Presently a unified treatment of microstructure dynamics in terrestrial snow from principles of ice crystal growth is hindered by the lack of models for the evolution of the bicontinuous ice matrix. To this end we developed a rigorous microstructure upscaling scheme which is based on common pore-scale (vapor diffusion) principles of crystal growth to predict the averaged evolution of the interface morphology. We derived a coupled set of evolution equations for the (volume averaged) ice volume fraction, surface area per unit volume, Gaussian curvature and first and second moment of the mean curvature distribution and demonstrate their correctness by a comparison to interface tracking of idealized grains. In a second step we use the model as a benchmark tool without a priori assumptions for a comparison to experiments of snow microstructure evolution via image analysis on 4D X-ray tomography data. The benchmarking allows quantifying uncertainties from local estimates of crystal growth velocities. Finally we demonstrate how the rigorous model facilitates a statistical assessment of common growth laws by combining 4D microstructure data with finite element numerics. The results show that the prediction of the surface area evolution from first principles demands further conceptual insight from ice crystal growth.