```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])          )        )       )```