The ringed-energy-radius and expansion of the long-exposed far-field central patterns of the high-energy (HEL) laser and its sampled one propagating in the turbulent atmosphere are compared by numerical calculation, the results show that: both of them are the same in the merely turbulent situation, and the thermal blooming leads to attached expansion of the pattern; the smaller the transmission of the sampler is, the less the effect of thermal blooming on the attached expansion of the pattern is; the attached expansion of the central pattern of the high-energy laser with respect to its sampled one is due to the thermal blooming. The atmospheric thermal blooming effects thus can be diagnosed by the methods of utilizing the beam wavefront sampler and comparing the characteristics of the far-field central patterns of the high-energy laser with its sampled one propagating in the turbulent atmosphere.