Abstract. It is well known that the representation of certain atmospheric conditions in
climate and weather models can still suffer from the limited grid resolution
that is facilitated by modern-day computer systems. Herein we study a simple
one-dimensional analogy to those models by using a single-column model
description of the atmosphere. The model employs an adaptive Cartesian mesh
that applies a high-resolution mesh only when and where it is required. The
so-called adaptive-grid model is described, and we report our findings
obtained for tests to evaluate the representation of the atmospheric boundary
layer, based on the first two GEWEX ABL Study (GABLS) inter-comparison cases.
The analysis shows that the adaptive-grid algorithm is indeed able to
dynamically coarsen and refine the numerical grid whilst maintaining an
accurate solution. This is an interesting result as in reality, transitional
dynamics (e.g. due to the diurnal cycle or due to changing synoptic
conditions) are the rule rather than the exception.
On the symmetry of a one-dimensional hydrogen atom
