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sbcblk.F90 in NEMO/trunk/cfgs/SPITZ12/MY_SRC – NEMO

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source: NEMO/trunk/cfgs/SPITZ12/MY_SRC/sbcblk.F90 @ 9769

Last change on this file since 9769 was 9769, checked in by clem, 6 years ago
remaining cp_ice_msh to be removed
File size: 70.8 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 Jules 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 JULES coupler)
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, tm_su, rn_cnd_s
49	USE icethd_dh ! for CALL ice_thd_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 iceforcing
69	PUBLIC blk_ice_flx ! routine called in iceforcing
70	PUBLIC blk_ice_qcn ! routine called in iceforcing
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	!!clem INTEGER , PARAMETER :: jpfld =10 ! maximum number of files to read
83	INTEGER , PARAMETER :: jpfld = 8 ! 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_tdif =10 ! 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: sbcblk.F90 6416 2016-04-01 12:22:17Z clem $
139	!! Software governed by the CeCILL licence (./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	IF( lk_mpp ) CALL mpp_sum ( sbc_blk_alloc )
151	IF( sbc_blk_alloc /= 0 ) CALL ctl_warn('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 :: ifpr, 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 ! " "
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, &
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', lwp )
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', lwp )
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%nfreqh /= 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	!!clem slf_i(jp_slp) = sn_slp ; slf_i(jp_tdif) = sn_tdif
218	!
219	lhftau = ln_taudif !- add an extra field if HF stress is used
220	!!clem jfld = jpfld - COUNT( (/.NOT.lhftau/) )
221	jfld = jpfld
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	DO ifpr= 1, jfld
227	ALLOCATE( sf(ifpr)%fnow(jpi,jpj,1) )
228	IF( slf_i(ifpr)%ln_tint ) ALLOCATE( sf(ifpr)%fdta(jpi,jpj,1,2) )
229	IF( slf_i(ifpr)%nfreqh > 0. .AND. MOD( 3600. * slf_i(ifpr)%nfreqh , REAL(nn_fsbc) * rdt) /= 0. ) &
230	& CALL ctl_warn( 'sbc_blk_init: sbcmod timestep rdt*nn_fsbc is NOT a submultiple of atmospheric forcing frequency.', &
231	& ' This is not ideal. You should consider changing either rdt or nn_fsbc value...' )
232
233	END DO
234	! !- fill the bulk structure with namelist informations
235	CALL fld_fill( sf, slf_i, cn_dir, 'sbc_blk_init', 'surface boundary condition -- bulk formulae', 'namsbc_blk' )
236	!
237	IF ( ln_wave ) THEN
238	!Activated wave module but neither drag nor stokes drift activated
239	IF ( .NOT.(ln_cdgw .OR. ln_sdw .OR. ln_tauwoc .OR. ln_stcor ) ) THEN
240	CALL ctl_warn( 'Ask for wave coupling but ln_cdgw=F, ln_sdw=F, ln_tauwoc=F, ln_stcor=F')
241	!drag coefficient read from wave model definable only with mfs bulk formulae and core
242	ELSEIF (ln_cdgw .AND. .NOT. ln_NCAR ) THEN
243	CALL ctl_stop( 'drag coefficient read from wave model definable only with mfs bulk formulae and core')
244	ELSEIF (ln_stcor .AND. .NOT. ln_sdw) THEN
245	CALL ctl_stop( 'Stokes-Coriolis term calculated only if activated Stokes Drift ln_sdw=T')
246	ENDIF
247	ELSE
248	IF ( ln_cdgw .OR. ln_sdw .OR. ln_tauwoc .OR. ln_stcor ) &
249	& CALL ctl_stop( 'Not Activated Wave Module (ln_wave=F) but asked coupling ', &
250	& 'with drag coefficient (ln_cdgw =T) ' , &
251	& 'or Stokes Drift (ln_sdw=T) ' , &
252	& 'or ocean stress modification due to waves (ln_tauwoc=T) ', &
253	& 'or Stokes-Coriolis term (ln_stcori=T)' )
254	ENDIF
255	!
256	!
257	IF(lwp) THEN !** Control print
258	!
259	WRITE(numout,) ! namelist
260	WRITE(numout,*) ' Namelist namsbc_blk (other than data information):'
261	WRITE(numout,*) ' "NCAR" algorithm (Large and Yeager 2008) ln_NCAR = ', ln_NCAR
262	WRITE(numout,*) ' "COARE 3.0" algorithm (Fairall et al. 2003) ln_COARE_3p0 = ', ln_COARE_3p0
263	WRITE(numout,*) ' "COARE 3.5" algorithm (Edson et al. 2013) ln_COARE_3p5 = ', ln_COARE_3p0
264	WRITE(numout,*) ' "ECMWF" algorithm (IFS cycle 31) ln_ECMWF = ', ln_ECMWF
265	WRITE(numout,*) ' add High freq.contribution to the stress module ln_taudif = ', ln_taudif
266	WRITE(numout,*) ' Air temperature and humidity reference height (m) rn_zqt = ', rn_zqt
267	WRITE(numout,*) ' Wind vector reference height (m) rn_zu = ', rn_zu
268	WRITE(numout,*) ' factor applied on precipitation (total & snow) rn_pfac = ', rn_pfac
269	WRITE(numout,*) ' factor applied on evaporation rn_efac = ', rn_efac
270	WRITE(numout,*) ' factor applied on ocean/ice velocity rn_vfac = ', rn_vfac
271	WRITE(numout,*) ' (form absolute (=0) to relative winds(=1))'
272	WRITE(numout,*) ' use ice-atm drag from Lupkes2012 ln_Cd_L12 = ', ln_Cd_L12
273	WRITE(numout,*) ' use ice-atm drag from Lupkes2015 ln_Cd_L15 = ', ln_Cd_L15
274	!
275	WRITE(numout,*)
276	SELECT CASE( nblk ) !* Print the choice of bulk algorithm
277	CASE( np_NCAR ) ; WRITE(numout,*) ' ==>>> "NCAR" algorithm (Large and Yeager 2008)'
278	CASE( np_COARE_3p0 ) ; WRITE(numout,*) ' ==>>> "COARE 3.0" algorithm (Fairall et al. 2003)'
279	CASE( np_COARE_3p5 ) ; WRITE(numout,*) ' ==>>> "COARE 3.5" algorithm (Edson et al. 2013)'
280	CASE( np_ECMWF ) ; WRITE(numout,*) ' ==>>> "ECMWF" algorithm (IFS cycle 31)'
281	END SELECT
282	!
283	ENDIF
284	!
285	END SUBROUTINE sbc_blk_init
286
287
288	SUBROUTINE sbc_blk( kt )
289	!!---------------------------------------------------------------------
290	!! * ROUTINE sbc_blk *
291	!!
292	!! ** Purpose : provide at each time step the surface ocean fluxes
293	!! (momentum, heat, freshwater and runoff)
294	!!
295	!! ** Method : (1) READ each fluxes in NetCDF files:
296	!! the 10m wind velocity (i-component) (m/s) at T-point
297	!! the 10m wind velocity (j-component) (m/s) at T-point
298	!! the 10m or 2m specific humidity ( % )
299	!! the solar heat (W/m2)
300	!! the Long wave (W/m2)
301	!! the 10m or 2m air temperature (Kelvin)
302	!! the total precipitation (rain+snow) (Kg/m2/s)
303	!! the snow (solid prcipitation) (kg/m2/s)
304	!! the tau diff associated to HF tau (N/m2) at T-point (ln_taudif=T)
305	!! (2) CALL blk_oce
306	!!
307	!! C A U T I O N : never mask the surface stress fields
308	!! the stress is assumed to be in the (i,j) mesh referential
309	!!
310	!! ** Action : defined at each time-step at the air-sea interface
311	!! - utau, vtau i- and j-component of the wind stress
312	!! - taum wind stress module at T-point
313	!! - wndm wind speed module at T-point over free ocean or leads in presence of sea-ice
314	!! - qns, qsr non-solar and solar heat fluxes
315	!! - emp upward mass flux (evapo. - precip.)
316	!! - sfx salt flux due to freezing/melting (non-zero only if ice is present)
317	!!
318	!! ** References : Large & Yeager, 2004 / Large & Yeager, 2008
319	!! Brodeau et al. Ocean Modelling 2010
320	!!----------------------------------------------------------------------
321	INTEGER, INTENT(in) :: kt ! ocean time step
322	!!---------------------------------------------------------------------
323	!
324	CALL fld_read( kt, nn_fsbc, sf ) ! input fields provided at the current time-step
325	!
326	! ! compute the surface ocean fluxes using bulk formulea
327	IF( MOD( kt - 1, nn_fsbc ) == 0 ) CALL blk_oce( kt, sf, sst_m, ssu_m, ssv_m )
328
329	#if defined key_cice
330	IF( MOD( kt - 1, nn_fsbc ) == 0 ) THEN
331	qlw_ice(:,:,1) = sf(jp_qlw )%fnow(:,:,1)
332	IF( ln_dm2dc ) THEN ; qsr_ice(:,:,1) = sbc_dcy( sf(jp_qsr)%fnow(:,:,1) )
333	ELSE ; qsr_ice(:,:,1) = sf(jp_qsr)%fnow(:,:,1)
334	ENDIF
335	tatm_ice(:,:) = sf(jp_tair)%fnow(:,:,1)
336	qatm_ice(:,:) = sf(jp_humi)%fnow(:,:,1)
337	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac
338	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac
339	wndi_ice(:,:) = sf(jp_wndi)%fnow(:,:,1)
340	wndj_ice(:,:) = sf(jp_wndj)%fnow(:,:,1)
341	ENDIF
342	#endif
343	!
344	END SUBROUTINE sbc_blk
345
346
347	SUBROUTINE blk_oce( kt, sf, pst, pu, pv )
348	!!---------------------------------------------------------------------
349	!! * ROUTINE blk_oce *
350	!!
351	!! ** Purpose : provide the momentum, heat and freshwater fluxes at
352	!! the ocean surface at each time step
353	!!
354	!! ** Method : bulk formulea for the ocean using atmospheric
355	!! fields read in sbc_read
356	!!
357	!! ** Outputs : - utau : i-component of the stress at U-point (N/m2)
358	!! - vtau : j-component of the stress at V-point (N/m2)
359	!! - taum : Wind stress module at T-point (N/m2)
360	!! - wndm : Wind speed module at T-point (m/s)
361	!! - qsr : Solar heat flux over the ocean (W/m2)
362	!! - qns : Non Solar heat flux over the ocean (W/m2)
363	!! - emp : evaporation minus precipitation (kg/m2/s)
364	!!
365	!! ** Nota : sf has to be a dummy argument for AGRIF on NEC
366	!!---------------------------------------------------------------------
367	INTEGER , INTENT(in ) :: kt ! time step index
368	TYPE(fld), INTENT(inout), DIMENSION(:) :: sf ! input data
369	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pst ! surface temperature [Celcius]
370	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pu ! surface current at U-point (i-component) [m/s]
371	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pv ! surface current at V-point (j-component) [m/s]
372	!
373	INTEGER :: ji, jj ! dummy loop indices
374	REAL(wp) :: zztmp ! local variable
375	REAL(wp), DIMENSION(jpi,jpj) :: zwnd_i, zwnd_j ! wind speed components at T-point
376	REAL(wp), DIMENSION(jpi,jpj) :: zsq ! specific humidity at pst
377	REAL(wp), DIMENSION(jpi,jpj) :: zqlw, zqsb ! long wave and sensible heat fluxes
378	REAL(wp), DIMENSION(jpi,jpj) :: zqla, zevap ! latent heat fluxes and evaporation
379	REAL(wp), DIMENSION(jpi,jpj) :: zst ! surface temperature in Kelvin
380	REAL(wp), DIMENSION(jpi,jpj) :: zU_zu ! bulk wind speed at height zu [m/s]
381	REAL(wp), DIMENSION(jpi,jpj) :: ztpot ! potential temperature of air at z=rn_zqt [K]
382	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa ! density of air [kg/m^3]
383	!!---------------------------------------------------------------------
384	!
385	! local scalars ( place there for vector optimisation purposes)
386	zst(:,:) = pst(:,:) + rt0 ! convert SST from Celcius to Kelvin (and set minimum value far above 0 K)
387
388	! ----------------------------------------------------------------------------- !
389	! 0 Wind components and module at T-point relative to the moving ocean !
390	! ----------------------------------------------------------------------------- !
391
392	! ... components ( U10m - U_oce ) at T-point (unmasked)
393	!!gm move zwnd_i (_j) set to zero inside the key_cyclone ???
394	zwnd_i(:,:) = 0._wp
395	zwnd_j(:,:) = 0._wp
396	#if defined key_cyclone
397	CALL wnd_cyc( kt, zwnd_i, zwnd_j ) ! add analytical tropical cyclone (Vincent et al. JGR 2012)
398	DO jj = 2, jpjm1
399	DO ji = fs_2, fs_jpim1 ! vect. opt.
400	sf(jp_wndi)%fnow(ji,jj,1) = sf(jp_wndi)%fnow(ji,jj,1) + zwnd_i(ji,jj)
401	sf(jp_wndj)%fnow(ji,jj,1) = sf(jp_wndj)%fnow(ji,jj,1) + zwnd_j(ji,jj)
402	END DO
403	END DO
404	#endif
405	DO jj = 2, jpjm1
406	DO ji = fs_2, fs_jpim1 ! vect. opt.
407	zwnd_i(ji,jj) = ( sf(jp_wndi)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( pu(ji-1,jj ) + pu(ji,jj) ) )
408	zwnd_j(ji,jj) = ( sf(jp_wndj)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( pv(ji ,jj-1) + pv(ji,jj) ) )
409	END DO
410	END DO
411	CALL lbc_lnk_multi( zwnd_i, 'T', -1., zwnd_j, 'T', -1. )
412	! ... scalar wind ( = \| U10m - U_oce \| ) at T-point (masked)
413	wndm(:,:) = SQRT( zwnd_i(:,:) * zwnd_i(:,:) &
414	& + zwnd_j(:,:) * zwnd_j(:,:) ) * tmask(:,:,1)
415
416	! ----------------------------------------------------------------------------- !
417	! I Radiative FLUXES !
418	! ----------------------------------------------------------------------------- !
419
420	! ocean albedo assumed to be constant + modify now Qsr to include the diurnal cycle ! Short Wave
421	zztmp = 1. - albo
422	IF( ln_dm2dc ) THEN ; qsr(:,:) = zztmp * sbc_dcy( sf(jp_qsr)%fnow(:,:,1) ) * tmask(:,:,1)
423	ELSE ; qsr(:,:) = zztmp * sf(jp_qsr)%fnow(:,:,1) * tmask(:,:,1)
424	ENDIF
425
426	zqlw(:,:) = ( sf(jp_qlw)%fnow(:,:,1) - Stef * zst(:,:)zst(:,:)zst(:,:)zst(:,:) ) tmask(:,:,1) ! Long Wave
427
428	! ----------------------------------------------------------------------------- !
429	! II Turbulent FLUXES !
430	! ----------------------------------------------------------------------------- !
431
432	! ... specific humidity at SST and IST tmask(
433	!!clem zsq(:,:) = 0.98 * q_sat( zst(:,:), sf(jp_slp)%fnow(:,:,1) )
434	zsq(:,:) = 0.98 * q_sat( zst(:,:), 101300. )
435	!!
436	!! Estimate of potential temperature at z=rn_zqt, based on adiabatic lapse-rate
437	!! (see Josey, Gulev & Yu, 2013) / doi=10.1016/B978-0-12-391851-2.00005-2
438	!! (since reanalysis products provide T at z, not theta !)
439	ztpot = sf(jp_tair)%fnow(:,:,1) + gamma_moist( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1) ) * rn_zqt
440
441	SELECT CASE( nblk ) !== transfer coefficients ==! Cd, Ch, Ce at T-point
442	!
443	CASE( np_NCAR ) ; CALL turb_ncar ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! NCAR-COREv2
444	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
445	CASE( np_COARE_3p0 ) ; CALL turb_coare ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! COARE v3.0
446	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
447	CASE( np_COARE_3p5 ) ; CALL turb_coare3p5( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! COARE v3.5
448	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
449	CASE( np_ECMWF ) ; CALL turb_ecmwf ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! ECMWF
450	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
451	CASE DEFAULT
452	CALL ctl_stop( 'STOP', 'sbc_oce: non-existing bulk formula selected' )
453	END SELECT
454
455	! ! Compute true air density :
456	IF( ABS(rn_zu - rn_zqt) > 0.01 ) THEN ! At zu: (probably useless to remove zrhogravrn_zu from SLP...)
457	!!clem zrhoa(:,:) = rho_air( t_zu(:,:) , q_zu(:,:) , sf(jp_slp)%fnow(:,:,1) )
458	zrhoa(:,:) = rho_air( t_zu(:,:) , q_zu(:,:) , 101300. )
459	ELSE ! At zt:
460	!!clem zrhoa(:,:) = rho_air( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1) )
461	zrhoa(:,:) = rho_air( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), 101300. )
462	END IF
463
464	!! CALL iom_put( "Cd_oce", Cd_atm) ! output value of pure ocean-atm. transfer coef.
465	!! CALL iom_put( "Ch_oce", Ch_atm) ! output value of pure ocean-atm. transfer coef.
466
467	DO jj = 1, jpj ! tau module, i and j component
468	DO ji = 1, jpi
469	zztmp = zrhoa(ji,jj) * zU_zu(ji,jj) * Cd_atm(ji,jj) ! using bulk wind speed
470	taum (ji,jj) = zztmp * wndm (ji,jj)
471	zwnd_i(ji,jj) = zztmp * zwnd_i(ji,jj)
472	zwnd_j(ji,jj) = zztmp * zwnd_j(ji,jj)
473	END DO
474	END DO
475
476	! ! add the HF tau contribution to the wind stress module
477	!!clem IF( lhftau ) taum(:,:) = taum(:,:) + sf(jp_tdif)%fnow(:,:,1)
478
479	CALL iom_put( "taum_oce", taum ) ! output wind stress module
480
481	! ... utau, vtau at U- and V_points, resp.
482	! Note the use of 0.5*(2-umask) in order to unmask the stress along coastlines
483	! Note the use of MAX(tmask(i,j),tmask(i+1,j) is to mask tau over ice shelves
484	DO jj = 1, jpjm1
485	DO ji = 1, fs_jpim1
486	utau(ji,jj) = 0.5 * ( 2. - umask(ji,jj,1) ) * ( zwnd_i(ji,jj) + zwnd_i(ji+1,jj ) ) &
487	& * MAX(tmask(ji,jj,1),tmask(ji+1,jj,1))
488	vtau(ji,jj) = 0.5 * ( 2. - vmask(ji,jj,1) ) * ( zwnd_j(ji,jj) + zwnd_j(ji ,jj+1) ) &
489	& * MAX(tmask(ji,jj,1),tmask(ji,jj+1,1))
490	END DO
491	END DO
492	CALL lbc_lnk_multi( utau, 'U', -1., vtau, 'V', -1. )
493
494	! Turbulent fluxes over ocean
495	! -----------------------------
496
497	! zqla used as temporary array, for rho*U (common term of bulk formulae):
498	zqla(:,:) = zrhoa(:,:) * zU_zu(:,:) * tmask(:,:,1)
499
500	IF( ABS( rn_zu - rn_zqt) < 0.01_wp ) THEN
501	!! q_air and t_air are given at 10m (wind reference height)
502	zevap(:,:) = rn_efacMAX( 0._wp, zqla(:,:)Ce_atm(:,:)*(zsq(:,:) - sf(jp_humi)%fnow(:,:,1)) ) ! Evaporation, using bulk wind speed
503	zqsb (:,:) = cp_air(sf(jp_humi)%fnow(:,:,1))zqla(:,:)Ch_atm(:,:)*(zst(:,:) - ztpot(:,:) ) ! Sensible Heat, using bulk wind speed
504	ELSE
505	!! q_air and t_air are not given at 10m (wind reference height)
506	! Values of temp. and hum. adjusted to height of wind during bulk algorithm iteration must be used!!!
507	zevap(:,:) = rn_efacMAX( 0._wp, zqla(:,:)Ce_atm(:,:)*(zsq(:,:) - q_zu(:,:) ) ) ! Evaporation, using bulk wind speed
508	zqsb (:,:) = cp_air(sf(jp_humi)%fnow(:,:,1))zqla(:,:)Ch_atm(:,:)*(zst(:,:) - t_zu(:,:) ) ! Sensible Heat, using bulk wind speed
509	ENDIF
510
511	zqla(:,:) = L_vap(zst(:,:)) * zevap(:,:) ! Latent Heat flux
512
513
514	IF(ln_ctl) THEN
515	CALL prt_ctl( tab2d_1=zqla , clinfo1=' blk_oce: zqla : ', tab2d_2=Ce_atm , clinfo2=' Ce_oce : ' )
516	CALL prt_ctl( tab2d_1=zqsb , clinfo1=' blk_oce: zqsb : ', tab2d_2=Ch_atm , clinfo2=' Ch_oce : ' )
517	CALL prt_ctl( tab2d_1=zqlw , clinfo1=' blk_oce: zqlw : ', tab2d_2=qsr, clinfo2=' qsr : ' )
518	CALL prt_ctl( tab2d_1=zsq , clinfo1=' blk_oce: zsq : ', tab2d_2=zst, clinfo2=' zst : ' )
519	CALL prt_ctl( tab2d_1=utau , clinfo1=' blk_oce: utau : ', mask1=umask, &
520	& tab2d_2=vtau , clinfo2= ' vtau : ', mask2=vmask )
521	CALL prt_ctl( tab2d_1=wndm , clinfo1=' blk_oce: wndm : ')
522	CALL prt_ctl( tab2d_1=zst , clinfo1=' blk_oce: zst : ')
523	ENDIF
524
525	! ----------------------------------------------------------------------------- !
526	! III Total FLUXES !
527	! ----------------------------------------------------------------------------- !
528	!
529	emp (:,:) = ( zevap(:,:) & ! mass flux (evap. - precip.)
530	& - sf(jp_prec)%fnow(:,:,1) * rn_pfac ) * tmask(:,:,1)
531	!
532	qns(:,:) = zqlw(:,:) - zqsb(:,:) - zqla(:,:) & ! Downward Non Solar
533	& - sf(jp_snow)%fnow(:,:,1) * rn_pfac * lfus & ! remove latent melting heat for solid precip
534	& - zevap(:,:) * pst(:,:) * rcp & ! remove evap heat content at SST
535	& + ( sf(jp_prec)%fnow(:,:,1) - sf(jp_snow)%fnow(:,:,1) ) * rn_pfac & ! add liquid precip heat content at Tair
536	& * ( sf(jp_tair)%fnow(:,:,1) - rt0 ) * rcp &
537	& + sf(jp_snow)%fnow(:,:,1) * rn_pfac & ! add solid precip heat content at min(Tair,Tsnow)
538	& * ( MIN( sf(jp_tair)%fnow(:,:,1), rt0_snow ) - rt0 ) * cpic
539	qns(:,:) = qns(:,:) * tmask(:,:,1)
540	!
541	#if defined key_si3
542	qns_oce(:,:) = zqlw(:,:) - zqsb(:,:) - zqla(:,:) ! non solar without emp (only needed by SI3)
543	qsr_oce(:,:) = qsr(:,:)
544	#endif
545	!
546	IF ( nn_ice == 0 ) THEN
547	CALL iom_put( "qlw_oce" , zqlw ) ! output downward longwave heat over the ocean
548	CALL iom_put( "qsb_oce" , - zqsb ) ! output downward sensible heat over the ocean
549	CALL iom_put( "qla_oce" , - zqla ) ! output downward latent heat over the ocean
550	CALL iom_put( "qemp_oce", qns-zqlw+zqsb+zqla ) ! output downward heat content of E-P over the ocean
551	CALL iom_put( "qns_oce" , qns ) ! output downward non solar heat over the ocean
552	CALL iom_put( "qsr_oce" , qsr ) ! output downward solar heat over the ocean
553	CALL iom_put( "qt_oce" , qns+qsr ) ! output total downward heat over the ocean
554	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! output total precipitation [kg/m2/s]
555	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! output solid precipitation [kg/m2/s]
556	CALL iom_put( 'snowpre', sprecip ) ! Snow
557	CALL iom_put( 'precip' , tprecip ) ! Total precipitation
558	ENDIF
559	!
560	IF(ln_ctl) THEN
561	CALL prt_ctl(tab2d_1=zqsb , clinfo1=' blk_oce: zqsb : ', tab2d_2=zqlw , clinfo2=' zqlw : ')
562	CALL prt_ctl(tab2d_1=zqla , clinfo1=' blk_oce: zqla : ', tab2d_2=qsr , clinfo2=' qsr : ')
563	CALL prt_ctl(tab2d_1=pst , clinfo1=' blk_oce: pst : ', tab2d_2=emp , clinfo2=' emp : ')
564	CALL prt_ctl(tab2d_1=utau , clinfo1=' blk_oce: utau : ', mask1=umask, &
565	& tab2d_2=vtau , clinfo2= ' vtau : ' , mask2=vmask )
566	ENDIF
567	!
568	END SUBROUTINE blk_oce
569
570
571
572	FUNCTION rho_air( ptak, pqa, pslp )
573	!!-------------------------------------------------------------------------------
574	!! * FUNCTION rho_air *
575	!!
576	!! ** Purpose : compute density of (moist) air using the eq. of state of the atmosphere
577	!!
578	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
579	!!-------------------------------------------------------------------------------
580	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
581	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg]
582	!!clem REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! pressure in [Pa]
583	REAL(wp), INTENT(in) :: pslp ! pressure in [Pa]
584	REAL(wp), DIMENSION(jpi,jpj) :: rho_air ! density of moist air [kg/m^3]
585	!!-------------------------------------------------------------------------------
586	!
587	rho_air = pslp / ( R_dryptak ( 1._wp + rctv0*pqa ) )
588	!
589	END FUNCTION rho_air
590
591
592	FUNCTION cp_air( pqa )
593	!!-------------------------------------------------------------------------------
594	!! * FUNCTION cp_air *
595	!!
596	!! ** Purpose : Compute specific heat (Cp) of moist air
597	!!
598	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
599	!!-------------------------------------------------------------------------------
600	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg]
601	REAL(wp), DIMENSION(jpi,jpj) :: cp_air ! specific heat of moist air [J/K/kg]
602	!!-------------------------------------------------------------------------------
603	!
604	Cp_air = Cp_dry + Cp_vap * pqa
605	!
606	END FUNCTION cp_air
607
608
609	FUNCTION q_sat( ptak, pslp )
610	!!----------------------------------------------------------------------------------
611	!! * FUNCTION q_sat *
612	!!
613	!! ** Purpose : Specific humidity at saturation in [kg/kg]
614	!! Based on accurate estimate of "e_sat"
615	!! aka saturation water vapor (Goff, 1957)
616	!!
617	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
618	!!----------------------------------------------------------------------------------
619	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
620	!!clem REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! sea level atmospheric pressure [Pa]
621	REAL(wp), INTENT(in) :: pslp ! sea level atmospheric pressure [Pa]
622	REAL(wp), DIMENSION(jpi,jpj) :: q_sat ! Specific humidity at saturation [kg/kg]
623	!
624	INTEGER :: ji, jj ! dummy loop indices
625	REAL(wp) :: ze_sat, ztmp ! local scalar
626	!!----------------------------------------------------------------------------------
627	!
628	DO jj = 1, jpj
629	DO ji = 1, jpi
630	!
631	ztmp = rt0 / ptak(ji,jj)
632	!
633	! Vapour pressure at saturation [hPa] : WMO, (Goff, 1957)
634	ze_sat = 10.*( 10.79574(1. - ztmp) - 5.028*LOG10(ptak(ji,jj)/rt0) &
635	& + 1.5047510.(-4)(1. - 10.*(-8.2969(ptak(ji,jj)/rt0 - 1.)) ) &
636	& + 0.4287310.(-3)(10.*(4.76955(1. - ztmp)) - 1.) + 0.78614 )
637	!
638	!!clem q_sat(ji,jj) = reps0 * ze_sat/( 0.01_wppslp(ji,jj) - (1._wp - reps0)ze_sat ) ! 0.01 because SLP is in [Pa]
639	q_sat(ji,jj) = reps0 * ze_sat/( 0.01_wppslp - (1._wp - reps0)ze_sat ) ! 0.01 because SLP is in [Pa]
640	!
641	END DO
642	END DO
643	!
644	END FUNCTION q_sat
645
646
647	FUNCTION gamma_moist( ptak, pqa )
648	!!----------------------------------------------------------------------------------
649	!! * FUNCTION gamma_moist *
650	!!
651	!! ** Purpose : Compute the moist adiabatic lapse-rate.
652	!! => http://glossary.ametsoc.org/wiki/Moist-adiabatic_lapse_rate
653	!! => http://www.geog.ucsb.edu/~joel/g266_s10/lecture_notes/chapt03/oh10_3_01/oh10_3_01.html
654	!!
655	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
656	!!----------------------------------------------------------------------------------
657	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
658	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! specific humidity [kg/kg]
659	REAL(wp), DIMENSION(jpi,jpj) :: gamma_moist ! moist adiabatic lapse-rate
660	!
661	INTEGER :: ji, jj ! dummy loop indices
662	REAL(wp) :: zrv, ziRT ! local scalar
663	!!----------------------------------------------------------------------------------
664	!
665	DO jj = 1, jpj
666	DO ji = 1, jpi
667	zrv = pqa(ji,jj) / (1. - pqa(ji,jj))
668	ziRT = 1. / (R_dry*ptak(ji,jj)) ! 1/RT
669	gamma_moist(ji,jj) = grav * ( 1. + cevapzrvziRT ) / ( Cp_dry + cevapcevapzrvreps0ziRT/ptak(ji,jj) )
670	END DO
671	END DO
672	!
673	END FUNCTION gamma_moist
674
675
676	FUNCTION L_vap( psst )
677	!!---------------------------------------------------------------------------------
678	!! * FUNCTION L_vap *
679	!!
680	!! ** Purpose : Compute the latent heat of vaporization of water from temperature
681	!!
682	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
683	!!----------------------------------------------------------------------------------
684	REAL(wp), DIMENSION(jpi,jpj) :: L_vap ! latent heat of vaporization [J/kg]
685	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! water temperature [K]
686	!!----------------------------------------------------------------------------------
687	!
688	L_vap = ( 2.501 - 0.00237 * ( psst(:,:) - rt0) ) * 1.e6
689	!
690	END FUNCTION L_vap
691
692	#if defined key_si3
693	!!----------------------------------------------------------------------
694	!! 'key_si3' SI3 sea-ice model
695	!!----------------------------------------------------------------------
696	!! blk_ice_tau : provide the air-ice stress
697	!! blk_ice_flx : provide the heat and mass fluxes at air-ice interface
698	!! blk_ice_qcn : provide ice surface temperature and snow/ice conduction flux (emulating JULES coupler)
699	!! Cdn10_Lupkes2012 : Lupkes et al. (2012) air-ice drag
700	!! Cdn10_Lupkes2015 : Lupkes et al. (2015) air-ice drag
701	!!----------------------------------------------------------------------
702
703	SUBROUTINE blk_ice_tau
704	!!---------------------------------------------------------------------
705	!! * ROUTINE blk_ice_tau *
706	!!
707	!! ** Purpose : provide the surface boundary condition over sea-ice
708	!!
709	!! ** Method : compute momentum using bulk formulation
710	!! formulea, ice variables and read atmospheric fields.
711	!! NB: ice drag coefficient is assumed to be a constant
712	!!---------------------------------------------------------------------
713	INTEGER :: ji, jj ! dummy loop indices
714	REAL(wp) :: zwndi_f , zwndj_f, zwnorm_f ! relative wind module and components at F-point
715	REAL(wp) :: zwndi_t , zwndj_t ! relative wind components at T-point
716	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa ! transfer coefficient for momentum (tau)
717	!!---------------------------------------------------------------------
718	!
719	! set transfer coefficients to default sea-ice values
720	Cd_atm(:,:) = Cd_ice
721	Ch_atm(:,:) = Cd_ice
722	Ce_atm(:,:) = Cd_ice
723
724	wndm_ice(:,:) = 0._wp !!gm brutal....
725
726	! ------------------------------------------------------------ !
727	! Wind module relative to the moving ice ( U10m - U_ice ) !
728	! ------------------------------------------------------------ !
729	! C-grid ice dynamics : U & V-points (same as ocean)
730	DO jj = 2, jpjm1
731	DO ji = fs_2, fs_jpim1 ! vect. opt.
732	zwndi_t = ( sf(jp_wndi)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( u_ice(ji-1,jj ) + u_ice(ji,jj) ) )
733	zwndj_t = ( sf(jp_wndj)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( v_ice(ji ,jj-1) + v_ice(ji,jj) ) )
734	wndm_ice(ji,jj) = SQRT( zwndi_t * zwndi_t + zwndj_t * zwndj_t ) * tmask(ji,jj,1)
735	END DO
736	END DO
737	CALL lbc_lnk( wndm_ice, 'T', 1. )
738	!
739	! Make ice-atm. drag dependent on ice concentration
740	IF ( ln_Cd_L12 ) THEN ! calculate new drag from Lupkes(2012) equations
741	CALL Cdn10_Lupkes2012( Cd_atm )
742	Ch_atm(:,:) = Cd_atm(:,:) ! momentum and heat transfer coef. are considered identical
743	ELSEIF( ln_Cd_L15 ) THEN ! calculate new drag from Lupkes(2015) equations
744	CALL Cdn10_Lupkes2015( Cd_atm, Ch_atm )
745	ENDIF
746
747	!! CALL iom_put( "Cd_ice", Cd_atm) ! output value of pure ice-atm. transfer coef.
748	!! CALL iom_put( "Ch_ice", Ch_atm) ! output value of pure ice-atm. transfer coef.
749
750	! local scalars ( place there for vector optimisation purposes)
751	! Computing density of air! Way denser that 1.2 over sea-ice !!!
752	!!clem zrhoa (:,:) = rho_air(sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1))
753	zrhoa (:,:) = rho_air(sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), 101300.)
754
755	!!gm brutal....
756	utau_ice (:,:) = 0._wp
757	vtau_ice (:,:) = 0._wp
758	!!gm end
759
760	! ------------------------------------------------------------ !
761	! Wind stress relative to the moving ice ( U10m - U_ice ) !
762	! ------------------------------------------------------------ !
763	! C-grid ice dynamics : U & V-points (same as ocean)
764	DO jj = 2, jpjm1
765	DO ji = fs_2, fs_jpim1 ! vect. opt.
766	utau_ice(ji,jj) = 0.5 * zrhoa(ji,jj) * Cd_atm(ji,jj) * ( wndm_ice(ji+1,jj ) + wndm_ice(ji,jj) ) &
767	& * ( 0.5 * (sf(jp_wndi)%fnow(ji+1,jj,1) + sf(jp_wndi)%fnow(ji,jj,1) ) - rn_vfac * u_ice(ji,jj) )
768	vtau_ice(ji,jj) = 0.5 * zrhoa(ji,jj) * Cd_atm(ji,jj) * ( wndm_ice(ji,jj+1 ) + wndm_ice(ji,jj) ) &
769	& * ( 0.5 * (sf(jp_wndj)%fnow(ji,jj+1,1) + sf(jp_wndj)%fnow(ji,jj,1) ) - rn_vfac * v_ice(ji,jj) )
770	END DO
771	END DO
772	CALL lbc_lnk_multi( utau_ice, 'U', -1., vtau_ice, 'V', -1. )
773	!
774	IF(ln_ctl) THEN
775	CALL prt_ctl(tab2d_1=utau_ice , clinfo1=' blk_ice: utau_ice : ', tab2d_2=vtau_ice , clinfo2=' vtau_ice : ')
776	CALL prt_ctl(tab2d_1=wndm_ice , clinfo1=' blk_ice: wndm_ice : ')
777	ENDIF
778	!
779	END SUBROUTINE blk_ice_tau
780
781
782	SUBROUTINE blk_ice_flx( ptsu, phs, phi, palb )
783	!!---------------------------------------------------------------------
784	!! * ROUTINE blk_ice_flx *
785	!!
786	!! ** Purpose : provide the heat and mass fluxes at air-ice interface
787	!!
788	!! ** Method : compute heat and freshwater exchanged
789	!! between atmosphere and sea-ice using bulk formulation
790	!! formulea, ice variables and read atmmospheric fields.
791	!!
792	!! caution : the net upward water flux has with mm/day unit
793	!!---------------------------------------------------------------------
794	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: ptsu ! sea ice surface temperature
795	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: phs ! snow thickness
796	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: phi ! ice thickness
797	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: palb ! ice albedo (all skies)
798	!!
799	INTEGER :: ji, jj, jl ! dummy loop indices
800	REAL(wp) :: zst3 ! local variable
801	REAL(wp) :: zcoef_dqlw, zcoef_dqla ! - -
802	REAL(wp) :: zztmp, z1_lsub ! - -
803	REAL(wp) :: zfr1, zfr2 ! local variables
804	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_st ! inverse of surface temperature
805	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_qlw ! long wave heat flux over ice
806	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_qsb ! sensible heat flux over ice
807	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_dqlw ! long wave heat sensitivity over ice
808	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_dqsb ! sensible heat sensitivity over ice
809	REAL(wp), DIMENSION(jpi,jpj) :: zevap, zsnw ! evaporation and snw distribution after wind blowing (SI3)
810	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa
811	!!---------------------------------------------------------------------
812	!
813	zcoef_dqlw = 4.0 * 0.95 * Stef ! local scalars
814	zcoef_dqla = -Ls * 11637800. * (-5897.8)
815	!
816	!!clem zrhoa(:,:) = rho_air( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1) )
817	zrhoa(:,:) = rho_air( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), 101300. )
818	!
819	zztmp = 1. / ( 1. - albo )
820	WHERE( ptsu(:,:,:) /= 0._wp ) ; z1_st(:,:,:) = 1._wp / ptsu(:,:,:)
821	ELSEWHERE ; z1_st(:,:,:) = 0._wp
822	END WHERE
823	! ! ========================== !
824	DO jl = 1, jpl ! Loop over ice categories !
825	! ! ========================== !
826	DO jj = 1 , jpj
827	DO ji = 1, jpi
828	! ----------------------------!
829	! I Radiative FLUXES !
830	! ----------------------------!
831	zst3 = ptsu(ji,jj,jl) * ptsu(ji,jj,jl) * ptsu(ji,jj,jl)
832	! Short Wave (sw)
833	qsr_ice(ji,jj,jl) = zztmp * ( 1. - palb(ji,jj,jl) ) * qsr(ji,jj)
834	! Long Wave (lw)
835	z_qlw(ji,jj,jl) = 0.95 * ( sf(jp_qlw)%fnow(ji,jj,1) - Stef * ptsu(ji,jj,jl) * zst3 ) * tmask(ji,jj,1)
836	! lw sensitivity
837	z_dqlw(ji,jj,jl) = zcoef_dqlw * zst3
838
839	! ----------------------------!
840	! II Turbulent FLUXES !
841	! ----------------------------!
842
843	! ... turbulent heat fluxes with Ch_atm recalculated in blk_ice_tau
844	! Sensible Heat
845	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))
846	! Latent Heat
847	qla_ice(ji,jj,jl) = rn_efac * MAX( 0.e0, zrhoa(ji,jj) * Ls * Ch_atm(ji,jj) * wndm_ice(ji,jj) * &
848	& ( 11637800. * EXP( -5897.8 * z1_st(ji,jj,jl) ) / zrhoa(ji,jj) - sf(jp_humi)%fnow(ji,jj,1) ) )
849	! Latent heat sensitivity for ice (Dqla/Dt)
850	IF( qla_ice(ji,jj,jl) > 0._wp ) THEN
851	dqla_ice(ji,jj,jl) = rn_efac * zcoef_dqla * Ch_atm(ji,jj) * wndm_ice(ji,jj) * &
852	& z1_st(ji,jj,jl)z1_st(ji,jj,jl) EXP(-5897.8 * z1_st(ji,jj,jl))
853	ELSE
854	dqla_ice(ji,jj,jl) = 0._wp
855	ENDIF
856
857	! Sensible heat sensitivity (Dqsb_ice/Dtn_ice)
858	z_dqsb(ji,jj,jl) = zrhoa(ji,jj) * cpa * Ch_atm(ji,jj) * wndm_ice(ji,jj)
859
860	! ----------------------------!
861	! III Total FLUXES !
862	! ----------------------------!
863	! Downward Non Solar flux
864	qns_ice (ji,jj,jl) = z_qlw (ji,jj,jl) - z_qsb (ji,jj,jl) - qla_ice (ji,jj,jl)
865	! Total non solar heat flux sensitivity for ice
866	dqns_ice(ji,jj,jl) = - ( z_dqlw(ji,jj,jl) + z_dqsb(ji,jj,jl) + dqla_ice(ji,jj,jl) )
867	END DO
868	!
869	END DO
870	!
871	END DO
872	!
873	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! total precipitation [kg/m2/s]
874	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! solid precipitation [kg/m2/s]
875	CALL iom_put( 'snowpre', sprecip ) ! Snow precipitation
876	CALL iom_put( 'precip' , tprecip ) ! Total precipitation
877
878	! --- evaporation --- !
879	z1_lsub = 1._wp / Lsub
880	evap_ice (:,:,:) = rn_efac * qla_ice (:,:,:) * z1_lsub ! sublimation
881	devap_ice(:,:,:) = rn_efac * dqla_ice(:,:,:) * z1_lsub ! d(sublimation)/dT
882	zevap (:,:) = rn_efac * ( emp(:,:) + tprecip(:,:) ) ! evaporation over ocean
883
884	! --- evaporation minus precipitation --- !
885	zsnw(:,:) = 0._wp
886	CALL ice_thd_snwblow( (1.-at_i_b(:,:)), zsnw ) ! snow distribution over ice after wind blowing
887	emp_oce(:,:) = ( 1._wp - at_i_b(:,:) ) * zevap(:,:) - ( tprecip(:,:) - sprecip(:,:) ) - sprecip(:,:) * (1._wp - zsnw )
888	emp_ice(:,:) = SUM( a_i_b(:,:,:) * evap_ice(:,:,:), dim=3 ) - sprecip(:,:) * zsnw
889	emp_tot(:,:) = emp_oce(:,:) + emp_ice(:,:)
890
891	! --- heat flux associated with emp --- !
892	qemp_oce(:,:) = - ( 1._wp - at_i_b(:,:) ) * zevap(:,:) * sst_m(:,:) * rcp & ! evap at sst
893	& + ( tprecip(:,:) - sprecip(:,:) ) * ( sf(jp_tair)%fnow(:,:,1) - rt0 ) * rcp & ! liquid precip at Tair
894	& + sprecip(:,:) * ( 1._wp - zsnw ) * & ! solid precip at min(Tair,Tsnow)
895	& ( ( MIN( sf(jp_tair)%fnow(:,:,1), rt0_snow ) - rt0 ) * cpic * tmask(:,:,1) - lfus )
896	qemp_ice(:,:) = sprecip(:,:) * zsnw * & ! solid precip (only)
897	& ( ( MIN( sf(jp_tair)%fnow(:,:,1), rt0_snow ) - rt0 ) * cpic * tmask(:,:,1) - lfus )
898
899	! --- total solar and non solar fluxes --- !
900	qns_tot(:,:) = ( 1._wp - at_i_b(:,:) ) * qns_oce(:,:) + SUM( a_i_b(:,:,:) * qns_ice(:,:,:), dim=3 ) &
901	& + qemp_ice(:,:) + qemp_oce(:,:)
902	qsr_tot(:,:) = ( 1._wp - at_i_b(:,:) ) * qsr_oce(:,:) + SUM( a_i_b(:,:,:) * qsr_ice(:,:,:), dim=3 )
903
904	! --- heat content of precip over ice in J/m3 (to be used in 1D-thermo) --- !
905	qprec_ice(:,:) = rhosn * ( ( MIN( sf(jp_tair)%fnow(:,:,1), rt0_snow ) - rt0 ) * cpic * tmask(:,:,1) - lfus )
906
907	! --- heat content of evap over ice in W/m2 (to be used in 1D-thermo) ---
908	DO jl = 1, jpl
909	qevap_ice(:,:,jl) = 0._wp ! should be -evap_ice(:,:,jl)( ( Tice - rt0 ) cpic * tmask(:,:,1) )
910	! ! But we do not have Tice => consider it at 0degC => evap=0
911	END DO
912
913	! --- shortwave radiation transmitted below the surface (W/m2, see Grenfell Maykut 77) --- !
914	zfr1 = ( 0.18 * ( 1.0 - cldf_ice ) + 0.35 * cldf_ice ) ! transmission when hi>10cm
915	zfr2 = ( 0.82 * ( 1.0 - cldf_ice ) + 0.65 * cldf_ice ) ! zfr2 such that zfr1 + zfr2 to equal 1
916	!
917	WHERE ( phs(:,:,:) <= 0._wp .AND. phi(:,:,:) < 0.1_wp ) ! linear decrease from hi=0 to 10cm
918	qsr_ice_tr(:,:,:) = qsr_ice(:,:,:) * ( zfr1 + zfr2 * ( 1._wp - phi(:,:,:) * 10._wp ) )
919	ELSEWHERE( phs(:,:,:) <= 0._wp .AND. phi(:,:,:) >= 0.1_wp ) ! constant (zfr1) when hi>10cm
920	qsr_ice_tr(:,:,:) = qsr_ice(:,:,:) * zfr1
921	ELSEWHERE ! zero when hs>0
922	qsr_ice_tr(:,:,:) = 0._wp
923	END WHERE
924	!
925	IF(ln_ctl) THEN
926	CALL prt_ctl(tab3d_1=qla_ice , clinfo1=' blk_ice: qla_ice : ', tab3d_2=z_qsb , clinfo2=' z_qsb : ', kdim=jpl)
927	CALL prt_ctl(tab3d_1=z_qlw , clinfo1=' blk_ice: z_qlw : ', tab3d_2=dqla_ice, clinfo2=' dqla_ice : ', kdim=jpl)
928	CALL prt_ctl(tab3d_1=z_dqsb , clinfo1=' blk_ice: z_dqsb : ', tab3d_2=z_dqlw , clinfo2=' z_dqlw : ', kdim=jpl)
929	CALL prt_ctl(tab3d_1=dqns_ice, clinfo1=' blk_ice: dqns_ice : ', tab3d_2=qsr_ice , clinfo2=' qsr_ice : ', kdim=jpl)
930	CALL prt_ctl(tab3d_1=ptsu , clinfo1=' blk_ice: ptsu : ', tab3d_2=qns_ice , clinfo2=' qns_ice : ', kdim=jpl)
931	CALL prt_ctl(tab2d_1=tprecip , clinfo1=' blk_ice: tprecip : ', tab2d_2=sprecip , clinfo2=' sprecip : ')
932	ENDIF
933	!
934	END SUBROUTINE blk_ice_flx
935
936
937	SUBROUTINE blk_ice_qcn( k_virtual_itd, ptsu, ptb, phs, phi )
938	!!---------------------------------------------------------------------
939	!! * ROUTINE blk_ice_qcn *
940	!!
941	!! ** Purpose : Compute surface temperature and snow/ice conduction flux
942	!! to force sea ice / snow thermodynamics
943	!! in the case JULES coupler is emulated
944	!!
945	!! ** Method : compute surface energy balance assuming neglecting heat storage
946	!! following the 0-layer Semtner (1976) approach
947	!!
948	!! ** Outputs : - ptsu : sea-ice / snow surface temperature (K)
949	!! - qcn_ice : surface inner conduction flux (W/m2)
950	!!
951	!!---------------------------------------------------------------------
952	INTEGER , INTENT(in ) :: k_virtual_itd ! single-category option
953	REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: ptsu ! sea ice / snow surface temperature
954	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: ptb ! sea ice base temperature
955	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: phs ! snow thickness
956	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: phi ! sea ice thickness
957	!
958	INTEGER , PARAMETER :: nit = 10 ! number of iterations
959	REAL(wp), PARAMETER :: zepsilon = 0.1_wp ! characteristic thickness for enhanced conduction
960	!
961	INTEGER :: ji, jj, jl ! dummy loop indices
962	INTEGER :: iter ! local integer
963	REAL(wp) :: zfac, zfac2, zfac3 ! local scalars
964	REAL(wp) :: zkeff_h, ztsu, ztsu0 !
965	REAL(wp) :: zqc, zqnet !
966	REAL(wp) :: zhe, zqa0 !
967	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zgfac ! enhanced conduction factor
968	!!---------------------------------------------------------------------
969
970	! -------------------------------------!
971	! I Enhanced conduction factor !
972	! -------------------------------------!
973	! Emulates the enhancement of conduction by unresolved thin ice (k_virtual_itd = 1/2)
974	! Fichefet and Morales Maqueda, JGR 1997
975	!
976	zgfac(:,:,:) = 1._wp
977
978	SELECT CASE ( k_virtual_itd )
979	!
980	CASE ( 1 , 2 )
981	!
982	zfac = 1._wp / ( rn_cnd_s + rcdic )
983	zfac2 = EXP(1._wp) * 0.5_wp * zepsilon
984	zfac3 = 2._wp / zepsilon
985	!
986	DO jl = 1, jpl
987	DO jj = 1 , jpj
988	DO ji = 1, jpi
989	zhe = ( rn_cnd_s * phi(ji,jj,jl) + rcdic * phs(ji,jj,jl) ) * zfac ! Effective thickness
990	IF( zhe >= zfac2 ) zgfac(ji,jj,jl) = MIN( 2._wp, 0.5_wp * ( 1._wp + LOG( zhe * zfac3 ) ) ) ! Enhanced conduction factor
991	END DO
992	END DO
993	END DO
994	!
995	END SELECT
996
997	! -------------------------------------------------------------!
998	! II Surface temperature and conduction flux !
999	! -------------------------------------------------------------!
1000	!
1001	zfac = rcdic * rn_cnd_s
1002	!
1003	DO jl = 1, jpl
1004	DO jj = 1 , jpj
1005	DO ji = 1, jpi
1006	!
1007	zkeff_h = zfac * zgfac(ji,jj,jl) / & ! Effective conductivity of the snow-ice system divided by thickness
1008	& ( rcdic * phs(ji,jj,jl) + rn_cnd_s * MAX( 0.01, phi(ji,jj,jl) ) )
1009	ztsu = ptsu(ji,jj,jl) ! Store current iteration temperature
1010	ztsu0 = ptsu(ji,jj,jl) ! Store initial surface temperature
1011	zqa0 = qsr_ice(ji,jj,jl) - qsr_ice_tr(ji,jj,jl) + qns_ice(ji,jj,jl) ! Net initial atmospheric heat flux
1012	!
1013	DO iter = 1, nit ! --- Iterative loop
1014	zqc = zkeff_h * ( ztsu - ptb(ji,jj) ) ! Conduction heat flux through snow-ice system (>0 downwards)
1015	zqnet = zqa0 + dqns_ice(ji,jj,jl) * ( ztsu - ptsu(ji,jj,jl) ) - zqc ! Surface energy budget
1016	ztsu = ztsu - zqnet / ( dqns_ice(ji,jj,jl) - zkeff_h ) ! Temperature update
1017	END DO
1018	!
1019	ptsu (ji,jj,jl) = MIN( rt0, ztsu )
1020	qcn_ice(ji,jj,jl) = zkeff_h * ( ptsu(ji,jj,jl) - ptb(ji,jj) )
1021	qns_ice(ji,jj,jl) = qns_ice(ji,jj,jl) + dqns_ice(ji,jj,jl) * ( ptsu(ji,jj,jl) - ztsu0 )
1022	qml_ice(ji,jj,jl) = ( qsr_ice(ji,jj,jl) - qsr_ice_tr(ji,jj,jl) + qns_ice(ji,jj,jl) - qcn_ice(ji,jj,jl) ) &
1023	& * MAX( 0._wp , SIGN( 1._wp, ptsu(ji,jj,jl) - rt0 ) )
1024
1025	END DO
1026	END DO
1027	!
1028	END DO
1029	!
1030	END SUBROUTINE blk_ice_qcn
1031
1032
1033	SUBROUTINE Cdn10_Lupkes2012( Cd )
1034	!!----------------------------------------------------------------------
1035	!! * ROUTINE Cdn10_Lupkes2012 *
1036	!!
1037	!! ** Purpose : Recompute the neutral air-ice drag referenced at 10m
1038	!! to make it dependent on edges at leads, melt ponds and flows.
1039	!! After some approximations, this can be resumed to a dependency
1040	!! on ice concentration.
1041	!!
1042	!! ** Method : The parameterization is taken from Lupkes et al. (2012) eq.(50)
1043	!! with the highest level of approximation: level4, eq.(59)
1044	!! The generic drag over a cell partly covered by ice can be re-written as follows:
1045	!!
1046	!! Cd = Cdw * (1-A) + Cdi * A + Ce * (1-A)*(nu+1/(10beta)) * A**mu
1047	!!
1048	!! Ce = 2.23e-3 , as suggested by Lupkes (eq. 59)
1049	!! nu = mu = beta = 1 , as suggested by Lupkes (eq. 59)
1050	!! A is the concentration of ice minus melt ponds (if any)
1051	!!
1052	!! This new drag has a parabolic shape (as a function of A) starting at
1053	!! Cdw(say 1.5e-3) for A=0, reaching 1.97e-3 for A~0.5
1054	!! and going down to Cdi(say 1.4e-3) for A=1
1055	!!
1056	!! It is theoretically applicable to all ice conditions (not only MIZ)
1057	!! => see Lupkes et al (2013)
1058	!!
1059	!! ** References : Lupkes et al. JGR 2012 (theory)
1060	!! Lupkes et al. GRL 2013 (application to GCM)
1061	!!
1062	!!----------------------------------------------------------------------
1063	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Cd
1064	REAL(wp), PARAMETER :: zCe = 2.23e-03_wp
1065	REAL(wp), PARAMETER :: znu = 1._wp
1066	REAL(wp), PARAMETER :: zmu = 1._wp
1067	REAL(wp), PARAMETER :: zbeta = 1._wp
1068	REAL(wp) :: zcoef
1069	!!----------------------------------------------------------------------
1070	zcoef = znu + 1._wp / ( 10._wp * zbeta )
1071
1072	! generic drag over a cell partly covered by ice
1073	!!Cd(:,:) = Cd_oce(:,:) * ( 1._wp - at_i_b(:,:) ) + & ! pure ocean drag
1074	!! & Cd_ice * at_i_b(:,:) + & ! pure ice drag
1075	!! & zCe * ( 1._wp - at_i_b(:,:) )*zcoef at_i_b(:,:)**zmu ! change due to sea-ice morphology
1076
1077	! ice-atm drag
1078	Cd(:,:) = Cd_ice + & ! pure ice drag
1079	& zCe * ( 1._wp - at_i_b(:,:) )*zcoef at_i_b(:,:)**(zmu-1._wp) ! change due to sea-ice morphology
1080
1081	END SUBROUTINE Cdn10_Lupkes2012
1082
1083
1084	SUBROUTINE Cdn10_Lupkes2015( Cd, Ch )
1085	!!----------------------------------------------------------------------
1086	!! * ROUTINE Cdn10_Lupkes2015 *
1087	!!
1088	!! ** pUrpose : Alternative turbulent transfert coefficients formulation
1089	!! between sea-ice and atmosphere with distinct momentum
1090	!! and heat coefficients depending on sea-ice concentration
1091	!! and atmospheric stability (no meltponds effect for now).
1092	!!
1093	!! ** Method : The parameterization is adapted from Lupkes et al. (2015)
1094	!! and ECHAM6 atmospheric model. Compared to Lupkes2012 scheme,
1095	!! it considers specific skin and form drags (Andreas et al. 2010)
1096	!! to compute neutral transfert coefficients for both heat and
1097	!! momemtum fluxes. Atmospheric stability effect on transfert
1098	!! coefficient is also taken into account following Louis (1979).
1099	!!
1100	!! ** References : Lupkes et al. JGR 2015 (theory)
1101	!! Lupkes et al. ECHAM6 documentation 2015 (implementation)
1102	!!
1103	!!----------------------------------------------------------------------
1104	!
1105	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Cd
1106	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Ch
1107	REAL(wp), DIMENSION(jpi,jpj) :: zst, zqo_sat, zqi_sat
1108	!
1109	! ECHAM6 constants
1110	REAL(wp), PARAMETER :: z0_skin_ice = 0.69e-3_wp ! Eq. 43 [m]
1111	REAL(wp), PARAMETER :: z0_form_ice = 0.57e-3_wp ! Eq. 42 [m]
1112	REAL(wp), PARAMETER :: z0_ice = 1.00e-3_wp ! Eq. 15 [m]
1113	REAL(wp), PARAMETER :: zce10 = 2.80e-3_wp ! Eq. 41
1114	REAL(wp), PARAMETER :: zbeta = 1.1_wp ! Eq. 41
1115	REAL(wp), PARAMETER :: zc = 5._wp ! Eq. 13
1116	REAL(wp), PARAMETER :: zc2 = zc * zc
1117	REAL(wp), PARAMETER :: zam = 2. * zc ! Eq. 14
1118	REAL(wp), PARAMETER :: zah = 3. * zc ! Eq. 30
1119	REAL(wp), PARAMETER :: z1_alpha = 1._wp / 0.2_wp ! Eq. 51
1120	REAL(wp), PARAMETER :: z1_alphaf = z1_alpha ! Eq. 56
1121	REAL(wp), PARAMETER :: zbetah = 1.e-3_wp ! Eq. 26
1122	REAL(wp), PARAMETER :: zgamma = 1.25_wp ! Eq. 26
1123	REAL(wp), PARAMETER :: z1_gamma = 1._wp / zgamma
1124	REAL(wp), PARAMETER :: r1_3 = 1._wp / 3._wp
1125	!
1126	INTEGER :: ji, jj ! dummy loop indices
1127	REAL(wp) :: zthetav_os, zthetav_is, zthetav_zu
1128	REAL(wp) :: zrib_o, zrib_i
1129	REAL(wp) :: zCdn_skin_ice, zCdn_form_ice, zCdn_ice
1130	REAL(wp) :: zChn_skin_ice, zChn_form_ice
1131	REAL(wp) :: z0w, z0i, zfmi, zfmw, zfhi, zfhw
1132	REAL(wp) :: zCdn_form_tmp
1133	!!----------------------------------------------------------------------
1134
1135	! Momentum Neutral Transfert Coefficients (should be a constant)
1136	zCdn_form_tmp = zce10 * ( LOG( 10._wp / z0_form_ice + 1._wp ) / LOG( rn_zu / z0_form_ice + 1._wp ) )**2 ! Eq. 40
1137	zCdn_skin_ice = ( vkarmn / LOG( rn_zu / z0_skin_ice + 1._wp ) )**2 ! Eq. 7
1138	zCdn_ice = zCdn_skin_ice ! Eq. 7 (cf Lupkes email for details)
1139	!zCdn_ice = 1.89e-3 ! old ECHAM5 value (cf Eq. 32)
1140
1141	! Heat Neutral Transfert Coefficients
1142	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)
1143
1144	! Atmospheric and Surface Variables
1145	zst(:,:) = sst_m(:,:) + rt0 ! convert SST from Celcius to Kelvin
1146	!!clem zqo_sat(:,:) = 0.98_wp * q_sat( zst(:,:) , sf(jp_slp)%fnow(:,:,1) ) ! saturation humidity over ocean [kg/kg]
1147	!!clem zqi_sat(:,:) = 0.98_wp * q_sat( tm_su(:,:), sf(jp_slp)%fnow(:,:,1) ) ! saturation humidity over ice [kg/kg]
1148	zqo_sat(:,:) = 0.98_wp * q_sat( zst(:,:) , 101300. ) ! saturation humidity over ocean [kg/kg]
1149	zqi_sat(:,:) = 0.98_wp * q_sat( tm_su(:,:), 101300. ) ! saturation humidity over ice [kg/kg]
1150	!
1151	DO jj = 2, jpjm1 ! reduced loop is necessary for reproducibility
1152	DO ji = fs_2, fs_jpim1
1153	! Virtual potential temperature [K]
1154	zthetav_os = zst(ji,jj) * ( 1._wp + rctv0 * zqo_sat(ji,jj) ) ! over ocean
1155	zthetav_is = tm_su(ji,jj) * ( 1._wp + rctv0 * zqi_sat(ji,jj) ) ! ocean ice
1156	zthetav_zu = t_zu (ji,jj) * ( 1._wp + rctv0 * q_zu(ji,jj) ) ! at zu
1157
1158	! Bulk Richardson Number (could use Ri_bulk function from aerobulk instead)
1159	zrib_o = grav / zthetav_os * ( zthetav_zu - zthetav_os ) * rn_zu / MAX( 0.5, wndm(ji,jj) )**2 ! over ocean
1160	zrib_i = grav / zthetav_is * ( zthetav_zu - zthetav_is ) * rn_zu / MAX( 0.5, wndm_ice(ji,jj) )**2 ! over ice
1161
1162	! Momentum and Heat Neutral Transfert Coefficients
1163	zCdn_form_ice = zCdn_form_tmp * at_i_b(ji,jj) * ( 1._wp - at_i_b(ji,jj) )**zbeta ! Eq. 40
1164	zChn_form_ice = zCdn_form_ice / ( 1._wp + ( LOG( z1_alphaf ) / vkarmn ) * SQRT( zCdn_form_ice ) ) ! Eq. 53
1165
1166	! Momentum and Heat Stability functions (possibility to use psi_m_ecmwf instead)
1167	z0w = rn_zu * EXP( -1._wp * vkarmn / SQRT( Cdn_oce(ji,jj) ) ) ! over water
1168	z0i = z0_skin_ice ! over ice (cf Lupkes email for details)
1169	IF( zrib_o <= 0._wp ) THEN
1170	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
1171	zfhw = ( 1._wp + ( zbetah * ( zthetav_os - zthetav_zu )*r1_3 / ( Chn_oce(ji,jj) MAX(0.01, wndm(ji,jj)) ) & ! Eq. 26
1172	& )zgamma )z1_gamma
1173	ELSE
1174	zfmw = 1._wp / ( 1._wp + zam * zrib_o / SQRT( 1._wp + zrib_o ) ) ! Eq. 12
1175	zfhw = 1._wp / ( 1._wp + zah * zrib_o / SQRT( 1._wp + zrib_o ) ) ! Eq. 28
1176	ENDIF
1177
1178	IF( zrib_i <= 0._wp ) THEN
1179	zfmi = 1._wp - zam * zrib_i / (1._wp + 3._wp * zc2 * zCdn_ice * SQRT( -zrib_i * ( rn_zu / z0i + 1._wp))) ! Eq. 9
1180	zfhi = 1._wp - zah * zrib_i / (1._wp + 3._wp * zc2 * zCdn_ice * SQRT( -zrib_i * ( rn_zu / z0i + 1._wp))) ! Eq. 25
1181	ELSE
1182	zfmi = 1._wp / ( 1._wp + zam * zrib_i / SQRT( 1._wp + zrib_i ) ) ! Eq. 11
1183	zfhi = 1._wp / ( 1._wp + zah * zrib_i / SQRT( 1._wp + zrib_i ) ) ! Eq. 27
1184	ENDIF
1185
1186	! Momentum Transfert Coefficients (Eq. 38)
1187	Cd(ji,jj) = zCdn_skin_ice * zfmi + &
1188	& 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) )
1189
1190	! Heat Transfert Coefficients (Eq. 49)
1191	Ch(ji,jj) = zChn_skin_ice * zfhi + &
1192	& 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) )
1193	!
1194	END DO
1195	END DO
1196	CALL lbc_lnk_multi( Cd, 'T', 1., Ch, 'T', 1. )
1197	!
1198	END SUBROUTINE Cdn10_Lupkes2015
1199
1200	#endif
1201
1202	!!======================================================================
1203	END MODULE sbcblk

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