We have observed variations at the several centimeter level in estimates of the vertical coordinate of site position. The estimates are obtained from our analysis of data acquired from the Swedish permanent Global Positioning System (GPS) network. The observed variations are strongly correlated with changes in the indirectly inferred accumulation of snow, which we assume collects on the radomes and pillars; the GPS sites could not be observed directly due to their remoteness. Numerical simulations which assume a simple geometry for the snow cover are used to study the effects of snow accumulation on GPS phase observables and hence on estimates of the vertical coordinate of site position obtained from these observables. Our results indicate that the variations in the vertical coordinate of site position can be fully explained by reasonable accumulations of snow which retard the GPS signals and enhance signal scattering effects. ¿ American Geophysical Union 1996