Why are the chinook winds coming down a mountain warm, as opposed to the katabatic winds which are cool?

MIKE MOSS SAYS:      Cathy,    Chinook winds refer specifically to synoptically driven winds over the central and northern Rockies that flow across the mountain ridge and then down the other side, some of the air being drawn downward from mid-troposhperic levels, and often replacing a previously existing polar or arctic airmass that was already in place on the lee side of the mountains. In addition to being driven across the mountains by large scale pressure patterns (high and low pressure centers) the air in a Chinook may have enough moisture on the windward side of the mountains to create clouds and precipitation as it flows up the windward slopes. By losing moisture in this way as the air ascends the slope on one side (cooling at something called the moist adiabatic rate)  the air is set up to warm by compression on the other side of the slope at a faster rate (called dry adiabatic) so that it is warmer at the same altitude than it was before it encountered the ridgeline. The combination of downslope flow, compressional warming and the replacement of a pre-existing cold air mass (and sometimes the disruption of a strong, shallow temperature inversion on the lee side of the mountains) can result in rapid warming on the downwind side of the mountain. In addition, depending on the stability of the airmass being pushed across the mountains, a mountain wave may form which involves strong up and down motion of the air for some distance to the lee of the mountains. This can result in strong wind gusts at the surface. Also, when moisture is removed from the air due to upslope precipitation on the windward side of the mountain, the air on the downslope side can end up especially dry, causing rapid melting and sublimation of snow, or strong drying of natural fire fuels and thus an enhanced potential for wildfire. These same kinds of winds in other locations have various names, but work on the same principle. The generic name for this phenomena is Foehn wind, and the Chinooks are considered a regional type of Foehn, as are the Santa Ana winds in the southwest associated with air forced across the Sierra Nevada range.

The most common meaning of a generic katabatic wind, on the other hand, refers to air near the slope of a mountain or ridgeline (or perhaps atop a plateau in some cases) that cools radiatively late in the day or at night, becomes cooler than the air at the same altitude farther away from the side of the mountain, and begins to flow downhill due to its greater density. This air doesn't originate on the other side of the ridge or at mid-levels of the troposphere and is not forced along by large scale high and low pressure systems, and while it will warm due to compression as it flows toward lower elevations, it will typically be colder than the air it replaces when it arrives there.

Some broader definitions of katabatic treat the word as describing any wind flowing toward a lower elevation. In that case, foehn winds would be a class of katabatic wind, and the katabatic wind I just described would be considered a small slope flow or part of a mountain-valley circulation. These circulations usually involve anabatic flows during the daytime, when solar heating of the surface, and thereby air in contact with the surface, results in air with a lower density and pressure than surrounding air, which then flows upslope, the opposite process from that producing localized katabatic flows.