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This is an example of a habit I have of
"beating some concepts to death."  The rather busy picture below illustrates how small changes in how air temperature changes with increasing altitude can determine whether the atmosphere will be stable or unstable.   Just for the purposes of illustration imagine riding a bicycle north from Swan and River Rd up the hill to Swan and Sunrise (fhe figure shows an elevation change of 1000 ft, it is actually quite a bit less than that). 



At far left the air temperature goes from 47o F to 41o F, a drop of 6o F.  This is a fairly rapid rate of decrease with increasing altitude and would make the atmosphere absolutely unstable.  The atmosphere wouldn't remain this way.  Air at the ground would rise, air higher up would sink, and the temperature profile would change (the rate of decrease with increasing altitude would lessen).  In some ways it would be like trying to pour vinegar on top of oil in a glass.  The lower density oil would rise because it would "want" to float on top of the higher density vinegar.

The next picture shows air temperature decreasing a little more slowly with increasing altitude.  This small change makes the atmosphere conditionally unstable (we won't go into what the conditions might be).  The atmosphere is often in this state. 

The atmosphere cools only 2o F in 1000 feet in the next picture.  This creates an absolutely stable atmosphere.  Air at the ground will remain at the ground and won't rise and mix with air higher up.  Compare this with the glass containing vinegar and a layer of oil on top.  The two layers won't mix.

Air temperature in the last figure actually increases with increasing altitude.  This is a temperature inversion and is very common on winter mornings.  The atmosphere is extremely stable under these conditions. 

Temperature inversions are something you can check out for yourself.  Head north on Swan Rd. on your bicycle early some winter morning.  You will pass through some pretty cold air as you cross the Rillito River.  By the time you get to Sunrise, the air can be 10 to 15 degrees warmer and will seem balmy compared to the cold air at the bottom of the hill.  If you're up for a real hill-climbing challenge continue north on Swan past Skyline.  You'll find a short but very steep section of road at the far north end of Swan.



And as long as we're talking about bicycle riding.  I was in France in July 2009 trying to ride my bike up some of the famous Tour de France mountain stages in the Alps.  One of the most famous is the Alpe d'Huez.  That's my bicycle below, a green "Gilmour" (Andy Gilmour is a local bicycle builder) at the top of the Alpe d'Huez.



I was back in France, in the Pyrrennees in 2010.  The next picture shows the last 3 or 4 km of the road to the summit of Mt. Ventoux, another famous Tour de France climb.