Why does lightning appear on cloudy days?

Lightning is a discharge phenomenon in thunderstorm clouds. The formation of thunderstorm clouds should meet certain conditions, that is, there should be enough water vapor in the air, the power to make wet air rise, and the air should be able to produce strong convection. Spring and summer are affected by the warm and humid airflow in the south, with humid air and strong solar radiation. The air near the ground is constantly heated up, and the upper cold air sinks, which is easy to form strong convection, so there are many thunderstorms and even hail. In winter, controlled by the continental cold air mass, the air is cold and dry, the solar radiation is weak, and the air is not easy to form violent convection, so thunderstorms rarely occur. But sometimes the weather is warmer in winter, and the power of warm and humid air is stronger. When the cold air in the north occasionally goes south, the warm and humid air is forced to rise, and the convection intensifies, so-called "thunder into winter" phenomenon will occur. Meteorologists also say that the occurrence of thunderstorms does not depend on the temperature itself, but on the upper and lower distribution of temperature. In other words, although the temperature is not high in winter, if the temperature difference between the upper and lower reaches a certain value, strong convection can also be formed, resulting in thunderstorms. Thundering in winter is rare in China, but when the air in Toronto is extremely unstable in winter, it is easy to have strong upward convection and form towering cumulonimbus clouds. Clouds are full of water vapor running up and down, which will generate static electricity. The upper end of the cloud will produce positive charge, the lower end of the cloud will produce negative charge, and the ground will be positively charged. Then, there is air as an insulator between positive and negative charges. If the voltage difference between positive and negative charges is large enough to break down the insulator.