Stochastic Model of Heat Transfer in the Atmospheric Surface Layer

A new stochastic model of heat transfer in the atmospheric surface layer is proposed. The model is based on the experimentally confirmed fact that the horizontal wind velocity can be treated as a random process. Accordingly, the model is formalized using a differential equation with random coefficients. Explicit formulas for the expectation and the second moment function of the solution to the heat transfer equation with random coefficients are given. The error induced by replacing the random coefficient of the equation with its expectation is estimated. An example is given demonstrating the efficiency of the proposed approach in the case of a Gaussian distribution of the horizontal wind velocity, when the expectation and the second moment function can be determined within the framework of model representations.