Severe haze or low-visibility events caused by abundant atmospheric aerosols have become a serious environmental issue in many countries. A framework based on deep convolutional neural networks containing more than 20 million parameters called HazeNet has been developed to forecast the occurrence of such events in two Asian megacities: Beijing and Shanghai. Trained using time-sequential regional maps of up to 16 meteorological and hydrological variables alongside surface visibility data over the past 41 years, the machine has achieved a good overall performance in identifying haze versus non-haze events, and thus their respective favorable meteorological and hydrological conditions, with a validation accuracy of 80 % in both the Beijing and Shanghai cases, exceeding the frequency of non-haze events or no-skill forecasting accuracy, and an F1 score specifically for haze events of nearly 0.5. Its performance is clearly better during months with high haze frequency, i.e., all months except dusty April and May in Beijing and from late autumn through all of winter in Shanghai. Certain valuable knowledge has also obtained from the training, such as the sensitivity of the machine's performance to the spatial scale of feature patterns, that could benefit future applications using meteorological and hydrological data. Furthermore, an unsupervised cluster analysis using features with a greatly reduced dimensionality produced by the trained HazeNet has, arguably for the first time, successfully categorized typical regional meteorological-hydrological regimes alongside local quantities associated with haze and non-haze events in the two targeted cities, providing substantial insights to advance our understandings of this environmental extreme. Interesting similarities in associated weather and hydrological regimes between haze and false alarm clusters or differences between haze and missing forecasting clusters have also been revealed, implying that factors, such as energy-consumption variation and long-range aerosol transport, could also influence the occurrence of hazes, even under unfavorable weather conditions.