Kinetic growth metamorphism lowers the mean number of bonds between the ice particles in snow. During the beginning state of snow metamorphism, at a large mean temperature gradient, significant particle growth occurs only at preferred growth sites. Three-dimensional approximations of the sink-source geometry are introduced to model particle growth and shrink rates. The calculations show that enhanced growth occurs at very small and at large sink-source distances. The consideration of growth rate enhancement by differences in radii of curvature between sink-source particles accounts for metamorphism at very low mean temperature gradients. Final particle size distributions and the reduction of the particle number density by metamorphism are calculated and may be compared with measured distributions.