```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]))        )       )```