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Episodic deluges in simulated hothouse climates


Earth’s distant past and potentially its future include extremely warm ‘hothouse’1 climate states, but little is known about how the atmosphere behaves in such states. One distinguishing characteristic of hothouse climates is that they feature lower-tropospheric radiative heating, rather than cooling, due to the closing of the water vapour infrared window regions2. Previous work has suggested that this could lead to temperature inversions and substantial changes in cloud cover3,4,5,6, but no previous modelling of the hothouse regime has resolved convective-scale turbulent air motions and cloud cover directly, thus leaving many questions about hothouse radiative heating unanswered. Here we conduct simulations that explicitly resolve convection and find that lower-tropospheric radiative heating in hothouse climates causes the hydrologic cycle to shift from a quasi-steady regime to a ‘relaxation oscillator’ regime, in which precipitation occurs in short and intense outbursts separated by multi-day dry spells. The transition to the oscillatory regime is accompanied by strongly enhanced local precipitation fluxes, a substantial increase in cloud cover, and a transiently positive (unstable) climate feedback parameter. Our results indicate that hothouse climates may feature a novel form of ‘temporal’ convective self-organization, with implications for both cloud coverage and erosion processes.

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Fig. 1: Transition to the relaxation oscillator regime due to increased insolation.
Fig. 2: The oscillatory regime is induced by LTRH.
Fig. 3: Mechanism of the oscillatory regime as revealed by high-frequency model output.
Fig. 4: Overview of the relaxation oscillator convective regime.

Data availability

Input data files and cloud-resolving model output associated with this work are available in a Zenodo repository at

Code availability

Source code for the stochastic two-layer model, processing cloud-resolving model output, and generating figures is available in a Zenodo repository at


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We are grateful to the authors of the cloud-resolving models used in this work: D. Romps, M. Khairoutdinov and G. Bryan. We also thank A. Dudhia for sharing with us the Reference Forward Model. We thank X. Wei for conducting exploratory simulations with SAM. J.T.S. thanks N. Jeevanjee, A. Match, N. Tarshish and Z. Kuang for discussions.

Author information




J.T.S. and R.D.W. designed the research. J.T.S. performed the simulations, analysed the results and prepared the figures. The manuscript was written jointly by J.T.S. and R.D.W.

Corresponding author

Correspondence to Jacob T. Seeley.

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The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 Errors in clear-sky RRTM radiative heating rates are corrected by using line-by-line radiative transfer.

Comparison of net (LW+SW; panels ad), longwave (LW; panels eh), and shortwave (SW; panels il) radiative heating rates as computed by RRTM (black) and PCM_LBL (red). The heating rates are computed for moist-adiabatic temperature-pressure profiles with surface temperatures ranging from 305 K to 335 K in 10-K increments (columns, left to right). All columns have a surface pressure of 101325 Pa, 75% tropospheric relative humidity, 400 ppm CO2, and an isothermal stratosphere at 160 K. Note that the discontinuous heating rates calculated by RRTM for the warmer atmospheres (around 20 km altitude) do not appear in the PCM_LBL results.

Extended Data Fig. 2 Top-of-atmosphere radiative fluxes and heating rates from DAM snapshots.

(ac) Outgoing longwave radiation (OLR) from a snapshot from the fixedSST_hires DAM simulation with a surface temperature of 305 K, computed by three different combinations of radiative transfer codes and approximations. Panel (a) is from RRTM alone, panel (b) shows the result of swapping out the clear-sky radiative fluxes from RRTM with those calculated by PCM_LBL, and panel (c) shows the result of swapping out each column’s clear-sky radiative fluxes for those calculated by PCM_LBL for the horizontal-mean column, which is the approach taken for the simulations associated with this work. Panel (d) shows the horizontal-mean longwave radiative heating rates for this snapshot. (eh) As in (ad), but for absorbed shortwave radiation (ASR). (ip) As in (ah), but for a snapshot from the simulation with a surface temperature of 330 K.

Extended Data Fig. 3 Tests of the robustness of the oscillatory transition.

Domain-mean precipitation from two periods of (a) the FCO2 simulation with mean SSTs of 306.1 K and 331.5 K; (b) the fixedSST suite at 305 K and 330 K; (c) the fixedSST_sm suite, which use the simplified microphysics parameterization described in the Methods; (d) fixed-SST simulations with finer horizontal resolution (Δx = 250 m; fixedSST_hires) or on a larger domain (Lx = 512 km; fixedSST_large). (e) The same quantity from simulations conducted with the System for Atmospheric Modeling (SAM)69 at fixed SSTs of 305 and 325 K. (f) As in (e), but for the Cloud Model 1 (CM1)70.

Extended Data Fig. 4 Mean profiles of temperature and cloud fraction.

From the fixedSST simulations, profiles of (a) mean temperature and (b) mean cloud fraction (fraction of grid cells with non-precipitating cloud condensate mass fraction greater than 10−5 kg/kg). In (a), the variability is indicated by the shading, which shows ±2 standard deviations of hourly-mean temperatures at each altitude. In (a), the dashed line shows the mean temperature profile from the simulation without evaporation of precipitating hydrometeors (prevap0) at 330 K.

Extended Data Fig. 5 Sign reversal of the climate feedback parameter indicates transient climate instability.

The feedback parameter λ is defined here as minus the change in net radiative flux at the top-of-atmosphere (TOA) per degree of surface warming (positive downward, so that a negative feedback indicates more radiation escaping to space with warming and hence climate stability, and a positive feedback indicates climate instability; this is often called the “Cess sensitivity”72). We calculated feedbacks using finite differences on a staggered surface temperature grid that interpolates between the surface temperatures of the fixedSST experiment. (a) The solid line shows clear-sky feedbacks calculated for TOA fluxes averaged over the final 100 days of the fixedSST simulations, while the dashed and dot-dashed lines show the feedbacks calculated using the time-mean columns from those simulations with actual or fixed 100% relative humidity profiles, respectively. (b) As in (a), but for the all-sky feedbacks from fixedSST experiments broken down into longwave and shortwave components. The dashed line shows the net all-sky feedback from the final 50 days of the LTRH_off experiment, which does not undergo a steady-to-oscillatory transition and remains stable at all temperatures. (c) Time-mean profiles of relative humidity (RH) in the fixedSST experiments, using temperature within the atmosphere as a vertical coordinate to emphasize the increases in upper-tropospheric relative humidity that occur during the oscillatory transition between 320 and 325 and K. Since the clear-sky climate instability is eliminated by using a fixed relative humidity of 100% (panel a), we attribute the clear-sky climate instability to the increase in upper-tropospheric RH, which lowers spectral emission temperatures and hence OLR.

Extended Data Fig. 6 Spatially-separated subdomains exhibit in-phase pulses of convection.

Timeseries of (a,c) moist static energy in the lowest model level (z = 12.5 m; MSEsurf), and (b,d) precipitation rate, averaged over five different subdomains of the fixedSST_large simulations at 305 K (top row) and 330 K (bottom row). The subdomains (color-coded in panel e) each have an area of 256 km2 and are located an average of 215 km apart from each other.

Extended Data Fig. 7 The steady-to-oscillatory transition in the convection-resolving model and the stochastic two-layer model.

(a) In the convection-resolving model, the radiative heating profile is switched from cool-climate-type to hothouse-type (LTRH_off to LTRH_on) on model day 0 (the transient_SO simulation). (b) In the two-layer model, the inhibition parameter is increased linearly in time between days 0 and 2 and held fixed thereafter.

Extended Data Fig. 8 Probability density functions (PDFs) of 6-hour local rain accumulations.

The precipitation data are from 20-day periods of (a) the fixedSST_large simulations, and (b) the transient_SO simulation in the steady and oscillatory regime. The PDFs are constructed by first dividing the model domains into watershed-sized subdomains (16 × 16 km2 for fixedSST_large, and 12 × 12 km2 for transient_SO). Precipitation is then accumulated in each subdomain for all 6-hour periods during the 20-day intervals, producing the 6-hour local rain accumulations from which the PDFs are constructed. The 99.9th percentile of each of the PDFs is indicated at the top of each plot.

Extended Data Fig. 9 The oscillatory transition occurs more readily for climates instellated by an M-star spectrum.

Comparison of tropospheric radiative heating rates (panels a,b) and timeseries of surface precipitation (panels c,d) in fixed-SST simulations with either the solar instellation spectrum or that of the M-star AD Leonis62. Panel (e) shows the spectral flux for these two stars (normalized to the same total flux), as well as the logarithm of the H2O absorption coefficient at a reference temperature and pressure.

Extended Data Table 1 Summary of key aspects of the suite of DAM simulations conducted for this work

Supplementary information

Supplementary Video 1

The supplementary video is an animation of DAM model output from the fixed-SST simulation at 330 K (from our fixedSST_hires suite; Extended Data Table 1). Each frame in the video consists of six panels showing, from top to bottom and left to right: buoyancy in the near-surface layer, wind speed in the near-surface layer, outgoing solar radiation, temperature anomaly in the near-surface layer, specific humidity anomaly in the near-surface layer, and accumulated rainfall over the preceding 6 h. Anomalies are calculated with respect to the horizontal and time mean. The sampling interval between frames is 15 min, and the animation covers 7 days of model time. The video is also available at

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Seeley, J.T., Wordsworth, R.D. Episodic deluges in simulated hothouse climates. Nature 599, 74–79 (2021).

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