Nowadays, many studies have been done to measure the urban extension and distribution horizontally. On the other hand, I am looking for your help to advise me for which kind of models and softwares that can measure the urban growth vertically.
Another option of software is Quantum GIS, which is opensource, highly customizable with LOTS of free plugins, developed using Pyhton (flexible, very popular between academics, good support community, and platform independent). Whatever software you eventually decide to use, the crucial aspect to have in mind is theory and method to approach your study phenomena. Your aims and goals, as well as the intended application are relevant to a more precise answer.