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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,...

A simple analytical formulation is presented for describing radiative transfer due to atmospheric water vapor. The radiative model is then applied to a global energy balance for earth, and the net infrared flux to space is expressed in terms of the mean surface temperature and atmospheric lapse rate. Water vapor and clouds are assumed to be the only sources of infrared opacity. When compared with empirical information, and for a global mean surface temperature of 288 K, the radiative model indicates a cloud top altitude for a single effective cloud of 6·8 km. Alternatively, when applied to a more realistic three-cloud formulation, the model predicts a comparable value of 6·5 km for an average cloud top altitude. With respect to changes in mean surface temperature, again comparing with empirical results, a discussion relating to the model suggests that the cloud top altitude decreases with decreasing surface temperature, which results in the surface temperature being roughly twice as sensitive to changes in factors such as planetary albedo than for the conventional assumption of a fixed cloud top altitude. Implications of this are discussed with respect to possible albedo changes due to atmospheric particulate matter as well as cloudiness as a climate feedback mechanism.

Radiative heat transfer in water clouds is studied by the method of discrete ordinates, taking into account not only scattering, absorption and emission by cloud droplets but also absorption and emission by water vapor in the cloud. According to Semuelson the method of discrete ordinates is not very amenable to studies involving the intermediate optical thickness, because of instabilities that are inherent in the method for the intermediate optical thickness. A method of avoiding these instabilities is shown in this paper. Numerical calculation for the spectral region from 5 to 40 μ was carried out on the model altostratus clouds, and that only for the window region on the model stratocumulus and nimbostratus clouds. The radiative temperature change in a very thin cloud is everywhere cooling. With increasing cloud thickness, however, the upper parts of the cloud undergo cooling, while the lower parts undergo heating. The rate of both heating and cooling is largest near the surface. In a semi-infinitely thick cloud the cloud top undergoes cooling at a rate of about 30°C/hr and effective cooling extends to about 100 m interior from the cloud boundary.

The effect of variation in cloudiness on the climate is considered in terms of 1) a relation between the radiation balance of the earth-atmosphere system and variations in the amount of cloud cover or effective cloud top height, 2) the effect on the surface temperature of variations in cloudiness, and 3) the dynamic coupling or “feedback” effects relating changes in surface temperature to the formation of clouds. The first two points are studied by numerical integration of a simple radiation flux model, and the third point is discussed qualitatively. Global-average radiation balance calculations show that an increase in the amount of low and middle level cloud cover (with cloud top height and cloud albedo fixed) decreases the surface temperature. But, this result for the global-average case does not hold near polar regions, where the albedo of the cloudy areas can he comparable to (or even smaller than) the albedo of the snow-covered cloudless areas, and where, especially in the winter season, th...

This paper describes the method of incorporating into the NCAR global circulation model the dynamic effect of mountains, the prediction of cloudiness for radiation calculations, and the calculation of ground surface temperature using a heat balance equation. Other aspects of the physics of the model and the finite-difference schemes are very similar to those discussed by the authors in 1967 and 1970. For the simulation of seasonal climate we specify two parameters: the sun's declination and the distribution of ocean surface temperatures. Since the prediction of cloudiness is parameterized in terms of the relative humidity and the vertical motion fields, solar and atmospheric radiation processes interact closely with the dynamics of the atmosphere through variations in the fields of cloudiness, temperature and water vapor. Coupling between radiation and dynamics helps to maintain stronger baroclinic activity in middle latitudes. Although a hydrologic cycle is included in the model atmosphere and t...