Learn English – Term for catchy tune that stays in your head

If the source of the water is rain on its way to the river on flat saturated ground and not an overflow from the river it is called ponding or ponded field, it is one of several types of flooding

Ponding is a type of flooding that can happen in relatively flat areas. Rain water falling in an area is normally stored in the ground, in canals or lakes, or is drained away, or pumped out. When more rainwater enters a water system than can be stored, or can leave the system, flooding occurs. In this case, rain is the source of the flood: not water coming from a river, but water on its way to the river. That's why it is also called "pluvial flood".
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It is the term used in scientific literature

An analytical solution is provided for predicting time dependent seepage into an array of equally spaced parallel ditch drains in a homogeneous and anisotropic soil medium underlain by an impervious layer and receiving water from a ponded horizontal field of infinite extent. The solution can account for both unequal levels of water in the adjacent drains and variable depths of ponding at the soil surface.
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The song itself can be said to be an earworm:

An earworm, sometimes known as a brainworm, sticky music, or stuck song syndrome, is a catchy piece of music that continually repeats through a person's mind after it is no longer playing.

This is not necessarily a derogatory term, although the experience is often negative.