Greenhouse gases, most importantly water vapor, increase the emissivity and decrease the albedo of clouds for thermal radiation. The modifications, which can be of order 10% for optically thick clouds, depend on the attenuation coefficient $α^{\{g\}}$ of the greenhouse gases, and also on the attenuation coefficient, $α^{\{c\}}$, the single-scattering albedo $\tilde ω^{\{c\}}$, and the scattering phase function $p^{\{c\}}(μ,μ')$ of the cloud particulates. Cold, high-altitude clouds with low partial pressures of water vapor have smaller emissivities for thermal radiation and larger albedos than otherwise identical but warmer low-altitude clouds with higher partial pressures of water vapor. In $2n$-stream scattering theory, these phenomena can be quantified with the intensity emissivities $\varepsilon_{i}$ of the streams $i=1,2,3,\ldots, 2n$, and with upward or downward flux emissivities, $\varepsilon_{\bf u}$ and $\varepsilon_{\bf d}$. The emissivities are the ratios of the outgoing thermal intensities or fluxes to those of a reference black cloud. Emission from optically-thick, isothermal clouds with scattering, as well as absorption and emission, is limb darkened. Intensity emissivities $\varepsilon_i$ for streams that are nearly normal to the cloud surface are larger than those of more nearly horizontal streams. The limb darkening increases with increasing values of the single scattering albedo $\tilde ω$. For fixed values of $\tildeω$, the onset of limb darkening with increasing zenith angle is more abrupt for phase functions with more forward scattering. Black clouds, which have only absorption and emission but no scattering, have unit (Lambertian) emissivities, $\varepsilon_i = 1$, for all stream directions.
Social Cost of Greenhouse Gases -- OPTiMEM and the Heat Conjecture(s)
Butterfly Sciences（蝴蝶科学）；Institute of Arctic and Alpine Research, University of Colorado Boulder（科罗拉多大学博尔德分校北极与高山研究所）；Global Monitoring Laboratory, National Oceanic and Atmospheric Administration（美国国家海洋和大气管理局全球监测实验室）；Center for Ecosystem Science and Society, Northern Arizona University（北亚利桑那大学生态系统科学与社会中心）；London Institute of Banking and Finance（伦敦银行与金融学院）；Climate Central（气候中心）；NOAA/NESDIS/NCEI（美国国家海洋和大气管理局国家环境卫星、数据和信息服务中心）
Model estimates for contribution of natural and anthropogenic CO$_2$ and CH$_4$ emissions into the atmosphere from the territory of Russia, China, USA and Canada to global climate changes in the 21st century
A Bridge Between Climate Science and Economics: OPTiMEM and the Heat Conjecture for Estimation of Social Cost of Greenhouse Gases
Butterfly Sciences（蝴蝶科学）；Institute of Arctic and Alpine Research, University of Colorado（科罗拉多大学极地高山研究所）；Center for Ecosystem Science and Society, Northern Arizona University（北亚利桑那大学生态系统科学与社会中心）；Chartered Governance Institute（特许治理学会）；Institute for Strategy, Resilience & Security, University College London（伦敦大学学院战略、韧性与安全研究所）；Climate Central（气候中心）
