How to explain the meteorological proverb "the river is foggy and sunny, and the mountain is foggy and rainy" with scientific knowledge?

There is fog on the river, indicating that the current weather situation is windless; On the other hand, it shows that the water surface temperature is lower than the high altitude, which is called "inversion temperature".

When the temperature is reversed, the weather conditions are generally stable, there is no convection up and down, and rainfall cannot be formed, so it is sunny.

There is fog on the mountain, that is, there is fog on the height.

The fog in the sky is formed by the condensation of water vapor in the updraft.

There is updraft and water vapor condensation, and there are some conditions for rain formation, but it may not rain.

Whether it must rain in foggy mountain areas depends on whether other conditions are met.

In some places, the mountains are covered with fog in the morning, and the sun disappears after it comes out.