| 1 |
module cv30_unsat_m |
| 2 |
|
| 3 |
implicit none |
| 4 |
|
| 5 |
contains |
| 6 |
|
| 7 |
SUBROUTINE cv30_unsat(icb, inb, t, q, qs, gz, u, v, p, ph, th, tv, lv, cpn, & |
| 8 |
ep, clw, m, ment, elij, delt, plcl, mp, qp, up, vp, wt, water, evap, b) |
| 9 |
|
| 10 |
! Unsaturated (precipitating) downdrafts |
| 11 |
|
| 12 |
use cv30_param_m, only: nl, sigd |
| 13 |
use cv_thermo_m, only: cpd, ginv, grav |
| 14 |
|
| 15 |
integer, intent(in):: icb(:) ! (ncum) |
| 16 |
! {2 <= icb <= nl - 3} |
| 17 |
|
| 18 |
integer, intent(in):: inb(:) ! (ncum) |
| 19 |
! first model level above the level of neutral buoyancy of the |
| 20 |
! parcel (1 <= inb <= nl - 1) |
| 21 |
|
| 22 |
real, intent(in):: t(:, :), q(:, :), qs(:, :) ! (ncum, nl) |
| 23 |
real, intent(in):: gz(:, :) ! (klon, klev) |
| 24 |
real, intent(in):: u(:, :), v(:, :) ! (klon, klev) |
| 25 |
real, intent(in):: p(:, :) ! (klon, klev) pressure at full level, in hPa |
| 26 |
real, intent(in):: ph(:, :) ! (ncum, klev + 1) |
| 27 |
real, intent(in):: th(:, :) ! (ncum, nl - 1) |
| 28 |
real, intent(in):: tv(:, :) ! (klon, klev) |
| 29 |
real, intent(in):: lv(:, :) ! (klon, klev) |
| 30 |
real, intent(in):: cpn(:, :) ! (klon, klev) |
| 31 |
real, intent(in):: ep(:, :) ! (ncum, klev) |
| 32 |
real, intent(in):: clw(:, :) ! (ncum, klev) |
| 33 |
real, intent(in):: m(:, :) ! (ncum, klev) |
| 34 |
real, intent(in):: ment(:, :, :) ! (ncum, klev, klev) |
| 35 |
real, intent(in):: elij(:, :, :) ! (ncum, klev, klev) |
| 36 |
real, intent(in):: delt |
| 37 |
real, intent(in):: plcl(:) ! (ncum) |
| 38 |
|
| 39 |
real, intent(out):: mp(:, :) ! (klon, klev) |
| 40 |
real, intent(out):: qp(:, :), up(:, :), vp(:, :) ! (ncum, nl) |
| 41 |
real, intent(out):: wt(:, :) ! (ncum, nl) |
| 42 |
real, intent(out):: water(:, :), evap(:, :) ! (ncum, nl) |
| 43 |
real, intent(out):: b(:, :) ! (ncum, nl - 1) |
| 44 |
|
| 45 |
! Local: |
| 46 |
|
| 47 |
real, parameter:: sigp = 0.15 |
| 48 |
! fraction of precipitation falling outside of cloud, \sig_s in |
| 49 |
! Emanuel (1991 928) |
| 50 |
|
| 51 |
integer ncum |
| 52 |
integer i, il, imax |
| 53 |
real tinv, delti |
| 54 |
real afac, afac1, afac2, bfac |
| 55 |
real pr1, sigt, b6, c6, revap, tevap, delth |
| 56 |
real amfac, amp2, xf, tf, fac2, ur, sru, fac, d, af, bf |
| 57 |
real ampmax |
| 58 |
real lvcp(size(icb), nl) ! (ncum, nl) |
| 59 |
real wdtrain(size(icb)) ! (ncum) |
| 60 |
logical lwork(size(icb)) ! (ncum) |
| 61 |
|
| 62 |
!------------------------------------------------------ |
| 63 |
|
| 64 |
ncum = size(icb) |
| 65 |
delti = 1. / delt |
| 66 |
tinv = 1. / 3. |
| 67 |
mp = 0. |
| 68 |
b = 0. |
| 69 |
|
| 70 |
do i = 1, nl |
| 71 |
do il = 1, ncum |
| 72 |
qp(il, i) = q(il, i) |
| 73 |
up(il, i) = u(il, i) |
| 74 |
vp(il, i) = v(il, i) |
| 75 |
wt(il, i) = 0.001 |
| 76 |
water(il, i) = 0. |
| 77 |
evap(il, i) = 0. |
| 78 |
lvcp(il, i) = lv(il, i) / cpn(il, i) |
| 79 |
enddo |
| 80 |
enddo |
| 81 |
|
| 82 |
! Check whether ep(inb) = 0. If so, skip precipitating downdraft |
| 83 |
! calculation. |
| 84 |
|
| 85 |
forall (il = 1:ncum) lwork(il) = ep(il, inb(il)) >= 1e-4 |
| 86 |
|
| 87 |
imax = nl - 1 |
| 88 |
do while (.not. any(inb >= imax .and. lwork) .and. imax >= 1) |
| 89 |
imax = imax - 1 |
| 90 |
end do |
| 91 |
|
| 92 |
downdraft_loop: DO i = imax, 1, - 1 |
| 93 |
! Integrate liquid water equation to find condensed water |
| 94 |
! and condensed water flux |
| 95 |
|
| 96 |
! Calculate detrained precipitation |
| 97 |
forall (il = 1:ncum, inb(il) >= i .and. lwork(il)) wdtrain(il) = grav & |
| 98 |
* (ep(il, i) * m(il, i) * clw(il, i) & |
| 99 |
+ sum(max(elij(il, :i - 1, i) - (1. - ep(il, i)) * clw(il, i), 0.) & |
| 100 |
* ment(il, :i - 1, i))) |
| 101 |
|
| 102 |
! Find rain water and evaporation using provisional |
| 103 |
! estimates of qp(i) and qp(i - 1) |
| 104 |
|
| 105 |
loop_horizontal: do il = 1, ncum |
| 106 |
if (i <= inb(il) .and. lwork(il)) then |
| 107 |
wt(il, i) = 45. |
| 108 |
|
| 109 |
if (i < inb(il)) then |
| 110 |
qp(il, i) = qp(il, i + 1) + (cpd * (t(il, i + 1) - t(il, i)) & |
| 111 |
+ gz(il, i + 1) - gz(il, i)) / lv(il, i) |
| 112 |
qp(il, i) = 0.5 * (qp(il, i) + q(il, i)) |
| 113 |
endif |
| 114 |
|
| 115 |
qp(il, i) = max(qp(il, i), 0.) |
| 116 |
qp(il, i) = min(qp(il, i), qs(il, i)) |
| 117 |
qp(il, inb(il)) = q(il, inb(il)) |
| 118 |
|
| 119 |
if (i == 1) then |
| 120 |
afac = p(il, 1) * (qs(il, 1) - qp(il, 1)) & |
| 121 |
/ (1e4 + 2000. * p(il, 1) * qs(il, 1)) |
| 122 |
else |
| 123 |
qp(il, i - 1) = qp(il, i) + (cpd * (t(il, i) - t(il, i - 1)) & |
| 124 |
+ gz(il, i) - gz(il, i - 1)) / lv(il, i) |
| 125 |
qp(il, i - 1) = 0.5 * (qp(il, i - 1) + q(il, i - 1)) |
| 126 |
qp(il, i - 1) = min(qp(il, i - 1), qs(il, i - 1)) |
| 127 |
qp(il, i - 1) = max(qp(il, i - 1), 0.) |
| 128 |
afac1 = p(il, i) * (qs(il, i) - qp(il, i)) & |
| 129 |
/ (1e4 + 2000. * p(il, i) * qs(il, i)) |
| 130 |
afac2 = p(il, i - 1) * (qs(il, i - 1) - qp(il, i - 1)) & |
| 131 |
/ (1e4 + 2000. * p(il, i - 1) * qs(il, i - 1)) |
| 132 |
afac = 0.5 * (afac1 + afac2) |
| 133 |
endif |
| 134 |
|
| 135 |
if (i == inb(il)) afac = 0. |
| 136 |
afac = max(afac, 0.) |
| 137 |
bfac = 1. / (sigd * wt(il, i)) |
| 138 |
|
| 139 |
if (i <= icb(il)) then |
| 140 |
! Prise en compte de la variation progressive de sigt dans |
| 141 |
! les couches icb et icb - 1 : |
| 142 |
! pour plcl <= ph(i + 1), pr1 = 0 |
| 143 |
! pour plcl >= ph(i), pr1 = 1 |
| 144 |
! pour ph(i + 1) < plcl < ph(i), pr1 est la proportion |
| 145 |
! \`a cheval sur le nuage. |
| 146 |
pr1 = max(0., min(1., & |
| 147 |
(plcl(il) - ph(il, i + 1)) / (ph(il, i) - ph(il, i + 1)))) |
| 148 |
sigt = sigp * pr1 + 1. - pr1 |
| 149 |
else |
| 150 |
! {i >= icb(il) + 1} |
| 151 |
sigt = sigp |
| 152 |
end if |
| 153 |
|
| 154 |
b6 = bfac * 50. * sigd * (ph(il, i) - ph(il, i + 1)) * sigt * afac |
| 155 |
c6 = water(il, i + 1) + bfac * wdtrain(il) - 50. * sigd * bfac & |
| 156 |
* (ph(il, i) - ph(il, i + 1)) * evap(il, i + 1) |
| 157 |
|
| 158 |
if (c6 > 0.) then |
| 159 |
revap = 0.5 * (- b6 + sqrt(b6 * b6 + 4. * c6)) |
| 160 |
evap(il, i) = sigt * afac * revap |
| 161 |
water(il, i) = revap * revap |
| 162 |
else |
| 163 |
evap(il, i) = - evap(il, i + 1) + 0.02 * (wdtrain(il) + sigd & |
| 164 |
* wt(il, i) * water(il, i + 1)) / (sigd * (ph(il, i) & |
| 165 |
- ph(il, i + 1))) |
| 166 |
end if |
| 167 |
|
| 168 |
! Calculate precipitating downdraft mass flux under |
| 169 |
! hydrostatic approximation |
| 170 |
|
| 171 |
test_above_surface: if (i /= 1) then |
| 172 |
tevap = max(0., evap(il, i)) |
| 173 |
delth = max(0.001, (th(il, i) - th(il, i - 1))) |
| 174 |
mp(il, i) = 100. * ginv * lvcp(il, i) * sigd * tevap & |
| 175 |
* (p(il, i - 1) - p(il, i)) / delth |
| 176 |
|
| 177 |
! If hydrostatic assumption fails, solve cubic |
| 178 |
! difference equation for downdraft theta and mass |
| 179 |
! flux from two simultaneous differential equations |
| 180 |
|
| 181 |
amfac = sigd * sigd * 70. * ph(il, i) & |
| 182 |
* (p(il, i - 1) - p(il, i)) & |
| 183 |
* (th(il, i) - th(il, i - 1)) / (tv(il, i) * th(il, i)) |
| 184 |
amp2 = abs(mp(il, i + 1) * mp(il, i + 1) - mp(il, i) & |
| 185 |
* mp(il, i)) |
| 186 |
|
| 187 |
if (amp2 > 0.1 * amfac) then |
| 188 |
xf = 100. * sigd * sigd * sigd * (ph(il, i) - ph(il, i + 1)) |
| 189 |
tf = b(il, i) - 5. * (th(il, i) - th(il, i - 1)) & |
| 190 |
* t(il, i) / (lvcp(il, i) * sigd * th(il, i)) |
| 191 |
af = xf * tf + mp(il, i + 1) * mp(il, i + 1) * tinv |
| 192 |
bf = 2. * (tinv * mp(il, i + 1))**3 + tinv & |
| 193 |
* mp(il, i + 1) * xf * tf + 50. * (p(il, i - 1) & |
| 194 |
- p(il, i)) * xf * tevap |
| 195 |
fac2 = 1. |
| 196 |
if (bf < 0.) fac2 = - 1. |
| 197 |
bf = abs(bf) |
| 198 |
ur = 0.25 * bf * bf - af * af * af * tinv * tinv * tinv |
| 199 |
|
| 200 |
if (ur >= 0.) then |
| 201 |
sru = sqrt(ur) |
| 202 |
fac = 1. |
| 203 |
if ((0.5 * bf - sru) < 0.) fac = - 1. |
| 204 |
mp(il, i) = mp(il, i + 1) * tinv + (0.5 * bf & |
| 205 |
+ sru)**tinv + fac * (abs(0.5 * bf - sru))**tinv |
| 206 |
else |
| 207 |
d = atan(2. * sqrt(- ur) / (bf + 1e-28)) |
| 208 |
if (fac2 < 0.)d = 3.14159 - d |
| 209 |
mp(il, i) = mp(il, i + 1) * tinv + 2. * sqrt(af * tinv) & |
| 210 |
* cos(d * tinv) |
| 211 |
endif |
| 212 |
|
| 213 |
mp(il, i) = max(0., mp(il, i)) |
| 214 |
|
| 215 |
! Il y a vraisemblablement une erreur dans la |
| 216 |
! ligne suivante : il faut diviser par (mp(il, |
| 217 |
! i) * sigd * grav) et non par (mp(il, i) + sigd |
| 218 |
! * 0.1). Et il faut bien revoir les facteurs |
| 219 |
! 100. |
| 220 |
b(il, i - 1) = b(il, i) + 100. * (p(il, i - 1) - p(il, i)) & |
| 221 |
* tevap / (mp(il, i) + sigd * 0.1) - 10. * (th(il, i) & |
| 222 |
- th(il, i - 1)) * t(il, i) / (lvcp(il, i) * sigd & |
| 223 |
* th(il, i)) |
| 224 |
b(il, i - 1) = max(b(il, i - 1), 0.) |
| 225 |
endif |
| 226 |
|
| 227 |
! Limit magnitude of mp(i) to meet CFL condition: |
| 228 |
ampmax = 2. * (ph(il, i) - ph(il, i + 1)) * delti |
| 229 |
amp2 = 2. * (ph(il, i - 1) - ph(il, i)) * delti |
| 230 |
ampmax = min(ampmax, amp2) |
| 231 |
mp(il, i) = min(mp(il, i), ampmax) |
| 232 |
|
| 233 |
! Force mp to decrease linearly to zero between cloud |
| 234 |
! base and the surface: |
| 235 |
if (p(il, i) > p(il, icb(il))) mp(il, i) = mp(il, icb(il)) & |
| 236 |
* (p(il, 1) - p(il, i)) / (p(il, 1) - p(il, icb(il))) |
| 237 |
endif test_above_surface |
| 238 |
|
| 239 |
! Find mixing ratio of precipitating downdraft |
| 240 |
|
| 241 |
if (i /= inb(il)) then |
| 242 |
qp(il, i) = q(il, i) |
| 243 |
|
| 244 |
if (mp(il, i) > mp(il, i + 1)) then |
| 245 |
qp(il, i) = qp(il, i + 1) * mp(il, i + 1) + q(il, i) & |
| 246 |
* (mp(il, i) - mp(il, i + 1)) + 100. * ginv * 0.5 & |
| 247 |
* sigd * (ph(il, i) - ph(il, i + 1)) & |
| 248 |
* (evap(il, i + 1) + evap(il, i)) |
| 249 |
qp(il, i) = qp(il, i) / mp(il, i) |
| 250 |
up(il, i) = up(il, i + 1) * mp(il, i + 1) + u(il, i) & |
| 251 |
* (mp(il, i) - mp(il, i + 1)) |
| 252 |
up(il, i) = up(il, i) / mp(il, i) |
| 253 |
vp(il, i) = vp(il, i + 1) * mp(il, i + 1) + v(il, i) & |
| 254 |
* (mp(il, i) - mp(il, i + 1)) |
| 255 |
vp(il, i) = vp(il, i) / mp(il, i) |
| 256 |
else |
| 257 |
if (mp(il, i + 1) > 1e-16) then |
| 258 |
qp(il, i) = qp(il, i + 1) + 100. * ginv * 0.5 * sigd & |
| 259 |
* (ph(il, i) - ph(il, i + 1)) * (evap(il, i + 1) & |
| 260 |
+ evap(il, i)) / mp(il, i + 1) |
| 261 |
up(il, i) = up(il, i + 1) |
| 262 |
vp(il, i) = vp(il, i + 1) |
| 263 |
endif |
| 264 |
endif |
| 265 |
|
| 266 |
qp(il, i) = min(qp(il, i), qs(il, i)) |
| 267 |
qp(il, i) = max(qp(il, i), 0.) |
| 268 |
endif |
| 269 |
endif |
| 270 |
end do loop_horizontal |
| 271 |
end DO downdraft_loop |
| 272 |
|
| 273 |
end SUBROUTINE cv30_unsat |
| 274 |
|
| 275 |
end module cv30_unsat_m |
Parent Directory
| 
Revision Log