Along with peak and trough divergences, the AO also can identify trend exhaustion points. Similar to the way RSI works (which identifies areas of extreme overbought and oversold areas) the AO direction diverging with price direction often occurs at end-of-trend areas as the above blue boxes show. Moreover, these end of trend areas are displayed even when RSI does not show overbought or oversold conditions. As you can see, in these blue box areas, the direction of the AO contradicts the direction of price indicating overbought and oversold areas.
I also term these areas as "momentum". This concept of momentum is different than the concept of momentum usually taught in trading courses. In trading courses, you will hear momentum defined as existing throughout a long trend. But in fact, this way of identifying momentum is useless because with their definition of momentum, it continues to exist after the real end of trend areas, until price confirmation exists indicating lower lows. But at that time money has already been lost.
Truly, in the world of physics, momentum is movement caused by an initial force on an object. Since acceleration is a component of force (and we are looking at a plot of market acceleration) you can see that in these blue areas the market is continuing in its direction as acceleration subsides. This is consistent with the physical definition of momentum, and so this new definition has scientific support.
Real price momentum reflect areas where weak hands require some kind of price confirmation before jumping in. This is consistent also with "following the leader", the leader being the initial force of the move, of which, again, acceleration is a component. If you instead follow acceleration, you can become the leader, that initial force, yourself.