q_t :: (real ~ "Hz" field (x(grid), y(grid), z(half)) on
(i = 1 .. nlon by j = 1 .. nlat by k = 1 .. nlev)
)
Scalar Form
q_t := ( - ( ave(( df(q, z ~ "1")
* (eta_p if 2 <= k and k <= nlev \\ 0.0)
), z)
/ df(p, z ~ "1")
)
- ( 1 / (h_x * h_y)
* ( (ave(h_y * u_aux * df(q, x), x) + ave(h_x * v_aux * df(q, y), y))
/ df(p, z ~ "1")
)
)
)
Dimensioned
q_t := ( - ( ave(( df(q, z ~ "1")
* (eta_p if 2 ~ "1" <= k and k <= nlev \\
0.0 ~ " kg s^-3 / m"
)
), z)
/ df(p, z ~ "1")
)
- ( 1 / (h_x * h_y)
* ( (ave(h_y * u_aux * df(q, x), x) + ave(h_x * v_aux * df(q, y), y))
/ df(p, z ~ "1")
)
)
)
Discretized
q_t := ( ( ( 1 / (hxt * hyt)
* ( - ave_h(hyu * u_aux * df_g(q, x), x)
- ave_h(hxv * v_aux * df_g(q, y), y)
)
)
- ave_g(df_h(q, z) * (eta_p if 2 <= k and k <= nlev \\ 0.0), z)
)
/ df_g(p, z)
)
CSE Eliminated
q_t := ((( ( ( 7.84806152880239E-8
* ( ( ( rdlam
* ( - varidx(t_151, [i, j, nlev])
- varidx(t_151, [i + 1, j, nlev])
)
)
+ ( rdth
* ( - varidx(t_155, [i, j, nlev])
- varidx(t_155, [i, j + 1, nlev])
)
)
)
/ (varidx(hxt, [i, j]) * varidx(hyt, [i, j]))
)
)
- 1 / 2 * varidx(t_166, [i, j, nlev])
)
/ (varidx(p, [i, j, k + 1]) - varidx(p, [i, j, k]))
) if
nlev <= k
) \\
(( ( ( 7.84806152880239E-8
* ( ( ( rdlam
* ( - varidx(t_151, [i, j, 1])
- varidx(t_151, [i + 1, j, 1])
)
)
+ ( rdth
* ( - varidx(t_155, [i, j, 1])
- varidx(t_155, [i, j + 1, 1])
)
)
)
/ (varidx(hxt, [i, j]) * varidx(hyt, [i, j]))
)
)
- 1 / 2 * varidx(t_166, [i, j, 2])
)
/ (varidx(p, [i, j, k + 1]) - varidx(p, [i, j, k]))
) if
k <= 1
) \\
( ( ( 7.84806152880239E-8
* ( ( ( rdlam
* (- varidx(t_151, [i, j, k]) - varidx(t_151, [i + 1, j, k]))
)
+ ( rdth
* (- varidx(t_155, [i, j, k]) - varidx(t_155, [i, j + 1, k]))
)
)
/ (varidx(hxt, [i, j]) * varidx(hyt, [i, j]))
)
)
- 1 / 2 * (varidx(t_166, [i, j, k]) + varidx(t_166, [i, j, k + 1]))
)
/ (varidx(p, [i, j, k + 1]) - varidx(p, [i, j, k]))
)
)