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sbcblk.F90 in NEMO/branches/2020/r4.0-HEAD_r12713_clem_dan_fixcpl/src/OCE/SBC – NEMO

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source: NEMO/branches/2020/r4.0-HEAD_r12713_clem_dan_fixcpl/src/OCE/SBC/sbcblk.F90 @ 12894

Last change on this file since 12894 was 12894, checked in by clem, 4 years ago
add parameterization of radiation from Marion Lebrun (2019)
Property svn:keywords set to `Id`
File size: 72.9 KB

Line
1	MODULE sbcblk
2	!!======================================================================
3	!! * MODULE sbcblk *
4	!! Ocean forcing: momentum, heat and freshwater flux formulation
5	!! Aerodynamic Bulk Formulas
6	!! SUCCESSOR OF "sbcblk_core"
7	!!=====================================================================
8	!! History : 1.0 ! 2004-08 (U. Schweckendiek) Original CORE code
9	!! 2.0 ! 2005-04 (L. Brodeau, A.M. Treguier) improved CORE bulk and its user interface
10	!! 3.0 ! 2006-06 (G. Madec) sbc rewritting
11	!! - ! 2006-12 (L. Brodeau) Original code for turb_core
12	!! 3.2 ! 2009-04 (B. Lemaire) Introduce iom_put
13	!! 3.3 ! 2010-10 (S. Masson) add diurnal cycle
14	!! 3.4 ! 2011-11 (C. Harris) Fill arrays required by CICE
15	!! 3.7 ! 2014-06 (L. Brodeau) simplification and optimization of CORE bulk
16	!! 4.0 ! 2016-06 (L. Brodeau) sbcblk_core becomes sbcblk and is not restricted to the CORE algorithm anymore
17	!! ! ==> based on AeroBulk (http://aerobulk.sourceforge.net/)
18	!! 4.0 ! 2016-10 (G. Madec) introduce a sbc_blk_init routine
19	!! 4.0 ! 2016-10 (M. Vancoppenolle) Introduce conduction flux emulator (M. Vancoppenolle)
20	!!----------------------------------------------------------------------
21
22	!!----------------------------------------------------------------------
23	!! sbc_blk_init : initialisation of the chosen bulk formulation as ocean surface boundary condition
24	!! sbc_blk : bulk formulation as ocean surface boundary condition
25	!! blk_oce : computes momentum, heat and freshwater fluxes over ocean
26	!! rho_air : density of (moist) air (depends on T_air, q_air and SLP
27	!! cp_air : specific heat of (moist) air (depends spec. hum. q_air)
28	!! q_sat : saturation humidity as a function of SLP and temperature
29	!! L_vap : latent heat of vaporization of water as a function of temperature
30	!! sea-ice case only :
31	!! blk_ice_tau : provide the air-ice stress
32	!! blk_ice_flx : provide the heat and mass fluxes at air-ice interface
33	!! blk_ice_qcn : provide ice surface temperature and snow/ice conduction flux (emulating conduction flux)
34	!! Cdn10_Lupkes2012 : Lupkes et al. (2012) air-ice drag
35	!! Cdn10_Lupkes2015 : Lupkes et al. (2015) air-ice drag
36	!!----------------------------------------------------------------------
37	USE oce ! ocean dynamics and tracers
38	USE dom_oce ! ocean space and time domain
39	USE phycst ! physical constants
40	USE fldread ! read input fields
41	USE sbc_oce ! Surface boundary condition: ocean fields
42	USE cyclone ! Cyclone 10m wind form trac of cyclone centres
43	USE sbcdcy ! surface boundary condition: diurnal cycle
44	USE sbcwave , ONLY : cdn_wave ! wave module
45	USE sbc_ice ! Surface boundary condition: ice fields
46	USE lib_fortran ! to use key_nosignedzero
47	#if defined key_si3
48	USE ice , ONLY : u_ice, v_ice, jpl, a_i_b, at_i_b, t_su, rn_cnd_s, hfx_err_dif, nn_qtrice
49	USE icevar ! for CALL ice_var_snwblow
50	#endif
51	USE sbcblk_algo_ncar ! => turb_ncar : NCAR - CORE (Large & Yeager, 2009)
52	USE sbcblk_algo_coare ! => turb_coare : COAREv3.0 (Fairall et al. 2003)
53	USE sbcblk_algo_coare3p5 ! => turb_coare3p5 : COAREv3.5 (Edson et al. 2013)
54	USE sbcblk_algo_ecmwf ! => turb_ecmwf : ECMWF (IFS cycle 31)
55	!
56	USE iom ! I/O manager library
57	USE in_out_manager ! I/O manager
58	USE lib_mpp ! distribued memory computing library
59	USE lbclnk ! ocean lateral boundary conditions (or mpp link)
60	USE prtctl ! Print control
61
62	IMPLICIT NONE
63	PRIVATE
64
65	PUBLIC sbc_blk_init ! called in sbcmod
66	PUBLIC sbc_blk ! called in sbcmod
67	#if defined key_si3
68	PUBLIC blk_ice_tau ! routine called in icesbc
69	PUBLIC blk_ice_flx ! routine called in icesbc
70	PUBLIC blk_ice_qcn ! routine called in icesbc
71	#endif
72
73	!!Lolo: should ultimately be moved in the module with all physical constants ?
74	!!gm : In principle, yes.
75	REAL(wp), PARAMETER :: Cp_dry = 1005.0 !: Specic heat of dry air, constant pressure [J/K/kg]
76	REAL(wp), PARAMETER :: Cp_vap = 1860.0 !: Specic heat of water vapor, constant pressure [J/K/kg]
77	REAL(wp), PARAMETER :: R_dry = 287.05_wp !: Specific gas constant for dry air [J/K/kg]
78	REAL(wp), PARAMETER :: R_vap = 461.495_wp !: Specific gas constant for water vapor [J/K/kg]
79	REAL(wp), PARAMETER :: reps0 = R_dry/R_vap !: ratio of gas constant for dry air and water vapor => ~ 0.622
80	REAL(wp), PARAMETER :: rctv0 = R_vap/R_dry !: for virtual temperature (== (1-eps)/eps) => ~ 0.608
81
82	INTEGER , PARAMETER :: jpfld =11 ! maximum number of files to read
83	INTEGER , PARAMETER :: jp_wndi = 1 ! index of 10m wind velocity (i-component) (m/s) at T-point
84	INTEGER , PARAMETER :: jp_wndj = 2 ! index of 10m wind velocity (j-component) (m/s) at T-point
85	INTEGER , PARAMETER :: jp_tair = 3 ! index of 10m air temperature (Kelvin)
86	INTEGER , PARAMETER :: jp_humi = 4 ! index of specific humidity ( % )
87	INTEGER , PARAMETER :: jp_qsr = 5 ! index of solar heat (W/m2)
88	INTEGER , PARAMETER :: jp_qlw = 6 ! index of Long wave (W/m2)
89	INTEGER , PARAMETER :: jp_prec = 7 ! index of total precipitation (rain+snow) (Kg/m2/s)
90	INTEGER , PARAMETER :: jp_snow = 8 ! index of snow (solid prcipitation) (kg/m2/s)
91	INTEGER , PARAMETER :: jp_slp = 9 ! index of sea level pressure (Pa)
92	INTEGER , PARAMETER :: jp_cc =10 ! index of cloud cover (-) range:0-1
93	INTEGER , PARAMETER :: jp_tdif =11 ! index of tau diff associated to HF tau (N/m2) at T-point
94
95	TYPE(FLD), ALLOCATABLE, DIMENSION(:) :: sf ! structure of input fields (file informations, fields read)
96
97	! !!! Bulk parameters
98	REAL(wp), PARAMETER :: cpa = 1000.5 ! specific heat of air (only used for ice fluxes now...)
99	REAL(wp), PARAMETER :: Ls = 2.839e6 ! latent heat of sublimation
100	REAL(wp), PARAMETER :: Stef = 5.67e-8 ! Stefan Boltzmann constant
101	REAL(wp), PARAMETER :: Cd_ice = 1.4e-3 ! transfer coefficient over ice
102	REAL(wp), PARAMETER :: albo = 0.066 ! ocean albedo assumed to be constant
103	!
104	! !!* Namelist namsbc_blk : bulk parameters
105	LOGICAL :: ln_NCAR ! "NCAR" algorithm (Large and Yeager 2008)
106	LOGICAL :: ln_COARE_3p0 ! "COARE 3.0" algorithm (Fairall et al. 2003)
107	LOGICAL :: ln_COARE_3p5 ! "COARE 3.5" algorithm (Edson et al. 2013)
108	LOGICAL :: ln_ECMWF ! "ECMWF" algorithm (IFS cycle 31)
109	!
110	LOGICAL :: ln_taudif ! logical flag to use the "mean of stress module - module of mean stress" data
111	REAL(wp) :: rn_pfac ! multiplication factor for precipitation
112	REAL(wp) :: rn_efac ! multiplication factor for evaporation
113	REAL(wp) :: rn_vfac ! multiplication factor for ice/ocean velocity in the calculation of wind stress
114	REAL(wp) :: rn_zqt ! z(q,t) : height of humidity and temperature measurements
115	REAL(wp) :: rn_zu ! z(u) : height of wind measurements
116	!!gm ref namelist initialize it so remove the setting to false below
117	LOGICAL :: ln_Cd_L12 = .FALSE. ! Modify the drag ice-atm depending on ice concentration (from Lupkes et al. JGR2012)
118	LOGICAL :: ln_Cd_L15 = .FALSE. ! Modify the drag ice-atm depending on ice concentration (from Lupkes et al. JGR2015)
119	!
120	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: Cd_atm ! transfer coefficient for momentum (tau)
121	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: Ch_atm ! transfer coefficient for sensible heat (Q_sens)
122	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: Ce_atm ! tansfert coefficient for evaporation (Q_lat)
123	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: t_zu ! air temperature at wind speed height (needed by Lupkes 2015 bulk scheme)
124	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: q_zu ! air spec. hum. at wind speed height (needed by Lupkes 2015 bulk scheme)
125	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: cdn_oce, chn_oce, cen_oce ! needed by Lupkes 2015 bulk scheme
126
127	INTEGER :: nblk ! choice of the bulk algorithm
128	! ! associated indices:
129	INTEGER, PARAMETER :: np_NCAR = 1 ! "NCAR" algorithm (Large and Yeager 2008)
130	INTEGER, PARAMETER :: np_COARE_3p0 = 2 ! "COARE 3.0" algorithm (Fairall et al. 2003)
131	INTEGER, PARAMETER :: np_COARE_3p5 = 3 ! "COARE 3.5" algorithm (Edson et al. 2013)
132	INTEGER, PARAMETER :: np_ECMWF = 4 ! "ECMWF" algorithm (IFS cycle 31)
133
134	!! * Substitutions
135	# include "vectopt_loop_substitute.h90"
136	!!----------------------------------------------------------------------
137	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
138	!! $Id$
139	!! Software governed by the CeCILL license (see ./LICENSE)
140	!!----------------------------------------------------------------------
141	CONTAINS
142
143	INTEGER FUNCTION sbc_blk_alloc()
144	!!-------------------------------------------------------------------
145	!! * ROUTINE sbc_blk_alloc *
146	!!-------------------------------------------------------------------
147	ALLOCATE( Cd_atm (jpi,jpj), Ch_atm (jpi,jpj), Ce_atm (jpi,jpj), t_zu(jpi,jpj), q_zu(jpi,jpj), &
148	& cdn_oce(jpi,jpj), chn_oce(jpi,jpj), cen_oce(jpi,jpj), STAT=sbc_blk_alloc )
149	!
150	CALL mpp_sum ( 'sbcblk', sbc_blk_alloc )
151	IF( sbc_blk_alloc /= 0 ) CALL ctl_stop( 'STOP', 'sbc_blk_alloc: failed to allocate arrays' )
152	END FUNCTION sbc_blk_alloc
153
154
155	SUBROUTINE sbc_blk_init
156	!!---------------------------------------------------------------------
157	!! * ROUTINE sbc_blk_init *
158	!!
159	!! ** Purpose : choose and initialize a bulk formulae formulation
160	!!
161	!! ** Method :
162	!!
163	!!----------------------------------------------------------------------
164	INTEGER :: jfpr, jfld ! dummy loop indice and argument
165	INTEGER :: ios, ierror, ioptio ! Local integer
166	!!
167	CHARACTER(len=100) :: cn_dir ! Root directory for location of atmospheric forcing files
168	TYPE(FLD_N), DIMENSION(jpfld) :: slf_i ! array of namelist informations on the fields to read
169	TYPE(FLD_N) :: sn_wndi, sn_wndj, sn_humi, sn_qsr ! informations about the fields to be read
170	TYPE(FLD_N) :: sn_qlw , sn_tair, sn_prec, sn_snow ! " "
171	TYPE(FLD_N) :: sn_slp , sn_tdif, sn_cc ! " "
172	NAMELIST/namsbc_blk/ sn_wndi, sn_wndj, sn_humi, sn_qsr, sn_qlw , & ! input fields
173	& sn_tair, sn_prec, sn_snow, sn_slp, sn_tdif, sn_cc, &
174	& ln_NCAR, ln_COARE_3p0, ln_COARE_3p5, ln_ECMWF, & ! bulk algorithm
175	& cn_dir , ln_taudif, rn_zqt, rn_zu, &
176	& rn_pfac, rn_efac, rn_vfac, ln_Cd_L12, ln_Cd_L15
177	!!---------------------------------------------------------------------
178	!
179	! ! allocate sbc_blk_core array
180	IF( sbc_blk_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'sbc_blk : unable to allocate standard arrays' )
181	!
182	! !** read bulk namelist
183	REWIND( numnam_ref ) !* Namelist namsbc_blk in reference namelist : bulk parameters
184	READ ( numnam_ref, namsbc_blk, IOSTAT = ios, ERR = 901)
185	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namsbc_blk in reference namelist' )
186	!
187	REWIND( numnam_cfg ) !* Namelist namsbc_blk in configuration namelist : bulk parameters
188	READ ( numnam_cfg, namsbc_blk, IOSTAT = ios, ERR = 902 )
189	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namsbc_blk in configuration namelist' )
190	!
191	IF(lwm) WRITE( numond, namsbc_blk )
192	!
193	! !** initialization of the chosen bulk formulae (+ check)
194	! !* select the bulk chosen in the namelist and check the choice
195	ioptio = 0
196	IF( ln_NCAR ) THEN ; nblk = np_NCAR ; ioptio = ioptio + 1 ; ENDIF
197	IF( ln_COARE_3p0 ) THEN ; nblk = np_COARE_3p0 ; ioptio = ioptio + 1 ; ENDIF
198	IF( ln_COARE_3p5 ) THEN ; nblk = np_COARE_3p5 ; ioptio = ioptio + 1 ; ENDIF
199	IF( ln_ECMWF ) THEN ; nblk = np_ECMWF ; ioptio = ioptio + 1 ; ENDIF
200	!
201	IF( ioptio /= 1 ) CALL ctl_stop( 'sbc_blk_init: Choose one and only one bulk algorithm' )
202	!
203	IF( ln_dm2dc ) THEN !* check: diurnal cycle on Qsr
204	IF( sn_qsr%freqh /= 24. ) CALL ctl_stop( 'sbc_blk_init: ln_dm2dc=T only with daily short-wave input' )
205	IF( sn_qsr%ln_tint ) THEN
206	CALL ctl_warn( 'sbc_blk_init: ln_dm2dc=T daily qsr time interpolation done by sbcdcy module', &
207	& ' ==> We force time interpolation = .false. for qsr' )
208	sn_qsr%ln_tint = .false.
209	ENDIF
210	ENDIF
211	! !* set the bulk structure
212	! !- store namelist information in an array
213	slf_i(jp_wndi) = sn_wndi ; slf_i(jp_wndj) = sn_wndj
214	slf_i(jp_qsr ) = sn_qsr ; slf_i(jp_qlw ) = sn_qlw
215	slf_i(jp_tair) = sn_tair ; slf_i(jp_humi) = sn_humi
216	slf_i(jp_prec) = sn_prec ; slf_i(jp_snow) = sn_snow
217	slf_i(jp_slp) = sn_slp ; slf_i(jp_cc) = sn_cc
218	slf_i(jp_tdif) = sn_tdif
219	!
220	lhftau = ln_taudif !- add an extra field if HF stress is used
221	jfld = jpfld - COUNT( (/.NOT.lhftau/) )
222	!
223	! !- allocate the bulk structure
224	ALLOCATE( sf(jfld), STAT=ierror )
225	IF( ierror > 0 ) CALL ctl_stop( 'STOP', 'sbc_blk_init: unable to allocate sf structure' )
226
227	! !- fill the bulk structure with namelist informations
228	CALL fld_fill( sf, slf_i, cn_dir, 'sbc_blk_init', 'surface boundary condition -- bulk formulae', 'namsbc_blk' )
229	!
230	DO jfpr = 1, jfld
231	!
232	IF( TRIM(sf(jfpr)%clrootname) == 'NOT USED' ) THEN !-- not used field --! (only now allocated and set to zero)
233	ALLOCATE( sf(jfpr)%fnow(jpi,jpj,1) )
234	sf(jfpr)%fnow(:,:,1) = 0._wp
235	ELSE !-- used field --!
236	ALLOCATE( sf(jfpr)%fnow(jpi,jpj,1) )
237	IF( slf_i(jfpr)%ln_tint ) ALLOCATE( sf(jfpr)%fdta(jpi,jpj,1,2) )
238	IF( slf_i(jfpr)%freqh > 0. .AND. MOD( NINT(3600. * slf_i(jfpr)%freqh), nn_fsbc * NINT(rdt) ) /= 0 ) &
239	& CALL ctl_warn( 'sbc_blk_init: sbcmod timestep rdt*nn_fsbc is NOT a submultiple of atmospheric forcing frequency.', &
240	& ' This is not ideal. You should consider changing either rdt or nn_fsbc value...' )
241	ENDIF
242	ENDDO
243	! fill cloud cover array with constant value if "not used"
244	IF( TRIM(sf(jp_cc)%clrootname) == 'NOT USED' ) sf(jp_cc)%fnow(:,:,1) = pp_cldf
245
246	IF ( ln_wave ) THEN
247	!Activated wave module but neither drag nor stokes drift activated
248	IF ( .NOT.(ln_cdgw .OR. ln_sdw .OR. ln_tauwoc .OR. ln_stcor ) ) THEN
249	CALL ctl_stop( 'STOP', 'Ask for wave coupling but ln_cdgw=F, ln_sdw=F, ln_tauwoc=F, ln_stcor=F' )
250	!drag coefficient read from wave model definable only with mfs bulk formulae and core
251	ELSEIF (ln_cdgw .AND. .NOT. ln_NCAR ) THEN
252	CALL ctl_stop( 'drag coefficient read from wave model definable only with NCAR and CORE bulk formulae')
253	ELSEIF (ln_stcor .AND. .NOT. ln_sdw) THEN
254	CALL ctl_stop( 'Stokes-Coriolis term calculated only if activated Stokes Drift ln_sdw=T')
255	ENDIF
256	ELSE
257	IF ( ln_cdgw .OR. ln_sdw .OR. ln_tauwoc .OR. ln_stcor ) &
258	& CALL ctl_stop( 'Not Activated Wave Module (ln_wave=F) but asked coupling ', &
259	& 'with drag coefficient (ln_cdgw =T) ' , &
260	& 'or Stokes Drift (ln_sdw=T) ' , &
261	& 'or ocean stress modification due to waves (ln_tauwoc=T) ', &
262	& 'or Stokes-Coriolis term (ln_stcori=T)' )
263	ENDIF
264	!
265	!
266	IF(lwp) THEN !** Control print
267	!
268	WRITE(numout,) ! namelist
269	WRITE(numout,*) ' Namelist namsbc_blk (other than data information):'
270	WRITE(numout,*) ' "NCAR" algorithm (Large and Yeager 2008) ln_NCAR = ', ln_NCAR
271	WRITE(numout,*) ' "COARE 3.0" algorithm (Fairall et al. 2003) ln_COARE_3p0 = ', ln_COARE_3p0
272	WRITE(numout,*) ' "COARE 3.5" algorithm (Edson et al. 2013) ln_COARE_3p5 = ', ln_COARE_3p0
273	WRITE(numout,*) ' "ECMWF" algorithm (IFS cycle 31) ln_ECMWF = ', ln_ECMWF
274	WRITE(numout,*) ' add High freq.contribution to the stress module ln_taudif = ', ln_taudif
275	WRITE(numout,*) ' Air temperature and humidity reference height (m) rn_zqt = ', rn_zqt
276	WRITE(numout,*) ' Wind vector reference height (m) rn_zu = ', rn_zu
277	WRITE(numout,*) ' factor applied on precipitation (total & snow) rn_pfac = ', rn_pfac
278	WRITE(numout,*) ' factor applied on evaporation rn_efac = ', rn_efac
279	WRITE(numout,*) ' factor applied on ocean/ice velocity rn_vfac = ', rn_vfac
280	WRITE(numout,*) ' (form absolute (=0) to relative winds(=1))'
281	WRITE(numout,*) ' use ice-atm drag from Lupkes2012 ln_Cd_L12 = ', ln_Cd_L12
282	WRITE(numout,*) ' use ice-atm drag from Lupkes2015 ln_Cd_L15 = ', ln_Cd_L15
283	!
284	WRITE(numout,*)
285	SELECT CASE( nblk ) !* Print the choice of bulk algorithm
286	CASE( np_NCAR ) ; WRITE(numout,*) ' ==>>> "NCAR" algorithm (Large and Yeager 2008)'
287	CASE( np_COARE_3p0 ) ; WRITE(numout,*) ' ==>>> "COARE 3.0" algorithm (Fairall et al. 2003)'
288	CASE( np_COARE_3p5 ) ; WRITE(numout,*) ' ==>>> "COARE 3.5" algorithm (Edson et al. 2013)'
289	CASE( np_ECMWF ) ; WRITE(numout,*) ' ==>>> "ECMWF" algorithm (IFS cycle 31)'
290	END SELECT
291	!
292	ENDIF
293	!
294	END SUBROUTINE sbc_blk_init
295
296
297	SUBROUTINE sbc_blk( kt )
298	!!---------------------------------------------------------------------
299	!! * ROUTINE sbc_blk *
300	!!
301	!! ** Purpose : provide at each time step the surface ocean fluxes
302	!! (momentum, heat, freshwater and runoff)
303	!!
304	!! ** Method : (1) READ each fluxes in NetCDF files:
305	!! the 10m wind velocity (i-component) (m/s) at T-point
306	!! the 10m wind velocity (j-component) (m/s) at T-point
307	!! the 10m or 2m specific humidity ( % )
308	!! the solar heat (W/m2)
309	!! the Long wave (W/m2)
310	!! the 10m or 2m air temperature (Kelvin)
311	!! the total precipitation (rain+snow) (Kg/m2/s)
312	!! the snow (solid prcipitation) (kg/m2/s)
313	!! the tau diff associated to HF tau (N/m2) at T-point (ln_taudif=T)
314	!! (2) CALL blk_oce
315	!!
316	!! C A U T I O N : never mask the surface stress fields
317	!! the stress is assumed to be in the (i,j) mesh referential
318	!!
319	!! ** Action : defined at each time-step at the air-sea interface
320	!! - utau, vtau i- and j-component of the wind stress
321	!! - taum wind stress module at T-point
322	!! - wndm wind speed module at T-point over free ocean or leads in presence of sea-ice
323	!! - qns, qsr non-solar and solar heat fluxes
324	!! - emp upward mass flux (evapo. - precip.)
325	!! - sfx salt flux due to freezing/melting (non-zero only if ice is present)
326	!!
327	!! ** References : Large & Yeager, 2004 / Large & Yeager, 2008
328	!! Brodeau et al. Ocean Modelling 2010
329	!!----------------------------------------------------------------------
330	INTEGER, INTENT(in) :: kt ! ocean time step
331	!!---------------------------------------------------------------------
332	!
333	CALL fld_read( kt, nn_fsbc, sf ) ! input fields provided at the current time-step
334	!
335	! ! compute the surface ocean fluxes using bulk formulea
336	IF( MOD( kt - 1, nn_fsbc ) == 0 ) CALL blk_oce( kt, sf, sst_m, ssu_m, ssv_m )
337
338	#if defined key_cice
339	IF( MOD( kt - 1, nn_fsbc ) == 0 ) THEN
340	qlw_ice(:,:,1) = sf(jp_qlw )%fnow(:,:,1)
341	IF( ln_dm2dc ) THEN ; qsr_ice(:,:,1) = sbc_dcy( sf(jp_qsr)%fnow(:,:,1) )
342	ELSE ; qsr_ice(:,:,1) = sf(jp_qsr)%fnow(:,:,1)
343	ENDIF
344	tatm_ice(:,:) = sf(jp_tair)%fnow(:,:,1)
345	qatm_ice(:,:) = sf(jp_humi)%fnow(:,:,1)
346	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac
347	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac
348	wndi_ice(:,:) = sf(jp_wndi)%fnow(:,:,1)
349	wndj_ice(:,:) = sf(jp_wndj)%fnow(:,:,1)
350	ENDIF
351	#endif
352	!
353	END SUBROUTINE sbc_blk
354
355
356	SUBROUTINE blk_oce( kt, sf, pst, pu, pv )
357	!!---------------------------------------------------------------------
358	!! * ROUTINE blk_oce *
359	!!
360	!! ** Purpose : provide the momentum, heat and freshwater fluxes at
361	!! the ocean surface at each time step
362	!!
363	!! ** Method : bulk formulea for the ocean using atmospheric
364	!! fields read in sbc_read
365	!!
366	!! ** Outputs : - utau : i-component of the stress at U-point (N/m2)
367	!! - vtau : j-component of the stress at V-point (N/m2)
368	!! - taum : Wind stress module at T-point (N/m2)
369	!! - wndm : Wind speed module at T-point (m/s)
370	!! - qsr : Solar heat flux over the ocean (W/m2)
371	!! - qns : Non Solar heat flux over the ocean (W/m2)
372	!! - emp : evaporation minus precipitation (kg/m2/s)
373	!!
374	!! ** Nota : sf has to be a dummy argument for AGRIF on NEC
375	!!---------------------------------------------------------------------
376	INTEGER , INTENT(in ) :: kt ! time step index
377	TYPE(fld), INTENT(inout), DIMENSION(:) :: sf ! input data
378	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pst ! surface temperature [Celcius]
379	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pu ! surface current at U-point (i-component) [m/s]
380	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pv ! surface current at V-point (j-component) [m/s]
381	!
382	INTEGER :: ji, jj ! dummy loop indices
383	REAL(wp) :: zztmp ! local variable
384	REAL(wp), DIMENSION(jpi,jpj) :: zwnd_i, zwnd_j ! wind speed components at T-point
385	REAL(wp), DIMENSION(jpi,jpj) :: zsq ! specific humidity at pst
386	REAL(wp), DIMENSION(jpi,jpj) :: zqlw, zqsb ! long wave and sensible heat fluxes
387	REAL(wp), DIMENSION(jpi,jpj) :: zqla, zevap ! latent heat fluxes and evaporation
388	REAL(wp), DIMENSION(jpi,jpj) :: zst ! surface temperature in Kelvin
389	REAL(wp), DIMENSION(jpi,jpj) :: zU_zu ! bulk wind speed at height zu [m/s]
390	REAL(wp), DIMENSION(jpi,jpj) :: ztpot ! potential temperature of air at z=rn_zqt [K]
391	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa ! density of air [kg/m^3]
392	!!---------------------------------------------------------------------
393	!
394	! local scalars ( place there for vector optimisation purposes)
395	zst(:,:) = pst(:,:) + rt0 ! convert SST from Celcius to Kelvin (and set minimum value far above 0 K)
396
397	! --- cloud cover --- !
398	cloud_fra(:,:) = sf(jp_cc)%fnow(:,:,1)
399
400	! ----------------------------------------------------------------------------- !
401	! 0 Wind components and module at T-point relative to the moving ocean !
402	! ----------------------------------------------------------------------------- !
403
404	! ... components ( U10m - U_oce ) at T-point (unmasked)
405	!!gm move zwnd_i (_j) set to zero inside the key_cyclone ???
406	zwnd_i(:,:) = 0._wp
407	zwnd_j(:,:) = 0._wp
408	#if defined key_cyclone
409	CALL wnd_cyc( kt, zwnd_i, zwnd_j ) ! add analytical tropical cyclone (Vincent et al. JGR 2012)
410	DO jj = 2, jpjm1
411	DO ji = fs_2, fs_jpim1 ! vect. opt.
412	sf(jp_wndi)%fnow(ji,jj,1) = sf(jp_wndi)%fnow(ji,jj,1) + zwnd_i(ji,jj)
413	sf(jp_wndj)%fnow(ji,jj,1) = sf(jp_wndj)%fnow(ji,jj,1) + zwnd_j(ji,jj)
414	END DO
415	END DO
416	#endif
417	DO jj = 2, jpjm1
418	DO ji = fs_2, fs_jpim1 ! vect. opt.
419	zwnd_i(ji,jj) = ( sf(jp_wndi)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( pu(ji-1,jj ) + pu(ji,jj) ) )
420	zwnd_j(ji,jj) = ( sf(jp_wndj)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( pv(ji ,jj-1) + pv(ji,jj) ) )
421	END DO
422	END DO
423	CALL lbc_lnk_multi( 'sbcblk', zwnd_i, 'T', -1., zwnd_j, 'T', -1. )
424	! ... scalar wind ( = \| U10m - U_oce \| ) at T-point (masked)
425	wndm(:,:) = SQRT( zwnd_i(:,:) * zwnd_i(:,:) &
426	& + zwnd_j(:,:) * zwnd_j(:,:) ) * tmask(:,:,1)
427
428	! ----------------------------------------------------------------------------- !
429	! I Radiative FLUXES !
430	! ----------------------------------------------------------------------------- !
431
432	! ocean albedo assumed to be constant + modify now Qsr to include the diurnal cycle ! Short Wave
433	zztmp = 1. - albo
434	IF( ln_dm2dc ) THEN ; qsr(:,:) = zztmp * sbc_dcy( sf(jp_qsr)%fnow(:,:,1) ) * tmask(:,:,1)
435	ELSE ; qsr(:,:) = zztmp * sf(jp_qsr)%fnow(:,:,1) * tmask(:,:,1)
436	ENDIF
437
438	zqlw(:,:) = ( sf(jp_qlw)%fnow(:,:,1) - Stef * zst(:,:)zst(:,:)zst(:,:)zst(:,:) ) tmask(:,:,1) ! Long Wave
439
440	! ----------------------------------------------------------------------------- !
441	! II Turbulent FLUXES !
442	! ----------------------------------------------------------------------------- !
443
444	! ... specific humidity at SST and IST tmask(
445	zsq(:,:) = 0.98 * q_sat( zst(:,:), sf(jp_slp)%fnow(:,:,1) )
446	!!
447	!! Estimate of potential temperature at z=rn_zqt, based on adiabatic lapse-rate
448	!! (see Josey, Gulev & Yu, 2013) / doi=10.1016/B978-0-12-391851-2.00005-2
449	!! (since reanalysis products provide T at z, not theta !)
450	ztpot = sf(jp_tair)%fnow(:,:,1) + gamma_moist( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1) ) * rn_zqt
451
452	SELECT CASE( nblk ) !== transfer coefficients ==! Cd, Ch, Ce at T-point
453	!
454	CASE( np_NCAR ) ; CALL turb_ncar ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! NCAR-COREv2
455	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
456	CASE( np_COARE_3p0 ) ; CALL turb_coare ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! COARE v3.0
457	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
458	CASE( np_COARE_3p5 ) ; CALL turb_coare3p5( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! COARE v3.5
459	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
460	CASE( np_ECMWF ) ; CALL turb_ecmwf ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! ECMWF
461	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
462	CASE DEFAULT
463	CALL ctl_stop( 'STOP', 'sbc_oce: non-existing bulk formula selected' )
464	END SELECT
465
466	! ! Compute true air density :
467	IF( ABS(rn_zu - rn_zqt) > 0.01 ) THEN ! At zu: (probably useless to remove zrhogravrn_zu from SLP...)
468	zrhoa(:,:) = rho_air( t_zu(:,:) , q_zu(:,:) , sf(jp_slp)%fnow(:,:,1) )
469	ELSE ! At zt:
470	zrhoa(:,:) = rho_air( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1) )
471	END IF
472
473	!! CALL iom_put( "Cd_oce", Cd_atm) ! output value of pure ocean-atm. transfer coef.
474	!! CALL iom_put( "Ch_oce", Ch_atm) ! output value of pure ocean-atm. transfer coef.
475
476	DO jj = 1, jpj ! tau module, i and j component
477	DO ji = 1, jpi
478	zztmp = zrhoa(ji,jj) * zU_zu(ji,jj) * Cd_atm(ji,jj) ! using bulk wind speed
479	taum (ji,jj) = zztmp * wndm (ji,jj)
480	zwnd_i(ji,jj) = zztmp * zwnd_i(ji,jj)
481	zwnd_j(ji,jj) = zztmp * zwnd_j(ji,jj)
482	END DO
483	END DO
484
485	! ! add the HF tau contribution to the wind stress module
486	IF( lhftau ) taum(:,:) = taum(:,:) + sf(jp_tdif)%fnow(:,:,1)
487
488	CALL iom_put( "taum_oce", taum ) ! output wind stress module
489
490	! ... utau, vtau at U- and V_points, resp.
491	! Note the use of 0.5*(2-umask) in order to unmask the stress along coastlines
492	! Note the use of MAX(tmask(i,j),tmask(i+1,j) is to mask tau over ice shelves
493	DO jj = 1, jpjm1
494	DO ji = 1, fs_jpim1
495	utau(ji,jj) = 0.5 * ( 2. - umask(ji,jj,1) ) * ( zwnd_i(ji,jj) + zwnd_i(ji+1,jj ) ) &
496	& * MAX(tmask(ji,jj,1),tmask(ji+1,jj,1))
497	vtau(ji,jj) = 0.5 * ( 2. - vmask(ji,jj,1) ) * ( zwnd_j(ji,jj) + zwnd_j(ji ,jj+1) ) &
498	& * MAX(tmask(ji,jj,1),tmask(ji,jj+1,1))
499	END DO
500	END DO
501	CALL lbc_lnk_multi( 'sbcblk', utau, 'U', -1., vtau, 'V', -1. )
502
503	! Turbulent fluxes over ocean
504	! -----------------------------
505
506	! zqla used as temporary array, for rho*U (common term of bulk formulae):
507	zqla(:,:) = zrhoa(:,:) * zU_zu(:,:) * tmask(:,:,1)
508
509	IF( ABS( rn_zu - rn_zqt) < 0.01_wp ) THEN
510	!! q_air and t_air are given at 10m (wind reference height)
511	zevap(:,:) = rn_efacMAX( 0._wp, zqla(:,:)Ce_atm(:,:)*(zsq(:,:) - sf(jp_humi)%fnow(:,:,1)) ) ! Evaporation, using bulk wind speed
512	zqsb (:,:) = cp_air(sf(jp_humi)%fnow(:,:,1))zqla(:,:)Ch_atm(:,:)*(zst(:,:) - ztpot(:,:) ) ! Sensible Heat, using bulk wind speed
513	ELSE
514	!! q_air and t_air are not given at 10m (wind reference height)
515	! Values of temp. and hum. adjusted to height of wind during bulk algorithm iteration must be used!!!
516	zevap(:,:) = rn_efacMAX( 0._wp, zqla(:,:)Ce_atm(:,:)*(zsq(:,:) - q_zu(:,:) ) ) ! Evaporation, using bulk wind speed
517	zqsb (:,:) = cp_air(sf(jp_humi)%fnow(:,:,1))zqla(:,:)Ch_atm(:,:)*(zst(:,:) - t_zu(:,:) ) ! Sensible Heat, using bulk wind speed
518	ENDIF
519
520	zqla(:,:) = L_vap(zst(:,:)) * zevap(:,:) ! Latent Heat flux
521
522
523	IF(ln_ctl) THEN
524	CALL prt_ctl( tab2d_1=zqla , clinfo1=' blk_oce: zqla : ', tab2d_2=Ce_atm , clinfo2=' Ce_oce : ' )
525	CALL prt_ctl( tab2d_1=zqsb , clinfo1=' blk_oce: zqsb : ', tab2d_2=Ch_atm , clinfo2=' Ch_oce : ' )
526	CALL prt_ctl( tab2d_1=zqlw , clinfo1=' blk_oce: zqlw : ', tab2d_2=qsr, clinfo2=' qsr : ' )
527	CALL prt_ctl( tab2d_1=zsq , clinfo1=' blk_oce: zsq : ', tab2d_2=zst, clinfo2=' zst : ' )
528	CALL prt_ctl( tab2d_1=utau , clinfo1=' blk_oce: utau : ', mask1=umask, &
529	& tab2d_2=vtau , clinfo2= ' vtau : ', mask2=vmask )
530	CALL prt_ctl( tab2d_1=wndm , clinfo1=' blk_oce: wndm : ')
531	CALL prt_ctl( tab2d_1=zst , clinfo1=' blk_oce: zst : ')
532	ENDIF
533
534	! ----------------------------------------------------------------------------- !
535	! III Total FLUXES !
536	! ----------------------------------------------------------------------------- !
537	!
538	emp (:,:) = ( zevap(:,:) & ! mass flux (evap. - precip.)
539	& - sf(jp_prec)%fnow(:,:,1) * rn_pfac ) * tmask(:,:,1)
540	!
541	qns(:,:) = zqlw(:,:) - zqsb(:,:) - zqla(:,:) & ! Downward Non Solar
542	& - sf(jp_snow)%fnow(:,:,1) * rn_pfac * rLfus & ! remove latent melting heat for solid precip
543	& - zevap(:,:) * pst(:,:) * rcp & ! remove evap heat content at SST
544	& + ( sf(jp_prec)%fnow(:,:,1) - sf(jp_snow)%fnow(:,:,1) ) * rn_pfac & ! add liquid precip heat content at Tair
545	& * ( sf(jp_tair)%fnow(:,:,1) - rt0 ) * rcp &
546	& + sf(jp_snow)%fnow(:,:,1) * rn_pfac & ! add solid precip heat content at min(Tair,Tsnow)
547	& * ( MIN( sf(jp_tair)%fnow(:,:,1), rt0 ) - rt0 ) * rcpi
548	qns(:,:) = qns(:,:) * tmask(:,:,1)
549	!
550	#if defined key_si3
551	qns_oce(:,:) = zqlw(:,:) - zqsb(:,:) - zqla(:,:) ! non solar without emp (only needed by SI3)
552	qsr_oce(:,:) = qsr(:,:)
553	#endif
554	!
555	IF ( nn_ice == 0 ) THEN
556	CALL iom_put( "qlw_oce" , zqlw ) ! output downward longwave heat over the ocean
557	CALL iom_put( "qsb_oce" , - zqsb ) ! output downward sensible heat over the ocean
558	CALL iom_put( "qla_oce" , - zqla ) ! output downward latent heat over the ocean
559	CALL iom_put( "qemp_oce", qns-zqlw+zqsb+zqla ) ! output downward heat content of E-P over the ocean
560	CALL iom_put( "qns_oce" , qns ) ! output downward non solar heat over the ocean
561	CALL iom_put( "qsr_oce" , qsr ) ! output downward solar heat over the ocean
562	CALL iom_put( "qt_oce" , qns+qsr ) ! output total downward heat over the ocean
563	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! output total precipitation [kg/m2/s]
564	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! output solid precipitation [kg/m2/s]
565	CALL iom_put( 'snowpre', sprecip ) ! Snow
566	CALL iom_put( 'precip' , tprecip ) ! Total precipitation
567	ENDIF
568	!
569	IF(ln_ctl) THEN
570	CALL prt_ctl(tab2d_1=zqsb , clinfo1=' blk_oce: zqsb : ', tab2d_2=zqlw , clinfo2=' zqlw : ')
571	CALL prt_ctl(tab2d_1=zqla , clinfo1=' blk_oce: zqla : ', tab2d_2=qsr , clinfo2=' qsr : ')
572	CALL prt_ctl(tab2d_1=pst , clinfo1=' blk_oce: pst : ', tab2d_2=emp , clinfo2=' emp : ')
573	CALL prt_ctl(tab2d_1=utau , clinfo1=' blk_oce: utau : ', mask1=umask, &
574	& tab2d_2=vtau , clinfo2= ' vtau : ' , mask2=vmask )
575	ENDIF
576	!
577	END SUBROUTINE blk_oce
578
579
580
581	FUNCTION rho_air( ptak, pqa, pslp )
582	!!-------------------------------------------------------------------------------
583	!! * FUNCTION rho_air *
584	!!
585	!! ** Purpose : compute density of (moist) air using the eq. of state of the atmosphere
586	!!
587	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
588	!!-------------------------------------------------------------------------------
589	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
590	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg]
591	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! pressure in [Pa]
592	REAL(wp), DIMENSION(jpi,jpj) :: rho_air ! density of moist air [kg/m^3]
593	!!-------------------------------------------------------------------------------
594	!
595	rho_air = pslp / ( R_dryptak ( 1._wp + rctv0*pqa ) )
596	!
597	END FUNCTION rho_air
598
599
600	FUNCTION cp_air( pqa )
601	!!-------------------------------------------------------------------------------
602	!! * FUNCTION cp_air *
603	!!
604	!! ** Purpose : Compute specific heat (Cp) of moist air
605	!!
606	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
607	!!-------------------------------------------------------------------------------
608	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg]
609	REAL(wp), DIMENSION(jpi,jpj) :: cp_air ! specific heat of moist air [J/K/kg]
610	!!-------------------------------------------------------------------------------
611	!
612	Cp_air = Cp_dry + Cp_vap * pqa
613	!
614	END FUNCTION cp_air
615
616
617	FUNCTION q_sat( ptak, pslp )
618	!!----------------------------------------------------------------------------------
619	!! * FUNCTION q_sat *
620	!!
621	!! ** Purpose : Specific humidity at saturation in [kg/kg]
622	!! Based on accurate estimate of "e_sat"
623	!! aka saturation water vapor (Goff, 1957)
624	!!
625	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
626	!!----------------------------------------------------------------------------------
627	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
628	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! sea level atmospheric pressure [Pa]
629	REAL(wp), DIMENSION(jpi,jpj) :: q_sat ! Specific humidity at saturation [kg/kg]
630	!
631	INTEGER :: ji, jj ! dummy loop indices
632	REAL(wp) :: ze_sat, ztmp ! local scalar
633	!!----------------------------------------------------------------------------------
634	!
635	DO jj = 1, jpj
636	DO ji = 1, jpi
637	!
638	ztmp = rt0 / ptak(ji,jj)
639	!
640	! Vapour pressure at saturation [hPa] : WMO, (Goff, 1957)
641	ze_sat = 10.*( 10.79574(1. - ztmp) - 5.028*LOG10(ptak(ji,jj)/rt0) &
642	& + 1.5047510.(-4)(1. - 10.*(-8.2969(ptak(ji,jj)/rt0 - 1.)) ) &
643	& + 0.4287310.(-3)(10.*(4.76955(1. - ztmp)) - 1.) + 0.78614 )
644	!
645	q_sat(ji,jj) = reps0 * ze_sat/( 0.01_wppslp(ji,jj) - (1._wp - reps0)ze_sat ) ! 0.01 because SLP is in [Pa]
646	!
647	END DO
648	END DO
649	!
650	END FUNCTION q_sat
651
652
653	FUNCTION gamma_moist( ptak, pqa )
654	!!----------------------------------------------------------------------------------
655	!! * FUNCTION gamma_moist *
656	!!
657	!! ** Purpose : Compute the moist adiabatic lapse-rate.
658	!! => http://glossary.ametsoc.org/wiki/Moist-adiabatic_lapse_rate
659	!! => http://www.geog.ucsb.edu/~joel/g266_s10/lecture_notes/chapt03/oh10_3_01/oh10_3_01.html
660	!!
661	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
662	!!----------------------------------------------------------------------------------
663	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
664	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! specific humidity [kg/kg]
665	REAL(wp), DIMENSION(jpi,jpj) :: gamma_moist ! moist adiabatic lapse-rate
666	!
667	INTEGER :: ji, jj ! dummy loop indices
668	REAL(wp) :: zrv, ziRT ! local scalar
669	!!----------------------------------------------------------------------------------
670	!
671	DO jj = 1, jpj
672	DO ji = 1, jpi
673	zrv = pqa(ji,jj) / (1. - pqa(ji,jj))
674	ziRT = 1. / (R_dry*ptak(ji,jj)) ! 1/RT
675	gamma_moist(ji,jj) = grav * ( 1. + rLevapzrvziRT ) / ( Cp_dry + rLevaprLevapzrvreps0ziRT/ptak(ji,jj) )
676	END DO
677	END DO
678	!
679	END FUNCTION gamma_moist
680
681
682	FUNCTION L_vap( psst )
683	!!---------------------------------------------------------------------------------
684	!! * FUNCTION L_vap *
685	!!
686	!! ** Purpose : Compute the latent heat of vaporization of water from temperature
687	!!
688	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
689	!!----------------------------------------------------------------------------------
690	REAL(wp), DIMENSION(jpi,jpj) :: L_vap ! latent heat of vaporization [J/kg]
691	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! water temperature [K]
692	!!----------------------------------------------------------------------------------
693	!
694	L_vap = ( 2.501 - 0.00237 * ( psst(:,:) - rt0) ) * 1.e6
695	!
696	END FUNCTION L_vap
697
698	#if defined key_si3
699	!!----------------------------------------------------------------------
700	!! 'key_si3' SI3 sea-ice model
701	!!----------------------------------------------------------------------
702	!! blk_ice_tau : provide the air-ice stress
703	!! blk_ice_flx : provide the heat and mass fluxes at air-ice interface
704	!! blk_ice_qcn : provide ice surface temperature and snow/ice conduction flux (emulating conduction flux)
705	!! Cdn10_Lupkes2012 : Lupkes et al. (2012) air-ice drag
706	!! Cdn10_Lupkes2015 : Lupkes et al. (2015) air-ice drag
707	!!----------------------------------------------------------------------
708
709	SUBROUTINE blk_ice_tau
710	!!---------------------------------------------------------------------
711	!! * ROUTINE blk_ice_tau *
712	!!
713	!! ** Purpose : provide the surface boundary condition over sea-ice
714	!!
715	!! ** Method : compute momentum using bulk formulation
716	!! formulea, ice variables and read atmospheric fields.
717	!! NB: ice drag coefficient is assumed to be a constant
718	!!---------------------------------------------------------------------
719	INTEGER :: ji, jj ! dummy loop indices
720	REAL(wp) :: zwndi_f , zwndj_f, zwnorm_f ! relative wind module and components at F-point
721	REAL(wp) :: zwndi_t , zwndj_t ! relative wind components at T-point
722	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa ! transfer coefficient for momentum (tau)
723	!!---------------------------------------------------------------------
724	!
725	! set transfer coefficients to default sea-ice values
726	Cd_atm(:,:) = Cd_ice
727	Ch_atm(:,:) = Cd_ice
728	Ce_atm(:,:) = Cd_ice
729
730	wndm_ice(:,:) = 0._wp !!gm brutal....
731
732	! ------------------------------------------------------------ !
733	! Wind module relative to the moving ice ( U10m - U_ice ) !
734	! ------------------------------------------------------------ !
735	! C-grid ice dynamics : U & V-points (same as ocean)
736	DO jj = 2, jpjm1
737	DO ji = fs_2, fs_jpim1 ! vect. opt.
738	zwndi_t = ( sf(jp_wndi)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( u_ice(ji-1,jj ) + u_ice(ji,jj) ) )
739	zwndj_t = ( sf(jp_wndj)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( v_ice(ji ,jj-1) + v_ice(ji,jj) ) )
740	wndm_ice(ji,jj) = SQRT( zwndi_t * zwndi_t + zwndj_t * zwndj_t ) * tmask(ji,jj,1)
741	END DO
742	END DO
743	CALL lbc_lnk( 'sbcblk', wndm_ice, 'T', 1. )
744	!
745	! Make ice-atm. drag dependent on ice concentration
746	IF ( ln_Cd_L12 ) THEN ! calculate new drag from Lupkes(2012) equations
747	CALL Cdn10_Lupkes2012( Cd_atm )
748	Ch_atm(:,:) = Cd_atm(:,:) ! momentum and heat transfer coef. are considered identical
749	ELSEIF( ln_Cd_L15 ) THEN ! calculate new drag from Lupkes(2015) equations
750	CALL Cdn10_Lupkes2015( Cd_atm, Ch_atm )
751	ENDIF
752
753	!! CALL iom_put( "Cd_ice", Cd_atm) ! output value of pure ice-atm. transfer coef.
754	!! CALL iom_put( "Ch_ice", Ch_atm) ! output value of pure ice-atm. transfer coef.
755
756	! local scalars ( place there for vector optimisation purposes)
757	! Computing density of air! Way denser that 1.2 over sea-ice !!!
758	zrhoa (:,:) = rho_air(sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1))
759
760	!!gm brutal....
761	utau_ice (:,:) = 0._wp
762	vtau_ice (:,:) = 0._wp
763	!!gm end
764
765	! ------------------------------------------------------------ !
766	! Wind stress relative to the moving ice ( U10m - U_ice ) !
767	! ------------------------------------------------------------ !
768	! C-grid ice dynamics : U & V-points (same as ocean)
769	DO jj = 2, jpjm1
770	DO ji = fs_2, fs_jpim1 ! vect. opt.
771	utau_ice(ji,jj) = 0.5 * zrhoa(ji,jj) * Cd_atm(ji,jj) * ( wndm_ice(ji+1,jj ) + wndm_ice(ji,jj) ) &
772	& * ( 0.5 * (sf(jp_wndi)%fnow(ji+1,jj,1) + sf(jp_wndi)%fnow(ji,jj,1) ) - rn_vfac * u_ice(ji,jj) )
773	vtau_ice(ji,jj) = 0.5 * zrhoa(ji,jj) * Cd_atm(ji,jj) * ( wndm_ice(ji,jj+1 ) + wndm_ice(ji,jj) ) &
774	& * ( 0.5 * (sf(jp_wndj)%fnow(ji,jj+1,1) + sf(jp_wndj)%fnow(ji,jj,1) ) - rn_vfac * v_ice(ji,jj) )
775	END DO
776	END DO
777	CALL lbc_lnk_multi( 'sbcblk', utau_ice, 'U', -1., vtau_ice, 'V', -1. )
778	!
779	!
780	IF(ln_ctl) THEN
781	CALL prt_ctl(tab2d_1=utau_ice , clinfo1=' blk_ice: utau_ice : ', tab2d_2=vtau_ice , clinfo2=' vtau_ice : ')
782	CALL prt_ctl(tab2d_1=wndm_ice , clinfo1=' blk_ice: wndm_ice : ')
783	ENDIF
784	!
785	END SUBROUTINE blk_ice_tau
786
787
788	SUBROUTINE blk_ice_flx( ptsu, phs, phi, palb )
789	!!---------------------------------------------------------------------
790	!! * ROUTINE blk_ice_flx *
791	!!
792	!! ** Purpose : provide the heat and mass fluxes at air-ice interface
793	!!
794	!! ** Method : compute heat and freshwater exchanged
795	!! between atmosphere and sea-ice using bulk formulation
796	!! formulea, ice variables and read atmmospheric fields.
797	!!
798	!! caution : the net upward water flux has with mm/day unit
799	!!---------------------------------------------------------------------
800	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: ptsu ! sea ice surface temperature
801	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: phs ! snow thickness
802	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: phi ! ice thickness
803	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: palb ! ice albedo (all skies)
804	!!
805	INTEGER :: ji, jj, jl ! dummy loop indices
806	REAL(wp) :: zst3 ! local variable
807	REAL(wp) :: zcoef_dqlw, zcoef_dqla ! - -
808	REAL(wp) :: zztmp, z1_rLsub ! - -
809	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_st ! inverse of surface temperature
810	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_qlw ! long wave heat flux over ice
811	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_qsb ! sensible heat flux over ice
812	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_dqlw ! long wave heat sensitivity over ice
813	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_dqsb ! sensible heat sensitivity over ice
814	REAL(wp), DIMENSION(jpi,jpj) :: zevap, zsnw ! evaporation and snw distribution after wind blowing (SI3)
815	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa
816	REAL(wp), DIMENSION(jpi,jpj) :: ztmp, ztmp2
817	REAL(wp), DIMENSION(jpi,jpj) :: ztri
818	!!---------------------------------------------------------------------
819	!
820	zcoef_dqlw = 4.0 * 0.95 * Stef ! local scalars
821	zcoef_dqla = -Ls * 11637800. * (-5897.8)
822	!
823	zrhoa(:,:) = rho_air( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1) )
824	!
825	zztmp = 1. / ( 1. - albo )
826	WHERE( ptsu(:,:,:) /= 0._wp ) ; z1_st(:,:,:) = 1._wp / ptsu(:,:,:)
827	ELSEWHERE ; z1_st(:,:,:) = 0._wp
828	END WHERE
829	! ! ========================== !
830	DO jl = 1, jpl ! Loop over ice categories !
831	! ! ========================== !
832	DO jj = 1 , jpj
833	DO ji = 1, jpi
834	! ----------------------------!
835	! I Radiative FLUXES !
836	! ----------------------------!
837	zst3 = ptsu(ji,jj,jl) * ptsu(ji,jj,jl) * ptsu(ji,jj,jl)
838	! Short Wave (sw)
839	qsr_ice(ji,jj,jl) = zztmp * ( 1. - palb(ji,jj,jl) ) * qsr(ji,jj)
840	! Long Wave (lw)
841	z_qlw(ji,jj,jl) = 0.95 * ( sf(jp_qlw)%fnow(ji,jj,1) - Stef * ptsu(ji,jj,jl) * zst3 ) * tmask(ji,jj,1)
842	! lw sensitivity
843	z_dqlw(ji,jj,jl) = zcoef_dqlw * zst3
844
845	! ----------------------------!
846	! II Turbulent FLUXES !
847	! ----------------------------!
848
849	! ... turbulent heat fluxes with Ch_atm recalculated in blk_ice_tau
850	! Sensible Heat
851	z_qsb(ji,jj,jl) = zrhoa(ji,jj) * cpa * Ch_atm(ji,jj) * wndm_ice(ji,jj) * (ptsu(ji,jj,jl) - sf(jp_tair)%fnow(ji,jj,1))
852	! Latent Heat
853	qla_ice(ji,jj,jl) = rn_efac * MAX( 0.e0, zrhoa(ji,jj) * Ls * Ch_atm(ji,jj) * wndm_ice(ji,jj) * &
854	& ( 11637800. * EXP( -5897.8 * z1_st(ji,jj,jl) ) / zrhoa(ji,jj) - sf(jp_humi)%fnow(ji,jj,1) ) )
855	! Latent heat sensitivity for ice (Dqla/Dt)
856	IF( qla_ice(ji,jj,jl) > 0._wp ) THEN
857	dqla_ice(ji,jj,jl) = rn_efac * zcoef_dqla * Ch_atm(ji,jj) * wndm_ice(ji,jj) * &
858	& z1_st(ji,jj,jl)z1_st(ji,jj,jl) EXP(-5897.8 * z1_st(ji,jj,jl))
859	ELSE
860	dqla_ice(ji,jj,jl) = 0._wp
861	ENDIF
862
863	! Sensible heat sensitivity (Dqsb_ice/Dtn_ice)
864	z_dqsb(ji,jj,jl) = zrhoa(ji,jj) * cpa * Ch_atm(ji,jj) * wndm_ice(ji,jj)
865
866	! ----------------------------!
867	! III Total FLUXES !
868	! ----------------------------!
869	! Downward Non Solar flux
870	qns_ice (ji,jj,jl) = z_qlw (ji,jj,jl) - z_qsb (ji,jj,jl) - qla_ice (ji,jj,jl)
871	! Total non solar heat flux sensitivity for ice
872	dqns_ice(ji,jj,jl) = - ( z_dqlw(ji,jj,jl) + z_dqsb(ji,jj,jl) + dqla_ice(ji,jj,jl) )
873	END DO
874	!
875	END DO
876	!
877	END DO
878	!
879	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! total precipitation [kg/m2/s]
880	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! solid precipitation [kg/m2/s]
881	CALL iom_put( 'snowpre', sprecip ) ! Snow precipitation
882	CALL iom_put( 'precip' , tprecip ) ! Total precipitation
883
884	! --- evaporation --- !
885	z1_rLsub = 1._wp / rLsub
886	evap_ice (:,:,:) = rn_efac * qla_ice (:,:,:) * z1_rLsub ! sublimation
887	devap_ice(:,:,:) = rn_efac * dqla_ice(:,:,:) * z1_rLsub ! d(sublimation)/dT
888	zevap (:,:) = rn_efac * ( emp(:,:) + tprecip(:,:) ) ! evaporation over ocean
889
890	! --- evaporation minus precipitation --- !
891	zsnw(:,:) = 0._wp
892	CALL ice_var_snwblow( (1.-at_i_b(:,:)), zsnw ) ! snow distribution over ice after wind blowing
893	emp_oce(:,:) = ( 1._wp - at_i_b(:,:) ) * zevap(:,:) - ( tprecip(:,:) - sprecip(:,:) ) - sprecip(:,:) * (1._wp - zsnw )
894	emp_ice(:,:) = SUM( a_i_b(:,:,:) * evap_ice(:,:,:), dim=3 ) - sprecip(:,:) * zsnw
895	emp_tot(:,:) = emp_oce(:,:) + emp_ice(:,:)
896
897	! --- heat flux associated with emp --- !
898	qemp_oce(:,:) = - ( 1._wp - at_i_b(:,:) ) * zevap(:,:) * sst_m(:,:) * rcp & ! evap at sst
899	& + ( tprecip(:,:) - sprecip(:,:) ) * ( sf(jp_tair)%fnow(:,:,1) - rt0 ) * rcp & ! liquid precip at Tair
900	& + sprecip(:,:) * ( 1._wp - zsnw ) * & ! solid precip at min(Tair,Tsnow)
901	& ( ( MIN( sf(jp_tair)%fnow(:,:,1), rt0 ) - rt0 ) * rcpi * tmask(:,:,1) - rLfus )
902	qemp_ice(:,:) = sprecip(:,:) * zsnw * & ! solid precip (only)
903	& ( ( MIN( sf(jp_tair)%fnow(:,:,1), rt0 ) - rt0 ) * rcpi * tmask(:,:,1) - rLfus )
904
905	! --- total solar and non solar fluxes --- !
906	qns_tot(:,:) = ( 1._wp - at_i_b(:,:) ) * qns_oce(:,:) + SUM( a_i_b(:,:,:) * qns_ice(:,:,:), dim=3 ) &
907	& + qemp_ice(:,:) + qemp_oce(:,:)
908	qsr_tot(:,:) = ( 1._wp - at_i_b(:,:) ) * qsr_oce(:,:) + SUM( a_i_b(:,:,:) * qsr_ice(:,:,:), dim=3 )
909
910	! --- heat content of precip over ice in J/m3 (to be used in 1D-thermo) --- !
911	qprec_ice(:,:) = rhos * ( ( MIN( sf(jp_tair)%fnow(:,:,1), rt0 ) - rt0 ) * rcpi * tmask(:,:,1) - rLfus )
912
913	! --- heat content of evap over ice in W/m2 (to be used in 1D-thermo) ---
914	DO jl = 1, jpl
915	qevap_ice(:,:,jl) = 0._wp ! should be -evap_ice(:,:,jl)( ( Tice - rt0 ) rcpi * tmask(:,:,1) )
916	! ! But we do not have Tice => consider it at 0degC => evap=0
917	END DO
918
919	! --- shortwave radiation transmitted thru the surface scattering layer (W/m2) --- !
920	IF( nn_qtrice == 0 ) THEN
921	! formulation derived from Grenfell and Maykut (1977), where transmission rate
922	! 1) depends on cloudiness
923	! 2) is 0 when there is any snow
924	! 3) tends to 1 for thin ice
925	ztri(:,:) = 0.18 * ( 1.0 - cloud_fra(:,:) ) + 0.35 * cloud_fra(:,:) ! surface transmission when hi>10cm
926	DO jl = 1, jpl
927	WHERE ( phs(:,:,jl) <= 0._wp .AND. phi(:,:,jl) < 0.1_wp ) ! linear decrease from hi=0 to 10cm
928	qtr_ice_top(:,:,jl) = qsr_ice(:,:,jl) * ( ztri(:,:) + ( 1._wp - ztri(:,:) ) * ( 1._wp - phi(:,:,jl) * 10._wp ) )
929	ELSEWHERE( phs(:,:,jl) <= 0._wp .AND. phi(:,:,jl) >= 0.1_wp ) ! constant (ztri) when hi>10cm
930	qtr_ice_top(:,:,jl) = qsr_ice(:,:,jl) * ztri(:,:)
931	ELSEWHERE ! zero when hs>0
932	qtr_ice_top(:,:,jl) = 0._wp
933	END WHERE
934	ENDDO
935	ELSEIF( nn_qtrice == 1 ) THEN
936	! formulation is derived from the thesis of M. Lebrun (2019).
937	! It represents the best fit using several sets of observations
938	! It comes with snow conductivities adapted to freezing/melting conditions (see icethd_zdf_bl99.F90)
939	qtr_ice_top(:,:,:) = 0.3_wp * qsr_ice(:,:,:)
940	ENDIF
941	!
942
943	IF( iom_use('evap_ao_cea') .OR. iom_use('hflx_evap_cea') ) THEN
944	ztmp(:,:) = zevap(:,:) * ( 1._wp - at_i_b(:,:) )
945	CALL iom_put( 'evap_ao_cea' , ztmp(:,:) * tmask(:,:,1) ) ! ice-free oce evap (cell average)
946	CALL iom_put( 'hflx_evap_cea', ztmp(:,:) * sst_m(:,:) * rcp * tmask(:,:,1) ) ! heat flux from evap (cell average)
947	ENDIF
948	IF( iom_use('hflx_rain_cea') ) THEN
949	ztmp(:,:) = rcp * ( SUM( (ptsu-rt0) * a_i_b, dim=3 ) + sst_m(:,:) * ( 1._wp - at_i_b(:,:) ) )
950	CALL iom_put( 'hflx_rain_cea', ( tprecip(:,:) - sprecip(:,:) ) * ztmp(:,:) ) ! heat flux from rain (cell average)
951	ENDIF
952	IF( iom_use('hflx_snow_cea') .OR. iom_use('hflx_snow_ao_cea') .OR. iom_use('hflx_snow_ai_cea') ) THEN
953	WHERE( SUM( a_i_b, dim=3 ) > 1.e-10 ) ; ztmp(:,:) = rcpi * SUM( (ptsu-rt0) * a_i_b, dim=3 ) / SUM( a_i_b, dim=3 )
954	ELSEWHERE ; ztmp(:,:) = rcp * sst_m(:,:)
955	ENDWHERE
956	ztmp2(:,:) = sprecip(:,:) * ( ztmp(:,:) - rLfus )
957	CALL iom_put('hflx_snow_cea' , ztmp2(:,:) ) ! heat flux from snow (cell average)
958	CALL iom_put('hflx_snow_ao_cea', ztmp2(:,:) * ( 1._wp - zsnw(:,:) ) ) ! heat flux from snow (over ocean)
959	CALL iom_put('hflx_snow_ai_cea', ztmp2(:,:) * zsnw(:,:) ) ! heat flux from snow (over ice)
960	ENDIF
961	!
962	IF(ln_ctl) THEN
963	CALL prt_ctl(tab3d_1=qla_ice , clinfo1=' blk_ice: qla_ice : ', tab3d_2=z_qsb , clinfo2=' z_qsb : ', kdim=jpl)
964	CALL prt_ctl(tab3d_1=z_qlw , clinfo1=' blk_ice: z_qlw : ', tab3d_2=dqla_ice, clinfo2=' dqla_ice : ', kdim=jpl)
965	CALL prt_ctl(tab3d_1=z_dqsb , clinfo1=' blk_ice: z_dqsb : ', tab3d_2=z_dqlw , clinfo2=' z_dqlw : ', kdim=jpl)
966	CALL prt_ctl(tab3d_1=dqns_ice, clinfo1=' blk_ice: dqns_ice : ', tab3d_2=qsr_ice , clinfo2=' qsr_ice : ', kdim=jpl)
967	CALL prt_ctl(tab3d_1=ptsu , clinfo1=' blk_ice: ptsu : ', tab3d_2=qns_ice , clinfo2=' qns_ice : ', kdim=jpl)
968	CALL prt_ctl(tab2d_1=tprecip , clinfo1=' blk_ice: tprecip : ', tab2d_2=sprecip , clinfo2=' sprecip : ')
969	ENDIF
970	!
971	END SUBROUTINE blk_ice_flx
972
973
974	SUBROUTINE blk_ice_qcn( ld_virtual_itd, ptsu, ptb, phs, phi )
975	!!---------------------------------------------------------------------
976	!! * ROUTINE blk_ice_qcn *
977	!!
978	!! ** Purpose : Compute surface temperature and snow/ice conduction flux
979	!! to force sea ice / snow thermodynamics
980	!! in the case conduction flux is emulated
981	!!
982	!! ** Method : compute surface energy balance assuming neglecting heat storage
983	!! following the 0-layer Semtner (1976) approach
984	!!
985	!! ** Outputs : - ptsu : sea-ice / snow surface temperature (K)
986	!! - qcn_ice : surface inner conduction flux (W/m2)
987	!!
988	!!---------------------------------------------------------------------
989	LOGICAL , INTENT(in ) :: ld_virtual_itd ! single-category option
990	REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: ptsu ! sea ice / snow surface temperature
991	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: ptb ! sea ice base temperature
992	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: phs ! snow thickness
993	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: phi ! sea ice thickness
994	!
995	INTEGER , PARAMETER :: nit = 10 ! number of iterations
996	REAL(wp), PARAMETER :: zepsilon = 0.1_wp ! characteristic thickness for enhanced conduction
997	!
998	INTEGER :: ji, jj, jl ! dummy loop indices
999	INTEGER :: iter ! local integer
1000	REAL(wp) :: zfac, zfac2, zfac3 ! local scalars
1001	REAL(wp) :: zkeff_h, ztsu, ztsu0 !
1002	REAL(wp) :: zqc, zqnet !
1003	REAL(wp) :: zhe, zqa0 !
1004	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zgfac ! enhanced conduction factor
1005	!!---------------------------------------------------------------------
1006
1007	! -------------------------------------!
1008	! I Enhanced conduction factor !
1009	! -------------------------------------!
1010	! Emulates the enhancement of conduction by unresolved thin ice (ld_virtual_itd = T)
1011	! Fichefet and Morales Maqueda, JGR 1997
1012	!
1013	zgfac(:,:,:) = 1._wp
1014
1015	IF( ld_virtual_itd ) THEN
1016	!
1017	zfac = 1._wp / ( rn_cnd_s + rcnd_i )
1018	zfac2 = EXP(1._wp) * 0.5_wp * zepsilon
1019	zfac3 = 2._wp / zepsilon
1020	!
1021	DO jl = 1, jpl
1022	DO jj = 1 , jpj
1023	DO ji = 1, jpi
1024	zhe = ( rn_cnd_s * phi(ji,jj,jl) + rcnd_i * phs(ji,jj,jl) ) * zfac ! Effective thickness
1025	IF( zhe >= zfac2 ) zgfac(ji,jj,jl) = MIN( 2._wp, 0.5_wp * ( 1._wp + LOG( zhe * zfac3 ) ) ) ! Enhanced conduction factor
1026	END DO
1027	END DO
1028	END DO
1029	!
1030	ENDIF
1031
1032	! -------------------------------------------------------------!
1033	! II Surface temperature and conduction flux !
1034	! -------------------------------------------------------------!
1035	!
1036	zfac = rcnd_i * rn_cnd_s
1037	!
1038	DO jl = 1, jpl
1039	DO jj = 1 , jpj
1040	DO ji = 1, jpi
1041	!
1042	zkeff_h = zfac * zgfac(ji,jj,jl) / & ! Effective conductivity of the snow-ice system divided by thickness
1043	& ( rcnd_i * phs(ji,jj,jl) + rn_cnd_s * MAX( 0.01, phi(ji,jj,jl) ) )
1044	ztsu = ptsu(ji,jj,jl) ! Store current iteration temperature
1045	ztsu0 = ptsu(ji,jj,jl) ! Store initial surface temperature
1046	zqa0 = qsr_ice(ji,jj,jl) - qtr_ice_top(ji,jj,jl) + qns_ice(ji,jj,jl) ! Net initial atmospheric heat flux
1047	!
1048	DO iter = 1, nit ! --- Iterative loop
1049	zqc = zkeff_h * ( ztsu - ptb(ji,jj) ) ! Conduction heat flux through snow-ice system (>0 downwards)
1050	zqnet = zqa0 + dqns_ice(ji,jj,jl) * ( ztsu - ptsu(ji,jj,jl) ) - zqc ! Surface energy budget
1051	ztsu = ztsu - zqnet / ( dqns_ice(ji,jj,jl) - zkeff_h ) ! Temperature update
1052	END DO
1053	!
1054	ptsu (ji,jj,jl) = MIN( rt0, ztsu )
1055	qcn_ice(ji,jj,jl) = zkeff_h * ( ptsu(ji,jj,jl) - ptb(ji,jj) )
1056	qns_ice(ji,jj,jl) = qns_ice(ji,jj,jl) + dqns_ice(ji,jj,jl) * ( ptsu(ji,jj,jl) - ztsu0 )
1057	qml_ice(ji,jj,jl) = ( qsr_ice(ji,jj,jl) - qtr_ice_top(ji,jj,jl) + qns_ice(ji,jj,jl) - qcn_ice(ji,jj,jl) ) &
1058	& * MAX( 0._wp , SIGN( 1._wp, ptsu(ji,jj,jl) - rt0 ) )
1059
1060	! --- Diagnose the heat loss due to changing non-solar flux (as in icethd_zdf_bl99) --- !
1061	hfx_err_dif(ji,jj) = hfx_err_dif(ji,jj) - ( dqns_ice(ji,jj,jl) * ( ptsu(ji,jj,jl) - ztsu0 ) ) * a_i_b(ji,jj,jl)
1062
1063	END DO
1064	END DO
1065	!
1066	END DO
1067	!
1068	END SUBROUTINE blk_ice_qcn
1069
1070
1071	SUBROUTINE Cdn10_Lupkes2012( Cd )
1072	!!----------------------------------------------------------------------
1073	!! * ROUTINE Cdn10_Lupkes2012 *
1074	!!
1075	!! ** Purpose : Recompute the neutral air-ice drag referenced at 10m
1076	!! to make it dependent on edges at leads, melt ponds and flows.
1077	!! After some approximations, this can be resumed to a dependency
1078	!! on ice concentration.
1079	!!
1080	!! ** Method : The parameterization is taken from Lupkes et al. (2012) eq.(50)
1081	!! with the highest level of approximation: level4, eq.(59)
1082	!! The generic drag over a cell partly covered by ice can be re-written as follows:
1083	!!
1084	!! Cd = Cdw * (1-A) + Cdi * A + Ce * (1-A)*(nu+1/(10beta)) * A**mu
1085	!!
1086	!! Ce = 2.23e-3 , as suggested by Lupkes (eq. 59)
1087	!! nu = mu = beta = 1 , as suggested by Lupkes (eq. 59)
1088	!! A is the concentration of ice minus melt ponds (if any)
1089	!!
1090	!! This new drag has a parabolic shape (as a function of A) starting at
1091	!! Cdw(say 1.5e-3) for A=0, reaching 1.97e-3 for A~0.5
1092	!! and going down to Cdi(say 1.4e-3) for A=1
1093	!!
1094	!! It is theoretically applicable to all ice conditions (not only MIZ)
1095	!! => see Lupkes et al (2013)
1096	!!
1097	!! ** References : Lupkes et al. JGR 2012 (theory)
1098	!! Lupkes et al. GRL 2013 (application to GCM)
1099	!!
1100	!!----------------------------------------------------------------------
1101	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Cd
1102	REAL(wp), PARAMETER :: zCe = 2.23e-03_wp
1103	REAL(wp), PARAMETER :: znu = 1._wp
1104	REAL(wp), PARAMETER :: zmu = 1._wp
1105	REAL(wp), PARAMETER :: zbeta = 1._wp
1106	REAL(wp) :: zcoef
1107	!!----------------------------------------------------------------------
1108	zcoef = znu + 1._wp / ( 10._wp * zbeta )
1109
1110	! generic drag over a cell partly covered by ice
1111	!!Cd(:,:) = Cd_oce(:,:) * ( 1._wp - at_i_b(:,:) ) + & ! pure ocean drag
1112	!! & Cd_ice * at_i_b(:,:) + & ! pure ice drag
1113	!! & zCe * ( 1._wp - at_i_b(:,:) )*zcoef at_i_b(:,:)**zmu ! change due to sea-ice morphology
1114
1115	! ice-atm drag
1116	Cd(:,:) = Cd_ice + & ! pure ice drag
1117	& zCe * ( 1._wp - at_i_b(:,:) )*zcoef at_i_b(:,:)**(zmu-1._wp) ! change due to sea-ice morphology
1118
1119	END SUBROUTINE Cdn10_Lupkes2012
1120
1121
1122	SUBROUTINE Cdn10_Lupkes2015( Cd, Ch )
1123	!!----------------------------------------------------------------------
1124	!! * ROUTINE Cdn10_Lupkes2015 *
1125	!!
1126	!! ** pUrpose : Alternative turbulent transfert coefficients formulation
1127	!! between sea-ice and atmosphere with distinct momentum
1128	!! and heat coefficients depending on sea-ice concentration
1129	!! and atmospheric stability (no meltponds effect for now).
1130	!!
1131	!! ** Method : The parameterization is adapted from Lupkes et al. (2015)
1132	!! and ECHAM6 atmospheric model. Compared to Lupkes2012 scheme,
1133	!! it considers specific skin and form drags (Andreas et al. 2010)
1134	!! to compute neutral transfert coefficients for both heat and
1135	!! momemtum fluxes. Atmospheric stability effect on transfert
1136	!! coefficient is also taken into account following Louis (1979).
1137	!!
1138	!! ** References : Lupkes et al. JGR 2015 (theory)
1139	!! Lupkes et al. ECHAM6 documentation 2015 (implementation)
1140	!!
1141	!!----------------------------------------------------------------------
1142	!
1143	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Cd
1144	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Ch
1145	REAL(wp), DIMENSION(jpi,jpj) :: ztm_su, zst, zqo_sat, zqi_sat
1146	!
1147	! ECHAM6 constants
1148	REAL(wp), PARAMETER :: z0_skin_ice = 0.69e-3_wp ! Eq. 43 [m]
1149	REAL(wp), PARAMETER :: z0_form_ice = 0.57e-3_wp ! Eq. 42 [m]
1150	REAL(wp), PARAMETER :: z0_ice = 1.00e-3_wp ! Eq. 15 [m]
1151	REAL(wp), PARAMETER :: zce10 = 2.80e-3_wp ! Eq. 41
1152	REAL(wp), PARAMETER :: zbeta = 1.1_wp ! Eq. 41
1153	REAL(wp), PARAMETER :: zc = 5._wp ! Eq. 13
1154	REAL(wp), PARAMETER :: zc2 = zc * zc
1155	REAL(wp), PARAMETER :: zam = 2. * zc ! Eq. 14
1156	REAL(wp), PARAMETER :: zah = 3. * zc ! Eq. 30
1157	REAL(wp), PARAMETER :: z1_alpha = 1._wp / 0.2_wp ! Eq. 51
1158	REAL(wp), PARAMETER :: z1_alphaf = z1_alpha ! Eq. 56
1159	REAL(wp), PARAMETER :: zbetah = 1.e-3_wp ! Eq. 26
1160	REAL(wp), PARAMETER :: zgamma = 1.25_wp ! Eq. 26
1161	REAL(wp), PARAMETER :: z1_gamma = 1._wp / zgamma
1162	REAL(wp), PARAMETER :: r1_3 = 1._wp / 3._wp
1163	!
1164	INTEGER :: ji, jj ! dummy loop indices
1165	REAL(wp) :: zthetav_os, zthetav_is, zthetav_zu
1166	REAL(wp) :: zrib_o, zrib_i
1167	REAL(wp) :: zCdn_skin_ice, zCdn_form_ice, zCdn_ice
1168	REAL(wp) :: zChn_skin_ice, zChn_form_ice
1169	REAL(wp) :: z0w, z0i, zfmi, zfmw, zfhi, zfhw
1170	REAL(wp) :: zCdn_form_tmp
1171	!!----------------------------------------------------------------------
1172
1173	! mean temperature
1174	WHERE( at_i_b(:,:) > 1.e-20 ) ; ztm_su(:,:) = SUM( t_su(:,:,:) * a_i_b(:,:,:) , dim=3 ) / at_i_b(:,:)
1175	ELSEWHERE ; ztm_su(:,:) = rt0
1176	ENDWHERE
1177
1178	! Momentum Neutral Transfert Coefficients (should be a constant)
1179	zCdn_form_tmp = zce10 * ( LOG( 10._wp / z0_form_ice + 1._wp ) / LOG( rn_zu / z0_form_ice + 1._wp ) )**2 ! Eq. 40
1180	zCdn_skin_ice = ( vkarmn / LOG( rn_zu / z0_skin_ice + 1._wp ) )**2 ! Eq. 7
1181	zCdn_ice = zCdn_skin_ice ! Eq. 7 (cf Lupkes email for details)
1182	!zCdn_ice = 1.89e-3 ! old ECHAM5 value (cf Eq. 32)
1183
1184	! Heat Neutral Transfert Coefficients
1185	zChn_skin_ice = vkarmn*2 / ( LOG( rn_zu / z0_ice + 1._wp ) LOG( rn_zu * z1_alpha / z0_skin_ice + 1._wp ) ) ! Eq. 50 + Eq. 52 (cf Lupkes email for details)
1186
1187	! Atmospheric and Surface Variables
1188	zst(:,:) = sst_m(:,:) + rt0 ! convert SST from Celcius to Kelvin
1189	zqo_sat(:,:) = 0.98_wp * q_sat( zst(:,:) , sf(jp_slp)%fnow(:,:,1) ) ! saturation humidity over ocean [kg/kg]
1190	zqi_sat(:,:) = 0.98_wp * q_sat( ztm_su(:,:), sf(jp_slp)%fnow(:,:,1) ) ! saturation humidity over ice [kg/kg]
1191	!
1192	DO jj = 2, jpjm1 ! reduced loop is necessary for reproducibility
1193	DO ji = fs_2, fs_jpim1
1194	! Virtual potential temperature [K]
1195	zthetav_os = zst(ji,jj) * ( 1._wp + rctv0 * zqo_sat(ji,jj) ) ! over ocean
1196	zthetav_is = ztm_su(ji,jj) * ( 1._wp + rctv0 * zqi_sat(ji,jj) ) ! ocean ice
1197	zthetav_zu = t_zu (ji,jj) * ( 1._wp + rctv0 * q_zu(ji,jj) ) ! at zu
1198
1199	! Bulk Richardson Number (could use Ri_bulk function from aerobulk instead)
1200	zrib_o = grav / zthetav_os * ( zthetav_zu - zthetav_os ) * rn_zu / MAX( 0.5, wndm(ji,jj) )**2 ! over ocean
1201	zrib_i = grav / zthetav_is * ( zthetav_zu - zthetav_is ) * rn_zu / MAX( 0.5, wndm_ice(ji,jj) )**2 ! over ice
1202
1203	! Momentum and Heat Neutral Transfert Coefficients
1204	zCdn_form_ice = zCdn_form_tmp * at_i_b(ji,jj) * ( 1._wp - at_i_b(ji,jj) )**zbeta ! Eq. 40
1205	zChn_form_ice = zCdn_form_ice / ( 1._wp + ( LOG( z1_alphaf ) / vkarmn ) * SQRT( zCdn_form_ice ) ) ! Eq. 53
1206
1207	! Momentum and Heat Stability functions (possibility to use psi_m_ecmwf instead)
1208	z0w = rn_zu * EXP( -1._wp * vkarmn / SQRT( Cdn_oce(ji,jj) ) ) ! over water
1209	z0i = z0_skin_ice ! over ice (cf Lupkes email for details)
1210	IF( zrib_o <= 0._wp ) THEN
1211	zfmw = 1._wp - zam * zrib_o / ( 1._wp + 3._wp * zc2 * Cdn_oce(ji,jj) * SQRT( -zrib_o * ( rn_zu / z0w + 1._wp ) ) ) ! Eq. 10
1212	zfhw = ( 1._wp + ( zbetah * ( zthetav_os - zthetav_zu )*r1_3 / ( Chn_oce(ji,jj) MAX(0.01, wndm(ji,jj)) ) & ! Eq. 26
1213	& )zgamma )z1_gamma
1214	ELSE
1215	zfmw = 1._wp / ( 1._wp + zam * zrib_o / SQRT( 1._wp + zrib_o ) ) ! Eq. 12
1216	zfhw = 1._wp / ( 1._wp + zah * zrib_o / SQRT( 1._wp + zrib_o ) ) ! Eq. 28
1217	ENDIF
1218
1219	IF( zrib_i <= 0._wp ) THEN
1220	zfmi = 1._wp - zam * zrib_i / (1._wp + 3._wp * zc2 * zCdn_ice * SQRT( -zrib_i * ( rn_zu / z0i + 1._wp))) ! Eq. 9
1221	zfhi = 1._wp - zah * zrib_i / (1._wp + 3._wp * zc2 * zCdn_ice * SQRT( -zrib_i * ( rn_zu / z0i + 1._wp))) ! Eq. 25
1222	ELSE
1223	zfmi = 1._wp / ( 1._wp + zam * zrib_i / SQRT( 1._wp + zrib_i ) ) ! Eq. 11
1224	zfhi = 1._wp / ( 1._wp + zah * zrib_i / SQRT( 1._wp + zrib_i ) ) ! Eq. 27
1225	ENDIF
1226
1227	! Momentum Transfert Coefficients (Eq. 38)
1228	Cd(ji,jj) = zCdn_skin_ice * zfmi + &
1229	& zCdn_form_ice * ( zfmi * at_i_b(ji,jj) + zfmw * ( 1._wp - at_i_b(ji,jj) ) ) / MAX( 1.e-06, at_i_b(ji,jj) )
1230
1231	! Heat Transfert Coefficients (Eq. 49)
1232	Ch(ji,jj) = zChn_skin_ice * zfhi + &
1233	& zChn_form_ice * ( zfhi * at_i_b(ji,jj) + zfhw * ( 1._wp - at_i_b(ji,jj) ) ) / MAX( 1.e-06, at_i_b(ji,jj) )
1234	!
1235	END DO
1236	END DO
1237	CALL lbc_lnk_multi( 'sbcblk', Cd, 'T', 1., Ch, 'T', 1. )
1238	!
1239	END SUBROUTINE Cdn10_Lupkes2015
1240
1241	#endif
1242
1243	!!======================================================================
1244	END MODULE sbcblk

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