Inverted troughs, also known as easterly waves in the tropics, are one of the factors that increase the chance of monsoon storms. Tracking hurricanes in both the Atlantic and East Pacific, you will notice the general movement in the tropics is from east to west. The storms are basically blown from east to west by the Trade Winds at latitudes close to the equator.
Within this air flow are waves, which form an inverted trough as they amplify (get bigger from top to bottom).
Generally troughs that form in the jet stream that runs across the United States dip south. An inverted trough is the opposite of that and extends northward. An area of low pressure forms at the tip of the inverted trough, creating an area of rising air, which usually results in enhanced storm development.
The inverted troughs that reach eastern Mexico travel west over the country with the tip of the inverted trough sometimes close enough to southern Arizona to increase afternoon storm chances.
Research out of Colorado State University suggests storm development is more likely along an inverted trough. Through analysis of an inverted trough tracked during the North American Monsoon Experiment (NAME), it was discovered the area of significant storm development is on the leading edge or western flank of the inverted trough. This is an area where winds at different levels of the atmosphere are blowing in varied directions, creating shear, which in turn creates an favorable area of storm formation.