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Precipitation efficiency constraint on climate change


Precipitation efficiency (PE) relates cloud condensation to precipitation and intrinsically binds atmospheric circulation to the hydrological cycle. Due to PE’s inherent microphysical dependencies, definitions and estimates vary immensely. Consequently, PE’s sensitivity to greenhouse warming and implications for climate change are poorly understood. Here, we quantify PE’s role in climate change by defining a simple index ϵ as the ratio of surface precipitation to condensed water path. This macroscopic metric is reconcilable with microphysical PE measures and higher ϵ is associated with stronger mean Walker circulation. We further find that state-of-the-art climate models disagree on the sign and magnitude of future ϵ changes. This sign disagreement originates from models’ convective parameterizations. Critically, models with increasing ϵ under greenhouse warming, in line with cloud-resolving simulations, show greater slowdown of the large-scale Hadley and Walker circulations and a two-fold greater increase in extreme rainfall than models with decreasing ϵ.

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Fig. 1: Climatology and correspondence of precipitation efficiency index ϵ with temperature.
Fig. 2: Time evolution of ϵ.
Fig. 3: Precipitation efficiency ϵ and the large-scale tropical circulation.
Fig. 4: Sensitivity of ϵ to surface temperature.
Fig. 5: Impact of ϵ on changes in temperature and atmospheric meridional circulation under greenhouse warming.
Fig. 6: Role of ϵ in climate change.

Data availability

TRMM data50 are obtained from and are interpolated from their native 0.25° by 0.25° resolution to 1° by 1° to match that of the MODIS monthly data available at Monthly surface temperature ( and SLP observations ( are also publicly available. Monthly mean Niño 3.4 SST data are obtained from ERA5 data are downloaded from!/dataset/reanalysis-era5-pressure-levels-monthly-means and interpolated from their native 0.25° by 0.25° grid to 1° by 1° resolution. The CMIP6 data supporting this study are available from Data from the CRM experiments and satellite-derived observations of \({\it{\epsilon }}\) are available at


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The authors thank N. Lutsko (Scripps Institution of Oceanography) for providing code to compute condensation rates in the cloud-resolving model. We thank S. Hu (Duke University) and A. A. Wing (Florida State University) for helpful ideas and discussions. We thank NASA, ECMWF and the CMIP6 group of the World Climate Research Programme for providing free and publicly available data. R.L.L. was supported by the National Science Foundation Grant 1352417 and the Yale University Graduate Fellowship. J.H.P.S. and A.V.F. acknowledge support from NOAA (NA20OAR4310377), the ARCHANGE project (ANR-18-MPGA-0001, the Government of the French Republic), NSF (AGS-2053096) and NASA (80NSSC21K0558). Additional support to A.V.F. was provided by the ARCHANGE project (ANR-18-MPGA-0001, the Government of the French Republic). T.S. was supported by EU H2020 grants 758005 and 821205.

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R.L.L. and J.H.P.S. conceived the study and performed the analysis and data visualization. R.L.L. wrote the original draft; R.L.L., J.H.P.S., A.V.F. and T.S. edited and reviewed the manuscript.

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Correspondence to Ryan L. Li.

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Nature Climate Change thanks Michael Byrne, Guy Dagan, Robert Wood and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Two precipitation efficiency measures in a cloud-resolving model.

Spatial scatterplot of microphysical precipitation efficiency \({\it{\epsilon }}_m\) against precipitation efficiency index \({\it{\epsilon }}\) for the SAM-L simulation (see methods) with 305 K SST.

Extended Data Fig. 2 Comparing metrics of precipitation efficiency.

Snapshots of (a) PE index \({\it{\epsilon }}\) from this study and (b) microphysical PE \({\it{\epsilon }}_m\)5 in the SAM-L simulation (see methods) with 305 K SST. The values at the top of each panel indicate domain averages. Cyan contours outline the region where the precipitable water exceeds 80% of its maximum value in the domain.

Extended Data Fig. 3 Precipitation efficiency and ENSO.

Scatterplot of the relative change of the observed regional precipitation efficiency index \({\it{\epsilon }}\) over the Indo-Pacific Warm Pool (WP; red) and over the Eastern Pacific (EP; blue) against the Nino 3.4 SST index. The solid and dashed lines represent the linear regression across blue and red points, respectively. Each dot is a monthly mean. WP and EP regions are defined in the text.

Extended Data Fig. 4 Decomposition of Changes in ϵ.

Multi-model mean (solid lines) and spread (shading) of normalized changes in precipitation efficiency index \(log({\it{\epsilon }}/{\it{\epsilon }}_0)\), surface precipitation \(log(P_s/P_{s0})\), and condensed water path \(- log(CWP/CWP_0)\) for (a) positive \(\partial {\it{\epsilon }}/\partial T_s\) models and (b) negative positive \(\partial {\it{\epsilon }}/\partial T_s\) models. Identical models as Fig. 4 are used.

Extended Data Fig. 5 Distribution of convection in the SAM experiments.

Cloud water mixing ratio and precipitable water in the (a) SAM-S and (b) SAM-L simulations. (a) and (b) have identical boundary conditions and physics (see methods) and only differ in the domain size. The purple grid in b demonstrates the relative size of the SAM-S grid. In b the convection is aggregated, under the clump of convection precipitable water exceeds 90 mm. PE is higher in b than in a.

Extended Data Fig. 6 Changes in the Zonal-Mean Atmospheric Circulation under Greenhouse Warming.

Response to warming of the annual- and zonal-mean streamfunction (\({{\Delta }}\psi\); colors) The zonal-mean circulation of the present climate is shown in solid (positive and counter-clockwise) and dotted (negative and clockwise) black lines. Hatching shows locations where 75% or more models agree in the sign of the response for all CMIP6 models used in this study.

Extended Data Fig. 7 Role of \({\it{\epsilon }}\) in Climate Change Normalized by Temperature.

As Fig. 6 except all data are normalized by Effective Climate Sensitivity before calculating the average and standard error.

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Supplementary Figs 1–4 and Table 1.

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Li, R.L., Studholme, J.H.P., Fedorov, A.V. et al. Precipitation efficiency constraint on climate change. Nat. Clim. Chang. 12, 642–648 (2022).

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