Abstract:What is it that makes atmospheric data assimilation come to be a discipline with its own theoretically mathematical foundation and formalism? In this article it is highlighted that the random variable is the fundamental concept of atmospheric data assimilation. This lies in two aspects. First, probability theory and mathematical statistics, which are oriented to random variables, can be used as the mathematical foundation of atmospheric data assimilation, and thus atmospheric data assimilation is equipped with its mathematical formalism which is derived from its criterion for an optimal estimate on the basis of estimation theory. So in this sense the essence of science for atmospheric data assimilation is built on the concept of random variable. Second, data under the concept of random variable can find a way to understand the clear step by step expansion of useful information contents used during the historical progress of atmospheric data assimilation, which helps to know a simple cognitional intrinsic logic of development of atmospheric data assimilation.