# Factorization of the mean

Three-dimensional model typically are unmanageable or demand huge computational efforts when applied to natural-scale geophysical mass flows, which can involve masses as large as $10^6$ to $10^{13}$ ${m}^3$. One way to make the problem more tractable is to assume that flows are long (or wide) relative to their depth, and to use depth-averaging in the direction normal to the sliding surface. This dramatically reduces the complexity associated with the flow from three-dimension to virtually shallow flow so that the computational cost is very low.