) × sin(ϖ), the characteristic of e × cos(λ − ϖ) as a single mode can be decomposed into two standing modes using the EOF method (Clement et al. 2001; Emile-Geay et al. 2007; Wang et al. 2012). Due to their comparable contributions to the total variance (51.8% vs 47.7%), the first two EOF-PCs of the equatorial insolation have similar magnitudes in terms of their temporal evolution, but with a phase shift of 90° (for ϖ) at the precessional band (Fig. A1a). The associated EOF spatial pattern is characterized by a September maximum and a March minimum for the EOF1 mode, and by a June maximum and December minimum for the EOF2 mode (Fig. A1b). These two orthogonal modes can also be represented as the seasonal insolation contrasts between the two equinoxes on 22 September (λ = 180°) and 20 March (λ = 0°), and between the two solstices on 21 June (λ = 90°) and 21 December (λ = 270°) (Huybers 2004). Associated climatic responses to these two insolation modes are summarized in the main text as Figs. 1–12 and are further supplemented by Figs. A2–A16 as follows.

Fig. A1.
Fig. A1.

(a) The first two EOF-PCs (black and gray lines) of the equatorial insolation from the CESMtransient experiment are shown along with the time series of climatic precession (red line). (b) The associated first two EOFs are shown as regression coefficients (W m−2) against the standardized EOF1-PC and EOF2-PC, respectively. The contribution of each EOF-PC to the total variance is shown as a percent in (a).

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A2.
Fig. A2.

(a) The time series of the eccentricity (red lines) and obliquity (black lines) since 20 ka used in the CESMtransient experiment (solid lines) and in the CESM slice experiments (dashed lines). (b) The time series of the global annual mean SST (red solid line) and ocean temperature at depths of 60–80 m (blue solid line) during the last 100 model years in experiment CESM0ka, and the SST time series (black solid line) during the last 50 model years in experiment CESMslab_0ka. (c)–(e) As in (b), but for 11, 17, and 6 ka, respectively. Vertical gray bars in (a) indicate four time slices of 17, 11, 6, and 0 ka. In (b)–(e), the linear trend for each solid line is shown as a dashed line, whereas those numbers mark the standard deviation (std) for each solid line and the slope for each dashed line.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A3.
Fig. A3.

The regressed monthly spatial pattern of the tropical Pacific SSTresidual (K) against its standardized EOF1-PC from the CESMtransient experiment, in which white shaded areas are not significant at the 95% confidence level.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A4.
Fig. A4.

The regressed monthly spatial pattern of the tropical Pacific SSTresidual (K) against its standardized EOF2-PC from the CESMtransient experiment, in which white shaded areas are not significant at the 95% confidence level.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A5.
Fig. A5.

The regressed monthly spatial pattern of the tropical Pacific SST (K) against its standardized EOF1-PC from the CESMtransient experiment, in which white shaded areas are not significant at the 95% confidence level.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A6.
Fig. A6.

The regressed monthly spatial pattern of the tropical Pacific SST (K) against its standardized EOF2-PC from the CESMtransient experiment, in which white shaded areas are not significant at the 95% confidence level.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A7.
Fig. A7.

Climatological differences for the monthly tropical Pacific SSTresidual (K) between 11 and 0 ka (or the time slice version of Figs. 2a–f) for the (left) CESMtransient experiment, (center) CESM slice experiments (CESM11ka and CESM0ka), and (right) differences between the left and center columns.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A8.
Fig. A8.

Climatological differences of the monthly tropical Pacific SST (K) between 11 and 0 ka (or the time slice version of Figs. 3a–f) for the (left) CESMtransient experiment, (center) CESM slice experiments (CESM11ka and CESM0ka), and (right) differences between the left and center columns.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A9.
Fig. A9.

Climatological differences of the monthly tropical Pacific SSTresidual (K) between 6 and 17 ka (or the time slice version of Figs. 2g–l) for the (left) CESMtransient experiment, (center) CESM slice experiments (CESM6ka and CESM17ka), and (right) differences between the left and center columns.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A10.
Fig. A10.

Climatological differences of the monthly tropical Pacific SST (K) between 6 and 17 ka (or the time slice version of Figs. 3g–l) for the (left) CESMtransient experiment, (center) CESM slice experiments (CESM6ka and CESM17ka), and (right) differences between the left and center columns.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A11.
Fig. A11.

(a) Climatological differences for the SSTeq annual cycle (shaded; K) and the equatorial insolation (black line; W m−2) between 11 and 0 ka from the CESMtransient experiment. (b) As in (a), but for differences between experiments CESM11ka and CESM0ka. (c) Discrepancies between (a) and (b). (d) As in (a), but for differences between experiments CESMslab_11ka and CESMslab_0ka. (e)–(h) As in (a)–(d), but for situations between 6 and 17 ka.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A12.
Fig. A12.

As in Fig. A8, but for the longitude–depth cross sections of monthly ocean temperature (shaded; K) along the latitudes 5°S–5°N. (left) Climatological differences between 11 and 0 ka from the CESMtransient experiment; (center) differences between experiment CESM11ka and CESM0ka; and (right) differences between the left and center columns.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A13.
Fig. A13.

As in Fig. A10, but for the longitude–depth cross sections of monthly ocean temperature (shaded; K) along the latitudes 5°S–5°N. (left) Climatological differences between 6 and 17 ka from the CESMtransient experiment; (center) differences between experiment CESM6ka and CESM17ka; and (right) differences between the left and center columns.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A14.
Fig. A14.

Climatological differences of mixed layer heat budget terms (K month−1) between experiment CESM11ka and CESM0ka (for comparison with Fig. 7). (a) Longitude–month profile of mixed layer temperature tendency along the latitudes 5°S–5°N; the remaining panels are as in (a), but for the (b) QTD+Adv, (c) Qresidual, (d) QTD, (e) QZA, (f) QBJ, (g) QTH, and (h) QTMA terms.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A15.
Fig. A15.

Regression coefficients for mixed layer heat budget terms (K month−1) against the standardized time series of the equinox insolation mode from the CESMtransient experiment. (a) Longitude–month profile of mixed layer temperature tendency along the latitudes 5°S–5°N; the remaining panels are as in (a), but for the (b) QTD+Adv, (c) Qresidual, (d) QTD, (e) QZA, (f) QBJ, (g) QTH, and (h) QTMA terms.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

Fig. A16.
Fig. A16.

Climatological differences of the monthly subsurface ocean temperature at depths of 60–80 m (K) between 11 and 0 ka. (left) Climatological differences from the CESMtransient experiment; (center) differences between experiment CESM11ka and CESM0ka; and (right) differences between the left and center columns.

Citation: Journal of Climate 32, 21; 10.1175/JCLI-D-18-0668.1

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