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Abstract The state dependence of cloud feedback—its variation with the mean state climate—has been found in many paleoclimate and contemporary climate simulations. Previous results have shown inconsistencies in the sign, magnitude, and underlying mechanisms of state dependence. To address this, we utilize a perturbed parameter ensemble (PPE) approach with fixed sea surface temperature (SST) in the Community Atmosphere Model, version 6. Our suites of PPEs span a wide range of global mean surface temperatures (GMSTs), with spatially uniform SST perturbations of −4, 0, 4, 8, 12, and 16 K from the preindustrial. The results reveal a nonmonotonic variation with GMSTs: Cloud feedback increases under both cooler and warmer-than-preindustrial conditions, with a rise of ∼0.1 W m⁻²K⁻¹under a 4-K colder climate and ∼0.4 W m⁻²K⁻¹under a 12-K warmer climate. This complexity arises from differing cloud feedback responses in high and low latitudes. In high latitudes, cloud feedback consistently rises with warming, likely driven by a moist adiabatic mechanism that influences cloud liquid water. The low-latitude feedback increases under both cooler and warmer conditions, likely influenced by changes in the lower-tropospheric stability. This stability shift is tied to nonlinearity in thermodynamic responses, particularly in the tropical latent heating, alongside potential state-dependent changes in tropical circulations. Under warmer-than-preindustrial conditions, the increase in cloud feedback with warming is negatively correlated with its preindustrial value. Our PPE approach takes the model parameter uncertainty into account and emphasizes the critical role of state dependence in understanding past and predicting future climates. Significance StatementThis study focuses on how cloud feedback—one of the most uncertain aspects of climate change—varies as global temperatures rise. We found that the cloud feedback decreases at first with warming and then increases, showing significant variation. This complexity stems from nonlinear thermodynamics, such as the Clapeyron–Clausius relationship, which describes how temperature affects moisture in the atmosphere. Our results indicate that the cloud feedback depends on the level of global warming, which is a significant factor rooted in fundamental physics. Recognizing this dependence is important for studies that aim to interpret past climates and predict future climate changes. 

This dataset originates from a new CESM2 CAM6 perturbed parameter ensemble (PPE) designed to explore climate and hydroclimate dynamics under a wide range of sea surface temperature (SST) conditions. The SST varies from 4 degrees Celsius colder to 16 degrees Celsius warmer than preindustrial levels, encompassing a broad spectrum of mean temperatures spanning the past 65 million years. This dataset offers valuable insights into climate and hydroclimate responses, as well as weather and climate extremes under diverse conditions.The dataset includes results from nine PPE simulations with different SST scenarios: preindustrial (PREI), 4K cooler (M04K), and 4K, 8K, 12K, and 16K warmer (P04K to P16K). For SSTs exceeding 8K warming, sea ice was removed to improve numerical stability. Each PPE set consists of 250 ensemble members, with 45 parameters related to microphysics, convection, turbulence, and aerosols perturbed using Latin Hypercube Sampling. An additional simulation with default parameter settings brings the total to 251 simulations, each running for five years using CAM6.3 (https://github.com/ESCOMP/CAM/tree/cam6_3_026; with additional paleo modifications).Post-processing converted the data into compressed NetCDF-4 format. All 251 runs were concatenated using ncecat to minimize the number of files. For example, the following file contains monthly surface temperature data from the preindustrial PPE: f.c6.F1850.f19_f19.paleo_ppe.sst_prei.ens251/atm/proc/tseries/month_1/f.c6.F1850.f19_f19.paleo_ppe.sst_prei.ens251.cam.h0.TS.000101-000512.ncA detailed variable list [https://rda.ucar.edu/OS/web/datasets/d651038/docs/detailed_vars.txt] can be found in the Documentation Tab.Parameter values are provided in the PPE Parameter File. More details can be found in the paper: Zhu et al. (2025). Investigating the State Dependence of Cloud Feedback Using a Suite of Perturbed Parameter Ensembles, Journal of Climate. 

Simulating the warmth and equability of past hothouse climates has been a challenge since the inception of paleoclimate modeling. The newest generation of Earth system models (ESMs) has shown substantial improvements in the ability to simulate the early Eocene global mean surface temperature (GMST) and equator-to-pole gradient. Results using the Community Earth System Model suggest that parameterizations of atmospheric radiation, convection, and clouds largely determine the Eocene GMST and are responsible for improvements in the new ESMs, but they have less direct influence on the equator-to-pole temperature gradient. ESMs still have difficulty simulating some regional and seasonal temperatures, although improved data reconstructions of chronology, spatial coverage, and seasonal resolution are needed for more robust model assessment. Looking forward, key processes including radiation and clouds need to be benchmarked and improved using more accurate models of limited domain/physics. Earth system processes need to be better explored, leveraging the increasing ESM resolution and complexity. 

Abstract. Climate field reconstruction (CFR) refers to the estimation of spatiotemporal climate fields (such as surface temperature) from a collection of pointwise paleoclimate proxy datasets. Such reconstructions can provide rich information on climate dynamics and provide an out-of-sample validation of climate models. However, most CFR workflows are complex and time-consuming, as they involve (i) preprocessing of the proxy records, climate model simulations, and instrumental observations; (ii) application of one or more statistical methods; and (iii) analysis and visualization of the reconstruction results. Historically, this process has lacked transparency and accessibility, limiting reproducibility and experimentation by non-specialists. This article presents an open-source and object-oriented Python package called cfr that aims to make CFR workflows easy to understand and conduct, saving climatologists from technical details and facilitating efficient and reproducible research. cfr provides user-friendly utilities for common CFR tasks such as proxy and climate data analysis and visualization, proxy system modeling, and modularized workflows for multiple reconstruction methods, enabling methodological intercomparisons within the same framework. The package is supported with extensive documentation of the application programming interface (API) and a growing number of tutorial notebooks illustrating its usage. As an example, we present two cfr-driven reconstruction experiments using the PAGES 2k temperature database applying the last millennium reanalysis (LMR) paleoclimate data assimilation (PDA) framework and the graphical expectation–maximization (GraphEM) algorithm, respectively.