Search Results
1. Introduction The nonequilibrium thermodynamics corresponding to climatological atmospheric entropy production is a fundamental problem that needs to be extensively explored. In the last several decades, entropy, related to nonequilibrium thermodynamics, has been applied to various problems in the atmospheric sciences, for example, the general circulation of the atmosphere ( Peixoto and Oort 1992 ; Johnson 1997 ; Goody 2000 ; Takamitsu and Kleidon 2005 ; Fraedrich and Lunkeit 2008
1. Introduction The nonequilibrium thermodynamics corresponding to climatological atmospheric entropy production is a fundamental problem that needs to be extensively explored. In the last several decades, entropy, related to nonequilibrium thermodynamics, has been applied to various problems in the atmospheric sciences, for example, the general circulation of the atmosphere ( Peixoto and Oort 1992 ; Johnson 1997 ; Goody 2000 ; Takamitsu and Kleidon 2005 ; Fraedrich and Lunkeit 2008
atmosphere and heats the atmosphere when it condenses. Energy transport is also associated with heating and cooling by radiation, dynamics, and water vapor phase change, which in turn alter entropy of the Earth system. Entropy is produced by heating and cooling by irreversible processes. In addition, entropy is carried by radiation. Entropy produced by a blackbody is, therefore, the sum of entropy produced by radiative cooling and entropy carried by the blackbody radiation ( Planck 1913 ). For the Earth
atmosphere and heats the atmosphere when it condenses. Energy transport is also associated with heating and cooling by radiation, dynamics, and water vapor phase change, which in turn alter entropy of the Earth system. Entropy is produced by heating and cooling by irreversible processes. In addition, entropy is carried by radiation. Entropy produced by a blackbody is, therefore, the sum of entropy produced by radiative cooling and entropy carried by the blackbody radiation ( Planck 1913 ). For the Earth
1. The MEP hypothesis Paltridge (1975 , 1978 ) first proposed that Earth’s climate structure might be explained from a hypothesis of maximum entropy production (MEP). If correct, this proposal would be of crucial importance to future climate research because it provides the hitherto missing global constraint of the second law of thermodynamics. Subsequent investigations have generally supported Paltridge’s work, but not to the degree that MEP is accepted as a useful principle in modern climate
1. The MEP hypothesis Paltridge (1975 , 1978 ) first proposed that Earth’s climate structure might be explained from a hypothesis of maximum entropy production (MEP). If correct, this proposal would be of crucial importance to future climate research because it provides the hitherto missing global constraint of the second law of thermodynamics. Subsequent investigations have generally supported Paltridge’s work, but not to the degree that MEP is accepted as a useful principle in modern climate
. Thus, the latent heat measurements are not direct and, as argued below, involve assumptions whose validity, while unquestionable for phase equilibrium, is not clear in the supercooled (metastable) domain (see appendix A ). Therefore, our second goal is to employ entropic considerations in order to facilitate an interpretation of difficult experiments and constrain the measurements. 2. The entropy constraint We regard a supercooled droplet as a thermodynamic system and the ambient air as the heat
. Thus, the latent heat measurements are not direct and, as argued below, involve assumptions whose validity, while unquestionable for phase equilibrium, is not clear in the supercooled (metastable) domain (see appendix A ). Therefore, our second goal is to employ entropic considerations in order to facilitate an interpretation of difficult experiments and constrain the measurements. 2. The entropy constraint We regard a supercooled droplet as a thermodynamic system and the ambient air as the heat
1. Entropy production rate and changes due to Earth’s absorptivity The central point of the comment by Gibbins and Haigh (2021 , hereinafter GH2021 ) is to recognize the significance of entropy storage within the Earth system, and that hence Earth is not in a steady state. Here, we summarize the main point of the comment. The rest of the three criticisms are addressed after this main point is discussed. Notations used in this reply follow those used in Kato and Rose (2020 , hereinafter KR
1. Entropy production rate and changes due to Earth’s absorptivity The central point of the comment by Gibbins and Haigh (2021 , hereinafter GH2021 ) is to recognize the significance of entropy storage within the Earth system, and that hence Earth is not in a steady state. Here, we summarize the main point of the comment. The rest of the three criticisms are addressed after this main point is discussed. Notations used in this reply follow those used in Kato and Rose (2020 , hereinafter KR
1. Introduction To motivate the study of the entropy budget, consider first an enclosed, dry atmosphere. For an enclosed atmosphere in a steady state, the sum of all the entropy sources must be zero (here, “sources” is shorthand for sources and sinks). In the case of an enclosed, dry atmosphere, all of the entropy sources are simply heat sources divided by the temperature. For example, possible heat sources include radiation ( Q ), conduction of heat (− ∇ · J , where J is the conductive
1. Introduction To motivate the study of the entropy budget, consider first an enclosed, dry atmosphere. For an enclosed atmosphere in a steady state, the sum of all the entropy sources must be zero (here, “sources” is shorthand for sources and sinks). In the case of an enclosed, dry atmosphere, all of the entropy sources are simply heat sources divided by the temperature. For example, possible heat sources include radiation ( Q ), conduction of heat (− ∇ · J , where J is the conductive
1. Introduction a. Motivation The climate is, fundamentally, an entropy-producing system. The movement of energy from warmer regions, where it is supplied to the climate, to cooler regions, where it leaves, is an inevitable consequence of the second law of thermodynamics and drives the motion and activity of the climate. The energy transfers are mediated by a myriad of irreversible processes: for example, wind, rain, and radiation. Each process produces entropy, which must be exported from the
1. Introduction a. Motivation The climate is, fundamentally, an entropy-producing system. The movement of energy from warmer regions, where it is supplied to the climate, to cooler regions, where it leaves, is an inevitable consequence of the second law of thermodynamics and drives the motion and activity of the climate. The energy transfers are mediated by a myriad of irreversible processes: for example, wind, rain, and radiation. Each process produces entropy, which must be exported from the
derived with a small number of reasonable assumptions. The subsequent formulation has accuracy that is comparable to other approximate formulations, but has the distinct advantage of having consistent formulations for other thermodynamical variables (e.g., total moist entropy and enthalpy). The new formulation is reasonably accurate, inexpensive, adaptable, and attractive for theoretical studies, which is a combination of characteristics that may be unrivaled by all other formulations that have been
derived with a small number of reasonable assumptions. The subsequent formulation has accuracy that is comparable to other approximate formulations, but has the distinct advantage of having consistent formulations for other thermodynamical variables (e.g., total moist entropy and enthalpy). The new formulation is reasonably accurate, inexpensive, adaptable, and attractive for theoretical studies, which is a combination of characteristics that may be unrivaled by all other formulations that have been
1. Introduction In Kato and Rose (2020 , hereinafter KR2020 ), a useful new dataset is introduced and explored that leverages the satellite-derived CERES data products to estimate Earth’s entropy production rates monthly since March 2000. The global entropy production rate is an underexplored variable that many have hypothesized could furnish a new predictive theory of the climate ( Paltridge 1975 ; Ozawa 2003 ; Martyushev and Seleznev 2006 ). The existence of such a thorough observational
1. Introduction In Kato and Rose (2020 , hereinafter KR2020 ), a useful new dataset is introduced and explored that leverages the satellite-derived CERES data products to estimate Earth’s entropy production rates monthly since March 2000. The global entropy production rate is an underexplored variable that many have hypothesized could furnish a new predictive theory of the climate ( Paltridge 1975 ; Ozawa 2003 ; Martyushev and Seleznev 2006 ). The existence of such a thorough observational
was put forth by PM03 , which has further been evaluated using observations by Montgomery et al. (2006) , Aberson et al. (2006) , and Bell and Montgomery (2008) and using numerical simulations by Persing and Montgomery (2005) and Cram et al. (2007) . The theory posits that the locally high-entropy air at low levels in the tropical cyclone’s eye can provide an additional source of energy that is not considered in E-MPI. This process has been referred to as the “superintensity” mechanism
was put forth by PM03 , which has further been evaluated using observations by Montgomery et al. (2006) , Aberson et al. (2006) , and Bell and Montgomery (2008) and using numerical simulations by Persing and Montgomery (2005) and Cram et al. (2007) . The theory posits that the locally high-entropy air at low levels in the tropical cyclone’s eye can provide an additional source of energy that is not considered in E-MPI. This process has been referred to as the “superintensity” mechanism
