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Past Earth warmed by tidal resonance-induced organization of clouds under a shorter day


Solar heating causes the periodic expansion and contraction of Earth’s atmosphere known as the atmospheric tide. This is observed at the surface as a semidiurnal pressure oscillation that appears to influence convection and rainfall. Roughly 0.5 to 1.0 billion years ago, when day length was roughly 21–22 hours, the tide would have been resonant, or close in frequency, with atmospheric Lamb waves of 10.5–11.0 hour periods. This ‘Lamb resonance’ would have amplified the pressure oscillation, perhaps strongly enough to affect the global or tropical climate. Here we run a general circulation model at different rotation rates to model the resonance and its impact on climate. The resonance exerts a dominant control on tropical cloud cover, convection and rainfall: sunrise and sunset are cloudy and rainy, whereas midday and midnight are clear and dry. Generally clear skies at noon lower the albedo, contributing 2–4 K warming in the global average, which would have helped counter the 10% fainter Sun. The hydrological cycle becomes more active, and the atmosphere moister. Our work highlights the role of tidally induced adiabatic expansion in controlling tropical precipitation, helping explain modern-day observations of a semidiurnal rainfall pattern.

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Fig. 1: Resonance at ~22 hours causes a sharp change in global climatology.
Fig. 2: The semidiurnal surface pressure anomaly increases at ~22 hours.
Fig. 3: Semidiurnal pressure amplitude and global mean surface temperature (relative to simulations with 24 hour day length) across all simulations.
Fig. 4: Convergence, clouds and precipitation are organized by the semidiurnal tide in resonance.
Fig. 5: Precipitation aligns more closely with temperature anomaly and divergence aloft than with low-level convergence.

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Data availability

Climate model output is archived in the Federated Research Data Repository ( The data are freely available under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence.

Code availability

The Community Earth System Model (CESM) version 1.2.1 used here is available at ExoCAM used here is available at, and its component ExoRT is available at Our Python code for post-processing and plotting is available via GitHub ( and Zenodo ( (ref. 57).


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Financial support was provided by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant (RGPIN-2018-05929) to C.G. High-performance computing resources were provided by the BC DRI Group and the Digital Research Alliance of Canada and by an NSERC Research Tools and Instruments grant (RTI-2020-00277) to C.G. We thank K. Zahnle, M. Farhat, P. Auclair-Desrotour, G. Boué, J. Laskar, A. Matthews, B. Khouider and K. Roy for informative discussions. We also thank S. Huber, E. Wiebe and E. Wolf for technical support.

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C.G. suggested the study. R.D. performed the model runs and numerical analysis and made the figures. Both authors contributed to the analysis and to writing the paper.

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Correspondence to Russell Deitrick.

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Nature Geoscience thanks Michael Schindelegger, Steve Woolnough and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: James Super, in collaboration with the Nature Geoscience team.

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Extended data

Extended Data Fig. 1 Horizontal maps of pressure anomaly across 16-25 hour day lengths.

The total pressure anomaly (left) and its diurnal (middle) and semidiurnal (right) modes are shown for all of the 30 ppm methane cases. The 22 and 24 hour cases are also shown in Fig. 2.

Extended Data Fig. 2 Semi-analytical calculation of the pressure anomaly from averaged GCM profiles.

Semidiurnal pressure anomaly are computed from the vertical structure equation, using output from the GCM. Top panels used the temperature profile and heating profiles from our WACCM 24 hour case (solid lines) and 22.5 hour case (dotted lines); bottom panels used profiles from our ExoCAM, 30 ppm CH4, 24 hour case (solid lines) and 22.25 hour case (dotted lines).

Extended Data Fig. 3 Semi-analytical calculation of imaginary component and phase of the pressure anomaly.

Imaginary component (left) and phase (right) of the semidiurnal pressure anomaly are computed from the vertical structure equation, using output from the GCM. Top panels used the temperature profile and heating profiles from our WACCM 24 hour case (solid lines) and resonant 22.5 hour case (dotted lines); bottom panels used the same from our ExoCAM, 30 ppm CH4, 24 hour case (solid lines) and resonant 22.25 hour case (dotted lines).

Extended Data Fig. 4 Horizontal maps of the cloud water path across 16-25 hour day lengths.

Cloud water path and cloud water path anomaly, plus the diurnal and semidiurnal modes, are shown for the full 30 ppm methane sequence. The cloud water path includes ice and liquid components and is vertically integrated.

Extended Data Fig. 5 Horizontal maps of precipitation across 16-25 hour day lengths.

Total precipitation and precipitation anomaly, plus the diurnal and semidiurnal modes, are shown for the full 30 ppm methane sequence.

Extended Data Fig. 6 Convection peaks at sunrise and sunset in resonance.

The deep convective mass flux (left column), deep convective heating rate (middle column), and horizontal divergence (right column) are shown as a function of pressure over the troposphere. All profiles are taken from the equator. The top row shows the fields at sunrise, the middle panels at noon, and the bottom panels at sunset.

Extended Data Fig. 7 Patterning seen in convection and rainfall.

The upper panels show the anomaly in mass flux due to shallow convection, the middle show the same due to deep convection, and the bottom panels show the precipitation. The latter is identical to that shown in Fig. 5 and is shown again here for comparison with convective fluxes.

Extended Data Fig. 8 Horizontal maps of the wind divergence field near tropopause across 16-25 hour day lengths.

The full divergence and divergence anomaly, plus the diurnal and semidiurnal modes, are shown for the full 30 ppm methane sequence at the 200 hPa level.

Extended Data Fig. 9 Horizontal maps of the wind divergence field near the surface across 16-25 hour day lengths.

The full divergence and divergence anomaly, plus the diurnal and semidiurnal modes, are shown for the full 30 ppm methane sequence at the 1000 hPa level.

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Deitrick, R., Goldblatt, C. Past Earth warmed by tidal resonance-induced organization of clouds under a shorter day. Nat. Geosci. 17, 675–682 (2024).

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