A stochastic approach to the solution to the differential equation of heat transfer in the atmosphere

Abstract

Abstract In this work, a model of heat transfer in the atmosphere is proposed. This model is based on a stochastic interpretation of the velocity vector components. Histograms of the wind speed distribution averaged over a relatively short time interval are obtained and analyzed. The proposed model is formulated based on empirical distributions. Explicit expressions for the first and the second-moment functions solving the heat transfer equation with random coefficients are presented. A function that estimates errors resulting from replacing a random coefficient in an equation with its mathematical expectation is also obtained. An example that demonstrates the effectiveness of the proposed approach in the case of a Gaussian distribution of the horizontal component of wind speed is presented. In this case, the first and second-moment functions in the frame of the proposed model are presented.