Abstract
Each component of both energy budget equations for the atmosphere and for the surface layer of the earth are parameterized by functions of the incident solar radiation at the top of the atmosphere, the temperature at the mid-atmosphere (500mb level) and at the earth surface. The parameterization includes the following two assumptions needful to simplify the model: (1) The condensation heat released into the atmosphere minus the vertically integrated divergence of total energy flux in the atmosphere is constant. (2) Time change of the heat energy stored in the earth surface layer is proportional to time change of the earth surface temperature, where the proportional coefficients are different between the hydrosphere and the lithosphere.
Simultaneous energy budget equations for the atmosphere and for the earth surface layer yield a non-homogeneous, one-order, linear ordinary differential equation of the temperature at the 500mb level or at the surface with respect to time. A homogeneous term of the equation is a function of the incident solar radiation at the top of the atmosphere. Integrating the equation with respect to time from 0°K for an initial value of the temperature at the 500mb level or the surface, the temperature rises gradually with the date of the year and comes to have seasonal variations after several years integration. Inspite of many rough assumptions, the computed seasonal variation of the temperature shows approximate agreement with the observation at each cases following respective the 500 mb level and the surface over land and over sea.
The responses of the temperature at the 500mb level and the surface are investigated over sea and over land against variation of cloud amount, surface albedo and sudden rise of the surface albedo, which follows the year's first snow covering over ground.
The phase lag in the seasonal variation of temperature against outer atmospheric solar radiation is analytically solved. The results show that the phase lag of temperature at the surface against outer atmospheric solar radiation depends on the oceanicity and is independent of the surface albedo. The phase lag at the 500mb level depends on the oceanity and even the surface albedo, which is larger over higher latitudes. Namely, the phase of the 500mb level temperature retards much more over lower latitudes, where the albedo is smaller than over higher latitudes.
