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module cv30_unsat_m |
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|
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implicit none |
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|
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contains |
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|
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SUBROUTINE cv30_unsat(icb, inb, t, q, qs, gz, u, v, p, ph, th, tv, lv, cpn, & |
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ep, clw, m, ment, elij, delt, plcl, mp, qp, up, vp, wt, water, evap, b) |
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|
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! Unsaturated (precipitating) downdrafts |
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|
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use cv30_param_m, only: nl, sigd |
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use cv_thermo_m, only: ginv |
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use SUPHEC_M, only: rg, rcpd |
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|
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integer, intent(in):: icb(:) ! (ncum) |
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! {2 <= icb <= nl - 3} |
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|
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integer, intent(in):: inb(:) ! (ncum) |
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! first model level above the level of neutral buoyancy of the |
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! parcel (1 <= inb <= nl - 1) |
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|
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real, intent(in):: t(:, :) ! (ncum, nl) temperature (K) |
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real, intent(in):: q(:, :), qs(:, :) ! (ncum, nl) |
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real, intent(in):: gz(:, :) ! (klon, klev) |
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real, intent(in):: u(:, :), v(:, :) ! (ncum, nl) |
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real, intent(in):: p(:, :) ! (klon, klev) pressure at full level, in hPa |
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real, intent(in):: ph(:, :) ! (ncum, klev + 1) |
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real, intent(in):: th(:, :) ! (ncum, nl - 1) potential temperature, in K |
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real, intent(in):: tv(:, :) ! (klon, klev) |
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|
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real, intent(in):: lv(:, :) ! (ncum, nl) |
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! specific latent heat of vaporization of water, in J kg-1 |
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|
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real, intent(in):: cpn(:, :) ! (ncum, nl) |
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! specific heat capacity at constant pressure of humid air, in J K-1 kg-1 |
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|
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real, intent(in):: ep(:, :) ! (ncum, klev) |
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real, intent(in):: clw(:, :) ! (ncum, klev) |
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real, intent(in):: m(:, :) ! (ncum, klev) |
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real, intent(in):: ment(:, :, :) ! (ncum, klev, klev) |
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real, intent(in):: elij(:, :, :) ! (ncum, klev, klev) |
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real, intent(in):: delt |
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real, intent(in):: plcl(:) ! (ncum) |
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|
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real, intent(out):: mp(:, :) |
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! (ncum, nl) Mass flux of the unsaturated downdraft, defined |
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! positive downward, in kg m-2 s-1. M_p in Emanuel (1991 928). |
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|
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real, intent(out):: qp(:, :), up(:, :), vp(:, :) ! (ncum, nl) |
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real, intent(out):: wt(:, :) ! (ncum, nl) |
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|
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real, intent(out):: water(:, :) ! (ncum, nl) |
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! precipitation mixing ratio, l_p in Emanuel (1991 928) |
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|
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real, intent(out):: evap(:, :) ! (ncum, nl) |
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! sigt * rate of evaporation of precipitation, in s-1 |
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! \sigma_s E in Emanuel (1991 928) |
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|
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real, intent(out):: b(:, :) ! (ncum, nl - 1) |
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|
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! Local: |
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|
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real, parameter:: sigp = 0.15 |
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! fraction of precipitation falling outside of cloud, \sig_s in |
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! Emanuel (1991 928) |
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|
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integer ncum |
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integer i, il, imax |
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real, parameter:: tinv = 1. / 3. |
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real delti |
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real afac, afac1, afac2, bfac |
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real pr1, sigt, b6, c6, revap, tevap |
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real xf, tf, fac2, ur, sru, fac, d, af, bf |
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real ampmax |
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real lvcp(size(icb), nl) ! (ncum, nl) L_v / C_p, in K |
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real wdtrain(size(icb)) ! (ncum) |
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logical lwork(size(icb)) ! (ncum) |
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|
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!------------------------------------------------------ |
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|
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ncum = size(icb) |
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delti = 1. / delt |
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mp = 0. |
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b = 0. |
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|
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do i = 1, nl |
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do il = 1, ncum |
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qp(il, i) = q(il, i) |
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up(il, i) = u(il, i) |
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vp(il, i) = v(il, i) |
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wt(il, i) = 0.001 |
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water(il, i) = 0. |
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evap(il, i) = 0. |
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lvcp(il, i) = lv(il, i) / cpn(il, i) |
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enddo |
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enddo |
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|
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! Check whether ep(inb) = 0. If so, skip precipitating downdraft |
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! calculation. |
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|
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forall (il = 1:ncum) lwork(il) = ep(il, inb(il)) >= 1e-4 |
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|
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imax = nl - 1 |
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do while (.not. any(inb >= imax .and. lwork) .and. imax >= 1) |
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imax = imax - 1 |
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end do |
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|
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downdraft_loop: DO i = imax, 1, - 1 |
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! Integrate liquid water equation to find condensed water |
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! and condensed water flux |
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|
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! Calculate detrained precipitation |
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forall (il = 1:ncum, inb(il) >= i .and. lwork(il)) wdtrain(il) = rg & |
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* (ep(il, i) * m(il, i) * clw(il, i) & |
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+ sum(max(elij(il, :i - 1, i) - (1. - ep(il, i)) * clw(il, i), 0.) & |
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* ment(il, :i - 1, i))) |
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|
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! Find rain water and evaporation using provisional |
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! estimates of qp(i) and qp(i - 1) |
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|
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loop_horizontal: do il = 1, ncum |
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if (i <= inb(il) .and. lwork(il)) then |
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wt(il, i) = 45. |
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|
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if (i < inb(il)) then |
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qp(il, i) = qp(il, i + 1) + (rcpd * (t(il, i + 1) - t(il, i)) & |
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+ gz(il, i + 1) - gz(il, i)) / lv(il, i) |
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qp(il, i) = 0.5 * (qp(il, i) + q(il, i)) |
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endif |
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|
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qp(il, i) = max(qp(il, i), 0.) |
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qp(il, i) = min(qp(il, i), qs(il, i)) |
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qp(il, inb(il)) = q(il, inb(il)) |
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|
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if (i == 1) then |
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afac = p(il, 1) * (qs(il, 1) - qp(il, 1)) & |
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/ (1e4 + 2000. * p(il, 1) * qs(il, 1)) |
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else |
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qp(il, i - 1) = qp(il, i) + (rcpd * (t(il, i) - t(il, i - 1)) & |
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+ gz(il, i) - gz(il, i - 1)) / lv(il, i) |
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qp(il, i - 1) = 0.5 * (qp(il, i - 1) + q(il, i - 1)) |
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qp(il, i - 1) = min(qp(il, i - 1), qs(il, i - 1)) |
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qp(il, i - 1) = max(qp(il, i - 1), 0.) |
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afac1 = p(il, i) * (qs(il, i) - qp(il, i)) & |
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/ (1e4 + 2000. * p(il, i) * qs(il, i)) |
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afac2 = p(il, i - 1) * (qs(il, i - 1) - qp(il, i - 1)) & |
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/ (1e4 + 2000. * p(il, i - 1) * qs(il, i - 1)) |
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afac = 0.5 * (afac1 + afac2) |
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endif |
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|
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if (i == inb(il)) afac = 0. |
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afac = max(afac, 0.) |
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bfac = 1. / (sigd * wt(il, i)) |
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|
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if (i <= icb(il)) then |
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! Prise en compte de la variation progressive de sigt dans |
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! les couches icb et icb - 1 : |
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! pour plcl <= ph(i + 1), pr1 = 0 |
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! pour plcl >= ph(i), pr1 = 1 |
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! pour ph(i + 1) < plcl < ph(i), pr1 est la proportion |
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! \`a cheval sur le nuage. |
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pr1 = max(0., min(1., & |
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(plcl(il) - ph(il, i + 1)) / (ph(il, i) - ph(il, i + 1)))) |
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sigt = sigp * pr1 + 1. - pr1 |
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else |
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! {i >= icb(il) + 1} |
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sigt = sigp |
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end if |
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|
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b6 = bfac * 50. * sigd * (ph(il, i) - ph(il, i + 1)) * sigt * afac |
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c6 = water(il, i + 1) + bfac * wdtrain(il) - 50. * sigd * bfac & |
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* (ph(il, i) - ph(il, i + 1)) * evap(il, i + 1) |
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|
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if (c6 > 0.) then |
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revap = 0.5 * (- b6 + sqrt(b6 * b6 + 4. * c6)) |
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evap(il, i) = sigt * afac * revap |
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water(il, i) = revap * revap |
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else |
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evap(il, i) = - evap(il, i + 1) + 0.02 * (wdtrain(il) + sigd & |
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* wt(il, i) * water(il, i + 1)) / (sigd * (ph(il, i) & |
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- ph(il, i + 1))) |
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end if |
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|
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! Calculate precipitating downdraft mass flux under |
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! hydrostatic approximation |
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|
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test_above_surface: if (i /= 1) then |
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tevap = max(0., evap(il, i)) |
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mp(il, i) = 100. * ginv * lvcp(il, i) * sigd * tevap & |
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* (p(il, i - 1) - p(il, i)) & |
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/ max(0.001, th(il, i) - th(il, i - 1)) |
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|
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! If hydrostatic assumption fails, solve cubic |
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! difference equation for downdraft theta and mass |
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! flux from two simultaneous differential equations |
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if (abs(mp(il, i + 1)**2 - mp(il, i)**2) > 0.1 * sigd**2 & |
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* 70. * ph(il, i) * (p(il, i - 1) - p(il, i)) & |
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* (th(il, i) - th(il, i - 1)) / (tv(il, i) * th(il, i))) & |
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then |
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xf = 100. * sigd**3 * (ph(il, i) - ph(il, i + 1)) |
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tf = b(il, i) - 5. * (th(il, i) - th(il, i - 1)) & |
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* t(il, i) / (lvcp(il, i) * sigd * th(il, i)) |
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af = xf * tf + mp(il, i + 1)**2 * tinv |
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bf = 2. * (tinv * mp(il, i + 1))**3 + tinv & |
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* mp(il, i + 1) * xf * tf + 50. * (p(il, i - 1) & |
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- p(il, i)) * xf * tevap |
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fac2 = 1. |
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if (bf < 0.) fac2 = - 1. |
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bf = abs(bf) |
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ur = 0.25 * bf * bf - af * af * af * tinv * tinv * tinv |
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|
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if (ur >= 0.) then |
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sru = sqrt(ur) |
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fac = 1. |
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if ((0.5 * bf - sru) < 0.) fac = - 1. |
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mp(il, i) = mp(il, i + 1) * tinv + (0.5 * bf & |
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+ sru)**tinv + fac * (abs(0.5 * bf - sru))**tinv |
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else |
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d = atan(2. * sqrt(- ur) / (bf + 1e-28)) |
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if (fac2 < 0.) d = 3.14159 - d |
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mp(il, i) = mp(il, i + 1) * tinv + 2. * sqrt(af * tinv) & |
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* cos(d * tinv) |
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endif |
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|
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mp(il, i) = max(0., mp(il, i)) |
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|
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! Il y a vraisemblablement une erreur dans la ligne |
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! suivante : il faut diviser par (mp(il, i) * sigd |
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! * rg) et non par (mp(il, i) + sigd * 0.1). Et il |
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! faut bien revoir les facteurs 100. |
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b(il, i - 1) = max(b(il, i) + 100. * (p(il, i - 1) & |
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- p(il, i)) * tevap / (mp(il, i) + sigd * 0.1) - 10. & |
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* (th(il, i) - th(il, i - 1)) * t(il, i) & |
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/ (lvcp(il, i) * sigd * th(il, i)), 0.) |
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endif |
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|
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! Limit magnitude of mp to meet CFL condition: |
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ampmax = 2. * (ph(il, i) - ph(il, i + 1)) * delti |
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ampmax = min(ampmax, 2. * (ph(il, i - 1) - ph(il, i)) * delti) |
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mp(il, i) = min(mp(il, i), ampmax) |
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|
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! Force mp to decrease linearly to zero between cloud |
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! base and the surface: |
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if (p(il, i) > p(il, icb(il))) mp(il, i) = mp(il, icb(il)) & |
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* (p(il, 1) - p(il, i)) / (p(il, 1) - p(il, icb(il))) |
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endif test_above_surface |
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|
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! Find mixing ratio of precipitating downdraft |
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|
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if (i /= inb(il)) then |
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qp(il, i) = q(il, i) |
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|
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if (mp(il, i) > mp(il, i + 1)) then |
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qp(il, i) = qp(il, i + 1) * mp(il, i + 1) + q(il, i) & |
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* (mp(il, i) - mp(il, i + 1)) + 100. * ginv * 0.5 & |
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* sigd * (ph(il, i) - ph(il, i + 1)) & |
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* (evap(il, i + 1) + evap(il, i)) |
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qp(il, i) = qp(il, i) / mp(il, i) |
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up(il, i) = up(il, i + 1) * mp(il, i + 1) + u(il, i) & |
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* (mp(il, i) - mp(il, i + 1)) |
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up(il, i) = up(il, i) / mp(il, i) |
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vp(il, i) = vp(il, i + 1) * mp(il, i + 1) + v(il, i) & |
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* (mp(il, i) - mp(il, i + 1)) |
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vp(il, i) = vp(il, i) / mp(il, i) |
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else |
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if (mp(il, i + 1) > 1e-16) then |
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qp(il, i) = qp(il, i + 1) + 100. * ginv * 0.5 * sigd & |
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* (ph(il, i) - ph(il, i + 1)) * (evap(il, i + 1) & |
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+ evap(il, i)) / mp(il, i + 1) |
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up(il, i) = up(il, i + 1) |
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vp(il, i) = vp(il, i + 1) |
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endif |
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endif |
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|
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qp(il, i) = min(qp(il, i), qs(il, i)) |
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qp(il, i) = max(qp(il, i), 0.) |
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endif |
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endif |
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end do loop_horizontal |
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end DO downdraft_loop |
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|
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end SUBROUTINE cv30_unsat |
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|
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end module cv30_unsat_m |
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