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sbc_phy.F90 in NEMO/trunk/src/OCE/SBC – NEMO

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source: NEMO/trunk/src/OCE/SBC/sbc_phy.F90 @ 14072

Last change on this file since 14072 was 14072, checked in by laurent, 3 years ago
Merging branch "2020/dev_r13648_ASINTER-04_laurent_bulk_ice", ticket #2369
File size: 58.7 KB

Rev	Line
[13655]	1	MODULE sbc_phy
[12015]	2	!!======================================================================
[13655]	3	!! * MODULE sbc_phy *
[12015]	4	!! A set of functions to compute air themodynamics parameters
	5	!! needed by Aerodynamic Bulk Formulas
	6	!!=====================================================================
[13655]	7	!! 4.x ! 2020 L. Brodeau from AeroBulk package (https://github.com/brodeau/aerobulk/)
[12015]	8	!!----------------------------------------------------------------------
	9
	10	!! virt_temp : virtual (aka sensible) temperature (potential or absolute)
	11	!! rho_air : density of (moist) air (depends on T_air, q_air and SLP
	12	!! visc_air : kinematic viscosity (aka Nu_air) of air from temperature
	13	!! L_vap : latent heat of vaporization of water as a function of temperature
	14	!! cp_air : specific heat of (moist) air (depends spec. hum. q_air)
	15	!! gamma_moist : adiabatic lapse-rate of moist air
[13655]	16	!! One_on_L : 1. / ( Obukhov length )
[12015]	17	!! Ri_bulk : bulk Richardson number aka BRN
	18	!! q_sat : saturation humidity as a function of SLP and temperature
	19	!! q_air_rh : specific humidity as a function of RH (fraction, not %), t_air and SLP
	20
	21	USE dom_oce ! ocean space and time domain
	22	USE phycst ! physical constants
	23
	24	IMPLICIT NONE
[14036]	25	!PRIVATE
	26	PUBLIC !! Haleluja that was the solution
[12015]	27
[13655]	28	INTEGER , PARAMETER, PUBLIC :: nb_iter0 = 5 ! Default number of itterations in bulk-param algorithms (can be overriden b.m.o `nb_iter` optional argument)
	29
[12015]	30	!! (mainly removed from sbcblk.F90)
	31	REAL(wp), PARAMETER, PUBLIC :: rCp_dry = 1005.0_wp !: Specic heat of dry air, constant pressure [J/K/kg]
	32	REAL(wp), PARAMETER, PUBLIC :: rCp_vap = 1860.0_wp !: Specic heat of water vapor, constant pressure [J/K/kg]
	33	REAL(wp), PARAMETER, PUBLIC :: R_dry = 287.05_wp !: Specific gas constant for dry air [J/K/kg]
	34	REAL(wp), PARAMETER, PUBLIC :: R_vap = 461.495_wp !: Specific gas constant for water vapor [J/K/kg]
	35	REAL(wp), PARAMETER, PUBLIC :: reps0 = R_dry/R_vap !: ratio of gas constant for dry air and water vapor => ~ 0.622
[12895]	36	REAL(wp), PARAMETER, PUBLIC :: rctv0 = R_vap/R_dry - 1._wp !: for virtual temperature (== (1-eps)/eps) => ~ 0.608
[12015]	37	REAL(wp), PARAMETER, PUBLIC :: rCp_air = 1000.5_wp !: specific heat of air (only used for ice fluxes now...)
	38	REAL(wp), PARAMETER, PUBLIC :: albo = 0.066_wp !: ocean albedo assumed to be constant
	39	!
	40	REAL(wp), PARAMETER, PUBLIC :: rho0_a = 1.2_wp !: Approx. of density of air [kg/m^3]
	41	REAL(wp), PARAMETER, PUBLIC :: rho0_w = 1025._wp !: Density of sea-water (ECMWF->1025) [kg/m^3]
	42	REAL(wp), PARAMETER, PUBLIC :: radrw = rho0_a/rho0_w !: Density ratio
	43	REAL(wp), PARAMETER, PUBLIC :: sq_radrw = SQRT(rho0_a/rho0_w)
	44	REAL(wp), PARAMETER, PUBLIC :: rCp0_w = 4190._wp !: Specific heat capacity of seawater (ECMWF 4190) [J/K/kg]
	45	REAL(wp), PARAMETER, PUBLIC :: rnu0_w = 1.e-6_wp !: kinetic viscosity of water [m^2/s]
	46	REAL(wp), PARAMETER, PUBLIC :: rk0_w = 0.6_wp !: thermal conductivity of water (at 20C) [W/m/K]
	47	!
[13655]	48	REAL(wp), PARAMETER, PUBLIC :: emiss_w = 0.98_wp !: Long-wave (thermal) emissivity of sea-water []
	49	!
	50	REAL(wp), PARAMETER, PUBLIC :: emiss_i = 0.996_wp !: " for ice and snow => but Rees 1993 suggests can be lower in winter on fresh snow... 0.72 ...
	51
	52	REAL(wp), PARAMETER, PUBLIC :: wspd_thrshld_ice = 0.2_wp !: minimum scalar wind speed accepted over sea-ice... [m/s]
	53
	54	!
[12015]	55	REAL(wp), PARAMETER, PUBLIC :: rdct_qsat_salt = 0.98_wp !: reduction factor on specific humidity at saturation (q_sat(T_s)) due to salt
	56	REAL(wp), PARAMETER, PUBLIC :: rtt0 = 273.16_wp !: triple point of temperature [K]
	57	!
	58	REAL(wp), PARAMETER, PUBLIC :: rcst_cs = -16._wp9.80665_wprho0_wrCp0_wrnu0_wrnu0_wrnu0_w/(rk0_w*rk0_w) !: for cool-skin parameterizations... (grav = 9.80665_wp)
	59	! => see eq.(14) in Fairall et al. 1996 (eq.(6) of Zeng aand Beljaars is WRONG! (typo?)
	60
[13655]	61	REAL(wp), PARAMETER, PUBLIC :: z0_sea_max = 0.0025_wp !: maximum realistic value for roughness length of sea-surface... [m]
[12015]	62
[13655]	63	REAL(wp), PUBLIC, SAVE :: pp_cldf = 0.81 !: cloud fraction over sea ice, summer CLIO value [-]
	64
	65
	66	REAL(wp), PARAMETER, PUBLIC :: Cx_min = 0.1E-3_wp ! smallest value allowed for bulk transfer coefficients (usually in stable conditions with now wind)
	67
	68	REAL(wp), PARAMETER :: &
	69	!! Constants for Goff formula in the presence of ice:
	70	& rAg_i = -9.09718_wp, &
	71	& rBg_i = -3.56654_wp, &
	72	& rCg_i = 0.876793_wp, &
	73	& rDg_i = LOG10(6.1071_wp)
	74
	75	REAL(wp), PARAMETER :: rc_louis = 5._wp
	76	REAL(wp), PARAMETER :: rc2_louis = rc_louis * rc_louis
	77	REAL(wp), PARAMETER :: ram_louis = 2. * rc_louis
	78	REAL(wp), PARAMETER :: rah_louis = 3. * rc_louis
	79
	80
	81	INTERFACE virt_temp
	82	MODULE PROCEDURE virt_temp_vctr, virt_temp_sclr
	83	END INTERFACE virt_temp
	84
	85	INTERFACE visc_air
	86	MODULE PROCEDURE visc_air_vctr, visc_air_sclr
	87	END INTERFACE visc_air
	88
[12015]	89	INTERFACE gamma_moist
	90	MODULE PROCEDURE gamma_moist_vctr, gamma_moist_sclr
	91	END INTERFACE gamma_moist
	92
	93	INTERFACE e_sat
	94	MODULE PROCEDURE e_sat_vctr, e_sat_sclr
	95	END INTERFACE e_sat
	96
[13655]	97	INTERFACE e_sat_ice
	98	MODULE PROCEDURE e_sat_ice_vctr, e_sat_ice_sclr
	99	END INTERFACE e_sat_ice
	100	INTERFACE de_sat_dt_ice
	101	MODULE PROCEDURE de_sat_dt_ice_vctr, de_sat_dt_ice_sclr
	102	END INTERFACE de_sat_dt_ice
	103
	104	INTERFACE Ri_bulk
	105	MODULE PROCEDURE Ri_bulk_vctr, Ri_bulk_sclr
	106	END INTERFACE Ri_bulk
	107
	108	INTERFACE q_sat
	109	MODULE PROCEDURE q_sat_vctr, q_sat_sclr
	110	END INTERFACE q_sat
	111
	112	INTERFACE dq_sat_dt_ice
	113	MODULE PROCEDURE dq_sat_dt_ice_vctr, dq_sat_dt_ice_sclr
	114	END INTERFACE dq_sat_dt_ice
	115
[12015]	116	INTERFACE L_vap
	117	MODULE PROCEDURE L_vap_vctr, L_vap_sclr
	118	END INTERFACE L_vap
	119
	120	INTERFACE rho_air
	121	MODULE PROCEDURE rho_air_vctr, rho_air_sclr
	122	END INTERFACE rho_air
	123
	124	INTERFACE cp_air
	125	MODULE PROCEDURE cp_air_vctr, cp_air_sclr
	126	END INTERFACE cp_air
	127
	128	INTERFACE alpha_sw
	129	MODULE PROCEDURE alpha_sw_vctr, alpha_sw_sclr
	130	END INTERFACE alpha_sw
	131
	132	INTERFACE bulk_formula
	133	MODULE PROCEDURE bulk_formula_vctr, bulk_formula_sclr
	134	END INTERFACE bulk_formula
	135
[13655]	136	INTERFACE qlw_net
	137	MODULE PROCEDURE qlw_net_vctr, qlw_net_sclr
	138	END INTERFACE qlw_net
[12015]	139
[13655]	140	INTERFACE f_m_louis
	141	MODULE PROCEDURE f_m_louis_vctr, f_m_louis_sclr
	142	END INTERFACE f_m_louis
[12015]	143
[13655]	144	INTERFACE f_h_louis
	145	MODULE PROCEDURE f_h_louis_vctr, f_h_louis_sclr
	146	END INTERFACE f_h_louis
	147
	148
[12015]	149	PUBLIC virt_temp
	150	PUBLIC rho_air
	151	PUBLIC visc_air
	152	PUBLIC L_vap
	153	PUBLIC cp_air
	154	PUBLIC gamma_moist
	155	PUBLIC One_on_L
	156	PUBLIC Ri_bulk
	157	PUBLIC q_sat
	158	PUBLIC q_air_rh
[13655]	159	PUBLIC dq_sat_dt_ice
[12015]	160	!:
	161	PUBLIC update_qnsol_tau
	162	PUBLIC alpha_sw
	163	PUBLIC bulk_formula
[13655]	164	PUBLIC qlw_net
	165	!
	166	PUBLIC f_m_louis, f_h_louis
	167	PUBLIC z0_from_Cd
	168	PUBLIC Cd_from_z0
	169	PUBLIC UN10_from_ustar
	170	PUBLIC UN10_from_CD
	171	PUBLIC z0tq_LKB
[12015]	172
[12340]	173	!! * Substitutions
	174	# include "do_loop_substitute.h90"
[12015]	175	!!----------------------------------------------------------------------
	176	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
	177	!! $Id: sbcblk.F90 10535 2019-01-16 17:36:47Z clem $
	178	!! Software governed by the CeCILL license (see ./LICENSE)
	179	!!----------------------------------------------------------------------
	180	CONTAINS
	181
[13655]	182
	183	FUNCTION virt_temp_sclr( pta, pqa )
[12015]	184	!!------------------------------------------------------------------------
	185	!!
[13655]	186	!! Compute the (absolute/potential) VIRTUAL temperature, based on the
[12015]	187	!! (absolute/potential) temperature and specific humidity
	188	!!
[13655]	189	!! If input temperature is absolute then output virtual temperature is absolute
	190	!! If input temperature is potential then output virtual temperature is potential
[12015]	191	!!
	192	!! Author: L. Brodeau, June 2019 / AeroBulk
	193	!! (https://github.com/brodeau/aerobulk/)
	194	!!------------------------------------------------------------------------
[13655]	195	REAL(wp) :: virt_temp_sclr !: virtual temperature [K]
	196	REAL(wp), INTENT(in) :: pta !: absolute or potential air temperature [K]
	197	REAL(wp), INTENT(in) :: pqa !: specific humidity of air [kg/kg]
[12015]	198	!!-------------------------------------------------------------------
	199	!
[13655]	200	virt_temp_sclr = pta * (1._wp + rctv0*pqa)
[12015]	201	!!
[13655]	202	!! This is exactly the same thing as:
	203	!! virt_temp_sclr = pta * ( pwa + reps0) / (reps0*(1.+pwa))
[12015]	204	!! with wpa (mixing ration) defined as : pwa = pqa/(1.-pqa)
	205	!
[13655]	206	END FUNCTION virt_temp_sclr
	207	!!
	208	FUNCTION virt_temp_vctr( pta, pqa )
	209	REAL(wp), DIMENSION(jpi,jpj) :: virt_temp_vctr !: virtual temperature [K]
	210	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pta !: absolute or potential air temperature [K]
	211	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa !: specific humidity of air [kg/kg]
	212	virt_temp_vctr(:,:) = pta(:,:) * (1._wp + rctv0*pqa(:,:))
	213	END FUNCTION virt_temp_vctr
	214	!===============================================================================================
[12015]	215
[13655]	216
	217	FUNCTION rho_air_vctr( ptak, pqa, ppa )
[12015]	218	!!-------------------------------------------------------------------------------
	219	!! * FUNCTION rho_air_vctr *
	220	!!
	221	!! ** Purpose : compute density of (moist) air using the eq. of state of the atmosphere
	222	!!
	223	!! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	224	!!-------------------------------------------------------------------------------
	225	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K]
	226	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg]
[13655]	227	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ppa ! pressure in [Pa]
[12015]	228	REAL(wp), DIMENSION(jpi,jpj) :: rho_air_vctr ! density of moist air [kg/m^3]
	229	!!-------------------------------------------------------------------------------
[13655]	230	rho_air_vctr = MAX( ppa / (R_dryptak ( 1._wp + rctv0*pqa )) , 0.8_wp )
[12015]	231	END FUNCTION rho_air_vctr
	232
[13655]	233	FUNCTION rho_air_sclr( ptak, pqa, ppa )
[12015]	234	!!-------------------------------------------------------------------------------
	235	!! * FUNCTION rho_air_sclr *
	236	!!
	237	!! ** Purpose : compute density of (moist) air using the eq. of state of the atmosphere
	238	!!
	239	!! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	240	!!-------------------------------------------------------------------------------
	241	REAL(wp), INTENT(in) :: ptak ! air temperature [K]
	242	REAL(wp), INTENT(in) :: pqa ! air specific humidity [kg/kg]
[13655]	243	REAL(wp), INTENT(in) :: ppa ! pressure in [Pa]
[12015]	244	REAL(wp) :: rho_air_sclr ! density of moist air [kg/m^3]
	245	!!-------------------------------------------------------------------------------
[13655]	246	rho_air_sclr = MAX( ppa / (R_dryptak ( 1._wp + rctv0*pqa )) , 0.8_wp )
[12015]	247	END FUNCTION rho_air_sclr
	248
	249
	250
[13655]	251
	252	FUNCTION visc_air_sclr(ptak)
[12015]	253	!!----------------------------------------------------------------------------------
[13655]	254	!! Air kinetic viscosity (m^2/s) given from air temperature in Kelvin
[12015]	255	!!
	256	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	257	!!----------------------------------------------------------------------------------
[13655]	258	REAL(wp) :: visc_air_sclr ! kinetic viscosity (m^2/s)
	259	REAL(wp), INTENT(in) :: ptak ! air temperature in (K)
[12015]	260	!
	261	REAL(wp) :: ztc, ztc2 ! local scalar
	262	!!----------------------------------------------------------------------------------
	263	!
[13655]	264	ztc = ptak - rt0 ! air temp, in deg. C
	265	ztc2 = ztc*ztc
	266	visc_air_sclr = 1.326e-5(1. + 6.542E-3ztc + 8.301e-6ztc2 - 4.84e-9ztc2*ztc)
	267	!
	268	END FUNCTION visc_air_sclr
	269
	270	FUNCTION visc_air_vctr(ptak)
	271	REAL(wp), DIMENSION(jpi,jpj) :: visc_air_vctr ! kinetic viscosity (m^2/s)
	272	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature in (K)
	273	INTEGER :: ji, jj ! dummy loop indices
[13305]	274	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
[13655]	275	visc_air_vctr(ji,jj) = visc_air_sclr( ptak(ji,jj) )
[12340]	276	END_2D
[13655]	277	END FUNCTION visc_air_vctr
[12015]	278
[13655]	279
[12015]	280	FUNCTION L_vap_vctr( psst )
	281	!!---------------------------------------------------------------------------------
	282	!! * FUNCTION L_vap_vctr *
	283	!!
	284	!! ** Purpose : Compute the latent heat of vaporization of water from temperature
	285	!!
	286	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	287	!!----------------------------------------------------------------------------------
	288	REAL(wp), DIMENSION(jpi,jpj) :: L_vap_vctr ! latent heat of vaporization [J/kg]
	289	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! water temperature [K]
	290	!!----------------------------------------------------------------------------------
	291	!
	292	L_vap_vctr = ( 2.501_wp - 0.00237_wp * ( psst(:,:) - rt0) ) * 1.e6_wp
	293	!
	294	END FUNCTION L_vap_vctr
	295
	296	FUNCTION L_vap_sclr( psst )
	297	!!---------------------------------------------------------------------------------
	298	!! * FUNCTION L_vap_sclr *
	299	!!
	300	!! ** Purpose : Compute the latent heat of vaporization of water from temperature
	301	!!
	302	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	303	!!----------------------------------------------------------------------------------
	304	REAL(wp) :: L_vap_sclr ! latent heat of vaporization [J/kg]
	305	REAL(wp), INTENT(in) :: psst ! water temperature [K]
	306	!!----------------------------------------------------------------------------------
	307	!
	308	L_vap_sclr = ( 2.501_wp - 0.00237_wp * ( psst - rt0) ) * 1.e6_wp
	309	!
	310	END FUNCTION L_vap_sclr
	311
	312
	313	FUNCTION cp_air_vctr( pqa )
	314	!!-------------------------------------------------------------------------------
	315	!! * FUNCTION cp_air_vctr *
	316	!!
	317	!! ** Purpose : Compute specific heat (Cp) of moist air
	318	!!
	319	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	320	!!-------------------------------------------------------------------------------
	321	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg]
	322	REAL(wp), DIMENSION(jpi,jpj) :: cp_air_vctr ! specific heat of moist air [J/K/kg]
	323	!!-------------------------------------------------------------------------------
	324	cp_air_vctr = rCp_dry + rCp_vap * pqa
	325	END FUNCTION cp_air_vctr
	326
	327	FUNCTION cp_air_sclr( pqa )
	328	!!-------------------------------------------------------------------------------
	329	!! * FUNCTION cp_air_sclr *
	330	!!
	331	!! ** Purpose : Compute specific heat (Cp) of moist air
	332	!!
	333	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	334	!!-------------------------------------------------------------------------------
	335	REAL(wp), INTENT(in) :: pqa ! air specific humidity [kg/kg]
	336	REAL(wp) :: cp_air_sclr ! specific heat of moist air [J/K/kg]
	337	!!-------------------------------------------------------------------------------
	338	cp_air_sclr = rCp_dry + rCp_vap * pqa
	339	END FUNCTION cp_air_sclr
	340
	341
	342
[13655]	343	!===============================================================================================
[12015]	344	FUNCTION gamma_moist_sclr( ptak, pqa )
	345	!!----------------------------------------------------------------------------------
	346	!! ** Purpose : Compute the moist adiabatic lapse-rate.
	347	!! => http://glossary.ametsoc.org/wiki/Moist-adiabatic_lapse_rate
	348	!! => http://www.geog.ucsb.edu/~joel/g266_s10/lecture_notes/chapt03/oh10_3_01/oh10_3_01.html
	349	!!
	350	!! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	351	!!----------------------------------------------------------------------------------
[13655]	352	REAL(wp) :: gamma_moist_sclr ! [K/m]
	353	REAL(wp), INTENT(in) :: ptak ! absolute air temperature [K] !#LB: double check it's absolute !!!
	354	REAL(wp), INTENT(in) :: pqa ! specific humidity [kg/kg]
[12015]	355	!
[13655]	356	REAL(wp) :: zta, zqa, zwa, ziRT, zLvap ! local scalars
[12015]	357	!!----------------------------------------------------------------------------------
	358	zta = MAX( ptak, 180._wp) ! prevents screw-up over masked regions where field == 0.
	359	zqa = MAX( pqa, 1.E-6_wp) ! " " "
	360	!!
	361	zwa = zqa / (1._wp - zqa) ! w is mixing ratio w = q/(1-q) \| q = w/(1+w)
	362	ziRT = 1._wp / (R_dry*zta) ! 1/RT
[13655]	363	zLvap = L_vap_sclr( ptak )
[12015]	364	!!
[13655]	365	gamma_moist_sclr = grav * ( 1._wp + zLvapzwaziRT ) / ( rCp_dry + zLvapzLvapzwareps0ziRT/zta )
	366	!!
[12015]	367	END FUNCTION gamma_moist_sclr
[13655]	368	!!
	369	FUNCTION gamma_moist_vctr( ptak, pqa )
	370	REAL(wp), DIMENSION(jpi,jpj) :: gamma_moist_vctr
	371	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak
	372	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa
	373	INTEGER :: ji, jj
	374	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
	375	gamma_moist_vctr(ji,jj) = gamma_moist_sclr( ptak(ji,jj), pqa(ji,jj) )
	376	END_2D
	377	END FUNCTION gamma_moist_vctr
	378	!===============================================================================================
[12015]	379
[13655]	380
[12015]	381	FUNCTION One_on_L( ptha, pqa, pus, pts, pqs )
	382	!!------------------------------------------------------------------------
	383	!!
[13655]	384	!! Evaluates the 1./(Obukhov length) from air temperature,
	385	!! air specific humidity, and frictional scales u, t and q*
[12015]	386	!!
[13655]	387	!! Author: L. Brodeau, June 2019 / AeroBulk
[12015]	388	!! (https://github.com/brodeau/aerobulk/)
	389	!!------------------------------------------------------------------------
[13655]	390	REAL(wp), DIMENSION(jpi,jpj) :: One_on_L !: 1./(Obukhov length) [m^-1]
	391	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptha !: reference potential temperature of air [K]
	392	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa !: reference specific humidity of air [kg/kg]
	393	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pus !: u*: friction velocity [m/s]
	394	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pts, pqs !: \theta* and q* friction aka turb. scales for temp. and spec. hum.
[12015]	395	!
	396	INTEGER :: ji, jj ! dummy loop indices
	397	REAL(wp) :: zqa ! local scalar
	398	!!-------------------------------------------------------------------
	399	!
[13305]	400	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
[13655]	401	!
	402	zqa = (1._wp + rctv0*pqa(ji,jj))
	403	!
	404	! The main concern is to know whether, the vertical turbulent flux of virtual temperature, < u' theta_v' > is estimated with:
	405	! a/ -u* [ theta* (1 + 0.61 q) + 0.61 theta q* ] => this is the one that seems correct! chose this one!
	406	! or
	407	! b/ -u* [ theta* + 0.61 theta q* ]
	408	!
	409	One_on_L(ji,jj) = gravvkarmn( pts(ji,jj)zqa + rctv0ptha(ji,jj)*pqs(ji,jj) ) &
	410	& / MAX( pus(ji,jj)pus(ji,jj)ptha(ji,jj)*zqa , 1.E-9_wp )
	411	!
[12340]	412	END_2D
[12015]	413	!
	414	One_on_L = SIGN( MIN(ABS(One_on_L),200._wp), One_on_L ) ! (prevent FPE from stupid values over masked regions...)
	415	!
	416	END FUNCTION One_on_L
	417
[13655]	418
	419	!===============================================================================================
	420	FUNCTION Ri_bulk_sclr( pz, psst, ptha, pssq, pqa, pub, pta_layer, pqa_layer )
[12015]	421	!!----------------------------------------------------------------------------------
	422	!! Bulk Richardson number according to "wide-spread equation"...
	423	!!
[13655]	424	!! Reminder: the Richardson number is the ratio "buoyancy" / "shear"
	425	!!
[12015]	426	!! ** Author: L. Brodeau, June 2019 / AeroBulk (https://github.com/brodeau/aerobulk/)
	427	!!----------------------------------------------------------------------------------
[13655]	428	REAL(wp) :: Ri_bulk_sclr
	429	REAL(wp), INTENT(in) :: pz ! height above the sea (aka "delta z") [m]
	430	REAL(wp), INTENT(in) :: psst ! SST [K]
	431	REAL(wp), INTENT(in) :: ptha ! pot. air temp. at height "pz" [K]
	432	REAL(wp), INTENT(in) :: pssq ! 0.98*q_sat(SST) [kg/kg]
	433	REAL(wp), INTENT(in) :: pqa ! air spec. hum. at height "pz" [kg/kg]
	434	REAL(wp), INTENT(in) :: pub ! bulk wind speed [m/s]
	435	REAL(wp), INTENT(in), OPTIONAL :: pta_layer ! when possible, a better guess of absolute temperature WITHIN the layer [K]
	436	REAL(wp), INTENT(in), OPTIONAL :: pqa_layer ! when possible, a better guess of specific humidity WITHIN the layer [kg/kg]
	437	!!
	438	LOGICAL :: l_ptqa_l_prvd = .FALSE.
	439	REAL(wp) :: zqa, zta, zgamma, zdthv, ztv, zsstv ! local scalars
	440	!!-------------------------------------------------------------------
	441	IF( PRESENT(pta_layer) .AND. PRESENT(pqa_layer) ) l_ptqa_l_prvd=.TRUE.
	442	!
	443	zsstv = virt_temp_sclr( psst, pssq ) ! virtual SST (absolute==potential because z=0!)
	444	!
	445	zdthv = virt_temp_sclr( ptha, pqa ) - zsstv ! air-sea delta of "virtual potential temperature"
	446	!
	447	!! ztv: estimate of the ABSOLUTE virtual temp. within the layer
	448	IF( l_ptqa_l_prvd ) THEN
	449	ztv = virt_temp_sclr( pta_layer, pqa_layer )
	450	ELSE
	451	zqa = 0.5_wp*( pqa + pssq ) ! ~ mean q within the layer...
	452	zta = 0.5_wp( psst + ptha - gamma_moist(ptha, zqa)pz ) ! ~ mean absolute temperature of air within the layer
	453	zta = 0.5_wp( psst + ptha - gamma_moist( zta, zqa)pz ) ! ~ mean absolute temperature of air within the layer
	454	zgamma = gamma_moist(zta, zqa) ! Adiabatic lapse-rate for moist air within the layer
	455	ztv = 0.5_wp( zsstv + virt_temp_sclr( ptha-zgammapz, pqa ) )
	456	END IF
	457	!
	458	Ri_bulk_sclr = gravzdthvpz / ( ztvpubpub ) ! the usual definition of Ri_bulk_sclr
	459	!
	460	END FUNCTION Ri_bulk_sclr
	461	!!
	462	FUNCTION Ri_bulk_vctr( pz, psst, ptha, pssq, pqa, pub, pta_layer, pqa_layer )
	463	REAL(wp), DIMENSION(jpi,jpj) :: Ri_bulk_vctr
[12015]	464	REAL(wp) , INTENT(in) :: pz ! height above the sea (aka "delta z") [m]
	465	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! SST [K]
	466	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptha ! pot. air temp. at height "pz" [K]
	467	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pssq ! 0.98*q_sat(SST) [kg/kg]
	468	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air spec. hum. at height "pz" [kg/kg]
	469	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pub ! bulk wind speed [m/s]
[13655]	470	REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pta_layer ! when possible, a better guess of absolute temperature WITHIN the layer [K]
	471	REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pqa_layer ! when possible, a better guess of specific humidity WITHIN the layer [kg/kg]
	472	!!
	473	LOGICAL :: l_ptqa_l_prvd = .FALSE.
	474	INTEGER :: ji, jj
	475	IF( PRESENT(pta_layer) .AND. PRESENT(pqa_layer) ) l_ptqa_l_prvd=.TRUE.
[13305]	476	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
[13655]	477	IF( l_ptqa_l_prvd ) THEN
	478	Ri_bulk_vctr(ji,jj) = Ri_bulk_sclr( pz, psst(ji,jj), ptha(ji,jj), pssq(ji,jj), pqa(ji,jj), pub(ji,jj), &
	479	& pta_layer=pta_layer(ji,jj ), pqa_layer=pqa_layer(ji,jj ) )
	480	ELSE
	481	Ri_bulk_vctr(ji,jj) = Ri_bulk_sclr( pz, psst(ji,jj), ptha(ji,jj), pssq(ji,jj), pqa(ji,jj), pub(ji,jj) )
	482	END IF
[12340]	483	END_2D
[13655]	484	END FUNCTION Ri_bulk_vctr
	485	!===============================================================================================
[12015]	486
[13655]	487	!===============================================================================================
[12015]	488	FUNCTION e_sat_sclr( ptak )
	489	!!----------------------------------------------------------------------------------
	490	!! * FUNCTION e_sat_sclr *
	491	!! < SCALAR argument version >
	492	!! ** Purpose : water vapor at saturation in [Pa]
	493	!! Based on accurate estimate by Goff, 1957
	494	!!
	495	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	496	!!
	497	!! Note: what rt0 should be here, is 273.16 (triple point of water) and not 273.15 like here
	498	!!----------------------------------------------------------------------------------
[13655]	499	REAL(wp) :: e_sat_sclr ! water vapor at saturation [kg/kg]
[12015]	500	REAL(wp), INTENT(in) :: ptak ! air temperature [K]
	501	REAL(wp) :: zta, ztmp ! local scalar
	502	!!----------------------------------------------------------------------------------
	503	zta = MAX( ptak , 180._wp ) ! air temp., prevents fpe0 errors dute to unrealistically low values over masked regions...
[13655]	504	ztmp = rt0 / zta !#LB: rt0 or rtt0 ???? (273.15 vs 273.16 )
[12015]	505	!
	506	! Vapour pressure at saturation [Pa] : WMO, (Goff, 1957)
	507	e_sat_sclr = 100.( 10.( 10.79574(1. - ztmp) - 5.028*LOG10(zta/rt0) &
	508	& + 1.5047510.(-4)(1. - 10.*(-8.2969(zta/rt0 - 1.)) ) &
	509	& + 0.4287310.(-3)(10.*(4.76955(1. - ztmp)) - 1.) + 0.78614) )
	510	!
	511	END FUNCTION e_sat_sclr
[13655]	512	!!
	513	FUNCTION e_sat_vctr(ptak)
	514	REAL(wp), DIMENSION(jpi,jpj) :: e_sat_vctr !: vapour pressure at saturation [Pa]
	515	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak !: temperature (K)
	516	INTEGER :: ji, jj ! dummy loop indices
	517	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
	518	e_sat_vctr(ji,jj) = e_sat_sclr(ptak(ji,jj))
	519	END_2D
	520	END FUNCTION e_sat_vctr
	521	!===============================================================================================
[12015]	522
[13655]	523	!===============================================================================================
	524	FUNCTION e_sat_ice_sclr(ptak)
	525	!!---------------------------------------------------------------------------------
	526	!! Same as "e_sat" but over ice rather than water!
	527	!!---------------------------------------------------------------------------------
	528	REAL(wp) :: e_sat_ice_sclr !: vapour pressure at saturation in presence of ice [Pa]
	529	REAL(wp), INTENT(in) :: ptak
	530	!!
	531	REAL(wp) :: zta, zle, ztmp
	532	!!---------------------------------------------------------------------------------
	533	zta = MAX( ptak , 180._wp ) ! air temp., prevents fpe0 errors dute to unrealistically low values over masked regions...
	534	ztmp = rtt0/zta
	535	!!
	536	zle = rAg_i(ztmp - 1._wp) + rBg_iLOG10(ztmp) + rCg_i*(1._wp - zta/rtt0) + rDg_i
	537	!!
	538	e_sat_ice_sclr = 100._wp * 10._wp**zle
	539	END FUNCTION e_sat_ice_sclr
	540	!!
	541	FUNCTION e_sat_ice_vctr(ptak)
	542	!! Same as "e_sat" but over ice rather than water!
	543	REAL(wp), DIMENSION(jpi,jpj) :: e_sat_ice_vctr !: vapour pressure at saturation in presence of ice [Pa]
	544	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak
	545	INTEGER :: ji, jj
[12015]	546	!!----------------------------------------------------------------------------------
[13655]	547	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
	548	e_sat_ice_vctr(ji,jj) = e_sat_ice_sclr( ptak(ji,jj) )
	549	END_2D
	550	END FUNCTION e_sat_ice_vctr
	551	!!
	552	FUNCTION de_sat_dt_ice_sclr(ptak)
	553	!!---------------------------------------------------------------------------------
	554	!! d [ e_sat_ice ] / dT (derivative / temperature)
	555	!! Analytical exact formulation: double checked!!!
	556	!! => DOUBLE-check possible / finite-difference version with "./bin/test_phymbl.x"
	557	!!---------------------------------------------------------------------------------
	558	REAL(wp) :: de_sat_dt_ice_sclr !: [Pa/K]
	559	REAL(wp), INTENT(in) :: ptak
[12015]	560	!!
[13655]	561	REAL(wp) :: zta, zde
	562	!!---------------------------------------------------------------------------------
	563	zta = MAX( ptak , 180._wp ) ! air temp., prevents fpe0 errors dute to unrealistically low values over masked regions...
[12015]	564	!!
[13655]	565	zde = -(rAg_irtt0)/(ztazta) - rBg_i/(zta*LOG(10._wp)) - rCg_i/rtt0
	566	!!
	567	de_sat_dt_ice_sclr = LOG(10._wp) * zde * e_sat_ice_sclr(zta)
	568	END FUNCTION de_sat_dt_ice_sclr
	569	!!
	570	FUNCTION de_sat_dt_ice_vctr(ptak)
	571	!! Same as "e_sat" but over ice rather than water!
	572	REAL(wp), DIMENSION(jpi,jpj) :: de_sat_dt_ice_vctr !: vapour pressure at saturation in presence of ice [Pa]
	573	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak
	574	INTEGER :: ji, jj
	575	!!----------------------------------------------------------------------------------
	576	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
	577	de_sat_dt_ice_vctr(ji,jj) = de_sat_dt_ice_sclr( ptak(ji,jj) )
	578	END_2D
	579	END FUNCTION de_sat_dt_ice_vctr
	580
	581
	582
	583	!===============================================================================================
	584
	585	!===============================================================================================
	586	FUNCTION q_sat_sclr( pta, ppa, l_ice )
	587	!!---------------------------------------------------------------------------------
	588	!! * FUNCTION q_sat_sclr *
	589	!!
	590	!! ** Purpose : Conputes specific humidity of air at saturation
	591	!!
[12015]	592	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	593	!!----------------------------------------------------------------------------------
[13655]	594	REAL(wp) :: q_sat_sclr
	595	REAL(wp), INTENT(in) :: pta !: absolute temperature of air [K]
	596	REAL(wp), INTENT(in) :: ppa !: atmospheric pressure [Pa]
	597	LOGICAL, INTENT(in), OPTIONAL :: l_ice !: we are above ice
	598	REAL(wp) :: ze_s
	599	LOGICAL :: lice
	600	!!----------------------------------------------------------------------------------
	601	lice = .FALSE.
	602	IF( PRESENT(l_ice) ) lice = l_ice
	603	IF( lice ) THEN
	604	ze_s = e_sat_ice( pta )
	605	ELSE
	606	ze_s = e_sat( pta ) ! Vapour pressure at saturation (Goff) :
	607	END IF
	608	q_sat_sclr = reps0ze_s/(ppa - (1._wp - reps0)ze_s)
	609	END FUNCTION q_sat_sclr
	610	!!
	611	FUNCTION q_sat_vctr( pta, ppa, l_ice )
	612	REAL(wp), DIMENSION(jpi,jpj) :: q_sat_vctr
	613	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pta !: absolute temperature of air [K]
	614	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ppa !: atmospheric pressure [Pa]
	615	LOGICAL, INTENT(in), OPTIONAL :: l_ice !: we are above ice
	616	LOGICAL :: lice
	617	INTEGER :: ji, jj
	618	!!----------------------------------------------------------------------------------
	619	lice = .FALSE.
	620	IF( PRESENT(l_ice) ) lice = l_ice
	621	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
	622	q_sat_vctr(ji,jj) = q_sat_sclr( pta(ji,jj) , ppa(ji,jj), l_ice=lice )
	623	END_2D
	624	END FUNCTION q_sat_vctr
	625	!===============================================================================================
	626
	627
	628	!===============================================================================================
	629	FUNCTION dq_sat_dt_ice_sclr( pta, ppa )
	630	!!---------------------------------------------------------------------------------
	631	!! * FUNCTION dq_sat_dt_ice_sclr *
	632	!! => d [ q_sat_ice(T) ] / dT
	633	!! Analytical exact formulation: double checked!!!
	634	!! => DOUBLE-check possible / finite-difference version with "./bin/test_phymbl.x"
	635	!!----------------------------------------------------------------------------------
	636	REAL(wp) :: dq_sat_dt_ice_sclr
	637	REAL(wp), INTENT(in) :: pta !: absolute temperature of air [K]
	638	REAL(wp), INTENT(in) :: ppa !: atmospheric pressure [Pa]
	639	REAL(wp) :: ze_s, zde_s_dt, ztmp
	640	!!----------------------------------------------------------------------------------
	641	ze_s = e_sat_ice_sclr( pta ) ! Vapour pressure at saturation in presence of ice (Goff)
	642	zde_s_dt = de_sat_dt_ice( pta )
[12015]	643	!
[13655]	644	ztmp = (reps0 - 1._wp)*ze_s + ppa
	645	!
	646	dq_sat_dt_ice_sclr = reps0ppazde_s_dt / ( ztmp*ztmp )
	647	!
	648	END FUNCTION dq_sat_dt_ice_sclr
	649	!!
	650	FUNCTION dq_sat_dt_ice_vctr( pta, ppa )
	651	REAL(wp), DIMENSION(jpi,jpj) :: dq_sat_dt_ice_vctr
	652	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pta !: absolute temperature of air [K]
	653	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ppa !: atmospheric pressure [Pa]
	654	INTEGER :: ji, jj
[12015]	655	!!----------------------------------------------------------------------------------
[13305]	656	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
[13655]	657	dq_sat_dt_ice_vctr(ji,jj) = dq_sat_dt_ice_sclr( pta(ji,jj) , ppa(ji,jj) )
[12340]	658	END_2D
[13655]	659	END FUNCTION dq_sat_dt_ice_vctr
	660	!===============================================================================================
[12015]	661
[13655]	662
	663	!===============================================================================================
	664	FUNCTION q_air_rh(prha, ptak, ppa)
[12015]	665	!!----------------------------------------------------------------------------------
	666	!! Specific humidity of air out of Relative Humidity
	667	!!
	668	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	669	!!----------------------------------------------------------------------------------
	670	REAL(wp), DIMENSION(jpi,jpj) :: q_air_rh
	671	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: prha !: relative humidity [fraction, not %!!!]
	672	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak !: air temperature [K]
[13655]	673	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ppa !: atmospheric pressure [Pa]
[12015]	674	!
	675	INTEGER :: ji, jj ! dummy loop indices
	676	REAL(wp) :: ze ! local scalar
	677	!!----------------------------------------------------------------------------------
	678	!
[13305]	679	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
[13655]	680	ze = prha(ji,jj)*e_sat_sclr(ptak(ji,jj))
	681	q_air_rh(ji,jj) = zereps0/(ppa(ji,jj) - (1. - reps0)ze)
[12340]	682	END_2D
[12015]	683	!
	684	END FUNCTION q_air_rh
	685
	686
[13655]	687	SUBROUTINE UPDATE_QNSOL_TAU( pzu, pTs, pqs, pTa, pqa, pust, ptst, pqst, pwnd, pUb, ppa, prlw, &
[12015]	688	& pQns, pTau, &
	689	& Qlat)
	690	!!----------------------------------------------------------------------------------
	691	!! Purpose: returns the non-solar heat flux to the ocean aka "Qlat + Qsen + Qlw"
	692	!! and the module of the wind stress => pTau = Tau
	693	!! ** Author: L. Brodeau, Sept. 2019 / AeroBulk (https://github.com/brodeau/aerobulk/)
	694	!!----------------------------------------------------------------------------------
	695	REAL(wp), INTENT(in) :: pzu ! height above the sea-level where all this takes place (normally 10m)
	696	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pTs ! water temperature at the air-sea interface [K]
	697	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqs ! satur. spec. hum. at T=pTs [kg/kg]
	698	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pTa ! potential air temperature at z=pzu [K]
	699	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! specific humidity at z=pzu [kg/kg]
	700	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pust ! u*
	701	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptst ! t*
	702	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqst ! q*
	703	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pwnd ! wind speed module at z=pzu [m/s]
	704	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pUb ! bulk wind speed at z=pzu (inc. pot. effect of gustiness etc) [m/s]
[13655]	705	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ppa ! sea-level atmospheric pressure [Pa]
[12015]	706	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: prlw ! downwelling longwave radiative flux [W/m^2]
	707	!
	708	REAL(wp), DIMENSION(jpi,jpj), INTENT(out) :: pQns ! non-solar heat flux to the ocean aka "Qlat + Qsen + Qlw" [W/m^2]]
	709	REAL(wp), DIMENSION(jpi,jpj), INTENT(out) :: pTau ! module of the wind stress [N/m^2]
	710	!
	711	REAL(wp), DIMENSION(jpi,jpj), OPTIONAL, INTENT(out) :: Qlat
	712	!
[13655]	713	REAL(wp) :: zdt, zdq, zCd, zCh, zCe, zz0, zQlat, zQsen, zQlw
[12015]	714	INTEGER :: ji, jj ! dummy loop indices
	715	!!----------------------------------------------------------------------------------
[13305]	716	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
[13655]	717	zdt = pTa(ji,jj) - pTs(ji,jj) ; zdt = SIGN( MAX(ABS(zdt),1.E-6_wp), zdt )
	718	zdq = pqa(ji,jj) - pqs(ji,jj) ; zdq = SIGN( MAX(ABS(zdq),1.E-9_wp), zdq )
	719	zz0 = pust(ji,jj)/pUb(ji,jj)
	720	zCd = zz0*zz0
	721	zCh = zz0*ptst(ji,jj)/zdt
	722	zCe = zz0*pqst(ji,jj)/zdq
[12015]	723
[13655]	724	CALL BULK_FORMULA( pzu, pTs(ji,jj), pqs(ji,jj), pTa(ji,jj), pqa(ji,jj), zCd, zCh, zCe, &
	725	& pwnd(ji,jj), pUb(ji,jj), ppa(ji,jj), &
	726	& pTau(ji,jj), zQsen, zQlat )
[12015]	727
[13655]	728	zQlw = qlw_net_sclr( prlw(ji,jj), pTs(ji,jj) ) ! Net longwave flux
[12015]	729
[13655]	730	pQns(ji,jj) = zQlat + zQsen + zQlw
[12015]	731
[13655]	732	IF( PRESENT(Qlat) ) Qlat(ji,jj) = zQlat
[12340]	733	END_2D
[12015]	734	END SUBROUTINE UPDATE_QNSOL_TAU
	735
	736
	737	SUBROUTINE BULK_FORMULA_SCLR( pzu, pTs, pqs, pTa, pqa, &
	738	& pCd, pCh, pCe, &
[13655]	739	& pwnd, pUb, ppa, &
[12615]	740	& pTau, pQsen, pQlat, &
	741	& pEvap, prhoa, pfact_evap )
[12015]	742	!!----------------------------------------------------------------------------------
	743	REAL(wp), INTENT(in) :: pzu ! height above the sea-level where all this takes place (normally 10m)
	744	REAL(wp), INTENT(in) :: pTs ! water temperature at the air-sea interface [K]
	745	REAL(wp), INTENT(in) :: pqs ! satur. spec. hum. at T=pTs [kg/kg]
	746	REAL(wp), INTENT(in) :: pTa ! potential air temperature at z=pzu [K]
	747	REAL(wp), INTENT(in) :: pqa ! specific humidity at z=pzu [kg/kg]
	748	REAL(wp), INTENT(in) :: pCd
	749	REAL(wp), INTENT(in) :: pCh
	750	REAL(wp), INTENT(in) :: pCe
	751	REAL(wp), INTENT(in) :: pwnd ! wind speed module at z=pzu [m/s]
	752	REAL(wp), INTENT(in) :: pUb ! bulk wind speed at z=pzu (inc. pot. effect of gustiness etc) [m/s]
[13655]	753	REAL(wp), INTENT(in) :: ppa ! sea-level atmospheric pressure [Pa]
[12015]	754	!!
	755	REAL(wp), INTENT(out) :: pTau ! module of the wind stress [N/m^2]
	756	REAL(wp), INTENT(out) :: pQsen ! [W/m^2]
	757	REAL(wp), INTENT(out) :: pQlat ! [W/m^2]
	758	!!
	759	REAL(wp), INTENT(out), OPTIONAL :: pEvap ! Evaporation [kg/m^2/s]
	760	REAL(wp), INTENT(out), OPTIONAL :: prhoa ! Air density at z=pzu [kg/m^3]
[12615]	761	REAL(wp), INTENT(in) , OPTIONAL :: pfact_evap ! ABOMINATION: corrective factor for evaporation (doing this against my will! /laurent)
[12015]	762	!!
[12615]	763	REAL(wp) :: ztaa, zgamma, zrho, zUrho, zevap, zfact_evap
[12015]	764	INTEGER :: jq
	765	!!----------------------------------------------------------------------------------
[12615]	766	zfact_evap = 1._wp
	767	IF( PRESENT(pfact_evap) ) zfact_evap = pfact_evap
[13655]	768
[12081]	769	!! Need ztaa, absolute temperature at pzu (formula to estimate rho_air needs absolute temperature, not the potential temperature "pTa")
	770	ztaa = pTa ! first guess...
	771	DO jq = 1, 4
[13655]	772	zgamma = gamma_moist( 0.5(ztaa+pTs) , pqa ) !#LB: why not "0.5(pqs+pqa)" rather then "pqa" ???
[12081]	773	ztaa = pTa - zgamma*pzu ! Absolute temp. is slightly colder...
	774	END DO
[13655]	775	zrho = rho_air(ztaa, pqa, ppa)
	776	zrho = rho_air(ztaa, pqa, ppa-zrhogravpzu) ! taking into account that we are pzu m above the sea level where SLP is given!
[12015]	777
[12081]	778	zUrho = pUbMAX(zrho, 1._wp) ! rhoU10
	779
	780	pTau = zUrho * pCd * pwnd ! Wind stress module
	781
	782	zevap = zUrho * pCe * (pqa - pqs)
	783	pQsen = zUrho * pCh * (pTa - pTs) * cp_air(pqa)
	784	pQlat = L_vap(pTs) * zevap
	785
[12615]	786	IF( PRESENT(pEvap) ) pEvap = - zfact_evap * zevap
[12081]	787	IF( PRESENT(prhoa) ) prhoa = zrho
	788
[12015]	789	END SUBROUTINE BULK_FORMULA_SCLR
[13655]	790	!!
[12615]	791	SUBROUTINE BULK_FORMULA_VCTR( pzu, pTs, pqs, pTa, pqa, &
	792	& pCd, pCh, pCe, &
[13655]	793	& pwnd, pUb, ppa, &
	794	& pTau, pQsen, pQlat, &
	795	& pEvap, prhoa, pfact_evap )
[12615]	796	!!----------------------------------------------------------------------------------
	797	REAL(wp), INTENT(in) :: pzu ! height above the sea-level where all this takes place (normally 10m)
	798	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pTs ! water temperature at the air-sea interface [K]
	799	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqs ! satur. spec. hum. at T=pTs [kg/kg]
	800	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pTa ! potential air temperature at z=pzu [K]
	801	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! specific humidity at z=pzu [kg/kg]
	802	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCd
	803	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCh
	804	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCe
	805	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pwnd ! wind speed module at z=pzu [m/s]
	806	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pUb ! bulk wind speed at z=pzu (inc. pot. effect of gustiness etc) [m/s]
[13655]	807	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ppa ! sea-level atmospheric pressure [Pa]
[12615]	808	!!
	809	REAL(wp), DIMENSION(jpi,jpj), INTENT(out) :: pTau ! module of the wind stress [N/m^2]
	810	REAL(wp), DIMENSION(jpi,jpj), INTENT(out) :: pQsen ! [W/m^2]
	811	REAL(wp), DIMENSION(jpi,jpj), INTENT(out) :: pQlat ! [W/m^2]
	812	!!
	813	REAL(wp), DIMENSION(jpi,jpj), INTENT(out), OPTIONAL :: pEvap ! Evaporation [kg/m^2/s]
	814	REAL(wp), DIMENSION(jpi,jpj), INTENT(out), OPTIONAL :: prhoa ! Air density at z=pzu [kg/m^3]
	815	REAL(wp), INTENT(in) , OPTIONAL :: pfact_evap ! ABOMINATION: corrective factor for evaporation (doing this against my will! /laurent)
	816	!!
	817	REAL(wp) :: ztaa, zgamma, zrho, zUrho, zevap, zfact_evap
	818	INTEGER :: ji, jj
	819	!!----------------------------------------------------------------------------------
	820	zfact_evap = 1._wp
	821	IF( PRESENT(pfact_evap) ) zfact_evap = pfact_evap
[12015]	822
[13305]	823	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
[12015]	824
[13655]	825	CALL BULK_FORMULA_SCLR( pzu, pTs(ji,jj), pqs(ji,jj), pTa(ji,jj), pqa(ji,jj), &
	826	& pCd(ji,jj), pCh(ji,jj), pCe(ji,jj), &
	827	& pwnd(ji,jj), pUb(ji,jj), ppa(ji,jj), &
	828	& pTau(ji,jj), pQsen(ji,jj), pQlat(ji,jj), &
	829	& pEvap=zevap, prhoa=zrho, pfact_evap=zfact_evap )
[12015]	830
[13655]	831	IF( PRESENT(pEvap) ) pEvap(ji,jj) = zevap
	832	IF( PRESENT(prhoa) ) prhoa(ji,jj) = zrho
[12615]	833	END_2D
	834	END SUBROUTINE BULK_FORMULA_VCTR
	835
	836
[12015]	837	FUNCTION alpha_sw_vctr( psst )
	838	!!---------------------------------------------------------------------------------
	839	!! * FUNCTION alpha_sw_vctr *
	840	!!
[13655]	841	!! ** Purpose : ROUGH estimate of the thermal expansion coefficient of sea-water at the surface (P =~ 1010 hpa)
[12015]	842	!!
	843	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	844	!!----------------------------------------------------------------------------------
	845	REAL(wp), DIMENSION(jpi,jpj) :: alpha_sw_vctr ! thermal expansion coefficient of sea-water [1/K]
	846	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! water temperature [K]
	847	!!----------------------------------------------------------------------------------
	848	alpha_sw_vctr = 2.1e-5_wp * MAX(psst(:,:)-rt0 + 3.2_wp, 0._wp)**0.79
	849	END FUNCTION alpha_sw_vctr
	850
	851	FUNCTION alpha_sw_sclr( psst )
	852	!!---------------------------------------------------------------------------------
	853	!! * FUNCTION alpha_sw_sclr *
	854	!!
[13655]	855	!! ** Purpose : ROUGH estimate of the thermal expansion coefficient of sea-water at the surface (P =~ 1010 hpa)
[12015]	856	!!
	857	!! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/)
	858	!!----------------------------------------------------------------------------------
	859	REAL(wp) :: alpha_sw_sclr ! thermal expansion coefficient of sea-water [1/K]
	860	REAL(wp), INTENT(in) :: psst ! sea-water temperature [K]
	861	!!----------------------------------------------------------------------------------
	862	alpha_sw_sclr = 2.1e-5_wp * MAX(psst-rt0 + 3.2_wp, 0._wp)**0.79
	863	END FUNCTION alpha_sw_sclr
	864
	865
[13655]	866	!===============================================================================================
	867	FUNCTION qlw_net_sclr( pdwlw, pts, l_ice )
	868	!!---------------------------------------------------------------------------------
	869	!! * FUNCTION qlw_net_sclr *
	870	!!
	871	!! ** Purpose : Estimate of the net longwave flux at the surface
	872	!!----------------------------------------------------------------------------------
	873	REAL(wp) :: qlw_net_sclr
	874	REAL(wp), INTENT(in) :: pdwlw !: downwelling longwave (aka infrared, aka thermal) radiation [W/m^2]
	875	REAL(wp), INTENT(in) :: pts !: surface temperature [K]
	876	LOGICAL, INTENT(in), OPTIONAL :: l_ice !: we are above ice
	877	REAL(wp) :: zemiss, zt2
	878	LOGICAL :: lice
	879	!!----------------------------------------------------------------------------------
	880	lice = .FALSE.
	881	IF( PRESENT(l_ice) ) lice = l_ice
	882	IF( lice ) THEN
	883	zemiss = emiss_i
	884	ELSE
	885	zemiss = emiss_w
	886	END IF
	887	zt2 = pts*pts
	888	qlw_net_sclr = zemiss( pdwlw - stefanzt2*zt2) ! zemiss used both as the IR albedo and IR emissivity...
	889	END FUNCTION qlw_net_sclr
	890	!!
	891	FUNCTION qlw_net_vctr( pdwlw, pts, l_ice )
	892	REAL(wp), DIMENSION(jpi,jpj) :: qlw_net_vctr
	893	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pdwlw !: downwelling longwave (aka infrared, aka thermal) radiation [W/m^2]
	894	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pts !: surface temperature [K]
	895	LOGICAL, INTENT(in), OPTIONAL :: l_ice !: we are above ice
	896	LOGICAL :: lice
	897	INTEGER :: ji, jj
	898	!!----------------------------------------------------------------------------------
	899	lice = .FALSE.
	900	IF( PRESENT(l_ice) ) lice = l_ice
	901	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
	902	qlw_net_vctr(ji,jj) = qlw_net_sclr( pdwlw(ji,jj) , pts(ji,jj), l_ice=lice )
	903	END_2D
	904	END FUNCTION qlw_net_vctr
	905	!===============================================================================================
[12015]	906
[13655]	907	FUNCTION z0_from_Cd( pzu, pCd, ppsi )
	908	REAL(wp), DIMENSION(jpi,jpj) :: z0_from_Cd !: roughness length [m]
	909	REAL(wp) , INTENT(in) :: pzu !: reference height zu [m]
	910	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCd !: (neutral or non-neutral) drag coefficient []
	911	REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: ppsi !: "Psi_m(pzu/L)" stability correction profile for momentum []
	912	!!
	913	!! If pCd is the NEUTRAL-STABILITY drag coefficient then ppsi must be 0 or not given
	914	!! If pCd is the drag coefficient (in stable or unstable conditions) then pssi must be provided
	915	!!----------------------------------------------------------------------------------
	916	IF( PRESENT(ppsi) ) THEN
	917	!! Cd provided is the actual Cd (not the neutral-stability CdN) :
	918	z0_from_Cd = pzu * EXP( - ( vkarmn/SQRT(pCd(:,:)) + ppsi(:,:) ) ) !LB: ok, double-checked!
	919	ELSE
	920	!! Cd provided is the neutral-stability Cd, aka CdN :
	921	z0_from_Cd = pzu * EXP( - vkarmn/SQRT(pCd(:,:)) ) !LB: ok, double-checked!
	922	END IF
	923	END FUNCTION z0_from_Cd
	924
	925	FUNCTION Cd_from_z0( pzu, pz0, ppsi )
	926	REAL(wp), DIMENSION(jpi,jpj) :: Cd_from_z0 !: (neutral or non-neutral) drag coefficient []
	927	REAL(wp) , INTENT(in) :: pzu !: reference height zu [m]
	928	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0 !: roughness length [m]
	929	REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: ppsi !: "Psi_m(pzu/L)" stability correction profile for momentum []
	930	!!
	931	!! If we want to return the NEUTRAL-STABILITY drag coefficient then ppsi must be 0 or not given
	932	!! If we want to return the stability-corrected Cd (i.e. in stable or unstable conditions) then pssi must be provided
	933	!!----------------------------------------------------------------------------------
	934	IF( PRESENT(ppsi) ) THEN
	935	!! The Cd we return is the actual Cd (not the neutral-stability CdN) :
	936	Cd_from_z0 = 1._wp / ( LOG( pzu / pz0(:,:) ) - ppsi(:,:) )
	937	ELSE
	938	!! The Cd we return is the neutral-stability Cd, aka CdN :
	939	Cd_from_z0 = 1._wp / LOG( pzu / pz0(:,:) )
	940	END IF
	941	Cd_from_z0 = vkarmn2 * Cd_from_z0 * Cd_from_z0
	942	END FUNCTION Cd_from_z0
	943
	944
	945	FUNCTION f_m_louis_sclr( pzu, pRib, pCdn, pz0 )
	946	!!----------------------------------------------------------------------------------
	947	!! Stability correction function for MOMENTUM
	948	!! Louis (1979)
	949	!!----------------------------------------------------------------------------------
	950	REAL(wp) :: f_m_louis_sclr ! term "f_m" in Eq.(6) when option "Louis" rather than "Psi(zeta) is chosen, Lupkes & Gryanik (2015),
	951	REAL(wp), INTENT(in) :: pzu ! reference height (height for pwnd) [m]
	952	REAL(wp), INTENT(in) :: pRib ! Bulk Richardson number
	953	REAL(wp), INTENT(in) :: pCdn ! neutral drag coefficient
	954	REAL(wp), INTENT(in) :: pz0 ! roughness length [m]
	955	!!----------------------------------------------------------------------------------
	956	REAL(wp) :: ztu, zts, zstab
	957	!!----------------------------------------------------------------------------------
	958	zstab = 0.5 + SIGN(0.5_wp, pRib) ; ! Unstable (Ri<0) => zstab = 0 \| Stable (Ri>0) => zstab = 1
	959	!
	960	ztu = pRib / ( 1._wp + 3._wp * rc2_louis * pCdn * SQRT( ABS( -pRib * ( pzu / pz0 + 1._wp) ) ) ) ! ABS is just here for when it's stable conditions and ztu is not used anyways
	961	zts = pRib / SQRT( ABS( 1._wp + pRib ) ) ! ABS is just here for when it's UNstable conditions and zts is not used anyways
	962	!
	963	f_m_louis_sclr = (1._wp - zstab) * ( 1._wp - ram_louis * ztu ) & ! Unstable Eq.(A6)
	964	& + zstab * 1._wp / ( 1._wp + ram_louis * zts ) ! Stable Eq.(A7)
	965	!
	966	END FUNCTION f_m_louis_sclr
	967	!!
	968	FUNCTION f_m_louis_vctr( pzu, pRib, pCdn, pz0 )
	969	REAL(wp), DIMENSION(jpi,jpj) :: f_m_louis_vctr
	970	REAL(wp), INTENT(in) :: pzu
	971	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pRib
	972	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCdn
	973	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0
	974	INTEGER :: ji, jj
	975	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
	976	f_m_louis_vctr(ji,jj) = f_m_louis_sclr( pzu, pRib(ji,jj), pCdn(ji,jj), pz0(ji,jj) )
	977	END_2D
	978	END FUNCTION f_m_louis_vctr
	979
	980
	981	FUNCTION f_h_louis_sclr( pzu, pRib, pChn, pz0 )
	982	!!----------------------------------------------------------------------------------
	983	!! Stability correction function for HEAT
	984	!! Louis (1979)
	985	!!----------------------------------------------------------------------------------
	986	REAL(wp) :: f_h_louis_sclr ! term "f_h" in Eq.(6) when option "Louis" rather than "Psi(zeta) is chosen, Lupkes & Gryanik (2015),
	987	REAL(wp), INTENT(in) :: pzu ! reference height (height for pwnd) [m]
	988	REAL(wp), INTENT(in) :: pRib ! Bulk Richardson number
	989	REAL(wp), INTENT(in) :: pChn ! neutral heat transfer coefficient
	990	REAL(wp), INTENT(in) :: pz0 ! roughness length [m]
	991	!!----------------------------------------------------------------------------------
	992	REAL(wp) :: ztu, zts, zstab
	993	!!----------------------------------------------------------------------------------
	994	zstab = 0.5 + SIGN(0.5_wp, pRib) ; ! Unstable (Ri<0) => zstab = 0 \| Stable (Ri>0) => zstab = 1
	995	!
	996	ztu = pRib / ( 1._wp + 3._wp * rc2_louis * pChn * SQRT( ABS(-pRib * ( pzu / pz0 + 1._wp) ) ) )
	997	zts = pRib / SQRT( ABS( 1._wp + pRib ) )
	998	!
	999	f_h_louis_sclr = (1._wp - zstab) * ( 1._wp - rah_louis * ztu ) & ! Unstable Eq.(A6)
	1000	& + zstab * 1._wp / ( 1._wp + rah_louis * zts ) ! Stable Eq.(A7) !#LB: in paper it's "ram_louis" and not "rah_louis" typo or what????
	1001	!
	1002	END FUNCTION f_h_louis_sclr
	1003	!!
	1004	FUNCTION f_h_louis_vctr( pzu, pRib, pChn, pz0 )
	1005	REAL(wp), DIMENSION(jpi,jpj) :: f_h_louis_vctr
	1006	REAL(wp), INTENT(in) :: pzu
	1007	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pRib
	1008	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pChn
	1009	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0
	1010	INTEGER :: ji, jj
	1011	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
	1012	f_h_louis_vctr(ji,jj) = f_h_louis_sclr( pzu, pRib(ji,jj), pChn(ji,jj), pz0(ji,jj) )
	1013	END_2D
	1014	END FUNCTION f_h_louis_vctr
	1015
	1016	FUNCTION UN10_from_ustar( pzu, pUzu, pus, ppsi )
	1017	!!----------------------------------------------------------------------------------
	1018	!! Provides the neutral-stability wind speed at 10 m
	1019	!!----------------------------------------------------------------------------------
	1020	REAL(wp), DIMENSION(jpi,jpj) :: UN10_from_ustar !: neutral stability wind speed at 10m [m/s]
	1021	REAL(wp), INTENT(in) :: pzu !: measurement heigh of wind speed [m]
	1022	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pUzu !: bulk wind speed at height pzu m [m/s]
	1023	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pus !: friction velocity [m/s]
	1024	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ppsi !: "Psi_m(pzu/L)" stability correction profile for momentum []
	1025	!!----------------------------------------------------------------------------------
	1026	UN10_from_ustar(:,:) = pUzu(:,:) - pus(:,:)/vkarmn * ( LOG(pzu/10._wp) - ppsi(:,:) )
	1027	!!
	1028	END FUNCTION UN10_from_ustar
	1029
	1030
	1031	FUNCTION UN10_from_CD( pzu, pUb, pCd, ppsi )
	1032	!!----------------------------------------------------------------------------------
	1033	!! Provides the neutral-stability wind speed at 10 m
	1034	!!----------------------------------------------------------------------------------
	1035	REAL(wp), DIMENSION(jpi,jpj) :: UN10_from_CD !: [m/s]
	1036	REAL(wp), INTENT(in) :: pzu !: measurement heigh of bulk wind speed
	1037	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pUb !: bulk wind speed at height pzu m [m/s]
	1038	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCd !: drag coefficient
	1039	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ppsi !: "Psi_m(pzu/L)" stability correction profile for momentum []
	1040	!!----------------------------------------------------------------------------------
	1041	!! Reminder: UN10 = u/vkarmn log(10/z0)
	1042	!! and: u* = sqrt(Cd) * Ub
	1043	!! u/vkarmn log( 10 / z0 )
	1044	UN10_from_CD(:,:) = SQRT(pCd(:,:))pUb/vkarmn LOG( 10._wp / z0_from_Cd( pzu, pCd(:,:), ppsi=ppsi(:,:) ) )
	1045	!!
	1046	END FUNCTION UN10_from_CD
	1047
	1048
	1049	FUNCTION z0tq_LKB( iflag, pRer, pz0 )
	1050	!!---------------------------------------------------------------------------------
	1051	!! * FUNCTION z0tq_LKB *
	1052	!!
	1053	!! ** Purpose : returns the "temperature/humidity roughness lengths"
	1054	!! * iflag==1 => temperature => returns: z_{0t}
	1055	!! * iflag==2 => humidity => returns: z_{0q}
	1056	!! from roughness reynold number "pRer" (i.e. [z_0 u*]/Nu_{air})
	1057	!! between 0 and 1000. Out of range "pRer" indicated by prt=-999.
	1058	!! and roughness length (for momentum)
	1059	!!
	1060	!! Based on Liu et al. (1979) JAS 36 1722-1723s
	1061	!!
	1062	!! Note: this is what is used into COARE 2.5 to estimate z_{0t} and z_{0q}
	1063	!!
	1064	!! ** Author: L. Brodeau, April 2020 / AeroBulk (https://github.com/brodeau/aerobulk/)
	1065	!!----------------------------------------------------------------------------------
	1066	REAL(wp), DIMENSION(jpi,jpj) :: z0tq_LKB
	1067	INTEGER, INTENT(in) :: iflag !: 1 => dealing with temperature; 2 => dealing with humidity
	1068	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pRer !: roughness Reynolds number [z_0 u*]/Nu_{air}
	1069	REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0 !: roughness length (for momentum) [m]
	1070	!-------------------------------------------------------------------
	1071	! Scalar Re_r relation from Liu et al.
	1072	REAL(wp), DIMENSION(8,2), PARAMETER :: &
	1073	& XA = (/ 0.177, 1.376, 1.026, 1.625, 4.661, 34.904, 1667.19, 5.88e5, &
	1074	& 0.292, 1.808, 1.393, 1.956, 4.994, 30.709, 1448.68, 2.98e5 /)
	1075	!!
	1076	REAL(wp), DIMENSION(8,2), PARAMETER :: &
	1077	& XB = (/ 0., 0.929, -0.599, -1.018, -1.475, -2.067, -2.907, -3.935, &
	1078	& 0., 0.826, -0.528, -0.870, -1.297, -1.845, -2.682, -3.616 /)
	1079	!!
	1080	REAL(wp), DIMENSION(0:8), PARAMETER :: &
	1081	& XRAN = (/ 0., 0.11, 0.825, 3.0, 10.0, 30.0, 100., 300., 1000. /)
	1082	!-------------------------------------------------------------------
	1083	!
	1084	!-------------------------------------------------------------------
	1085	! Scalar Re_r relation from Moana Wave data.
	1086	!
	1087	! real*8 A(9,2),B(9,2),RAN(9),pRer,prt
	1088	! integer iflag
	1089	! DATA A/0.177,2.7e3,1.03,1.026,1.625,4.661,34.904,1667.19,5.88E5,
	1090	! & 0.292,3.7e3,1.4,1.393,1.956,4.994,30.709,1448.68,2.98E5/
	1091	! DATA B/0.,4.28,0,-0.599,-1.018,-1.475,-2.067,-2.907,-3.935,
	1092	! & 0.,4.28,0,-0.528,-0.870,-1.297,-1.845,-2.682,-3.616/
	1093	! DATA RAN/0.11,.16,1.00,3.0,10.0,30.0,100.,300.,1000./
	1094	!-------------------------------------------------------------------
	1095
	1096	LOGICAL :: lfound=.FALSE.
	1097	REAL(wp) :: zrr
	1098	INTEGER :: ji, jj, jm
	1099
	1100	z0tq_LKB(:,:) = -999._wp
	1101
	1102	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
	1103
	1104	zrr = pRer(ji,jj)
	1105	lfound = .FALSE.
	1106
	1107	IF( (zrr > 0.).AND.(zrr < 1000.) ) THEN
	1108	jm = 0
	1109	DO WHILE ( .NOT. lfound )
	1110	jm = jm + 1
	1111	lfound = ( (zrr > XRAN(jm-1)) .AND. (zrr <= XRAN(jm)) )
	1112	END DO
	1113
	1114	z0tq_LKB(ji,jj) = XA(jm,iflag)zrrXB(jm,iflag) pz0(ji,jj)/zrr
	1115
	1116	END IF
	1117
	1118	END_2D
	1119
	1120	z0tq_LKB(:,:) = MIN( MAX(ABS(z0tq_LKB(:,:)), 1.E-9) , 0.05_wp )
	1121
	1122	END FUNCTION z0tq_LKB
	1123
	1124
[12015]	1125	!!======================================================================
[13655]	1126	END MODULE sbc_phy

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