High sensitivity temperature-programmed desorption mass spectrometry (TPDMS) was employed in order to investigate the desorption kinetics of CCl4 from thin (similar to 500 ML (ML: monolayer)) amorphous D2O ice films. TPDMS experiments demonstrate that at low coverages CCl4 is trapped in the pores near the surface of microscopically rough ice. Three distinct desorption features, mu, delta-, and epsilon-CCl4, consistent with the release of trapped CCl4 were observed. The mu-, delta-, and epsilon-CCl4 desorption yields demonstrate high sensitivity to the temperature and rate of ice film deposition. We interpret these results as evidence of the existence of three metastable forms of microporous amorphous ice, I-mu, I-delta, and I-epsilon. Measurements of the relative desorption yields from CCl4 species trapped at the surface of ice films prepared at different temperatures and deposition rates were used in order to estimate the barriers to the diffusion of D2O on the surface of I-delta (E-D delta) and I-epsilon (E-D epsilon). The values obtained were E-D delta = 5 +/- 1 kcal mol(-1) and E-D epsilon = 9 +/- 2 kcal mol(-1). We suggest that I-mu, I-delta, and I-epsilon can be characterized respectively by the relative abundances of two-. three-, and four-coordinated D2O molecules at the ice surface. A proposed phase diagram for thin D2O ice films is presented.