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Two annual cycles of the Pacific cold tongue under orbital precession


The Pacific cold tongue annual cycle in sea surface temperature is presumed to be driven by Earth’s axial tilt1,2,3,4,5 (tilt effect), and thus its phasing should be fixed relative to the calendar. However, its phase and amplitude change dramatically and consistently under various configurations of orbital precession in several Earth System models. Here, we show that the cold tongue possesses another annual cycle driven by the variation in Earth–Sun distance (distance effect) from orbital eccentricity. As the two cycles possess slightly different periodicities6, their interference results in a complex evolution of the net seasonality over a precession cycle. The amplitude from the distance effect increases linearly with eccentricity and is comparable to the amplitude from the tilt effect for the largest eccentricity values over the last million years (e value approximately 0.05)7. Mechanistically, the distance effect on the cold tongue arises through a seasonal longitudinal shift in the Walker circulation and subsequent annual wind forcing on the tropical Pacific dynamic ocean–atmosphere system. The finding calls for reassessment of current understanding of the Pacific cold tongue annual cycle and re-evaluation of tropical Pacific palaeoclimate records for annual cycle phase changes.

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Fig. 1: Schematic of the Earth’s orbital configuration.
Fig. 2: Annual cycles of equatorial Pacific SSTs for three different Earth System models show a remarkable and consistent seasonal variation with the LOP.
Fig. 3: Variation of the cold tongue annual cycle to LOP arises from the sum of the tilt and distance effect contributions.
Fig. 4: The distance effect on the longitude position of the Walker circulation as diagnosed by the energy flux potential.

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Data availability

The iCESM 1.2, HadCM3, CESM 1.2 and ICM output variables used in this study are available at ref. 57 ( GFDL CM 2.1 model output is available at ref. 58 and EC Earth output at ref. 59.

Code availability

The CESM 1.2 code is publicly available at Analytical codes used in this paper are available in ref. 57 (


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We thank D. Battisti for providing the ICM code, W. Boos for providing code for the energy flux diagnostic, D. Pollard and M. Erb for providing code for the fixed-angle calendar conversion, S. White and R. Shen for advice on palaeoproxy records, and B. Raney and J. Bosmans for providing the GFDL and EC Earth model output, respectively. J.C.H.C. acknowledges support from a Visiting Professorship at Academia Sinica, funded by the Ministry of Science and Technology, Taiwan, under grant no. 110-2811-M-001-554. A.R.A. acknowledges support from National Science Foundation award 1903640. C.R.T. acknowledges funding from the National Center for Atmosphere Research Advanced Study Program postdoctoral fellowship. This research used the Savio computational cluster resource provided by the Berkeley Research Computing program at the University of California, Berkeley (supported by the UC Berkeley Chancellor, Vice Chancellor for Research and Chief Information Officer). High-performance computing support on Cheyenne ( was provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation.

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Authors and Affiliations



J.C.H.C., A.R.A. and A.J.B. conceived the study. J.C.H.C. conducted the CESM simulations and led the data analysis, writing of the manuscript and design of figures. D.J.V. and A.R.A. undertook the ICM simulations and analysis. P.A.N. provided the energy flux analysis. W.H.G.R. and C.R.T. conducted the HadCM3 and iCESM 1.2 model simulations, respectively. All authors contributed to the writing of this manuscript.

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Correspondence to John C. H. Chiang.

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Nature thanks Shang-Ping Xie and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Modern-day observed Pacific cold tongue annual cycle.

(a) SST averaged over 6°S–6°N, showing the cold tongue annual cycle with the cold peak in boreal fall and warm peak in boreal spring. Note that the time axis is such that 0 is the start of the year and 12 is the end; mid-January is thus 0.5. (b-c) SST and 10m winds for (b) October (cold peak), and (c) April (warm peak). Data is from ERA-Interim60, averaged over 1979–2018. The M_Map package41 is used to generate the maps for (b) and (c), using coastline data from the Global Self-consistent, Hierarchical, High-resolution Geography Database42.

Extended Data Fig. 2 The seasonal cycle of insolation at the equator for different orbital configurations, including those used in Fig. 2.

In all cases, downward solar radiation at top-of-atmosphere is averaged over 6°S–6°N, and the blue dashed line is for the tilt-only (e = 0) case. (a) Pre-industrial case. (b) difference from the tilt-only case for LOP = 90°, e = 0.0493 (black line), and pre-industrial (green line). (c) LOP = 0°, e = 0.0493. (d) LOP = 90°, e = 0.0493. (e) LOP = 180°, e = 0.0493. (f) LOP = 270°, e = 0.0493. Insolation data is from the GFDL CM 2.1 simulations of Erb et al. (2015)12. Panel (b) shows the contrast in the amplitude of insolation changes between the e = 0.0493 case (~ 42W/m2) and the pre-industrial case (~15W/m2) where the eccentricity is ~1/3 as large.

Extended Data Fig. 3 Cold tongue annual cycle in EC Earth also shows consistent variation with changing LOP.

Plotted is the climatological monthly mean SST averaged over 6°S–6°N (same as Fig. 2) for the (a) Precession maximum, minimum obliquity (Pmax), (b) Precession minimum, minimum obliquity (Pmin), and (c) Minimum obliquity with circular orbit (Tmin) runs in Bosmans et al. (2015)50. To facilitate comparison, an offset is added to each panel so that the annual mean SST averaged over 145–275°E is the same as for the observational data as shown in Extended Data Fig. 1a, 27.44 °C. The orbital parameters are slightly different, but Pmax corresponds approximately to the LOP = 90° simulation, Pmin to LOP = 270° simulation, and Tmin to the e = 0 simulation. The column positioning of the panels corresponds to the equivalent LOP or e = 0 case in Fig. 2. See Methods section on 'Earth System Model simulations' for the orbital parameters and details of the simulations.

Extended Data Fig. 4 Variation of the cold tongue SST annual cycle to LOP in CESM LOP for e = 0.01 and e = 0.02, and their fits to equation 1.

(a) Cold tongue SST (averaged over 6°S–6°N, 140–90°W) for e = 0.01 and varying longitude of perihelion. The annual mean is removed before plotting. (b) Least-square surface fit of the data in (a), using equation 1. (c) and (d): same as (a) and (b) respectively, except for e = 0.02. See Table 1 for the fitted coefficients.

Extended Data Fig. 5 CESM 1.2 annual cycle of equatorial Pacific SST under different combinations of tilt and distance effects.

Plotted is climatological monthly mean SST averaged over 6°S–6°N across the Pacific. In all cases, LOP = 0°. To facilitate comparison, an offset is added to each panel so that the annual mean SST averaged over 145°E–85°W is the same as for the observational data as shown in Extended Data Fig. 1a, 27.44 °C. (a) e = 0.05, obliquity = 23.439° (tilt and distance run); (b) e = 0.05, obliquity = 0° (distance-only run); (c) e = 0.00, obliquity = 23.439° (tilt-only run); (d) sum of the annual cycles of (b) and (c), added to the annual mean of (a); and (e) e = 0, obliquity = 0° (zero annual forcing run).

Extended Data Fig. 6 Equatorial thermocline response in the CESM LOP simulations connects the western equatorial Pacific zonal wind stress change to cold tongue changes.

LOP cases (a) 90°, (b) 180°, (c) 270°, and (d) 0° are shown. Contours show the 6°S–6°N averaged temperature anomaly at mean thermocline depth for e = 0.04, for the stated LOP. The temperature averaged across all LOP cases is first subtracted out, to remove the influence of the tilt effect from the thermocline. The contour interval is 0.5K, and dashed values are negative; the zero contour is not shown. For clarity, only values east of 170°E are plotted. The eastward propagation of thermocline anomalies is visually apparent. Shading represents the corresponding zonal wind stress anomaly averaged over 6°S–6°N; the average across all LOP cases is first subtracted out, to remove the influence of the tilt effect. Only values in the western Pacific (west of 160°W) are plotted. Positive values indicate westerlies. Although only four LOP cases are shown here, a deeper thermocline (as indicated by warmer temperature) in the western Pacific is accompanied by a westerly wind stress anomaly (and vice versa) for all LOP cases.

Extended Data Fig. 7 An intermediate coupled model (ICM) with imposed distance effect annually-varying wind forcing generates a cold tongue annual cycle.

All fields as shown are averaged over 6°S–6°N. (a) Distance effect zonal wind anomalies from the lowest model level of the CESM 1.2 coupled to a slab ocean (contour interval 0.75m/s, dashed contours are negative, zero contour omitted) and the SST response of the ICM to the applied wind forcing (shaded). This shows the cold tongue annual cycle in SST generated by the winds. (b) Full zonal wind (CESM 1.2 slab ocean + ICM) anomalies up to 160°W (shaded) and ICM thermocline depth anomalies east of 170°E (contour interval 2m, dashed contours are negative, zero contour omitted). This shows the connection between the winds and the cold tongue through thermocline changes. (c) SST anomalies due to the distance effect orbital forcing in the CESM 1.2 coupled to a slab ocean, showing the peak warming around December from the thermodynamic response to the distance effect insolation. The magnitude of the SST change here is not directly comparable with that of the ICM in panel (a), because of the lack of ocean dynamical feedback in the slab ocean that would alter the thermodynamic SST response. See Methods section on ‘Simulations with an ICM of the tropical Pacific’ for details.

Extended Data Fig. 8 Seasonal longitudinal shift in the Walker circulation due to the distance effect.

The difference between the distance-only run and zero annual forcing run (former minus latter) for various climate fields averaged over March–June (following aphelion) in the left column, and September–December (following perihelion) in the right column. (a-b) Precipitation (shaded) and wind stress (vectors). (c-d) Zonal overturning circulation at the equator displayed as vectors, with the x-component being the divergent component of the zonal wind (in m/s) averaged 10°S-10°N and y-component being the pressure vertical velocity (in Pa/s) multiplied by 250, also averaged 10°S-10°N. The green bar in (c-d) indicates the approximate longitudes of the Maritime Continent. (e-f) 200mb velocity potential. (g-h) Surface pressure. The precipitation in panels (a-b) show a shift in the location of equatorial rainfall between the Maritime Continent and western equatorial Pacific between March–June and September–December, associated with changing equatorial trades over the western equatorial Pacific. The zonal overturning circulation in panels (c-d) show anomalous subsidence over the Maritime continent and anomalous uplift over the western equatorial Pacific in March–June, indicating an eastward shift in the main uplift region of the Walker circulation; the opposite occurs for September–December. The velocity potential change in panels (e-f) shows a predominantly zonal wavenumber 1 pattern with the nodal point over the Maritime continent, reversing in sign between March–June and September–December. The surface pressure change in panels (g-h) show a see-saw in atmospheric mass between Africa/Indian ocean and the Pacific, again with the nodal point at the Maritime continent. Thus, all fields shown are consistent with a seasonal longitudinal shift of the Walker circulation towards the east in March–June and towards the west in September–December. The M_Map package41 is used to generate the maps, using coastline data from the Global Self-consistent, Hierarchical, High-resolution Geography Database42.

Extended Data Fig. 9 Consistent cold tongue annual cycle changes between the iCESM 1.2 and CESM LOP simulations.

Plotted is the climatological monthly mean SST averaged over 6°S–6°N, for (top row) iCESM 1.240, and (2rd row) CESM LOP. The numbers on the top row denote the longitude of perihelion (where 90° = perihelion at winter solstice, 180° = at vernal equinox, 270° = at summer solstice, and 0° = at autumn equinox), and the last column from simulations setting eccentricity to zero. To facilitate comparison, an offset is added to each panel so that the annual mean SST averaged over 145°E–85°W is the same as for the observational data as shown in Extended Data Fig. 1a, 27.44 °C. Despite the short integration time for the CESM LOP, the cold tongue seasonal cycle changes are qualitatively similar with the longer iCESM 1.2 simulations.

Extended Data Table 1 Summary table of CESM 1.2 simulations used in this study and their orbital configurations

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Chiang, J.C.H., Atwood, A.R., Vimont, D.J. et al. Two annual cycles of the Pacific cold tongue under orbital precession. Nature 611, 295–300 (2022).

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