A physics-based open atmosphere boundary condition for height-coordinate atmospheric models

The most common boundary condition (BC) imposed at the model top in many nonhydrostatic, height-based models is a rigid lid (no mass-flux) complemented by an absorbing sponge layer. This BC is unphysical and not appropriate for large-scale heating and cooling processes present in the upper atmosphere with a high model top. To address this problem, we have derived a physics-based open atmosphere BC from first principles that allows fluid to smoothly exit and enter the model domain during heating and cooling processes, respectively. The new BC is derived from both the compressible and hydrostatic continuity equation and accounts for bulk and surface heating as well as horizontal divergence by modeling the velocity normal to the model top (vertical velocity). This physics-based BC was implemented in two height-based, spectral element nonhydrostatic atmospheric models and tested on both 1D and 3D atmospheric test cases using two idealized heating tests targeted toward high altitude applications. The numerical results indicate that the BC is stable using explicit, fully implicit, and horizontally explicit, vertical implicit (HEVI) time integrators. Unlike the rigid BC, the proposed BC produces stable numerical results without producing spurious oscillations near the model top. Unlike sponge layers, the proposed BC does not require any tuning parameters since all parameters are consistent with the BCs used in many hydrostatic models. •A new open boundary condition (BC) has been derived for high altitude (HA) applications.•This physics-based BC was implemented in two height-based nonhydrostatic atmospheric models: NUMA and NEPTUNE.•Unlike the rigid BC and sponge BC, the proposed BC does not produce spurious oscillations.