12 - Boundary Conditions

Summary

Introduction

In the earlier chapters, the reader has been introduced to various equations of motion of the atmosphere, such as non-divergent vorticity equation, shallow water barotropic equations, quasi-geostrophic equations, and baroclinic equations. The aforementioned model equations for the atmosphere represents both an initial value problem and a boundary-value problem. For global atmospheric models, the required boundary conditions would correspond to both upper and lower boundaries of the atmosphere. There are no lateral boundaries for a global model as the model computational domain is naturally periodic. However, for regional atmospheric models that have a limited area of computational domain, the governing equations cannot be solved without specifying the nature of the lateral-boundary conditions. These lateralboundary conditions for limited area models provide a means of obtaining the values of the dependent variables at these boundary points that correspond to lateral boundaries. For operational meteorological forecasts that employ a limited area regional atmospheric model, the lateral boundary values are obtained by interpolation from values of dependent variables at grid points of a previously run global atmospheric forecast model. For non-operational researchers working with a limited area regional atmospheric model, the lateral boundary values are obtained from archived and gridded regional or global analysis, the latter obtained by combining the optimal atmospheric model output with all possible atmospheric observations.

Both global and regional models require the upper and lower boundary values to be assigned. Real atmosphere does not have a definite upper value. However, unlike the real atmosphere, the model atmosphere does not extend to infinity; hence, it is necessary to define an artificial upper boundary for the model atmosphere and provide upper boundary values for the dependent variables at these artificial upper boundaries. The choice of the upper artificial boundary or lid impacts the computational costs. Upward-propagating internal-gravity waves that are generated by mountains or by deeply convective and organized systems can extend to great heights in the atmosphere. The most commonly employed upper boundary conditions in atmospheric models such as the rigid lid condition or free surface condition can reflect these vertically propagating internal gravity waves and distort the model solution.