By introducing the temporal correction coefficient, which is defined as the ratio between the closed loop wavefront residual error and the open loop error induced by atmospheric turbulence, and the measured signal to noise ratio, the temporal correction effectiveness of adaptive optical system for light wave atmospheric propagation is studied. Its dependence on the power law exponent of the turbulence, the cut off frequency, the measured signal to noise ratio, the time delay and the closed loop bandwidth is analyzed. The optimal closed loop bandwidth is given. The temporal compensation effectiveness of 61 element weak light adaptive optical system is also analyzed.