Heat radiation transfer in the Earth atmosphere

There are three types of heat radiation transfer in the Earth atmosphere calculation are compared at this work. They are: direct (exact precise) line-by-line calculation, exact Lebesgue average method calculation and fast approximate Lebesgue calculation. An approximate Lebesgue calculation use simplified procedure of Lebesgue’s coefficient assembly. The difference between the direct and the both Lebesgue's methods don't exceed 5%. The computing resources retrenchment are more than 10000 times in Lebesgue's calculations. The fast procedure of Lebesgue's coefficient assembly leads to additional essential operations economy. All calculations are executing by the finite-analytic discrete scheme for the even-odd kinetic equations set. The fast procedure Lebesgue's coefficient assembly makes it possible to execute a set of similar calculations of atmospheric radiations. The database of fast Lebesgue's coefficient assembly might be used by unqualified users on the base of any transport code.