Lee Troughs

This is a sample lesson page from the Certificate of Achievement in Weather Forecasting offered by the Penn State Department of Meteorology. Any questions about this program can be directed to: Steve Seman


When you've finished with this page, you should be able to discuss how lee troughs form (aloft and at the surface), and what their implications are for surface convergence and lower tropospheric moisture transport.


The upper-air pattern is critically important to mesoscale forecasters for a number of reasons, some of which you already saw in our discussion of the big picture at 500 mb. Another reason that the upper-level pattern is important is that it can affect where surface boundaries develop. One such way this can happen is with the development of "lee troughs."

When strong westerly winds blow across the Rockies, a trough typically forms in the lee of the mountains (the side facing away from the wind, where winds blow down the slope) over the western high plains. For the record, similar troughs can form sometimes in the lee of the Appalachians and other smaller mountain ranges, too. These troughs are called lee troughs because of the location where they develop. The 700-mb chart at 12Z on January 1, 2004 (right image below), shows a classic height pattern consistent with fairly strong southwesterly winds that set the stage for a lee trough to form (note the trough that is evident east of the Rockies).

Left: Topographic map of the US. Right: Pattern of 700-mb heights conducive to the formation of a lee trough.
(Left) The Rocky Mountains (high resolution). (Right) The 700-mb analysis at 12Z on January 1, 2004, shows a classic height pattern consistent with fairly strong southwesterly winds and the formation of a lee trough east of the Rockies.
Credit: Earth System Research Laboratory

How does a lee trough form east of the Rockies (and, to a lesser extent, east of the shorter Appalachians)? In your previous studies, you learned about absolute vorticity, which we expressed as z + f (relative vorticity plus planetary vorticity). Monitoring the change in an air parcel's 500-mb absolute vorticity with time and linking to mass convergence or divergence indicates that absolute vorticity is not a "conserved" property. In other words, an air parcel's 500-mb vorticity changes in time -- it's not constant, or "conserved." We're in luck, however, because Ertel's Potential Vorticity is a conservative property for relatively large-scale motions in the atmosphere. Mathematically,

Equation for Ertel's Potential Vorticity
The conservation of Ertel's potential vorticity involves the give-and-take between relative vorticity, the Coriolis parameter and the height of an air parcel or air column.
Credit: David Babb

where z is relative vorticity, f is planetary vorticity, (z + f)/H is Ertel's Potential Vorticity and H is the height of an air parcel (or air column). The above equation asserts that the ratio of an air parcel's (or air column's) absolute vorticity to its height is always conserved.

Conceptually, this relationship should make sense to you, as visualized in this animation of a parcel with a changing rate of spin. A parcel (or column) that spins faster (has greater absolute vorticity) must also get taller as convergence occurs (remember that mass and angular momentum are also conserved). Meanwhile, a parcel (or column) that spins slower (less absolute vorticity) must get shorter as divergence occurs.

Therefore, assuming the absolute vorticity of an air column is positive (cyclonic), any stretching in the vertical results in an increase in cyclonic spin (in other words, an increase in absolute vorticity). Let's see if we can apply this idea to the interaction between westerlies and mountains in the mid-latitudes to see how a lee trough forms.

Suppose a column of air extending from the ground to the tropopause moves directly eastward toward the Rockies (see below). Further assume that its relative vorticity is zero (no shear or curvature) and that the planetary vorticity is 10 x 10-5 seconds-1. With these assumptions in mind, let's follow the air column up a mountain (as illustrated by the chalkboard diagram below). Clearly, H starts to decrease since the distance from the surface to the top of the troposphere is smaller on top of the mountain.

A chalkboard diagram showing an air column passing over a mountain range and forming a lee trough.
Assuming a westerly wind, an eastward-moving air column (parcel) ascending the windward slopes of the Rockies must make an anticyclonic turn in order to conserve Ertel's Potential Vorticity. After reaching the summit and descending the lee side of the mountains, the column's relative vorticity must increase to offset the increasing H and the decreasing f. Thus, the column transitions to a cyclonic turn, forming a lee trough east of the Rockies.
Credit: David Babb

In order to conserve Ertel's Potential Vorticity, the column makes an anticyclonic turn and heads southward. Why southward? First, both z (relative vorticity) and f (planetary vorticity) must decrease in order to offset the decrease in H. Recall that the initial relative vorticity was zero, so a decrease in z translates to negative (anticyclonic) relative vorticity. Okay, once the column reaches the summit and starts to descend the lee slopes, H increases (the column stretches vertically). The only way to offset this increase in H is for the relative vorticity of the southward-moving column (toward lower values of planetary vorticity) to increase. Thus, the column starts a cyclonic turn, gradually tracing out a trough east of the Rockies. This cyclonic turn is consistent with the vertical stretching and column spin-up that I discussed earlier.

Once the air parcel completes the cyclonic turn and heads northward, relative vorticity will start to decrease to offset the increase in f (remember, planetary vorticity increases with increasing latitude). The parcel will eventually start an anticyclonic turn that will cause it to move in a southward direction. In essence, steady westerly flow over the Rockies results in a lee trough east of the mountains and then an dampening series of wave-like motions farther east. The presence of an upper-air trough in the lee of the mountain range can make the region ripe for cyclogenesis.

But, lee troughs aren't just an upper-air feature. After parcels in the fast southwesterly flow pass the crest of the Rockies, they blow down the slopes of the eastern side of the Rockies and warm via compression. That warming lowers the density of local air columns, resulting in the formation of a surface trough of low pressure. For example, note surface trough at 12Z on January 1, 2004 (the same time as the 700-mb map above).

Given the surface lee trough that forms as well, in response to the warming of downsloping air columns via compression, lee troughs create a zone of surface convergence. But, that's not the whole story with respect to their impact on surface weather. Lee troughs can also help draw moist air northward from the Gulf of Mexico as wind flow in the lower troposphere turns more southerly ahead of the trough. Indeed, lee troughs can aid in the formation of dry lines (recall that dry lines are boundaries between moist and dry air). For example, the strong southwesterly flow aloft over the southern Rockies, as seen on this 700-mb analysis from 12Z on June 10, 2004, resulted in the formation of a lee trough. Within the lee trough that developed along the Texas / New Mexico border, a dry line developed (check out the 12Z surface weather map from the date) as moist air from the Gulf of Mexico accelerated northward east of the trough, increasing dew-point gradients and thereby helping to create the dry line.

Increased low-level moisture (higher dew points) acts to reduce CIN, as you've learned, which can make the environment more favorable for thunderstorm development. So, there's no doubt that forecasters want to keep their eye on the formation of lee troughs! We'll certainly encounter them again. With this background out of the way, let's turn our attention more generally to surface boundaries and the roles that they play in initiating deep, moist convection. Read on.