Hybrid σ-p Coordinate Choices for a Global Model

A methodology for choosing a hybrid sigma-p ( sigma-pressure) vertical coordinate of the Simmons-Strufing form for a global model is presented. The method focuses on properties of the vertical derivative of the terrain-following coefficient, which affect the smoothness and shape of layer thickness profiles and determines the coordinate's monotonicity over variable terrain. The method is applied to characterize and interrelate existing hybrid coordinate choices in NWP and climate models, then to design new coordinates with specific properties. Offline tests indicate that the new coordinates reduce stratospheric errors in models due to vertical truncation effects in the computation of the pressure gradient force over steep terrain. When implemented in a global model, the new coordinates significantly reduce vorticity and divergence errors at all altitudes in idealized simulations. In forecasting experiments with a global model, the new coordinates slightly reduce the stability of the semi-implicit time scheme. Resetting the reference pressure in the scheme to similar to 800 hPa solves the problem for every coordinate except the Sangster-Arakawa-Lamb hybrid, which remains intrinsically less stable than the others. Impacts of different coordinates on forecast skill are neutral or weakly positive, with the new hybrid coordinates yielding slight improvements relative to earlier hybrid choices. This essentially neutral impact indirectly endorses the wide variety of hybrid coordinate choices currently used in NWP and climate models, with the proviso that these tests do not address the impact over longer time scales or on data assimilation.