The states of thermal equilibrium (incorporating an adjustment of super-adiabatic stratification) as well as that of pure radiative equilibrium of the atmosphere are computed as the asymptotic steady state approached in an initial value problem. Recent measurements of absorptivities obtained for a wide range of pressure are used, and the scheme of computation is sufficiently general to include the effect of several layers of clouds. The atmosphere in thermal equilibrium has an isothermal lower stratosphere and an inversion in the upper stratosphere which are features observed in middle latitudes. The role of various gaseous absorbers (i.e., water vapor, carbon dioxide, and ozone), as well as the role of the clouds, is investigated by computing thermal equilibrium with and without one or two of these elements. The existence of ozone has very little effect on the equilibrium temperature of the earth's surface but a very important effect on the temperature throughout the stratosphere; the absorption of solar radiation by ozone in the upper and middle stratosphere, in addition to maintaining the warm temperature in that region, appears also to be necessary for the maintenance of the isothermal layer or slight inversion just above the tropopause. The thermal equilibrium state in the absence of solar insolation is computed by setting the temperature of the earth's surface at the observed polar value. In this case, the stratospheric temperature decreases monotonically with increasing altitude, whereas the corresponding state of pure radiative equilibrium has an inversion just above the level of the tropopause. A series of thermal equilibriums is computed for the distributions of absorbers typical of different latitudes. According to these results, the latitudinal variation of the distributions of ozone and water vapor may be partly responsible for the latitudinal variation of the thickness of the isothermal part of the stratosphere. Finally, the state of local radiative equilibrium of the stratosphere overlying a troposphere with the observed distribution of temperature is computed for each season and latitude. In the upper stratosphere of the winter hemisphere, a large latitudinal temperature gradient appears at the latitude of the polar-night jet stream, while in the upper statosphere of the summer hemisphere, the equilibrium temperature varies little with latitude. These features are consistent with the observed atmosphere. However, the computations predict an extremely cold polar night temperature in the upper stratosphere and a latitudinal decrease (toward the cold pole) of equilibrium temperature in the middle or lower stratosphere for winter and fall. This disagrees with observation, and suggests that explicit introduction of the dynamics of large scale motion is necessary.

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A series of 2-week predictions were made with a general circulation model for 12 winter cases selected from the period 1964-69. All were January cases. The same prediction model-the most sophisticated and probably the most realistic model of those we tested in 1967-was used throughout. The model was hemispheric and had an N = 4 0 grid (grid size of about 270 km a t midlatitudes) with nine vertical levels. A detailed description of the model's performance is attempted by making statistical analyses of the forecast results compared with observed data. The analyses also provide useful insight into the dynamical behavior of the long waves in the middle latitude zone. The verification study reveals the practical limit of predictability with the 1967 version of the Geophysical Fluid Dynamics Laboratory model. For example, the correlation coefficient between prediction and observation of the 500-mb geopotential deviation from January normal stays above zero until the 10th day. A spectral study of the planetary and cyclone waves was also made. The behavior of the ultralong wave in this model is disappointing, but cyclone waves are reasonably well predicted until the eighth day.

Two-week predictions were made for two winter cases by applying the Geophysical Fluid Dynamics Laboratory high-resolution, nine-level, hemispheric, moist general circulation model. Three versions of the model are discussed: Experiment 1 includes the orography but not the radiative transfer or the turbulent exchange of heat and moisture with the lower boundary; Experiment 2 accounts for all of these effects as well as land-sea contrast; Experiment 3 allows, in addition, the difference in thermal properties between the land-ice and sea-ice surfaces, as well as an 80% relative humidity condensation criterion reduced from the 100% criterion in Experiments 1 and 2. The computed results are compared with observed data in terms of the evolution of individual cyclonic and anticyclonic patterns, the zonal mean structure of temperature, wind, and humidity, the precipitation over the United States, and the hemispheric energetics. The forecast near sea level was considerably improved in Experiments 2 and 3 over Experiment 1. The experiment succeeded in forecasting the birth of second and third generation extratropical cyclones and their behavior thereafter. The hemispheric sum of precipitation was increased five times in Experiment 2 over that in Experiment 1, and even more in Experiment 3, the greatest contribution occurring in the Tropics. Two winter cases were considered. The correlation coefficients between the observed and the forecast patterns for the change of 500-mb geopotential height from the initial time remained above 0.5 for 13 days in one case and for 9 days in the other. There are, however, several defects in the model. The forecast temperature was too low. In the flow pattern the intensities of the Highs and Lows weakened appreciably after 6 or 8 days, reflecting the fact that the forecast of eddy kinetic energy was less than the observed. On the other hand, the intensity of the tropospheric westerlies was too great.

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