| A functional relation between two chemical species puts observational constraints on attempts to model the atmosphere. For example, adequate representation of these relations is important when modeling the depletion of stratospheric ozone by nitrous oxide. Previous work has shown a case where a linear functional relation is not preserved in the tracer transport scheme of the Higher Order Methods Modeling Environment (HOMME), which is the spectral element dynamics core used by the Community Atmosphere Model (CAM). Application of a certain simple tracer chemistry reaction before each model time step can test whether the scheme actually preserves linear tracer correlations (LCs) to machine precision. Using this method, we confirm previous results that, the implementation of the default shape-preserving filter of HOMME used in the transport scheme does not preserve LCs. However, since we prove that this limiter along with a few other limiter algorithms do in fact preserve LCs in exact arithmetic, we suggest that these limiter algorithms exacerbate the growth of roundoff error in elements where tracers have very different magnitudes. Nevertheless, we manage to put forth a limiting scheme that improves the tracer correlation problem. We also derive another new limiter that relies on multiplicative rescaling of nodal values within a given element. This algorithm does not rely on iterations for convergence and thus has the advantage of being more computationally efficient than the current default CAM-SE limiter. Results also show that the default limiter does not always introduce the lowest amount of L2 error, which contradicts its purpose, since it was derived to minimize error in the L2 norm. |
