Аннотация:Abstract. Experts in the field of mathematical modeling of the climate systemhave different views on the class of models that should be employed to analyze andpredict climate for time scales corresponding to climatic processes. In this paper,we investigate the properties of a model constructed using the hydrostatichypothesis. A one-dimensional (horizontally homogeneous) hydrostatic model of adry atmosphere is considered. Air is considered an ideal gas. The source of heat isthe external short-wave radiation flux entering the upper boundary of theatmosphere. This energy is partly absorbed by atmospheric layers and theunderlying surface, partly returned to space. The atmospheric layers and theunderlying surface radiate in the long-wave range. In general, the absorptioncoefficient and heat capacity are specific for the atmospheric layers and areeverywhere positive. In the model, the radiation balance of a segment of theatmospheric column above a unit area of the underlying surface determines thechange in the internal energy and the volume occupied by the segment. Thepressure value always remains equal to the weight of a part of the atmosphericcolumn above the segment (hydrostatic hypothesis). The underlying surface isalways in the state of radiation equilibrium. Under these assumptions: a) there is asingle equilibrium vertical temperature distribution in the column andcorresponding air pressure and density distributions (they are calculated using thehydrostatic assumption and the equation of a state of the ideal gas); b) thetemperature distribution is asymptotically stable, i.e. any other initial distribution ofnon-negative temperature values tends with time to equilibrium uniformly on thevertical. Thus, one can expect that the numerical analogs of the model consideredin this work will also be stable, which is important for the computationalimplementation of both the one-dimensional model and its three-dimensionalversions.Keywords. Dry atmosphere, one-dimensional model, hydrostatic hypothesis,equilibrium state, asymptotic stability.