A police radar is designed to detect vehicle speed and has a limited distance due to a low transmitted power and a small-size antenna.
The same principle (Doppler effect) can be and is used in weather radar. A larger antenna is needed as well as a higher transmitted power. FM-CW mode with a wideband signal frequency sweep is used to detect rain drops and heavy clouds.
A simple device that can detect clouds and rain is a radiometer; a sensitive microwave receiver with a suitable antenna works quite well, detecting water emission at microwaves.