Energy Balance Models Incorporating Transport of Thermal and Latent Energy

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  • 1 Corporate Research Science Laboratories, Exxon Research and Engineering Co., Annandale, NJ 08801
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Abstract

Standard latitudinally resolved energy balance models describe conservation of energy on a sphere subject to solar heating, cooling by infrared radiation and diffusive redistribution of energy according to a Fourier type heat flow with flux proportional to the gradient of temperature. The model determines the distribution of temperature with latitude T(x). Here we consider a similar model, the two phase model, in which we allow for transport of both thermal energy of air and latent heat associated with water vapor.

We use the two phase model to calculate climate change, i.e., ΔT(x), as a function of varying insolation and changing concentration of atmospheric CO2 under the assumption that relative humidity does not change. We compare the results with calculations from standard energy balance models and general circulation models. The distribution of warming with latitude for doubled atmospheric CO2 found with the two phase model agrees far better with the pattern of warming found in GCM studies than do results found with the standard model. In particular, the two phase model, like the GCM, shows greater manning at the poles than at the equator. In the two phase model, polar amplification can be explained in terms of a temperature dependent effective diffusion coefficient that increases with warming. Amplification of warming toward the poles occurs in the two phase model because the ability of the system to transport heat increases as the system warms.

Abstract

Standard latitudinally resolved energy balance models describe conservation of energy on a sphere subject to solar heating, cooling by infrared radiation and diffusive redistribution of energy according to a Fourier type heat flow with flux proportional to the gradient of temperature. The model determines the distribution of temperature with latitude T(x). Here we consider a similar model, the two phase model, in which we allow for transport of both thermal energy of air and latent heat associated with water vapor.

We use the two phase model to calculate climate change, i.e., ΔT(x), as a function of varying insolation and changing concentration of atmospheric CO2 under the assumption that relative humidity does not change. We compare the results with calculations from standard energy balance models and general circulation models. The distribution of warming with latitude for doubled atmospheric CO2 found with the two phase model agrees far better with the pattern of warming found in GCM studies than do results found with the standard model. In particular, the two phase model, like the GCM, shows greater manning at the poles than at the equator. In the two phase model, polar amplification can be explained in terms of a temperature dependent effective diffusion coefficient that increases with warming. Amplification of warming toward the poles occurs in the two phase model because the ability of the system to transport heat increases as the system warms.

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