The theoretical foundations of the exponential and power-law analytical formulations for the size–frequency and intensity–frequency distributions of the convective vortices, including dust devils, are re-examined. Jaynes’ general statistical arguments based on Shannon’s entropy maximum principle leading to an exponential distribution are supplemented by Rényi’s maximum entropy principle which is shown to lead to a power-law distribution. In both cases, a key ingredient of the theory is the a priori knowledge of a first finite moment of the distribution. Applications to statistics of convective vortices, including dust devils, on Earth and Mars are discussed. The existence of a finite expectation value of the vortex diameter related to the absolute value of the Obukhov length scale in the atmospheric boundary layer allows a quantitative explanation of a burst of convective vortex activity observed at the InSight landing site in northern autumn on Mars.

重新审视了包括尘卷风在内的对流涡旋的大小-频率和强度-频率分布的指数和幂律分析公式的理论基础。Jaynes 基于香农熵最大原理导致指数分布的一般统计论点得到 Rényi 最大熵原理的补充，该原理被证明导致幂律分布。在这两种情况下，该理论的一个关键要素是对分布的第一个有限矩的先验知识。讨论了地球和火星上对流涡旋（包括尘暴）统计的应用。