A trough and a cyclonic vortex are both weather patterns that can be identified on a weather map.
A trough is a region of low atmospheric pressure, which is typically associated with the formation of clouds and precipitation. On a weather map, a trough is represented by a curved line with arrows pointing in the direction of the winds along the trough. The arrows pointing towards each other indicates the winds are converging, which can lead to lift and thunderstorm development.
A cyclonic vortex is a rotating weather system that is characterized by a center of low pressure. The winds circulate around the center in a counter-clockwise direction in the Northern Hemisphere and clockwise direction in the Southern Hemisphere. This is known as the "cyclonic flow" or "cyclonic circulation" The circulation can be seen as a large spiral pattern on the map, which is usually represented by a series of closed isobars. This feature is often seen as a low pressure system and usually produces clouds, rain and sometimes severe weather.
Troughs and cyclonic vortexes can be identified on a weather map by looking for regions of low pressure, represented by contours of low pressure called isobars, and by looking for the characteristic flow patterns of the winds around these systems. They can also be identified by analyzing satellite images, which can show the clouds and precipitation associated with these systems.