Often if there is not any real weather happening, the lack of real weather return can allow for other returns that are really noise to surround the area near the actual radar dish or array. If you think about it this makes sense. Signal to noise ratios would naturally enhance noise when a legitimate signal is not present. The things that would produce the noise include ground clutter and anomalous propagation. The reason it is always centered nearby the radar station is because areas further away will be at lower angles on a curved earth compared to areas closer to the radar station. When significant weather targets exist in the area, the Signal becomes much stronger for that weather return. Thus the noise that remains fairly constant is not a significant return energy compared to the signal so it is filtered out and thus your weather radar map does not show the noise.
Often if there is not any real weather happening, the lack of real weather return can allow for other returns that are really noise to surround the area near the actual radar dish or array. If you think about it this makes sense. Signal to noise ratios would naturally enhance noise when a legitimate signal is not present. The things that would produce the noise include ground clutter and anomalous propagation. The reason it is always centered nearby the radar station is because areas further away will be at lower angles on a curved earth compared to areas closer to the radar station. When significant weather targets exist in the area, the Signal becomes much stronger for that weather return. Thus the noise that remains fairly constant is not a significant return energy compared to the signal so it is filtered out and thus your weather radar map does not show the noise.
https://blog.foreflight.com/2015/07/30/when-the-radar-lies/