Surfaces in the Outer Solar System are sufficiently cold (< 50 K) that amorphous solid water (ASW) should be present. One property of ASW is its porosity, which allows for volatile species to condense within the internal pore network. The extent of this interior pore network can potentially have a strong effect on the chemical evolution of any icy surface. Previous laboratory studies have mainly focused on porosity in the context of thin interstellar ice mantles. Here we were interested in investigating to what extent the porosity and subsequent gas adsorption properties of ASW change as one moves towards thicker samples more representative of ices found in the outer solar system. Here we present some of our most recent results that examine the interconnectivity of the internal pore structure of ASW as a function of sample thickness, which we determine using a combination of infrared spectroscopy, ultraviolet-visible spectroscopy and microbalance gravimetry.