We have measured the electron-stimulated desorption of metastable molecular nitrogen (N-2*) from N-2 condensed onto solid thin films of water of varying preparation. Structures seen in the N-2* yield function permit the quantity of N-2 at the film-vacuum interface to be monitored and hence allow one to study changes in the effective surface area of the water film. This latter quantity is itself related to the porosity of the film. When deposited onto porous water, N-2 molecules penetrate into the film and throughout its pores covering their large surface area. Under these conditions, the signal of desorbing N-2* particles is inversely proportional to the surface area of the pores. We present a simple model for N-2 film growth on a porous film. Its mathematical formulation allows the pore area and pore volume of amorphous water films to be measured. The surface region of crystalline water films is also found to be rough. Moreover, the porosity of solid water films is found to be dependent on the substrate on which the film is grown.