Unfortunately the link is broken, so I cannot see how this has been done.
I can however, based on what you have said and my understanding of it, point out how things could be done.
The following is how I identify Ponding / Water Storage Areas - possibly you could modify this to fit your needs.
1) Take a contour dataset and convert this to a TIN and then to raster (This raster dataset is your untouched original)
2) Can be done in two ways (a or b)
a) Take the original raster from 1 and perform a "Surface Fill" (located in the Spatial Analyst - Hydrolocial Tools), These may be tweaking required to get a decent result, but basically this tool fills all the holes or depressions in the raster surface to create a hydrological surface that allows for water to pass freely over it. Effectively this should "fill in" the sinkholes in the contour dataset.
b) Is similar to a, except you use the topo to raster interpolation in 3D or Spatial Analyst. One of the parameters in this interpolation is the number of iterations the interpolation is allowed to run, the more the process runs, the more smooth the surface will become. Effectively the result is similar to a.
3) After you have run a or b you can use the raster calculator to subtract the original raster (1) by the modified raster (2a or b), the result will be a raster with values from 0 to -xxx. Where 0 are areas where there was not alteration to the raster from filling in depressions and the -xxx are areas where the were depressions filled.
4) Running the contour tool on this raster will give you the contours of the sink holes. From the 0 contour down to the deepest - If you want it the other way around simply subtract Raster 1 from Raster 2a or b.
I am not sure if I have helped you or missed the point completely, but hopefully once the correct link is put up I can see what you needed.
Good luck, I look forward to reading the article.