Modern AD radars try to avoid being affected by weather, by design. The acquisition process is much the same with any radar, although fighter radars cover, generally, about 120 degrees based on the aircraft centreline, more using electronic scanning - not 360 yet.
Due to a different beam width, search mode requires consecutive sweeps at stepped elevations, but the display is not much difference, apart from using a range/closure against azimuth display rather than the plan display you would be used to. That causes a distortion of the display, but offers much better azimuth resolution at closer ranges, where it counts.
Other modes are available.