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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.
Classical weather radar systems are pulse radars, as effectively all civil and military radar systems. They are using doppler speed detection in addition (like other radar systems, too). For an overview of technical principle, see Weather radar - Wikipedia, the free encyclopedia
Police speed trap uses small band CW doppler and thus can't determine distances or perform a distance filtered measurement.
The basic design of a traffic radar usually sends out a continuous tone and determines the vehicle speed by measuring the doppler shift. Weather (and most other) a emit a string of pulses to measure range. Most weather radars are of this type.
I don't see how you could easily interchange the two applications.
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