Curvature terms

The curvature (Coriolis) terms have slightly different forms depending on the projections. They are expressed for the latitude-longitude projection as

$$f_{u,crv} = v \left[ f + {\frac{u}{R_e}} {\rm tan}\left(\phi_r\right) \right] - w \left( \frac{u}{R_e} + e \right)$$ (300)

$$f_{v,crv} = -u \left[ f + {\frac{u}{R_e }} {\rm tan}\left(\phi_r\right) \right] - \frac{v \, w}{R_e}$$ (301)

$$f_{w,crv} = \frac{\left(v^2 + u^2\right)}{R_e} + e\,u$$ (302)

For a conformal projection ($m_x=m_y=m$), the curvature terms can be expressed as

$$f_{u,crv} = v \left( f + u {\frac{\partial m}{\partial y}} - v {\frac{\partial m}{\partial x}} \right) \,-\, e \, w \,-\, \frac{u \, w}{R_e}$$ (303)

$$f_{v,crv} = -u \left( f + u {\frac{\partial m}{\partial y}} - v {\frac{\partial m}{\partial x}} \right) \,-\, \frac{v \, w}{R_e}$$ (304)

$$f_{w,crv} = e \, u \,+\, \left( \frac{u^2 + v^2}{R_e} \right)$$ (305)

where the Coriolis parameter, $f$, is defined as

$$f = 2 {\rm sin}\left(\phi_r\right) \Omega_r$$ (306)

and the curvature term factor is

$$e = 2 {\rm cos}\left(\phi_r\right) \Omega_r$$ (307)

where $\Omega_r=2\pi/86400$.