[13655] | 1 | ! AeroBulk / 2020 / L. Brodeau |
---|
| 2 | ! |
---|
| 3 | ! When using AeroBulk to produce scientific work, please acknowledge with the following citation: |
---|
| 4 | ! |
---|
| 5 | ! Brodeau, L., B. Barnier, S. Gulev, and C. Woods, 2016: Climatologically |
---|
| 6 | ! significant effects of some approximations in the bulk parameterizations of |
---|
| 7 | ! turbulent air-sea fluxes. J. Phys. Oceanogr., doi:10.1175/JPO-D-16-0169.1. |
---|
| 8 | ! |
---|
| 9 | ! |
---|
| 10 | MODULE sbcblk_algo_ice_cdn |
---|
| 11 | !!==================================================================================== |
---|
| 12 | !! Author: Laurent Brodeau, January 2020 |
---|
| 13 | !!==================================================================================== |
---|
| 14 | USE par_kind, ONLY: wp |
---|
| 15 | USE par_oce, ONLY: jpi, jpj, Nis0, Nie0, Njs0, Nje0, nn_hls |
---|
| 16 | USE phycst ! physical constants |
---|
[13719] | 17 | USE sbc_phy ! Catalog of functions for physical/meteorological parameters in the marine boundary layer |
---|
[13655] | 18 | |
---|
| 19 | IMPLICIT NONE |
---|
| 20 | PRIVATE |
---|
| 21 | |
---|
| 22 | PUBLIC :: CdN10_f_LU12, CdN_f_LU12_eq36, CdN10_f_LU13, CdN_f_LG15, CdN_f_LG15_light |
---|
| 23 | |
---|
| 24 | REAL(wp), PARAMETER :: rCe_0 = 2.23E-3_wp !LOLO: this one can be more accurate when sea-ice data => Lupkes et al (2013), Eq.(1) |
---|
| 25 | REAL(wp), PARAMETER :: rNu_0 = 1._wp |
---|
| 26 | REAL(wp), PARAMETER :: rMu_0 = 1._wp |
---|
| 27 | REAL(wp), PARAMETER :: rbeta_0 = 1.4_wp ! (Eq.47) MIZ |
---|
| 28 | |
---|
| 29 | REAL(wp), PARAMETER :: rhmin_0 = 0.286_wp ! Eq.(25) |
---|
| 30 | REAL(wp), PARAMETER :: rhmax_0 = 0.534_wp ! Eq.(25) |
---|
| 31 | REAL(wp), PARAMETER :: rDmin_0 = 8._wp ! Eq.(27) |
---|
| 32 | REAL(wp), PARAMETER :: rDmax_0 = 300._wp ! Eq.(27) |
---|
| 33 | REAL(wp), PARAMETER :: rz0_w_0 = 3.27E-4 ! fixed roughness length over water (paragraph below Eq.36) |
---|
| 34 | |
---|
| 35 | !!============================================================ |
---|
| 36 | REAL(wp), PARAMETER :: rce10_i_0 = 3.46e-3_wp ! (Eq.48) MIZ |
---|
| 37 | |
---|
| 38 | REAL(wp), PARAMETER :: ralpha_0 = 0.2_wp ! (Eq.12) (ECHAM6 value) |
---|
| 39 | |
---|
| 40 | !! * Substitutions |
---|
| 41 | # include "do_loop_substitute.h90" |
---|
| 42 | !!---------------------------------------------------------------------- |
---|
| 43 | CONTAINS |
---|
| 44 | |
---|
| 45 | |
---|
| 46 | FUNCTION CdN10_f_LU12( pfrice, pz0w, pSc, phf, pDi ) |
---|
| 47 | !!---------------------------------------------------------------------- |
---|
| 48 | !! *** ROUTINE CdN10_f_LU12 *** |
---|
| 49 | !! |
---|
| 50 | !! GENERAL FORM OF EQUATION 22 of Lupkes et al. 2012 |
---|
| 51 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 52 | !! |
---|
| 53 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
---|
| 54 | !! drag referenced at 10m to make it dependent on edges at |
---|
| 55 | !! leads, melt ponds and flows (to be added to the "skin" |
---|
| 56 | !! contribution. After some |
---|
| 57 | !! approximations, this can be resumed to a dependency on |
---|
| 58 | !! ice concentration. |
---|
| 59 | !! |
---|
| 60 | !! ** References : Lupkes et al. JGR 2012 (theory) |
---|
| 61 | !! |
---|
| 62 | !!---------------------------------------------------------------------- |
---|
| 63 | REAL(wp), DIMENSION(jpi,jpj) :: CdN10_f_LU12 ! neutral FORM drag coefficient contribution over sea-ice |
---|
| 64 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc, phf and pDi all provided... |
---|
| 65 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0w ! roughness length over water [m] |
---|
| 66 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pSc ! shletering function [0-1] (Sc->1 for large distance between floes, ->0 for small distances) |
---|
| 67 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: phf ! mean freeboard of floes [m] |
---|
| 68 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pDi ! cross wind dimension of the floe (aka effective edge length for form drag) [m] |
---|
| 69 | !!---------------------------------------------------------------------- |
---|
| 70 | LOGICAL :: l_known_Sc=.FALSE., l_known_hf=.FALSE., l_known_Di=.FALSE. |
---|
| 71 | REAL(wp) :: ztmp, zrlog, zfri, zfrw, zSc, zhf, zDi |
---|
| 72 | INTEGER :: ji, jj |
---|
| 73 | !!---------------------------------------------------------------------- |
---|
| 74 | l_known_Sc = PRESENT(pSc) |
---|
| 75 | l_known_hf = PRESENT(phf) |
---|
| 76 | l_known_Di = PRESENT(pDi) |
---|
| 77 | |
---|
| 78 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
---|
| 79 | |
---|
| 80 | zfri = pfrice(ji,jj) |
---|
| 81 | zfrw = (1._wp - zfri) |
---|
| 82 | |
---|
| 83 | IF(l_known_Sc) THEN |
---|
| 84 | zSc = pSc(ji,jj) |
---|
| 85 | ELSE |
---|
| 86 | !! Sc parameterized in terms of A (ice fraction): |
---|
| 87 | zSc = zfrw**(1._wp / ( 10._wp * rBeta_0 )) ! Eq.(31) |
---|
| 88 | END IF |
---|
| 89 | |
---|
| 90 | IF(l_known_hf) THEN |
---|
| 91 | zhf = phf(ji,jj) |
---|
| 92 | ELSE |
---|
| 93 | !! hf parameterized in terms of A (ice fraction): |
---|
| 94 | zhf = rhmax_0*zfri + rhmin_0*zfrw ! Eq.(25) |
---|
| 95 | END IF |
---|
| 96 | |
---|
| 97 | IF(l_known_Di) THEN |
---|
| 98 | zDi = pDi(ji,jj) |
---|
| 99 | ELSE |
---|
| 100 | !! Di parameterized in terms of A (ice fraction): |
---|
| 101 | ztmp = 1._wp / ( 1._wp - (rDmin_0/rDmax_0)**(1._wp/rBeta_0) ) ! A* Eq.(27) |
---|
| 102 | zDi = rDmin_0 * ( ztmp/(ztmp - zfri) )**rBeta_0 ! Eq.(26) |
---|
| 103 | END IF |
---|
| 104 | |
---|
| 105 | ztmp = 1._wp/pz0w(ji,jj) |
---|
| 106 | zrlog = LOG(zhf*ztmp) / LOG(10._wp*ztmp) |
---|
| 107 | |
---|
| 108 | CdN10_f_LU12(:,:) = 0.5_wp* 0.3_wp * zrlog*zrlog * zSc*zSc * zhf/zDi * zfri ! Eq.(22) |
---|
| 109 | !! 1/2 Ce |
---|
| 110 | |
---|
| 111 | END_2D |
---|
| 112 | END FUNCTION CdN10_f_LU12 |
---|
| 113 | |
---|
| 114 | |
---|
| 115 | FUNCTION CdN_f_LU12_eq36( pzu, pfrice ) |
---|
| 116 | REAL(wp), DIMENSION(jpi,jpj) :: CdN_f_LU12_eq36 ! neutral FORM drag coefficient contribution over sea-ice |
---|
| 117 | REAL(wp), INTENT(in) :: pzu ! reference height [m] |
---|
| 118 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc, phf and pDi all provided... |
---|
| 119 | !!---------------------------------------------------------------------- |
---|
| 120 | REAL(wp) :: ztmp, zrlog, zfri, zhf, zDi |
---|
| 121 | INTEGER :: ji, jj |
---|
| 122 | !!---------------------------------------------------------------------- |
---|
| 123 | !zhf = 0.28 ! h_fc |
---|
| 124 | zhf = 0.41 ! h_fc |
---|
| 125 | zDi = rDmin_0 |
---|
| 126 | |
---|
| 127 | ztmp = 1._wp/rz0_w_0 |
---|
| 128 | zrlog = LOG(zhf*ztmp) / LOG(pzu*ztmp) |
---|
| 129 | |
---|
| 130 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
---|
| 131 | |
---|
| 132 | zfri = pfrice(ji,jj) |
---|
| 133 | |
---|
| 134 | CdN_f_LU12_eq36(:,:) = 0.5_wp* 0.3_wp * zrlog*zrlog * zhf/zDi * (1._wp - zfri)**rBeta_0 ! Eq.(35) & (36) |
---|
| 135 | !! 1/2 Ce |
---|
| 136 | END_2D |
---|
| 137 | END FUNCTION CdN_f_LU12_eq36 |
---|
| 138 | |
---|
| 139 | |
---|
| 140 | |
---|
| 141 | |
---|
| 142 | FUNCTION CdN10_f_LU13( pfrice ) |
---|
| 143 | !!---------------------------------------------------------------------- |
---|
| 144 | !! *** ROUTINE CdN10_f_LU13 *** |
---|
| 145 | !! |
---|
| 146 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
---|
| 147 | !! drag referenced at 10m to make it dependent on edges at |
---|
| 148 | !! leads, melt ponds and flows (to be added to the "skin" |
---|
| 149 | !! contribution. After some |
---|
| 150 | !! approximations, this can be resumed to a dependency on |
---|
| 151 | !! ice concentration. |
---|
| 152 | !! |
---|
| 153 | !! ** Method : The parameterization is taken from Lupkes et al. (2012) eq.(50) |
---|
| 154 | !! with the highest level of approximation: level4, eq.(59) |
---|
| 155 | !! The generic drag over a cell partly covered by ice can be re-written as follows: |
---|
| 156 | !! |
---|
| 157 | !! Cd = Cdw * (1-A) + Cdi * A + Ce * (1-A)**(nu+1/(10*beta)) * A**mu |
---|
| 158 | !! |
---|
| 159 | !! Ce = 2.23e-3 , as suggested by Lupkes (eq. 59) |
---|
| 160 | !! nu = mu = beta = 1 , as suggested by Lupkes (eq. 59) |
---|
| 161 | !! A is the concentration of ice minus melt ponds (if any) |
---|
| 162 | !! |
---|
| 163 | !! This new drag has a parabolic shape (as a function of A) starting at |
---|
| 164 | !! Cdw(say 1.5e-3) for A=0, reaching 1.97e-3 for A~0.5 |
---|
| 165 | !! and going down to Cdi(say 1.4e-3) for A=1 |
---|
| 166 | !! |
---|
| 167 | !! It is theoretically applicable to all ice conditions (not only MIZ) |
---|
| 168 | !! => see Lupkes et al (2013) |
---|
| 169 | !! |
---|
| 170 | !! ** References : Lupkes et al. JGR 2012 (theory) |
---|
| 171 | !! Lupkes et al. GRL 2013 (application to GCM) |
---|
| 172 | !! |
---|
| 173 | !!---------------------------------------------------------------------- |
---|
| 174 | REAL(wp), DIMENSION(jpi,jpj) :: CdN10_f_LU13 ! neutral FORM drag coefficient contribution over sea-ice |
---|
| 175 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b |
---|
| 176 | |
---|
| 177 | !!---------------------------------------------------------------------- |
---|
| 178 | REAL(wp) :: zcoef |
---|
| 179 | !!---------------------------------------------------------------------- |
---|
| 180 | zcoef = rNu_0 + 1._wp / ( 10._wp * rBeta_0 ) |
---|
| 181 | |
---|
| 182 | !! We are not an AGCM, we are an OGCM!!! => we drop term "(1 - A)*Cd_w" |
---|
| 183 | !! => so we keep only the last rhs terms of Eq.(1) of Lupkes et al, 2013 that we divide by "A": |
---|
| 184 | !! (we multiply Cd_i_s and Cd_i_f by A later, when applying ocean-ice partitioning... |
---|
| 185 | |
---|
| 186 | CdN10_f_LU13(:,:) = rCe_0 * pfrice(:,:)**(rMu_0 - 1._wp) * (1._wp - pfrice(:,:))**zcoef |
---|
| 187 | !! => seems okay for winter 100% sea-ice as second rhs term vanishes as pfrice == 1.... |
---|
| 188 | |
---|
| 189 | END FUNCTION CdN10_f_LU13 |
---|
| 190 | |
---|
| 191 | |
---|
| 192 | FUNCTION CdN_f_LG15( pzu, pfrice, pz0i, pSc, phf, pDi ) |
---|
| 193 | !!---------------------------------------------------------------------- |
---|
| 194 | !! *** ROUTINE CdN_f_LG15 *** |
---|
| 195 | !! |
---|
| 196 | !! GENERAL FORM OF EQUATION 21 of Lupkes & Gryanik (2015) |
---|
| 197 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 198 | !! |
---|
| 199 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
---|
| 200 | !! drag referenced at 10m to make it dependent on edges at |
---|
| 201 | !! leads, melt ponds and flows (to be added to the "skin" |
---|
| 202 | !! contribution. After some |
---|
| 203 | !! approximations, this can be resumed to a dependency on |
---|
| 204 | !! ice concentration. |
---|
| 205 | !! |
---|
| 206 | !! ** References : Lupkes & Gryanik (2015) |
---|
| 207 | !! |
---|
| 208 | !!---------------------------------------------------------------------- |
---|
| 209 | REAL(wp), DIMENSION(jpi,jpj) :: CdN_f_LG15 ! neutral FORM drag coefficient contribution over sea-ice |
---|
| 210 | REAL(wp), INTENT(in ) :: pzu ! reference height [m] |
---|
| 211 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc, phf and pDi all provided... |
---|
| 212 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0i ! roughness length over ICE [m] (in LU12, it's over water ???) |
---|
| 213 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pSc ! shletering function [0-1] (Sc->1 for large distance between floes, ->0 for small distances) |
---|
| 214 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: phf ! mean freeboard of floes [m] |
---|
| 215 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pDi ! cross wind dimension of the floe (aka effective edge length for form drag) [m] |
---|
| 216 | !!---------------------------------------------------------------------- |
---|
| 217 | LOGICAL :: l_known_Sc=.FALSE., l_known_hf=.FALSE., l_known_Di=.FALSE. |
---|
| 218 | REAL(wp) :: ztmp, zrlog, zfri, zfrw, zSc, zhf, zDi |
---|
| 219 | INTEGER :: ji, jj |
---|
| 220 | !!---------------------------------------------------------------------- |
---|
| 221 | l_known_Sc = PRESENT(pSc) |
---|
| 222 | l_known_hf = PRESENT(phf) |
---|
| 223 | l_known_Di = PRESENT(pDi) |
---|
| 224 | |
---|
| 225 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
---|
| 226 | |
---|
| 227 | zfri = pfrice(ji,jj) |
---|
| 228 | zfrw = (1._wp - zfri) |
---|
| 229 | |
---|
| 230 | IF(l_known_Sc) THEN |
---|
| 231 | zSc = pSc(ji,jj) |
---|
| 232 | ELSE |
---|
| 233 | !! Sc parameterized in terms of A (ice fraction): |
---|
| 234 | zSc = zfrw**(1._wp / ( 10._wp * rBeta_0 )) ! Eq.(31) |
---|
| 235 | END IF |
---|
| 236 | |
---|
| 237 | IF(l_known_hf) THEN |
---|
| 238 | zhf = phf(ji,jj) |
---|
| 239 | ELSE |
---|
| 240 | !! hf parameterized in terms of A (ice fraction): |
---|
| 241 | zhf = rhmax_0*zfri + rhmin_0*zfrw ! Eq.(25) |
---|
| 242 | END IF |
---|
| 243 | |
---|
| 244 | IF(l_known_Di) THEN |
---|
| 245 | zDi = pDi(ji,jj) |
---|
| 246 | ELSE |
---|
| 247 | !! Di parameterized in terms of A (ice fraction): |
---|
| 248 | ztmp = 1._wp / ( 1._wp - (rDmin_0/rDmax_0)**(1._wp/rBeta_0) ) ! A* Eq.(27) |
---|
| 249 | zDi = rDmin_0 * ( ztmp/(ztmp - zfri) )**rBeta_0 ! Eq.(26) |
---|
| 250 | END IF |
---|
| 251 | |
---|
| 252 | ztmp = 1._wp/pz0i(ji,jj) |
---|
| 253 | zrlog = LOG(zhf*ztmp/2.718_wp) / LOG(pzu*ztmp) !LOLO: adding number "e" !!! |
---|
| 254 | |
---|
| 255 | CdN_f_LG15(:,:) = 0.5_wp* 0.4_wp * zrlog*zrlog * zSc*zSc * zhf/zDi * zfri ! Eq.(21) Lukes & Gryanik (2015) |
---|
| 256 | !! 1/2 Ce |
---|
| 257 | |
---|
| 258 | END_2D |
---|
| 259 | END FUNCTION CdN_f_LG15 |
---|
| 260 | |
---|
| 261 | |
---|
| 262 | |
---|
| 263 | FUNCTION CdN_f_LG15_light( pzu, pfrice, pz0w ) |
---|
| 264 | !!---------------------------------------------------------------------- |
---|
| 265 | !! *** ROUTINE CdN_f_LG15_light *** |
---|
| 266 | !! |
---|
| 267 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
---|
| 268 | !! drag referenced at 10m to make it dependent on edges at |
---|
| 269 | !! leads, melt ponds and flows (to be added to the "skin" |
---|
| 270 | !! contribution. After some |
---|
| 271 | !! approximations, this can be resumed to a dependency on |
---|
| 272 | !! ice concentration. |
---|
| 273 | !! |
---|
| 274 | !! ** References : Lupkes & Gryanik (2015) |
---|
| 275 | !! |
---|
| 276 | !!---------------------------------------------------------------------- |
---|
| 277 | REAL(wp), DIMENSION(jpi,jpj) :: CdN_f_LG15_light ! neutral FORM drag coefficient contribution over sea-ice |
---|
| 278 | REAL(wp), INTENT(in) :: pzu ! reference height [m] |
---|
| 279 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b |
---|
| 280 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0w ! roughness length over water [m] |
---|
| 281 | !!---------------------------------------------------------------------- |
---|
| 282 | REAL(wp) :: ztmp, zrlog, zfri |
---|
| 283 | INTEGER :: ji, jj |
---|
| 284 | !!---------------------------------------------------------------------- |
---|
| 285 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
---|
| 286 | |
---|
| 287 | zfri = pfrice(ji,jj) |
---|
| 288 | |
---|
| 289 | ztmp = 1._wp / pz0w(ji,jj) |
---|
| 290 | zrlog = LOG( 10._wp * ztmp ) / LOG( pzu * ztmp ) ! part of (Eq.46) |
---|
| 291 | |
---|
| 292 | CdN_f_LG15_light(:,:) = rce10_i_0 *zrlog*zrlog * zfri * (1._wp - zfri)**rbeta_0 ! (Eq.46) [ index 1 is for ice, 2 for water ] |
---|
| 293 | |
---|
| 294 | END_2D |
---|
| 295 | END FUNCTION CdN_f_LG15_light |
---|
| 296 | |
---|
| 297 | |
---|
| 298 | |
---|
| 299 | !!====================================================================== |
---|
| 300 | END MODULE sbcblk_algo_ice_cdn |
---|