Based on the equation of atmospheric pollutant mass conservation, the meteorological factors which affect air pollution are constructed and daily increment of air quality index (AQI) is taken as the object to quantitatively classify the air pollution potential. The atmospheric circulation background is divided into cold, mixed and warm-air circulations in autumn and winter by the Q-type cluster analysis method. Then the meteorological factor and its thresholds for distinguishing three types of atmospheric circulation are studied. Based on autumn-winter atmospheric data during 2017-2019, the five-grade prediction models of pollution potential are established, and the discriminant accuracies are 80.0%, 71.0% and 74.7% for cold, mixed and warm-air circulations respectively by the use of the Bayes discriminant analysis method. The mean accuracy of three air types reaches 75.2%. When the five-grade prediction models of pollution potential are tested with autumn-winter atmospheric data during 2015-2017, the mean accuracy of the three air types can reach 63.6%. Through comparison of atmospheric self-purification index (ASI) and the results from the five-grade prediction models of pollution potential with daily increment of AQI in autumn and winter from 2019 to 2021, the five-grade prediction models of pollution potential discriminant results are more consistent with the daily increment trend of AQI than ASI, and the correlation coefficient exceeds 0.67. The correct times of the five-grade prediction models of pollution potential for extremely favorable and extremely unfavorable pollutant diffusions are significantly more than by AQI.