Test of a cubic spline interface for physical processes with a 1-D third-order spectral element model

A common way to introduce physical processes into numerical models of the atmosphere is to call the parameterization at every grid point. This can lead to considerable errors. A simple 1-D example is proposed to illustrate that when a physical process occurs at one grid point only, a considerable sampling errormay occur, with the result that only a fraction of the true impact of this process is seen. The interface to the physical parameterization in numerical weather predictionmodel using a third-order 1-D spectral element method(SEM3) model is investigated by homogeneous advection. In SEM3, the grid points, called principal nodes, are at boundaries of computational intervals and two more collocation points in the interior of each cell. This article argues that it is sufficient to do the physical parameterization for principal nodes only that creating the interior grid-point values of physics schemes by linear interpolation. This is called the spline interface method. A simple condensation mode...