Final generic form of prognostic equations including all sources

The mass prognostic equations can be written including all of the aforementioned diffusion and relation terms as

$$\begin{split} {\frac{\left( \partial\mu_d\,\varphi \right) }{... ...ppa_w \,\mu_d \,\left(\varphi -\varphi_{ref}\right) \end{split}$$ (121)

To summarize: $\delta_{u,v}=1$ for $\varphi=u,v$ (divergence damping), otherwise $\delta_{u,v}=0$ for all other variables, and $\delta_{w}=1$ only when $\varphi=w$. Again, ${\cal{F}}_{u,v,w}$ represents the pressure gradient and curvature terms for the wind component equations. Note that $K_r=0$ so that there is no lateral boundary forcing for global scale applications. Finally, it is also possible (especially for high resolution runs) to include second order physically-based horizontal diffusion as $D_{h \varphi}^2$.