Generalized expressions of the traditional terrain-following coordinates is as follows:
sig = (zeta - zeta_b) / (zeta - zeta_t)
Z = (1-sig) Z_b + sig Z_t
Z=Z_b + (Z_t - Z_b)*sig,
Gv^1/2 = dz / dzeta = (Z_t - Z_b) / H where H = zeta_t - zeta_b,
(dz/dx)_zeta = (1-sig) * dZ_b/dx + sig * dZ_T/dx,
(dxi/dx)_z = - Gv^{-1/2} (dz/dx)_zeta,
For the atmospheric model, we assume
- zeta_b=0 and zeta_t = Z_t = (constant)
Generalized expressions of the traditional terrain-following coordinates is as follows:
sig = (zeta - zeta_b) / (zeta - zeta_t)
Z = (1-sig) Z_b + sig Z_t
Z=Z_b + (Z_t - Z_b)*sig,
Gv^1/2 = dz / dzeta = (Z_t - Z_b) / H where H = zeta_t - zeta_b,
(dz/dx)_zeta = (1-sig) * dZ_b/dx + sig * dZ_T/dx,
(dxi/dx)_z = - Gv^{-1/2} (dz/dx)_zeta,
For the atmospheric model, we assume