Water collected between towers

Water collected between towers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

In a two-dimensional world, we begin with any bar-chart (or row of close-packed 'towers', each of unit width), and then it rains, filling any convex enclosures in the chart with water.

9               ██           9               ██    
8               ██           8               ██    
7     ██        ██           7     ██░░░░░░░░██    
6     ██  ██    ██           6     ██░░██░░░░██    
5 ██  ██  ██  ████           5 ██░░██░░██░░████    
4 ██  ██  ████████           4 ██░░██░░████████    
3 ██████  ████████           3 ██████░░████████    
2 ████████████████  ██       2 ████████████████░░██
1 ████████████████████       1 ████████████████████

In the example above, a bar chart representing the values [5, 3, 7, 2, 6, 4, 5, 9, 1, 2] has filled with 14 units of water.

Write a function, in your language, from an array of heights, to the corresponding number of such water units.

(See, for example, 'Water collected between towers' on Stack Overflow, from which this example is taken).