Thermal distortion parameters are proposed to evaluate the intensity of thermal blooming effect of repetitively long pulse laser. A numerical simulation model of thermal blooming effect of repetitively long pulse laser is established, and experiments are carried out. By comparing the simulation results with the experimental results, we find that the experimental results are agree well with the simulation results in terms of spot shape and size, which verifies the reliability of the mathematical-physical model of repetitively long pulse laser and the simulation algorithm. On this basis, the quantitative relationships between the spot expansion and the thermal distortion parameters caused by the repetitively long pulse thermal blooming effect, named scaling laws of thermal blooming effect of repetitively long pulse laser, are obtained by a large number of numerical simulations under different atmosphere parameters and launching system parameters.