Ice mechanical properties, and hence the response of glaciers to climate change, depend strongly on the presence of liquid water at ice-grain boundaries. The propagation velocities of radar and seismic waves are also highly sensitive to this water. Mixing laws, typically the Looyenga and Riznichenko formulae, have traditionally been used to quantify liquid water content within glaciers from such velocity data; however, it has become apparent that these mixing laws are geometrically inconsistent. We present an inclusion-based effective medium approximation in which we model water inclusions within solid ice. Two types of inclusions are used: spherical inclusions to represent water in the grain junction nodes, and high-aspect ratio spheroidal inclusions to represent water in the grain boundary veins. We apply this model to radar and seismic data from a polythermal glacier in Svalbard to quantify both inclusion geometry and the unfrozen water content within the warm ice.