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sbcblk.F90 @ 10986

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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 cyclone ! Cyclone 10m wind form trac of cyclone centres
43	USE sbcdcy ! surface boundary condition: diurnal cycle
44	USE sbcwave , ONLY : cdn_wave ! wave module
45	USE sbc_ice ! Surface boundary condition: ice fields
46	USE lib_fortran ! to use key_nosignedzero
47	#if defined key_si3
48	USE ice , ONLY : u_ice, v_ice, jpl, a_i_b, at_i_b, t_su, rn_cnd_s, hfx_err_dif
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 icesbc
69	PUBLIC blk_ice_flx ! routine called in icesbc
70	PUBLIC blk_ice_qcn ! routine called in icesbc
71	#endif
72
73	!!Lolo: should ultimately be moved in the module with all physical constants ?
74	!!gm : In principle, yes.
75	REAL(wp), PARAMETER :: Cp_dry = 1005.0 !: Specic heat of dry air, constant pressure [J/K/kg]
76	REAL(wp), PARAMETER :: Cp_vap = 1860.0 !: Specic heat of water vapor, constant pressure [J/K/kg]
77	REAL(wp), PARAMETER :: R_dry = 287.05_wp !: Specific gas constant for dry air [J/K/kg]
78	REAL(wp), PARAMETER :: R_vap = 461.495_wp !: Specific gas constant for water vapor [J/K/kg]
79	REAL(wp), PARAMETER :: reps0 = R_dry/R_vap !: ratio of gas constant for dry air and water vapor => ~ 0.622
80	REAL(wp), PARAMETER :: rctv0 = R_vap/R_dry !: for virtual temperature (== (1-eps)/eps) => ~ 0.608
81
82	INTEGER , PARAMETER :: jpfld =10 ! maximum number of files to read
83	INTEGER , PARAMETER :: jp_wndi = 1 ! index of 10m wind velocity (i-component) (m/s) at T-point
84	INTEGER , PARAMETER :: jp_wndj = 2 ! index of 10m wind velocity (j-component) (m/s) at T-point
85	INTEGER , PARAMETER :: jp_tair = 3 ! index of 10m air temperature (Kelvin)
86	INTEGER , PARAMETER :: jp_humi = 4 ! index of specific humidity ( % )
87	INTEGER , PARAMETER :: jp_qsr = 5 ! index of solar heat (W/m2)
88	INTEGER , PARAMETER :: jp_qlw = 6 ! index of Long wave (W/m2)
89	INTEGER , PARAMETER :: jp_prec = 7 ! index of total precipitation (rain+snow) (Kg/m2/s)
90	INTEGER , PARAMETER :: jp_snow = 8 ! index of snow (solid prcipitation) (kg/m2/s)
91	INTEGER , PARAMETER :: jp_slp = 9 ! index of sea level pressure (Pa)
92	INTEGER , PARAMETER :: jp_tdif =10 ! index of tau diff associated to HF tau (N/m2) at T-point
93
94	TYPE(FLD), ALLOCATABLE, DIMENSION(:) :: sf ! structure of input fields (file informations, fields read)
95
96	! !!! Bulk parameters
97	REAL(wp), PARAMETER :: cpa = 1000.5 ! specific heat of air (only used for ice fluxes now...)
98	REAL(wp), PARAMETER :: Ls = 2.839e6 ! latent heat of sublimation
99	REAL(wp), PARAMETER :: Stef = 5.67e-8 ! Stefan Boltzmann constant
100	REAL(wp), PARAMETER :: Cd_ice = 1.4e-3 ! transfer coefficient over ice
101	REAL(wp), PARAMETER :: albo = 0.066 ! ocean albedo assumed to be constant
102	!
103	! !!* Namelist namsbc_blk : bulk parameters
104	LOGICAL :: ln_NCAR ! "NCAR" algorithm (Large and Yeager 2008)
105	LOGICAL :: ln_COARE_3p0 ! "COARE 3.0" algorithm (Fairall et al. 2003)
106	LOGICAL :: ln_COARE_3p5 ! "COARE 3.5" algorithm (Edson et al. 2013)
107	LOGICAL :: ln_ECMWF ! "ECMWF" algorithm (IFS cycle 31)
108	!
109	LOGICAL :: ln_taudif ! logical flag to use the "mean of stress module - module of mean stress" data
110	REAL(wp) :: rn_pfac ! multiplication factor for precipitation
111	REAL(wp) :: rn_efac ! multiplication factor for evaporation
112	REAL(wp) :: rn_vfac ! multiplication factor for ice/ocean velocity in the calculation of wind stress
113	REAL(wp) :: rn_zqt ! z(q,t) : height of humidity and temperature measurements
114	REAL(wp) :: rn_zu ! z(u) : height of wind measurements
115	!!gm ref namelist initialize it so remove the setting to false below
116	LOGICAL :: ln_Cd_L12 = .FALSE. ! Modify the drag ice-atm depending on ice concentration (from Lupkes et al. JGR2012)
117	LOGICAL :: ln_Cd_L15 = .FALSE. ! Modify the drag ice-atm depending on ice concentration (from Lupkes et al. JGR2015)
118	!
119	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: Cd_atm ! transfer coefficient for momentum (tau)
120	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: Ch_atm ! transfer coefficient for sensible heat (Q_sens)
121	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: Ce_atm ! tansfert coefficient for evaporation (Q_lat)
122	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: t_zu ! air temperature at wind speed height (needed by Lupkes 2015 bulk scheme)
123	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: q_zu ! air spec. hum. at wind speed height (needed by Lupkes 2015 bulk scheme)
124	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: cdn_oce, chn_oce, cen_oce ! needed by Lupkes 2015 bulk scheme
125
126	INTEGER :: nblk ! choice of the bulk algorithm
127	! ! associated indices:
128	INTEGER, PARAMETER :: np_NCAR = 1 ! "NCAR" algorithm (Large and Yeager 2008)
129	INTEGER, PARAMETER :: np_COARE_3p0 = 2 ! "COARE 3.0" algorithm (Fairall et al. 2003)
130	INTEGER, PARAMETER :: np_COARE_3p5 = 3 ! "COARE 3.5" algorithm (Edson et al. 2013)
131	INTEGER, PARAMETER :: np_ECMWF = 4 ! "ECMWF" algorithm (IFS cycle 31)
132
133	!! * Substitutions
134	# include "vectopt_loop_substitute.h90"
135	!!----------------------------------------------------------------------
136	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
137	!! $Id$
138	!! Software governed by the CeCILL license (see ./LICENSE)
139	!!----------------------------------------------------------------------
140	CONTAINS
141
142	INTEGER FUNCTION sbc_blk_alloc()
143	!!-------------------------------------------------------------------
144	!! * ROUTINE sbc_blk_alloc *
145	!!-------------------------------------------------------------------
146	ALLOCATE( Cd_atm (jpi,jpj), Ch_atm (jpi,jpj), Ce_atm (jpi,jpj), t_zu(jpi,jpj), q_zu(jpi,jpj), &
147	& cdn_oce(jpi,jpj), chn_oce(jpi,jpj), cen_oce(jpi,jpj), STAT=sbc_blk_alloc )
148	!
149	CALL mpp_sum ( 'sbcblk', sbc_blk_alloc )
150	IF( sbc_blk_alloc /= 0 ) CALL ctl_stop( 'STOP', 'sbc_blk_alloc: failed to allocate arrays' )
151	END FUNCTION sbc_blk_alloc
152
153
154	SUBROUTINE sbc_blk_init
155	!!---------------------------------------------------------------------
156	!! * ROUTINE sbc_blk_init *
157	!!
158	!! ** Purpose : choose and initialize a bulk formulae formulation
159	!!
160	!! ** Method :
161	!!
162	!!----------------------------------------------------------------------
163	INTEGER :: ifpr, jfld ! dummy loop indice and argument
164	INTEGER :: ios, ierror, ioptio ! Local integer
165	!!
166	CHARACTER(len=100) :: cn_dir ! Root directory for location of atmospheric forcing files
167	TYPE(FLD_N), DIMENSION(jpfld) :: slf_i ! array of namelist informations on the fields to read
168	TYPE(FLD_N) :: sn_wndi, sn_wndj, sn_humi, sn_qsr ! informations about the fields to be read
169	TYPE(FLD_N) :: sn_qlw , sn_tair, sn_prec, sn_snow ! " "
170	TYPE(FLD_N) :: sn_slp , sn_tdif ! " "
171	NAMELIST/namsbc_blk/ sn_wndi, sn_wndj, sn_humi, sn_qsr, sn_qlw , & ! input fields
172	& sn_tair, sn_prec, sn_snow, sn_slp, sn_tdif, &
173	& ln_NCAR, ln_COARE_3p0, ln_COARE_3p5, ln_ECMWF, & ! bulk algorithm
174	& cn_dir , ln_taudif, rn_zqt, rn_zu, &
175	& rn_pfac, rn_efac, rn_vfac, ln_Cd_L12, ln_Cd_L15
176	!!---------------------------------------------------------------------
177	!
178	! ! allocate sbc_blk_core array
179	IF( sbc_blk_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'sbc_blk : unable to allocate standard arrays' )
180	!
181	! !** read bulk namelist
182	REWIND( numnam_ref ) !* Namelist namsbc_blk in reference namelist : bulk parameters
183	READ ( numnam_ref, namsbc_blk, IOSTAT = ios, ERR = 901)
184	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namsbc_blk in reference namelist', lwp )
185	!
186	REWIND( numnam_cfg ) !* Namelist namsbc_blk in configuration namelist : bulk parameters
187	READ ( numnam_cfg, namsbc_blk, IOSTAT = ios, ERR = 902 )
188	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namsbc_blk in configuration namelist', lwp )
189	!
190	IF(lwm .AND. nprint > 2) WRITE( numond, namsbc_blk )
191	!
192	! !** initialization of the chosen bulk formulae (+ check)
193	! !* select the bulk chosen in the namelist and check the choice
194	ioptio = 0
195	IF( ln_NCAR ) THEN ; nblk = np_NCAR ; ioptio = ioptio + 1 ; ENDIF
196	IF( ln_COARE_3p0 ) THEN ; nblk = np_COARE_3p0 ; ioptio = ioptio + 1 ; ENDIF
197	IF( ln_COARE_3p5 ) THEN ; nblk = np_COARE_3p5 ; ioptio = ioptio + 1 ; ENDIF
198	IF( ln_ECMWF ) THEN ; nblk = np_ECMWF ; ioptio = ioptio + 1 ; ENDIF
199	!
200	IF( ioptio /= 1 ) CALL ctl_stop( 'sbc_blk_init: Choose one and only one bulk algorithm' )
201	!
202	IF( ln_dm2dc ) THEN !* check: diurnal cycle on Qsr
203	IF( sn_qsr%nfreqh /= 24 ) CALL ctl_stop( 'sbc_blk_init: ln_dm2dc=T only with daily short-wave input' )
204	IF( sn_qsr%ln_tint ) THEN
205	CALL ctl_warn( 'sbc_blk_init: ln_dm2dc=T daily qsr time interpolation done by sbcdcy module', &
206	& ' ==> We force time interpolation = .false. for qsr' )
207	sn_qsr%ln_tint = .false.
208	ENDIF
209	ENDIF
210	! !* set the bulk structure
211	! !- store namelist information in an array
212	slf_i(jp_wndi) = sn_wndi ; slf_i(jp_wndj) = sn_wndj
213	slf_i(jp_qsr ) = sn_qsr ; slf_i(jp_qlw ) = sn_qlw
214	slf_i(jp_tair) = sn_tair ; slf_i(jp_humi) = sn_humi
215	slf_i(jp_prec) = sn_prec ; slf_i(jp_snow) = sn_snow
216	slf_i(jp_slp) = sn_slp ; slf_i(jp_tdif) = sn_tdif
217	!
218	lhftau = ln_taudif !- add an extra field if HF stress is used
219	jfld = jpfld - COUNT( (/.NOT.lhftau/) )
220	!
221	! !- allocate the bulk structure
222	ALLOCATE( sf(jfld), STAT=ierror )
223	IF( ierror > 0 ) CALL ctl_stop( 'STOP', 'sbc_blk_init: unable to allocate sf structure' )
224	DO ifpr= 1, jfld
225	ALLOCATE( sf(ifpr)%fnow(jpi,jpj,1) )
226	IF( slf_i(ifpr)%ln_tint ) ALLOCATE( sf(ifpr)%fdta(jpi,jpj,1,2) )
227	IF( slf_i(ifpr)%nfreqh > 0. .AND. MOD( 3600. * slf_i(ifpr)%nfreqh , REAL(nn_fsbc) * rdt) /= 0. ) &
228	& CALL ctl_warn( 'sbc_blk_init: sbcmod timestep rdt*nn_fsbc is NOT a submultiple of atmospheric forcing frequency.', &
229	& ' This is not ideal. You should consider changing either rdt or nn_fsbc value...' )
230
231	END DO
232	! !- fill the bulk structure with namelist informations
233	CALL fld_fill( sf, slf_i, cn_dir, 'sbc_blk_init', 'surface boundary condition -- bulk formulae', 'namsbc_blk' )
234	!
235	IF ( ln_wave ) THEN
236	!Activated wave module but neither drag nor stokes drift activated
237	IF ( .NOT.(ln_cdgw .OR. ln_sdw .OR. ln_tauwoc .OR. ln_stcor ) ) THEN
238	CALL ctl_stop( 'STOP', 'Ask for wave coupling but ln_cdgw=F, ln_sdw=F, ln_tauwoc=F, ln_stcor=F' )
239	!drag coefficient read from wave model definable only with mfs bulk formulae and core
240	ELSEIF (ln_cdgw .AND. .NOT. ln_NCAR ) THEN
241	CALL ctl_stop( 'drag coefficient read from wave model definable only with NCAR and CORE bulk formulae')
242	ELSEIF (ln_stcor .AND. .NOT. ln_sdw) THEN
243	CALL ctl_stop( 'Stokes-Coriolis term calculated only if activated Stokes Drift ln_sdw=T')
244	ENDIF
245	ELSE
246	IF ( ln_cdgw .OR. ln_sdw .OR. ln_tauwoc .OR. ln_stcor ) &
247	& CALL ctl_stop( 'Not Activated Wave Module (ln_wave=F) but asked coupling ', &
248	& 'with drag coefficient (ln_cdgw =T) ' , &
249	& 'or Stokes Drift (ln_sdw=T) ' , &
250	& 'or ocean stress modification due to waves (ln_tauwoc=T) ', &
251	& 'or Stokes-Coriolis term (ln_stcori=T)' )
252	ENDIF
253	!
254	!
255	IF(lwp) THEN !** Control print
256	!
257	WRITE(numout,) ! namelist
258	WRITE(numout,*) ' Namelist namsbc_blk (other than data information):'
259	WRITE(numout,*) ' "NCAR" algorithm (Large and Yeager 2008) ln_NCAR = ', ln_NCAR
260	WRITE(numout,*) ' "COARE 3.0" algorithm (Fairall et al. 2003) ln_COARE_3p0 = ', ln_COARE_3p0
261	WRITE(numout,*) ' "COARE 3.5" algorithm (Edson et al. 2013) ln_COARE_3p5 = ', ln_COARE_3p0
262	WRITE(numout,*) ' "ECMWF" algorithm (IFS cycle 31) ln_ECMWF = ', ln_ECMWF
263	WRITE(numout,*) ' add High freq.contribution to the stress module ln_taudif = ', ln_taudif
264	WRITE(numout,*) ' Air temperature and humidity reference height (m) rn_zqt = ', rn_zqt
265	WRITE(numout,*) ' Wind vector reference height (m) rn_zu = ', rn_zu
266	WRITE(numout,*) ' factor applied on precipitation (total & snow) rn_pfac = ', rn_pfac
267	WRITE(numout,*) ' factor applied on evaporation rn_efac = ', rn_efac
268	WRITE(numout,*) ' factor applied on ocean/ice velocity rn_vfac = ', rn_vfac
269	WRITE(numout,*) ' (form absolute (=0) to relative winds(=1))'
270	WRITE(numout,*) ' use ice-atm drag from Lupkes2012 ln_Cd_L12 = ', ln_Cd_L12
271	WRITE(numout,*) ' use ice-atm drag from Lupkes2015 ln_Cd_L15 = ', ln_Cd_L15
272	!
273	WRITE(numout,*)
274	SELECT CASE( nblk ) !* Print the choice of bulk algorithm
275	CASE( np_NCAR ) ; WRITE(numout,*) ' ==>>> "NCAR" algorithm (Large and Yeager 2008)'
276	CASE( np_COARE_3p0 ) ; WRITE(numout,*) ' ==>>> "COARE 3.0" algorithm (Fairall et al. 2003)'
277	CASE( np_COARE_3p5 ) ; WRITE(numout,*) ' ==>>> "COARE 3.5" algorithm (Edson et al. 2013)'
278	CASE( np_ECMWF ) ; WRITE(numout,*) ' ==>>> "ECMWF" algorithm (IFS cycle 31)'
279	END SELECT
280	IF(lflush) CALL FLUSH(numout)
281	!
282	ENDIF
283	!
284	END SUBROUTINE sbc_blk_init
285
286
287	SUBROUTINE sbc_blk( kt )
288	!!---------------------------------------------------------------------
289	!! * ROUTINE sbc_blk *
290	!!
291	!! ** Purpose : provide at each time step the surface ocean fluxes
292	!! (momentum, heat, freshwater and runoff)
293	!!
294	!! ** Method : (1) READ each fluxes in NetCDF files:
295	!! the 10m wind velocity (i-component) (m/s) at T-point
296	!! the 10m wind velocity (j-component) (m/s) at T-point
297	!! the 10m or 2m specific humidity ( % )
298	!! the solar heat (W/m2)
299	!! the Long wave (W/m2)
300	!! the 10m or 2m air temperature (Kelvin)
301	!! the total precipitation (rain+snow) (Kg/m2/s)
302	!! the snow (solid prcipitation) (kg/m2/s)
303	!! the tau diff associated to HF tau (N/m2) at T-point (ln_taudif=T)
304	!! (2) CALL blk_oce
305	!!
306	!! C A U T I O N : never mask the surface stress fields
307	!! the stress is assumed to be in the (i,j) mesh referential
308	!!
309	!! ** Action : defined at each time-step at the air-sea interface
310	!! - utau, vtau i- and j-component of the wind stress
311	!! - taum wind stress module at T-point
312	!! - wndm wind speed module at T-point over free ocean or leads in presence of sea-ice
313	!! - qns, qsr non-solar and solar heat fluxes
314	!! - emp upward mass flux (evapo. - precip.)
315	!! - sfx salt flux due to freezing/melting (non-zero only if ice is present)
316	!!
317	!! ** References : Large & Yeager, 2004 / Large & Yeager, 2008
318	!! Brodeau et al. Ocean Modelling 2010
319	!!----------------------------------------------------------------------
320	INTEGER, INTENT(in) :: kt ! ocean time step
321	!!---------------------------------------------------------------------
322	!
323	CALL fld_read( kt, nn_fsbc, sf ) ! input fields provided at the current time-step
324	!
325	! ! compute the surface ocean fluxes using bulk formulea
326	IF( MOD( kt - 1, nn_fsbc ) == 0 ) CALL blk_oce( kt, sf, sst_m, ssu_m, ssv_m )
327
328	#if defined key_cice
329	IF( MOD( kt - 1, nn_fsbc ) == 0 ) THEN
330	qlw_ice(:,:,1) = sf(jp_qlw )%fnow(:,:,1)
331	IF( ln_dm2dc ) THEN ; qsr_ice(:,:,1) = sbc_dcy( sf(jp_qsr)%fnow(:,:,1) )
332	ELSE ; qsr_ice(:,:,1) = sf(jp_qsr)%fnow(:,:,1)
333	ENDIF
334	tatm_ice(:,:) = sf(jp_tair)%fnow(:,:,1)
335	qatm_ice(:,:) = sf(jp_humi)%fnow(:,:,1)
336	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac
337	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac
338	wndi_ice(:,:) = sf(jp_wndi)%fnow(:,:,1)
339	wndj_ice(:,:) = sf(jp_wndj)%fnow(:,:,1)
340	ENDIF
341	#endif
342	!
343	END SUBROUTINE sbc_blk
344
345
346	SUBROUTINE blk_oce( kt, sf, pst, pu, pv )
347	!!---------------------------------------------------------------------
348	!! * ROUTINE blk_oce *
349	!!
350	!! ** Purpose : provide the momentum, heat and freshwater fluxes at
351	!! the ocean surface at each time step
352	!!
353	!! ** Method : bulk formulea for the ocean using atmospheric
354	!! fields read in sbc_read
355	!!
356	!! ** Outputs : - utau : i-component of the stress at U-point (N/m2)
357	!! - vtau : j-component of the stress at V-point (N/m2)
358	!! - taum : Wind stress module at T-point (N/m2)
359	!! - wndm : Wind speed module at T-point (m/s)
360	!! - qsr : Solar heat flux over the ocean (W/m2)
361	!! - qns : Non Solar heat flux over the ocean (W/m2)
362	!! - emp : evaporation minus precipitation (kg/m2/s)
363	!!
364	!! ** Nota : sf has to be a dummy argument for AGRIF on NEC
365	!!---------------------------------------------------------------------
366	INTEGER , INTENT(in ) :: kt ! time step index
367	TYPE(fld), INTENT(inout), DIMENSION(:) :: sf ! input data
368	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pst ! surface temperature [Celcius]
369	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pu ! surface current at U-point (i-component) [m/s]
370	REAL(wp) , INTENT(in) , DIMENSION(:,:) :: pv ! surface current at V-point (j-component) [m/s]
371	!
372	INTEGER :: ji, jj ! dummy loop indices
373	REAL(wp) :: zztmp ! local variable
374	REAL(wp), DIMENSION(jpi,jpj) :: zwnd_i, zwnd_j ! wind speed components at T-point
375	REAL(wp), DIMENSION(jpi,jpj) :: zsq ! specific humidity at pst
376	REAL(wp), DIMENSION(jpi,jpj) :: zqlw, zqsb ! long wave and sensible heat fluxes
377	REAL(wp), DIMENSION(jpi,jpj) :: zqla, zevap ! latent heat fluxes and evaporation
378	REAL(wp), DIMENSION(jpi,jpj) :: zst ! surface temperature in Kelvin
379	REAL(wp), DIMENSION(jpi,jpj) :: zU_zu ! bulk wind speed at height zu [m/s]
380	REAL(wp), DIMENSION(jpi,jpj) :: ztpot ! potential temperature of air at z=rn_zqt [K]
381	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa ! density of air [kg/m^3]
382	!!---------------------------------------------------------------------
383	!
384	! local scalars ( place there for vector optimisation purposes)
385	zst(:,:) = pst(:,:) + rt0 ! convert SST from Celcius to Kelvin (and set minimum value far above 0 K)
386
387	! ----------------------------------------------------------------------------- !
388	! 0 Wind components and module at T-point relative to the moving ocean !
389	! ----------------------------------------------------------------------------- !
390
391	! ... components ( U10m - U_oce ) at T-point (unmasked)
392	!!gm move zwnd_i (_j) set to zero inside the key_cyclone ???
393	zwnd_i(:,:) = 0._wp
394	zwnd_j(:,:) = 0._wp
395	#if defined key_cyclone
396	CALL wnd_cyc( kt, zwnd_i, zwnd_j ) ! add analytical tropical cyclone (Vincent et al. JGR 2012)
397	DO jj = 2, jpjm1
398	DO ji = fs_2, fs_jpim1 ! vect. opt.
399	sf(jp_wndi)%fnow(ji,jj,1) = sf(jp_wndi)%fnow(ji,jj,1) + zwnd_i(ji,jj)
400	sf(jp_wndj)%fnow(ji,jj,1) = sf(jp_wndj)%fnow(ji,jj,1) + zwnd_j(ji,jj)
401	END DO
402	END DO
403	#endif
404	DO jj = 2, jpjm1
405	DO ji = fs_2, fs_jpim1 ! vect. opt.
406	zwnd_i(ji,jj) = ( sf(jp_wndi)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( pu(ji-1,jj ) + pu(ji,jj) ) )
407	zwnd_j(ji,jj) = ( sf(jp_wndj)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( pv(ji ,jj-1) + pv(ji,jj) ) )
408	END DO
409	END DO
410	CALL lbc_lnk_multi( 'sbcblk', zwnd_i, 'T', -1., zwnd_j, 'T', -1. )
411	! ... scalar wind ( = \| U10m - U_oce \| ) at T-point (masked)
412	wndm(:,:) = SQRT( zwnd_i(:,:) * zwnd_i(:,:) &
413	& + zwnd_j(:,:) * zwnd_j(:,:) ) * tmask(:,:,1)
414
415	! ----------------------------------------------------------------------------- !
416	! I Radiative FLUXES !
417	! ----------------------------------------------------------------------------- !
418
419	! ocean albedo assumed to be constant + modify now Qsr to include the diurnal cycle ! Short Wave
420	zztmp = 1. - albo
421	IF( ln_dm2dc ) THEN ; qsr(:,:) = zztmp * sbc_dcy( sf(jp_qsr)%fnow(:,:,1) ) * tmask(:,:,1)
422	ELSE ; qsr(:,:) = zztmp * sf(jp_qsr)%fnow(:,:,1) * tmask(:,:,1)
423	ENDIF
424
425	zqlw(:,:) = ( sf(jp_qlw)%fnow(:,:,1) - Stef * zst(:,:)zst(:,:)zst(:,:)zst(:,:) ) tmask(:,:,1) ! Long Wave
426
427	! ----------------------------------------------------------------------------- !
428	! II Turbulent FLUXES !
429	! ----------------------------------------------------------------------------- !
430
431	! ... specific humidity at SST and IST tmask(
432	zsq(:,:) = 0.98 * q_sat( zst(:,:), sf(jp_slp)%fnow(:,:,1) )
433	!!
434	!! Estimate of potential temperature at z=rn_zqt, based on adiabatic lapse-rate
435	!! (see Josey, Gulev & Yu, 2013) / doi=10.1016/B978-0-12-391851-2.00005-2
436	!! (since reanalysis products provide T at z, not theta !)
437	ztpot = sf(jp_tair)%fnow(:,:,1) + gamma_moist( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1) ) * rn_zqt
438
439	SELECT CASE( nblk ) !== transfer coefficients ==! Cd, Ch, Ce at T-point
440	!
441	CASE( np_NCAR ) ; CALL turb_ncar ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! NCAR-COREv2
442	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
443	CASE( np_COARE_3p0 ) ; CALL turb_coare ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! COARE v3.0
444	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
445	CASE( np_COARE_3p5 ) ; CALL turb_coare3p5( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! COARE v3.5
446	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
447	CASE( np_ECMWF ) ; CALL turb_ecmwf ( rn_zqt, rn_zu, zst, ztpot, zsq, sf(jp_humi)%fnow, wndm, & ! ECMWF
448	& Cd_atm, Ch_atm, Ce_atm, t_zu, q_zu, zU_zu, cdn_oce, chn_oce, cen_oce )
449	CASE DEFAULT
450	CALL ctl_stop( 'STOP', 'sbc_oce: non-existing bulk formula selected' )
451	END SELECT
452
453	! ! Compute true air density :
454	IF( ABS(rn_zu - rn_zqt) > 0.01 ) THEN ! At zu: (probably useless to remove zrhogravrn_zu from SLP...)
455	zrhoa(:,:) = rho_air( t_zu(:,:) , q_zu(:,:) , sf(jp_slp)%fnow(:,:,1) )
456	ELSE ! At zt:
457	zrhoa(:,:) = rho_air( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1) )
458	END IF
459
460	!! CALL iom_put( "Cd_oce", Cd_atm) ! output value of pure ocean-atm. transfer coef.
461	!! CALL iom_put( "Ch_oce", Ch_atm) ! output value of pure ocean-atm. transfer coef.
462
463	DO jj = 1, jpj ! tau module, i and j component
464	DO ji = 1, jpi
465	zztmp = zrhoa(ji,jj) * zU_zu(ji,jj) * Cd_atm(ji,jj) ! using bulk wind speed
466	taum (ji,jj) = zztmp * wndm (ji,jj)
467	zwnd_i(ji,jj) = zztmp * zwnd_i(ji,jj)
468	zwnd_j(ji,jj) = zztmp * zwnd_j(ji,jj)
469	END DO
470	END DO
471
472	! ! add the HF tau contribution to the wind stress module
473	IF( lhftau ) taum(:,:) = taum(:,:) + sf(jp_tdif)%fnow(:,:,1)
474
475	CALL iom_put( "taum_oce", taum ) ! output wind stress module
476
477	! ... utau, vtau at U- and V_points, resp.
478	! Note the use of 0.5*(2-umask) in order to unmask the stress along coastlines
479	! Note the use of MAX(tmask(i,j),tmask(i+1,j) is to mask tau over ice shelves
480	DO jj = 1, jpjm1
481	DO ji = 1, fs_jpim1
482	utau(ji,jj) = 0.5 * ( 2. - umask(ji,jj,1) ) * ( zwnd_i(ji,jj) + zwnd_i(ji+1,jj ) ) &
483	& * MAX(tmask(ji,jj,1),tmask(ji+1,jj,1))
484	vtau(ji,jj) = 0.5 * ( 2. - vmask(ji,jj,1) ) * ( zwnd_j(ji,jj) + zwnd_j(ji ,jj+1) ) &
485	& * MAX(tmask(ji,jj,1),tmask(ji,jj+1,1))
486	END DO
487	END DO
488	CALL lbc_lnk_multi( 'sbcblk', utau, 'U', -1., vtau, 'V', -1. )
489
490	! Turbulent fluxes over ocean
491	! -----------------------------
492
493	! zqla used as temporary array, for rho*U (common term of bulk formulae):
494	zqla(:,:) = zrhoa(:,:) * zU_zu(:,:) * tmask(:,:,1)
495
496	IF( ABS( rn_zu - rn_zqt) < 0.01_wp ) THEN
497	!! q_air and t_air are given at 10m (wind reference height)
498	zevap(:,:) = rn_efacMAX( 0._wp, zqla(:,:)Ce_atm(:,:)*(zsq(:,:) - sf(jp_humi)%fnow(:,:,1)) ) ! Evaporation, using bulk wind speed
499	zqsb (:,:) = cp_air(sf(jp_humi)%fnow(:,:,1))zqla(:,:)Ch_atm(:,:)*(zst(:,:) - ztpot(:,:) ) ! Sensible Heat, using bulk wind speed
500	ELSE
501	!! q_air and t_air are not given at 10m (wind reference height)
502	! Values of temp. and hum. adjusted to height of wind during bulk algorithm iteration must be used!!!
503	zevap(:,:) = rn_efacMAX( 0._wp, zqla(:,:)Ce_atm(:,:)*(zsq(:,:) - q_zu(:,:) ) ) ! Evaporation, using bulk wind speed
504	zqsb (:,:) = cp_air(sf(jp_humi)%fnow(:,:,1))zqla(:,:)Ch_atm(:,:)*(zst(:,:) - t_zu(:,:) ) ! Sensible Heat, using bulk wind speed
505	ENDIF
506
507	zqla(:,:) = L_vap(zst(:,:)) * zevap(:,:) ! Latent Heat flux
508
509
510	IF(ln_ctl) THEN
511	CALL prt_ctl( tab2d_1=zqla , clinfo1=' blk_oce: zqla : ', tab2d_2=Ce_atm , clinfo2=' Ce_oce : ' )
512	CALL prt_ctl( tab2d_1=zqsb , clinfo1=' blk_oce: zqsb : ', tab2d_2=Ch_atm , clinfo2=' Ch_oce : ' )
513	CALL prt_ctl( tab2d_1=zqlw , clinfo1=' blk_oce: zqlw : ', tab2d_2=qsr, clinfo2=' qsr : ' )
514	CALL prt_ctl( tab2d_1=zsq , clinfo1=' blk_oce: zsq : ', tab2d_2=zst, clinfo2=' zst : ' )
515	CALL prt_ctl( tab2d_1=utau , clinfo1=' blk_oce: utau : ', mask1=umask, &
516	& tab2d_2=vtau , clinfo2= ' vtau : ', mask2=vmask )
517	CALL prt_ctl( tab2d_1=wndm , clinfo1=' blk_oce: wndm : ')
518	CALL prt_ctl( tab2d_1=zst , clinfo1=' blk_oce: zst : ')
519	ENDIF
520
521	! ----------------------------------------------------------------------------- !
522	! III Total FLUXES !
523	! ----------------------------------------------------------------------------- !
524	!
525	emp (:,:) = ( zevap(:,:) & ! mass flux (evap. - precip.)
526	& - sf(jp_prec)%fnow(:,:,1) * rn_pfac ) * tmask(:,:,1)
527	!
528	qns(:,:) = zqlw(:,:) - zqsb(:,:) - zqla(:,:) & ! Downward Non Solar
529	& - sf(jp_snow)%fnow(:,:,1) * rn_pfac * rLfus & ! remove latent melting heat for solid precip
530	& - zevap(:,:) * pst(:,:) * rcp & ! remove evap heat content at SST
531	& + ( sf(jp_prec)%fnow(:,:,1) - sf(jp_snow)%fnow(:,:,1) ) * rn_pfac & ! add liquid precip heat content at Tair
532	& * ( sf(jp_tair)%fnow(:,:,1) - rt0 ) * rcp &
533	& + sf(jp_snow)%fnow(:,:,1) * rn_pfac & ! add solid precip heat content at min(Tair,Tsnow)
534	& * ( MIN( sf(jp_tair)%fnow(:,:,1), rt0 ) - rt0 ) * rcpi
535	qns(:,:) = qns(:,:) * tmask(:,:,1)
536	!
537	#if defined key_si3
538	qns_oce(:,:) = zqlw(:,:) - zqsb(:,:) - zqla(:,:) ! non solar without emp (only needed by SI3)
539	qsr_oce(:,:) = qsr(:,:)
540	#endif
541	!
542	IF ( nn_ice == 0 ) THEN
543	CALL iom_put( "qlw_oce" , zqlw ) ! output downward longwave heat over the ocean
544	CALL iom_put( "qsb_oce" , - zqsb ) ! output downward sensible heat over the ocean
545	CALL iom_put( "qla_oce" , - zqla ) ! output downward latent heat over the ocean
546	CALL iom_put( "qemp_oce", qns-zqlw+zqsb+zqla ) ! output downward heat content of E-P over the ocean
547	CALL iom_put( "qns_oce" , qns ) ! output downward non solar heat over the ocean
548	CALL iom_put( "qsr_oce" , qsr ) ! output downward solar heat over the ocean
549	CALL iom_put( "qt_oce" , qns+qsr ) ! output total downward heat over the ocean
550	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! output total precipitation [kg/m2/s]
551	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! output solid precipitation [kg/m2/s]
552	CALL iom_put( 'snowpre', sprecip ) ! Snow
553	CALL iom_put( 'precip' , tprecip ) ! Total precipitation
554	ENDIF
555	!
556	IF(ln_ctl) THEN
557	CALL prt_ctl(tab2d_1=zqsb , clinfo1=' blk_oce: zqsb : ', tab2d_2=zqlw , clinfo2=' zqlw : ')
558	CALL prt_ctl(tab2d_1=zqla , clinfo1=' blk_oce: zqla : ', tab2d_2=qsr , clinfo2=' qsr : ')
559	CALL prt_ctl(tab2d_1=pst , clinfo1=' blk_oce: pst : ', tab2d_2=emp , clinfo2=' emp : ')
560	CALL prt_ctl(tab2d_1=utau , clinfo1=' blk_oce: utau : ', mask1=umask, &
561	& tab2d_2=vtau , clinfo2= ' vtau : ' , mask2=vmask )
562	ENDIF
563	!
564	END SUBROUTINE blk_oce
565
566
567
568	FUNCTION rho_air( ptak, pqa, pslp )
569	!!-------------------------------------------------------------------------------
570	!! * FUNCTION rho_air *
571	!!
572	!! ** Purpose : compute density of (moist) air using the eq. of state of the atmosphere
573	!!
574	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
575	!!-------------------------------------------------------------------------------
576	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
577	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg]
578	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! pressure in [Pa]
579	REAL(wp), DIMENSION(jpi,jpj) :: rho_air ! density of moist air [kg/m^3]
580	!!-------------------------------------------------------------------------------
581	!
582	rho_air = pslp / ( R_dryptak ( 1._wp + rctv0*pqa ) )
583	!
584	END FUNCTION rho_air
585
586
587	FUNCTION cp_air( pqa )
588	!!-------------------------------------------------------------------------------
589	!! * FUNCTION cp_air *
590	!!
591	!! ** Purpose : Compute specific heat (Cp) of moist air
592	!!
593	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
594	!!-------------------------------------------------------------------------------
595	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg]
596	REAL(wp), DIMENSION(jpi,jpj) :: cp_air ! specific heat of moist air [J/K/kg]
597	!!-------------------------------------------------------------------------------
598	!
599	Cp_air = Cp_dry + Cp_vap * pqa
600	!
601	END FUNCTION cp_air
602
603
604	FUNCTION q_sat( ptak, pslp )
605	!!----------------------------------------------------------------------------------
606	!! * FUNCTION q_sat *
607	!!
608	!! ** Purpose : Specific humidity at saturation in [kg/kg]
609	!! Based on accurate estimate of "e_sat"
610	!! aka saturation water vapor (Goff, 1957)
611	!!
612	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
613	!!----------------------------------------------------------------------------------
614	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
615	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! sea level atmospheric pressure [Pa]
616	REAL(wp), DIMENSION(jpi,jpj) :: q_sat ! Specific humidity at saturation [kg/kg]
617	!
618	INTEGER :: ji, jj ! dummy loop indices
619	REAL(wp) :: ze_sat, ztmp ! local scalar
620	!!----------------------------------------------------------------------------------
621	!
622	DO jj = 1, jpj
623	DO ji = 1, jpi
624	!
625	ztmp = rt0 / ptak(ji,jj)
626	!
627	! Vapour pressure at saturation [hPa] : WMO, (Goff, 1957)
628	ze_sat = 10.*( 10.79574(1. - ztmp) - 5.028*LOG10(ptak(ji,jj)/rt0) &
629	& + 1.5047510.(-4)(1. - 10.*(-8.2969(ptak(ji,jj)/rt0 - 1.)) ) &
630	& + 0.4287310.(-3)(10.*(4.76955(1. - ztmp)) - 1.) + 0.78614 )
631	!
632	q_sat(ji,jj) = reps0 * ze_sat/( 0.01_wppslp(ji,jj) - (1._wp - reps0)ze_sat ) ! 0.01 because SLP is in [Pa]
633	!
634	END DO
635	END DO
636	!
637	END FUNCTION q_sat
638
639
640	FUNCTION gamma_moist( ptak, pqa )
641	!!----------------------------------------------------------------------------------
642	!! * FUNCTION gamma_moist *
643	!!
644	!! ** Purpose : Compute the moist adiabatic lapse-rate.
645	!! => http://glossary.ametsoc.org/wiki/Moist-adiabatic_lapse_rate
646	!! => http://www.geog.ucsb.edu/~joel/g266_s10/lecture_notes/chapt03/oh10_3_01/oh10_3_01.html
647	!!
648	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
649	!!----------------------------------------------------------------------------------
650	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
651	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! specific humidity [kg/kg]
652	REAL(wp), DIMENSION(jpi,jpj) :: gamma_moist ! moist adiabatic lapse-rate
653	!
654	INTEGER :: ji, jj ! dummy loop indices
655	REAL(wp) :: zrv, ziRT ! local scalar
656	!!----------------------------------------------------------------------------------
657	!
658	DO jj = 1, jpj
659	DO ji = 1, jpi
660	zrv = pqa(ji,jj) / (1. - pqa(ji,jj))
661	ziRT = 1. / (R_dry*ptak(ji,jj)) ! 1/RT
662	gamma_moist(ji,jj) = grav * ( 1. + rLevapzrvziRT ) / ( Cp_dry + rLevaprLevapzrvreps0ziRT/ptak(ji,jj) )
663	END DO
664	END DO
665	!
666	END FUNCTION gamma_moist
667
668
669	FUNCTION L_vap( psst )
670	!!---------------------------------------------------------------------------------
671	!! * FUNCTION L_vap *
672	!!
673	!! ** Purpose : Compute the latent heat of vaporization of water from temperature
674	!!
675	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk)
676	!!----------------------------------------------------------------------------------
677	REAL(wp), DIMENSION(jpi,jpj) :: L_vap ! latent heat of vaporization [J/kg]
678	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! water temperature [K]
679	!!----------------------------------------------------------------------------------
680	!
681	L_vap = ( 2.501 - 0.00237 * ( psst(:,:) - rt0) ) * 1.e6
682	!
683	END FUNCTION L_vap
684
685	#if defined key_si3
686	!!----------------------------------------------------------------------
687	!! 'key_si3' SI3 sea-ice model
688	!!----------------------------------------------------------------------
689	!! blk_ice_tau : provide the air-ice stress
690	!! blk_ice_flx : provide the heat and mass fluxes at air-ice interface
691	!! blk_ice_qcn : provide ice surface temperature and snow/ice conduction flux (emulating conduction flux)
692	!! Cdn10_Lupkes2012 : Lupkes et al. (2012) air-ice drag
693	!! Cdn10_Lupkes2015 : Lupkes et al. (2015) air-ice drag
694	!!----------------------------------------------------------------------
695
696	SUBROUTINE blk_ice_tau
697	!!---------------------------------------------------------------------
698	!! * ROUTINE blk_ice_tau *
699	!!
700	!! ** Purpose : provide the surface boundary condition over sea-ice
701	!!
702	!! ** Method : compute momentum using bulk formulation
703	!! formulea, ice variables and read atmospheric fields.
704	!! NB: ice drag coefficient is assumed to be a constant
705	!!---------------------------------------------------------------------
706	INTEGER :: ji, jj ! dummy loop indices
707	REAL(wp) :: zwndi_f , zwndj_f, zwnorm_f ! relative wind module and components at F-point
708	REAL(wp) :: zwndi_t , zwndj_t ! relative wind components at T-point
709	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa ! transfer coefficient for momentum (tau)
710	!!---------------------------------------------------------------------
711	!
712	! set transfer coefficients to default sea-ice values
713	Cd_atm(:,:) = Cd_ice
714	Ch_atm(:,:) = Cd_ice
715	Ce_atm(:,:) = Cd_ice
716
717	wndm_ice(:,:) = 0._wp !!gm brutal....
718
719	! ------------------------------------------------------------ !
720	! Wind module relative to the moving ice ( U10m - U_ice ) !
721	! ------------------------------------------------------------ !
722	! C-grid ice dynamics : U & V-points (same as ocean)
723	DO jj = 2, jpjm1
724	DO ji = fs_2, fs_jpim1 ! vect. opt.
725	zwndi_t = ( sf(jp_wndi)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( u_ice(ji-1,jj ) + u_ice(ji,jj) ) )
726	zwndj_t = ( sf(jp_wndj)%fnow(ji,jj,1) - rn_vfac * 0.5 * ( v_ice(ji ,jj-1) + v_ice(ji,jj) ) )
727	wndm_ice(ji,jj) = SQRT( zwndi_t * zwndi_t + zwndj_t * zwndj_t ) * tmask(ji,jj,1)
728	END DO
729	END DO
730	CALL lbc_lnk( 'sbcblk', wndm_ice, 'T', 1. )
731	!
732	! Make ice-atm. drag dependent on ice concentration
733	IF ( ln_Cd_L12 ) THEN ! calculate new drag from Lupkes(2012) equations
734	CALL Cdn10_Lupkes2012( Cd_atm )
735	Ch_atm(:,:) = Cd_atm(:,:) ! momentum and heat transfer coef. are considered identical
736	ELSEIF( ln_Cd_L15 ) THEN ! calculate new drag from Lupkes(2015) equations
737	CALL Cdn10_Lupkes2015( Cd_atm, Ch_atm )
738	ENDIF
739
740	!! CALL iom_put( "Cd_ice", Cd_atm) ! output value of pure ice-atm. transfer coef.
741	!! CALL iom_put( "Ch_ice", Ch_atm) ! output value of pure ice-atm. transfer coef.
742
743	! local scalars ( place there for vector optimisation purposes)
744	! Computing density of air! Way denser that 1.2 over sea-ice !!!
745	zrhoa (:,:) = rho_air(sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1))
746
747	!!gm brutal....
748	utau_ice (:,:) = 0._wp
749	vtau_ice (:,:) = 0._wp
750	!!gm end
751
752	! ------------------------------------------------------------ !
753	! Wind stress relative to the moving ice ( U10m - U_ice ) !
754	! ------------------------------------------------------------ !
755	! C-grid ice dynamics : U & V-points (same as ocean)
756	DO jj = 2, jpjm1
757	DO ji = fs_2, fs_jpim1 ! vect. opt.
758	utau_ice(ji,jj) = 0.5 * zrhoa(ji,jj) * Cd_atm(ji,jj) * ( wndm_ice(ji+1,jj ) + wndm_ice(ji,jj) ) &
759	& * ( 0.5 * (sf(jp_wndi)%fnow(ji+1,jj,1) + sf(jp_wndi)%fnow(ji,jj,1) ) - rn_vfac * u_ice(ji,jj) )
760	vtau_ice(ji,jj) = 0.5 * zrhoa(ji,jj) * Cd_atm(ji,jj) * ( wndm_ice(ji,jj+1 ) + wndm_ice(ji,jj) ) &
761	& * ( 0.5 * (sf(jp_wndj)%fnow(ji,jj+1,1) + sf(jp_wndj)%fnow(ji,jj,1) ) - rn_vfac * v_ice(ji,jj) )
762	END DO
763	END DO
764	CALL lbc_lnk_multi( 'sbcblk', utau_ice, 'U', -1., vtau_ice, 'V', -1. )
765	!
766	!
767	IF(ln_ctl) THEN
768	CALL prt_ctl(tab2d_1=utau_ice , clinfo1=' blk_ice: utau_ice : ', tab2d_2=vtau_ice , clinfo2=' vtau_ice : ')
769	CALL prt_ctl(tab2d_1=wndm_ice , clinfo1=' blk_ice: wndm_ice : ')
770	ENDIF
771	!
772	END SUBROUTINE blk_ice_tau
773
774
775	SUBROUTINE blk_ice_flx( ptsu, phs, phi, palb )
776	!!---------------------------------------------------------------------
777	!! * ROUTINE blk_ice_flx *
778	!!
779	!! ** Purpose : provide the heat and mass fluxes at air-ice interface
780	!!
781	!! ** Method : compute heat and freshwater exchanged
782	!! between atmosphere and sea-ice using bulk formulation
783	!! formulea, ice variables and read atmmospheric fields.
784	!!
785	!! caution : the net upward water flux has with mm/day unit
786	!!---------------------------------------------------------------------
787	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: ptsu ! sea ice surface temperature
788	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: phs ! snow thickness
789	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: phi ! ice thickness
790	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: palb ! ice albedo (all skies)
791	!!
792	INTEGER :: ji, jj, jl ! dummy loop indices
793	REAL(wp) :: zst3 ! local variable
794	REAL(wp) :: zcoef_dqlw, zcoef_dqla ! - -
795	REAL(wp) :: zztmp, z1_rLsub ! - -
796	REAL(wp) :: zfr1, zfr2 ! local variables
797	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_st ! inverse of surface temperature
798	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_qlw ! long wave heat flux over ice
799	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_qsb ! sensible heat flux over ice
800	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_dqlw ! long wave heat sensitivity over ice
801	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z_dqsb ! sensible heat sensitivity over ice
802	REAL(wp), DIMENSION(jpi,jpj) :: zevap, zsnw ! evaporation and snw distribution after wind blowing (SI3)
803	REAL(wp), DIMENSION(jpi,jpj) :: zrhoa
804	!!---------------------------------------------------------------------
805	!
806	zcoef_dqlw = 4.0 * 0.95 * Stef ! local scalars
807	zcoef_dqla = -Ls * 11637800. * (-5897.8)
808	!
809	zrhoa(:,:) = rho_air( sf(jp_tair)%fnow(:,:,1), sf(jp_humi)%fnow(:,:,1), sf(jp_slp)%fnow(:,:,1) )
810	!
811	zztmp = 1. / ( 1. - albo )
812	WHERE( ptsu(:,:,:) /= 0._wp ) ; z1_st(:,:,:) = 1._wp / ptsu(:,:,:)
813	ELSEWHERE ; z1_st(:,:,:) = 0._wp
814	END WHERE
815	! ! ========================== !
816	DO jl = 1, jpl ! Loop over ice categories !
817	! ! ========================== !
818	DO jj = 1 , jpj
819	DO ji = 1, jpi
820	! ----------------------------!
821	! I Radiative FLUXES !
822	! ----------------------------!
823	zst3 = ptsu(ji,jj,jl) * ptsu(ji,jj,jl) * ptsu(ji,jj,jl)
824	! Short Wave (sw)
825	qsr_ice(ji,jj,jl) = zztmp * ( 1. - palb(ji,jj,jl) ) * qsr(ji,jj)
826	! Long Wave (lw)
827	z_qlw(ji,jj,jl) = 0.95 * ( sf(jp_qlw)%fnow(ji,jj,1) - Stef * ptsu(ji,jj,jl) * zst3 ) * tmask(ji,jj,1)
828	! lw sensitivity
829	z_dqlw(ji,jj,jl) = zcoef_dqlw * zst3
830
831	! ----------------------------!
832	! II Turbulent FLUXES !
833	! ----------------------------!
834
835	! ... turbulent heat fluxes with Ch_atm recalculated in blk_ice_tau
836	! Sensible Heat
837	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))
838	! Latent Heat
839	qla_ice(ji,jj,jl) = rn_efac * MAX( 0.e0, zrhoa(ji,jj) * Ls * Ch_atm(ji,jj) * wndm_ice(ji,jj) * &
840	& ( 11637800. * EXP( -5897.8 * z1_st(ji,jj,jl) ) / zrhoa(ji,jj) - sf(jp_humi)%fnow(ji,jj,1) ) )
841	! Latent heat sensitivity for ice (Dqla/Dt)
842	IF( qla_ice(ji,jj,jl) > 0._wp ) THEN
843	dqla_ice(ji,jj,jl) = rn_efac * zcoef_dqla * Ch_atm(ji,jj) * wndm_ice(ji,jj) * &
844	& z1_st(ji,jj,jl)z1_st(ji,jj,jl) EXP(-5897.8 * z1_st(ji,jj,jl))
845	ELSE
846	dqla_ice(ji,jj,jl) = 0._wp
847	ENDIF
848
849	! Sensible heat sensitivity (Dqsb_ice/Dtn_ice)
850	z_dqsb(ji,jj,jl) = zrhoa(ji,jj) * cpa * Ch_atm(ji,jj) * wndm_ice(ji,jj)
851
852	! ----------------------------!
853	! III Total FLUXES !
854	! ----------------------------!
855	! Downward Non Solar flux
856	qns_ice (ji,jj,jl) = z_qlw (ji,jj,jl) - z_qsb (ji,jj,jl) - qla_ice (ji,jj,jl)
857	! Total non solar heat flux sensitivity for ice
858	dqns_ice(ji,jj,jl) = - ( z_dqlw(ji,jj,jl) + z_dqsb(ji,jj,jl) + dqla_ice(ji,jj,jl) )
859	END DO
860	!
861	END DO
862	!
863	END DO
864	!
865	tprecip(:,:) = sf(jp_prec)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! total precipitation [kg/m2/s]
866	sprecip(:,:) = sf(jp_snow)%fnow(:,:,1) * rn_pfac * tmask(:,:,1) ! solid precipitation [kg/m2/s]
867	CALL iom_put( 'snowpre', sprecip ) ! Snow precipitation
868	CALL iom_put( 'precip' , tprecip ) ! Total precipitation
869
870	! --- evaporation --- !
871	z1_rLsub = 1._wp / rLsub
872	evap_ice (:,:,:) = rn_efac * qla_ice (:,:,:) * z1_rLsub ! sublimation
873	devap_ice(:,:,:) = rn_efac * dqla_ice(:,:,:) * z1_rLsub ! d(sublimation)/dT
874	zevap (:,:) = rn_efac * ( emp(:,:) + tprecip(:,:) ) ! evaporation over ocean
875
876	! --- evaporation minus precipitation --- !
877	zsnw(:,:) = 0._wp
878	CALL ice_thd_snwblow( (1.-at_i_b(:,:)), zsnw ) ! snow distribution over ice after wind blowing
879	emp_oce(:,:) = ( 1._wp - at_i_b(:,:) ) * zevap(:,:) - ( tprecip(:,:) - sprecip(:,:) ) - sprecip(:,:) * (1._wp - zsnw )
880	emp_ice(:,:) = SUM( a_i_b(:,:,:) * evap_ice(:,:,:), dim=3 ) - sprecip(:,:) * zsnw
881	emp_tot(:,:) = emp_oce(:,:) + emp_ice(:,:)
882
883	! --- heat flux associated with emp --- !
884	qemp_oce(:,:) = - ( 1._wp - at_i_b(:,:) ) * zevap(:,:) * sst_m(:,:) * rcp & ! evap at sst
885	& + ( tprecip(:,:) - sprecip(:,:) ) * ( sf(jp_tair)%fnow(:,:,1) - rt0 ) * rcp & ! liquid precip at Tair
886	& + sprecip(:,:) * ( 1._wp - zsnw ) * & ! solid precip at min(Tair,Tsnow)
887	& ( ( MIN( sf(jp_tair)%fnow(:,:,1), rt0 ) - rt0 ) * rcpi * tmask(:,:,1) - rLfus )
888	qemp_ice(:,:) = sprecip(:,:) * zsnw * & ! solid precip (only)
889	& ( ( MIN( sf(jp_tair)%fnow(:,:,1), rt0 ) - rt0 ) * rcpi * tmask(:,:,1) - rLfus )
890
891	! --- total solar and non solar fluxes --- !
892	qns_tot(:,:) = ( 1._wp - at_i_b(:,:) ) * qns_oce(:,:) + SUM( a_i_b(:,:,:) * qns_ice(:,:,:), dim=3 ) &
893	& + qemp_ice(:,:) + qemp_oce(:,:)
894	qsr_tot(:,:) = ( 1._wp - at_i_b(:,:) ) * qsr_oce(:,:) + SUM( a_i_b(:,:,:) * qsr_ice(:,:,:), dim=3 )
895
896	! --- heat content of precip over ice in J/m3 (to be used in 1D-thermo) --- !
897	qprec_ice(:,:) = rhos * ( ( MIN( sf(jp_tair)%fnow(:,:,1), rt0 ) - rt0 ) * rcpi * tmask(:,:,1) - rLfus )
898
899	! --- heat content of evap over ice in W/m2 (to be used in 1D-thermo) ---
900	DO jl = 1, jpl
901	qevap_ice(:,:,jl) = 0._wp ! should be -evap_ice(:,:,jl)( ( Tice - rt0 ) rcpi * tmask(:,:,1) )
902	! ! But we do not have Tice => consider it at 0degC => evap=0
903	END DO
904
905	! --- shortwave radiation transmitted below the surface (W/m2, see Grenfell Maykut 77) --- !
906	zfr1 = ( 0.18 * ( 1.0 - cldf_ice ) + 0.35 * cldf_ice ) ! transmission when hi>10cm
907	zfr2 = ( 0.82 * ( 1.0 - cldf_ice ) + 0.65 * cldf_ice ) ! zfr2 such that zfr1 + zfr2 to equal 1
908	!
909	WHERE ( phs(:,:,:) <= 0._wp .AND. phi(:,:,:) < 0.1_wp ) ! linear decrease from hi=0 to 10cm
910	qtr_ice_top(:,:,:) = qsr_ice(:,:,:) * ( zfr1 + zfr2 * ( 1._wp - phi(:,:,:) * 10._wp ) )
911	ELSEWHERE( phs(:,:,:) <= 0._wp .AND. phi(:,:,:) >= 0.1_wp ) ! constant (zfr1) when hi>10cm
912	qtr_ice_top(:,:,:) = qsr_ice(:,:,:) * zfr1
913	ELSEWHERE ! zero when hs>0
914	qtr_ice_top(:,:,:) = 0._wp
915	END WHERE
916	!
917	IF(ln_ctl) THEN
918	CALL prt_ctl(tab3d_1=qla_ice , clinfo1=' blk_ice: qla_ice : ', tab3d_2=z_qsb , clinfo2=' z_qsb : ', kdim=jpl)
919	CALL prt_ctl(tab3d_1=z_qlw , clinfo1=' blk_ice: z_qlw : ', tab3d_2=dqla_ice, clinfo2=' dqla_ice : ', kdim=jpl)
920	CALL prt_ctl(tab3d_1=z_dqsb , clinfo1=' blk_ice: z_dqsb : ', tab3d_2=z_dqlw , clinfo2=' z_dqlw : ', kdim=jpl)
921	CALL prt_ctl(tab3d_1=dqns_ice, clinfo1=' blk_ice: dqns_ice : ', tab3d_2=qsr_ice , clinfo2=' qsr_ice : ', kdim=jpl)
922	CALL prt_ctl(tab3d_1=ptsu , clinfo1=' blk_ice: ptsu : ', tab3d_2=qns_ice , clinfo2=' qns_ice : ', kdim=jpl)
923	CALL prt_ctl(tab2d_1=tprecip , clinfo1=' blk_ice: tprecip : ', tab2d_2=sprecip , clinfo2=' sprecip : ')
924	ENDIF
925	!
926	END SUBROUTINE blk_ice_flx
927
928
929	SUBROUTINE blk_ice_qcn( ld_virtual_itd, ptsu, ptb, phs, phi )
930	!!---------------------------------------------------------------------
931	!! * ROUTINE blk_ice_qcn *
932	!!
933	!! ** Purpose : Compute surface temperature and snow/ice conduction flux
934	!! to force sea ice / snow thermodynamics
935	!! in the case conduction flux is emulated
936	!!
937	!! ** Method : compute surface energy balance assuming neglecting heat storage
938	!! following the 0-layer Semtner (1976) approach
939	!!
940	!! ** Outputs : - ptsu : sea-ice / snow surface temperature (K)
941	!! - qcn_ice : surface inner conduction flux (W/m2)
942	!!
943	!!---------------------------------------------------------------------
944	LOGICAL , INTENT(in ) :: ld_virtual_itd ! single-category option
945	REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: ptsu ! sea ice / snow surface temperature
946	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: ptb ! sea ice base temperature
947	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: phs ! snow thickness
948	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: phi ! sea ice thickness
949	!
950	INTEGER , PARAMETER :: nit = 10 ! number of iterations
951	REAL(wp), PARAMETER :: zepsilon = 0.1_wp ! characteristic thickness for enhanced conduction
952	!
953	INTEGER :: ji, jj, jl ! dummy loop indices
954	INTEGER :: iter ! local integer
955	REAL(wp) :: zfac, zfac2, zfac3 ! local scalars
956	REAL(wp) :: zkeff_h, ztsu, ztsu0 !
957	REAL(wp) :: zqc, zqnet !
958	REAL(wp) :: zhe, zqa0 !
959	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zgfac ! enhanced conduction factor
960	!!---------------------------------------------------------------------
961
962	! -------------------------------------!
963	! I Enhanced conduction factor !
964	! -------------------------------------!
965	! Emulates the enhancement of conduction by unresolved thin ice (ld_virtual_itd = T)
966	! Fichefet and Morales Maqueda, JGR 1997
967	!
968	zgfac(:,:,:) = 1._wp
969
970	IF( ld_virtual_itd ) THEN
971	!
972	zfac = 1._wp / ( rn_cnd_s + rcnd_i )
973	zfac2 = EXP(1._wp) * 0.5_wp * zepsilon
974	zfac3 = 2._wp / zepsilon
975	!
976	DO jl = 1, jpl
977	DO jj = 1 , jpj
978	DO ji = 1, jpi
979	zhe = ( rn_cnd_s * phi(ji,jj,jl) + rcnd_i * phs(ji,jj,jl) ) * zfac ! Effective thickness
980	IF( zhe >= zfac2 ) zgfac(ji,jj,jl) = MIN( 2._wp, 0.5_wp * ( 1._wp + LOG( zhe * zfac3 ) ) ) ! Enhanced conduction factor
981	END DO
982	END DO
983	END DO
984	!
985	ENDIF
986
987	! -------------------------------------------------------------!
988	! II Surface temperature and conduction flux !
989	! -------------------------------------------------------------!
990	!
991	zfac = rcnd_i * rn_cnd_s
992	!
993	DO jl = 1, jpl
994	DO jj = 1 , jpj
995	DO ji = 1, jpi
996	!
997	zkeff_h = zfac * zgfac(ji,jj,jl) / & ! Effective conductivity of the snow-ice system divided by thickness
998	& ( rcnd_i * phs(ji,jj,jl) + rn_cnd_s * MAX( 0.01, phi(ji,jj,jl) ) )
999	ztsu = ptsu(ji,jj,jl) ! Store current iteration temperature
1000	ztsu0 = ptsu(ji,jj,jl) ! Store initial surface temperature
1001	zqa0 = qsr_ice(ji,jj,jl) - qtr_ice_top(ji,jj,jl) + qns_ice(ji,jj,jl) ! Net initial atmospheric heat flux
1002	!
1003	DO iter = 1, nit ! --- Iterative loop
1004	zqc = zkeff_h * ( ztsu - ptb(ji,jj) ) ! Conduction heat flux through snow-ice system (>0 downwards)
1005	zqnet = zqa0 + dqns_ice(ji,jj,jl) * ( ztsu - ptsu(ji,jj,jl) ) - zqc ! Surface energy budget
1006	ztsu = ztsu - zqnet / ( dqns_ice(ji,jj,jl) - zkeff_h ) ! Temperature update
1007	END DO
1008	!
1009	ptsu (ji,jj,jl) = MIN( rt0, ztsu )
1010	qcn_ice(ji,jj,jl) = zkeff_h * ( ptsu(ji,jj,jl) - ptb(ji,jj) )
1011	qns_ice(ji,jj,jl) = qns_ice(ji,jj,jl) + dqns_ice(ji,jj,jl) * ( ptsu(ji,jj,jl) - ztsu0 )
1012	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) ) &
1013	& * MAX( 0._wp , SIGN( 1._wp, ptsu(ji,jj,jl) - rt0 ) )
1014
1015	! --- Diagnose the heat loss due to changing non-solar flux (as in icethd_zdf_bl99) --- !
1016	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)
1017
1018	END DO
1019	END DO
1020	!
1021	END DO
1022	!
1023	END SUBROUTINE blk_ice_qcn
1024
1025
1026	SUBROUTINE Cdn10_Lupkes2012( Cd )
1027	!!----------------------------------------------------------------------
1028	!! * ROUTINE Cdn10_Lupkes2012 *
1029	!!
1030	!! ** Purpose : Recompute the neutral air-ice drag referenced at 10m
1031	!! to make it dependent on edges at leads, melt ponds and flows.
1032	!! After some approximations, this can be resumed to a dependency
1033	!! on ice concentration.
1034	!!
1035	!! ** Method : The parameterization is taken from Lupkes et al. (2012) eq.(50)
1036	!! with the highest level of approximation: level4, eq.(59)
1037	!! The generic drag over a cell partly covered by ice can be re-written as follows:
1038	!!
1039	!! Cd = Cdw * (1-A) + Cdi * A + Ce * (1-A)*(nu+1/(10beta)) * A**mu
1040	!!
1041	!! Ce = 2.23e-3 , as suggested by Lupkes (eq. 59)
1042	!! nu = mu = beta = 1 , as suggested by Lupkes (eq. 59)
1043	!! A is the concentration of ice minus melt ponds (if any)
1044	!!
1045	!! This new drag has a parabolic shape (as a function of A) starting at
1046	!! Cdw(say 1.5e-3) for A=0, reaching 1.97e-3 for A~0.5
1047	!! and going down to Cdi(say 1.4e-3) for A=1
1048	!!
1049	!! It is theoretically applicable to all ice conditions (not only MIZ)
1050	!! => see Lupkes et al (2013)
1051	!!
1052	!! ** References : Lupkes et al. JGR 2012 (theory)
1053	!! Lupkes et al. GRL 2013 (application to GCM)
1054	!!
1055	!!----------------------------------------------------------------------
1056	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Cd
1057	REAL(wp), PARAMETER :: zCe = 2.23e-03_wp
1058	REAL(wp), PARAMETER :: znu = 1._wp
1059	REAL(wp), PARAMETER :: zmu = 1._wp
1060	REAL(wp), PARAMETER :: zbeta = 1._wp
1061	REAL(wp) :: zcoef
1062	!!----------------------------------------------------------------------
1063	zcoef = znu + 1._wp / ( 10._wp * zbeta )
1064
1065	! generic drag over a cell partly covered by ice
1066	!!Cd(:,:) = Cd_oce(:,:) * ( 1._wp - at_i_b(:,:) ) + & ! pure ocean drag
1067	!! & Cd_ice * at_i_b(:,:) + & ! pure ice drag
1068	!! & zCe * ( 1._wp - at_i_b(:,:) )*zcoef at_i_b(:,:)**zmu ! change due to sea-ice morphology
1069
1070	! ice-atm drag
1071	Cd(:,:) = Cd_ice + & ! pure ice drag
1072	& zCe * ( 1._wp - at_i_b(:,:) )*zcoef at_i_b(:,:)**(zmu-1._wp) ! change due to sea-ice morphology
1073
1074	END SUBROUTINE Cdn10_Lupkes2012
1075
1076
1077	SUBROUTINE Cdn10_Lupkes2015( Cd, Ch )
1078	!!----------------------------------------------------------------------
1079	!! * ROUTINE Cdn10_Lupkes2015 *
1080	!!
1081	!! ** pUrpose : Alternative turbulent transfert coefficients formulation
1082	!! between sea-ice and atmosphere with distinct momentum
1083	!! and heat coefficients depending on sea-ice concentration
1084	!! and atmospheric stability (no meltponds effect for now).
1085	!!
1086	!! ** Method : The parameterization is adapted from Lupkes et al. (2015)
1087	!! and ECHAM6 atmospheric model. Compared to Lupkes2012 scheme,
1088	!! it considers specific skin and form drags (Andreas et al. 2010)
1089	!! to compute neutral transfert coefficients for both heat and
1090	!! momemtum fluxes. Atmospheric stability effect on transfert
1091	!! coefficient is also taken into account following Louis (1979).
1092	!!
1093	!! ** References : Lupkes et al. JGR 2015 (theory)
1094	!! Lupkes et al. ECHAM6 documentation 2015 (implementation)
1095	!!
1096	!!----------------------------------------------------------------------
1097	!
1098	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Cd
1099	REAL(wp), DIMENSION(:,:), INTENT(inout) :: Ch
1100	REAL(wp), DIMENSION(jpi,jpj) :: ztm_su, zst, zqo_sat, zqi_sat
1101	!
1102	! ECHAM6 constants
1103	REAL(wp), PARAMETER :: z0_skin_ice = 0.69e-3_wp ! Eq. 43 [m]
1104	REAL(wp), PARAMETER :: z0_form_ice = 0.57e-3_wp ! Eq. 42 [m]
1105	REAL(wp), PARAMETER :: z0_ice = 1.00e-3_wp ! Eq. 15 [m]
1106	REAL(wp), PARAMETER :: zce10 = 2.80e-3_wp ! Eq. 41
1107	REAL(wp), PARAMETER :: zbeta = 1.1_wp ! Eq. 41
1108	REAL(wp), PARAMETER :: zc = 5._wp ! Eq. 13
1109	REAL(wp), PARAMETER :: zc2 = zc * zc
1110	REAL(wp), PARAMETER :: zam = 2. * zc ! Eq. 14
1111	REAL(wp), PARAMETER :: zah = 3. * zc ! Eq. 30
1112	REAL(wp), PARAMETER :: z1_alpha = 1._wp / 0.2_wp ! Eq. 51
1113	REAL(wp), PARAMETER :: z1_alphaf = z1_alpha ! Eq. 56
1114	REAL(wp), PARAMETER :: zbetah = 1.e-3_wp ! Eq. 26
1115	REAL(wp), PARAMETER :: zgamma = 1.25_wp ! Eq. 26
1116	REAL(wp), PARAMETER :: z1_gamma = 1._wp / zgamma
1117	REAL(wp), PARAMETER :: r1_3 = 1._wp / 3._wp
1118	!
1119	INTEGER :: ji, jj ! dummy loop indices
1120	REAL(wp) :: zthetav_os, zthetav_is, zthetav_zu
1121	REAL(wp) :: zrib_o, zrib_i
1122	REAL(wp) :: zCdn_skin_ice, zCdn_form_ice, zCdn_ice
1123	REAL(wp) :: zChn_skin_ice, zChn_form_ice
1124	REAL(wp) :: z0w, z0i, zfmi, zfmw, zfhi, zfhw
1125	REAL(wp) :: zCdn_form_tmp
1126	!!----------------------------------------------------------------------
1127
1128	! mean temperature
1129	WHERE( at_i_b(:,:) > 1.e-20 ) ; ztm_su(:,:) = SUM( t_su(:,:,:) * a_i_b(:,:,:) , dim=3 ) / at_i_b(:,:)
1130	ELSEWHERE ; ztm_su(:,:) = rt0
1131	ENDWHERE
1132
1133	! Momentum Neutral Transfert Coefficients (should be a constant)
1134	zCdn_form_tmp = zce10 * ( LOG( 10._wp / z0_form_ice + 1._wp ) / LOG( rn_zu / z0_form_ice + 1._wp ) )**2 ! Eq. 40
1135	zCdn_skin_ice = ( vkarmn / LOG( rn_zu / z0_skin_ice + 1._wp ) )**2 ! Eq. 7
1136	zCdn_ice = zCdn_skin_ice ! Eq. 7 (cf Lupkes email for details)
1137	!zCdn_ice = 1.89e-3 ! old ECHAM5 value (cf Eq. 32)
1138
1139	! Heat Neutral Transfert Coefficients
1140	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)
1141
1142	! Atmospheric and Surface Variables
1143	zst(:,:) = sst_m(:,:) + rt0 ! convert SST from Celcius to Kelvin
1144	zqo_sat(:,:) = 0.98_wp * q_sat( zst(:,:) , sf(jp_slp)%fnow(:,:,1) ) ! saturation humidity over ocean [kg/kg]
1145	zqi_sat(:,:) = 0.98_wp * q_sat( ztm_su(:,:), sf(jp_slp)%fnow(:,:,1) ) ! saturation humidity over ice [kg/kg]
1146	!
1147	DO jj = 2, jpjm1 ! reduced loop is necessary for reproducibility
1148	DO ji = fs_2, fs_jpim1
1149	! Virtual potential temperature [K]
1150	zthetav_os = zst(ji,jj) * ( 1._wp + rctv0 * zqo_sat(ji,jj) ) ! over ocean
1151	zthetav_is = ztm_su(ji,jj) * ( 1._wp + rctv0 * zqi_sat(ji,jj) ) ! ocean ice
1152	zthetav_zu = t_zu (ji,jj) * ( 1._wp + rctv0 * q_zu(ji,jj) ) ! at zu
1153
1154	! Bulk Richardson Number (could use Ri_bulk function from aerobulk instead)
1155	zrib_o = grav / zthetav_os * ( zthetav_zu - zthetav_os ) * rn_zu / MAX( 0.5, wndm(ji,jj) )**2 ! over ocean
1156	zrib_i = grav / zthetav_is * ( zthetav_zu - zthetav_is ) * rn_zu / MAX( 0.5, wndm_ice(ji,jj) )**2 ! over ice
1157
1158	! Momentum and Heat Neutral Transfert Coefficients
1159	zCdn_form_ice = zCdn_form_tmp * at_i_b(ji,jj) * ( 1._wp - at_i_b(ji,jj) )**zbeta ! Eq. 40
1160	zChn_form_ice = zCdn_form_ice / ( 1._wp + ( LOG( z1_alphaf ) / vkarmn ) * SQRT( zCdn_form_ice ) ) ! Eq. 53
1161
1162	! Momentum and Heat Stability functions (possibility to use psi_m_ecmwf instead)
1163	z0w = rn_zu * EXP( -1._wp * vkarmn / SQRT( Cdn_oce(ji,jj) ) ) ! over water
1164	z0i = z0_skin_ice ! over ice (cf Lupkes email for details)
1165	IF( zrib_o <= 0._wp ) THEN
1166	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
1167	zfhw = ( 1._wp + ( zbetah * ( zthetav_os - zthetav_zu )*r1_3 / ( Chn_oce(ji,jj) MAX(0.01, wndm(ji,jj)) ) & ! Eq. 26
1168	& )zgamma )z1_gamma
1169	ELSE
1170	zfmw = 1._wp / ( 1._wp + zam * zrib_o / SQRT( 1._wp + zrib_o ) ) ! Eq. 12
1171	zfhw = 1._wp / ( 1._wp + zah * zrib_o / SQRT( 1._wp + zrib_o ) ) ! Eq. 28
1172	ENDIF
1173
1174	IF( zrib_i <= 0._wp ) THEN
1175	zfmi = 1._wp - zam * zrib_i / (1._wp + 3._wp * zc2 * zCdn_ice * SQRT( -zrib_i * ( rn_zu / z0i + 1._wp))) ! Eq. 9
1176	zfhi = 1._wp - zah * zrib_i / (1._wp + 3._wp * zc2 * zCdn_ice * SQRT( -zrib_i * ( rn_zu / z0i + 1._wp))) ! Eq. 25
1177	ELSE
1178	zfmi = 1._wp / ( 1._wp + zam * zrib_i / SQRT( 1._wp + zrib_i ) ) ! Eq. 11
1179	zfhi = 1._wp / ( 1._wp + zah * zrib_i / SQRT( 1._wp + zrib_i ) ) ! Eq. 27
1180	ENDIF
1181
1182	! Momentum Transfert Coefficients (Eq. 38)
1183	Cd(ji,jj) = zCdn_skin_ice * zfmi + &
1184	& 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) )
1185
1186	! Heat Transfert Coefficients (Eq. 49)
1187	Ch(ji,jj) = zChn_skin_ice * zfhi + &
1188	& 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) )
1189	!
1190	END DO
1191	END DO
1192	CALL lbc_lnk_multi( 'sbcblk', Cd, 'T', 1., Ch, 'T', 1. )
1193	!
1194	END SUBROUTINE Cdn10_Lupkes2015
1195
1196	#endif
1197
1198	!!======================================================================
1199	END MODULE sbcblk

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source: NEMO/branches/UKMO/NEMO_4.0_mirror_text_diagnostics/src/OCE/SBC/sbcblk.F90 @ 10986

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