Newer
Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
! AeroBulk / 2020 / L. Brodeau
!
! When using AeroBulk to produce scientific work, please acknowledge with the following citation:
!
! Brodeau, L., B. Barnier, S. Gulev, and C. Woods, 2016: Climatologically
! significant effects of some approximations in the bulk parameterizations of
! turbulent air-sea fluxes. J. Phys. Oceanogr., doi:10.1175/JPO-D-16-0169.1.
!
!
MODULE sbcblk_algo_ice_cdn
!!====================================================================================
!! Author: Laurent Brodeau, January 2020
!!====================================================================================
USE par_kind, ONLY: wp
USE par_oce, ONLY: jpi, jpj, Nis0, Nie0, Njs0, Nje0, nn_hls, ntsi, ntsj, ntei, ntej
USE phycst ! physical constants
USE sbc_phy ! Catalog of functions for physical/meteorological parameters in the marine boundary layer
IMPLICIT NONE
PRIVATE
PUBLIC :: CdN10_f_LU12, CdN_f_LU12_eq36, CdN10_f_LU13, CdN_f_LG15, CdN_f_LG15_light
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)
REAL(wp), PARAMETER :: rNu_0 = 1._wp
REAL(wp), PARAMETER :: rMu_0 = 1._wp
REAL(wp), PARAMETER :: rbeta_0 = 1.4_wp ! (Eq.47) MIZ
REAL(wp), PARAMETER :: rhmin_0 = 0.286_wp ! Eq.(25)
REAL(wp), PARAMETER :: rhmax_0 = 0.534_wp ! Eq.(25)
REAL(wp), PARAMETER :: rDmin_0 = 8._wp ! Eq.(27)
REAL(wp), PARAMETER :: rDmax_0 = 300._wp ! Eq.(27)
REAL(wp), PARAMETER :: rz0_w_0 = 3.27E-4 ! fixed roughness length over water (paragraph below Eq.36)
!!============================================================
REAL(wp), PARAMETER :: rce10_i_0 = 3.46e-3_wp ! (Eq.48) MIZ
REAL(wp), PARAMETER :: ralpha_0 = 0.2_wp ! (Eq.12) (ECHAM6 value)
!! * Substitutions
# include "do_loop_substitute.h90"
!!----------------------------------------------------------------------
CONTAINS
Guillaume Samson
committed
FUNCTION CdN10_f_LU12( pfrice, pz0w, pSc2, phf, pDi )
!!----------------------------------------------------------------------
!! *** ROUTINE CdN10_f_LU12 ***
!!
!! GENERAL FORM OF EQUATION 22 of Lupkes et al. 2012
!! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
!!
!! ** Purpose : Computes the "form" contribution of the neutral air-ice
!! drag referenced at 10m to make it dependent on edges at
!! leads, melt ponds and flows (to be added to the "skin"
!! contribution. After some
!! approximations, this can be resumed to a dependency on
!! ice concentration.
!!
!! ** References : Lupkes et al. JGR 2012 (theory)
!!
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj) :: CdN10_f_LU12 ! neutral FORM drag coefficient contribution over sea-ice
Guillaume Samson
committed
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc2, phf and pDi all provided...
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0w ! roughness length over water [m]
Guillaume Samson
committed
REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pSc2 ! squared shletering function [0-1] (Sc->1 for large distance between floes, ->0 for small distances)
REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: phf ! mean freeboard of floes [m]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pDi ! cross wind dimension of the floe (aka effective edge length for form drag) [m]
!!----------------------------------------------------------------------
Guillaume Samson
committed
LOGICAL :: l_known_Sc2=.FALSE., l_known_hf=.FALSE., l_known_Di=.FALSE.
REAL(wp) :: ztmp, zrlog, zfri, zfrw, zSc2, zhf, zDi
INTEGER :: ji, jj
!!----------------------------------------------------------------------
Guillaume Samson
committed
l_known_Sc2 = PRESENT(pSc2)
l_known_hf = PRESENT(phf)
l_known_Di = PRESENT(pDi)
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zfri = pfrice(ji,jj)
zfrw = (1._wp - zfri)
Guillaume Samson
committed
IF(l_known_Sc2) THEN
zSc2 = pSc2(ji,jj)
Guillaume Samson
committed
!! Sc**2 parameterized in terms of A (ice fraction):
zSc2 = zfrw**(1._wp / ( 10._wp * rBeta_0 )) ! Eq.(31)
END IF
IF(l_known_hf) THEN
zhf = phf(ji,jj)
ELSE
!! hf parameterized in terms of A (ice fraction):
zhf = rhmax_0*zfri + rhmin_0*zfrw ! Eq.(25)
END IF
IF(l_known_Di) THEN
zDi = pDi(ji,jj)
ELSE
!! Di parameterized in terms of A (ice fraction):
ztmp = 1._wp / ( 1._wp - (rDmin_0/rDmax_0)**(1._wp/rBeta_0) ) ! A* Eq.(27)
zDi = rDmin_0 * ( ztmp/(ztmp - zfri) )**rBeta_0 ! Eq.(26)
END IF
ztmp = 1._wp/pz0w(ji,jj)
zrlog = LOG(zhf*ztmp) / LOG(10._wp*ztmp)
Guillaume Samson
committed
CdN10_f_LU12(ji,jj) = 0.5_wp* 0.3_wp * zrlog*zrlog * zSc2 * zhf/zDi * zfri ! Eq.(22)
!! 1/2 Ce
END_2D
END FUNCTION CdN10_f_LU12
FUNCTION CdN_f_LU12_eq36( pzu, pfrice )
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj) :: CdN_f_LU12_eq36 ! neutral FORM drag coefficient contribution over sea-ice
REAL(wp), INTENT(in) :: pzu ! reference height [m]
Guillaume Samson
committed
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc2, phf and pDi all provided...
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
!!----------------------------------------------------------------------
REAL(wp) :: ztmp, zrlog, zfri, zhf, zDi
INTEGER :: ji, jj
!!----------------------------------------------------------------------
!zhf = 0.28 ! h_fc
zhf = 0.41 ! h_fc
zDi = rDmin_0
ztmp = 1._wp/rz0_w_0
zrlog = LOG(zhf*ztmp) / LOG(pzu*ztmp)
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zfri = pfrice(ji,jj)
CdN_f_LU12_eq36(ji,jj) = 0.5_wp* 0.3_wp * zrlog*zrlog * zhf/zDi * (1._wp - zfri)**rBeta_0 ! Eq.(35) & (36)
!! 1/2 Ce
END_2D
END FUNCTION CdN_f_LU12_eq36
FUNCTION CdN10_f_LU13( pfrice )
!!----------------------------------------------------------------------
!! *** ROUTINE CdN10_f_LU13 ***
!!
!! ** Purpose : Computes the "form" contribution of the neutral air-ice
!! drag referenced at 10m to make it dependent on edges at
!! leads, melt ponds and flows (to be added to the "skin"
!! contribution. After some
!! approximations, this can be resumed to a dependency on
!! ice concentration.
!!
!! ** Method : The parameterization is taken from Lupkes et al. (2012) eq.(50)
!! with the highest level of approximation: level4, eq.(59)
!! The generic drag over a cell partly covered by ice can be re-written as follows:
!!
!! Cd = Cdw * (1-A) + Cdi * A + Ce * (1-A)**(nu+1/(10*beta)) * A**mu
!!
!! Ce = 2.23e-3 , as suggested by Lupkes (eq. 59)
!! nu = mu = beta = 1 , as suggested by Lupkes (eq. 59)
!! A is the concentration of ice minus melt ponds (if any)
!!
!! This new drag has a parabolic shape (as a function of A) starting at
!! Cdw(say 1.5e-3) for A=0, reaching 1.97e-3 for A~0.5
!! and going down to Cdi(say 1.4e-3) for A=1
!!
!! It is theoretically applicable to all ice conditions (not only MIZ)
!! => see Lupkes et al (2013)
!!
!! ** References : Lupkes et al. JGR 2012 (theory)
!! Lupkes et al. GRL 2013 (application to GCM)
!!
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj) :: CdN10_f_LU13 ! neutral FORM drag coefficient contribution over sea-ice
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b
!!----------------------------------------------------------------------
INTEGER :: ji, jj
REAL(wp) :: zcoef
!!----------------------------------------------------------------------
zcoef = rNu_0 + 1._wp / ( 10._wp * rBeta_0 )
!! We are not an AGCM, we are an OGCM!!! => we drop term "(1 - A)*Cd_w"
!! => so we keep only the last rhs terms of Eq.(1) of Lupkes et al, 2013 that we divide by "A":
!! (we multiply Cd_i_s and Cd_i_f by A later, when applying ocean-ice partitioning...
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
CdN10_f_LU13(ji,jj) = rCe_0 * pfrice(ji,jj)**(rMu_0 - 1._wp) * (1._wp - pfrice(ji,jj))**zcoef
END_2D
!! => seems okay for winter 100% sea-ice as second rhs term vanishes as pfrice == 1....
END FUNCTION CdN10_f_LU13
Guillaume Samson
committed
FUNCTION CdN_f_LG15( pzu, pfrice, pz0i, pSc2, phf, pDi )
!!----------------------------------------------------------------------
!! *** ROUTINE CdN_f_LG15 ***
!!
!! GENERAL FORM OF EQUATION 21 of Lupkes & Gryanik (2015)
!! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
!!
!! ** Purpose : Computes the "form" contribution of the neutral air-ice
!! drag referenced at 10m to make it dependent on edges at
!! leads, melt ponds and flows (to be added to the "skin"
!! contribution. After some
!! approximations, this can be resumed to a dependency on
!! ice concentration.
!!
!! ** References : Lupkes & Gryanik (2015)
!!
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj) :: CdN_f_LG15 ! neutral FORM drag coefficient contribution over sea-ice
REAL(wp), INTENT(in ) :: pzu ! reference height [m]
Guillaume Samson
committed
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc2, phf and pDi all provided...
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0i ! roughness length over ICE [m] (in LU12, it's over water ???)
Guillaume Samson
committed
REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pSc2 ! squared shletering function [0-1] (Sc->1 for large distance between floes, ->0 for small distances)
REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: phf ! mean freeboard of floes [m]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pDi ! cross wind dimension of the floe (aka effective edge length for form drag) [m]
!!----------------------------------------------------------------------
Guillaume Samson
committed
LOGICAL :: l_known_Sc2=.FALSE., l_known_hf=.FALSE., l_known_Di=.FALSE.
REAL(wp) :: ztmp, zrlog, zfri, zfrw, zSc2, zhf, zDi
INTEGER :: ji, jj
!!----------------------------------------------------------------------
Guillaume Samson
committed
l_known_Sc2 = PRESENT(pSc2)
l_known_hf = PRESENT(phf)
l_known_Di = PRESENT(pDi)
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zfri = pfrice(ji,jj)
zfrw = (1._wp - zfri)
Guillaume Samson
committed
IF(l_known_Sc2) THEN
zSc2 = pSc2(ji,jj)
Guillaume Samson
committed
!! Sc**2 parameterized in terms of A (ice fraction):
zSc2 = zfrw**(1._wp / ( 10._wp * rBeta_0 )) ! Eq.(31)
END IF
IF(l_known_hf) THEN
zhf = phf(ji,jj)
ELSE
!! hf parameterized in terms of A (ice fraction):
zhf = rhmax_0*zfri + rhmin_0*zfrw ! Eq.(25)
END IF
IF(l_known_Di) THEN
zDi = pDi(ji,jj)
ELSE
!! Di parameterized in terms of A (ice fraction):
ztmp = 1._wp / ( 1._wp - (rDmin_0/rDmax_0)**(1._wp/rBeta_0) ) ! A* Eq.(27)
zDi = rDmin_0 * ( ztmp/(ztmp - zfri) )**rBeta_0 ! Eq.(26)
END IF
ztmp = 1._wp/pz0i(ji,jj)
zrlog = LOG(zhf*ztmp/2.718_wp) / LOG(pzu*ztmp) !LOLO: adding number "e" !!!
Guillaume Samson
committed
CdN_f_LG15(ji,jj) = 0.5_wp* 0.4_wp * zrlog*zrlog * zSc2 * zhf/zDi * zfri ! Eq.(21) Lukes & Gryanik (2015)
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
!! 1/2 Ce
END_2D
END FUNCTION CdN_f_LG15
FUNCTION CdN_f_LG15_light( pzu, pfrice, pz0w )
!!----------------------------------------------------------------------
!! *** ROUTINE CdN_f_LG15_light ***
!!
!! ** Purpose : Computes the "form" contribution of the neutral air-ice
!! drag referenced at 10m to make it dependent on edges at
!! leads, melt ponds and flows (to be added to the "skin"
!! contribution. After some
!! approximations, this can be resumed to a dependency on
!! ice concentration.
!!
!! ** References : Lupkes & Gryanik (2015)
!!
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj) :: CdN_f_LG15_light ! neutral FORM drag coefficient contribution over sea-ice
REAL(wp), INTENT(in) :: pzu ! reference height [m]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0w ! roughness length over water [m]
!!----------------------------------------------------------------------
REAL(wp) :: ztmp, zrlog, zfri
INTEGER :: ji, jj
!!----------------------------------------------------------------------
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zfri = pfrice(ji,jj)
ztmp = 1._wp / pz0w(ji,jj)
zrlog = LOG( 10._wp * ztmp ) / LOG( pzu * ztmp ) ! part of (Eq.46)
CdN_f_LG15_light(ji,jj) = rce10_i_0 *zrlog*zrlog * zfri * (1._wp - zfri)**rbeta_0 ! (Eq.46) [ index 1 is for ice, 2 for water ]
END_2D
END FUNCTION CdN_f_LG15_light
!!======================================================================
END MODULE sbcblk_algo_ice_cdn