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sbcblk.F90

Last change on this file was 15813, checked in by clem, 13 months ago
SI3: change heat budget to avoid supercooling. The rest: cosmetics
Property svn:keywords set to `Id`
File size: 75.4 KB

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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 trc_oce ! share SMS/Ocean variables
43	USE cyclone ! Cyclone 10m wind form trac of cyclone centres
44	USE sbcdcy ! surface boundary condition: diurnal cycle
45	USE sbcwave , ONLY : cdn_wave ! wave module
46	USE sbc_ice ! Surface boundary condition: ice fields
47	USE lib_fortran ! to use key_nosignedzero
48	#if defined key_si3
49	USE ice , ONLY : u_ice, v_ice, jpl, a_i_b, at_i_b, t_su, rn_cnd_s, hfx_err_dif, nn_qtrice
50	USE icevar ! for CALL ice_var_snwblow
51	#endif
52	USE sbcblk_algo_ncar ! => turb_ncar : NCAR - CORE (Large & Yeager, 2009)
53	USE sbcblk_algo_coare ! => turb_coare : COAREv3.0 (Fairall et al. 2003)
54	USE sbcblk_algo_coare3p5 ! => turb_coare3p5 : COAREv3.5 (Edson et al. 2013)
55	USE sbcblk_algo_ecmwf ! => turb_ecmwf : ECMWF (IFS cycle 31)
56	!
57	USE iom ! I/O manager library
58	USE in_out_manager ! I/O manager
59	USE lib_mpp ! distribued memory computing library
60	USE lbclnk ! ocean lateral boundary conditions (or mpp link)
61	USE prtctl ! Print control
62
63	IMPLICIT NONE
64	PRIVATE
65
66	PUBLIC sbc_blk_init ! called in sbcmod
67	PUBLIC sbc_blk ! called in sbcmod
68	#if defined key_si3
69	PUBLIC blk_ice_tau ! routine called in icesbc
70	PUBLIC blk_ice_flx ! routine called in icesbc
71	PUBLIC blk_ice_qcn ! routine called in icesbc
72	#endif
73
74	!!Lolo: should ultimately be moved in the module with all physical constants ?
75	!!gm : In principle, yes.
76	REAL(wp), PARAMETER :: Cp_dry = 1005.0 !: Specic heat of dry air, constant pressure [J/K/kg]
77	REAL(wp), PARAMETER :: Cp_vap = 1860.0 !: Specic heat of water vapor, constant pressure [J/K/kg]
78	REAL(wp), PARAMETER :: R_dry = 287.05_wp !: Specific gas constant for dry air [J/K/kg]
79	REAL(wp), PARAMETER :: R_vap = 461.495_wp !: Specific gas constant for water vapor [J/K/kg]
80	REAL(wp), PARAMETER :: reps0 = R_dry/R_vap !: ratio of gas constant for dry air and water vapor => ~ 0.622
81	REAL(wp), PARAMETER :: rctv0 = R_vap/R_dry - 1._wp !: for virtual temperature (== (1-eps)/eps) => ~ 0.608
82
83	INTEGER , PARAMETER :: jpfld =11 ! maximum number of files to read
84	INTEGER , PARAMETER :: jp_wndi = 1 ! index of 10m wind velocity (i-component) (m/s) at T-point
85	INTEGER , PARAMETER :: jp_wndj = 2 ! index of 10m wind velocity (j-component) (m/s) at T-point
86	INTEGER , PARAMETER :: jp_tair = 3 ! index of 10m air temperature (Kelvin)
87	INTEGER , PARAMETER :: jp_humi = 4 ! index of specific humidity ( % )
88	INTEGER , PARAMETER :: jp_qsr = 5 ! index of solar heat (W/m2)
89	INTEGER , PARAMETER :: jp_qlw = 6 ! index of Long wave (W/m2)
90	INTEGER , PARAMETER :: jp_prec = 7 ! index of total precipitation (rain+snow) (Kg/m2/s)
91	INTEGER , PARAMETER :: jp_snow = 8 ! index of snow (solid prcipitation) (kg/m2/s)
92	INTEGER , PARAMETER :: jp_slp = 9 ! index of sea level pressure (Pa)
93	INTEGER , PARAMETER :: jp_cc =10 ! index of cloud cover (-) range:0-1
94	INTEGER , PARAMETER :: jp_tdif =11 ! index of tau diff associated to HF tau (N/m2) at T-point
95
96	TYPE(FLD), ALLOCATABLE, DIMENSION(:) :: sf ! structure of input fields (file informations, fields read)
97
98	! !!! Bulk parameters
99	REAL(wp), PARAMETER :: cpa = 1000.5 ! specific heat of air (only used for ice fluxes now...)
100	REAL(wp), PARAMETER :: Ls = 2.839e6 ! latent heat of sublimation
101	REAL(wp), PARAMETER :: Stef = 5.67e-8 ! Stefan Boltzmann constant
102	REAL(wp), PARAMETER :: Cd_ice = 1.4e-3 ! transfer coefficient over ice
103	REAL(wp), PARAMETER :: albo = 0.066 ! ocean albedo assumed to be constant
104	!
105	! !!* Namelist namsbc_blk : bulk parameters
106	LOGICAL :: ln_NCAR ! "NCAR" algorithm (Large and Yeager 2008)
107	LOGICAL :: ln_COARE_3p0 ! "COARE 3.0" algorithm (Fairall et al. 2003)
108	LOGICAL :: ln_COARE_3p5 ! "COARE 3.5" algorithm (Edson et al. 2013)
109	LOGICAL :: ln_ECMWF ! "ECMWF" algorithm (IFS cycle 31)
110	!
111	LOGICAL :: ln_taudif ! logical flag to use the "mean of stress module - module of mean stress" data
112	REAL(wp) :: rn_pfac ! multiplication factor for precipitation
113	REAL(wp) :: rn_efac ! multiplication factor for evaporation
114	REAL(wp) :: rn_vfac ! multiplication factor for ice/ocean velocity in the calculation of wind stress
115	REAL(wp) :: rn_zqt ! z(q,t) : height of humidity and temperature measurements
116	REAL(wp) :: rn_zu ! z(u) : height of wind measurements
117	!!gm ref namelist initialize it so remove the setting to false below
118	LOGICAL :: ln_Cd_L12 = .FALSE. ! Modify the drag ice-atm depending on ice concentration (from Lupkes et al. JGR2012)
119	LOGICAL :: ln_Cd_L15 = .FALSE. ! Modify the drag ice-atm depending on ice concentration (from Lupkes et al. JGR2015)
120	!
121	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: Cd_atm ! transfer coefficient for momentum (tau)
122	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: Ch_atm ! transfer coefficient for sensible heat (Q_sens)
123	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: Ce_atm ! tansfert coefficient for evaporation (Q_lat)
124	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: t_zu ! air temperature at wind speed height (needed by Lupkes 2015 bulk scheme)
125	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: q_zu ! air spec. hum. at wind speed height (needed by Lupkes 2015 bulk scheme)
126	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: cdn_oce, chn_oce, cen_oce ! needed by Lupkes 2015 bulk scheme
127
128	INTEGER :: nblk ! choice of the bulk algorithm
129	! ! associated indices:
130	INTEGER, PARAMETER :: np_NCAR = 1 ! "NCAR" algorithm (Large and Yeager 2008)
131	INTEGER, PARAMETER :: np_COARE_3p0 = 2 ! "COARE 3.0" algorithm (Fairall et al. 2003)
132	INTEGER, PARAMETER :: np_COARE_3p5 = 3 ! "COARE 3.5" algorithm (Edson et al. 2013)
133	INTEGER, PARAMETER :: np_ECMWF = 4 ! "ECMWF" algorithm (IFS cycle 31)
134
135	!! * Substitutions
136	# include "vectopt_loop_substitute.h90"
137	!!----------------------------------------------------------------------
138	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
139	!! $Id$
140	!! Software governed by the CeCILL license (see ./LICENSE)
141	!!----------------------------------------------------------------------
142	CONTAINS
143
144	INTEGER FUNCTION sbc_blk_alloc()
145	!!-------------------------------------------------------------------
146	!! * ROUTINE sbc_blk_alloc *
147	!!-------------------------------------------------------------------
148	ALLOCATE( Cd_atm (jpi,jpj), Ch_atm (jpi,jpj), Ce_atm (jpi,jpj), t_zu(jpi,jpj), q_zu(jpi,jpj), &
149	& cdn_oce(jpi,jpj), chn_oce(jpi,jpj), cen_oce(jpi,jpj), STAT=sbc_blk_alloc )
150	!
151	CALL mpp_sum ( 'sbcblk', sbc_blk_alloc )
152	IF( sbc_blk_alloc /= 0 ) CALL ctl_stop( 'STOP', 'sbc_blk_alloc: failed to allocate arrays' )
153	END FUNCTION sbc_blk_alloc
154
155
156	SUBROUTINE sbc_blk_init
157	!!---------------------------------------------------------------------
158	!! * ROUTINE sbc_blk_init *
159	!!
160	!! ** Purpose : choose and initialize a bulk formulae formulation
161	!!
162	!! ** Method :
163	!!
164	!!----------------------------------------------------------------------
165	INTEGER :: jfpr, jfld ! dummy loop indice and argument
166	INTEGER :: ios, ierror, ioptio ! Local integer
167	!!
168	CHARACTER(len=100) :: cn_dir ! Root directory for location of atmospheric forcing files
169	TYPE(FLD_N), DIMENSION(jpfld) :: slf_i ! array of namelist informations on the fields to read
170	TYPE(FLD_N) :: sn_wndi, sn_wndj, sn_humi, sn_qsr ! informations about the fields to be read
171	TYPE(FLD_N) :: sn_qlw , sn_tair, sn_prec, sn_snow ! " "
172	TYPE(FLD_N) :: sn_slp , sn_tdif, sn_cc ! " "
173	NAMELIST/namsbc_blk/ sn_wndi, sn_wndj, sn_humi, sn_qsr, sn_qlw , & ! input fields
174	& sn_tair, sn_prec, sn_snow, sn_slp, sn_tdif, sn_cc, &
175	& ln_NCAR, ln_COARE_3p0, ln_COARE_3p5, ln_ECMWF, & ! bulk algorithm
176	& cn_dir , ln_taudif, rn_zqt, rn_zu, &
177	& rn_pfac, rn_efac, rn_vfac, ln_Cd_L12, ln_Cd_L15
178	!!---------------------------------------------------------------------
179	!
180	! ! allocate sbc_blk_core array
181	IF( sbc_blk_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'sbc_blk : unable to allocate standard arrays' )
182	!
183	! !** read bulk namelist
184	REWIND( numnam_ref ) !* Namelist namsbc_blk in reference namelist : bulk parameters
185	READ ( numnam_ref, namsbc_blk, IOSTAT = ios, ERR = 901)
186	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namsbc_blk in reference namelist' )
187	!
188	REWIND( numnam_cfg ) !* Namelist namsbc_blk in configuration namelist : bulk parameters
189	READ ( numnam_cfg, namsbc_blk, IOSTAT = ios, ERR = 902 )
190	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namsbc_blk in configuration namelist' )
191	!
192	IF(lwm) WRITE( numond, namsbc_blk )
193	!
194	! !** initialization of the chosen bulk formulae (+ check)
195	! !* select the bulk chosen in the namelist and check the choice
196	ioptio = 0
197	IF( ln_NCAR ) THEN ; nblk = np_NCAR ; ioptio = ioptio + 1 ; ENDIF
198	IF( ln_COARE_3p0 ) THEN ; nblk = np_COARE_3p0 ; ioptio = ioptio + 1 ; ENDIF
199	IF( ln_COARE_3p5 ) THEN ; nblk = np_COARE_3p5 ; ioptio = ioptio + 1 ; ENDIF
200	IF( ln_ECMWF ) THEN ; nblk = np_ECMWF ; ioptio = ioptio + 1 ; ENDIF
201	!
202	IF( ioptio /= 1 ) CALL ctl_stop( 'sbc_blk_init: Choose one and only one bulk algorithm' )
203	!
204	IF( ln_dm2dc ) THEN !* check: diurnal cycle on Qsr
205	IF( sn_qsr%freqh /= 24. ) CALL ctl_stop( 'sbc_blk_init: ln_dm2dc=T only with daily short-wave input' )
206	IF( sn_qsr%ln_tint ) THEN
207	CALL ctl_warn( 'sbc_blk_init: ln_dm2dc=T daily qsr time interpolation done by sbcdcy module', &
208	& ' ==> We force time interpolation = .false. for qsr' )
209	sn_qsr%ln_tint = .false.
210	ENDIF
211	ENDIF
212	! !* set the bulk structure
213	! !- store namelist information in an array
214	slf_i(jp_wndi) = sn_wndi ; slf_i(jp_wndj) = sn_wndj
215	slf_i(jp_qsr ) = sn_qsr ; slf_i(jp_qlw ) = sn_qlw
216	slf_i(jp_tair) = sn_tair ; slf_i(jp_humi) = sn_humi
217	slf_i(jp_prec) = sn_prec ; slf_i(jp_snow) = sn_snow
218	slf_i(jp_slp) = sn_slp ; slf_i(jp_cc) = sn_cc
219	slf_i(jp_tdif) = sn_tdif
220	!
221	lhftau = ln_taudif !- add an extra field if HF stress is used
222	jfld = jpfld - COUNT( (/.NOT.lhftau/) )
223	!
224	! !- allocate the bulk structure
225	ALLOCATE( sf(jfld), STAT=ierror )
226	IF( ierror > 0 ) CALL ctl_stop( 'STOP', 'sbc_blk_init: unable to allocate sf structure' )
227
228	! !- fill the bulk structure with namelist informations
229	CALL fld_fill( sf, slf_i, cn_dir, 'sbc_blk_init', 'surface boundary condition -- bulk formulae', 'namsbc_blk' )
230	!
231	DO jfpr = 1, jfld
232	!
233	IF( TRIM(sf(jfpr)%clrootname) == 'NOT USED' ) THEN !-- not used field --! (only now allocated and set to zero)
234	ALLOCATE( sf(jfpr)%fnow(jpi,jpj,1) )
235	sf(jfpr)%fnow(:,:,1) = 0._wp
236	ELSE !-- used field --!
237	ALLOCATE( sf(jfpr)%fnow(jpi,jpj,1) )
238	IF( slf_i(jfpr)%ln_tint ) ALLOCATE( sf(jfpr)%fdta(jpi,jpj,1,2) )
239	IF( slf_i(jfpr)%freqh > 0. .AND. MOD( NINT(3600. * slf_i(jfpr)%freqh), nn_fsbc * NINT(rdt) ) /= 0 ) &
240	& CALL ctl_warn( 'sbc_blk_init: sbcmod timestep rdt*nn_fsbc is NOT a submultiple of atmospheric forcing frequency.', &
241	& ' This is not ideal. You should consider changing either rdt or nn_fsbc value...' )
242	ENDIF
243	ENDDO
244	! fill cloud cover array with constant value if "not used"
245	IF( TRIM(sf(jp_cc)%clrootname) == 'NOT USED' ) sf(jp_cc)%fnow(:,:,1) = pp_cldf
246
247	IF ( ln_wave ) THEN
248	!Activated wave module but neither drag nor stokes drift activated
249	IF ( .NOT.(ln_cdgw .OR. ln_sdw .OR. ln_tauwoc .OR. ln_stcor ) ) THEN
250	CALL ctl_stop( 'STOP', 'Ask for wave coupling but ln_cdgw=F, ln_sdw=F, ln_tauwoc=F, ln_stcor=F' )
251	!drag coefficient read from wave model definable only with mfs bulk formulae and core
252	ELSEIF (ln_cdgw .AND. .NOT. ln_NCAR ) THEN
253	CALL ctl_stop( 'drag coefficient read from wave model definable only with NCAR and CORE bulk formulae')
254	ELSEIF (ln_stcor .AND. .NOT. ln_sdw) THEN
255	CALL ctl_stop( 'Stokes-Coriolis term calculated only if activated Stokes Drift ln_sdw=T')
256	ENDIF
257	ELSE
258	IF ( ln_cdgw .OR. ln_sdw .OR. ln_tauwoc .OR. ln_stcor ) &
259	& CALL ctl_stop( 'Not Activated Wave Module (ln_wave=F) but asked coupling ', &
260	& 'with drag coefficient (ln_cdgw =T) ' , &
261	& 'or Stokes Drift (ln_sdw=T) ' , &
262	& 'or ocean stress modification due to waves (ln_tauwoc=T) ', &
263	& 'or Stokes-Coriolis term (ln_stcori=T)' )
264	ENDIF
265	!
266	!
267	IF(lwp) THEN !** Control print
268	!
269	WRITE(numout,) ! namelist
270	WRITE(numout,*) ' Namelist namsbc_blk (other than data information):'
271	WRITE(numout,*) ' "NCAR" algorithm (Large and Yeager 2008) ln_NCAR = ', ln_NCAR
272	WRITE(numout,*) ' "COARE 3.0" algorithm (Fairall et al. 2003) ln_COARE_3p0 = ', ln_COARE_3p0
273	WRITE(numout,*) ' "COARE 3.5" algorithm (Edson et al. 2013) ln_COARE_3p5 = ', ln_COARE_3p5
274	WRITE(numout,*) ' "ECMWF" algorithm (IFS cycle 31) ln_ECMWF = ', ln_ECMWF
275	WRITE(numout,*) ' add High freq.contribution to the stress module ln_taudif = ', ln_taudif
276	WRITE(numout,*) ' Air temperature and humidity reference height (m) rn_zqt = ', rn_zqt
277	WRITE(numout,*) ' Wind vector reference height (m) rn_zu = ', rn_zu
278	WRITE(numout,*) ' factor applied on precipitation (total & snow) rn_pfac = ', rn_pfac
279	WRITE(numout,*) ' factor applied on evaporation rn_efac = ', rn_efac
280	WRITE(numout,*) ' factor applied on ocean/ice velocity rn_vfac = ', rn_vfac
281	WRITE(numout,*) ' (form absolute (=0) to relative winds(=1))'
282	WRITE(numout,*) ' use ice-atm drag from Lupkes2012 ln_Cd_L12 = ', ln_Cd_L12
283	WRITE(numout,*) ' use ice-atm drag from Lupkes2015 ln_Cd_L15 = ', ln_Cd_L15
284	!
285	WRITE(numout,*)
286	SELECT CASE( nblk ) !* Print the choice of bulk algorithm
287	CASE( np_NCAR ) ; WRITE(numout,*) ' ==>>> "NCAR" algorithm (Large and Yeager 2008)'
288	CASE( np_COARE_3p0 ) ; WRITE(numout,*) ' ==>>> "COARE 3.0" algorithm (Fairall et al. 2003)'
289	CASE( np_COARE_3p5 ) ; WRITE(numout,*) ' ==>>> "COARE 3.5" algorithm (Edson et al. 2013)'
290	CASE( np_ECMWF ) ; WRITE(numout,*) ' ==>>> "ECMWF" algorithm (IFS cycle 31)'
291	END SELECT
292	!
293	ENDIF
294	!
295	END SUBROUTINE sbc_blk_init
296
297
298	SUBROUTINE sbc_blk( kt )
299	!!---------------------------------------------------------------------
300	!! * ROUTINE sbc_blk *
301	!!
302	!! ** Purpose : provide at each time step the surface ocean fluxes
303	!! (momentum, heat, freshwater and runoff)
304	!!
305	!! ** Method : (1) READ each fluxes in NetCDF files:
306	!! the 10m wind velocity (i-component) (m/s) at T-point
307	!! the 10m wind velocity (j-component) (m/s) at T-point
308	!! the 10m or 2m specific humidity ( % )
309	!! the solar heat (W/m2)
310	!! the Long wave (W/m2)
311	!! the 10m or 2m air temperature (Kelvin)
312	!! the total precipitation (rain+snow) (Kg/m2/s)
313	!! the snow (solid prcipitation) (kg/m2/s)
314	!! the tau diff associated to HF tau (N/m2) at T-point (ln_taudif=T)
315	!! (2) CALL blk_oce
316	!!
317	!! C A U T I O N : never mask the surface stress fields
318	!! the stress is assumed to be in the (i,j) mesh referential
319	!!
320	!! ** Action : defined at each time-step at the air-sea interface
321	!! - utau, vtau i- and j-component of the wind stress
322	!! - taum wind stress module at T-point
323	!! - wndm wind speed module at T-point over free ocean or leads in presence of sea-ice
324	!! - qns, qsr non-solar and solar heat fluxes
325	!! - emp upward mass flux (evapo. - precip.)
326	!! - sfx salt flux due to freezing/melting (non-zero only if ice is present)
327	!!
328	!! ** References : Large & Yeager, 2004 / Large & Yeager, 2008
329	!! Brodeau et al. Ocean Modelling 2010
330	!!----------------------------------------------------------------------
331	INTEGER, INTENT(in) :: kt ! ocean time step
332	!!---------------------------------------------------------------------
333	!
334	CALL fld_read( kt, nn_fsbc, sf ) ! input fields provided at the current time-step
335	!
336	! ! compute the surface ocean fluxes using bulk formulea
337	IF( MOD( kt - 1, nn_fsbc ) == 0 ) CALL blk_oce( kt, sf, sst_m, ssu_m, ssv_m )
338
339	#if defined key_cice
340	IF( MOD( kt - 1, nn_fsbc ) == 0 ) THEN
341	qlw_ice(:,:,1) = sf(jp_qlw )%fnow(:,:,1)
342	IF( ln_dm2dc ) THEN ; qsr_ice(:,:,1) = sbc_dcy( sf(jp_qsr)%fnow(:,:,1) )
343	ELSE ; qsr_ice(:,:,1) = sf(jp_qsr)%fnow(:,:,1)
344	ENDIF
345	tatm_ice(:,:) = sf(jp_tair)%fnow(:,:,1)
346	qatm_ice(:,:) = sf(jp_humi)%fnow(:,:,1)
347	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac
348	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac
349	wndi_ice(:,:) = sf(jp_wndi)%fnow(:,:,1)
350	wndj_ice(:,:) = sf(jp_wndj)%fnow(:,:,1)
351	ENDIF
352	#endif
353	!
354	END SUBROUTINE sbc_blk
355
356
357	SUBROUTINE blk_oce( kt, sf, pst, pu, pv )
358	!!---------------------------------------------------------------------
359	!! * ROUTINE blk_oce *
360	!!
361	!! ** Purpose : provide the momentum, heat and freshwater fluxes at
362	!! the ocean surface at each time step
363	!!
364	!! ** Method : bulk formulea for the ocean using atmospheric
365	!! fields read in sbc_read
366	!!
367	!! ** Outputs : - utau : i-component of the stress at U-point (N/m2)
368	!! - vtau : j-component of the stress at V-point (N/m2)
369	!! - taum : Wind stress module at T-point (N/m2)
370	!! - wndm : Wind speed module at T-point (m/s)
371	!! - qsr : Solar heat flux over the ocean (W/m2)
372	!! - qns : Non Solar heat flux over the ocean (W/m2)
373	!! - emp : evaporation minus precipitation (kg/m2/s)
374	!!
375	!! ** Nota : sf has to be a dummy argument for AGRIF on NEC
376	!!---------------------------------------------------------------------
377	INTEGER , INTENT(in ) :: kt ! time step index
378	TYPE(fld), INTENT(inout), DIMENSION(:) :: sf ! input data
379	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pst ! surface temperature [Celcius]
380	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pu ! surface current at U-point (i-component) [m/s]
381	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pv ! surface current at V-point (j-component) [m/s]
382	!
383	INTEGER :: ji, jj ! dummy loop indices
384	REAL(wp) :: zztmp ! local variable
385	REAL(wp), DIMENSION(jpi,jpj) :: zwnd_i, zwnd_j ! wind speed components at T-point
386	REAL(wp), DIMENSION(jpi,jpj) :: zsq ! specific humidity at pst
387	REAL(wp), DIMENSION(jpi,jpj) :: zqlw, zqsb ! long wave and sensible heat fluxes
388	REAL(wp), DIMENSION(jpi,jpj) :: zqla, zevap ! latent heat fluxes and evaporation
389	REAL(wp), DIMENSION(jpi,jpj) :: zst ! surface temperature in Kelvin
390	REAL(wp), DIMENSION(jpi,jpj) :: zU_zu ! bulk wind speed at height zu [m/s]
391	REAL(wp), DIMENSION(jpi,jpj) :: ztpot ! potential temperature of air at z=rn_zqt [K]
392	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa ! density of air [kg/m^3]
393	REAL(wp), DIMENSION(jpi,jpj) :: zcptrain, zcptsnw, zcptn ! Heat content per unit mass (J/kg)
394	!!---------------------------------------------------------------------
395	!
396	! Heat content per unit mass (J/kg)
397	zcptrain(:,:) = ( sf(jp_tair)%fnow(:,:,1) - rt0 ) * rcp * tmask(:,:,1)
398	zcptsnw (:,:) = ( MIN( sf(jp_tair)%fnow(:,:,1), rt0 ) - rt0 ) * rcpi * tmask(:,:,1)
399	zcptn (:,:) = pst(:,:) * rcp * tmask(:,:,1)
400	!
401	! local scalars ( place there for vector optimisation purposes)
402	zst(:,:) = pst(:,:) + rt0 ! convert SST from Celcius to Kelvin (and set minimum value far above 0 K)
403
404	! --- cloud cover --- !
405	cloud_fra(:,:) = sf(jp_cc)%fnow(:,:,1)
406
407	! ----------------------------------------------------------------------------- !
408	! 0 Wind components and module at T-point relative to the moving ocean !
409	! ----------------------------------------------------------------------------- !
410
411	! ... components ( U10m - U_oce ) at T-point (unmasked)
412	!!gm move zwnd_i (_j) set to zero inside the key_cyclone ???
413	zwnd_i(:,:) = 0._wp
414	zwnd_j(:,:) = 0._wp
415	#if defined key_cyclone
416	CALL wnd_cyc( kt, zwnd_i, zwnd_j ) ! add analytical tropical cyclone (Vincent et al. JGR 2012)
417	DO jj = 2, jpjm1
418	DO ji = fs_2, fs_jpim1 ! vect. opt.
419	sf(jp_wndi)%fnow(ji,jj,1) = sf(jp_wndi)%fnow(ji,jj,1) + zwnd_i(ji,jj)
420	sf(jp_wndj)%fnow(ji,jj,1) = sf(jp_wndj)%fnow(ji,jj,1) + zwnd_j(ji,jj)
421	END DO
422	END DO
423	#endif
424	! mask the wind in case it is not masked in the input file otherwise we end up with twice the stress at the coast
425	! (see calculation of utau/vtau below)
426	DO jj = 2, jpjm1
427	DO ji = fs_2, fs_jpim1 ! vect. opt.
428	zwnd_i(ji,jj) = ( sf(jp_wndi)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( pu(ji-1,jj ) + pu(ji,jj) ) ) * tmask(ji,jj,1)
429	zwnd_j(ji,jj) = ( sf(jp_wndj)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( pv(ji ,jj-1) + pv(ji,jj) ) ) * tmask(ji,jj,1)
430	END DO
431	END DO
432	CALL lbc_lnk_multi( 'sbcblk', zwnd_i, 'T', -1., zwnd_j, 'T', -1. )
433	! ... scalar wind ( = \| U10m - U_oce \| ) at T-point (masked)
434	wndm(:,:) = SQRT( zwnd_i(:,:) * zwnd_i(:,:) &
435	& + zwnd_j(:,:) * zwnd_j(:,:) )
436
437	! ----------------------------------------------------------------------------- !
438	! I Radiative FLUXES !
439	! ----------------------------------------------------------------------------- !
440
441	! ocean albedo assumed to be constant + modify now Qsr to include the diurnal cycle ! Short Wave
442	zztmp = 1. - albo
443	IF( ln_dm2dc ) THEN ; qsr(:,:) = zztmp * sbc_dcy( sf(jp_qsr)%fnow(:,:,1) ) * tmask(:,:,1)
444	ELSE ; qsr(:,:) = zztmp * sf(jp_qsr)%fnow(:,:,1) * tmask(:,:,1)
445	ENDIF
446
447	#if defined key_top
448	IF( ln_trcdc2dm ) THEN ! diurnal cycle in TOP
449	IF( ln_dm2dc ) THEN ; qsr_mean(:,:) = zztmp * sf(jp_qsr)%fnow(:,:,1) * tmask(:,:,1)
450	ELSE ; ncpl_qsr_freq = sf(jp_qsr)%freqh * 3600 ! qsr_mean will be computed in TOP
451	ENDIF
452	ENDIF
453	#endif
454
455	zqlw(:,:) = ( sf(jp_qlw)%fnow(:,:,1) - Stef * zst(:,:)zst(:,:)zst(:,:)zst(:,:) ) tmask(:,:,1) ! Long Wave
456
457	! ----------------------------------------------------------------------------- !
458	! II Turbulent FLUXES !
459	! ----------------------------------------------------------------------------- !
460
461	! ... specific humidity at SST and IST tmask(
462	zsq(:,:) = 0.98 * q_sat( zst(:,:), sf(jp_slp)%fnow(:,:,1) )
463	!!
464	!! Estimate of potential temperature at z=rn_zqt, based on adiabatic lapse-rate
465	!! (see Josey, Gulev & Yu, 2013) / doi=10.1016/B978-0-12-391851-2.00005-2
466	!! (since reanalysis products provide T at z, not theta !)
467	ztpot = sf(jp_tair)%fnow(:,:,1) + gamma_moist( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1) ) * rn_zqt
468
469	SELECT CASE( nblk ) !== transfer coefficients ==! Cd, Ch, Ce at T-point
470	!
471	CASE( np_NCAR ) ; CALL turb_ncar ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! NCAR-COREv2
472	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
473	CASE( np_COARE_3p0 ) ; CALL turb_coare ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! COARE v3.0
474	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
475	CASE( np_COARE_3p5 ) ; CALL turb_coare3p5( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! COARE v3.5
476	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
477	CASE( np_ECMWF ) ; CALL turb_ecmwf ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! ECMWF
478	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
479	CASE DEFAULT
480	CALL ctl_stop( 'STOP', 'sbc_oce: non-existing bulk formula selected' )
481	END SELECT
482
483	! ! Compute true air density :
484	IF( ABS(rn_zu - rn_zqt) > 0.01 ) THEN ! At zu: (probably useless to remove zrhogravrn_zu from SLP...)
485	zrhoa(:,:) = rho_air( t_zu(:,:) , q_zu(:,:) , sf(jp_slp)%fnow(:,:,1) )
486	ELSE ! At zt:
487	zrhoa(:,:) = rho_air( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1) )
488	END IF
489
490	!! CALL iom_put( "Cd_oce", Cd_atm) ! output value of pure ocean-atm. transfer coef.
491	!! CALL iom_put( "Ch_oce", Ch_atm) ! output value of pure ocean-atm. transfer coef.
492
493	DO jj = 1, jpj ! tau module, i and j component
494	DO ji = 1, jpi
495	zztmp = zrhoa(ji,jj) * zU_zu(ji,jj) * Cd_atm(ji,jj) ! using bulk wind speed
496	taum (ji,jj) = zztmp * wndm (ji,jj)
497	zwnd_i(ji,jj) = zztmp * zwnd_i(ji,jj)
498	zwnd_j(ji,jj) = zztmp * zwnd_j(ji,jj)
499	END DO
500	END DO
501
502	! ! add the HF tau contribution to the wind stress module
503	IF( lhftau ) taum(:,:) = taum(:,:) + sf(jp_tdif)%fnow(:,:,1)
504
505	CALL iom_put( "taum_oce", taum ) ! output wind stress module
506
507	! ... utau, vtau at U- and V_points, resp.
508	! Note the use of 0.5*(2-umask) in order to unmask the stress along coastlines
509	! Note the use of MAX(tmask(i,j),tmask(i+1,j) is to mask tau over ice shelves
510	DO jj = 1, jpjm1
511	DO ji = 1, fs_jpim1
512	utau(ji,jj) = 0.5 * ( 2. - umask(ji,jj,1) ) * ( zwnd_i(ji,jj) + zwnd_i(ji+1,jj ) ) &
513	& * MAX(tmask(ji,jj,1),tmask(ji+1,jj,1))
514	vtau(ji,jj) = 0.5 * ( 2. - vmask(ji,jj,1) ) * ( zwnd_j(ji,jj) + zwnd_j(ji ,jj+1) ) &
515	& * MAX(tmask(ji,jj,1),tmask(ji,jj+1,1))
516	END DO
517	END DO
518	CALL lbc_lnk_multi( 'sbcblk', utau, 'U', -1., vtau, 'V', -1. )
519
520	! Turbulent fluxes over ocean
521	! -----------------------------
522
523	! zqla used as temporary array, for rho*U (common term of bulk formulae):
524	zqla(:,:) = zrhoa(:,:) * zU_zu(:,:) * tmask(:,:,1)
525
526	IF( ABS( rn_zu - rn_zqt) < 0.01_wp ) THEN
527	!! q_air and t_air are given at 10m (wind reference height)
528	zevap(:,:) = rn_efacMAX( 0._wp, zqla(:,:)Ce_atm(:,:)*(zsq(:,:) - sf(jp_humi)%fnow(:,:,1)) ) ! Evaporation, using bulk wind speed
529	zqsb (:,:) = cp_air(sf(jp_humi)%fnow(:,:,1))zqla(:,:)Ch_atm(:,:)*(zst(:,:) - ztpot(:,:) ) ! Sensible Heat, using bulk wind speed
530	ELSE
531	!! q_air and t_air are not given at 10m (wind reference height)
532	! Values of temp. and hum. adjusted to height of wind during bulk algorithm iteration must be used!!!
533	zevap(:,:) = rn_efacMAX( 0._wp, zqla(:,:)Ce_atm(:,:)*(zsq(:,:) - q_zu(:,:) ) ) ! Evaporation, using bulk wind speed
534	zqsb (:,:) = cp_air(sf(jp_humi)%fnow(:,:,1))zqla(:,:)Ch_atm(:,:)*(zst(:,:) - t_zu(:,:) ) ! Sensible Heat, using bulk wind speed
535	ENDIF
536
537	zqla(:,:) = L_vap(zst(:,:)) * zevap(:,:) ! Latent Heat flux
538
539
540	IF(ln_ctl) THEN
541	CALL prt_ctl( tab2d_1=zqla , clinfo1=' blk_oce: zqla : ', tab2d_2=Ce_atm , clinfo2=' Ce_oce : ' )
542	CALL prt_ctl( tab2d_1=zqsb , clinfo1=' blk_oce: zqsb : ', tab2d_2=Ch_atm , clinfo2=' Ch_oce : ' )
543	CALL prt_ctl( tab2d_1=zqlw , clinfo1=' blk_oce: zqlw : ', tab2d_2=qsr, clinfo2=' qsr : ' )
544	CALL prt_ctl( tab2d_1=zsq , clinfo1=' blk_oce: zsq : ', tab2d_2=zst, clinfo2=' zst : ' )
545	CALL prt_ctl( tab2d_1=utau , clinfo1=' blk_oce: utau : ', mask1=umask, &
546	& tab2d_2=vtau , clinfo2= ' vtau : ', mask2=vmask )
547	CALL prt_ctl( tab2d_1=wndm , clinfo1=' blk_oce: wndm : ')
548	CALL prt_ctl( tab2d_1=zst , clinfo1=' blk_oce: zst : ')
549	ENDIF
550
551	! ----------------------------------------------------------------------------- !
552	! III Total FLUXES !
553	! ----------------------------------------------------------------------------- !
554	!
555	emp (:,:) = ( zevap(:,:) & ! mass flux (evap. - precip.)
556	& - sf(jp_prec)%fnow(:,:,1) * rn_pfac ) * tmask(:,:,1)
557	!
558	qns(:,:) = zqlw(:,:) - zqsb(:,:) - zqla(:,:) & ! Downward Non Solar
559	& - sf(jp_snow)%fnow(:,:,1) * rn_pfac * rLfus & ! remove latent melting heat for solid precip
560	& - zevap(:,:) * zcptn(:,:) & ! remove evap heat content at SST
561	& + ( sf(jp_prec)%fnow(:,:,1) - sf(jp_snow)%fnow(:,:,1) ) * rn_pfac & ! add liquid precip heat content at Tair
562	& * zcptrain(:,:) &
563	& + sf(jp_snow)%fnow(:,:,1) * rn_pfac & ! add solid precip heat content at min(Tair,Tsnow)
564	& * zcptsnw(:,:)
565	qns(:,:) = qns(:,:) * tmask(:,:,1)
566	!
567	#if defined key_si3
568	qns_oce(:,:) = zqlw(:,:) - zqsb(:,:) - zqla(:,:) ! non solar without emp (only needed by SI3)
569	qsr_oce(:,:) = qsr(:,:)
570	#endif
571	!
572	IF ( nn_ice == 0 ) THEN
573	CALL iom_put( "qlw_oce" , zqlw ) ! output downward longwave heat over the ocean
574	CALL iom_put( "qsb_oce" , - zqsb ) ! output downward sensible heat over the ocean
575	CALL iom_put( "qla_oce" , - zqla ) ! output downward latent heat over the ocean
576	CALL iom_put( "qemp_oce", qns-zqlw+zqsb+zqla ) ! output downward heat content of E-P over the ocean
577	CALL iom_put( "qns_oce" , qns ) ! output downward non solar heat over the ocean
578	CALL iom_put( "qsr_oce" , qsr ) ! output downward solar heat over the ocean
579	CALL iom_put( "qt_oce" , qns+qsr ) ! output total downward heat over the ocean
580	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! output total precipitation [kg/m2/s]
581	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! output solid precipitation [kg/m2/s]
582	CALL iom_put( 'snowpre', sprecip ) ! Snow
583	CALL iom_put( 'precip' , tprecip ) ! Total precipitation
584	ENDIF
585	!
586	IF(ln_ctl) THEN
587	CALL prt_ctl(tab2d_1=zqsb , clinfo1=' blk_oce: zqsb : ', tab2d_2=zqlw , clinfo2=' zqlw : ')
588	CALL prt_ctl(tab2d_1=zqla , clinfo1=' blk_oce: zqla : ', tab2d_2=qsr , clinfo2=' qsr : ')
589	CALL prt_ctl(tab2d_1=pst , clinfo1=' blk_oce: pst : ', tab2d_2=emp , clinfo2=' emp : ')
590	CALL prt_ctl(tab2d_1=utau , clinfo1=' blk_oce: utau : ', mask1=umask, &
591	& tab2d_2=vtau , clinfo2= ' vtau : ' , mask2=vmask )
592	ENDIF
593	!
594	END SUBROUTINE blk_oce
595
596
597
598	FUNCTION rho_air( ptak, pqa, pslp )
599	!!-------------------------------------------------------------------------------
600	!! * FUNCTION rho_air *
601	!!
602	!! ** Purpose : compute density of (moist) air using the eq. of state of the atmosphere
603	!!
604	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
605	!!-------------------------------------------------------------------------------
606	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
607	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg]
608	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! pressure in [Pa]
609	REAL(wp), DIMENSION(jpi,jpj) :: rho_air ! density of moist air [kg/m^3]
610	!!-------------------------------------------------------------------------------
611	!
612	rho_air = pslp / ( R_dryptak ( 1._wp + rctv0*pqa ) )
613	!
614	END FUNCTION rho_air
615
616
617	FUNCTION cp_air( pqa )
618	!!-------------------------------------------------------------------------------
619	!! * FUNCTION cp_air *
620	!!
621	!! ** Purpose : Compute specific heat (Cp) of moist air
622	!!
623	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
624	!!-------------------------------------------------------------------------------
625	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg]
626	REAL(wp), DIMENSION(jpi,jpj) :: cp_air ! specific heat of moist air [J/K/kg]
627	!!-------------------------------------------------------------------------------
628	!
629	Cp_air = Cp_dry + Cp_vap * pqa
630	!
631	END FUNCTION cp_air
632
633
634	FUNCTION q_sat( ptak, pslp )
635	!!----------------------------------------------------------------------------------
636	!! * FUNCTION q_sat *
637	!!
638	!! ** Purpose : Specific humidity at saturation in [kg/kg]
639	!! Based on accurate estimate of "e_sat"
640	!! aka saturation water vapor (Goff, 1957)
641	!!
642	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
643	!!----------------------------------------------------------------------------------
644	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
645	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! sea level atmospheric pressure [Pa]
646	REAL(wp), DIMENSION(jpi,jpj) :: q_sat ! Specific humidity at saturation [kg/kg]
647	!
648	INTEGER :: ji, jj ! dummy loop indices
649	REAL(wp) :: ze_sat, ztmp ! local scalar
650	!!----------------------------------------------------------------------------------
651	!
652	DO jj = 1, jpj
653	DO ji = 1, jpi
654	!
655	ztmp = rt0 / ptak(ji,jj)
656	!
657	! Vapour pressure at saturation [hPa] : WMO, (Goff, 1957)
658	ze_sat = 10.*( 10.79574(1. - ztmp) - 5.028*LOG10(ptak(ji,jj)/rt0) &
659	& + 1.5047510.(-4)(1. - 10.*(-8.2969(ptak(ji,jj)/rt0 - 1.)) ) &
660	& + 0.4287310.(-3)(10.*(4.76955(1. - ztmp)) - 1.) + 0.78614 )
661	!
662	q_sat(ji,jj) = reps0 * ze_sat/( 0.01_wppslp(ji,jj) - (1._wp - reps0)ze_sat ) ! 0.01 because SLP is in [Pa]
663	!
664	END DO
665	END DO
666	!
667	END FUNCTION q_sat
668
669
670	FUNCTION gamma_moist( ptak, pqa )
671	!!----------------------------------------------------------------------------------
672	!! * FUNCTION gamma_moist *
673	!!
674	!! ** Purpose : Compute the moist adiabatic lapse-rate.
675	!! => http://glossary.ametsoc.org/wiki/Moist-adiabatic_lapse_rate
676	!! => http://www.geog.ucsb.edu/~joel/g266_s10/lecture_notes/chapt03/oh10_3_01/oh10_3_01.html
677	!!
678	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
679	!!----------------------------------------------------------------------------------
680	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
681	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! specific humidity [kg/kg]
682	REAL(wp), DIMENSION(jpi,jpj) :: gamma_moist ! moist adiabatic lapse-rate
683	!
684	INTEGER :: ji, jj ! dummy loop indices
685	REAL(wp) :: zrv, ziRT ! local scalar
686	!!----------------------------------------------------------------------------------
687	!
688	DO jj = 1, jpj
689	DO ji = 1, jpi
690	zrv = pqa(ji,jj) / (1. - pqa(ji,jj))
691	ziRT = 1. / (R_dry*ptak(ji,jj)) ! 1/RT
692	gamma_moist(ji,jj) = grav * ( 1. + rLevapzrvziRT ) / ( Cp_dry + rLevaprLevapzrvreps0ziRT/ptak(ji,jj) )
693	END DO
694	END DO
695	!
696	END FUNCTION gamma_moist
697
698
699	FUNCTION L_vap( psst )
700	!!---------------------------------------------------------------------------------
701	!! * FUNCTION L_vap *
702	!!
703	!! ** Purpose : Compute the latent heat of vaporization of water from temperature
704	!!
705	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
706	!!----------------------------------------------------------------------------------
707	REAL(wp), DIMENSION(jpi,jpj) :: L_vap ! latent heat of vaporization [J/kg]
708	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! water temperature [K]
709	!!----------------------------------------------------------------------------------
710	!
711	L_vap = ( 2.501 - 0.00237 * ( psst(:,:) - rt0) ) * 1.e6
712	!
713	END FUNCTION L_vap
714
715	#if defined key_si3
716	!!----------------------------------------------------------------------
717	!! 'key_si3' SI3 sea-ice model
718	!!----------------------------------------------------------------------
719	!! blk_ice_tau : provide the air-ice stress
720	!! blk_ice_flx : provide the heat and mass fluxes at air-ice interface
721	!! blk_ice_qcn : provide ice surface temperature and snow/ice conduction flux (emulating conduction flux)
722	!! Cdn10_Lupkes2012 : Lupkes et al. (2012) air-ice drag
723	!! Cdn10_Lupkes2015 : Lupkes et al. (2015) air-ice drag
724	!!----------------------------------------------------------------------
725
726	SUBROUTINE blk_ice_tau
727	!!---------------------------------------------------------------------
728	!! * ROUTINE blk_ice_tau *
729	!!
730	!! ** Purpose : provide the surface boundary condition over sea-ice
731	!!
732	!! ** Method : compute momentum using bulk formulation
733	!! formulea, ice variables and read atmospheric fields.
734	!! NB: ice drag coefficient is assumed to be a constant
735	!!---------------------------------------------------------------------
736	INTEGER :: ji, jj ! dummy loop indices
737	REAL(wp) :: zwndi_f , zwndj_f, zwnorm_f ! relative wind module and components at F-point
738	REAL(wp) :: zwndi_t , zwndj_t ! relative wind components at T-point
739	REAL(wp) :: zztmp1 , zztmp2 ! temporary values
740	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa ! transfer coefficient for momentum (tau)
741	!!---------------------------------------------------------------------
742	!
743	! set transfer coefficients to default sea-ice values
744	Cd_atm(:,:) = Cd_ice
745	Ch_atm(:,:) = Cd_ice
746	Ce_atm(:,:) = Cd_ice
747
748	wndm_ice(:,:) = 0._wp !!gm brutal....
749
750	! ------------------------------------------------------------ !
751	! Wind module relative to the moving ice ( U10m - U_ice ) !
752	! ------------------------------------------------------------ !
753	! C-grid ice dynamics : U & V-points (same as ocean)
754	DO jj = 2, jpjm1
755	DO ji = fs_2, fs_jpim1 ! vect. opt.
756	zwndi_t = ( sf(jp_wndi)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( u_ice(ji-1,jj ) + u_ice(ji,jj) ) )
757	zwndj_t = ( sf(jp_wndj)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( v_ice(ji ,jj-1) + v_ice(ji,jj) ) )
758	wndm_ice(ji,jj) = SQRT( zwndi_t * zwndi_t + zwndj_t * zwndj_t ) * tmask(ji,jj,1)
759	END DO
760	END DO
761	CALL lbc_lnk( 'sbcblk', wndm_ice, 'T', 1. )
762	!
763	! Make ice-atm. drag dependent on ice concentration
764	IF ( ln_Cd_L12 ) THEN ! calculate new drag from Lupkes(2012) equations
765	CALL Cdn10_Lupkes2012( Cd_atm )
766	Ch_atm(:,:) = Cd_atm(:,:) ! momentum and heat transfer coef. are considered identical
767	ELSEIF( ln_Cd_L15 ) THEN ! calculate new drag from Lupkes(2015) equations
768	CALL Cdn10_Lupkes2015( Cd_atm, Ch_atm )
769	ENDIF
770
771	!! CALL iom_put( "Cd_ice", Cd_atm) ! output value of pure ice-atm. transfer coef.
772	!! CALL iom_put( "Ch_ice", Ch_atm) ! output value of pure ice-atm. transfer coef.
773
774	! local scalars ( place there for vector optimisation purposes)
775	! Computing density of air! Way denser that 1.2 over sea-ice !!!
776	zrhoa (:,:) = rho_air(sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1))
777
778	! ------------------------------------------------------------ !
779	! Wind stress relative to the moving ice ( U10m - U_ice ) !
780	! ------------------------------------------------------------ !
781	zztmp1 = rn_vfac * 0.5_wp
782	DO jj = 2, jpj ! at T point
783	DO ji = 2, jpi
784	zztmp2 = zrhoa(ji,jj) * Cd_atm(ji,jj) * wndm_ice(ji,jj)
785	utau_ice(ji,jj) = zztmp2 * ( sf(jp_wndi)%fnow(ji,jj,1) - zztmp1 * ( u_ice(ji-1,jj ) + u_ice(ji,jj) ) )
786	vtau_ice(ji,jj) = zztmp2 * ( sf(jp_wndj)%fnow(ji,jj,1) - zztmp1 * ( v_ice(ji ,jj-1) + v_ice(ji,jj) ) )
787	END DO
788	END DO
789	!
790	DO jj = 2, jpjm1 ! U & V-points (same as ocean).
791	DO ji = fs_2, fs_jpim1 ! vect. opt.
792	! take care of the land-sea mask to avoid "pollution" of coastal stress. p[uv]taui used in frazil and rheology
793	zztmp1 = 0.5_wp * ( 2. - umask(ji,jj,1) ) * MAX( tmask(ji,jj,1),tmask(ji+1,jj ,1) )
794	zztmp2 = 0.5_wp * ( 2. - vmask(ji,jj,1) ) * MAX( tmask(ji,jj,1),tmask(ji ,jj+1,1) )
795	utau_ice(ji,jj) = zztmp1 * ( utau_ice(ji,jj) + utau_ice(ji+1,jj ) )
796	vtau_ice(ji,jj) = zztmp2 * ( vtau_ice(ji,jj) + vtau_ice(ji ,jj+1) )
797	END DO
798	END DO
799	CALL lbc_lnk_multi( 'sbcblk', utau_ice, 'U', -1., vtau_ice, 'V', -1. )
800	!
801	!
802	IF(ln_ctl) THEN
803	CALL prt_ctl(tab2d_1=utau_ice , clinfo1=' blk_ice: utau_ice : ', tab2d_2=vtau_ice , clinfo2=' vtau_ice : ')
804	CALL prt_ctl(tab2d_1=wndm_ice , clinfo1=' blk_ice: wndm_ice : ')
805	ENDIF
806	!
807	END SUBROUTINE blk_ice_tau
808
809
810	SUBROUTINE blk_ice_flx( ptsu, phs, phi, palb )
811	!!---------------------------------------------------------------------
812	!! * ROUTINE blk_ice_flx *
813	!!
814	!! ** Purpose : provide the heat and mass fluxes at air-ice interface
815	!!
816	!! ** Method : compute heat and freshwater exchanged
817	!! between atmosphere and sea-ice using bulk formulation
818	!! formulea, ice variables and read atmmospheric fields.
819	!!
820	!! caution : the net upward water flux has with mm/day unit
821	!!---------------------------------------------------------------------
822	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: ptsu ! sea ice surface temperature
823	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: phs ! snow thickness
824	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: phi ! ice thickness
825	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: palb ! ice albedo (all skies)
826	!!
827	INTEGER :: ji, jj, jl ! dummy loop indices
828	REAL(wp) :: zst3 ! local variable
829	REAL(wp) :: zcoef_dqlw, zcoef_dqla ! - -
830	REAL(wp) :: zztmp, z1_rLsub ! - -
831	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_st ! inverse of surface temperature
832	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_qlw ! long wave heat flux over ice
833	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_qsb ! sensible heat flux over ice
834	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_dqlw ! long wave heat sensitivity over ice
835	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_dqsb ! sensible heat sensitivity over ice
836	REAL(wp), DIMENSION(jpi,jpj) :: zevap, zsnw ! evaporation and snw distribution after wind blowing (SI3)
837	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa
838	REAL(wp), DIMENSION(jpi,jpj) :: ztri
839	REAL(wp), DIMENSION(jpi,jpj) :: zcptrain, zcptsnw, zcptn ! Heat content per unit mass (J/kg)
840	!!---------------------------------------------------------------------
841	!
842	zcoef_dqlw = 4.0 * 0.95 * Stef ! local scalars
843	zcoef_dqla = -Ls * 11637800. * (-5897.8)
844	!
845	zrhoa(:,:) = rho_air( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1) )
846	!
847	! Heat content per unit mass (J/kg)
848	zcptrain(:,:) = ( sf(jp_tair)%fnow(:,:,1) - rt0 ) * rcp * tmask(:,:,1)
849	zcptsnw (:,:) = ( MIN( sf(jp_tair)%fnow(:,:,1), rt0 ) - rt0 ) * rcpi * tmask(:,:,1)
850	zcptn (:,:) = sst_m(:,:) * rcp * tmask(:,:,1)
851	!
852	zztmp = 1. / ( 1. - albo )
853	WHERE( ptsu(:,:,:) /= 0._wp ) ; z1_st(:,:,:) = 1._wp / ptsu(:,:,:)
854	ELSEWHERE ; z1_st(:,:,:) = 0._wp
855	END WHERE
856	! ! ========================== !
857	DO jl = 1, jpl ! Loop over ice categories !
858	! ! ========================== !
859	DO jj = 1 , jpj
860	DO ji = 1, jpi
861	! ----------------------------!
862	! I Radiative FLUXES !
863	! ----------------------------!
864	zst3 = ptsu(ji,jj,jl) * ptsu(ji,jj,jl) * ptsu(ji,jj,jl)
865	! Short Wave (sw)
866	qsr_ice(ji,jj,jl) = zztmp * ( 1. - palb(ji,jj,jl) ) * qsr(ji,jj)
867	! Long Wave (lw)
868	z_qlw(ji,jj,jl) = 0.95 * ( sf(jp_qlw)%fnow(ji,jj,1) - Stef * ptsu(ji,jj,jl) * zst3 ) * tmask(ji,jj,1)
869	! lw sensitivity
870	z_dqlw(ji,jj,jl) = zcoef_dqlw * zst3
871
872	! ----------------------------!
873	! II Turbulent FLUXES !
874	! ----------------------------!
875
876	! ... turbulent heat fluxes with Ch_atm recalculated in blk_ice_tau
877	! Sensible Heat
878	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))
879	! Latent Heat
880	qla_ice(ji,jj,jl) = rn_efac * MAX( 0.e0, zrhoa(ji,jj) * Ls * Ch_atm(ji,jj) * wndm_ice(ji,jj) * &
881	& ( 11637800. * EXP( -5897.8 * z1_st(ji,jj,jl) ) / zrhoa(ji,jj) - sf(jp_humi)%fnow(ji,jj,1) ) )
882	! Latent heat sensitivity for ice (Dqla/Dt)
883	IF( qla_ice(ji,jj,jl) > 0._wp ) THEN
884	dqla_ice(ji,jj,jl) = rn_efac * zcoef_dqla * Ch_atm(ji,jj) * wndm_ice(ji,jj) * &
885	& z1_st(ji,jj,jl)z1_st(ji,jj,jl) EXP(-5897.8 * z1_st(ji,jj,jl))
886	ELSE
887	dqla_ice(ji,jj,jl) = 0._wp
888	ENDIF
889
890	! Sensible heat sensitivity (Dqsb_ice/Dtn_ice)
891	z_dqsb(ji,jj,jl) = zrhoa(ji,jj) * cpa * Ch_atm(ji,jj) * wndm_ice(ji,jj)
892
893	! ----------------------------!
894	! III Total FLUXES !
895	! ----------------------------!
896	! Downward Non Solar flux
897	qns_ice (ji,jj,jl) = z_qlw (ji,jj,jl) - z_qsb (ji,jj,jl) - qla_ice (ji,jj,jl)
898	! Total non solar heat flux sensitivity for ice
899	dqns_ice(ji,jj,jl) = - ( z_dqlw(ji,jj,jl) + z_dqsb(ji,jj,jl) + dqla_ice(ji,jj,jl) )
900	END DO
901	!
902	END DO
903	!
904	END DO
905	!
906	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! total precipitation [kg/m2/s]
907	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! solid precipitation [kg/m2/s]
908	CALL iom_put( 'snowpre', sprecip ) ! Snow precipitation
909	CALL iom_put( 'precip' , tprecip ) ! Total precipitation
910
911	! --- evaporation --- !
912	z1_rLsub = 1._wp / rLsub
913	evap_ice (:,:,:) = rn_efac * qla_ice (:,:,:) * z1_rLsub ! sublimation
914	devap_ice(:,:,:) = rn_efac * dqla_ice(:,:,:) * z1_rLsub ! d(sublimation)/dT
915	zevap (:,:) = rn_efac * ( emp(:,:) + tprecip(:,:) ) ! evaporation over ocean
916
917	! --- evaporation minus precipitation --- !
918	zsnw(:,:) = 0._wp
919	CALL ice_var_snwblow( (1.-at_i_b(:,:)), zsnw ) ! snow distribution over ice after wind blowing
920	emp_oce(:,:) = ( 1._wp - at_i_b(:,:) ) * zevap(:,:) - ( tprecip(:,:) - sprecip(:,:) ) - sprecip(:,:) * (1._wp - zsnw )
921	emp_ice(:,:) = SUM( a_i_b(:,:,:) * evap_ice(:,:,:), dim=3 ) - sprecip(:,:) * zsnw
922	emp_tot(:,:) = emp_oce(:,:) + emp_ice(:,:)
923
924	! --- heat flux associated with emp --- !
925	qemp_oce(:,:) = - ( 1._wp - at_i_b(:,:) ) * zevap(:,:) * zcptn(:,:) & ! evap at sst
926	& + ( tprecip(:,:) - sprecip(:,:) ) * zcptrain(:,:) & ! liquid precip at Tair
927	& + sprecip(:,:) * ( 1._wp - zsnw ) * ( zcptsnw (:,:) - rLfus ) ! solid precip at min(Tair,Tsnow)
928	qemp_ice(:,:) = sprecip(:,:) * zsnw * ( zcptsnw (:,:) - rLfus ) ! solid precip (only)
929
930	! --- total solar and non solar fluxes --- !
931	qns_tot(:,:) = ( 1._wp - at_i_b(:,:) ) * qns_oce(:,:) + SUM( a_i_b(:,:,:) * qns_ice(:,:,:), dim=3 ) &
932	& + qemp_ice(:,:) + qemp_oce(:,:)
933	qsr_tot(:,:) = ( 1._wp - at_i_b(:,:) ) * qsr_oce(:,:) + SUM( a_i_b(:,:,:) * qsr_ice(:,:,:), dim=3 )
934
935	! --- heat content of precip over ice in J/m3 (to be used in 1D-thermo) --- !
936	qprec_ice(:,:) = rhos * ( zcptsnw(:,:) - rLfus )
937
938	! --- heat content of evap over ice in W/m2 (to be used in 1D-thermo) ---
939	DO jl = 1, jpl
940	qevap_ice(:,:,jl) = 0._wp ! should be -evap_ice(:,:,jl)( ( Tice - rt0 ) rcpi * tmask(:,:,1) )
941	! ! But we do not have Tice => consider it at 0degC => evap=0
942	END DO
943
944	! --- shortwave radiation transmitted thru the surface scattering layer (W/m2) --- !
945	IF( nn_qtrice == 0 ) THEN
946	! formulation derived from Grenfell and Maykut (1977), where transmission rate
947	! 1) depends on cloudiness
948	! 2) is 0 when there is any snow
949	! 3) tends to 1 for thin ice
950	ztri(:,:) = 0.18 * ( 1.0 - cloud_fra(:,:) ) + 0.35 * cloud_fra(:,:) ! surface transmission when hi>10cm
951	DO jl = 1, jpl
952	WHERE ( phs(:,:,jl) <= 0._wp .AND. phi(:,:,jl) < 0.1_wp ) ! linear decrease from hi=0 to 10cm
953	qtr_ice_top(:,:,jl) = qsr_ice(:,:,jl) * ( ztri(:,:) + ( 1._wp - ztri(:,:) ) * ( 1._wp - phi(:,:,jl) * 10._wp ) )
954	ELSEWHERE( phs(:,:,jl) <= 0._wp .AND. phi(:,:,jl) >= 0.1_wp ) ! constant (ztri) when hi>10cm
955	qtr_ice_top(:,:,jl) = qsr_ice(:,:,jl) * ztri(:,:)
956	ELSEWHERE ! zero when hs>0
957	qtr_ice_top(:,:,jl) = 0._wp
958	END WHERE
959	ENDDO
960	ELSEIF( nn_qtrice == 1 ) THEN
961	! formulation is derived from the thesis of M. Lebrun (2019).
962	! It represents the best fit using several sets of observations
963	! It comes with snow conductivities adapted to freezing/melting conditions (see icethd_zdf_bl99.F90)
964	qtr_ice_top(:,:,:) = 0.3_wp * qsr_ice(:,:,:)
965	ENDIF
966	!
967
968	IF( iom_use('evap_ao_cea') .OR. iom_use('hflx_evap_cea') ) THEN
969	CALL iom_put( 'evap_ao_cea' , zevap(:,:) * ( 1._wp - at_i_b(:,:) ) * tmask(:,:,1) ) ! ice-free oce evap (cell average)
970	CALL iom_put( 'hflx_evap_cea', zevap(:,:) * ( 1._wp - at_i_b(:,:) ) * tmask(:,:,1) * zcptn(:,:) ) ! heat flux from evap (cell average)
971	ENDIF
972	IF( iom_use('rain') .OR. iom_use('rain_ao_cea') .OR. iom_use('hflx_rain_cea') ) THEN
973	CALL iom_put( 'rain' , tprecip(:,:) - sprecip(:,:) ) ! liquid precipitation
974	CALL iom_put( 'rain_ao_cea' , ( tprecip(:,:) - sprecip(:,:) ) * ( 1._wp - at_i_b(:,:) ) ) ! liquid precipitation over ocean (cell average)
975	CALL iom_put( 'hflx_rain_cea', ( tprecip(:,:) - sprecip(:,:) ) * zcptrain(:,:) ) ! heat flux from rain (cell average)
976	ENDIF
977	IF( iom_use('snow_ao_cea') .OR. iom_use('snow_ai_cea') .OR. &
978	& iom_use('hflx_snow_cea') .OR. iom_use('hflx_snow_ao_cea') .OR. iom_use('hflx_snow_ai_cea') ) THEN
979	CALL iom_put( 'snow_ao_cea' , sprecip(:,:) * ( 1._wp - zsnw(:,:) ) ) ! Snow over ice-free ocean (cell average)
980	CALL iom_put( 'snow_ai_cea' , sprecip(:,:) * zsnw(:,:) ) ! Snow over sea-ice (cell average)
981	CALL iom_put( 'hflx_snow_cea' , sprecip(:,:) * ( zcptsnw(:,:) - rLfus ) ) ! heat flux from snow (cell average)
982	CALL iom_put( 'hflx_snow_ao_cea', sprecip(:,:) * ( zcptsnw(:,:) - rLfus ) * ( 1._wp - zsnw(:,:) ) ) ! heat flux from snow (over ocean)
983	CALL iom_put( 'hflx_snow_ai_cea', sprecip(:,:) * ( zcptsnw(:,:) - rLfus ) * zsnw(:,:) ) ! heat flux from snow (over ice)
984	ENDIF
985	IF( iom_use('hflx_prec_cea') ) THEN ! heat flux from precip (cell average)
986	CALL iom_put('hflx_prec_cea' , sprecip(:,:) * ( zcptsnw (:,:) - rLfus ) &
987	& + ( tprecip(:,:) - sprecip(:,:) ) * zcptrain(:,:) )
988	ENDIF
989	!
990	IF( iom_use('subl_ai_cea') .OR. iom_use('hflx_subl_cea') ) THEN
991	CALL iom_put( 'subl_ai_cea' , SUM( a_i_b(:,:,:) * evap_ice(:,:,:), dim=3 ) * tmask(:,:,1) ) ! Sublimation over sea-ice (cell average)
992	CALL iom_put( 'hflx_subl_cea', SUM( a_i_b(:,:,:) * qevap_ice(:,:,:), dim=3 ) * tmask(:,:,1) ) ! Heat flux from sublimation (cell average)
993	ENDIF
994
995	IF(ln_ctl) THEN
996	CALL prt_ctl(tab3d_1=qla_ice , clinfo1=' blk_ice: qla_ice : ', tab3d_2=z_qsb , clinfo2=' z_qsb : ', kdim=jpl)
997	CALL prt_ctl(tab3d_1=z_qlw , clinfo1=' blk_ice: z_qlw : ', tab3d_2=dqla_ice, clinfo2=' dqla_ice : ', kdim=jpl)
998	CALL prt_ctl(tab3d_1=z_dqsb , clinfo1=' blk_ice: z_dqsb : ', tab3d_2=z_dqlw , clinfo2=' z_dqlw : ', kdim=jpl)
999	CALL prt_ctl(tab3d_1=dqns_ice, clinfo1=' blk_ice: dqns_ice : ', tab3d_2=qsr_ice , clinfo2=' qsr_ice : ', kdim=jpl)
1000	CALL prt_ctl(tab3d_1=ptsu , clinfo1=' blk_ice: ptsu : ', tab3d_2=qns_ice , clinfo2=' qns_ice : ', kdim=jpl)
1001	CALL prt_ctl(tab2d_1=tprecip , clinfo1=' blk_ice: tprecip : ', tab2d_2=sprecip , clinfo2=' sprecip : ')
1002	ENDIF
1003	!
1004	END SUBROUTINE blk_ice_flx
1005
1006
1007	SUBROUTINE blk_ice_qcn( ld_virtual_itd, ptsu, ptb, phs, phi )
1008	!!---------------------------------------------------------------------
1009	!! * ROUTINE blk_ice_qcn *
1010	!!
1011	!! ** Purpose : Compute surface temperature and snow/ice conduction flux
1012	!! to force sea ice / snow thermodynamics
1013	!! in the case conduction flux is emulated
1014	!!
1015	!! ** Method : compute surface energy balance assuming neglecting heat storage
1016	!! following the 0-layer Semtner (1976) approach
1017	!!
1018	!! ** Outputs : - ptsu : sea-ice / snow surface temperature (K)
1019	!! - qcn_ice : surface inner conduction flux (W/m2)
1020	!!
1021	!!---------------------------------------------------------------------
1022	LOGICAL , INTENT(in ) :: ld_virtual_itd ! single-category option
1023	REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: ptsu ! sea ice / snow surface temperature
1024	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: ptb ! sea ice base temperature
1025	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: phs ! snow thickness
1026	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: phi ! sea ice thickness
1027	!
1028	INTEGER , PARAMETER :: nit = 10 ! number of iterations
1029	REAL(wp), PARAMETER :: zepsilon = 0.1_wp ! characteristic thickness for enhanced conduction
1030	!
1031	INTEGER :: ji, jj, jl ! dummy loop indices
1032	INTEGER :: iter ! local integer
1033	REAL(wp) :: zfac, zfac2, zfac3 ! local scalars
1034	REAL(wp) :: zkeff_h, ztsu, ztsu0 !
1035	REAL(wp) :: zqc, zqnet !
1036	REAL(wp) :: zhe, zqa0 !
1037	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zgfac ! enhanced conduction factor
1038	!!---------------------------------------------------------------------
1039
1040	! -------------------------------------!
1041	! I Enhanced conduction factor !
1042	! -------------------------------------!
1043	! Emulates the enhancement of conduction by unresolved thin ice (ld_virtual_itd = T)
1044	! Fichefet and Morales Maqueda, JGR 1997
1045	!
1046	zgfac(:,:,:) = 1._wp
1047
1048	IF( ld_virtual_itd ) THEN
1049	!
1050	zfac = 1._wp / ( rn_cnd_s + rcnd_i )
1051	zfac2 = EXP(1._wp) * 0.5_wp * zepsilon
1052	zfac3 = 2._wp / zepsilon
1053	!
1054	DO jl = 1, jpl
1055	DO jj = 1 , jpj
1056	DO ji = 1, jpi
1057	zhe = ( rn_cnd_s * phi(ji,jj,jl) + rcnd_i * phs(ji,jj,jl) ) * zfac ! Effective thickness
1058	IF( zhe >= zfac2 ) zgfac(ji,jj,jl) = MIN( 2._wp, 0.5_wp * ( 1._wp + LOG( zhe * zfac3 ) ) ) ! Enhanced conduction factor
1059	END DO
1060	END DO
1061	END DO
1062	!
1063	ENDIF
1064
1065	! -------------------------------------------------------------!
1066	! II Surface temperature and conduction flux !
1067	! -------------------------------------------------------------!
1068	!
1069	zfac = rcnd_i * rn_cnd_s
1070	!
1071	DO jl = 1, jpl
1072	DO jj = 1 , jpj
1073	DO ji = 1, jpi
1074	!
1075	zkeff_h = zfac * zgfac(ji,jj,jl) / & ! Effective conductivity of the snow-ice system divided by thickness
1076	& ( rcnd_i * phs(ji,jj,jl) + rn_cnd_s * MAX( 0.01, phi(ji,jj,jl) ) )
1077	ztsu = ptsu(ji,jj,jl) ! Store current iteration temperature
1078	ztsu0 = ptsu(ji,jj,jl) ! Store initial surface temperature
1079	zqa0 = qsr_ice(ji,jj,jl) - qtr_ice_top(ji,jj,jl) + qns_ice(ji,jj,jl) ! Net initial atmospheric heat flux
1080	!
1081	DO iter = 1, nit ! --- Iterative loop
1082	zqc = zkeff_h * ( ztsu - ptb(ji,jj) ) ! Conduction heat flux through snow-ice system (>0 downwards)
1083	zqnet = zqa0 + dqns_ice(ji,jj,jl) * ( ztsu - ptsu(ji,jj,jl) ) - zqc ! Surface energy budget
1084	ztsu = ztsu - zqnet / ( dqns_ice(ji,jj,jl) - zkeff_h ) ! Temperature update
1085	END DO
1086	!
1087	ptsu (ji,jj,jl) = MIN( rt0, ztsu )
1088	qcn_ice(ji,jj,jl) = zkeff_h * ( ptsu(ji,jj,jl) - ptb(ji,jj) )
1089	qns_ice(ji,jj,jl) = qns_ice(ji,jj,jl) + dqns_ice(ji,jj,jl) * ( ptsu(ji,jj,jl) - ztsu0 )
1090	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) ) &
1091	& * MAX( 0._wp , SIGN( 1._wp, ptsu(ji,jj,jl) - rt0 ) )
1092
1093	! --- Diagnose the heat loss due to changing non-solar flux (as in icethd_zdf_bl99) --- !
1094	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)
1095
1096	END DO
1097	END DO
1098	!
1099	END DO
1100	!
1101	END SUBROUTINE blk_ice_qcn
1102
1103
1104	SUBROUTINE Cdn10_Lupkes2012( Cd )
1105	!!----------------------------------------------------------------------
1106	!! * ROUTINE Cdn10_Lupkes2012 *
1107	!!
1108	!! ** Purpose : Recompute the neutral air-ice drag referenced at 10m
1109	!! to make it dependent on edges at leads, melt ponds and flows.
1110	!! After some approximations, this can be resumed to a dependency
1111	!! on ice concentration.
1112	!!
1113	!! ** Method : The parameterization is taken from Lupkes et al. (2012) eq.(50)
1114	!! with the highest level of approximation: level4, eq.(59)
1115	!! The generic drag over a cell partly covered by ice can be re-written as follows:
1116	!!
1117	!! Cd = Cdw * (1-A) + Cdi * A + Ce * (1-A)*(nu+1/(10beta)) * A**mu
1118	!!
1119	!! Ce = 2.23e-3 , as suggested by Lupkes (eq. 59)
1120	!! nu = mu = beta = 1 , as suggested by Lupkes (eq. 59)
1121	!! A is the concentration of ice minus melt ponds (if any)
1122	!!
1123	!! This new drag has a parabolic shape (as a function of A) starting at
1124	!! Cdw(say 1.5e-3) for A=0, reaching 1.97e-3 for A~0.5
1125	!! and going down to Cdi(say 1.4e-3) for A=1
1126	!!
1127	!! It is theoretically applicable to all ice conditions (not only MIZ)
1128	!! => see Lupkes et al (2013)
1129	!!
1130	!! ** References : Lupkes et al. JGR 2012 (theory)
1131	!! Lupkes et al. GRL 2013 (application to GCM)
1132	!!
1133	!!----------------------------------------------------------------------
1134	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Cd
1135	REAL(wp), PARAMETER :: zCe = 2.23e-03_wp
1136	REAL(wp), PARAMETER :: znu = 1._wp
1137	REAL(wp), PARAMETER :: zmu = 1._wp
1138	REAL(wp), PARAMETER :: zbeta = 1._wp
1139	REAL(wp) :: zcoef
1140	!!----------------------------------------------------------------------
1141	zcoef = znu + 1._wp / ( 10._wp * zbeta )
1142
1143	! generic drag over a cell partly covered by ice
1144	!!Cd(:,:) = Cd_oce(:,:) * ( 1._wp - at_i_b(:,:) ) + & ! pure ocean drag
1145	!! & Cd_ice * at_i_b(:,:) + & ! pure ice drag
1146	!! & zCe * ( 1._wp - at_i_b(:,:) )*zcoef at_i_b(:,:)**zmu ! change due to sea-ice morphology
1147
1148	! ice-atm drag
1149	Cd(:,:) = Cd_ice + & ! pure ice drag
1150	& zCe * ( 1._wp - at_i_b(:,:) )*zcoef at_i_b(:,:)**(zmu-1._wp) ! change due to sea-ice morphology
1151
1152	END SUBROUTINE Cdn10_Lupkes2012
1153
1154
1155	SUBROUTINE Cdn10_Lupkes2015( Cd, Ch )
1156	!!----------------------------------------------------------------------
1157	!! * ROUTINE Cdn10_Lupkes2015 *
1158	!!
1159	!! ** pUrpose : Alternative turbulent transfert coefficients formulation
1160	!! between sea-ice and atmosphere with distinct momentum
1161	!! and heat coefficients depending on sea-ice concentration
1162	!! and atmospheric stability (no meltponds effect for now).
1163	!!
1164	!! ** Method : The parameterization is adapted from Lupkes et al. (2015)
1165	!! and ECHAM6 atmospheric model. Compared to Lupkes2012 scheme,
1166	!! it considers specific skin and form drags (Andreas et al. 2010)
1167	!! to compute neutral transfert coefficients for both heat and
1168	!! momemtum fluxes. Atmospheric stability effect on transfert
1169	!! coefficient is also taken into account following Louis (1979).
1170	!!
1171	!! ** References : Lupkes et al. JGR 2015 (theory)
1172	!! Lupkes et al. ECHAM6 documentation 2015 (implementation)
1173	!!
1174	!!----------------------------------------------------------------------
1175	!
1176	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Cd
1177	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Ch
1178	REAL(wp), DIMENSION(jpi,jpj) :: ztm_su, zst, zqo_sat, zqi_sat
1179	!
1180	! ECHAM6 constants
1181	REAL(wp), PARAMETER :: z0_skin_ice = 0.69e-3_wp ! Eq. 43 [m]
1182	REAL(wp), PARAMETER :: z0_form_ice = 0.57e-3_wp ! Eq. 42 [m]
1183	REAL(wp), PARAMETER :: z0_ice = 1.00e-3_wp ! Eq. 15 [m]
1184	REAL(wp), PARAMETER :: zce10 = 2.80e-3_wp ! Eq. 41
1185	REAL(wp), PARAMETER :: zbeta = 1.1_wp ! Eq. 41
1186	REAL(wp), PARAMETER :: zc = 5._wp ! Eq. 13
1187	REAL(wp), PARAMETER :: zc2 = zc * zc
1188	REAL(wp), PARAMETER :: zam = 2. * zc ! Eq. 14
1189	REAL(wp), PARAMETER :: zah = 3. * zc ! Eq. 30
1190	REAL(wp), PARAMETER :: z1_alpha = 1._wp / 0.2_wp ! Eq. 51
1191	REAL(wp), PARAMETER :: z1_alphaf = z1_alpha ! Eq. 56
1192	REAL(wp), PARAMETER :: zbetah = 1.e-3_wp ! Eq. 26
1193	REAL(wp), PARAMETER :: zgamma = 1.25_wp ! Eq. 26
1194	REAL(wp), PARAMETER :: z1_gamma = 1._wp / zgamma
1195	REAL(wp), PARAMETER :: r1_3 = 1._wp / 3._wp
1196	!
1197	INTEGER :: ji, jj ! dummy loop indices
1198	REAL(wp) :: zthetav_os, zthetav_is, zthetav_zu
1199	REAL(wp) :: zrib_o, zrib_i
1200	REAL(wp) :: zCdn_skin_ice, zCdn_form_ice, zCdn_ice
1201	REAL(wp) :: zChn_skin_ice, zChn_form_ice
1202	REAL(wp) :: z0w, z0i, zfmi, zfmw, zfhi, zfhw
1203	REAL(wp) :: zCdn_form_tmp
1204	!!----------------------------------------------------------------------
1205
1206	! mean temperature
1207	WHERE( at_i_b(:,:) > 1.e-20 ) ; ztm_su(:,:) = SUM( t_su(:,:,:) * a_i_b(:,:,:) , dim=3 ) / at_i_b(:,:)
1208	ELSEWHERE ; ztm_su(:,:) = rt0
1209	ENDWHERE
1210
1211	! Momentum Neutral Transfert Coefficients (should be a constant)
1212	zCdn_form_tmp = zce10 * ( LOG( 10._wp / z0_form_ice + 1._wp ) / LOG( rn_zu / z0_form_ice + 1._wp ) )**2 ! Eq. 40
1213	zCdn_skin_ice = ( vkarmn / LOG( rn_zu / z0_skin_ice + 1._wp ) )**2 ! Eq. 7
1214	zCdn_ice = zCdn_skin_ice ! Eq. 7 (cf Lupkes email for details)
1215	!zCdn_ice = 1.89e-3 ! old ECHAM5 value (cf Eq. 32)
1216
1217	! Heat Neutral Transfert Coefficients
1218	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)
1219
1220	! Atmospheric and Surface Variables
1221	zst(:,:) = sst_m(:,:) + rt0 ! convert SST from Celcius to Kelvin
1222	zqo_sat(:,:) = 0.98_wp * q_sat( zst(:,:) , sf(jp_slp)%fnow(:,:,1) ) ! saturation humidity over ocean [kg/kg]
1223	zqi_sat(:,:) = 0.98_wp * q_sat( ztm_su(:,:), sf(jp_slp)%fnow(:,:,1) ) ! saturation humidity over ice [kg/kg]
1224	!
1225	DO jj = 2, jpjm1 ! reduced loop is necessary for reproducibility
1226	DO ji = fs_2, fs_jpim1
1227	! Virtual potential temperature [K]
1228	zthetav_os = zst(ji,jj) * ( 1._wp + rctv0 * zqo_sat(ji,jj) ) ! over ocean
1229	zthetav_is = ztm_su(ji,jj) * ( 1._wp + rctv0 * zqi_sat(ji,jj) ) ! ocean ice
1230	zthetav_zu = t_zu (ji,jj) * ( 1._wp + rctv0 * q_zu(ji,jj) ) ! at zu
1231
1232	! Bulk Richardson Number (could use Ri_bulk function from aerobulk instead)
1233	zrib_o = grav / zthetav_os * ( zthetav_zu - zthetav_os ) * rn_zu / MAX( 0.5, wndm(ji,jj) )**2 ! over ocean
1234	zrib_i = grav / zthetav_is * ( zthetav_zu - zthetav_is ) * rn_zu / MAX( 0.5, wndm_ice(ji,jj) )**2 ! over ice
1235
1236	! Momentum and Heat Neutral Transfert Coefficients
1237	zCdn_form_ice = zCdn_form_tmp * at_i_b(ji,jj) * ( 1._wp - at_i_b(ji,jj) )**zbeta ! Eq. 40
1238	zChn_form_ice = zCdn_form_ice / ( 1._wp + ( LOG( z1_alphaf ) / vkarmn ) * SQRT( zCdn_form_ice ) ) ! Eq. 53
1239
1240	! Momentum and Heat Stability functions (possibility to use psi_m_ecmwf instead)
1241	z0w = rn_zu * EXP( -1._wp * vkarmn / SQRT( Cdn_oce(ji,jj) ) ) ! over water
1242	z0i = z0_skin_ice ! over ice (cf Lupkes email for details)
1243	IF( zrib_o <= 0._wp ) THEN
1244	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
1245	zfhw = ( 1._wp + ( zbetah * ( zthetav_os - zthetav_zu )*r1_3 / ( Chn_oce(ji,jj) MAX(0.01, wndm(ji,jj)) ) & ! Eq. 26
1246	& )zgamma )z1_gamma
1247	ELSE
1248	zfmw = 1._wp / ( 1._wp + zam * zrib_o / SQRT( 1._wp + zrib_o ) ) ! Eq. 12
1249	zfhw = 1._wp / ( 1._wp + zah * zrib_o / SQRT( 1._wp + zrib_o ) ) ! Eq. 28
1250	ENDIF
1251
1252	IF( zrib_i <= 0._wp ) THEN
1253	zfmi = 1._wp - zam * zrib_i / (1._wp + 3._wp * zc2 * zCdn_ice * SQRT( -zrib_i * ( rn_zu / z0i + 1._wp))) ! Eq. 9
1254	zfhi = 1._wp - zah * zrib_i / (1._wp + 3._wp * zc2 * zCdn_ice * SQRT( -zrib_i * ( rn_zu / z0i + 1._wp))) ! Eq. 25
1255	ELSE
1256	zfmi = 1._wp / ( 1._wp + zam * zrib_i / SQRT( 1._wp + zrib_i ) ) ! Eq. 11
1257	zfhi = 1._wp / ( 1._wp + zah * zrib_i / SQRT( 1._wp + zrib_i ) ) ! Eq. 27
1258	ENDIF
1259
1260	! Momentum Transfert Coefficients (Eq. 38)
1261	Cd(ji,jj) = zCdn_skin_ice * zfmi + &
1262	& 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) )
1263
1264	! Heat Transfert Coefficients (Eq. 49)
1265	Ch(ji,jj) = zChn_skin_ice * zfhi + &
1266	& 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) )
1267	!
1268	END DO
1269	END DO
1270	CALL lbc_lnk_multi( 'sbcblk', Cd, 'T', 1., Ch, 'T', 1. )
1271	!
1272	END SUBROUTINE Cdn10_Lupkes2015
1273
1274	#endif
1275
1276	!!======================================================================
1277	END MODULE sbcblk

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