Derivation of Model Topography

The Fourth-Order model necessitates representation of the topography. The problem of the representation of the topography at grid points is addressed. The attempted was to derive an envelope topography. The TI is obtained by taking local mean plus one standard deviation at each grid point and sigma filtering it. The method was greatly influenced by large standard deviations at steep mountains. The O1 topography is the local mean. The S1 is obtained by Sigma filtering in both latitude and longitude the mean O1. The S2 is when the operation is applied twice and S3 thrice, the Q3 is the sigma filtered local mean of the upper third quantile of the source data.