v_t :: (real ~ " m s^-2" field (x(grid), y(half), z(half)) on
(i = 1 .. nlon by j = 1 .. nlat by k = 1 .. nlev)
)
Scalar Form
v_t := ( 1 / h_y * ave(ave(- h_x * u_aux, x), y) * protect(Z)
- (R_d * T) / h_y * df(ln_p, y) * (q * (1 / epsilon - 1) + 1)
- ( ave(( df(v, z ~ "1")
* (eta_p if 2 <= k and k <= nlev \\ 0.0)
), z)
/ df(p, z ~ "1")
)
- 1 / h_y * df(E + phi, y)
)
Dimensioned
v_t := ( 1 / h_y * ave(ave(- h_x * u_aux, x), y) * protect(Z)
- ( (R_d * T) / h_y
* df(ln_p, y)
* (q * (1 / epsilon - 1 ~ "1") + 1 ~ "1")
)
- ( ave(( df(v, z ~ "1")
* (eta_p if 2 ~ "1" <= k and k <= nlev \\
0.0 ~ " kg s^-3 / m"
)
), z)
/ df(p, z ~ "1")
)
- 1 / h_y * df(E + phi, y)
)
Discretized
v_t := ( ( 1 / hyv
* ( ( R_d
* ave_g(T, y)
* df_g(ln_p, y)
* (ave_g(q, y) * (1 - 1 / epsilon) - 1)
)
- df_g(E + phi, y)
- ave_g(ave_h(hxu * u_aux, x), y) * protect(ave_h(Z, x))
)
)
- ( ave_g(( df_h(v, z)
* (ave_g(eta_p, y) if 2 <= k and k <= nlev \\ 0.0)
), z)
/ df_g(ave_g(p, y), z)
)
)
CSE Eliminated
v_t := ((( 1 / 2 * varidx(t_219, [i, j, nlev]) / varidx(t_49, [i, j, nlev])
+ ( ( rdth * ( ( 1.56961230576048E-7
* ( (varidx(E, [i, j, k]) + varidx(phi, [i, j, nlev]))
- varidx(E, [i, j + 1, k])
- varidx(phi, [i, j + 1, nlev])
)
)
+ ( 2.25270758122744E-5
* (( 0.30391234671126
* ( varidx(q, [i, j, nlev])
+ varidx(q, [i, j + 1, nlev])
)
) + 1)
* (varidx(ln_p, [i, j, k]) - varidx(ln_p, [i, j + 1, k]))
* (varidx(T, [i, j, k]) + varidx(T, [i, j + 1, k]))
)
)
+ ( 1 / 16
* (varidx(Z, [i, j, k]) + varidx(Z, [i - 1, j, k]))
* ( ( varidx(hxu, [i, j])
* varidx(t_47, [i, j, nlev])
* varidx(u, [i, j, nlev])
)
+ ( varidx(hxu, [i, j + 1])
* varidx(t_47, [i, j + 1, nlev])
* varidx(u, [i, j + 1, nlev])
)
+ ( varidx(hxu, [i - 1, j])
* varidx(t_47, [i - 1, j, nlev])
* varidx(u, [i - 1, j, nlev])
)
+ ( varidx(hxu, [i - 1, j + 1])
* varidx(t_47, [i - 1, j + 1, nlev])
* varidx(u, [i - 1, j + 1, nlev])
)
)
)
)
/ varidx(hyv, [i, j])
)
) if
nlev <= k
) \\
( 1 / 2 * varidx(t_219, [i, j, 2]) / varidx(t_49, [i, j, 1])
+ ( ( rdth * ( ( 1.56961230576048E-7
* ( (varidx(E, [i, j, k]) + varidx(phi, [i, j, 1]))
- varidx(E, [i, j + 1, k])
- varidx(phi, [i, j + 1, 1])
)
)
+ ( 2.25270758122744E-5
* (( 0.30391234671126
* (varidx(q, [i, j, 1]) + varidx(q, [i, j + 1, 1]))
) + 1)
* (varidx(ln_p, [i, j, k]) - varidx(ln_p, [i, j + 1, k]))
* (varidx(T, [i, j, k]) + varidx(T, [i, j + 1, k]))
)
)
+ ( 1 / 16
* (varidx(Z, [i, j, k]) + varidx(Z, [i - 1, j, k]))
* ( ( varidx(hxu, [i, j])
* varidx(t_47, [i, j, 1])
* varidx(u, [i, j, 1])
)
+ ( varidx(hxu, [i, j + 1])
* varidx(t_47, [i, j + 1, 1])
* varidx(u, [i, j + 1, 1])
)
+ ( varidx(hxu, [i - 1, j])
* varidx(t_47, [i - 1, j, 1])
* varidx(u, [i - 1, j, 1])
)
+ ( varidx(hxu, [i - 1, j + 1])
* varidx(t_47, [i - 1, j + 1, 1])
* varidx(u, [i - 1, j + 1, 1])
)
)
)
)
/ varidx(hyv, [i, j])
)
) if k <= 1 \\
( ( 1 / 2
* ( (varidx(t_219, [i, j, k]) + varidx(t_219, [i, j, k + 1]))
/ varidx(t_49, [i, j, k])
)
)
+ ( ( rdth * ( ( 1.56961230576048E-7
* ( (varidx(E, [i, j, k]) + varidx(phi, [i, j, k]))
- varidx(E, [i, j + 1, k])
- varidx(phi, [i, j + 1, k])
)
)
+ ( 2.25270758122744E-5
* (( 0.30391234671126
* (varidx(q, [i, j, k]) + varidx(q, [i, j + 1, k]))
) + 1)
* (varidx(ln_p, [i, j, k]) - varidx(ln_p, [i, j + 1, k]))
* (varidx(T, [i, j, k]) + varidx(T, [i, j + 1, k]))
)
)
+ ( 1 / 16
* (varidx(Z, [i, j, k]) + varidx(Z, [i - 1, j, k]))
* ( ( varidx(hxu, [i, j])
* varidx(t_47, [i, j, k])
* varidx(u, [i, j, k])
)
+ ( varidx(hxu, [i, j + 1])
* varidx(t_47, [i, j + 1, k])
* varidx(u, [i, j + 1, k])
)
+ ( varidx(hxu, [i - 1, j])
* varidx(t_47, [i - 1, j, k])
* varidx(u, [i - 1, j, k])
)
+ ( varidx(hxu, [i - 1, j + 1])
* varidx(t_47, [i - 1, j + 1, k])
* varidx(u, [i - 1, j + 1, k])
)
)
)
)
/ varidx(hyv, [i, j])
)
)
)