A Diffuse Thin Cloud Atmospheric Structure as a Feedback Mechanism in Global Climatic Modeling

Abstract

This paper describes the first step in the development of another global climatic model in which the structure of the atmosphere and consequently its optical properties are dynamically coupled to the surface temperature. Rather than considering clouds as discrete entities, we structure the atmosphere as a diffuse thin cloud by utilizing the fundamental thermodynamics of the cooling of moist air of fixed surface relative humidity maintaining vertical mechanical equilibrium. Vertical convective thermal mixing is parameterized as is the amount of condensate that is “rained” out. The remaining condensate is distributed as spherical droplets by an assumed distribution function. The modified two-stream approximation employing a Gaussian quadrature is used to solve the radiative transfer equation. The reflectivity and transmissivity of the model atmosphere and a given amount of aerosol are then calculated. These quantities, together with a parameterization of surface reflectivity to surface temperature, serve to determine the total albedo to solar radiation. The infrared flux is calculated employing the emissivity technique of Rodgers. The radiative dynamical coupling to surface temperature is such that the solar energy absorbed descreases and the emitted infrared increases with an increase in surface temperature, each with about the same magnitude of 0.0026 cal cm⁻² min⁻¹ (°K)⁻¹. Thus both provide stabilizing negative feedback. In applying the diffuse cloud model atmosphere to climate assessment we have at this stage considered only global annual average surface temperature, calculating that temperature which gives radiation balance. The sensitivity of the “climate” to variations in aerosol optical density, atmospheric carbon dioxide, and the solar constant is calculated and the results are comparable to those obtained by others using very different models. In general, our model exhibits slightly greater stability.