| 1 | MODULE icethd_pnd |
|---|
| 2 | !!====================================================================== |
|---|
| 3 | !! *** MODULE icethd_pnd *** |
|---|
| 4 | !! sea-ice: Melt ponds on top of sea ice |
|---|
| 5 | !!====================================================================== |
|---|
| 6 | !! history : ! 2012 (O. Lecomte) Adaptation from Flocco and Turner |
|---|
| 7 | !! ! 2017 (M. Vancoppenolle, O. Lecomte, C. Rousset) Implementation |
|---|
| 8 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
|---|
| 9 | !!---------------------------------------------------------------------- |
|---|
| 10 | #if defined key_si3 |
|---|
| 11 | !!---------------------------------------------------------------------- |
|---|
| 12 | !! 'key_si3' : SI3 sea-ice model |
|---|
| 13 | !!---------------------------------------------------------------------- |
|---|
| 14 | !! ice_thd_pnd_init : some initialization and namelist read |
|---|
| 15 | !! ice_thd_pnd : main calling routine |
|---|
| 16 | !!---------------------------------------------------------------------- |
|---|
| 17 | USE phycst ! physical constants |
|---|
| 18 | USE dom_oce ! ocean space and time domain |
|---|
| 19 | USE ice ! sea-ice: variables |
|---|
| 20 | USE ice1D ! sea-ice: thermodynamics variables |
|---|
| 21 | USE icetab ! sea-ice: 1D <==> 2D transformation |
|---|
| 22 | ! |
|---|
| 23 | USE in_out_manager ! I/O manager |
|---|
| 24 | USE lib_mpp ! MPP library |
|---|
| 25 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
|---|
| 26 | USE timing ! Timing |
|---|
| 27 | |
|---|
| 28 | IMPLICIT NONE |
|---|
| 29 | PRIVATE |
|---|
| 30 | |
|---|
| 31 | PUBLIC ice_thd_pnd_init ! routine called by icestp.F90 |
|---|
| 32 | PUBLIC ice_thd_pnd ! routine called by icestp.F90 |
|---|
| 33 | |
|---|
| 34 | INTEGER :: nice_pnd ! choice of the type of pond scheme |
|---|
| 35 | ! ! associated indices: |
|---|
| 36 | INTEGER, PARAMETER :: np_pndNO = 0 ! No pond scheme |
|---|
| 37 | INTEGER, PARAMETER :: np_pndCST = 1 ! Constant ice pond scheme |
|---|
| 38 | INTEGER, PARAMETER :: np_pndLEV = 2 ! Level ice pond scheme |
|---|
| 39 | INTEGER, PARAMETER :: np_pndTOPO = 3 ! Level ice pond scheme |
|---|
| 40 | |
|---|
| 41 | !! * Substitutions |
|---|
| 42 | # include "vectopt_loop_substitute.h90" |
|---|
| 43 | !!---------------------------------------------------------------------- |
|---|
| 44 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
|---|
| 45 | !! $Id$ |
|---|
| 46 | !! Software governed by the CeCILL license (see ./LICENSE) |
|---|
| 47 | !!---------------------------------------------------------------------- |
|---|
| 48 | CONTAINS |
|---|
| 49 | |
|---|
| 50 | SUBROUTINE ice_thd_pnd |
|---|
| 51 | !!------------------------------------------------------------------- |
|---|
| 52 | !! *** ROUTINE ice_thd_pnd *** |
|---|
| 53 | !! |
|---|
| 54 | !! ** Purpose : change melt pond fraction and thickness |
|---|
| 55 | !! |
|---|
| 56 | !! Note: Melt ponds affect currently affect radiative transfer |
|---|
| 57 | !! They carry no heat, and the melt water they carry is not |
|---|
| 58 | !! exchanged with the ocean |
|---|
| 59 | !! |
|---|
| 60 | !! This means freshwater is directly released after surface & bottom melt in ice_thd_dh |
|---|
| 61 | !! |
|---|
| 62 | !! A wfx_pnd has been coded for diagnostic purposes |
|---|
| 63 | !! Each time wfx_pnd is updated, wfx_sum / wfx_snw_sum must be updated |
|---|
| 64 | !! |
|---|
| 65 | !!! The current diagnostic lacks a contribution from drainage |
|---|
| 66 | !! |
|---|
| 67 | !!------------------------------------------------------------------- |
|---|
| 68 | ! |
|---|
| 69 | SELECT CASE ( nice_pnd ) |
|---|
| 70 | ! |
|---|
| 71 | CASE (np_pndCST) ; CALL pnd_CST !== Constant melt ponds ==! |
|---|
| 72 | ! |
|---|
| 73 | CASE (np_pndLEV) ; CALL pnd_LEV !== Level ice melt ponds ==! |
|---|
| 74 | ! |
|---|
| 75 | CASE (np_pndTOPO) ; CALL pnd_TOPO !== Topographic melt ponds ==! |
|---|
| 76 | ! |
|---|
| 77 | END SELECT |
|---|
| 78 | ! |
|---|
| 79 | END SUBROUTINE ice_thd_pnd |
|---|
| 80 | |
|---|
| 81 | |
|---|
| 82 | SUBROUTINE pnd_CST |
|---|
| 83 | !!------------------------------------------------------------------- |
|---|
| 84 | !! *** ROUTINE pnd_CST *** |
|---|
| 85 | !! |
|---|
| 86 | !! ** Purpose : Compute melt pond evolution |
|---|
| 87 | !! |
|---|
| 88 | !! ** Method : Melt pond fraction and thickness are prescribed |
|---|
| 89 | !! to non-zero values when t_su = 0C |
|---|
| 90 | !! |
|---|
| 91 | !! ** Tunable parameters : pond fraction (rn_apnd), pond depth (rn_hpnd) |
|---|
| 92 | !! |
|---|
| 93 | !! ** Note : Coupling with such melt ponds is only radiative |
|---|
| 94 | !! Advection, ridging, rafting... are bypassed |
|---|
| 95 | !! |
|---|
| 96 | !! ** References : Bush, G.W., and Trump, D.J. (2017) |
|---|
| 97 | !!------------------------------------------------------------------- |
|---|
| 98 | INTEGER :: ji ! loop indices |
|---|
| 99 | !!------------------------------------------------------------------- |
|---|
| 100 | DO ji = 1, npti |
|---|
| 101 | ! |
|---|
| 102 | IF( a_i_1d(ji) > 0._wp .AND. t_su_1d(ji) >= rt0 ) THEN |
|---|
| 103 | h_ip_1d(ji) = rn_hpnd |
|---|
| 104 | a_ip_1d(ji) = rn_apnd * a_i_1d(ji) |
|---|
| 105 | h_il_1d(ji) = 0._wp ! no pond lids whatsoever |
|---|
| 106 | ELSE |
|---|
| 107 | h_ip_1d(ji) = 0._wp |
|---|
| 108 | a_ip_1d(ji) = 0._wp |
|---|
| 109 | h_il_1d(ji) = 0._wp |
|---|
| 110 | ENDIF |
|---|
| 111 | ! |
|---|
| 112 | END DO |
|---|
| 113 | ! |
|---|
| 114 | END SUBROUTINE pnd_CST |
|---|
| 115 | |
|---|
| 116 | |
|---|
| 117 | SUBROUTINE pnd_LEV |
|---|
| 118 | !!------------------------------------------------------------------- |
|---|
| 119 | !! *** ROUTINE pnd_LEV *** |
|---|
| 120 | !! |
|---|
| 121 | !! ** Purpose : Compute melt pond evolution |
|---|
| 122 | !! |
|---|
| 123 | !! ** Method : A fraction of meltwater is accumulated in ponds and sent to ocean when surface is freezing |
|---|
| 124 | !! We work with volumes and then redistribute changes into thickness and concentration |
|---|
| 125 | !! assuming linear relationship between the two. |
|---|
| 126 | !! |
|---|
| 127 | !! ** Action : - pond growth: Vp = Vp + dVmelt --- from Holland et al 2012 --- |
|---|
| 128 | !! dVmelt = (1-r)/rhow * ( rhoi*dh_i + rhos*dh_s ) * a_i |
|---|
| 129 | !! dh_i = meltwater from ice surface melt |
|---|
| 130 | !! dh_s = meltwater from snow melt |
|---|
| 131 | !! (1-r) = fraction of melt water that is not flushed |
|---|
| 132 | !! |
|---|
| 133 | !! - limtations: a_ip must not exceed (1-r)*a_i |
|---|
| 134 | !! h_ip must not exceed 0.5*h_i |
|---|
| 135 | !! |
|---|
| 136 | !! - pond shrinking: |
|---|
| 137 | !! if lids: Vp = Vp -dH * a_ip |
|---|
| 138 | !! dH = lid thickness change. Retrieved from this eq.: --- from Flocco et al 2010 --- |
|---|
| 139 | !! |
|---|
| 140 | !! rhoi * Lf * dH/dt = ki * MAX(Tp-Tsu,0) / H |
|---|
| 141 | !! H = lid thickness |
|---|
| 142 | !! Lf = latent heat of fusion |
|---|
| 143 | !! Tp = -2C |
|---|
| 144 | !! |
|---|
| 145 | !! And solved implicitely as: |
|---|
| 146 | !! H(t+dt)**2 -H(t) * H(t+dt) -ki * (Tp-Tsu) * dt / (rhoi*Lf) = 0 |
|---|
| 147 | !! |
|---|
| 148 | !! if no lids: Vp = Vp * exp(0.01*MAX(Tp-Tsu,0)/Tp) --- from Holland et al 2012 --- |
|---|
| 149 | !! |
|---|
| 150 | !! - Flushing: w = -perm/visc * rho_oce * grav * Hp / Hi --- from Flocco et al 2007 --- |
|---|
| 151 | !! perm = permability of sea-ice |
|---|
| 152 | !! visc = water viscosity |
|---|
| 153 | !! Hp = height of top of the pond above sea-level |
|---|
| 154 | !! Hi = ice thickness thru which there is flushing |
|---|
| 155 | !! |
|---|
| 156 | !! - Corrections: remove melt ponds when lid thickness is 10 times the pond thickness |
|---|
| 157 | !! |
|---|
| 158 | !! - pond thickness and area is retrieved from pond volume assuming a linear relationship between h_ip and a_ip: |
|---|
| 159 | !! a_ip/a_i = a_ip_frac = h_ip / zaspect |
|---|
| 160 | !! |
|---|
| 161 | !! ** Tunable parameters : ln_pnd_lids, rn_apnd_max, rn_apnd_min |
|---|
| 162 | !! |
|---|
| 163 | !! ** Note : mostly stolen from CICE |
|---|
| 164 | !! |
|---|
| 165 | !! ** References : Flocco and Feltham (JGR, 2007) |
|---|
| 166 | !! Flocco et al (JGR, 2010) |
|---|
| 167 | !! Holland et al (J. Clim, 2012) |
|---|
| 168 | !!------------------------------------------------------------------- |
|---|
| 169 | |
|---|
| 170 | REAL(wp), DIMENSION(nlay_i) :: ztmp ! temporary array |
|---|
| 171 | !! |
|---|
| 172 | REAL(wp), PARAMETER :: zaspect = 0.8_wp ! pond aspect ratio |
|---|
| 173 | REAL(wp), PARAMETER :: zTp = -2._wp ! reference temperature |
|---|
| 174 | REAL(wp), PARAMETER :: zvisc = 1.79e-3_wp ! water viscosity |
|---|
| 175 | !! |
|---|
| 176 | REAL(wp) :: zfr_mlt, zdv_mlt ! fraction and volume of available meltwater retained for melt ponding |
|---|
| 177 | REAL(wp) :: zdv_frz, zdv_flush ! Amount of melt pond that freezes, flushes |
|---|
| 178 | REAL(wp) :: zhp ! heigh of top of pond lid wrt ssh |
|---|
| 179 | REAL(wp) :: zv_ip_max ! max pond volume allowed |
|---|
| 180 | REAL(wp) :: zdT ! zTp-t_su |
|---|
| 181 | REAL(wp) :: zsbr ! Brine salinity |
|---|
| 182 | REAL(wp) :: zperm ! permeability of sea ice |
|---|
| 183 | REAL(wp) :: zfac, zdum ! temporary arrays |
|---|
| 184 | REAL(wp) :: z1_rhow, z1_aspect, z1_Tp ! inverse |
|---|
| 185 | !! |
|---|
| 186 | INTEGER :: ji, jk ! loop indices |
|---|
| 187 | |
|---|
| 188 | !!------------------------------------------------------------------- |
|---|
| 189 | |
|---|
| 190 | z1_rhow = 1._wp / rhow |
|---|
| 191 | z1_aspect = 1._wp / zaspect |
|---|
| 192 | z1_Tp = 1._wp / zTp |
|---|
| 193 | |
|---|
| 194 | DO ji = 1, npti |
|---|
| 195 | ! !----------------------------------------------------! |
|---|
| 196 | IF( h_i_1d(ji) < rn_himin .OR. a_i_1d(ji) < epsi10 ) THEN ! Case ice thickness < rn_himin or tiny ice fraction ! |
|---|
| 197 | ! !----------------------------------------------------! |
|---|
| 198 | !--- Remove ponds on thin ice or tiny ice fractions |
|---|
| 199 | a_ip_1d(ji) = 0._wp |
|---|
| 200 | h_ip_1d(ji) = 0._wp |
|---|
| 201 | h_il_1d(ji) = 0._wp |
|---|
| 202 | ! !--------------------------------! |
|---|
| 203 | ELSE ! Case ice thickness >= rn_himin ! |
|---|
| 204 | ! !--------------------------------! |
|---|
| 205 | v_ip_1d(ji) = h_ip_1d(ji) * a_ip_1d(ji) ! retrieve volume from thickness |
|---|
| 206 | v_il_1d(ji) = h_il_1d(ji) * a_ip_1d(ji) |
|---|
| 207 | ! |
|---|
| 208 | !------------------! |
|---|
| 209 | ! case ice melting ! |
|---|
| 210 | !------------------! |
|---|
| 211 | ! |
|---|
| 212 | !--- available meltwater for melt ponding ---! |
|---|
| 213 | zdum = -( dh_i_sum(ji)*rhoi + dh_s_mlt(ji)*rhos ) * z1_rhow * a_i_1d(ji) |
|---|
| 214 | zfr_mlt = rn_apnd_min + ( rn_apnd_max - rn_apnd_min ) * at_i_1d(ji) ! = ( 1 - r ) = fraction of melt water that is not flushed |
|---|
| 215 | zdv_mlt = MAX( 0._wp, zfr_mlt * zdum ) ! >0, max for roundoff errors? |
|---|
| 216 | ! |
|---|
| 217 | !--- overflow ---! |
|---|
| 218 | ! If pond area exceeds zfr_mlt * a_i_1d(ji) then reduce the pond volume |
|---|
| 219 | ! a_ip_max = zfr_mlt * a_i |
|---|
| 220 | ! => from zaspect = h_ip / (a_ip / a_i), set v_ip_max as: |
|---|
| 221 | zv_ip_max = zfr_mlt**2 * a_i_1d(ji) * zaspect |
|---|
| 222 | zdv_mlt = MAX( 0._wp, MIN( zdv_mlt, zv_ip_max - v_ip_1d(ji) ) ) |
|---|
| 223 | |
|---|
| 224 | ! If pond depth exceeds half the ice thickness then reduce the pond volume |
|---|
| 225 | ! h_ip_max = 0.5 * h_i |
|---|
| 226 | ! => from zaspect = h_ip / (a_ip / a_i), set v_ip_max as: |
|---|
| 227 | zv_ip_max = z1_aspect * a_i_1d(ji) * 0.25 * h_i_1d(ji) * h_i_1d(ji) ! MV dimensions are wrong here or comment is unclear |
|---|
| 228 | zdv_mlt = MAX( 0._wp, MIN( zdv_mlt, zv_ip_max - v_ip_1d(ji) ) ) |
|---|
| 229 | |
|---|
| 230 | !--- Pond growing ---! |
|---|
| 231 | v_ip_1d(ji) = v_ip_1d(ji) + zdv_mlt |
|---|
| 232 | ! |
|---|
| 233 | !--- Lid melting ---! |
|---|
| 234 | IF( ln_pnd_lids ) v_il_1d(ji) = MAX( 0._wp, v_il_1d(ji) - zdv_mlt ) ! must be bounded by 0 |
|---|
| 235 | |
|---|
| 236 | ! |
|---|
| 237 | !--- mass flux ---! |
|---|
| 238 | IF( zdv_mlt > 0._wp ) THEN |
|---|
| 239 | ! MV add comment on what that mass flux means |
|---|
| 240 | zfac = zdv_mlt * rhow * r1_rdtice ! melt pond mass flux < 0 [kg.m-2.s-1] |
|---|
| 241 | wfx_pnd_1d(ji) = wfx_pnd_1d(ji) - zfac |
|---|
| 242 | ! |
|---|
| 243 | ! MV |
|---|
| 244 | ! why surface melt and snow fluxes must be adjusted is not clear |
|---|
| 245 | ! sounds like things are counted twice |
|---|
| 246 | ! |
|---|
| 247 | zdum = zfac / ( wfx_snw_sum_1d(ji) + wfx_sum_1d(ji) ) ! adjust ice/snow melting flux > 0 to balance melt pond flux |
|---|
| 248 | wfx_snw_sum_1d(ji) = wfx_snw_sum_1d(ji) * (1._wp + zdum) |
|---|
| 249 | wfx_sum_1d(ji) = wfx_sum_1d(ji) * (1._wp + zdum) |
|---|
| 250 | ENDIF |
|---|
| 251 | |
|---|
| 252 | !-------------------! |
|---|
| 253 | ! case ice freezing ! i.e. t_su_1d(ji) < (zTp+rt0) |
|---|
| 254 | !-------------------! |
|---|
| 255 | ! |
|---|
| 256 | zdT = MAX( zTp+rt0 - t_su_1d(ji), 0._wp ) |
|---|
| 257 | ! |
|---|
| 258 | !--- Pond contraction (due to refreezing) ---! |
|---|
| 259 | IF( ln_pnd_lids ) THEN |
|---|
| 260 | ! |
|---|
| 261 | !--- Lid growing and subsequent pond shrinking ---! |
|---|
| 262 | zdv_frz = 0.5_wp * MAX( 0._wp, -v_il_1d(ji) + & ! Flocco 2010 (eq. 5) solved implicitly as aH**2 + bH + c = 0 |
|---|
| 263 | & SQRT( v_il_1d(ji)**2 + a_ip_1d(ji)**2 * 4._wp * rcnd_i * zdT * rdt_ice / (rLfus * rhow) ) ) ! max for roundoff errors |
|---|
| 264 | |
|---|
| 265 | ! Lid growing |
|---|
| 266 | v_il_1d(ji) = MAX( 0._wp, v_il_1d(ji) + zdv_frz ) |
|---|
| 267 | |
|---|
| 268 | ! Pond shrinking |
|---|
| 269 | v_ip_1d(ji) = MAX( 0._wp, v_ip_1d(ji) - zdv_frz ) |
|---|
| 270 | |
|---|
| 271 | ELSE |
|---|
| 272 | ! Pond shrinking |
|---|
| 273 | v_ip_1d(ji) = v_ip_1d(ji) * EXP( 0.01_wp * zdT * z1_Tp ) ! Holland 2012 (eq. 6) |
|---|
| 274 | ENDIF |
|---|
| 275 | ! |
|---|
| 276 | !--- Set new pond area and depth ---! assuming linear relation between h_ip and a_ip_frac |
|---|
| 277 | ! v_ip = h_ip * a_ip |
|---|
| 278 | ! a_ip/a_i = a_ip_frac = h_ip / zaspect (cf Holland 2012, fitting SHEBA so that knowing v_ip we can distribute it to a_ip and h_ip) |
|---|
| 279 | a_ip_1d(ji) = MIN( a_i_1d(ji), SQRT( v_ip_1d(ji) * z1_aspect * a_i_1d(ji) ) ) ! make sure a_ip < a_i |
|---|
| 280 | h_ip_1d(ji) = zaspect * a_ip_1d(ji) / a_i_1d(ji) |
|---|
| 281 | |
|---|
| 282 | !---------------! |
|---|
| 283 | ! Pond flushing ! |
|---|
| 284 | !---------------! |
|---|
| 285 | ! height of top of the pond above sea-level |
|---|
| 286 | zhp = ( h_i_1d(ji) * ( rau0 - rhoi ) + h_ip_1d(ji) * ( rau0 - rhow * a_ip_1d(ji) / a_i_1d(ji) ) ) * r1_rau0 |
|---|
| 287 | |
|---|
| 288 | ! Calculate the permeability of the ice (Assur 1958, see Flocco 2010) |
|---|
| 289 | DO jk = 1, nlay_i |
|---|
| 290 | zsbr = - 1.2_wp & |
|---|
| 291 | & - 21.8_wp * ( t_i_1d(ji,jk) - rt0 ) & |
|---|
| 292 | & - 0.919_wp * ( t_i_1d(ji,jk) - rt0 )**2 & |
|---|
| 293 | & - 0.0178_wp * ( t_i_1d(ji,jk) - rt0 )**3 |
|---|
| 294 | ! zsbr = - ( t_i_1d(ji,jk) - rt0 ) / rTmlt |
|---|
| 295 | ztmp(jk) = sz_i_1d(ji,jk) / zsbr |
|---|
| 296 | END DO |
|---|
| 297 | |
|---|
| 298 | zperm = MAX( 0._wp, 3.e-08_wp * MINVAL(ztmp)**3 ) |
|---|
| 299 | |
|---|
| 300 | ! Do the drainage using Darcy's law |
|---|
| 301 | zdv_flush = -zperm * rau0 * grav * zhp * rdt_ice / (zvisc * h_i_1d(ji)) * a_ip_1d(ji) |
|---|
| 302 | zdv_flush = MAX( zdv_flush, -v_ip_1d(ji) ) |
|---|
| 303 | v_ip_1d(ji) = v_ip_1d(ji) + zdv_flush |
|---|
| 304 | |
|---|
| 305 | ! MV --- why pond drainage does not give back water into freshwater flux ? |
|---|
| 306 | |
|---|
| 307 | !--- Set new pond area and depth ---! assuming linear relation between h_ip and a_ip_frac |
|---|
| 308 | a_ip_1d(ji) = MIN( a_i_1d(ji), SQRT( v_ip_1d(ji) * z1_aspect * a_i_1d(ji) ) ) ! make sure a_ip < a_i |
|---|
| 309 | h_ip_1d(ji) = zaspect * a_ip_1d(ji) / a_i_1d(ji) |
|---|
| 310 | |
|---|
| 311 | !--- Corrections and lid thickness ---! |
|---|
| 312 | IF( ln_pnd_lids ) THEN |
|---|
| 313 | !--- retrieve lid thickness from volume ---! |
|---|
| 314 | IF( a_ip_1d(ji) > epsi10 ) THEN ; h_il_1d(ji) = v_il_1d(ji) / a_ip_1d(ji) |
|---|
| 315 | ELSE ; h_il_1d(ji) = 0._wp |
|---|
| 316 | ENDIF |
|---|
| 317 | !--- remove ponds if lids are much larger than ponds ---! |
|---|
| 318 | IF ( h_il_1d(ji) > h_ip_1d(ji) * 10._wp ) THEN |
|---|
| 319 | a_ip_1d(ji) = 0._wp |
|---|
| 320 | h_ip_1d(ji) = 0._wp |
|---|
| 321 | h_il_1d(ji) = 0._wp |
|---|
| 322 | ENDIF |
|---|
| 323 | ENDIF |
|---|
| 324 | ! |
|---|
| 325 | ENDIF |
|---|
| 326 | |
|---|
| 327 | END DO |
|---|
| 328 | ! |
|---|
| 329 | END SUBROUTINE pnd_LEV |
|---|
| 330 | |
|---|
| 331 | SUBROUTINE pnd_TOPO (aice, aicen, & |
|---|
| 332 | vice, vicen, & |
|---|
| 333 | vsnon, & |
|---|
| 334 | ticen, salin, & |
|---|
| 335 | a_ip_frac, h_ip, & |
|---|
| 336 | Tsfc ) |
|---|
| 337 | |
|---|
| 338 | !!------------------------------------------------------------------- |
|---|
| 339 | !! *** ROUTINE pnd_TOPO *** |
|---|
| 340 | !! |
|---|
| 341 | !! ** Purpose : Compute melt pond evolution |
|---|
| 342 | !! |
|---|
| 343 | !! ** Purpose : Compute melt pond evolution based on the ice |
|---|
| 344 | !! topography as inferred from the ice thickness |
|---|
| 345 | !! distribution. |
|---|
| 346 | !! |
|---|
| 347 | !! ** Method : This code is initially based on Flocco and Feltham |
|---|
| 348 | !! (2007) and Flocco et al. (2010). More to come... |
|---|
| 349 | !! |
|---|
| 350 | !! ** Tunable parameters : |
|---|
| 351 | !! |
|---|
| 352 | !! ** Note : |
|---|
| 353 | !! |
|---|
| 354 | !! ** References |
|---|
| 355 | !! Flocco, D. and D. L. Feltham, 2007. A continuum model of melt pond |
|---|
| 356 | !! evolution on Arctic sea ice. J. Geophys. Res. 112, C08016, doi: |
|---|
| 357 | !! 10.1029/2006JC003836. |
|---|
| 358 | !! Flocco, D., D. L. Feltham and A. K. Turner, 2010. Incorporation of |
|---|
| 359 | !! a physically based melt pond scheme into the sea ice component of a |
|---|
| 360 | !! climate model. J. Geophys. Res. 115, C08012, |
|---|
| 361 | !! doi: 10.1029/2009JC005568. |
|---|
| 362 | !! |
|---|
| 363 | !!------------------------------------------------------------------- |
|---|
| 364 | |
|---|
| 365 | !js 190423: the lid on melt ponds appears only in the analog subroutine of CICE 5.1.2 |
|---|
| 366 | |
|---|
| 367 | REAL (wp), DIMENSION (jpi,jpj), & |
|---|
| 368 | INTENT(IN) :: & |
|---|
| 369 | aice, & ! total ice area fraction |
|---|
| 370 | vice ! total ice volume (m) |
|---|
| 371 | |
|---|
| 372 | REAL (wp), DIMENSION (jpi,jpj,jpl), & |
|---|
| 373 | INTENT(IN) :: & |
|---|
| 374 | aicen, & ! ice area fraction, per category |
|---|
| 375 | vsnon, & ! snow volume, per category (m) |
|---|
| 376 | vicen ! ice volume, per category (m) |
|---|
| 377 | |
|---|
| 378 | REAL (wp), DIMENSION (jpi,jpj,nlay_i,jpl), & |
|---|
| 379 | INTENT(IN) :: & |
|---|
| 380 | ticen, & ! ice temperature per category (K) |
|---|
| 381 | salin |
|---|
| 382 | |
|---|
| 383 | REAL (wp), DIMENSION (jpi,jpj,jpl), & |
|---|
| 384 | INTENT(INOUT) :: & |
|---|
| 385 | a_ip_frac , & ! pond area fraction of ice, per ice category |
|---|
| 386 | h_ip ! pond depth, per ice category (m) |
|---|
| 387 | |
|---|
| 388 | REAL (wp), DIMENSION (jpi,jpj,jpl), & |
|---|
| 389 | INTENT(IN) :: & |
|---|
| 390 | Tsfc ! snow/sea ice surface temperature |
|---|
| 391 | |
|---|
| 392 | ! local variables |
|---|
| 393 | REAL (wp), DIMENSION (jpi,jpj,jpl) :: & |
|---|
| 394 | zTsfcn, & ! ice/snow surface temperature (C) |
|---|
| 395 | zvolpn ! pond volume per unit area, per category (m) |
|---|
| 396 | |
|---|
| 397 | REAL (wp), DIMENSION (jpi,jpj,jpl) :: & |
|---|
| 398 | zrfrac, & ! fraction of available meltwater retained for melt ponding |
|---|
| 399 | zapondn,& ! pond area fraction, per category |
|---|
| 400 | zhpondn ! pond depth, per category (m) |
|---|
| 401 | |
|---|
| 402 | REAL (wp), DIMENSION (jpi,jpj) :: & |
|---|
| 403 | zvolp, & ! total volume of pond, per unit area of pond (m) |
|---|
| 404 | zwfx_tmp ! temporary array for melt water |
|---|
| 405 | |
|---|
| 406 | REAL (wp) :: & |
|---|
| 407 | zhi, & ! ice thickness (m) |
|---|
| 408 | zTavg, & ! mean surface temperature across categories (C) |
|---|
| 409 | z1_rhow, & ! inverse freshwater density |
|---|
| 410 | zdTs, & ! temperature difference for freeze-up (C) |
|---|
| 411 | zvpold, & ! dummy pond volume |
|---|
| 412 | zdvn ! change in melt pond volume for fresh water budget |
|---|
| 413 | |
|---|
| 414 | INTEGER, DIMENSION (jpi*jpj) :: & |
|---|
| 415 | indxi, indxj ! compressed indices for cells with ice melting |
|---|
| 416 | |
|---|
| 417 | INTEGER :: ij,icells,ji,jj,jl ! loop indices |
|---|
| 418 | |
|---|
| 419 | REAL (wp), PARAMETER :: & |
|---|
| 420 | ! MV ouate de phoque!!! constants hard coded ???? |
|---|
| 421 | ! 917 = rhoice |
|---|
| 422 | ! 0.334 =Lfus!!!! |
|---|
| 423 | zr1_rlfus = 1._wp / 0.334e+6 / 917._wp , & ! (J/m^3) |
|---|
| 424 | zTp = -0.15_wp, & ! pond freezing temperature (C) |
|---|
| 425 | zmin_volp = 1.e-4_wp, & ! minimum pond volume (m) |
|---|
| 426 | zrexp = 0.01_wp, & ! constant melt pond freeze-up rate |
|---|
| 427 | z01 = 0.01_wp, & |
|---|
| 428 | z25 = 0.25_wp, & |
|---|
| 429 | z5 = 0.5_wp |
|---|
| 430 | |
|---|
| 431 | z1_rhow = 1. / rhow |
|---|
| 432 | |
|---|
| 433 | !--------------------------------------------------------------- |
|---|
| 434 | ! Initialization |
|---|
| 435 | !--------------------------------------------------------------- |
|---|
| 436 | zhpondn (:,:,:) = 0._wp |
|---|
| 437 | zapondn (:,:,:) = 0._wp |
|---|
| 438 | zvolpn (:,:,:) = 0._wp |
|---|
| 439 | |
|---|
| 440 | zTsfcn(:,:,:) = Tsfc(:,:,:) - rt0 ! Convert in Celsius |
|---|
| 441 | |
|---|
| 442 | IF ( ln_pnd_fw ) THEN |
|---|
| 443 | v_ip_b(:,:,:) = v_ip(:,:,:) |
|---|
| 444 | ELSE |
|---|
| 445 | v_ip_b(:,:,:) = 0._wp |
|---|
| 446 | ENDIF |
|---|
| 447 | |
|---|
| 448 | !------------------------------------------------------------------ |
|---|
| 449 | ! Available melt water for melt ponding and corresponding fraction |
|---|
| 450 | !------------------------------------------------------------------ |
|---|
| 451 | !js 03/05/19 unset restriction on sign of wfx_pnd_in; mask values close to zero for future division |
|---|
| 452 | !wfx_pnd_in(:,:) = MAX( wfx_sum(:,:) + wfx_snw_sum(:,:), 0._wp ) ! available meltwater for melt ponding |
|---|
| 453 | !wfx_pnd_in(:,:) = MAX( wfx_sum(:,:) + wfx_snw_sum(:,:) , epsi10 ) * MAX( 0._wp, SIGN( 1._wp, wfx_sum(:,:) + wfx_snw_sum(:,:) - epsi10 ) ) |
|---|
| 454 | !wfx_pnd_in(:,:) = (wfx_sum(:,:) + wfx_snw_sum(:,:)) * MAX( 0._wp, SIGN( 1._wp, ABS(wfx_sum(:,:) + wfx_snw_sum(:,:)) - epsi10 ) ) |
|---|
| 455 | |
|---|
| 456 | ! MV |
|---|
| 457 | ! NB: wfx_pnd_in can be slightly negative for very small values (why?) |
|---|
| 458 | ! This can in some occasions give negative |
|---|
| 459 | ! v_ip in the first category, which then gives crazy pond |
|---|
| 460 | ! fractions and crashes the code as soon as the melt-pond |
|---|
| 461 | ! radiative coupling is activated |
|---|
| 462 | ! if we understand and remove why wfx_sum or wfx_snw could be |
|---|
| 463 | ! negative, then, we can remove the MAX |
|---|
| 464 | ! NB: I now changed to wfx_snw_sum, this may fix the problem. |
|---|
| 465 | ! We should check |
|---|
| 466 | |
|---|
| 467 | |
|---|
| 468 | ! OLI 07/2017: when we (MV & OL) first started the inclusion of melt |
|---|
| 469 | ! ponds in the model, we removed the Holland et al. (2012, see |
|---|
| 470 | ! CESM scheme above) parameterization. I put it back here, |
|---|
| 471 | ! because I think it is needed. In summary, the sinks of FW for |
|---|
| 472 | ! ponds are: 1/ Runoff through cracks/leads => depends on the |
|---|
| 473 | ! total ice area only |
|---|
| 474 | ! 2/ overflow, including Lüthje et al. (2006) limitation |
|---|
| 475 | ! (max a_ip fraction function of h_i). This is in |
|---|
| 476 | ! fact an other form of runoff that depends on the |
|---|
| 477 | ! ITD |
|---|
| 478 | ! 3/ Flushing - losses by permeability |
|---|
| 479 | ! 4/ Refreezing |
|---|
| 480 | ! 5/ Removal of ponds on thin ice |
|---|
| 481 | ! I think 1 is needed because it is different from 2. However, |
|---|
| 482 | ! test runs should/could be done, to check the sensitivity and |
|---|
| 483 | ! the real usefulness of that stuff. |
|---|
| 484 | ! Note : the Holland et al. param was wrongly wired in NEMO3.1 (using |
|---|
| 485 | ! a_i instead of at_i), which might well explain why I had a too |
|---|
| 486 | ! weak melt pond cover in my simulations (compared to MODIS, in |
|---|
| 487 | ! situ obs. and CICE simulations. |
|---|
| 488 | |
|---|
| 489 | !js 23/04/19: rewired back to a fraction with a_i |
|---|
| 490 | !!! zrfrac(:,:,:) = rn_pnd_fracmin + ( rn_pnd_fracmax - rn_pnd_fracmin ) * aicen(:,:,:) |
|---|
| 491 | ! MV2020 |
|---|
| 492 | zrfrac(:,:,:) = rn_apnd_min + ( rn_apnd_max - rn_apnd_min ) * at_i_1d(:) ! = ( 1 - r ) = fraction of melt water that is not flushed |
|---|
| 493 | zwfx_tmp(:,:) = 0._wp |
|---|
| 494 | |
|---|
| 495 | !--- Add retained melt water to melt ponds |
|---|
| 496 | ! v_ip should never be negative, otherwise code crashes |
|---|
| 497 | ! Rq MV: as far as I saw, UM5 can create very small negative v_ip values |
|---|
| 498 | ! hence I added the max, which was not required with Prather (1 yr run) |
|---|
| 499 | ! OLI: Here I use vt_ip, so I don't know if the max is |
|---|
| 500 | ! required... |
|---|
| 501 | !zvolp(:,:) = MAX(vt_ip(:,:),0._wp) + zrfrac(:,:) * wfx_pnd_in(:,:) * z1_rhow * rdt_ice ! Total available melt water, to be distributed as melt ponds |
|---|
| 502 | ! OLI: 07/2017 Bugfix above, removed " * aice(:,:)" |
|---|
| 503 | !js 19/04/18: change zrfrac to use aicen |
|---|
| 504 | |
|---|
| 505 | zvolp(:,:) = vt_ip(:,:) |
|---|
| 506 | |
|---|
| 507 | DO jl = 1, jpl |
|---|
| 508 | ! Melt water, to be distributed as melt ponds |
|---|
| 509 | zvolp(:,:) = zvolp(:,:) - zrfrac(:,:,jl) & |
|---|
| 510 | * ( dh_i_pnd(:,:,jl)*rhoic + dh_s_pnd(:,:,jl)*rhosn ) & |
|---|
| 511 | * z1_rhow * a_i(:,:,jl) |
|---|
| 512 | ! MV ---> use expression from level ice melt ponds (dv_mlt) |
|---|
| 513 | |
|---|
| 514 | END DO |
|---|
| 515 | |
|---|
| 516 | |
|---|
| 517 | !!! MV ---> rewrite this accounting for level ice melt ponds |
|---|
| 518 | !!! 1) wfx_pnd_in is obsolete, ln_pnd_fw as well |
|---|
| 519 | !!! 2) |
|---|
| 520 | !!! wfx_sum |
|---|
| 521 | !!! |
|---|
| 522 | !!! |
|---|
| 523 | !js 03/05/19: we truncate negative values after calculating zvolp, in a |
|---|
| 524 | ! similar manner to the subroutine ice_thd_pnd_cesm. Variation dh_i_pnd and |
|---|
| 525 | ! dh_s_pnd are negative, indicating a loss of ice or snow. But we can expect them |
|---|
| 526 | ! to be negative for some reasons. We keep this behaviour as it is, for |
|---|
| 527 | ! fluxes conservation reasons. If some dh are positive, then we remove water |
|---|
| 528 | ! indirectly from the ponds. |
|---|
| 529 | zvolp(:,:) = MAX( zvolp(:,:) , 0._wp ) |
|---|
| 530 | |
|---|
| 531 | |
|---|
| 532 | ! Fresh water flux going into the ponds |
|---|
| 533 | wfx_pnd_in(:,:) = wfx_pnd_in(:,:) + rhow * ( zvolp(:,:) - vt_ip(:,:) ) * r1_rdtice |
|---|
| 534 | |
|---|
| 535 | !--- Remove retained meltwater from surface fluxes |
|---|
| 536 | IF ( ln_pnd_fw ) THEN |
|---|
| 537 | !wfx_snw_sum(:,:) = wfx_snw_sum(:,:) * ( 1. - zrfrac(:,:) ) |
|---|
| 538 | !wfx_sum(:,:) = wfx_sum(:,:) * ( 1. - zrfrac(:,:) ) |
|---|
| 539 | |
|---|
| 540 | !js 190419: we change the code to use a_i in zrfrac. To be tested, but |
|---|
| 541 | !it should be conservative. zwfx_tmp is the flux accumulated in the |
|---|
| 542 | !ponds. wfx_pnd_in is the total surface melt fluxes. |
|---|
| 543 | zwfx_tmp(:,:) = MAX( wfx_sum(:,:) + wfx_snw_sum(:,:) , epsi10 ) & |
|---|
| 544 | & * MAX( 0._wp, SIGN( 1._wp, ABS(wfx_sum(:,:) + wfx_snw_sum(:,:)) - epsi10 ) ) |
|---|
| 545 | WHERE ( ABS(zwfx_tmp(:,:)) > epsi10 ) |
|---|
| 546 | zwfx_tmp(:,:) = wfx_pnd_in(:,:) / zwfx_tmp(:,:) |
|---|
| 547 | ELSEWHERE |
|---|
| 548 | zwfx_tmp(:,:) = 0._wp |
|---|
| 549 | ENDWHERE |
|---|
| 550 | |
|---|
| 551 | wfx_sum(:,:) = ( 1._wp - zwfx_tmp(:,:) ) * wfx_sum(:,:) |
|---|
| 552 | wfx_snw_sum(:,:) = ( 1._wp - zwfx_tmp(:,:) ) * wfx_snw_sum(:,:) |
|---|
| 553 | ENDIF |
|---|
| 554 | |
|---|
| 555 | |
|---|
| 556 | |
|---|
| 557 | !----------------------------------------------------------------- |
|---|
| 558 | ! Identify grid cells with ponds |
|---|
| 559 | !----------------------------------------------------------------- |
|---|
| 560 | |
|---|
| 561 | icells = 0 |
|---|
| 562 | DO jj = 1, jpj |
|---|
| 563 | DO ji = 1, jpi |
|---|
| 564 | IF ( aice(ji,jj) > epsi10 ) THEN |
|---|
| 565 | zhi = vice(ji,jj) / aice(ji,jj) |
|---|
| 566 | ELSE |
|---|
| 567 | zhi = 0._wp |
|---|
| 568 | END IF |
|---|
| 569 | |
|---|
| 570 | IF ( aice(ji,jj) > z01 .and. zhi > rn_himin .and. & |
|---|
| 571 | zvolp(ji,jj) > zmin_volp*aice(ji,jj)) THEN |
|---|
| 572 | icells = icells + 1 |
|---|
| 573 | indxi(icells) = ji |
|---|
| 574 | indxj(icells) = jj |
|---|
| 575 | ELSE ! remove ponds on thin ice, or too small ponds |
|---|
| 576 | zvolpn(ji,jj,:) = 0._wp |
|---|
| 577 | zvolp (ji,jj) = 0._wp |
|---|
| 578 | |
|---|
| 579 | a_ip(ji,jj,:) = 0._wp |
|---|
| 580 | v_ip(ji,jj,:) = 0._wp |
|---|
| 581 | a_ip_frac(ji,jj,:) = 0._wp |
|---|
| 582 | h_ip(ji,jj,:) = 0._wp |
|---|
| 583 | |
|---|
| 584 | vt_ip(ji,jj) = 0._wp |
|---|
| 585 | at_ip(ji,jj) = 0._wp |
|---|
| 586 | |
|---|
| 587 | ! IF ( ln_pnd_fw ) & !--- Give freshwater to the ocean |
|---|
| 588 | ! wfx_pnd_out(ji,jj) = wfx_pnd_out(ji,jj) + zvolp(ji,jj) * rhow * r1_rdtice |
|---|
| 589 | END IF |
|---|
| 590 | END DO ! ji |
|---|
| 591 | END DO ! jj |
|---|
| 592 | |
|---|
| 593 | |
|---|
| 594 | |
|---|
| 595 | !!! MV sounds like this should be replaced by lid |
|---|
| 596 | |
|---|
| 597 | DO ij = 1, icells |
|---|
| 598 | |
|---|
| 599 | ji = indxi(ij) |
|---|
| 600 | jj = indxj(ij) |
|---|
| 601 | |
|---|
| 602 | !-------------------------------------------------------------- |
|---|
| 603 | ! Shrink pond due to refreezing |
|---|
| 604 | !-------------------------------------------------------------- |
|---|
| 605 | ! OLI 07/2017: Done like for empirical melt pond scheme (CESM). |
|---|
| 606 | ! Therefore, I chose to put this part of the code before the main |
|---|
| 607 | ! routines ice_thd_pnd_area/depth (contrary to the original code), |
|---|
| 608 | ! seeing the freeze-up as a global sink of |
|---|
| 609 | ! freshwater for melt ponds in the whole grid cell. If this was done |
|---|
| 610 | ! after, I would need to make an additional assumption on the shape of |
|---|
| 611 | ! melt ponds, which I don't want to do (for the CESM scheme, this |
|---|
| 612 | ! assumption was on the aspect ratio). So I remove some water due to |
|---|
| 613 | ! refreezing first (using zTavg instead of zTsfcn in each category) and |
|---|
| 614 | ! then let the FF07 routines do their job for the fractional areas and |
|---|
| 615 | ! depths of melt ponds. |
|---|
| 616 | ! The whole ice lid related stuff from FF07 was thus removed and replaced |
|---|
| 617 | ! by this. As mentionned below, this should be improved, but is much |
|---|
| 618 | ! easier to conserve heat and freshwater this way. |
|---|
| 619 | |
|---|
| 620 | ! Average surface temperature is needed to compute freeze-up at the cell |
|---|
| 621 | ! scale |
|---|
| 622 | zTavg = 0._wp |
|---|
| 623 | DO jl = 1, jpl |
|---|
| 624 | zTavg = zTavg + zTsfcn(ji,jj,jl)*aicen(ji,jj,jl) |
|---|
| 625 | END DO |
|---|
| 626 | zTavg = zTavg / aice(ji,jj) |
|---|
| 627 | |
|---|
| 628 | ! The freezing temperature for meltponds is assumed slightly below 0C, |
|---|
| 629 | ! as if meltponds had a little salt in them (hence the use of zTp). |
|---|
| 630 | ! The salt budget is not |
|---|
| 631 | ! altered for meltponds, but if it were then an actual pond freezing |
|---|
| 632 | ! temperature could be computed. |
|---|
| 633 | |
|---|
| 634 | zdTs = MAX ( zTp - zTavg, 0. ) |
|---|
| 635 | |
|---|
| 636 | zvpold = zvolp(ji,jj) |
|---|
| 637 | |
|---|
| 638 | zvolp(ji,jj) = zvolp(ji,jj) * EXP( zrexp * zdTs / zTp ) |
|---|
| 639 | |
|---|
| 640 | !--- Dump meltwater due to refreezing ( of course this is wrong |
|---|
| 641 | !--- but this parameterization is too simple ) |
|---|
| 642 | ! IF ( ln_pnd_fw ) & |
|---|
| 643 | ! wfx_pnd_out(ji,jj) = wfx_pnd_out(ji,jj) + rhow * ( zvpold - zvolp(ji,jj) ) * r1_rdtice |
|---|
| 644 | ! ! OLI 07/2017 : Bugfix above, zvpold - zvolp instead of the |
|---|
| 645 | ! ! opposite, otherwise negative contribution |
|---|
| 646 | |
|---|
| 647 | !-------------------------------------------------------------- |
|---|
| 648 | ! calculate pond area and depth |
|---|
| 649 | !-------------------------------------------------------------- |
|---|
| 650 | zdvn = 0._wp |
|---|
| 651 | CALL ice_thd_pnd_area(aice(ji,jj),vice(ji,jj), & |
|---|
| 652 | aicen(ji,jj,:), vicen(ji,jj,:), vsnon(ji,jj,:), & |
|---|
| 653 | ticen(ji,jj,:,:), salin(ji,jj,:,:), & |
|---|
| 654 | zvolpn(ji,jj,:), zvolp(ji,jj), & |
|---|
| 655 | zapondn(ji,jj,:),zhpondn(ji,jj,:), zdvn) |
|---|
| 656 | ! outputs are |
|---|
| 657 | ! - zdvn |
|---|
| 658 | ! - zvolpn |
|---|
| 659 | ! - zvolp |
|---|
| 660 | ! - zapondn |
|---|
| 661 | ! - zhpondn |
|---|
| 662 | |
|---|
| 663 | ! IF ( ln_pnd_fw ) & |
|---|
| 664 | ! wfx_pnd_out(ji,jj) = wfx_pnd_out(ji,jj) + zdvn * rhow * r1_rdtice ! update flux from ponds to ocean |
|---|
| 665 | |
|---|
| 666 | !--------------------------------------------------------------- |
|---|
| 667 | ! Update pond volume and fraction |
|---|
| 668 | !--------------------------------------------------------------- |
|---|
| 669 | DO jl = 1, jpl |
|---|
| 670 | a_ip(ji,jj,jl) = zapondn(ji,jj,jl) |
|---|
| 671 | v_ip(ji,jj,jl) = zvolpn(ji,jj,jl) |
|---|
| 672 | a_ip_frac(ji,jj,jl) = a_ip(ji,jj,jl) / MAX(aicen(ji,jj,jl), epsi10) & |
|---|
| 673 | * MAX(0._wp, SIGN(1._wp, aicen(ji,jj,jl) - epsi10)) |
|---|
| 674 | h_ip (ji,jj,jl) = zhpondn(ji,jj,jl) |
|---|
| 675 | END DO |
|---|
| 676 | END DO ! ij |
|---|
| 677 | |
|---|
| 678 | IF ( ln_pnd_fw ) THEN |
|---|
| 679 | !js 15/05/19: water going out of the ponds give a positive freshwater |
|---|
| 680 | ! flux. |
|---|
| 681 | wfx_pnd_out(:,:) = SUM(MAX(0._wp, v_ip_b(:,:,:) - v_ip(:,:,:)), DIM=3) * rhow * r1_rdtice |
|---|
| 682 | ELSE |
|---|
| 683 | wfx_pnd_out(:,:) = 0._wp |
|---|
| 684 | ENDIF |
|---|
| 685 | |
|---|
| 686 | END SUBROUTINE pnd_TOPO |
|---|
| 687 | |
|---|
| 688 | SUBROUTINE ice_thd_pnd_area(aice, vice, & |
|---|
| 689 | aicen, vicen, vsnon, ticen, & |
|---|
| 690 | salin, zvolpn, zvolp, & |
|---|
| 691 | zapondn,zhpondn,dvolp) |
|---|
| 692 | |
|---|
| 693 | !!------------------------------------------------------------------- |
|---|
| 694 | !! *** ROUTINE ice_thd_pnd_area *** |
|---|
| 695 | !! |
|---|
| 696 | !! ** Purpose : Given the total volume of meltwater, update |
|---|
| 697 | !! pond fraction (a_ip) and depth (should be volume) |
|---|
| 698 | !! |
|---|
| 699 | !! ** |
|---|
| 700 | !! |
|---|
| 701 | !!------------------------------------------------------------------ |
|---|
| 702 | |
|---|
| 703 | REAL (wp), INTENT(IN) :: & |
|---|
| 704 | aice, vice |
|---|
| 705 | |
|---|
| 706 | REAL (wp), DIMENSION(jpl), INTENT(IN) :: & |
|---|
| 707 | aicen, vicen, vsnon |
|---|
| 708 | |
|---|
| 709 | REAL (wp), DIMENSION(nlay_i,jpl), INTENT(IN) :: & |
|---|
| 710 | ticen, salin |
|---|
| 711 | |
|---|
| 712 | REAL (wp), DIMENSION(jpl), INTENT(INOUT) :: & |
|---|
| 713 | zvolpn |
|---|
| 714 | |
|---|
| 715 | REAL (wp), INTENT(INOUT) :: & |
|---|
| 716 | zvolp, dvolp |
|---|
| 717 | |
|---|
| 718 | REAL (wp), DIMENSION(jpl), INTENT(OUT) :: & |
|---|
| 719 | zapondn, zhpondn |
|---|
| 720 | |
|---|
| 721 | INTEGER :: & |
|---|
| 722 | n, ns, & |
|---|
| 723 | m_index, & |
|---|
| 724 | permflag |
|---|
| 725 | |
|---|
| 726 | REAL (wp), DIMENSION(jpl) :: & |
|---|
| 727 | hicen, & |
|---|
| 728 | hsnon, & |
|---|
| 729 | asnon, & |
|---|
| 730 | rhos, & ! OLI 07/2017 : for now this is useless, but will be useful with new snow scheme |
|---|
| 731 | alfan, & |
|---|
| 732 | betan, & |
|---|
| 733 | cum_max_vol, & |
|---|
| 734 | reduced_aicen |
|---|
| 735 | |
|---|
| 736 | REAL (wp), DIMENSION(0:jpl) :: & |
|---|
| 737 | cum_max_vol_tmp |
|---|
| 738 | |
|---|
| 739 | REAL (wp) :: & |
|---|
| 740 | hpond, & |
|---|
| 741 | drain, & |
|---|
| 742 | floe_weight, & |
|---|
| 743 | pressure_head, & |
|---|
| 744 | hsl_rel, & |
|---|
| 745 | deltah, & |
|---|
| 746 | perm, & |
|---|
| 747 | msno |
|---|
| 748 | |
|---|
| 749 | REAL (wp), parameter :: & |
|---|
| 750 | viscosity = 1.79e-3_wp, & ! kinematic water viscosity in kg/m/s |
|---|
| 751 | z0 = 0.0_wp , & |
|---|
| 752 | c1 = 1.0_wp , & |
|---|
| 753 | p4 = 0.4_wp , & |
|---|
| 754 | p6 = 0.6_wp |
|---|
| 755 | |
|---|
| 756 | !-----------| |
|---|
| 757 | ! | |
|---|
| 758 | ! |-----------| |
|---|
| 759 | !___________|___________|______________________________________sea-level |
|---|
| 760 | ! | | |
|---|
| 761 | ! | |---^--------| |
|---|
| 762 | ! | | | | |
|---|
| 763 | ! | | | |-----------| |------- |
|---|
| 764 | ! | | |alfan(n)| | | |
|---|
| 765 | ! | | | | |--------------| |
|---|
| 766 | ! | | | | | | |
|---|
| 767 | !---------------------------v------------------------------------------- |
|---|
| 768 | ! | | ^ | | | |
|---|
| 769 | ! | | | | |--------------| |
|---|
| 770 | ! | | |betan(n)| | | |
|---|
| 771 | ! | | | |-----------| |------- |
|---|
| 772 | ! | | | | |
|---|
| 773 | ! | |---v------- | |
|---|
| 774 | ! | | |
|---|
| 775 | ! |-----------| |
|---|
| 776 | ! | |
|---|
| 777 | !-----------| |
|---|
| 778 | |
|---|
| 779 | !------------------------------------------------------------------- |
|---|
| 780 | ! initialize |
|---|
| 781 | !------------------------------------------------------------------- |
|---|
| 782 | |
|---|
| 783 | rhos(:) = rhosn ! OLI 07/2017 : same has above |
|---|
| 784 | |
|---|
| 785 | DO n = 1, jpl |
|---|
| 786 | |
|---|
| 787 | zapondn(n) = z0 |
|---|
| 788 | zhpondn(n) = z0 |
|---|
| 789 | |
|---|
| 790 | !---------------------------------------- |
|---|
| 791 | ! X) compute the effective snow fraction |
|---|
| 792 | !---------------------------------------- |
|---|
| 793 | IF (aicen(n) < epsi10) THEN |
|---|
| 794 | hicen(n) = z0 |
|---|
| 795 | hsnon(n) = z0 |
|---|
| 796 | reduced_aicen(n) = z0 |
|---|
| 797 | asnon(n) = z0 !js: in CICE 5.1.2: make sense as the compiler may not initiate the variables |
|---|
| 798 | ELSE |
|---|
| 799 | hicen(n) = vicen(n) / aicen(n) |
|---|
| 800 | hsnon(n) = vsnon(n) / aicen(n) |
|---|
| 801 | reduced_aicen(n) = c1 ! n=jpl |
|---|
| 802 | |
|---|
| 803 | !js: initial code in NEMO_DEV |
|---|
| 804 | !IF (n < jpl) reduced_aicen(n) = aicen(n) & |
|---|
| 805 | ! * (-0.024_wp*hicen(n) + 0.832_wp) |
|---|
| 806 | |
|---|
| 807 | !js: from CICE 5.1.2: this limit reduced_aicen to 0.2 when hicen is too large |
|---|
| 808 | IF (n < jpl) reduced_aicen(n) = aicen(n) & |
|---|
| 809 | * max(0.2_wp,(-0.024_wp*hicen(n) + 0.832_wp)) |
|---|
| 810 | |
|---|
| 811 | asnon(n) = reduced_aicen(n) ! effective snow fraction (empirical) |
|---|
| 812 | ! MV should check whether this makes sense to have the same effective snow fraction in here |
|---|
| 813 | ! OLI: it probably doesn't |
|---|
| 814 | END IF |
|---|
| 815 | |
|---|
| 816 | ! This choice for alfa and beta ignores hydrostatic equilibium of categories. |
|---|
| 817 | ! Hydrostatic equilibium of the entire ITD is accounted for below, assuming |
|---|
| 818 | ! a surface topography implied by alfa=0.6 and beta=0.4, and rigidity across all |
|---|
| 819 | ! categories. alfa and beta partition the ITD - they are areas not thicknesses! |
|---|
| 820 | ! Multiplying by hicen, alfan and betan (below) are thus volumes per unit area. |
|---|
| 821 | ! Here, alfa = 60% of the ice area (and since hice is constant in a category, |
|---|
| 822 | ! alfan = 60% of the ice volume) in each category lies above the reference line, |
|---|
| 823 | ! and 40% below. Note: p6 is an arbitrary choice, but alfa+beta=1 is required. |
|---|
| 824 | |
|---|
| 825 | ! MV: |
|---|
| 826 | ! Note that this choice is not in the original FF07 paper and has been adopted in CICE |
|---|
| 827 | ! No reason why is explained in the doc, but I guess there is a reason. I'll try to investigate, maybe |
|---|
| 828 | |
|---|
| 829 | ! Where does that choice come from ? => OLI : Coz' Chuck Norris said so... |
|---|
| 830 | |
|---|
| 831 | alfan(n) = 0.6 * hicen(n) |
|---|
| 832 | betan(n) = 0.4 * hicen(n) |
|---|
| 833 | |
|---|
| 834 | cum_max_vol(n) = z0 |
|---|
| 835 | cum_max_vol_tmp(n) = z0 |
|---|
| 836 | |
|---|
| 837 | END DO ! jpl |
|---|
| 838 | |
|---|
| 839 | cum_max_vol_tmp(0) = z0 |
|---|
| 840 | drain = z0 |
|---|
| 841 | dvolp = z0 |
|---|
| 842 | |
|---|
| 843 | !---------------------------------------------------------- |
|---|
| 844 | ! x) Drain overflow water, update pond fraction and volume |
|---|
| 845 | !---------------------------------------------------------- |
|---|
| 846 | |
|---|
| 847 | !-------------------------------------------------------------------------- |
|---|
| 848 | ! the maximum amount of water that can be contained up to each ice category |
|---|
| 849 | !-------------------------------------------------------------------------- |
|---|
| 850 | |
|---|
| 851 | ! MV |
|---|
| 852 | ! If melt ponds are too deep to be sustainable given the ITD (OVERFLOW) |
|---|
| 853 | ! Then the excess volume cum_max_vol(jl) drains out of the system |
|---|
| 854 | ! It should be added to wfx_pnd_out |
|---|
| 855 | ! END MV |
|---|
| 856 | !js 18/04/19: XXX do something about this flux thing |
|---|
| 857 | |
|---|
| 858 | DO n = 1, jpl-1 ! last category can not hold any volume |
|---|
| 859 | |
|---|
| 860 | IF (alfan(n+1) >= alfan(n) .and. alfan(n+1) > z0) THEN |
|---|
| 861 | |
|---|
| 862 | ! total volume in level including snow |
|---|
| 863 | cum_max_vol_tmp(n) = cum_max_vol_tmp(n-1) + & |
|---|
| 864 | (alfan(n+1) - alfan(n)) * sum(reduced_aicen(1:n)) |
|---|
| 865 | |
|---|
| 866 | ! subtract snow solid volumes from lower categories in current level |
|---|
| 867 | DO ns = 1, n |
|---|
| 868 | cum_max_vol_tmp(n) = cum_max_vol_tmp(n) & |
|---|
| 869 | - rhos(ns)/rhow * & ! free air fraction that can be filled by water |
|---|
| 870 | asnon(ns) * & ! effective areal fraction of snow in that category |
|---|
| 871 | max(min(hsnon(ns)+alfan(ns)-alfan(n), alfan(n+1)-alfan(n)), z0) |
|---|
| 872 | END DO |
|---|
| 873 | |
|---|
| 874 | ELSE ! assume higher categories unoccupied |
|---|
| 875 | cum_max_vol_tmp(n) = cum_max_vol_tmp(n-1) |
|---|
| 876 | END IF |
|---|
| 877 | !IF (cum_max_vol_tmp(n) < z0) THEN |
|---|
| 878 | ! CALL abort_ice('negative melt pond volume') |
|---|
| 879 | !END IF |
|---|
| 880 | END DO |
|---|
| 881 | cum_max_vol_tmp(jpl) = cum_max_vol_tmp(jpl-1) ! last category holds no volume |
|---|
| 882 | cum_max_vol (1:jpl) = cum_max_vol_tmp(1:jpl) |
|---|
| 883 | |
|---|
| 884 | !---------------------------------------------------------------- |
|---|
| 885 | ! is there more meltwater than can be held in the floe? |
|---|
| 886 | !---------------------------------------------------------------- |
|---|
| 887 | IF (zvolp >= cum_max_vol(jpl)) THEN |
|---|
| 888 | drain = zvolp - cum_max_vol(jpl) + epsi10 |
|---|
| 889 | zvolp = zvolp - drain ! update meltwater volume available |
|---|
| 890 | dvolp = drain ! this is the drained water |
|---|
| 891 | IF (zvolp < epsi10) THEN |
|---|
| 892 | dvolp = dvolp + zvolp |
|---|
| 893 | zvolp = z0 |
|---|
| 894 | END IF |
|---|
| 895 | END IF |
|---|
| 896 | |
|---|
| 897 | ! height and area corresponding to the remaining volume |
|---|
| 898 | |
|---|
| 899 | CALL ice_thd_pnd_depth(reduced_aicen, asnon, hsnon, rhos, alfan, zvolp, cum_max_vol, hpond, m_index) |
|---|
| 900 | |
|---|
| 901 | DO n=1, m_index |
|---|
| 902 | !zhpondn(n) = hpond - alfan(n) + alfan(1) ! here oui choulde update |
|---|
| 903 | ! ! volume instead, no ? |
|---|
| 904 | zhpondn(n) = max((hpond - alfan(n) + alfan(1)), z0) !js: from CICE 5.1.2 |
|---|
| 905 | zapondn(n) = reduced_aicen(n) |
|---|
| 906 | ! in practise, pond fraction depends on the empirical snow fraction |
|---|
| 907 | ! so in turn on ice thickness |
|---|
| 908 | END DO |
|---|
| 909 | !zapond = sum(zapondn(1:m_index)) !js: from CICE 5.1.2; not in Icepack1.1.0-6-gac6195d |
|---|
| 910 | |
|---|
| 911 | !------------------------------------------------------------------------ |
|---|
| 912 | ! Drainage through brine network (permeability) |
|---|
| 913 | !------------------------------------------------------------------------ |
|---|
| 914 | !!! drainage due to ice permeability - Darcy's law |
|---|
| 915 | |
|---|
| 916 | ! sea water level |
|---|
| 917 | msno = z0 |
|---|
| 918 | DO n=1,jpl |
|---|
| 919 | msno = msno + vsnon(n) * rhos(n) |
|---|
| 920 | END DO |
|---|
| 921 | floe_weight = (msno + rhoic*vice + rau0*zvolp) / aice |
|---|
| 922 | hsl_rel = floe_weight / rau0 & |
|---|
| 923 | - ((sum(betan(:)*aicen(:))/aice) + alfan(1)) |
|---|
| 924 | |
|---|
| 925 | deltah = hpond - hsl_rel |
|---|
| 926 | pressure_head = grav * rau0 * max(deltah, z0) |
|---|
| 927 | |
|---|
| 928 | ! drain if ice is permeable |
|---|
| 929 | permflag = 0 |
|---|
| 930 | IF (pressure_head > z0) THEN |
|---|
| 931 | DO n = 1, jpl-1 |
|---|
| 932 | IF (hicen(n) /= z0) THEN |
|---|
| 933 | !IF (hicen(n) > z0) THEN !js: from CICE 5.1.2 |
|---|
| 934 | perm = 0._wp ! MV ugly dummy patch |
|---|
| 935 | CALL ice_thd_pnd_perm(ticen(:,n), salin(:,n), perm) |
|---|
| 936 | IF (perm > z0) permflag = 1 |
|---|
| 937 | |
|---|
| 938 | drain = perm*zapondn(n)*pressure_head*rdt_ice / & |
|---|
| 939 | (viscosity*hicen(n)) |
|---|
| 940 | dvolp = dvolp + min(drain, zvolp) |
|---|
| 941 | zvolp = max(zvolp - drain, z0) |
|---|
| 942 | IF (zvolp < epsi10) THEN |
|---|
| 943 | dvolp = dvolp + zvolp |
|---|
| 944 | zvolp = z0 |
|---|
| 945 | END IF |
|---|
| 946 | END IF |
|---|
| 947 | END DO |
|---|
| 948 | |
|---|
| 949 | ! adjust melt pond dimensions |
|---|
| 950 | IF (permflag > 0) THEN |
|---|
| 951 | ! recompute pond depth |
|---|
| 952 | CALL ice_thd_pnd_depth(reduced_aicen, asnon, hsnon, rhos, alfan, zvolp, cum_max_vol, hpond, m_index) |
|---|
| 953 | DO n=1, m_index |
|---|
| 954 | zhpondn(n) = hpond - alfan(n) + alfan(1) |
|---|
| 955 | zapondn(n) = reduced_aicen(n) |
|---|
| 956 | END DO |
|---|
| 957 | !zapond = sum(zapondn(1:m_index)) !js: from CICE 5.1.2; not in Icepack1.1.0-6-gac6195d |
|---|
| 958 | END IF |
|---|
| 959 | END IF ! pressure_head |
|---|
| 960 | |
|---|
| 961 | !------------------------------- |
|---|
| 962 | ! X) remove water from the snow |
|---|
| 963 | !------------------------------- |
|---|
| 964 | !------------------------------------------------------------------------ |
|---|
| 965 | ! total melt pond volume in category does not include snow volume |
|---|
| 966 | ! snow in melt ponds is not melted |
|---|
| 967 | !------------------------------------------------------------------------ |
|---|
| 968 | |
|---|
| 969 | ! Calculate pond volume for lower categories |
|---|
| 970 | DO n=1,m_index-1 |
|---|
| 971 | zvolpn(n) = zapondn(n) * zhpondn(n) & ! what is not in the snow |
|---|
| 972 | - (rhos(n)/rhow) * asnon(n) * min(hsnon(n), zhpondn(n)) |
|---|
| 973 | END DO |
|---|
| 974 | |
|---|
| 975 | ! Calculate pond volume for highest category = remaining pond volume |
|---|
| 976 | |
|---|
| 977 | ! The following is completely unclear to Martin at least |
|---|
| 978 | ! Could we redefine properly and recode in a more readable way ? |
|---|
| 979 | |
|---|
| 980 | ! m_index = last category with melt pond |
|---|
| 981 | |
|---|
| 982 | IF (m_index == 1) zvolpn(m_index) = zvolp ! volume of mw in 1st category is the total volume of melt water |
|---|
| 983 | |
|---|
| 984 | IF (m_index > 1) THEN |
|---|
| 985 | IF (zvolp > sum(zvolpn(1:m_index-1))) THEN |
|---|
| 986 | zvolpn(m_index) = zvolp - sum(zvolpn(1:m_index-1)) |
|---|
| 987 | ELSE |
|---|
| 988 | zvolpn(m_index) = z0 |
|---|
| 989 | zhpondn(m_index) = z0 |
|---|
| 990 | zapondn(m_index) = z0 |
|---|
| 991 | ! If remaining pond volume is negative reduce pond volume of |
|---|
| 992 | ! lower category |
|---|
| 993 | IF (zvolp+epsi10 < sum(zvolpn(1:m_index-1))) & |
|---|
| 994 | zvolpn(m_index-1) = zvolpn(m_index-1) - sum(zvolpn(1:m_index-1)) + zvolp |
|---|
| 995 | END IF |
|---|
| 996 | END IF |
|---|
| 997 | |
|---|
| 998 | DO n=1,m_index |
|---|
| 999 | IF (zapondn(n) > epsi10) THEN |
|---|
| 1000 | zhpondn(n) = zvolpn(n) / zapondn(n) |
|---|
| 1001 | ELSE |
|---|
| 1002 | dvolp = dvolp + zvolpn(n) |
|---|
| 1003 | zhpondn(n) = z0 |
|---|
| 1004 | zvolpn(n) = z0 |
|---|
| 1005 | zapondn(n) = z0 |
|---|
| 1006 | END IF |
|---|
| 1007 | END DO |
|---|
| 1008 | DO n = m_index+1, jpl |
|---|
| 1009 | zhpondn(n) = z0 |
|---|
| 1010 | zapondn(n) = z0 |
|---|
| 1011 | zvolpn (n) = z0 |
|---|
| 1012 | END DO |
|---|
| 1013 | |
|---|
| 1014 | END SUBROUTINE ice_thd_pnd_area |
|---|
| 1015 | |
|---|
| 1016 | |
|---|
| 1017 | SUBROUTINE ice_thd_pnd_depth(aicen, asnon, hsnon, rhos, alfan, zvolp, cum_max_vol, hpond, m_index) |
|---|
| 1018 | !!------------------------------------------------------------------- |
|---|
| 1019 | !! *** ROUTINE ice_thd_pnd_depth *** |
|---|
| 1020 | !! |
|---|
| 1021 | !! ** Purpose : Compute melt pond depth |
|---|
| 1022 | !!------------------------------------------------------------------- |
|---|
| 1023 | |
|---|
| 1024 | REAL (wp), DIMENSION(jpl), INTENT(IN) :: & |
|---|
| 1025 | aicen, & |
|---|
| 1026 | asnon, & |
|---|
| 1027 | hsnon, & |
|---|
| 1028 | rhos, & |
|---|
| 1029 | alfan, & |
|---|
| 1030 | cum_max_vol |
|---|
| 1031 | |
|---|
| 1032 | REAL (wp), INTENT(IN) :: & |
|---|
| 1033 | zvolp |
|---|
| 1034 | |
|---|
| 1035 | REAL (wp), INTENT(OUT) :: & |
|---|
| 1036 | hpond |
|---|
| 1037 | |
|---|
| 1038 | INTEGER, INTENT(OUT) :: & |
|---|
| 1039 | m_index |
|---|
| 1040 | |
|---|
| 1041 | INTEGER :: n, ns |
|---|
| 1042 | |
|---|
| 1043 | REAL (wp), DIMENSION(0:jpl+1) :: & |
|---|
| 1044 | hitl, & |
|---|
| 1045 | aicetl |
|---|
| 1046 | |
|---|
| 1047 | REAL (wp) :: & |
|---|
| 1048 | rem_vol, & |
|---|
| 1049 | area, & |
|---|
| 1050 | vol, & |
|---|
| 1051 | tmp, & |
|---|
| 1052 | z0 = 0.0_wp |
|---|
| 1053 | |
|---|
| 1054 | !---------------------------------------------------------------- |
|---|
| 1055 | ! hpond is zero if zvolp is zero - have we fully drained? |
|---|
| 1056 | !---------------------------------------------------------------- |
|---|
| 1057 | |
|---|
| 1058 | IF (zvolp < epsi10) THEN |
|---|
| 1059 | hpond = z0 |
|---|
| 1060 | m_index = 0 |
|---|
| 1061 | ELSE |
|---|
| 1062 | |
|---|
| 1063 | !---------------------------------------------------------------- |
|---|
| 1064 | ! Calculate the category where water fills up to |
|---|
| 1065 | !---------------------------------------------------------------- |
|---|
| 1066 | |
|---|
| 1067 | !----------| |
|---|
| 1068 | ! | |
|---|
| 1069 | ! | |
|---|
| 1070 | ! |----------| -- -- |
|---|
| 1071 | !__________|__________|_________________________________________ ^ |
|---|
| 1072 | ! | | rem_vol ^ | Semi-filled |
|---|
| 1073 | ! | |----------|-- -- -- - ---|-- ---- -- -- --v layer |
|---|
| 1074 | ! | | | | |
|---|
| 1075 | ! | | | |hpond |
|---|
| 1076 | ! | | |----------| | |------- |
|---|
| 1077 | ! | | | | | | |
|---|
| 1078 | ! | | | |---v-----| |
|---|
| 1079 | ! | | m_index | | | |
|---|
| 1080 | !------------------------------------------------------------- |
|---|
| 1081 | |
|---|
| 1082 | m_index = 0 ! 1:m_index categories have water in them |
|---|
| 1083 | DO n = 1, jpl |
|---|
| 1084 | IF (zvolp <= cum_max_vol(n)) THEN |
|---|
| 1085 | m_index = n |
|---|
| 1086 | IF (n == 1) THEN |
|---|
| 1087 | rem_vol = zvolp |
|---|
| 1088 | ELSE |
|---|
| 1089 | rem_vol = zvolp - cum_max_vol(n-1) |
|---|
| 1090 | END IF |
|---|
| 1091 | exit ! to break out of the loop |
|---|
| 1092 | END IF |
|---|
| 1093 | END DO |
|---|
| 1094 | m_index = min(jpl-1, m_index) |
|---|
| 1095 | |
|---|
| 1096 | !---------------------------------------------------------------- |
|---|
| 1097 | ! semi-filled layer may have m_index different snow in it |
|---|
| 1098 | !---------------------------------------------------------------- |
|---|
| 1099 | |
|---|
| 1100 | !----------------------------------------------------------- ^ |
|---|
| 1101 | ! | alfan(m_index+1) |
|---|
| 1102 | ! | |
|---|
| 1103 | !hitl(3)--> |----------| | |
|---|
| 1104 | !hitl(2)--> |------------| * * * * *| | |
|---|
| 1105 | !hitl(1)--> |----------|* * * * * * |* * * * * | | |
|---|
| 1106 | !hitl(0)-->------------------------------------------------- | ^ |
|---|
| 1107 | ! various snow from lower categories | |alfa(m_index) |
|---|
| 1108 | |
|---|
| 1109 | ! hitl - heights of the snow layers from thinner and current categories |
|---|
| 1110 | ! aicetl - area of each snow depth in this layer |
|---|
| 1111 | |
|---|
| 1112 | hitl(:) = z0 |
|---|
| 1113 | aicetl(:) = z0 |
|---|
| 1114 | DO n = 1, m_index |
|---|
| 1115 | hitl(n) = max(min(hsnon(n) + alfan(n) - alfan(m_index), & |
|---|
| 1116 | alfan(m_index+1) - alfan(m_index)), z0) |
|---|
| 1117 | aicetl(n) = asnon(n) |
|---|
| 1118 | |
|---|
| 1119 | aicetl(0) = aicetl(0) + (aicen(n) - asnon(n)) |
|---|
| 1120 | END DO |
|---|
| 1121 | |
|---|
| 1122 | hitl(m_index+1) = alfan(m_index+1) - alfan(m_index) |
|---|
| 1123 | aicetl(m_index+1) = z0 |
|---|
| 1124 | |
|---|
| 1125 | !---------------------------------------------------------------- |
|---|
| 1126 | ! reorder array according to hitl |
|---|
| 1127 | ! snow heights not necessarily in height order |
|---|
| 1128 | !---------------------------------------------------------------- |
|---|
| 1129 | |
|---|
| 1130 | DO ns = 1, m_index+1 |
|---|
| 1131 | DO n = 0, m_index - ns + 1 |
|---|
| 1132 | IF (hitl(n) > hitl(n+1)) THEN ! swap order |
|---|
| 1133 | tmp = hitl(n) |
|---|
| 1134 | hitl(n) = hitl(n+1) |
|---|
| 1135 | hitl(n+1) = tmp |
|---|
| 1136 | tmp = aicetl(n) |
|---|
| 1137 | aicetl(n) = aicetl(n+1) |
|---|
| 1138 | aicetl(n+1) = tmp |
|---|
| 1139 | END IF |
|---|
| 1140 | END DO |
|---|
| 1141 | END DO |
|---|
| 1142 | |
|---|
| 1143 | !---------------------------------------------------------------- |
|---|
| 1144 | ! divide semi-filled layer into set of sublayers each vertically homogenous |
|---|
| 1145 | !---------------------------------------------------------------- |
|---|
| 1146 | |
|---|
| 1147 | !hitl(3)---------------------------------------------------------------- |
|---|
| 1148 | ! | * * * * * * * * |
|---|
| 1149 | ! |* * * * * * * * * |
|---|
| 1150 | !hitl(2)---------------------------------------------------------------- |
|---|
| 1151 | ! | * * * * * * * * | * * * * * * * * |
|---|
| 1152 | ! |* * * * * * * * * |* * * * * * * * * |
|---|
| 1153 | !hitl(1)---------------------------------------------------------------- |
|---|
| 1154 | ! | * * * * * * * * | * * * * * * * * | * * * * * * * * |
|---|
| 1155 | ! |* * * * * * * * * |* * * * * * * * * |* * * * * * * * * |
|---|
| 1156 | !hitl(0)---------------------------------------------------------------- |
|---|
| 1157 | ! aicetl(0) aicetl(1) aicetl(2) aicetl(3) |
|---|
| 1158 | |
|---|
| 1159 | ! move up over layers incrementing volume |
|---|
| 1160 | DO n = 1, m_index+1 |
|---|
| 1161 | |
|---|
| 1162 | area = sum(aicetl(:)) - & ! total area of sub-layer |
|---|
| 1163 | (rhos(n)/rau0) * sum(aicetl(n:jpl+1)) ! area of sub-layer occupied by snow |
|---|
| 1164 | |
|---|
| 1165 | vol = (hitl(n) - hitl(n-1)) * area ! thickness of sub-layer times area |
|---|
| 1166 | |
|---|
| 1167 | IF (vol >= rem_vol) THEN ! have reached the sub-layer with the depth within |
|---|
| 1168 | hpond = rem_vol / area + hitl(n-1) + alfan(m_index) - alfan(1) |
|---|
| 1169 | |
|---|
| 1170 | exit |
|---|
| 1171 | ELSE ! still in sub-layer below the sub-layer with the depth |
|---|
| 1172 | rem_vol = rem_vol - vol |
|---|
| 1173 | END IF |
|---|
| 1174 | |
|---|
| 1175 | END DO |
|---|
| 1176 | |
|---|
| 1177 | END IF |
|---|
| 1178 | |
|---|
| 1179 | END SUBROUTINE ice_thd_pnd_depth |
|---|
| 1180 | |
|---|
| 1181 | |
|---|
| 1182 | SUBROUTINE ice_thd_pnd_perm(ticen, salin, perm) |
|---|
| 1183 | !!------------------------------------------------------------------- |
|---|
| 1184 | !! *** ROUTINE ice_thd_pnd_perm *** |
|---|
| 1185 | !! |
|---|
| 1186 | !! ** Purpose : Determine the liquid fraction of brine in the ice |
|---|
| 1187 | !! and its permeability |
|---|
| 1188 | !!------------------------------------------------------------------- |
|---|
| 1189 | |
|---|
| 1190 | REAL (wp), DIMENSION(nlay_i), INTENT(IN) :: & |
|---|
| 1191 | ticen, & ! internal ice temperature (K) |
|---|
| 1192 | salin ! salinity (ppt) !js: ppt according to cice |
|---|
| 1193 | |
|---|
| 1194 | REAL (wp), INTENT(OUT) :: & |
|---|
| 1195 | perm ! permeability |
|---|
| 1196 | |
|---|
| 1197 | REAL (wp) :: & |
|---|
| 1198 | Sbr ! brine salinity |
|---|
| 1199 | |
|---|
| 1200 | REAL (wp), DIMENSION(nlay_i) :: & |
|---|
| 1201 | Tin, & ! ice temperature |
|---|
| 1202 | phi ! liquid fraction |
|---|
| 1203 | |
|---|
| 1204 | INTEGER :: k |
|---|
| 1205 | |
|---|
| 1206 | !----------------------------------------------------------------- |
|---|
| 1207 | ! Compute ice temperatures from enthalpies using quadratic formula |
|---|
| 1208 | !----------------------------------------------------------------- |
|---|
| 1209 | |
|---|
| 1210 | DO k = 1,nlay_i |
|---|
| 1211 | Tin(k) = ticen(k) - rt0 !js: from K to degC |
|---|
| 1212 | END DO |
|---|
| 1213 | |
|---|
| 1214 | !----------------------------------------------------------------- |
|---|
| 1215 | ! brine salinity and liquid fraction |
|---|
| 1216 | !----------------------------------------------------------------- |
|---|
| 1217 | |
|---|
| 1218 | DO k = 1, nlay_i |
|---|
| 1219 | |
|---|
| 1220 | Sbr = - Tin(k) / rTmlt ! Consistent expression with SI3 (linear liquidus) |
|---|
| 1221 | ! Best expression to date is that one |
|---|
| 1222 | ! Sbr = - 18.7 * Tin(k) − 0.519 * Tin(k)**2 − 0.00535 * Tin(k) ***3 |
|---|
| 1223 | phi(k) = salin(k) / Sbr |
|---|
| 1224 | |
|---|
| 1225 | END DO |
|---|
| 1226 | |
|---|
| 1227 | !----------------------------------------------------------------- |
|---|
| 1228 | ! permeability |
|---|
| 1229 | !----------------------------------------------------------------- |
|---|
| 1230 | |
|---|
| 1231 | perm = 3.0e-08_wp * (minval(phi))**3 ! Golden et al. (2007) |
|---|
| 1232 | |
|---|
| 1233 | END SUBROUTINE ice_thd_pnd_perm |
|---|
| 1234 | |
|---|
| 1235 | |
|---|
| 1236 | !---------------------------------------------------------------------------------------------------------------------- |
|---|
| 1237 | |
|---|
| 1238 | SUBROUTINE ice_thd_pnd_init |
|---|
| 1239 | !!------------------------------------------------------------------- |
|---|
| 1240 | !! *** ROUTINE ice_thd_pnd_init *** |
|---|
| 1241 | !! |
|---|
| 1242 | !! ** Purpose : Physical constants and parameters linked to melt ponds |
|---|
| 1243 | !! over sea ice |
|---|
| 1244 | !! |
|---|
| 1245 | !! ** Method : Read the namthd_pnd namelist and check the melt pond |
|---|
| 1246 | !! parameter values called at the first timestep (nit000) |
|---|
| 1247 | !! |
|---|
| 1248 | !! ** input : Namelist namthd_pnd |
|---|
| 1249 | !!------------------------------------------------------------------- |
|---|
| 1250 | INTEGER :: ios, ioptio ! Local integer |
|---|
| 1251 | !! |
|---|
| 1252 | NAMELIST/namthd_pnd/ ln_pnd, ln_pnd_LEV , rn_apnd_min, rn_apnd_max, & |
|---|
| 1253 | & ln_pnd_CST , rn_apnd, rn_hpnd, & |
|---|
| 1254 | & ln_pnd_TOPO , & |
|---|
| 1255 | & ln_pnd_lids, ln_pnd_alb |
|---|
| 1256 | !!------------------------------------------------------------------- |
|---|
| 1257 | ! |
|---|
| 1258 | REWIND( numnam_ice_ref ) ! Namelist namthd_pnd in reference namelist : Melt Ponds |
|---|
| 1259 | READ ( numnam_ice_ref, namthd_pnd, IOSTAT = ios, ERR = 901) |
|---|
| 1260 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namthd_pnd in reference namelist' ) |
|---|
| 1261 | REWIND( numnam_ice_cfg ) ! Namelist namthd_pnd in configuration namelist : Melt Ponds |
|---|
| 1262 | READ ( numnam_ice_cfg, namthd_pnd, IOSTAT = ios, ERR = 902 ) |
|---|
| 1263 | 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namthd_pnd in configuration namelist' ) |
|---|
| 1264 | IF(lwm) WRITE ( numoni, namthd_pnd ) |
|---|
| 1265 | ! |
|---|
| 1266 | IF(lwp) THEN ! control print |
|---|
| 1267 | WRITE(numout,*) |
|---|
| 1268 | WRITE(numout,*) 'ice_thd_pnd_init: ice parameters for melt ponds' |
|---|
| 1269 | WRITE(numout,*) '~~~~~~~~~~~~~~~~' |
|---|
| 1270 | WRITE(numout,*) ' Namelist namicethd_pnd:' |
|---|
| 1271 | WRITE(numout,*) ' Melt ponds activated or not ln_pnd = ', ln_pnd |
|---|
| 1272 | WRITE(numout,*) ' Topographic melt pond scheme ln_pnd_TOPO = ', ln_pnd_TOPO |
|---|
| 1273 | WRITE(numout,*) ' Level ice melt pond scheme ln_pnd_LEV = ', ln_pnd_LEV |
|---|
| 1274 | WRITE(numout,*) ' Minimum ice fraction that contributes to melt ponds rn_apnd_min = ', rn_apnd_min |
|---|
| 1275 | WRITE(numout,*) ' Maximum ice fraction that contributes to melt ponds rn_apnd_max = ', rn_apnd_max |
|---|
| 1276 | WRITE(numout,*) ' Constant ice melt pond scheme ln_pnd_CST = ', ln_pnd_CST |
|---|
| 1277 | WRITE(numout,*) ' Prescribed pond fraction rn_apnd = ', rn_apnd |
|---|
| 1278 | WRITE(numout,*) ' Prescribed pond depth rn_hpnd = ', rn_hpnd |
|---|
| 1279 | WRITE(numout,*) ' Frozen lids on top of melt ponds ln_pnd_lids = ', ln_pnd_lids |
|---|
| 1280 | WRITE(numout,*) ' Melt ponds affect albedo or not ln_pnd_alb = ', ln_pnd_alb |
|---|
| 1281 | ENDIF |
|---|
| 1282 | ! |
|---|
| 1283 | ! !== set the choice of ice pond scheme ==! |
|---|
| 1284 | ioptio = 0 |
|---|
| 1285 | IF( .NOT.ln_pnd ) THEN ; ioptio = ioptio + 1 ; nice_pnd = np_pndNO ; ENDIF |
|---|
| 1286 | IF( ln_pnd_CST ) THEN ; ioptio = ioptio + 1 ; nice_pnd = np_pndCST ; ENDIF |
|---|
| 1287 | IF( ln_pnd_LEV ) THEN ; ioptio = ioptio + 1 ; nice_pnd = np_pndLEV ; ENDIF |
|---|
| 1288 | IF( ioptio /= 1 ) & |
|---|
| 1289 | & CALL ctl_stop( 'ice_thd_pnd_init: choose either none (ln_pnd=F) or only one pond scheme (ln_pnd_LEV or ln_pnd_CST)' ) |
|---|
| 1290 | ! |
|---|
| 1291 | SELECT CASE( nice_pnd ) |
|---|
| 1292 | CASE( np_pndNO ) |
|---|
| 1293 | IF( ln_pnd_alb ) THEN ; ln_pnd_alb = .FALSE. ; CALL ctl_warn( 'ln_pnd_alb=false when no ponds' ) ; ENDIF |
|---|
| 1294 | IF( ln_pnd_lids ) THEN ; ln_pnd_lids = .FALSE. ; CALL ctl_warn( 'ln_pnd_lids=false when no ponds' ) ; ENDIF |
|---|
| 1295 | CASE( np_pndCST ) |
|---|
| 1296 | IF( ln_pnd_lids ) THEN ; ln_pnd_lids = .FALSE. ; CALL ctl_warn( 'ln_pnd_lids=false when constant ponds' ) ; ENDIF |
|---|
| 1297 | END SELECT |
|---|
| 1298 | ! |
|---|
| 1299 | END SUBROUTINE ice_thd_pnd_init |
|---|
| 1300 | |
|---|
| 1301 | #else |
|---|
| 1302 | !!---------------------------------------------------------------------- |
|---|
| 1303 | !! Default option Empty module NO SI3 sea-ice model |
|---|
| 1304 | !!---------------------------------------------------------------------- |
|---|
| 1305 | #endif |
|---|
| 1306 | |
|---|
| 1307 | !!====================================================================== |
|---|
| 1308 | END MODULE icethd_pnd |
|---|
