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source: branches/ORCHIDEE_2_2/ORCHIDEE/src_sechiba/diffuco.f90 @ 6189

Last change on this file since 6189 was 6189, checked in by josefine.ghattas, 5 years ago
As done in the trunk rev [6188]: Corrections done by A. Jornet. These errors crashed the model only in coupled mode with serveral treadds OMP.
Property svn:keywords set to `Revision Date HeadURL Date Author Revision`
File size: 133.1 KB

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1	! ================================================================================================================================
2	! MODULE : diffuco
3	!
4	! CONTACT : orchidee-help _at_ listes.ipsl.fr
5	!
6	! LICENCE : IPSL (2006)
7	! This software is governed by the CeCILL licence see ORCHIDEE/ORCHIDEE_CeCILL.LIC
8	!
9	!>\BRIEF This module calculates the limiting coefficients, both aerodynamic
10	!! and hydrological, for the turbulent heat fluxes.
11	!!
12	!!\n DESCRIPTION: The aerodynamic resistance R_a is used to limit
13	!! the transport of fluxes from the surface layer of vegetation to the point in the atmosphere at which
14	!! interaction with the LMDZ atmospheric circulation model takes place. The aerodynamic resistance is
15	!! calculated either within the module r_aerod (if the surface drag coefficient is provided by the LMDZ, and
16	!! if the flag 'ldq_cdrag_from_gcm' is set to TRUE) or r_aero (if the surface drag coefficient must be calculated).\n
17	!!
18	!! Within ORCHIDEE, evapotranspiration is a function of the Evaporation Potential, but is modulated by a
19	!! series of resistances (canopy and aerodynamic) of the surface layer, here represented by beta.\n
20	!!
21	!! DESCRIPTION :
22	!! \latexonly
23	!! \input{diffuco_intro.tex}
24	!! \endlatexonly
25	!! \n
26	!!
27	!! This module calculates the beta for several different scenarios:
28	!! - diffuco_snow calculates the beta coefficient for sublimation by snow,
29	!! - diffuco_inter calculates the beta coefficient for interception loss by each type of vegetation,
30	!! - diffuco_bare calculates the beta coefficient for bare soil,
31	!! - diffuco_trans_co2 calculates the beta coefficient for transpiration for each type of vegetation, using Farqhar's formula
32	!! - chemistry_bvoc calculates the beta coefficient for emissions of biogenic compounds \n
33	!!
34	!! Finally, the module diffuco_comb computes the combined $\alpha$ and $\beta$ coefficients for use
35	!! elsewhere in the module. \n
36
37	!! RECENT CHANGE(S): Nathalie le 28 mars 2006 - sur proposition de Fred Hourdin, ajout
38	!! d'un potentiometre pour regler la resistance de la vegetation (rveg is now in pft_parameters)
39	!! October 2018: Removed diffuco_trans using Jarvis formula for calculation of beta coefficient
40	!!
41	!! REFERENCE(S) : None
42	!!
43	!! SVN :
44	!! $HeadURL$
45	!! $Date$
46	!! $Revision$
47	!! \n
48	!_ ================================================================================================================================
49
50	MODULE diffuco
51
52	! modules used :
53	USE constantes
54	USE constantes_soil
55	USE qsat_moisture
56	USE sechiba_io_p
57	USE ioipsl
58	USE pft_parameters
59	USE grid
60	USE time, ONLY : one_day, dt_sechiba
61	USE ioipsl_para
62	USE xios_orchidee
63	USE chemistry, ONLY : chemistry_initialize, chemistry_bvoc, chemistry_clear
64	IMPLICIT NONE
65
66	! public routines :
67	PRIVATE
68	PUBLIC :: diffuco_main, diffuco_initialize, diffuco_finalize, diffuco_clear
69
70	INTERFACE Arrhenius_modified
71	MODULE PROCEDURE Arrhenius_modified_0d, Arrhenius_modified_1d
72	END INTERFACE
73
74	!
75	! variables used inside diffuco module : declaration and initialisation
76	!
77	REAL(r_std), ALLOCATABLE, SAVE, DIMENSION (:) :: wind !! Wind module (m s^{-1})
78	!$OMP THREADPRIVATE(wind)
79
80	CONTAINS
81
82
83	!! =============================================================================================================================
84	!! SUBROUTINE: diffuco_initialize
85	!!
86	!>\BRIEF Allocate module variables, read from restart file or initialize with default values
87	!!
88	!! DESCRIPTION: Allocate module variables, read from restart file or initialize with default values.
89	!! Call chemistry_initialize for initialization of variables needed for the calculations of BVOCs.
90	!!
91	!! RECENT CHANGE(S): None
92	!!
93	!! REFERENCE(S): None
94	!!
95	!! FLOWCHART: None
96	!! \n
97	!_ ==============================================================================================================================
98	SUBROUTINE diffuco_initialize (kjit, kjpindex, index, &
99	rest_id, lalo, neighbours, resolution, &
100	rstruct, q_cdrag)
101
102	!! 0. Variable and parameter declaration
103	!! 0.1 Input variables
104	INTEGER(i_std), INTENT(in) :: kjit !! Time step number (-)
105	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
106	INTEGER(i_std),DIMENSION (kjpindex), INTENT (in) :: index !! Indeces of the points on the map (-)
107	INTEGER(i_std),INTENT (in) :: rest_id !! _Restart_ file identifier (-)
108	REAL(r_std),DIMENSION (kjpindex,2), INTENT (in) :: lalo !! Geographical coordinates
109	INTEGER(i_std),DIMENSION (kjpindex,NbNeighb),INTENT (in):: neighbours !! Vector of neighbours for each
110	REAL(r_std),DIMENSION (kjpindex,2), INTENT(in) :: resolution !! The size in km of each grid-box in X and Y
111
112	!! 0.2 Output variables
113	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: rstruct !! Structural resistance for the vegetation
114
115	!! 0.3 Modified variables
116	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
117
118	!! 0.4 Local variables
119	INTEGER :: ilai
120	INTEGER :: jv
121	INTEGER :: ier
122	CHARACTER(LEN=4) :: laistring
123	CHARACTER(LEN=80) :: var_name
124	!_ ================================================================================================================================
125
126	!! 1. Define flag ldq_cdrag_from_gcm. This flag determines if the cdrag should be taken from the GCM or be calculated.
127	!! The default value is true if the q_cdrag variables was already initialized. This is the case when coupled to the LMDZ.
128
129	!Config Key = CDRAG_FROM_GCM
130	!Config Desc = Keep cdrag coefficient from gcm.
131	!Config If = OK_SECHIBA
132	!Config Def = y
133	!Config Help = Set to .TRUE. if you want q_cdrag coming from GCM (if q_cdrag on initialization is non zero).
134	!Config Keep cdrag coefficient from gcm for latent and sensible heat fluxes.
135	!Config Units = [FLAG]
136	IF ( ABS(MAXVAL(q_cdrag)) .LE. EPSILON(q_cdrag)) THEN
137	ldq_cdrag_from_gcm = .FALSE.
138	ELSE
139	ldq_cdrag_from_gcm = .TRUE.
140	ENDIF
141	CALL getin_p('CDRAG_from_GCM', ldq_cdrag_from_gcm)
142	IF (printlev>=2) WRITE(numout,*) "ldq_cdrag_from_gcm = ",ldq_cdrag_from_gcm
143
144	!! 2. Allocate module variables
145	ALLOCATE (wind(kjpindex),stat=ier)
146	IF (ier /= 0) CALL ipslerr_p(3,'diffuco_initialize','Problem in allocate of variable wind','','')
147
148	!! 3. Read variables from restart file
149	IF (printlev>=3) WRITE (numout,*) 'Read DIFFUCO variables from restart file'
150
151	CALL ioconf_setatt_p('UNITS', 's/m')
152	CALL ioconf_setatt_p('LONG_NAME','Structural resistance')
153	CALL restget_p (rest_id, 'rstruct', nbp_glo, nvm, 1, kjit, .TRUE., rstruct, "gather", nbp_glo, index_g)
154	IF ( ALL(rstruct(:,:) == val_exp) ) THEN
155	DO jv = 1, nvm
156	rstruct(:,jv) = rstruct_const(jv)
157	ENDDO
158	ENDIF
159
160	!! 4. Initialize chemistry module
161	IF (printlev>=3) WRITE(numout,*) "ok_bvoc:",ok_bvoc
162	IF ( ok_bvoc ) CALL chemistry_initialize(kjpindex, lalo, neighbours, resolution)
163
164	END SUBROUTINE diffuco_initialize
165
166
167
168	!! ================================================================================================================================
169	!! SUBROUTINE : diffuco_main
170	!!
171	!>\BRIEF The root subroutine for the module, which calls all other required
172	!! subroutines.
173	!!
174	!! DESCRIPTION :
175
176	!! This is the main subroutine for the module.
177	!! First it calculates the surface drag coefficient (via a call to diffuco_aero), using available parameters to determine
178	!! the stability of air in the surface layer by calculating the Richardson Nubmber. If a value for the
179	!! surface drag coefficient is passed down from the atmospheric model and and if the flag 'ldq_cdrag_from_gcm'
180	!! is set to TRUE, then the subroutine diffuco_aerod is called instead. This calculates the aerodynamic coefficient. \n
181	!!
182	!! Following this, an estimation of the saturated humidity at the surface is made (via a call
183	!! to qsatcalc in the module qsat_moisture). Following this the beta coefficients for sublimation (via
184	!! diffuco_snow), interception (diffuco_inter), bare soil (diffuco_bare), and transpiration (via
185	!! diffuco_trans_co2) are calculated in sequence. Finally
186	!! the alpha and beta coefficients are combined (diffuco_comb). \n
187	!!
188	!! The surface drag coefficient is calculated for use within the module enerbil. It is required to to
189	!! calculate the aerodynamic coefficient for every flux. \n
190	!!
191	!! The various beta coefficients are used within the module enerbil for modifying the rate of evaporation,
192	!! as appropriate for the surface. As explained in Chapter 2 of Guimberteau (2010), that module (enerbil)
193	!! calculates the rate of evaporation essentially according to the expression $E = /beta E_{pot}$, where
194	!! E is the total evaporation and $E_{pot}$ the evaporation potential. If $\beta = 1$, there would be
195	!! essentially no resistance to evaporation, whereas should $\beta = 0$, there would be no evaporation and
196	!! the surface layer would be subject to some very stong hydrological stress. \n
197	!!
198	!! The following processes are calculated:
199	!! - call diffuco_aero for aerodynamic transfer coeficient
200	!! - call diffuco_snow for partial beta coefficient: sublimation
201	!! - call diffuco_inter for partial beta coefficient: interception for each type of vegetation
202	!! - call diffuco_bare for partial beta coefficient: bare soil
203	!! - call diffuco_trans_co2 for partial beta coefficient: transpiration for each type of vegetation, using Farqhar's formula
204	!! - call diffuco_comb for alpha and beta coefficient
205	!! - call chemistry_bvoc for alpha and beta coefficients for biogenic emissions
206	!!
207	!! RECENT CHANGE(S): None
208	!!
209	!! MAIN OUTPUT VARIABLE(S): humrel, q_cdrag, vbeta, vbeta1, vbeta4,
210	!! vbeta2, vbeta3, rveget, cimean
211	!!
212	!! REFERENCE(S) :
213	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
214	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
215	!! Circulation Model. Journal of Climate, 6, pp.248-273.
216	!! - de Rosnay, P, 1999. ReprÃ©sentation des interactions sol-plante-atmosphÃšre dans le modÃšle de circulation gÃ©nÃ©rale
217	!! du LMD, 1999. PhD Thesis, UniversitÃ© Paris 6, available (25/01/12):
218	!! http://www.ecmwf.int/staff/patricia_de_rosnay/publications.html#8
219	!! - Ducharne, A, 1997. Le cycle de l'eau: modÃ©lisation de l'hydrologie continentale, Ã©tude de ses interactions avec
220	!! le climat, PhD Thesis, UniversitÃ© Paris 6
221	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influences de l'irrigation
222	!! sur le cycle de l'eau, PhD Thesis, available (25/01/12):
223	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
224	!! - LathiÃšre, J, 2005. Evolution des Ã©missions de composÃ©s organiques et azotÃ©s par la biosphÃšre continentale dans le
225	!! modÃšle LMDz-INCA-ORCHIDEE, UniversitÃ© Paris 6
226	!!
227	!! FLOWCHART :
228	!! \latexonly
229	!! \includegraphics[scale=0.5]{diffuco_main_flowchart.png}
230	!! \endlatexonly
231	!! \n
232	!_ ================================================================================================================================
233
234	SUBROUTINE diffuco_main (kjit, kjpindex, index, indexveg, indexlai, u, v, &
235	& zlev, z0m, z0h, roughheight, temp_sol, temp_air, temp_growth, rau, q_cdrag, qsurf, qair, pb, &
236	& evap_bare_lim, evap_bare_lim_ns, evapot, evapot_corr, snow, flood_frac, flood_res, frac_nobio, snow_nobio, totfrac_nobio, &
237	& swnet, swdown, coszang, ccanopy, humrel, veget, veget_max, lai, qsintveg, qsintmax, assim_param, &
238	& vbeta , vbeta1, vbeta2, vbeta3, vbeta3pot, vbeta4, vbeta5, gsmean, rveget, rstruct, cimean, gpp, co2_to_bm, &
239	& lalo, neighbours, resolution, ptnlev1, precip_rain, frac_age, tot_bare_soil, frac_snow_veg, frac_snow_nobio, &
240	& hist_id, hist2_id)
241
242	!! 0. Variable and parameter declaration
243
244	!! 0.1 Input variables
245
246	INTEGER(i_std), INTENT(in) :: kjit !! Time step number (-)
247	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
248	INTEGER(i_std),INTENT (in) :: hist_id !! _History_ file identifier (-)
249	INTEGER(i_std),INTENT (in) :: hist2_id !! _History_ file 2 identifier (-)
250	INTEGER(i_std),DIMENSION (kjpindex), INTENT (in) :: index !! Indeces of the points on the map (-)
251	INTEGER(i_std),DIMENSION (kjpindex*(nlai+1)), INTENT (in) :: indexlai !! Indeces of the points on the 3D map
252	INTEGER(i_std),DIMENSION (kjpindex*nvm), INTENT (in) :: indexveg !! Indeces of the points on the 3D map (-)
253	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind speed (m s^{-1})
254	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Northward Lowest level wind speed (m s^{-1})
255	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: zlev !! Height of first layer (m)
256	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: z0m !! Surface roughness Length for momentum (m)
257	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: z0h !! Surface roughness Length for heat (m)
258	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: roughheight !! Effective height for roughness (m)
259	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_sol !! Skin temperature (K)
260	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_air !! Lowest level temperature (K)
261	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_growth !! Growth temperature (Â°C) - Is equal to t2m_month
262	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! Air Density (kg m^{-3})
263	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsurf !! Near surface air specific humidity (kg kg^{-1})
264	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level air specific humidity (kg kg^{-1})
265	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: snow !! Snow mass (kg)
266	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: flood_frac !! Fraction of floodplains
267	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: flood_res !! Reservoir in floodplains (estimation to avoid over-evaporation)
268	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: pb !! Surface level pressure (hPa)
269	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: evap_bare_lim !! Limit to the bare soil evaporation when the
270	!! 11-layer hydrology is used (-)
271	REAL(r_std),DIMENSION (kjpindex,nstm), INTENT (inout) :: evap_bare_lim_ns !! Limit to the bare soil evaporation when the
272	!! 11-layer hydrology is used (-)
273	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: evapot !! Soil Potential Evaporation (mm day^{-1})
274	!! NdN This variable does not seem to be used at
275	!! all in diffuco
276	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: evapot_corr !! Soil Potential Evaporation
277	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT (in) :: frac_nobio !! Fraction of ice,lakes,cities,... (-)
278	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT (in) :: snow_nobio !! Snow on ice,lakes,cities,... (kg m^{-2})
279	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: totfrac_nobio !! Total fraction of ice+lakes+cities+... (-)
280	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: swnet !! Net surface short-wave flux (W m^{-2})
281	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: swdown !! Down-welling surface short-wave flux (W m^{-2})
282	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: coszang !! Cosine of the solar zenith angle (unitless)
283	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: ccanopy !! CO2 concentration inside the canopy (ppm)
284	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget !! Fraction of vegetation type (-)
285	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget_max !! Max. fraction of vegetation type (LAI->infty)
286	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: lai !! Leaf area index (m^2 m^{-2})
287	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintveg !! Water on vegetation due to interception (kg m^{-2})
288	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintmax !! Maximum water on vegetation for interception
289	!! (kg m^{-2})
290	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: co2_to_bm !! virtual gpp ((gC m^{-2} s^{-1}), total area)
291	REAL(r_std),DIMENSION (kjpindex,nvm,npco2), INTENT (in) :: assim_param !! min+max+opt temps, vcmax, vjmax
292	!! for photosynthesis (K ??)
293	REAL(r_std),DIMENSION (kjpindex,2), INTENT (in) :: lalo !! Geographical coordinates
294	INTEGER(i_std),DIMENSION (kjpindex,NbNeighb),INTENT (in):: neighbours !! Vector of neighbours for each
295	!! grid point (1=N, 2=E, 3=S, 4=W)
296	REAL(r_std),DIMENSION (kjpindex,2), INTENT(in) :: resolution !! The size in km of each grid-box in X and Y
297	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: ptnlev1 !! 1st level of soil temperature (Kelvin)
298	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: precip_rain !! Rain precipitation expressed in mm/tstep
299	REAL(r_std),DIMENSION (kjpindex,nvm,nleafages), INTENT (in) :: frac_age !! Age efficiency for isoprene emissions (from STOMATE)
300	REAL(r_std),DIMENSION (kjpindex), INTENT(in) :: tot_bare_soil !! Total evaporating bare soil fraction
301	REAL(r_std),DIMENSION (kjpindex), INTENT(in) :: frac_snow_veg !! Snow cover fraction on vegeted area
302	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT(in):: frac_snow_nobio !! Snow cover fraction on non-vegeted area
303
304	!! 0.2 Output variables
305
306	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta !! Total beta coefficient (-)
307	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta1 !! Beta for sublimation (-)
308	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta4 !! Beta for bare soil evaporation (-)
309	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta5 !! Beta for floodplains
310	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: gsmean !! Mean stomatal conductance to CO2 (mol m-2 s-1)
311	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta2 !! Beta for interception loss (-)
312	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta3 !! Beta for transpiration (-)
313	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta3pot !! Beta for potential transpiration
314	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: rveget !! Stomatal resistance for the whole canopy (s m^{-1})
315	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: rstruct !! Structural resistance for the vegetation
316	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: cimean !! Mean leaf Ci (ppm)
317	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT(out) :: gpp !! Assimilation ((gC m^{-2} s^{-1}), total area)
318
319	!! 0.3 Modified variables
320
321	REAL(r_std),DIMENSION (kjpindex, nvm), INTENT (inout) :: humrel !! Soil moisture stress (within range 0 to 1)
322	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: q_cdrag !! Surface drag coefficient (-)
323
324	!! 0.4 Local variables
325
326	REAL(r_std),DIMENSION (kjpindex,nvm) :: vbeta23 !! Beta for fraction of wetted foliage that will
327	!! transpire once intercepted water has evaporated (-)
328	REAL(r_std),DIMENSION (kjpindex) :: raero !! Aerodynamic resistance (s m^{-1})
329	INTEGER(i_std) :: ilai
330	CHARACTER(LEN=4) :: laistring
331	CHARACTER(LEN=80) :: var_name !! To store variables names for I/O
332	REAL(r_std),DIMENSION(kjpindex) :: qsatt !! Surface saturated humidity (kg kg^{-1})
333	REAL(r_std),DIMENSION (kjpindex,nvm) :: cim !! Intercellular CO2 over nlai
334
335	!_ ================================================================================================================================
336
337	wind(:) = SQRT (u(:)u(:) + v(:)v(:))
338
339	!! 1. Calculate the different coefficients
340
341	IF (.NOT.ldq_cdrag_from_gcm) THEN
342	! Case 1a)
343	CALL diffuco_aero (kjpindex, kjit, u, v, zlev, z0h, z0m, roughheight, temp_sol, temp_air, &
344	qsurf, qair, snow, q_cdrag)
345	ENDIF
346
347	! Case 1b)
348	CALL diffuco_raerod (kjpindex, u, v, q_cdrag, raero)
349
350	!! 2. Make an estimation of the saturated humidity at the surface
351
352	CALL qsatcalc (kjpindex, temp_sol, pb, qsatt)
353
354	!! 3. Calculate the beta coefficient for sublimation
355
356	CALL diffuco_snow (kjpindex, qair, qsatt, rau, u, v, q_cdrag, &
357	snow, frac_nobio, totfrac_nobio, snow_nobio, frac_snow_veg, frac_snow_nobio, &
358	vbeta1)
359
360
361	CALL diffuco_flood (kjpindex, qair, qsatt, rau, u, v, q_cdrag, evapot, evapot_corr, &
362	& flood_frac, flood_res, vbeta5)
363
364	!! 4. Calculate the beta coefficient for interception
365
366	CALL diffuco_inter (kjpindex, qair, qsatt, rau, u, v, q_cdrag, humrel, veget, &
367	& qsintveg, qsintmax, rstruct, vbeta2, vbeta23)
368
369
370	!! 5. Calculate the beta coefficient for transpiration
371
372	CALL diffuco_trans_co2 (kjpindex, swdown, pb, qsurf, qair, temp_air, temp_growth, rau, u, v, q_cdrag, humrel, &
373	assim_param, ccanopy, &
374	veget, veget_max, lai, qsintveg, qsintmax, vbeta3, vbeta3pot, &
375	rveget, rstruct, cimean, gsmean, gpp, &
376	co2_to_bm, vbeta23, hist_id, indexveg, indexlai, index, kjit, cim)
377
378	!
379	!biogenic emissions
380	!
381	IF ( ok_bvoc ) THEN
382	CALL chemistry_bvoc (kjpindex, swdown, coszang, temp_air, &
383	temp_sol, ptnlev1, precip_rain, humrel, veget_max, &
384	lai, frac_age, lalo, ccanopy, cim, wind, snow, &
385	veget, hist_id, hist2_id, kjit, index, &
386	indexlai, indexveg)
387	ENDIF
388	!
389	! combination of coefficient : alpha and beta coefficient
390	! beta coefficient for bare soil
391	!
392
393	CALL diffuco_bare (kjpindex, evap_bare_lim, evap_bare_lim_ns, vbeta2, vbeta3, vbeta4)
394
395	!! 6. Combine the alpha and beta coefficients
396
397	! Ajout qsintmax dans les arguments de la routine.... Nathalie / le 13-03-2006
398	CALL diffuco_comb (kjpindex, humrel, rau, u, v, q_cdrag, pb, qair, temp_sol, temp_air, snow, &
399	& veget, lai, tot_bare_soil, vbeta1, vbeta2, vbeta3, vbeta4, &
400	& evap_bare_lim, evap_bare_lim_ns, veget_max, vbeta, qsintmax)
401
402	CALL xios_orchidee_send_field("q_cdrag",q_cdrag)
403	CALL xios_orchidee_send_field("raero",raero)
404	CALL xios_orchidee_send_field("wind",wind)
405	CALL xios_orchidee_send_field("qsatt",qsatt)
406	CALL xios_orchidee_send_field("coszang",coszang)
407	CALL xios_orchidee_send_field('cim', cim)
408
409	IF ( .NOT. almaoutput ) THEN
410	CALL histwrite_p(hist_id, 'raero', kjit, raero, kjpindex, index)
411	CALL histwrite_p(hist_id, 'cdrag', kjit, q_cdrag, kjpindex, index)
412	CALL histwrite_p(hist_id, 'Wind', kjit, wind, kjpindex, index)
413	CALL histwrite_p(hist_id, 'qsatt', kjit, qsatt, kjpindex, index)
414	CALL histwrite_p(hist_id, 'cim', kjit, cim, kjpindex*nvm, indexveg)
415
416	IF ( hist2_id > 0 ) THEN
417	CALL histwrite_p(hist2_id, 'raero', kjit, raero, kjpindex, index)
418	CALL histwrite_p(hist2_id, 'cdrag', kjit, q_cdrag, kjpindex, index)
419	CALL histwrite_p(hist2_id, 'Wind', kjit, wind, kjpindex, index)
420	CALL histwrite_p(hist2_id, 'qsatt', kjit, qsatt, kjpindex, index)
421	ENDIF
422	ELSE
423	CALL histwrite_p(hist_id, 'cim', kjit, cim, kjpindex*nvm, indexveg)
424	ENDIF
425
426	IF (printlev>=3) WRITE (numout,*) ' diffuco_main done '
427
428	END SUBROUTINE diffuco_main
429
430	!! =============================================================================================================================
431	!! SUBROUTINE: diffuco_finalize
432	!!
433	!>\BRIEF Write to restart file
434	!!
435	!! DESCRIPTION: This subroutine writes the module variables and variables calculated in diffuco
436	!! to restart file
437	!!
438	!! RECENT CHANGE(S): None
439	!! REFERENCE(S): None
440	!! FLOWCHART: None
441	!! \n
442	!_ ==============================================================================================================================
443	SUBROUTINE diffuco_finalize (kjit, kjpindex, rest_id, rstruct )
444
445	!! 0. Variable and parameter declaration
446	!! 0.1 Input variables
447	INTEGER(i_std), INTENT(in) :: kjit !! Time step number (-)
448	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
449	INTEGER(i_std),INTENT (in) :: rest_id !! _Restart_ file identifier (-)
450	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: rstruct !! Structural resistance for the vegetation
451
452	!! 0.4 Local variables
453	INTEGER :: ilai
454	CHARACTER(LEN=4) :: laistring
455	CHARACTER(LEN=80) :: var_name
456
457	!_ ================================================================================================================================
458
459	!! 1. Prepare the restart file for the next simulation
460	IF (printlev>=3) WRITE (numout,*) 'Complete restart file with DIFFUCO variables '
461
462	CALL restput_p (rest_id, 'rstruct', nbp_glo, nvm, 1, kjit, rstruct, 'scatter', nbp_glo, index_g)
463
464	END SUBROUTINE diffuco_finalize
465
466
467	!! ================================================================================================================================
468	!! SUBROUTINE : diffuco_clear
469	!!
470	!>\BRIEF Housekeeping module to deallocate the variables
471	!! rstruct and raero
472	!!
473	!! DESCRIPTION : Housekeeping module to deallocate the variables
474	!! rstruct and raero
475	!!
476	!! RECENT CHANGE(S) : None
477	!!
478	!! MAIN OUTPUT VARIABLE(S) : None
479	!!
480	!! REFERENCE(S) : None
481	!!
482	!! FLOWCHART : None
483	!! \n
484	!_ ================================================================================================================================
485
486	SUBROUTINE diffuco_clear()
487
488	! Deallocate and reset variables in chemistry module
489	CALL chemistry_clear
490
491	END SUBROUTINE diffuco_clear
492
493
494	!! ================================================================================================================================
495	!! SUBROUTINE : diffuco_aero
496	!!
497	!>\BRIEF This module first calculates the surface drag
498	!! coefficient, for cases in which the surface drag coefficient is NOT provided by the coupled
499	!! atmospheric model LMDZ or when the flag ldq_cdrag_from_gcm is set to FALSE
500	!!
501	!! DESCRIPTION : Computes the surface drag coefficient, for cases
502	!! in which it is NOT provided by the coupled atmospheric model LMDZ. The module first uses the
503	!! meteorolgical input to calculate the Richardson Number, which is an indicator of atmospheric
504	!! stability in the surface layer. The formulation used to find this surface drag coefficient is
505	!! dependent on the stability determined. \n
506	!!
507	!! Designation of wind speed
508	!! \latexonly
509	!! \input{diffucoaero1.tex}
510	!! \endlatexonly
511	!!
512	!! Calculation of geopotential. This is the definition of Geopotential height (e.g. Jacobson
513	!! eqn.4.47, 2005). (required for calculation of the Richardson Number)
514	!! \latexonly
515	!! \input{diffucoaero2.tex}
516	!! \endlatexonly
517	!!
518	!! \latexonly
519	!! \input{diffucoaero3.tex}
520	!! \endlatexonly
521	!!
522	!! Calculation of the virtual air temperature at the surface (required for calculation
523	!! of the Richardson Number)
524	!! \latexonly
525	!! \input{diffucoaero4.tex}
526	!! \endlatexonly
527	!!
528	!! Calculation of the virtual surface temperature (required for calculation of th
529	!! Richardson Number)
530	!! \latexonly
531	!! \input{diffucoaero5.tex}
532	!! \endlatexonly
533	!!
534	!! Calculation of the squared wind shear (required for calculation of the Richardson
535	!! Number)
536	!! \latexonly
537	!! \input{diffucoaero6.tex}
538	!! \endlatexonly
539	!!
540	!! Calculation of the Richardson Number. The Richardson Number is defined as the ratio
541	!! of potential to kinetic energy, or, in the context of atmospheric science, of the
542	!! generation of energy by wind shear against consumption
543	!! by static stability and is an indicator of flow stability (i.e. for when laminar flow
544	!! becomes turbulent and vise versa). It is approximated using the expression below:
545	!! \latexonly
546	!! \input{diffucoaero7.tex}
547	!! \endlatexonly
548	!!
549	!! The Richardson Number hence calculated is subject to a minimum value:
550	!! \latexonly
551	!! \input{diffucoaero8.tex}
552	!! \endlatexonly
553	!!
554	!! Computing the drag coefficient. We add the add the height of the vegetation to the
555	!! level height to take into account that the level 'seen' by the vegetation is actually
556	!! the top of the vegetation. Then we we can subtract the displacement height.
557	!! \latexonly
558	!! \input{diffucoaero9.tex}
559	!! \endlatexonly
560	!!
561	!! For the stable case (i.e $R_i$ $\geq$ 0)
562	!! \latexonly
563	!! \input{diffucoaero10.tex}
564	!! \endlatexonly
565	!!
566	!! \latexonly
567	!! \input{diffucoaero11.tex}
568	!! \endlatexonly
569	!!
570	!! For the unstable case (i.e. $R_i$ < 0)
571	!! \latexonly
572	!! \input{diffucoaero12.tex}
573	!! \endlatexonly
574	!!
575	!! \latexonly
576	!! \input{diffucoaero13.tex}
577	!! \endlatexonly
578	!!
579	!! If the Drag Coefficient becomes too small than the surface may uncouple from the atmosphere.
580	!! To prevent this, a minimum limit to the drag coefficient is defined as:
581	!!
582	!! \latexonly
583	!! \input{diffucoaero14.tex}
584	!! \endlatexonly
585	!!
586	!! RECENT CHANGE(S): None
587	!!
588	!! MAIN OUTPUT VARIABLE(S): q_cdrag
589	!!
590	!! REFERENCE(S) :
591	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
592	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
593	!! Circulation Model. Journal of Climate, 6, pp.248-273
594	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influences de l'irrigation
595	!! sur le cycle de l'eau, PhD Thesis, available from:
596	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
597	!! - Jacobson M.Z., Fundamentals of Atmospheric Modeling (2nd Edition), published Cambridge
598	!! University Press, ISBN 0-521-54865-9
599	!!
600	!! FLOWCHART :
601	!! \latexonly
602	!! \includegraphics[scale=0.5]{diffuco_aero_flowchart.png}
603	!! \endlatexonly
604	!! \n
605	!_ ================================================================================================================================
606
607	SUBROUTINE diffuco_aero (kjpindex, kjit, u, v, zlev, z0h, z0m, roughheight, temp_sol, temp_air, &
608	qsurf, qair, snow, q_cdrag)
609
610	!! 0. Variable and parameter declaration
611
612	!! 0.1 Input variables
613
614	INTEGER(i_std), INTENT(in) :: kjpindex, kjit !! Domain size
615	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind speed (m s^{-1})
616	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Northward Lowest level wind speed (m s^{-1})
617	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: zlev !! Height of first atmospheric layer (m)
618	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: z0h !! Surface roughness Length for heat (m)
619	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: z0m !! Surface roughness Length for momentum (m)
620	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: roughheight !! Effective roughness height (m)
621	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_sol !! Ground temperature (K)
622	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_air !! Lowest level temperature (K)
623	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsurf !! near surface specific air humidity (kg kg^{-1})
624	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level specific air humidity (kg kg^{-1})
625	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: snow !! Snow mass (kg)
626
627	!! 0.2 Output variables
628
629	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: q_cdrag !! Surface drag coefficient (-)
630
631	!! 0.3 Modified variables
632
633	!! 0.4 Local variables
634
635	INTEGER(i_std) :: ji, jv
636	REAL(r_std) :: speed, zg, zdphi, ztvd, ztvs, zdu2
637	REAL(r_std) :: zri, cd_neut, zscf, cd_tmp
638	!_ ================================================================================================================================
639
640	!! 1. Initialisation
641
642	! test if we have to work with q_cdrag or to calcul it
643	DO ji=1,kjpindex
644
645	!! 1a).1 Designation of wind speed
646	!! \latexonly
647	!! \input{diffucoaero1.tex}
648	!! \endlatexonly
649	speed = wind(ji)
650
651	!! 1a).2 Calculation of geopotentiel
652	!! This is the definition of Geopotential height (e.g. Jacobson eqn.4.47, 2005). (required
653	!! for calculation of the Richardson Number)
654	!! \latexonly
655	!! \input{diffucoaero2.tex}
656	!! \endlatexonly
657	zg = zlev(ji) * cte_grav
658
659	!! \latexonly
660	!! \input{diffucoaero3.tex}
661	!! \endlatexonly
662	zdphi = zg/cp_air
663
664	!! 1a).3 Calculation of the virtual air temperature at the surface
665	!! required for calculation of the Richardson Number
666	!! \latexonly
667	!! \input{diffucoaero4.tex}
668	!! \endlatexonly
669	ztvd = (temp_air(ji) + zdphi / (un + rvtmp2 * qair(ji))) * (un + retv * qair(ji))
670
671	!! 1a).4 Calculation of the virtual surface temperature
672	!! required for calculation of the Richardson Number
673	!! \latexonly
674	!! \input{diffucoaero5.tex}
675	!! \endlatexonly
676	ztvs = temp_sol(ji) * (un + retv * qsurf(ji))
677
678	!! 1a).5 Calculation of the squared wind shear
679	!! required for calculation of the Richardson Number
680	!! \latexonly
681	!! \input{diffucoaero6.tex}
682	!! \endlatexonly
683	zdu2 = MAX(cepdu2,speed**2)
684
685	!! 1a).6 Calculation of the Richardson Number
686	!! The Richardson Number is defined as the ratio of potential to kinetic energy, or, in the
687	!! context of atmospheric science, of the generation of energy by wind shear against consumption
688	!! by static stability and is an indicator of flow stability (i.e. for when laminar flow
689	!! becomes turbulent and vise versa).\n
690	!! It is approximated using the expression below:
691	!! \latexonly
692	!! \input{diffucoaero7.tex}
693	!! \endlatexonly
694	zri = zg * (ztvd - ztvs) / (zdu2 * ztvd)
695
696	!! The Richardson Number hence calculated is subject to a minimum value:
697	!! \latexonly
698	!! \input{diffucoaero8.tex}
699	!! \endlatexonly
700	zri = MAX(MIN(zri,5.),-5.)
701
702	!! 1a).7 Computing the drag coefficient
703	!! We add the add the height of the vegetation to the level height to take into account
704	!! that the level 'seen' by the vegetation is actually the top of the vegetation. Then we
705	!! we can subtract the displacement height.
706	!! \latexonly
707	!! \input{diffucoaero9.tex}
708	!! \endlatexonly
709
710	!! 7.0 Snow smoothering
711	!! Snow induces low levels of turbulence.
712	!! Sensible heat fluxes can therefore be reduced of ~1/3. Pomeroy et al., 1998
713	cd_neut = ct_karman ** 2. / ( LOG( (zlev(ji) + roughheight(ji)) / z0m(ji) ) * LOG( (zlev(ji) + roughheight(ji)) / z0h(ji) ) )
714
715	!! 1a).7.1 - for the stable case (i.e $R_i$ $\geq$ 0)
716	IF (zri .GE. zero) THEN
717
718	!! \latexonly
719	!! \input{diffucoaero10.tex}
720	!! \endlatexonly
721	zscf = SQRT(un + cd * ABS(zri))
722
723	!! \latexonly
724	!! \input{diffucoaero11.tex}
725	!! \endlatexonly
726	cd_tmp=cd_neut/(un + trois * cb * zri * zscf)
727	ELSE
728
729	!! 1a).7.2 - for the unstable case (i.e. $R_i$ < 0)
730	!! \latexonly
731	!! \input{diffucoaero12.tex}
732	!! \endlatexonly
733	zscf = un / (un + trois * cb * cc * cd_neut * SQRT(ABS(zri) * &
734	& ((zlev(ji) + roughheight(ji)) / z0m(ji))))
735
736	!! \latexonly
737	!! \input{diffucoaero13.tex}
738	!! \endlatexonly
739	cd_tmp=cd_neut * (un - trois * cb * zri * zscf)
740	ENDIF
741
742	!! If the Drag Coefficient becomes too small than the surface may uncouple from the atmosphere.
743	!! To prevent this, a minimum limit to the drag coefficient is defined as:
744
745	!! \latexonly
746	!! \input{diffucoaero14.tex}
747	!! \endlatexonly
748	!!
749	q_cdrag(ji) = MAX(cd_tmp, min_qc/MAX(speed,min_wind))
750
751	! In some situations it might be useful to give an upper limit on the cdrag as well.
752	! The line here should then be uncommented.
753	!q_cdrag(ji) = MIN(q_cdrag(ji), 0.5/MAX(speed,min_wind))
754
755	END DO
756
757	IF (printlev>=3) WRITE (numout,*) ' not ldqcdrag_from_gcm : diffuco_aero done '
758
759	END SUBROUTINE diffuco_aero
760
761
762	!! ================================================================================================================================
763	!! SUBROUTINE : diffuco_snow
764	!!
765	!>\BRIEF This subroutine computes the beta coefficient for snow sublimation.
766	!!
767	!! DESCRIPTION : This routine computes beta coefficient for snow sublimation, which
768	!! integrates the snow on both vegetation and other surface types (e.g. ice, lakes,
769	!! cities etc.) \n
770	!!
771	!! A critical depth of snow (snowcri) is defined to calculate the fraction of each grid-cell
772	!! that is covered with snow (snow/snowcri) while the remaining part is snow-free.
773	!! We also carry out a first calculation of sublimation (subtest) to lower down the beta
774	!! coefficient if necessary (if subtest > snow). This is a predictor-corrector test.
775	!!
776	!! RECENT CHANGE(S): None
777	!!
778	!! MAIN OUTPUT VARIABLE(S): ::vbeta1
779	!!
780	!! REFERENCE(S) :
781	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
782	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
783	!! Circulation Model. Journal of Climate, 6, pp. 248-273
784	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influences de l'irrigation
785	!! sur le cycle de l'eau, PhD Thesis, available from:
786	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
787	!!
788	!! FLOWCHART : None
789	!! \n
790	!_ ================================================================================================================================
791
792	SUBROUTINE diffuco_snow (kjpindex, qair, qsatt, rau, u, v,q_cdrag, &
793	& snow, frac_nobio, totfrac_nobio, snow_nobio, frac_snow_veg, frac_snow_nobio, &
794	vbeta1)
795
796	!! 0. Variable and parameter declaration
797
798	!! 0.1 Input variables
799
800	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
801	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level specific air humidity (kg kg^{-1})
802	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsatt !! Surface saturated humidity (kg kg^{-1})
803	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! Air density (kg m^{-3})
804	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind speed (m s^{-1})
805	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Northward Lowest level wind speed (m s^{-1})
806	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
807	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: snow !! Snow mass (kg m^{-2})
808	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT (in) :: frac_nobio !! Fraction of ice, lakes, cities etc. (-)
809	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT (in) :: snow_nobio !! Snow on ice, lakes, cities etc. (-)
810	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: totfrac_nobio !! Total fraction of ice, lakes, cities etc. (-)
811	REAL(r_std),DIMENSION (kjpindex), INTENT(in) :: frac_snow_veg !! Snow cover fraction on vegeted area
812	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT(in) :: frac_snow_nobio!! Snow cover fraction on non-vegeted area
813
814	!! 0.2 Output variables
815
816	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta1 !! Beta for sublimation (dimensionless ratio)
817
818	!! 0.3 Modified variables
819
820	!! 0.4 Local variables
821
822	REAL(r_std) :: subtest !! Sublimation for test (kg m^{-2})
823	REAL(r_std) :: zrapp !! Modified factor (ratio)
824	REAL(r_std) :: speed !! Wind speed (m s^{-1})
825	REAL(r_std) :: vbeta1_add !! Beta for sublimation (ratio)
826	INTEGER(i_std) :: ji, jv !! Indices (-)
827	!_ ================================================================================================================================
828
829	!! 1. Calculate beta coefficient for snow sublimation on the vegetation\n
830
831	DO ji=1,kjpindex ! Loop over # pixels - domain size
832
833	! Fraction of mesh that can sublimate snow
834	vbeta1(ji) = (un - totfrac_nobio(ji)) * frac_snow_veg(ji)
835
836	! Limitation of sublimation in case of snow amounts smaller than the atmospheric demand.
837	speed = MAX(min_wind, wind(ji))
838
839	subtest = dt_sechiba * vbeta1(ji) * speed * q_cdrag(ji) * rau(ji) * &
840	& ( qsatt(ji) - qair(ji) )
841
842	IF ( subtest .GT. min_sechiba ) THEN
843	zrapp = snow(ji) / subtest
844	IF ( zrapp .LT. un ) THEN
845	vbeta1(ji) = vbeta1(ji) * zrapp
846	ENDIF
847	ENDIF
848
849	END DO ! Loop over # pixels - domain size
850
851	!! 2. Add the beta coefficients calculated from other surfaces types (snow on ice,lakes, cities...)
852
853	DO jv = 1, nnobio ! Loop over # other surface types
854	!!$ !
855	!!$ IF ( jv .EQ. iice ) THEN
856	!!$ !
857	!!$ ! Land ice is of course a particular case
858	!!$ !
859	!!$ DO ji=1,kjpindex
860	!!$ vbeta1(ji) = vbeta1(ji) + frac_nobio(ji,jv)
861	!!$ ENDDO
862	!!$ !
863	!!$ ELSE
864	!
865	DO ji=1,kjpindex ! Loop over # pixels - domain size
866
867	vbeta1_add = frac_nobio(ji,jv) * frac_snow_nobio(ji, jv)
868
869	! Limitation of sublimation in case of snow amounts smaller than
870	! the atmospheric demand.
871	speed = MAX(min_wind, wind(ji))
872
873	!! Limitation of sublimation by the snow accumulated on the ground
874	!! A first approximation is obtained with the old values of
875	!! qair and qsol_sat: function of temp-sol and pb. (see call of qsatcalc)
876	subtest = dt_sechiba * vbeta1_add * speed * q_cdrag(ji) * rau(ji) * &
877	& ( qsatt(ji) - qair(ji) )
878
879	IF ( subtest .GT. min_sechiba ) THEN
880	zrapp = snow_nobio(ji,jv) / subtest
881	IF ( zrapp .LT. un ) THEN
882	vbeta1_add = vbeta1_add * zrapp
883	ENDIF
884	ENDIF
885
886	vbeta1(ji) = vbeta1(ji) + vbeta1_add
887
888	ENDDO ! Loop over # pixels - domain size
889
890	!!$ ENDIF
891
892	ENDDO ! Loop over # other surface types
893
894	IF (printlev>=3) WRITE (numout,*) ' diffuco_snow done '
895
896	END SUBROUTINE diffuco_snow
897
898
899	!! ================================================================================================================================
900	!! SUBROUTINE : diffuco_flood
901	!!
902	!>\BRIEF This routine computes partial beta coefficient : floodplains
903	!!
904	!! DESCRIPTION :
905	!!
906	!! RECENT CHANGE(S): None
907	!!
908	!! MAIN OUTPUT VARIABLE(S) : vbeta5
909	!!
910	!! REFERENCE(S) : None
911	!!
912	!! FLOWCHART : None
913	!! \n
914	!_ ================================================================================================================================
915
916	SUBROUTINE diffuco_flood (kjpindex, qair, qsatt, rau, u, v, q_cdrag, evapot, evapot_corr, &
917	& flood_frac, flood_res, vbeta5)
918
919	! interface description
920	! input scalar
921	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size
922	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level specific humidity
923	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsatt !! Surface saturated humidity
924	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! Density
925	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Lowest level wind speed
926	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Lowest level wind speed
927	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
928	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: flood_res !! water mass in flood reservoir
929	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: flood_frac !! fraction of floodplains
930	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: evapot !! Potential evaporation
931	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: evapot_corr!! Potential evaporation2
932	! output fields
933	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta5 !! Beta for floodplains
934
935	! local declaration
936	REAL(r_std) :: subtest, zrapp, speed
937	INTEGER(i_std) :: ji, jv
938
939	!_ ================================================================================================================================
940	!
941	! beta coefficient for sublimation for floodplains
942	!
943	DO ji=1,kjpindex
944	!
945	IF (evapot(ji) .GT. min_sechiba) THEN
946	vbeta5(ji) = flood_frac(ji) *evapot_corr(ji)/evapot(ji)
947	ELSE
948	vbeta5(ji) = flood_frac(ji)
949	ENDIF
950	!
951	! -- Limitation of evaporation in case of water amounts smaller than
952	! the atmospheric demand.
953
954	!
955	speed = MAX(min_wind, SQRT (u(ji)u(ji) + v(ji)v(ji)))
956	!
957	subtest = dt_sechiba * vbeta5(ji) * speed * q_cdrag(ji) * rau(ji) * &
958	& ( qsatt(ji) - qair(ji) )
959	!
960	IF ( subtest .GT. min_sechiba ) THEN
961	zrapp = flood_res(ji) / subtest
962	IF ( zrapp .LT. un ) THEN
963	vbeta5(ji) = vbeta5(ji) * zrapp
964	ENDIF
965	ENDIF
966	!
967	END DO
968
969	IF (printlev>=3) WRITE (numout,*) ' diffuco_flood done '
970
971	END SUBROUTINE diffuco_flood
972
973
974	!! ================================================================================================================================
975	!! SUBROUTINE : diffuco_inter
976	!!
977	!>\BRIEF This routine computes the partial beta coefficient
978	!! for the interception for each type of vegetation
979	!!
980	!! DESCRIPTION : We first calculate the dry and wet parts of each PFT (wet part = qsintveg/qsintmax).
981	!! The former is submitted to transpiration only (vbeta3 coefficient, calculated in
982	!! diffuco_trans_co2), while the latter is first submitted to interception loss
983	!! (vbeta2 coefficient) and then to transpiration once all the intercepted water has been evaporated
984	!! (vbeta23 coefficient). Interception loss is also submitted to a predictor-corrector test,
985	!! as for snow sublimation. \n
986	!!
987	!! \latexonly
988	!! \input{diffucointer1.tex}
989	!! \endlatexonly
990	!! Calculate the wet fraction of vegetation as the ration between the intercepted water and the maximum water
991	!! on the vegetation. This ratio defines the wet portion of vegetation that will be submitted to interception loss.
992	!!
993	!! \latexonly
994	!! \input{diffucointer2.tex}
995	!! \endlatexonly
996	!!
997	!! Calculation of $\beta_3$, the canopy transpiration resistance
998	!! \latexonly
999	!! \input{diffucointer3.tex}
1000	!! \endlatexonly
1001	!!
1002	!! We here determine the limitation of interception loss by the water stored on the leaf.
1003	!! A first approximation of interception loss is obtained using the old values of
1004	!! qair and qsol_sat, which are functions of temp-sol and pb. (see call of 'qsatcalc')
1005	!! \latexonly
1006	!! \input{diffucointer4.tex}
1007	!! \endlatexonly
1008	!!
1009	!! \latexonly
1010	!! \input{diffucointer5.tex}
1011	!! \endlatexonly
1012	!!
1013	!! \latexonly
1014	!! \input{diffucointer6.tex}
1015	!! \endlatexonly
1016	!!
1017	!! Once the whole water stored on foliage has evaporated, transpiration can take place on the fraction
1018	!! 'zqsvegrap'.
1019	!! \latexonly
1020	!! \input{diffucointer7.tex}
1021	!! \endlatexonly
1022	!!
1023	!! RECENT CHANGE(S): None
1024	!!
1025	!! MAIN OUTPUT VARIABLE(S): ::vbeta2, ::vbeta23
1026	!!
1027	!! REFERENCE(S) :
1028	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
1029	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
1030	!! Circulation Model. Journal of Climate, 6, pp. 248-273
1031	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influences de l'irrigation
1032	!! sur le cycle de l'eau, PhD Thesis, available from:
1033	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
1034	!! - Perrier, A, 1975. Etude physique de l'Ã©vaporation dans les conditions naturelles. Annales
1035	!! Agronomiques, 26(1-18): pp. 105-123, pp. 229-243
1036	!!
1037	!! FLOWCHART : None
1038	!! \n
1039	!_ ================================================================================================================================
1040
1041	SUBROUTINE diffuco_inter (kjpindex, qair, qsatt, rau, u, v, q_cdrag, humrel, veget, &
1042	& qsintveg, qsintmax, rstruct, vbeta2, vbeta23)
1043
1044	!! 0 Variable and parameter declaration
1045
1046	!! 0.1 Input variables
1047
1048	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
1049	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level specific air humidity (kg kg^{-1})
1050	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsatt !! Surface saturated humidity (kg kg^{-1})
1051	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! Air Density (kg m^{-3})
1052	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind speed (m s^{-1})
1053	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Northward Lowest level wind speed (m s^{-1})
1054	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
1055	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: humrel !! Soil moisture stress (within range 0 to 1)
1056	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget !! vegetation fraction for each type (fraction)
1057	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintveg !! Water on vegetation due to interception (kg m^{-2})
1058	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintmax !! Maximum water on vegetation (kg m^{-2})
1059	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: rstruct !! architectural resistance (s m^{-1})
1060
1061	!! 0.2 Output variables
1062
1063	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta2 !! Beta for interception loss (-)
1064	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta23 !! Beta for fraction of wetted foliage that will
1065	!! transpire (-)
1066
1067	!! 0.4 Local variables
1068
1069	INTEGER(i_std) :: ji, jv !! (-), (-)
1070	REAL(r_std) :: zqsvegrap, ziltest, zrapp, speed !!
1071	!_ ================================================================================================================================
1072
1073	!! 1. Initialize
1074
1075	vbeta2(:,:) = zero
1076	vbeta23(:,:) = zero
1077
1078	!! 2. The beta coefficient for interception by vegetation.
1079
1080	DO jv = 2,nvm
1081
1082	DO ji=1,kjpindex
1083
1084	IF (veget(ji,jv) .GT. min_sechiba .AND. qsintveg(ji,jv) .GT. zero ) THEN
1085
1086	zqsvegrap = zero
1087	IF (qsintmax(ji,jv) .GT. min_sechiba ) THEN
1088
1089	!! \latexonly
1090	!! \input{diffucointer1.tex}
1091	!! \endlatexonly
1092	!!
1093	!! We calculate the wet fraction of vegetation as the ration between the intercepted water and the maximum water
1094	!! on the vegetation. This ratio defines the wet portion of vegetation that will be submitted to interception loss.
1095	!!
1096	zqsvegrap = MAX(zero, qsintveg(ji,jv) / qsintmax(ji,jv))
1097	END IF
1098
1099	!! \latexonly
1100	!! \input{diffucointer2.tex}
1101	!! \endlatexonly
1102	speed = MAX(min_wind, wind(ji))
1103
1104	!! Calculation of $\beta_3$, the canopy transpiration resistance
1105	!! \latexonly
1106	!! \input{diffucointer3.tex}
1107	!! \endlatexonly
1108	vbeta2(ji,jv) = veget(ji,jv) * zqsvegrap * (un / (un + speed * q_cdrag(ji) * rstruct(ji,jv)))
1109
1110	!! We here determine the limitation of interception loss by the water stored on the leaf.
1111	!! A first approximation of interception loss is obtained using the old values of
1112	!! qair and qsol_sat, which are functions of temp-sol and pb. (see call of 'qsatcalc')
1113	!! \latexonly
1114	!! \input{diffucointer4.tex}
1115	!! \endlatexonly
1116	ziltest = dt_sechiba * vbeta2(ji,jv) * speed * q_cdrag(ji) * rau(ji) * &
1117	& ( qsatt(ji) - qair(ji) )
1118
1119	IF ( ziltest .GT. min_sechiba ) THEN
1120
1121	!! \latexonly
1122	!! \input{diffucointer5.tex}
1123	!! \endlatexonly
1124	zrapp = qsintveg(ji,jv) / ziltest
1125	IF ( zrapp .LT. un ) THEN
1126
1127	!! \latexonly
1128	!! \input{diffucointer6.tex}
1129	!! \endlatexonly
1130	!!
1131	!! Once the whole water stored on foliage has evaporated, transpiration can take place on the fraction
1132	!! 'zqsvegrap'.
1133	IF ( humrel(ji,jv) >= min_sechiba ) THEN
1134	vbeta23(ji,jv) = MAX(vbeta2(ji,jv) - vbeta2(ji,jv) * zrapp, zero)
1135	ELSE
1136	! We don't want transpiration when the soil cannot deliver it
1137	vbeta23(ji,jv) = zero
1138	ENDIF
1139
1140	!! \latexonly
1141	!! \input{diffucointer7.tex}
1142	!! \endlatexonly
1143	vbeta2(ji,jv) = vbeta2(ji,jv) * zrapp
1144	ENDIF
1145	ENDIF
1146	END IF
1147	! ! Autre formulation possible pour l'evaporation permettant une transpiration sur tout le feuillage
1148	! !commenter si formulation Nathalie sinon Tristan
1149	! speed = MAX(min_wind, wind(ji))
1150	!
1151	! vbeta23(ji,jv) = MAX(zero, veget(ji,jv) * (un / (un + speed * q_cdrag(ji) * rstruct(ji,jv))) - vbeta2(ji,jv))
1152
1153	END DO
1154
1155	END DO
1156
1157	IF (printlev>=3) WRITE (numout,*) ' diffuco_inter done '
1158
1159	END SUBROUTINE diffuco_inter
1160
1161
1162	!! ==============================================================================================================================
1163	!! SUBROUTINE : diffuco_bare
1164	!!
1165	!>\BRIEF This routine computes the partial beta coefficient corresponding to
1166	!! bare soil
1167	!!
1168	!! DESCRIPTION : Bare soil evaporation is submitted to a maximum possible flow (evap_bare_lim)
1169	!!
1170	!! Calculation of wind speed
1171	!! \latexonly
1172	!! \input{diffucobare1.tex}
1173	!! \endlatexonly
1174	!!
1175	!! The calculation of $\beta_4$
1176	!! \latexonly
1177	!! \input{diffucobare2.tex}
1178	!! \endlatexonly
1179	!!
1180	!! RECENT CHANGE(S): None
1181	!!
1182	!! MAIN OUTPUT VARIABLE(S): ::vbeta4
1183	!!
1184	!! REFERENCE(S) :
1185	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
1186	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
1187	!! Circulation Model. Journal of Climate, 6, pp.248-273
1188	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influences de l'irrigation
1189	!! sur le cycle de l'eau, PhD Thesis, available from:
1190	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
1191	!!
1192	!! FLOWCHART : None
1193	!! \n
1194	!_ ================================================================================================================================
1195
1196	SUBROUTINE diffuco_bare (kjpindex, evap_bare_lim, evap_bare_lim_ns, vbeta2, vbeta3, vbeta4)
1197
1198	!! 0. Variable and parameter declaration
1199
1200	!! 0.1 Input variables
1201	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
1202	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: vbeta2 !! Beta for Interception
1203	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: vbeta3 !! Beta for Transpiration
1204
1205	!! 0.2 Output variables
1206	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta4 !! Beta for bare soil evaporation (-)
1207
1208	!! 0.3 Modified variables
1209	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: evap_bare_lim !! limiting factor for bare soil evaporation
1210	!! when the 11-layer hydrology is used (-)
1211	REAL(r_std),DIMENSION (kjpindex,nstm), INTENT (inout) :: evap_bare_lim_ns !! limiting factor for bare soil evaporation
1212	!! when the 11-layer hydrology is used (-)
1213	!! 0.4 Local variables
1214	INTEGER(i_std) :: ji
1215
1216	!_ ================================================================================================================================
1217
1218	!! 1. Calculation of the soil resistance and the beta (beta_4) for bare soil
1219
1220	! To use the new version of hydrol_split_soil and ensure the water conservation, we must have throughout sechiba at all time:
1221	! a) evap_bare_lim(ji) = SUM(evap_bare_lim_ns(ji,:)soiltile(ji,:)vegtot(ji))
1222	! b) all the terms (vbeta4, evap_bare_lim, evap_bare_lim_ns) =0 if evap_bare_lim(ji) LE min_sechiba
1223	! This must also be kept true in diffuco_comb
1224
1225	DO ji = 1, kjpindex
1226
1227	! The limitation by 1-beta2-beta3 is due to the fact that evaporation under vegetation is possible
1228	!! \latexonly
1229	!! \input{diffucobare3.tex}
1230	!! \endlatexonly
1231
1232	IF ( (evap_bare_lim(ji) .GT. min_sechiba) .AND. &
1233	! in this case we can't have vegtot LE min_sechina, cf hydrol_soil
1234	(un - SUM(vbeta2(ji,:)+vbeta3(ji,:)) .GT. min_sechiba) ) THEN
1235	! eventually, none of the left-hand term is close to zero
1236
1237	vbeta4(ji) = MIN(evap_bare_lim(ji), un - SUM(vbeta2(ji,:)+vbeta3(ji,:)))
1238	! so that vbeta does not exceed 1
1239
1240	ELSE ! instead of having very small vbeta4, we set everything to zero
1241	vbeta4(ji) = zero
1242	evap_bare_lim(ji) = zero
1243	evap_bare_lim_ns(ji,:) = zero
1244	ENDIF
1245
1246	END DO
1247
1248	IF (printlev>=3) WRITE (numout,*) ' diffuco_bare done '
1249
1250	END SUBROUTINE diffuco_bare
1251
1252
1253	!! ==============================================================================================================================
1254	!! SUBROUTINE : diffuco_trans_co2
1255	!!
1256	!>\BRIEF This subroutine computes carbon assimilation and stomatal
1257	!! conductance, following respectively Farqhuar et al. (1980) and Ball et al. (1987).
1258	!!
1259	!! DESCRIPTION :\n
1260	!! *** General:\n
1261	!! The equations are different depending on the photosynthesis mode (C3 versus C4).\n
1262	!! Assimilation and conductance are computed over 20 levels of LAI and then
1263	!! integrated at the canopy level.\n
1264	!! This routine also computes partial beta coefficient: transpiration for each
1265	!! type of vegetation.\n
1266	!! There is a main loop on the PFTs, then inner loops on the points where
1267	!! assimilation has to be calculated.\n
1268	!! This subroutine is called at each sechiba time step by sechiba_main.\n
1269	!! *** Details:
1270	!! - Integration at the canopy level\n
1271	!! \latexonly
1272	!! \input{diffuco_trans_co2_1.1.tex}
1273	!! \endlatexonly
1274	!! - Light''s extinction \n
1275	!! The available light follows a simple Beer extinction law.
1276	!! The extinction coefficients (ext_coef) are PFT-dependant constants and are defined in constant_co2.f90.\n
1277	!! \latexonly
1278	!! \input{diffuco_trans_co2_1.2.tex}
1279	!! \endlatexonly
1280	!! - Estimation of relative humidity of air (for calculation of the stomatal conductance)\n
1281	!! \latexonly
1282	!! \input{diffuco_trans_co2_1.3.tex}
1283	!! \endlatexonly
1284	!! - Calculation of the water limitation factor\n
1285	!! \latexonly
1286	!! \input{diffuco_trans_co2_2.1.tex}
1287	!! \endlatexonly
1288	!! - Calculation of temperature dependent parameters for C4 plants\n
1289	!! \latexonly
1290	!! \input{diffuco_trans_co2_2.2.tex}
1291	!! \endlatexonly
1292	!! - Calculation of temperature dependent parameters for C3 plants\n
1293	!! \latexonly
1294	!! \input{diffuco_trans_co2_2.3.tex}
1295	!! \endlatexonly
1296	!! - Vmax scaling\n
1297	!! Vmax is scaled into the canopy due to reduction of nitrogen
1298	!! (Johnson and Thornley,1984).\n
1299	!! \latexonly
1300	!! \input{diffuco_trans_co2_2.4.1.tex}
1301	!! \endlatexonly
1302	!! - Assimilation for C4 plants (Collatz et al., 1992)\n
1303	!! \latexonly
1304	!! \input{diffuco_trans_co2_2.4.2.tex}
1305	!! \endlatexonly
1306	!! - Assimilation for C3 plants (Farqhuar et al., 1980)\n
1307	!! \latexonly
1308	!! \input{diffuco_trans_co2_2.4.3.tex}
1309	!! \endlatexonly
1310	!! - Estimation of the stomatal conductance (Ball et al., 1987)\n
1311	!! \latexonly
1312	!! \input{diffuco_trans_co2_2.4.4.tex}
1313	!! \endlatexonly
1314	!!
1315	!! RECENT CHANGE(S):
1316	!!
1317	!! 2018/11 replaced t2m and q2m by temp_air and qair; prognostic variables on first atmospheric model layer
1318	!!
1319	!! 2006/06 N. de Noblet
1320	!! - addition of q2m and t2m as input parameters for the
1321	!! calculation of Rveget
1322	!! - introduction of vbeta23
1323	!!
1324	!! MAIN OUTPUT VARIABLE(S): beta coefficients, resistances, CO2 intercellular
1325	!! concentration
1326	!!
1327	!! REFERENCE(S) :
1328	!! - Ball, J., T. Woodrow, and J. Berry (1987), A model predicting stomatal
1329	!! conductance and its contribution to the control of photosynthesis under
1330	!! different environmental conditions, Prog. Photosynthesis, 4, 221â 224.
1331	!! - Collatz, G., M. Ribas-Carbo, and J. Berry (1992), Coupled photosynthesis
1332	!! stomatal conductance model for leaves of C4 plants, Aust. J. Plant Physiol.,
1333	!! 19, 519â538.
1334	!! - Farquhar, G., S. von Caemmener, and J. Berry (1980), A biochemical model of
1335	!! photosynthesis CO2 fixation in leaves of C3 species, Planta, 149, 78â90.
1336	!! - Johnson, I. R., and J. Thornley (1984), A model of instantaneous and daily
1337	!! canopy photosynthesis, J Theor. Biol., 107, 531 545
1338	!! - McMurtrie, R.E., Rook, D.A. and Kelliher, F.M., 1990. Modelling the yield of Pinus radiata on a
1339	!! site limited by water and nitrogen. For. Ecol. Manage., 30: 381-413
1340	!! - Bounoua, L., Hall, F. G., Sellers, P. J., Kumar, A., Collatz, G. J., Tucker, C. J., and Imhoff, M. L. (2010), Quantifying the
1341	!! negative feedback of vegetation to greenhouse warming: A modeling approach, Geophysical Research Letters, 37, Artn L23701,
1342	!! Doi 10.1029/2010gl045338
1343	!! - Bounoua, L., Collatz, G. J., Sellers, P. J., Randall, D. A., Dazlich, D. A., Los, S. O., Berry, J. A., Fung, I.,
1344	!! Tucker, C. J., Field, C. B., and Jensen, T. G. (1999), Interactions between vegetation and climate: Radiative and physiological
1345	!! effects of doubled atmospheric co2, Journal of Climate, 12, 309-324, Doi 10.1175/1520-0442(1999)012<0309:Ibvacr>2.0.Co;2
1346	!! - Sellers, P. J., Bounoua, L., Collatz, G. J., Randall, D. A., Dazlich, D. A., Los, S. O., Berry, J. A., Fung, I.,
1347	!! Tucker, C. J., Field, C. B., and Jensen, T. G. (1996), Comparison of radiative and physiological effects of doubled atmospheric
1348	!! co2 on climate, Science, 271, 1402-1406, DOI 10.1126/science.271.5254.1402
1349	!! - Lewis, J. D., Ward, J. K., and Tissue, D. T. (2010), Phosphorus supply drives nonlinear responses of cottonwood
1350	!! (populus deltoides) to increases in co2 concentration from glacial to future concentrations, New Phytologist, 187, 438-448,
1351	!! DOI 10.1111/j.1469-8137.2010.03307.x
1352	!! - Kattge, J., Knorr, W., Raddatz, T., and Wirth, C. (2009), Quantifying photosynthetic capacity and its relationship to leaf
1353	!! nitrogen content for global-scale terrestrial biosphere models, Global Change Biology, 15, 976-991,
1354	!! DOI 10.1111/j.1365-2486.2008.01744.x
1355	!!
1356	!! FLOWCHART : None
1357	!! \n
1358	!_ ================================================================================================================================
1359
1360	SUBROUTINE diffuco_trans_co2 (kjpindex, swdown, pb, qsurf, qair, temp_air, temp_growth, rau, u, v, q_cdrag, humrel, &
1361	assim_param, Ca, &
1362	veget, veget_max, lai, qsintveg, qsintmax, vbeta3, vbeta3pot, rveget, rstruct, &
1363	cimean, gsmean, gpp, &
1364	co2_to_bm, vbeta23, hist_id, indexveg, indexlai, index, kjit, cim)
1365
1366	!
1367	!! 0. Variable and parameter declaration
1368	!
1369
1370	!
1371	!! 0.1 Input variables
1372	!
1373	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (unitless)
1374	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: swdown !! Downwelling short wave flux
1375	!! @tex ($W m^{-2}$) @endtex
1376	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: pb !! Lowest level pressure (hPa)
1377	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsurf !! Near surface specific humidity
1378	!! @tex ($kg kg^{-1}$) @endtex
1379	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Specific humidity at first atmospheric model layer
1380	!! @tex ($kg kg^{-1}$) @endtex
1381	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_air !! Air temperature at first atmospheric model layer (K)
1382	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_growth !! Growth temperature (Â°C) - Is equal to t2m_month
1383	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! air density @tex ($kg m^{-3}$) @endtex
1384	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Lowest level wind speed
1385	!! @tex ($m s^{-1}$) @endtex
1386	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Lowest level wind speed
1387	!! @tex ($m s^{-1}$) @endtex
1388	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
1389	REAL(r_std),DIMENSION (kjpindex,nvm,npco2), INTENT (in) :: assim_param !! min+max+opt temps (K), vcmax, vjmax for
1390	!! photosynthesis
1391	!! @tex ($\mu mol m^{-2} s^{-1}$) @endtex
1392	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: Ca !! CO2 concentration inside the canopy
1393	!! @tex ($\mu mol mol^{-1}$) @endtex
1394	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: humrel !! Soil moisture stress (0-1,unitless)
1395	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget !! Coverage fraction of vegetation for each PFT
1396	!! depending on LAI (0-1, unitless)
1397	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget_max !! Maximum vegetation fraction of each PFT inside
1398	!! the grid box (0-1, unitless)
1399	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: lai !! Leaf area index @tex ($m^2 m^{-2}$) @endtex
1400	!! @tex ($m s^{-1}$) @endtex
1401	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintveg !! Water on vegetation due to interception
1402	!! @tex ($kg m^{-2}$) @endte
1403	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintmax !! Maximum water on vegetation
1404	!! @tex ($kg m^{-2}$) @endtex
1405	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: vbeta23 !! Beta for fraction of wetted foliage that will
1406	!! transpire (unitless)
1407	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: co2_to_bm !! virtual gpp ((gC m^{-2} s^{-1}), total area)
1408	INTEGER(i_std),INTENT (in) :: hist_id !! _History_ file identifier (-)
1409	INTEGER(i_std),DIMENSION (kjpindex*nvm), INTENT (in) :: indexveg !! Indeces of the points on the 3D map (-)
1410	INTEGER(i_std),DIMENSION (kjpindex*(nlai+1)), INTENT (in) :: indexlai !! Indeces of the points on the 3D map
1411	INTEGER(i_std),DIMENSION (kjpindex), INTENT (in) :: index !! Indeces of the points on the map (-)
1412	INTEGER(i_std), INTENT(in) :: kjit !! Time step number (-)
1413	!
1414	!! 0.2 Output variables
1415	!
1416	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta3 !! Beta for Transpiration (unitless)
1417	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta3pot !! Beta for Potential Transpiration
1418	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: rveget !! stomatal resistance of vegetation
1419	!! @tex ($s m^{-1}$) @endtex
1420	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: rstruct !! structural resistance @tex ($s m^{-1}$) @endtex
1421	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: cimean !! mean intercellular CO2 concentration
1422	!! @tex ($\mu mol mol^{-1}$) @endtex
1423	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: gsmean !! mean stomatal conductance to CO2 (umol m-2 s-1)
1424	REAL(r_Std),DIMENSION (kjpindex,nvm), INTENT (out) :: gpp
1425	!! Assimilation ((gC m^{-2} s^{-1}), total area)
1426	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: cim !! Intercellular CO2 over nlai
1427	!
1428	!! 0.3 Modified variables
1429	!
1430
1431	!
1432	!! 0.4 Local variables
1433	!
1434	REAL(r_std),DIMENSION (kjpindex,nvm) :: vcmax !! maximum rate of carboxylation
1435	!! @tex ($\mu mol CO2 m^{-2} s^{-1}$) @endtex
1436	INTEGER(i_std) :: ji, jv, jl, limit_photo !! indices (unitless)
1437	REAL(r_std), DIMENSION(kjpindex,nlai+1) :: info_limitphoto
1438	REAL(r_std), DIMENSION(kjpindex,nvm,nlai) :: leaf_ci !! intercellular CO2 concentration (ppm)
1439	REAL(r_std), DIMENSION(kjpindex) :: leaf_ci_lowest !! intercellular CO2 concentration at the lowest
1440	!! LAI level
1441	!! @tex ($\mu mol mol^{-1}$) @endtex
1442	INTEGER(i_std), DIMENSION(kjpindex) :: ilai !! counter for loops on LAI levels (unitless)
1443	REAL(r_std), DIMENSION(kjpindex) :: zqsvegrap !! relative water quantity in the water
1444	!! interception reservoir (0-1,unitless)
1445	REAL(r_std) :: speed !! wind speed @tex ($m s^{-1}$) @endtex
1446	! Assimilation
1447	LOGICAL, DIMENSION(kjpindex) :: assimilate !! where assimilation is to be calculated
1448	!! (unitless)
1449	LOGICAL, DIMENSION(kjpindex) :: calculate !! where assimilation is to be calculated for
1450	!! in the PFTs loop (unitless)
1451	INTEGER(i_std) :: nic,inic,icinic !! counter/indices (unitless)
1452	INTEGER(i_std), DIMENSION(kjpindex) :: index_calc !! index (unitless)
1453	INTEGER(i_std) :: nia,inia,nina,inina,iainia !! counter/indices (unitless)
1454	INTEGER(i_std), DIMENSION(kjpindex) :: index_assi,index_non_assi !! indices (unitless)
1455	REAL(r_std), DIMENSION(kjpindex, nlai+1) :: vc2 !! rate of carboxylation (at a specific LAI level)
1456	!! @tex ($\mu mol CO2 m^{-2} s^{-1}$) @endtex
1457	REAL(r_std), DIMENSION(kjpindex, nlai+1) :: vj2 !! rate of Rubisco regeneration (at a specific LAI
1458	!! level) @tex ($\mu mol e- m^{-2} s^{-1}$) @endtex
1459	REAL(r_std), DIMENSION(kjpindex, nlai+1) :: assimi !! assimilation (at a specific LAI level)
1460	!! @tex ($\mu mol m^{-2} s^{-1}$) @endtex
1461	!! (temporary variables)
1462	REAL(r_std), DIMENSION(kjpindex) :: gstop !! stomatal conductance to H2O at topmost level
1463	!! @tex ($m s^{-1}$) @endtex
1464	REAL(r_std), DIMENSION(kjpindex,nlai+1) :: gs !! stomatal conductance to CO2
1465	!! @tex ($\mol m^{-2} s^{-1}$) @endtex
1466	REAL(r_std), DIMENSION(kjpindex,nlai) :: templeafci
1467
1468
1469	REAL(r_std), DIMENSION(kjpindex) :: gamma_star !! CO2 compensation point (ppm)
1470	!! @tex ($\mu mol mol^{-1}$) @endtex
1471
1472	REAL(r_std), DIMENSION(kjpindex) :: air_relhum !! air relative humidity at 2m
1473	!! @tex ($kg kg^{-1}$) @endtex
1474	REAL(r_std), DIMENSION(kjpindex) :: VPD !! Vapor Pressure Deficit (kPa)
1475	REAL(r_std), DIMENSION(kjpindex) :: water_lim !! water limitation factor (0-1,unitless)
1476
1477	REAL(r_std), DIMENSION(kjpindex) :: gstot !! total stomatal conductance to H2O
1478	!! Final unit is
1479	!! @tex ($m s^{-1}$) @endtex
1480	REAL(r_std), DIMENSION(kjpindex) :: assimtot !! total assimilation
1481	!! @tex ($\mu mol CO2 m^{-2} s^{-1}$) @endtex
1482	REAL(r_std), DIMENSION(kjpindex) :: Rdtot !! Total Day respiration (respiratory CO2 release other than by photorespiration) (mumol CO2 mâ2 sâ1)
1483	REAL(r_std), DIMENSION(kjpindex) :: leaf_gs_top !! leaf stomatal conductance to H2O at topmost level
1484	!! @tex ($\mol H2O m^{-2} s^{-1}$) @endtex
1485	REAL(r_std), DIMENSION(nlai+1) :: laitab !! tabulated LAI steps @tex ($m^2 m^{-2}$) @endtex
1486	REAL(r_std), DIMENSION(kjpindex) :: qsatt !! surface saturated humidity at 2m (??)
1487	!! @tex ($g g^{-1}$) @endtex
1488	REAL(r_std), DIMENSION(nvm,nlai) :: light !! fraction of light that gets through upper LAI
1489	!! levels (0-1,unitless)
1490	REAL(r_std), DIMENSION(kjpindex) :: T_Vcmax !! Temperature dependance of Vcmax (unitless)
1491	REAL(r_std), DIMENSION(kjpindex) :: S_Vcmax_acclim_temp !! Entropy term for Vcmax
1492	!! accounting for acclimation to temperature (J K-1 mol-1)
1493	REAL(r_std), DIMENSION(kjpindex) :: T_Jmax !! Temperature dependance of Jmax
1494	REAL(r_std), DIMENSION(kjpindex) :: S_Jmax_acclim_temp !! Entropy term for Jmax
1495	!! accounting for acclimation toxs temperature (J K-1 mol-1)
1496	REAL(r_std), DIMENSION(kjpindex) :: T_gm !! Temperature dependance of gmw
1497	REAL(r_std), DIMENSION(kjpindex) :: T_Rd !! Temperature dependance of Rd (unitless)
1498	REAL(r_std), DIMENSION(kjpindex) :: T_Kmc !! Temperature dependance of KmC (unitless)
1499	REAL(r_std), DIMENSION(kjpindex) :: T_KmO !! Temperature dependance of KmO (unitless)
1500	REAL(r_std), DIMENSION(kjpindex) :: T_Sco !! Temperature dependance of Sco
1501	REAL(r_std), DIMENSION(kjpindex) :: T_gamma_star !! Temperature dependance of gamma_star (unitless)
1502	REAL(r_std), DIMENSION(kjpindex) :: vc !! Maximum rate of Rubisco activity-limited carboxylation (mumol CO2 mâ2 sâ1)
1503	REAL(r_std), DIMENSION(kjpindex) :: vj !! Maximum rate of e- transport under saturated light (mumol CO2 mâ2 sâ1)
1504	REAL(r_std), DIMENSION(kjpindex) :: gm !! Mesophyll diffusion conductance (molCO2 mâ2 sâ1 barâ1)
1505	REAL(r_std), DIMENSION(kjpindex) :: g0var
1506	REAL(r_std), DIMENSION(kjpindex,nlai+1) :: Rd !! Day respiration (respiratory CO2 release other than by photorespiration) (mumol CO2 mâ2 sâ1)
1507	REAL(r_std), DIMENSION(kjpindex) :: Kmc !! MichaelisâMenten constant of Rubisco for CO2 (mubar)
1508	REAL(r_std), DIMENSION(kjpindex) :: KmO !! MichaelisâMenten constant of Rubisco for O2 (mubar)
1509	REAL(r_std), DIMENSION(kjpindex) :: Sco !! Relative CO2 /O2 specificity factor for Rubisco (bar bar-1)
1510	REAL(r_std), DIMENSION(kjpindex) :: gb_co2 !! Boundary-layer conductance (molCO2 mâ2 sâ1 barâ1)
1511	REAL(r_std), DIMENSION(kjpindex) :: gb_h2o !! Boundary-layer conductance (molH2O mâ2 sâ1 barâ1)
1512	REAL(r_std), DIMENSION(kjpindex) :: fvpd !! Factor for describing the effect of leaf-to-air vapour difference on gs (-)
1513	REAL(r_std), DIMENSION(kjpindex) :: low_gamma_star !! Half of the reciprocal of Sc/o (bar bar-1)
1514	REAL(r_std) :: N_Vcmax !! Nitrogen level dependance of Vcmacx and Jmax
1515	REAL(r_std) :: fcyc !! Fraction of electrons at PSI that follow cyclic transport around PSI (-)
1516	REAL(r_std) :: z !! A lumped parameter (see Yin et al. 2009) ( mol mol-1)
1517	REAL(r_std) :: Rm !! Day respiration in the mesophyll (umol CO2 mâ2 sâ1)
1518	REAL(r_std) :: Cs_star !! Cs -based CO2 compensation point in the absence of Rd (ubar)
1519	REAL(r_std), DIMENSION(kjpindex) :: Iabs !! Photon flux density absorbed by leaf photosynthetic pigments (umol photon mâ2 sâ1)
1520	REAL(r_std), DIMENSION(kjpindex) :: Jmax !! Maximum value of J under saturated light (umol eâ mâ2 sâ1)
1521	REAL(r_std), DIMENSION(kjpindex, nlai+1) :: JJ !! Rate of eâ transport (umol eâ mâ2 sâ1)
1522	REAL(r_std) :: J2 !! Rate of all eâ transport through PSII (umol eâ mâ2 sâ1)
1523	REAL(r_std) :: VpJ2 !! eâ transport-limited PEP carboxylation rate (umol CO2 mâ2 sâ1)
1524	REAL(r_std) :: A_1, A_3 !! Lowest First and third roots of the analytical solution for a general cubic equation (see Appendix A of Yin et al. 2009) (umol CO2 mâ2 sâ1)
1525	REAL(r_std) :: A_1_tmp, A_3_tmp !! Temporary First and third roots of the analytical solution for a general cubic equation (see Appendix A of Yin et al. 2009) (umol CO2 mâ2 sâ1)
1526	REAL(r_std) :: Obs !! Bundle-sheath oxygen partial pressure (ubar)
1527	REAL(r_std), DIMENSION(kjpindex, nlai+1) :: Cc !! Chloroplast CO2 partial pressure (ubar)
1528	REAL(r_std) :: ci_star !! Ci -based CO2 compensation point in the absence of Rd (ubar)
1529	REAL(r_std) :: a,b,c,d,m,f,j,g,h,i,l,p,q,r !! Variables used for solving the cubic equation (see Yin et al. (2009))
1530	REAL(r_std) :: QQ,UU,PSI,x1,x2,x3 !! Variables used for solving the cubic equation (see Yin et al. (2009))
1531
1532	REAL(r_std) :: cresist !! coefficient for resistances (??)
1533	REAL(r_std), DIMENSION(kjpindex) :: laisum !! when calculating cim over nlai
1534
1535	! @defgroup Photosynthesis Photosynthesis
1536	! @{
1537	! 1. Preliminary calculations\n
1538	!_ ================================================================================================================================
1539
1540	cim(:,:)=zero
1541	leaf_ci(:,:,:) = zero
1542
1543	!
1544	! 1.1 Calculate LAI steps\n
1545	! The integration at the canopy level is done over nlai fixed levels.
1546	!! \latexonly
1547	!! \input{diffuco_trans_co2_1.1.tex}
1548	!! \endlatexonly
1549	! @}
1550	! @codeinc
1551	DO jl = 1, nlai+1
1552	laitab(jl) = laimax(EXP(lai_level_depthREAL(jl-1,r_std))-1.)/(EXP(lai_level_depth*REAL(nlai,r_std))-un)
1553	ENDDO
1554	! @endcodeinc
1555
1556	! @addtogroup Photosynthesis
1557	! @{
1558	!
1559	! 1.2 Calculate light fraction for each LAI step\n
1560	! The available light follows a simple Beer extinction law.
1561	! The extinction coefficients (ext_coef) are PFT-dependant constants and are defined in constant_co2.f90.
1562	!! \latexonly
1563	!! \input{diffuco_trans_co2_1.2.tex}
1564	!! \endlatexonly
1565	! @}
1566	! @codeinc
1567	DO jl = 1, nlai
1568	DO jv = 1, nvm
1569	light(jv,jl) = exp( -ext_coeff(jv)*laitab(jl) )
1570	ENDDO
1571	ENDDO
1572	! @endcodeinc
1573	!
1574	! Photosynthesis parameters
1575	!
1576
1577	IF (downregulation_co2) THEN
1578	DO jv= 1, nvm
1579	vcmax(:,jv) = assim_param(:,jv,ivcmax)(un-downregulation_co2_coeff(jv)log(Ca(:)/downregulation_co2_baselevel))
1580	ENDDO
1581	ELSE
1582	vcmax(:,:) = assim_param(:,:,ivcmax)
1583	ENDIF
1584
1585	! DO jv = 1, nvm
1586	! vcmax(:,:) = Vcmax25(jv)
1587	! ENDDO
1588
1589	! @addtogroup Photosynthesis
1590	! @{
1591	!
1592	! 1.3 Estimate relative humidity of air (for calculation of the stomatal conductance).\n
1593	!! \latexonly
1594	!! \input{diffuco_trans_co2_1.3.tex}
1595	!! \endlatexonly
1596	! @}
1597	!
1598
1599	CALL qsatcalc (kjpindex, temp_air, pb, qsatt)
1600	air_relhum(:) = &
1601	( qair(:) * pb(:) / (Tetens_1+qair(:)* Tetens_2) ) / &
1602	( qsatt(:)pb(:) / (Tetens_1+qsatt(:)Tetens_2 ) )
1603
1604
1605	VPD(:) = ( qsatt(:)pb(:) / (Tetens_1+qsatt(:)Tetens_2 ) ) &
1606	- ( qair(:) * pb(:) / (Tetens_1+qair(:)* Tetens_2) )
1607	! VPD is needed in kPa
1608	VPD(:) = VPD(:)/10.
1609
1610	!
1611	! 2. beta coefficient for vegetation transpiration
1612	!
1613	rstruct(:,1) = rstruct_const(1)
1614	rveget(:,:) = undef_sechiba
1615	!
1616	vbeta3(:,:) = zero
1617	vbeta3pot(:,:) = zero
1618	gsmean(:,:) = zero
1619	gpp(:,:) = zero
1620	!
1621	cimean(:,1) = Ca(:)
1622	!
1623	! @addtogroup Photosynthesis
1624	! @{
1625	! 2. Loop over vegetation types\n
1626	! @}
1627	!
1628	DO jv = 2,nvm
1629	gamma_star(:)=zero
1630	Kmo(:)=zero
1631	Kmc(:)=zero
1632	gm(:)=zero
1633	g0var(:) =zero
1634
1635	Cc(:,:)=zero
1636	Vc2(:,:)=zero
1637	JJ(:,:)=zero
1638	info_limitphoto(:,:)=zero
1639	gs(:,:)=zero
1640	templeafci(:,:)=zero
1641	assimi(:,:)=zero
1642	Rd(:,:)=zero
1643
1644	!
1645	! @addtogroup Photosynthesis
1646	! @{
1647	!
1648	! 2.1 Initializations\n
1649	!! \latexonly
1650	!! \input{diffuco_trans_co2_2.1.tex}
1651	!! \endlatexonly
1652	! @}
1653	!
1654	! beta coefficient for vegetation transpiration
1655	!
1656	rstruct(:,jv) = rstruct_const(jv)
1657	cimean(:,jv) = Ca(:)
1658	!
1659	!! mask that contains points where there is photosynthesis
1660	!! For the sake of vectorisation [DISPENSABLE], computations are done only for convenient points.
1661	!! nia is the number of points where the assimilation is calculated and nina the number of points where photosynthesis is not
1662	!! calculated (based on criteria on minimum or maximum values on LAI, vegetation fraction, shortwave incoming radiation,
1663	!! temperature and relative humidity).
1664	!! For the points where assimilation is not calculated, variables are initialized to specific values.
1665	!! The assimilate(kjpindex) array contains the logical value (TRUE/FALSE) relative to this photosynthesis calculation.
1666	!! The index_assi(kjpindex) array indexes the nia points with assimilation, whereas the index_no_assi(kjpindex) array indexes
1667	!! the nina points with no assimilation.
1668	nia=0
1669	nina=0
1670	!
1671	DO ji=1,kjpindex
1672	!
1673	IF ( ( lai(ji,jv) .GT. 0.01 ) .AND. &
1674	( veget_max(ji,jv) .GT. min_sechiba ) ) THEN
1675
1676	IF ( ( veget(ji,jv) .GT. min_sechiba ) .AND. &
1677	( swdown(ji) .GT. min_sechiba ) .AND. &
1678	( humrel(ji,jv) .GT. min_sechiba) .AND. &
1679	( temp_growth(ji) .GT. tphoto_min(jv) ) .AND. &
1680	( temp_growth(ji) .LT. tphoto_max(jv) ) ) THEN
1681	!
1682	assimilate(ji) = .TRUE.
1683	nia=nia+1
1684	index_assi(nia)=ji
1685	!
1686	ELSE
1687	!
1688	assimilate(ji) = .FALSE.
1689	nina=nina+1
1690	index_non_assi(nina)=ji
1691	!
1692	ENDIF
1693	ELSE
1694	!
1695	assimilate(ji) = .FALSE.
1696	nina=nina+1
1697	index_non_assi(nina)=ji
1698	!
1699	ENDIF
1700	!
1701
1702	ENDDO
1703	!
1704
1705	gstot(:) = zero
1706	gstop(:) = zero
1707	assimtot(:) = zero
1708	Rdtot(:)=zero
1709	leaf_gs_top(:) = zero
1710	!
1711	zqsvegrap(:) = zero
1712	WHERE (qsintmax(:,jv) .GT. min_sechiba)
1713	!! relative water quantity in the water interception reservoir
1714	zqsvegrap(:) = MAX(zero, qsintveg(:,jv) / qsintmax(:,jv))
1715	ENDWHERE
1716	!
1717	!! Calculates the water limitation factor.
1718	water_lim(:) = humrel(:,jv)
1719
1720	! give a default value of ci for all pixel that do not assimilate
1721	DO jl=1,nlai
1722	DO inina=1,nina
1723	leaf_ci(index_non_assi(inina),jv,jl) = Ca(index_non_assi(inina))
1724	ENDDO
1725	ENDDO
1726	!
1727	ilai(:) = 1
1728	!
1729	! Here is the calculation of assimilation and stomatal conductance
1730	! based on the work of Farquahr, von Caemmerer and Berry (FvCB model)
1731	! as described in Yin et al. 2009
1732	! Yin et al. developed a extended version of the FvCB model for C4 plants
1733	! and proposed an analytical solution for both photosynthesis pathways (C3 and C4)
1734	! Photosynthetic parameters used are those reported in Yin et al.
1735	! Except For Vcmax25, relationships between Vcmax25 and Jmax25 for which we use
1736	! Medlyn et al. (2002) and Kattge & Knorr (2007)
1737	! Because these 2 references do not consider mesophyll conductance, we neglect this term
1738	! in the formulations developed by Yin et al.
1739	! Consequently, gm (the mesophyll conductance) tends to the infinite
1740	! This is of importance because as stated by Kattge & Knorr and Medlyn et al.,
1741	! values of Vcmax and Jmax derived with different model parametrizations are not
1742	! directly comparable and the published values of Vcmax and Jmax had to be standardized
1743	! to one consistent formulation and parametrization
1744
1745	! See eq. 6 of Yin et al. (2009)
1746	! Parametrization of Medlyn et al. (2002) - from Bernacchi et al. (2001)
1747	T_KmC(:) = Arrhenius(kjpindex,temp_air,298.,E_KmC(jv))
1748	T_KmO(:) = Arrhenius(kjpindex,temp_air,298.,E_KmO(jv))
1749	T_Sco(:) = Arrhenius(kjpindex,temp_air,298.,E_Sco(jv))
1750	T_gamma_star(:) = Arrhenius(kjpindex,temp_air,298.,E_gamma_star(jv))
1751
1752
1753	! Parametrization of Yin et al. (2009) - from Bernacchi et al. (2001)
1754	T_Rd(:) = Arrhenius(kjpindex,temp_air,298.,E_Rd(jv))
1755
1756
1757	! For C3 plants, we assume that the Entropy term for Vcmax and Jmax
1758	! acclimates to temperature as shown by Kattge & Knorr (2007) - Eq. 9 and 10
1759	! and that Jmax and Vcmax respond to temperature following a modified Arrhenius function
1760	! (with a decrease of these parameters for high temperature) as in Medlyn et al. (2002)
1761	! and Kattge & Knorr (2007).
1762	! In Yin et al. (2009), temperature dependance to Vcmax is based only on a Arrhenius function
1763	! Concerning this apparent unconsistency, have a look to the section 'Limitation of
1764	! Photosynthesis by gm' of Bernacchi (2002) that may provide an explanation
1765
1766	! Growth temperature tested by Kattge & Knorr range from 11 to 35Â°C
1767	! So, we limit the relationship between these lower and upper limits
1768	S_Jmax_acclim_temp(:) = aSJ(jv) + bSJ(jv) * MAX(11., MIN(temp_growth(:),35.))
1769	T_Jmax(:) = Arrhenius_modified(kjpindex,temp_air,298.,E_Jmax(jv),D_Jmax(jv),S_Jmax_acclim_temp)
1770
1771	S_Vcmax_acclim_temp(:) = aSV(jv) + bSV(jv) * MAX(11., MIN(temp_growth(:),35.))
1772	T_Vcmax(:) = Arrhenius_modified(kjpindex,temp_air,298.,E_Vcmax(jv),D_Vcmax(jv),S_Vcmax_acclim_temp)
1773
1774
1775
1776	vc(:) = vcmax(:,jv) * T_Vcmax(:)
1777	! As shown by Kattge & Knorr (2007), we make use
1778	! of Jmax25/Vcmax25 ratio (rJV) that acclimates to temperature for C3 plants
1779	! rJV is written as a function of the growth temperature
1780	! rJV = arJV + brJV * T_month
1781	! See eq. 10 of Kattge & Knorr (2007)
1782	! and Table 3 for Values of arJV anf brJV
1783	! Growth temperature is monthly temperature (expressed in Â°C) - See first paragraph of
1784	! section Methods/Data of Kattge & Knorr
1785	vj(:) = ( arJV(jv) + brJV(jv) * MAX(11., MIN(temp_growth(:),35.)) ) * vcmax(:,jv) * T_Jmax(:)
1786
1787	T_gm(:) = Arrhenius_modified(kjpindex,temp_air,298.,E_gm(jv),D_gm(jv),S_gm(jv))
1788	gm(:) = gm25(jv) * T_gm(:) * MAX(1-stress_gm(jv), water_lim(:))
1789
1790	g0var(:) = g0(jv)* MAX(1-stress_gs(jv), water_lim(:))
1791	! @endcodeinc
1792	!
1793	KmC(:)=KmC25(jv)*T_KmC(:)
1794	KmO(:)=KmO25(jv)*T_KmO(:)
1795	Sco(:)=Sco25(jv)*T_sco(:)
1796	gamma_star(:) = gamma_star25(jv)*T_gamma_star(:)
1797
1798
1799
1800	! low_gamma_star is defined by Yin et al. (2009)
1801	! as the half of the reciprocal of Sco - See Table 2
1802	low_gamma_star(:) = 0.5 / Sco(:)
1803
1804	! VPD expressed in kPa
1805	! Note : MIN(1.-min_sechiba,MAX(min_sechiba,(a1(jv) - b1(jv) * VPD(:)))) is always between 0-1 not including 0 and 1
1806	fvpd(:) = 1. / ( 1. / MIN(1.-min_sechiba,MAX(min_sechiba,(a1(jv) - b1(jv) * VPD(:)))) - 1. ) &
1807	* MAX(1-stress_gs(jv), water_lim(:))
1808
1809	! leaf boundary layer conductance
1810	! conversion from a conductance in (m s-1) to (mol H2O m-2 s-1)
1811	! from Pearcy et al. (1991, see below)
1812	gb_h2o(:) = gb_ref * 44.6 * (tp_00/temp_air(:)) * (pb(:)/pb_std)
1813
1814	! conversion from (mol H2O m-2 s-1) to (mol CO2 m-2 s-1)
1815	gb_co2(:) = gb_h2o(:) / ratio_H2O_to_CO2
1816
1817	!
1818	! @addtogroup Photosynthesis
1819	! @{
1820	!
1821	! 2.4 Loop over LAI discretized levels to estimate assimilation and conductance\n
1822	! @}
1823	!
1824	!! The calculate(kjpindex) array is of type logical to indicate wether we have to sum over this LAI fixed level (the LAI of
1825	!! the point for the PFT is lower or equal to the LAI level value). The number of such points is incremented in nic and the
1826	!! corresponding point is indexed in the index_calc array.
1827	JJ(:,:)=zero
1828	vc2(:,:)=zero
1829	vj2(:,:)=zero
1830	Cc(:,:)=zero
1831	gs(:,:)=zero
1832	assimi(:,:)=zero
1833	Rd(:,:)=zero
1834
1835	DO jl = 1, nlai
1836	!
1837	nic=0
1838	calculate(:) = .FALSE.
1839	!
1840	IF (nia .GT. 0) then
1841	DO inia=1,nia
1842	calculate(index_assi(inia)) = (laitab(jl) .LE. lai(index_assi(inia),jv) )
1843	IF ( calculate(index_assi(inia)) ) THEN
1844	nic=nic+1
1845	index_calc(nic)=index_assi(inia)
1846	ENDIF
1847	ENDDO
1848	ENDIF
1849	!
1850	! @addtogroup Photosynthesis
1851	! @{
1852	!
1853	! 2.4.1 Vmax is scaled into the canopy due to reduction of nitrogen
1854	!! (Johnson and Thornley,1984).\n
1855	!! \latexonly
1856	!! \input{diffuco_trans_co2_2.4.1.tex}
1857	!! \endlatexonly
1858	! @}
1859	!
1860	N_Vcmax = ( un - .7_r_std * ( un - light(jv,jl) ) )
1861	!
1862
1863	vc2(:,jl) = vc(:) * N_Vcmax * MAX(1-stress_vcmax(jv), water_lim(:))
1864	vj2(:,jl) = vj(:) * N_Vcmax * MAX(1-stress_vcmax(jv), water_lim(:))
1865
1866	! see Comment in legend of Fig. 6 of Yin et al. (2009)
1867	! Rd25 is assumed to equal 0.01 Vcmax25
1868	Rd(:,jl) = vcmax(:,jv) * N_Vcmax * 0.01 * T_Rd(:) * MAX(1-stress_vcmax(jv), water_lim(:))
1869
1870	Iabs(:)=swdown(:)W_to_molRG_to_PARext_coeff(jv)light(jv,jl)
1871
1872	! eq. 4 of Yin et al (2009)
1873	Jmax(:)=vj2(:,jl)
1874	JJ(:,jl) = ( alpha_LL(jv) * Iabs(:) + Jmax(:) - sqrt((alpha_LL(jv) * Iabs(:) + Jmax(:) )**2. &
1875	- 4 * theta(jv) * Jmax(:) * alpha_LL(jv) * Iabs(:)) ) &
1876	/ ( 2 * theta(jv))
1877
1878	!
1879	IF ( is_c4(jv) ) THEN
1880	!
1881	! @addtogroup Photosynthesis
1882	! @{
1883	!
1884	! 2.4.2 Assimilation for C4 plants (Collatz et al., 1992)\n
1885	!! \latexonly
1886	!! \input{diffuco_trans_co2_2.4.2.tex}
1887	!! \endlatexonly
1888	! @}
1889	!
1890	!
1891	!
1892	IF (nic .GT. 0) THEN
1893	DO inic=1,nic
1894
1895	! Analytical resolution of the Assimilation based Yin et al. (2009)
1896	icinic=index_calc(inic)
1897
1898	! Eq. 28 of Yin et al. (2009)
1899	fcyc= 1. - ( 4.(1.-fpsir(jv))(1.+fQ(jv)) + 3.h_protons(jv)fpseudo(jv) ) / &
1900	( 3.h_protons(jv) - 4.(1.-fpsir(jv)))
1901
1902	! See paragraph after eq. (20b) of Yin et al.
1903	Rm=Rd(icinic,jl)/2.
1904
1905	! We assume that cs_star equals ci_star (see Comment in legend of Fig. 6 of Yin et al. (2009)
1906	! Equation 26 of Yin et al. (2009)
1907	Cs_star = (gbs(jv) * low_gamma_star(icinic) * Oi - &
1908	( 1. + low_gamma_star(icinic) * alpha(jv) / 0.047) * Rd(icinic,jl) + Rm ) &
1909	/ ( gbs(jv) + kp(jv) )
1910
1911	! eq. 11 of Yin et al (2009)
1912	J2 = JJ(icinic,jl) / ( 1. - fpseudo(jv) / ( 1. - fcyc ) )
1913
1914	! Equation right after eq. (20d) of Yin et al. (2009)
1915	z = ( 2. + fQ(jv) - fcyc ) / ( h_protons(jv) * (1. - fcyc ))
1916
1917	VpJ2 = fpsir(jv) * J2 * z / 2.
1918
1919	A_3=9999.
1920
1921	! See eq. right after eq. 18 of Yin et al. (2009)
1922	DO limit_photo=1,2
1923	! Is Vc limiting the Assimilation
1924	IF ( limit_photo .EQ. 1 ) THEN
1925	a = 1. + kp(jv) / gbs(jv)
1926	b = 0.
1927	x1 = Vc2(icinic,jl)
1928	x2 = KmC(icinic)/KmO(icinic)
1929	x3 = KmC(icinic)
1930	! Is J limiting the Assimilation
1931	ELSE
1932	a = 1.
1933	b = VpJ2
1934	x1 = (1.- fpsir(jv)) * J2 * z / 3.
1935	x2 = 7. * low_gamma_star(icinic) / 3.
1936	x3 = 0.
1937	ENDIF
1938
1939	m=fvpd(icinic)-g0var(icinic)/gb_co2(icinic)
1940	d=g0var(icinic)(Ca(icinic)-Cs_star) + fvpd(icinic)Rd(icinic,jl)
1941	f=(b-Rm-low_gamma_star(icinic)Oigbs(jv))x1d + agbs(jv)x1Ca(icinic)d
1942	j=(b-Rm+gbs(jv)x3 + x2gbs(jv)Oi)m + (alpha(jv)x2/0.047-1.)d &
1943	+ agbs(jv)(Ca(icinic)*m - d/gb_co2(icinic) - (Ca(icinic) - Cs_star ))
1944
1945	g=(b-Rm-low_gamma_star(icinic)Oigbs(jv))x1m - (alpha(jv)low_gamma_star(icinic)/0.047+1.)x1*d &
1946	+ agbs(jv)x1(Ca(icinic)m - d/gb_co2(icinic) - (Ca(icinic)-Cs_star ))
1947
1948	h=-((alpha(jv)low_gamma_star(icinic)/0.047+1.)x1m + (agbs(jv)x1(m-1.))/gb_co2(icinic) )
1949	i= ( b-Rm + gbs(jv)x3 + x2gbs(jv)Oi )d + agbs(jv)Ca(icinic)*d
1950	l= ( alpha(jv)x2/0.047 - 1.)m - (agbs(jv)(m-1.))/gb_co2(icinic)
1951
1952	p = (j-(h-l*Rd(icinic,jl))) / l
1953	q = (i+j*Rd(icinic,jl)-g) / l
1954	r = -(f-i*Rd(icinic,jl)) / l
1955
1956	! See Yin et al. (2009) and Baldocchi (1994)
1957	QQ = ( (p*2._r_std) - 3._r_std q) / 9._r_std
1958	UU = ( 2._r_std* (p*3._r_std) - 9._r_std pq + 27._r_std r) /54._r_std
1959
1960	IF ( (QQ .GE. 0._r_std) .AND. (ABS(UU/(QQ**1.5_r_std) ) .LE. 1._r_std) ) THEN
1961	PSI = ACOS(UU/(QQ**1.5_r_std))
1962	A_3_tmp = -2._r_std * SQRT(QQ) * COS(( PSI + 4._r_std * PI)/3._r_std ) - p / 3._r_std
1963	IF (( A_3_tmp .LT. A_3 )) THEN
1964	A_3 = A_3_tmp
1965	info_limitphoto(icinic,jl)=2.
1966	ELSE
1967	! In case, J is not limiting the assimilation
1968	! we have to re-initialise a, b, x1, x2 and x3 values
1969	! in agreement with a Vc-limited assimilation
1970	a = 1. + kp(jv) / gbs(jv)
1971	b = 0.
1972	x1 = Vc2(icinic,jl)
1973	x2 = KmC(icinic)/KmO(icinic)
1974	x3 = KmC(icinic)
1975	info_limitphoto(icinic,jl)=1.
1976	ENDIF
1977	ENDIF
1978
1979	IF ( ( A_3 .EQ. 9999. ) .OR. ( A_3 .LT. (-Rd(icinic,jl)) ) ) THEN
1980	IF ( printlev>=4 ) THEN
1981	WRITE(numout,*) 'We have a problem in diffuco_trans_co2 for A_3'
1982	WRITE(numout,*) 'no real positive solution found for pft:',jv
1983	WRITE(numout,*) 'temp_air:',temp_air(icinic)
1984	WRITE(numout,*) 'vpd:',vpd(icinic)
1985	END IF
1986	A_3 = -Rd(icinic,jl)
1987	ENDIF
1988	assimi(icinic,jl) = A_3
1989
1990	IF ( ABS( assimi(icinic,jl) + Rd(icinic,jl) ) .LT. min_sechiba ) THEN
1991	gs(icinic,jl) = g0var(icinic)
1992	!leaf_ci keeps its initial value (Ca).
1993	ELSE
1994	! Eq. 24 of Yin et al. (2009)
1995	Obs = ( alpha(jv) * assimi(icinic,jl) ) / ( 0.047 * gbs(jv) ) + Oi
1996	! Eq. 23 of Yin et al. (2009)
1997	Cc(icinic,jl) = ( ( assimi(icinic,jl) + Rd(icinic,jl) ) * ( x2 * Obs + x3 ) + low_gamma_star(icinic) &
1998	* Obs * x1 ) &
1999	/ MAX(min_sechiba, x1 - ( assimi(icinic,jl) + Rd(icinic,jl) ))
2000	! Eq. 22 of Yin et al. (2009)
2001	leaf_ci(icinic,jv,jl) = ( Cc(icinic,jl) - ( b - assimi(icinic,jl) - Rm ) / gbs(jv) ) / a
2002	! Eq. 25 of Yin et al. (2009)
2003	! It should be Cs instead of Ca but it seems that
2004	! other equations in Appendix C make use of Ca
2005	gs(icinic,jl) = g0var(icinic) + ( assimi(icinic,jl) + Rd(icinic,jl) ) / &
2006	( Ca(icinic) - Cs_star ) * fvpd(icinic)
2007	ENDIF
2008	ENDDO
2009	ENDDO
2010	ENDIF
2011	ELSE
2012	!
2013	! @addtogroup Photosynthesis
2014	! @{
2015	!
2016	! 2.4.3 Assimilation for C3 plants (Farqhuar et al., 1980)\n
2017	!! \latexonly
2018	!! \input{diffuco_trans_co2_2.4.3.tex}
2019	!! \endlatexonly
2020	! @}
2021	!
2022	!
2023	IF (nic .GT. 0) THEN
2024	DO inic=1,nic
2025	icinic=index_calc(inic)
2026
2027	A_1=9999.
2028
2029	! See eq. right after eq. 18 of Yin et al. (2009)
2030	DO limit_photo=1,2
2031	! Is Vc limiting the Assimilation
2032	IF ( limit_photo .EQ. 1 ) THEN
2033	x1 = vc2(icinic,jl)
2034	! It should be O not Oi (comment from Vuichard)
2035	x2 = KmC(icinic) * ( 1. + 2gamma_star(icinic)Sco(icinic) / KmO(icinic) )
2036	! Is J limiting the Assimilation
2037	ELSE
2038	x1 = JJ(icinic,jl)/4.
2039	x2 = 2. * gamma_star(icinic)
2040	ENDIF
2041
2042
2043	! See Appendix B of Yin et al. (2009)
2044	a = g0var(icinic) * ( x2 + gamma_star(icinic) ) + &
2045	( g0var(icinic) / gm(icinic) + fvpd(icinic) ) * ( x1 - Rd(icinic,jl) )
2046	b = Ca(icinic) * ( x1 - Rd(icinic,jl) ) - gamma_star(icinic) * x1 - Rd(icinic,jl) * x2
2047	c = Ca(icinic) + x2 + ( 1./gm(icinic) + 1./gb_co2(icinic) ) * ( x1 - Rd(icinic,jl) )
2048	d = x2 + gamma_star(icinic) + ( x1 - Rd(icinic,jl) ) / gm(icinic)
2049	m = 1./gm(icinic) + ( g0var(icinic)/gm(icinic) + fvpd(icinic) ) * ( 1./gm(icinic) + 1./gb_co2(icinic) )
2050
2051	p = - ( d + (x1 - Rd(icinic,jl) ) / gm(icinic) + a * ( 1./gm(icinic) + 1./gb_co2(icinic) ) + &
2052	( g0var(icinic)/gm(icinic) + fvpd(icinic) ) * c ) / m
2053
2054	q = ( d * ( x1 - Rd(icinic,jl) ) + ac + ( g0var(icinic)/gm(icinic) + fvpd(icinic) ) b ) / m
2055	r = - a * b / m
2056
2057	! See Yin et al. (2009)
2058	QQ = ( (p*2._r_std) - 3._r_std q) / 9._r_std
2059	UU = ( 2._r_std* (p*3._r_std) - 9._r_std pq + 27._r_std r) /54._r_std
2060
2061	IF ( (QQ .GE. 0._r_std) .AND. (ABS(UU/(QQ**1.5_r_std) ) .LE. 1._r_std) ) THEN
2062	PSI = ACOS(UU/(QQ**1.5_r_std))
2063	A_1_tmp = -2._r_std * SQRT(QQ) * COS( PSI / 3._r_std ) - p / 3._r_std
2064	IF (( A_1_tmp .LT. A_1 )) THEN
2065	A_1 = A_1_tmp
2066	info_limitphoto(icinic,jl)=2.
2067	ELSE
2068	! In case, J is not limiting the assimilation
2069	! we have to re-initialise x1 and x2 values
2070	! in agreement with a Vc-limited assimilation
2071	x1 = vc2(icinic,jl)
2072	! It should be O not Oi (comment from Vuichard)
2073	x2 = KmC(icinic) * ( 1. + 2gamma_star(icinic)Sco(icinic) / KmO(icinic) )
2074	info_limitphoto(icinic,jl)=1.
2075	ENDIF
2076	ENDIF
2077	ENDDO
2078	IF ( (A_1 .EQ. 9999.) .OR. ( A_1 .LT. (-Rd(icinic,jl)) ) ) THEN
2079	IF ( printlev>=4 ) THEN
2080	WRITE(numout,*) 'We have a problem in diffuco_trans_co2 for A_1'
2081	WRITE(numout,*) 'no real positive solution found for pft:',jv
2082	WRITE(numout,*) 'temp_air:',temp_air(icinic)
2083	WRITE(numout,*) 'vpd:',vpd(icinic)
2084	END IF
2085	A_1 = -Rd(icinic,jl)
2086	ENDIF
2087	assimi(icinic,jl) = A_1
2088
2089	IF ( ABS( assimi(icinic,jl) + Rd(icinic,jl) ) .LT. min_sechiba ) THEN
2090	gs(icinic,jl) = g0var(icinic)
2091	ELSE
2092	! Eq. 18 of Yin et al. (2009)
2093	Cc(icinic,jl) = ( gamma_star(icinic) * x1 + ( assimi(icinic,jl) + Rd(icinic,jl) ) * x2 ) &
2094	/ MAX( min_sechiba, x1 - ( assimi(icinic,jl) + Rd(icinic,jl) ) )
2095	! Eq. 17 of Yin et al. (2009)
2096	leaf_ci(icinic,jv,jl) = Cc(icinic,jl) + assimi(icinic,jl) / gm(icinic)
2097	! See eq. right after eq. 15 of Yin et al. (2009)
2098	ci_star = gamma_star(icinic) - Rd(icinic,jl) / gm(icinic)
2099	!
2100	! Eq. 15 of Yin et al. (2009)
2101	gs(icinic,jl) = g0var(icinic) + ( assimi(icinic,jl) + Rd(icinic,jl) ) / ( leaf_ci(icinic,jv,jl) &
2102	- ci_star ) * fvpd(icinic)
2103	ENDIF
2104	ENDDO
2105	ENDIF
2106	ENDIF
2107	!
2108	IF (nic .GT. 0) THEN
2109	!
2110	DO inic=1,nic
2111	!
2112	! @addtogroup Photosynthesis
2113	! @{
2114	!
2115	!! 2.4.4 Estimatation of the stomatal conductance (Ball et al., 1987).\n
2116	!! \latexonly
2117	!! \input{diffuco_trans_co2_2.4.4.tex}
2118	!! \endlatexonly
2119	! @}
2120	!
2121	icinic=index_calc(inic)
2122	!
2123	! keep stomatal conductance of topmost level
2124	!
2125	IF ( jl .EQ. 1 ) THEN
2126	leaf_gs_top(icinic) = gs(icinic,jl)
2127	!
2128	ENDIF
2129	!
2130	! @addtogroup Photosynthesis
2131	! @{
2132	!
2133	!! 2.4.5 Integration at the canopy level\n
2134	!! \latexonly
2135	!! \input{diffuco_trans_co2_2.4.5.tex}
2136	!! \endlatexonly
2137	! @}
2138	! total assimilation and conductance
2139	assimtot(icinic) = assimtot(icinic) + &
2140	assimi(icinic,jl) * (laitab(jl+1)-laitab(jl))
2141	Rdtot(icinic) = Rdtot(icinic) + &
2142	Rd(icinic,jl) * (laitab(jl+1)-laitab(jl))
2143	gstot(icinic) = gstot(icinic) + &
2144	gs(icinic,jl) * (laitab(jl+1)-laitab(jl))
2145	!
2146	ilai(icinic) = jl
2147	!
2148	ENDDO
2149	!
2150	ENDIF
2151	ENDDO ! loop over LAI steps
2152
2153	IF(jv==testpft) THEN
2154	templeafci(:,:)=leaf_ci(:,testpft,:)
2155	CALL histwrite_p(hist_id, 'Cc', kjit, Cc, kjpindex*(nlai+1), indexlai)
2156	CALL histwrite_p(hist_id, 'Vc', kjit, Vc2, kjpindex*(nlai+1), indexlai)
2157	CALL histwrite_p(hist_id, 'Vj', kjit, JJ, kjpindex*(nlai+1), indexlai)
2158	CALL histwrite_p(hist_id, 'limitphoto', kjit, info_limitphoto, kjpindex*(nlai+1), indexlai)
2159	CALL histwrite_p(hist_id, 'gammastar', kjit, gamma_star, kjpindex,index)
2160	CALL histwrite_p(hist_id, 'Kmo', kjit, Kmo, kjpindex,index)
2161	CALL histwrite_p(hist_id, 'Kmc', kjit, Kmc, kjpindex,index)
2162	CALL histwrite_p(hist_id, 'gm', kjit, gm, kjpindex, index)
2163	CALL histwrite_p(hist_id, 'gs', kjit, gs, kjpindex*(nlai+1), indexlai)
2164	CALL histwrite_p(hist_id, 'leafci', kjit, templeafci, kjpindex*(nlai), indexlai)
2165	CALL histwrite_p(hist_id, 'assimi', kjit, assimi, kjpindex*(nlai+1), indexlai)
2166	CALL histwrite_p(hist_id, 'Rd', kjit, Rd, kjpindex*(nlai+1), indexlai)
2167	ENDIF
2168	!! Calculated intercellular CO2 over nlai needed for the chemistry module
2169	cim(:,jv)=0.
2170	laisum(:)=0
2171	DO jl=1,nlai
2172	WHERE (laitab(jl) .LE. lai(:,jv) )
2173	cim(:,jv)= cim(:,jv)+leaf_ci(:,jv,jl)*(laitab(jl+1)-laitab(jl))
2174	laisum(:)=laisum(:)+ (laitab(jl+1)-laitab(jl))
2175	ENDWHERE
2176	ENDDO
2177	WHERE (laisum(:)>0)
2178	cim(:,jv)= cim(:,jv)/laisum(:)
2179	ENDWHERE
2180
2181
2182	!
2183	!! 2.5 Calculate resistances
2184	!
2185	IF (nia .GT. 0) THEN
2186	!
2187	DO inia=1,nia
2188	!
2189	iainia=index_assi(inia)
2190
2191	!! Mean stomatal conductance for CO2 (mol m-2 s-1)
2192	gsmean(iainia,jv) = gstot(iainia)
2193	!
2194	! cimean is the "mean ci" calculated in such a way that assimilation
2195	! calculated in enerbil is equivalent to assimtot
2196	!
2197	IF ( ABS(gsmean(iainia,jv)-g0var(iainia)*laisum(iainia)) .GT. min_sechiba) THEN
2198	cimean(iainia,jv) = (fvpd(iainia)*(assimtot(iainia)+Rdtot(iainia))) /&
2199	(gsmean(iainia,jv)-g0var(iainia)*laisum(iainia)) + gamma_star(iainia)
2200	ELSE
2201	cimean(iainia,jv) = gamma_star(iainia)
2202	ENDIF
2203
2204	! conversion from umol m-2 (PFT) s-1 to gC m-2 (mesh area) tstep-1
2205	gpp(iainia,jv) = assimtot(iainia)12e-6veget_max(iainia,jv)*dt_sechiba
2206
2207	!
2208	! conversion from mol/m^2/s to m/s
2209	!
2210	! As in Pearcy, Schulze and Zimmermann
2211	! Measurement of transpiration and leaf conductance
2212	! Chapter 8 of Plant Physiological Ecology
2213	! Field methods and instrumentation, 1991
2214	! Editors:
2215	!
2216	! Robert W. Pearcy,
2217	! James R. Ehleringer,
2218	! Harold A. Mooney,
2219	! Philip W. Rundel
2220	!
2221	! ISBN: 978-0-412-40730-7 (Print) 978-94-010-9013-1 (Online)
2222
2223	gstot(iainia) = mol_to_m_1 (temp_air(iainia)/tp_00)&
2224	(pb_std/pb(iainia))gstot(iainia)ratio_H2O_to_CO2
2225	gstop(iainia) = mol_to_m_1 * (temp_air(iainia)/tp_00)*&
2226	(pb_std/pb(iainia))leaf_gs_top(iainia)ratio_H2O_to_CO2*&
2227	laitab(ilai(iainia)+1)
2228	!
2229	rveget(iainia,jv) = un/gstop(iainia)
2230
2231	!
2232	!
2233	! rstruct is the difference between rtot (=1./gstot) and rveget
2234	!
2235	! Correction Nathalie - le 27 Mars 2006 - Interdire a rstruct d'etre negatif
2236	!rstruct(iainia,jv) = un/gstot(iainia) - &
2237	! rveget(iainia,jv)
2238	rstruct(iainia,jv) = MAX( un/gstot(iainia) - &
2239	rveget(iainia,jv), min_sechiba)
2240	!
2241	!
2242	!! wind is a global variable of the diffuco module.
2243	speed = MAX(min_wind, wind(iainia))
2244	!
2245	! beta for transpiration
2246	!
2247	! Corrections Nathalie - 28 March 2006 - on advices of Fred Hourdin
2248	!! Introduction of a potentiometer rveg_pft to settle the rveg+rstruct sum problem in the coupled mode.
2249	!! rveg_pft=1 in the offline mode. rveg_pft is a global variable declared in the diffuco module.
2250	!vbeta3(iainia,jv) = veget_max(iainia,jv) * &
2251	! (un - zqsvegrap(iainia)) * &
2252	! (un / (un + speed * q_cdrag(iainia) * (rveget(iainia,jv) + &
2253	! rstruct(iainia,jv))))
2254	!! Global resistance of the canopy to evaporation
2255	cresist=(un / (un + speed * q_cdrag(iainia) * &
2256	veget(iainia,jv)/veget_max(iainia,jv) * &
2257	(rveg_pft(jv)*(rveget(iainia,jv) + rstruct(iainia,jv)))))
2258
2259	IF ( humrel(iainia,jv) >= min_sechiba ) THEN
2260	vbeta3(iainia,jv) = veget(iainia,jv) * &
2261	(un - zqsvegrap(iainia)) * cresist + &
2262	MIN( vbeta23(iainia,jv), veget(iainia,jv) * &
2263	zqsvegrap(iainia) * cresist )
2264	ELSE
2265	! Because of a minimum conductance g0, vbeta3 cannot be zero even if humrel=0
2266	! in the above equation.
2267	! Here, we force transpiration to be zero when the soil cannot deliver it
2268	vbeta3(iainia,jv) = zero
2269	END IF
2270
2271	! vbeta3pot for computation of potential transpiration (needed for irrigation)
2272	vbeta3pot(iainia,jv) = MAX(zero, veget(iainia,jv) * cresist)
2273	!
2274	!
2275	ENDDO
2276	!
2277	ENDIF
2278	!
2279	END DO ! loop over vegetation types
2280	!
2281
2282	! Add virtual gpp (co2_to_bm) to the gpp.
2283	! Virtual gpp can be created when introducing new pft or for correction of carbon fluxes
2284	! for instance for adjustment of Ra at end of the day.
2285	gpp(:,:) = gpp(:,:) + co2_to_bm(:,:)
2286
2287	IF (printlev>=3) WRITE (numout,*) ' diffuco_trans_co2 done '
2288
2289
2290	END SUBROUTINE diffuco_trans_co2
2291
2292
2293	!! ================================================================================================================================
2294	!! SUBROUTINE : diffuco_comb
2295	!!
2296	!>\BRIEF This routine combines the previous partial beta
2297	!! coefficients and calculates the total alpha and complete beta coefficients.
2298	!!
2299	!! DESCRIPTION : Those integrated coefficients are used to calculate (in enerbil.f90) the total evapotranspiration
2300	!! from the grid-cell. \n
2301	!!
2302	!! In the case that air is more humid than surface, dew deposition can occur (negative latent heat flux).
2303	!! In this instance, for temperature above zero, all of the beta coefficients are set to 0, except for
2304	!! interception (vbeta2) and bare soil (vbeta4 with zero soil resistance). The amount of water that is
2305	!! intercepted by leaves is calculated based on the value of LAI of the surface. In the case of freezing
2306	!! temperatures, water is added to the snow reservoir, and so vbeta4 and vbeta2 are set to 0, and the
2307	!! total vbeta is set to 1.\n
2308	!!
2309	!! \latexonly
2310	!! \input{diffucocomb1.tex}
2311	!! \endlatexonly
2312	!!
2313	!! The beta and alpha coefficients are initially set to 1.
2314	!! \latexonly
2315	!! \input{diffucocomb2.tex}
2316	!! \endlatexonly
2317	!!
2318	!! If snow is lower than the critical value:
2319	!! \latexonly
2320	!! \input{diffucocomb3.tex}
2321	!! \endlatexonly
2322	!! If in the presence of dew:
2323	!! \latexonly
2324	!! \input{diffucocomb4.tex}
2325	!! \endlatexonly
2326	!!
2327	!! Determine where the water goes (soil, vegetation, or snow)
2328	!! when air moisture exceeds saturation.
2329	!! \latexonly
2330	!! \input{diffucocomb5.tex}
2331	!! \endlatexonly
2332	!!
2333	!! If it is not freezing dew is put into the interception reservoir and onto the bare soil. If it is freezing,
2334	!! water is put into the snow reservoir.
2335	!! Now modify vbetas where necessary: for soil and snow
2336	!! \latexonly
2337	!! \input{diffucocomb6.tex}
2338	!! \endlatexonly
2339	!!
2340	!! and for vegetation
2341	!! \latexonly
2342	!! \input{diffucocomb7.tex}
2343	!! \endlatexonly
2344	!!
2345	!! Then compute part of dew that can be intercepted by leafs.
2346	!!
2347	!! There will be no transpiration when air moisture is too high, under any circumstance
2348	!! \latexonly
2349	!! \input{diffucocomb8.tex}
2350	!! \endlatexonly
2351	!!
2352	!! There will also be no interception loss on bare soil, under any circumstance.
2353	!! \latexonly
2354	!! \input{diffucocomb9.tex}
2355	!! \endlatexonly
2356	!!
2357	!! The flowchart details the 'decision tree' which underlies the module.
2358	!!
2359	!! RECENT CHANGE(S): None
2360	!!
2361	!! MAIN OUTPUT VARIABLE(S): vbeta1, vbeta4, humrel, vbeta2, vbeta3, vbeta
2362	!!
2363	!! REFERENCE(S) :
2364	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
2365	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
2366	!! Circulation Model. Journal of Climate, 6, pp.248-273
2367	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influences de l'irrigation
2368	!! sur le cycle de l'eau, PhD Thesis, available from:
2369	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
2370	!!
2371	!! FLOWCHART :
2372	!! \latexonly
2373	!! \includegraphics[scale=0.25]{diffuco_comb_flowchart.png}
2374	!! \endlatexonly
2375	!! \n
2376	!_ ================================================================================================================================
2377
2378	SUBROUTINE diffuco_comb (kjpindex, humrel, rau, u, v, q_cdrag, pb, qair, temp_sol, temp_air, &
2379	& snow, veget, lai, tot_bare_soil, vbeta1, vbeta2, vbeta3 , vbeta4, &
2380	& evap_bare_lim, evap_bare_lim_ns, veget_max, vbeta, qsintmax)
2381
2382	! Ajout qsintmax dans les arguments de la routine Nathalie / le 13-03-2006
2383
2384	!! 0. Variable and parameter declaration
2385
2386	!! 0.1 Input variables
2387
2388	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
2389	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! Air Density (kg m^{-3})
2390	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind speed (m s^{-1})
2391	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Nortward Lowest level wind speed (m s^{-1})
2392	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
2393	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: pb !! Lowest level pressure (hPa)
2394	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level specific air humidity (kg kg^{-1})
2395	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_sol !! Skin temperature (K)
2396	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_air !! Lower air temperature (K)
2397	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: snow !! Snow mass (kg)
2398	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget !! Fraction of vegetation type (fraction)
2399	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: lai !! Leaf area index (m^2 m^{-2})
2400	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintmax !! Maximum water on vegetation (kg m^{-2})
2401	REAL(r_std), DIMENSION (kjpindex), INTENT(in) :: tot_bare_soil!! Total evaporating bare soil fraction
2402	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget_max !! Max. fraction of vegetation type (LAI->infty)
2403
2404	!! 0.2 Output variables
2405
2406	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta !! Total beta coefficient (-)
2407
2408	!! 0.3 Modified variables
2409
2410	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: vbeta1 !! Beta for sublimation (-)
2411	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: vbeta4 !! Beta for Bare soil evaporation (-)
2412	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (inout) :: humrel !! Soil moisture stress (within range 0 to 1)
2413	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (inout) :: vbeta2 !! Beta for interception loss (-)
2414	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (inout) :: vbeta3 !! Beta for Transpiration (-)
2415	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: evap_bare_lim !! limiting factor for bare soil evaporation
2416	!! when the 11-layer hydrology is used (-)
2417	REAL(r_std),DIMENSION (kjpindex,nstm), INTENT (inout):: evap_bare_lim_ns !! limiting factor for bare soil evaporation
2418	!! when the 11-layer hydrology is used (-)
2419	!! 0.4 Local variables
2420
2421	INTEGER(i_std) :: ji, jv
2422	REAL(r_std) :: zevtest, zsoil_moist, zrapp
2423	REAL(r_std), DIMENSION(kjpindex) :: qsatt
2424	LOGICAL, DIMENSION(kjpindex) :: toveg, tosnow
2425	REAL(r_std) :: coeff_dew_veg
2426	REAL(r_std), DIMENSION(kjpindex) :: vegtot
2427	!_ ================================================================================================================================
2428
2429	!! 1 If we are in presence of dew
2430
2431	CALL qsatcalc (kjpindex, temp_sol, pb, qsatt)
2432
2433
2434	!! 1.1 Determine where the water goes
2435	!! Determine where the water goes (soil, vegetation, or snow)
2436	!! when air moisture exceeds saturation.
2437	!! \latexonly
2438	!! \input{diffucocomb5.tex}
2439	!! \endlatexonly
2440	toveg(:) = .FALSE.
2441	tosnow(:) = .FALSE.
2442	DO ji = 1, kjpindex
2443	IF ( qsatt(ji) .LT. qair(ji) ) THEN
2444	IF (temp_air(ji) .GT. tp_00) THEN
2445	!! If it is not freezing dew is put into the
2446	!! interception reservoir and onto the bare soil.
2447	toveg(ji) = .TRUE.
2448	ELSE
2449	!! If it is freezing water is put into the
2450	!! snow reservoir.
2451	tosnow(ji) = .TRUE.
2452	ENDIF
2453	ENDIF
2454	END DO
2455
2456	!! 1.2 Now modify vbetas where necessary.
2457
2458	!! 1.2.1 Soil and snow
2459	!! \latexonly
2460	!! \input{diffucocomb6.tex}
2461	!! \endlatexonly
2462
2463	! We need to keep consistency between evap_bare_lim, evap_bare_lim_ns and vbeta4 (thus vevapnu)
2464	! or we have a water conservation issue in hydrol_split_soil
2465
2466	DO ji = 1, kjpindex
2467
2468	IF ( toveg(ji) ) THEN
2469
2470	vbeta1(ji) = zero
2471	vegtot(ji) = SUM(veget_max(ji,:))
2472
2473	IF ( (tot_bare_soil(ji) .GT. min_sechiba) .AND. (vegtot(ji).GT. min_sechiba) ) THEN
2474
2475	vbeta4(ji) = tot_bare_soil(ji)
2476
2477	! We now have to redefine evap_bare_lim & evap_bare_lim_ns
2478	IF (evap_bare_lim(ji) .GT. min_sechiba) THEN
2479	evap_bare_lim_ns(ji,:) = evap_bare_lim_ns(ji,:) * vbeta4(ji) / evap_bare_lim(ji)
2480	ELSE ! we must re-invent evap_bare_lim_ns => uniform across soiltiles
2481	evap_bare_lim_ns(ji,:) = tot_bare_soil(ji)/vegtot(ji)
2482	ENDIF
2483
2484	evap_bare_lim(ji) = vbeta4(ji)
2485	! consistent with evap_bare_lim(ji) = SUM(evap_bare_lim_ns(ji,:)soiltile(ji,:)vegtot(ji))
2486	! as SUM(soiltile(ji,:)) = 1
2487
2488	ELSE
2489	vbeta4(ji) = zero
2490	evap_bare_lim_ns(ji,:) = zero
2491	evap_bare_lim(ji) = zero
2492	ENDIF
2493	ENDIF
2494
2495	IF ( tosnow(ji) ) THEN
2496	vbeta1(ji) = un
2497	vbeta4(ji) = zero
2498	evap_bare_lim_ns(ji,:) = zero
2499	evap_bare_lim(ji) = zero
2500	ENDIF
2501
2502	ENDDO
2503
2504	!! 1.2.2 Vegetation and interception loss
2505	!! \latexonly
2506	!! \input{diffucocomb7.tex}
2507	!! \endlatexonly
2508	DO jv = 1, nvm
2509
2510	DO ji = 1, kjpindex
2511
2512	IF ( toveg(ji) ) THEN
2513	IF (qsintmax(ji,jv) .GT. min_sechiba) THEN
2514
2515	! Compute part of dew that can be intercepted by leafs.
2516	IF ( lai(ji,jv) .GT. min_sechiba) THEN
2517	IF (lai(ji,jv) .GT. 1.5) THEN
2518	coeff_dew_veg= &
2519	& dew_veg_poly_coeff(6)lai(ji,jv)*5 &
2520	& - dew_veg_poly_coeff(5)lai(ji,jv)*4 &
2521	& + dew_veg_poly_coeff(4)lai(ji,jv)*3 &
2522	& - dew_veg_poly_coeff(3)lai(ji,jv)*2 &
2523	& + dew_veg_poly_coeff(2)*lai(ji,jv) &
2524	& + dew_veg_poly_coeff(1)
2525	ELSE
2526	coeff_dew_veg=un
2527	ENDIF
2528	ELSE
2529	coeff_dew_veg=zero
2530	ENDIF
2531	IF (jv .EQ. 1) THEN
2532	! This line may not work with CWRR when frac_bare is distributed among three soiltiles
2533	! Fortunately, qsintmax(ji,1)=0 (LAI=0 in PFT1) so we never pass here
2534	vbeta2(ji,jv) = coeff_dew_veg*tot_bare_soil(ji)
2535	ELSE
2536	vbeta2(ji,jv) = coeff_dew_veg*veget(ji,jv)
2537	ENDIF
2538	ELSE
2539	vbeta2(ji,jv) = zero ! if qsintmax=0, vbeta2=0
2540	ENDIF
2541	ENDIF
2542	IF ( tosnow(ji) ) vbeta2(ji,jv) = zero
2543
2544	ENDDO
2545
2546	ENDDO
2547
2548	!! 1.2.3 Vegetation and transpiration
2549	!! There will be no transpiration when air moisture is too high, under any circumstance
2550	!! \latexonly
2551	!! \input{diffucocomb8.tex}
2552	!! \endlatexonly
2553	DO jv = 1, nvm
2554	DO ji = 1, kjpindex
2555	IF ( qsatt(ji) .LT. qair(ji) ) THEN
2556	vbeta3(ji,jv) = zero
2557	humrel(ji,jv) = zero
2558	ENDIF
2559	ENDDO
2560	ENDDO
2561
2562
2563	!! 1.2.4 Overrules 1.2.2
2564	!! There will also be no interception loss on bare soil, under any circumstance.
2565	!! \latexonly
2566	!! \input{diffucocomb9.tex}
2567	!! \endlatexonly
2568	DO ji = 1, kjpindex
2569	IF ( qsatt(ji) .LT. qair(ji) ) THEN
2570	vbeta2(ji,1) = zero
2571	ENDIF
2572	ENDDO
2573
2574	!! 2 Now calculate vbeta in all cases (the equality needs to hold for enerbil to be consistent)
2575
2576	DO ji = 1, kjpindex
2577	vbeta(ji) = vbeta4(ji) + SUM(vbeta2(ji,:)) + SUM(vbeta3(ji,:))
2578
2579	IF (vbeta(ji) .LT. min_sechiba) THEN
2580	vbeta(ji) = zero
2581	vbeta4(ji) = zero
2582	vbeta2(ji,:)= zero
2583	vbeta3(ji,:)= zero
2584	evap_bare_lim_ns(ji,:) = zero
2585	evap_bare_lim(ji) = zero
2586	END IF
2587	ENDDO
2588
2589	CALL xios_orchidee_send_field("evap_bare_lim",evap_bare_lim)
2590	CALL xios_orchidee_send_field("evap_bare_lim_ns",evap_bare_lim_ns)
2591
2592	IF (printlev>=3) WRITE (numout,*) ' diffuco_comb done '
2593
2594	END SUBROUTINE diffuco_comb
2595
2596
2597	!! ================================================================================================================================
2598	!! SUBROUTINE : diffuco_raerod
2599	!!
2600	!>\BRIEF Computes the aerodynamic resistance, for cases in which the
2601	!! surface drag coefficient is provided by the coupled atmospheric model LMDZ and when the flag
2602	!! 'ldq_cdrag_from_gcm' is set to TRUE
2603	!!
2604	!! DESCRIPTION : Simply computes the aerodynamic resistance, for cases in which the
2605	!! surface drag coefficient is provided by the coupled atmospheric model LMDZ. If the surface drag coefficient
2606	!! is not provided by the LMDZ or signalled by the flag 'ldq_cdrag_from_gcm' set to FALSE, then the subroutine
2607	!! diffuco_aero is called instead of this one.
2608	!!
2609	!! Calculation of the aerodynamic resistance, for diganostic purposes. First calculate wind speed:
2610	!! \latexonly
2611	!! \input{diffucoaerod1.tex}
2612	!! \endlatexonly
2613	!!
2614	!! next calculate ::raero
2615	!! \latexonly
2616	!! \input{diffucoaerod2.tex}
2617	!! \endlatexonly
2618	!!
2619	!! RECENT CHANGE(S): None
2620	!!
2621	!! MAIN OUTPUT VARIABLE(S): ::raero
2622	!!
2623	!! REFERENCE(S) :
2624	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
2625	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
2626	!! Circulation Model. Journal of Climate, 6, pp.248-273
2627	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influence de l'irrigation
2628	!! sur le cycle de l'eau, PhD Thesis, available from:
2629	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
2630	!!
2631	!! FLOWCHART : None
2632	!! \n
2633	!_ ================================================================================================================================
2634
2635	SUBROUTINE diffuco_raerod (kjpindex, u, v, q_cdrag, raero)
2636
2637	IMPLICIT NONE
2638
2639	!! 0. Variable and parameter declaration
2640
2641	!! 0.1 Input variables
2642
2643	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
2644	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind velocity (m s^{-1})
2645	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Northward Lowest level wind velocity (m s^{-1})
2646	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
2647
2648	!! 0.2 Output variables
2649
2650	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: raero !! Aerodynamic resistance (s m^{-1})
2651
2652	!! 0.3 Modified variables
2653
2654	!! 0.4 Local variables
2655
2656	INTEGER(i_std) :: ji !! (-)
2657	REAL(r_std) :: speed !! (m s^{-1})
2658	!_ ================================================================================================================================
2659
2660	!! 1. Simple calculation of the aerodynamic resistance, for diganostic purposes.
2661
2662	DO ji=1,kjpindex
2663
2664	!! \latexonly
2665	!! \input{diffucoaerod1.tex}
2666	!! \endlatexonly
2667	speed = MAX(min_wind, wind(ji))
2668
2669	!! \latexonly
2670	!! \input{diffucoaerod2.tex}
2671	!! \endlatexonly
2672	raero(ji) = un / (q_cdrag(ji)*speed)
2673
2674	ENDDO
2675
2676	END SUBROUTINE diffuco_raerod
2677
2678
2679	FUNCTION Arrhenius (kjpindex,temp,ref_temp,energy_act) RESULT ( val_arrhenius )
2680	!! 0.1 Input variables
2681
2682	INTEGER(i_std),INTENT(in) :: kjpindex !! Domain size (-)
2683	REAL(r_std),DIMENSION(kjpindex),INTENT(in) :: temp !! Temperature (K)
2684	REAL(r_std), INTENT(in) :: ref_temp !! Temperature of reference (K)
2685	REAL(r_std),INTENT(in) :: energy_act !! Activation Energy (J mol-1)
2686
2687	!! 0.2 Result
2688
2689	REAL(r_std), DIMENSION(kjpindex) :: val_arrhenius !! Temperature dependance based on
2690	!! a Arrhenius function (-)
2691
2692	val_arrhenius(:)=EXP(((temp(:)-ref_temp)energy_act)/(ref_tempRR*(temp(:))))
2693	END FUNCTION Arrhenius
2694
2695	FUNCTION Arrhenius_modified_1d (kjpindex,temp,ref_temp,energy_act,energy_deact,entropy) RESULT ( val_arrhenius )
2696	!! 0.1 Input variables
2697
2698	INTEGER(i_std),INTENT(in) :: kjpindex !! Domain size (-)
2699	REAL(r_std),DIMENSION(kjpindex),INTENT(in) :: temp !! Temperature (K)
2700	REAL(r_std), INTENT(in) :: ref_temp !! Temperature of reference (K)
2701	REAL(r_std),INTENT(in) :: energy_act !! Activation Energy (J mol-1)
2702	REAL(r_std),INTENT(in) :: energy_deact !! Deactivation Energy (J mol-1)
2703	REAL(r_std),DIMENSION(kjpindex),INTENT(in) :: entropy !! Entropy term (J K-1 mol-1)
2704
2705	!! 0.2 Result
2706
2707	REAL(r_std), DIMENSION(kjpindex) :: val_arrhenius !! Temperature dependance based on
2708	!! a Arrhenius function (-)
2709
2710	val_arrhenius(:)=EXP(((temp(:)-ref_temp)energy_act)/(ref_tempRR*(temp(:)))) &
2711	* (1. + EXP( (ref_temp * entropy(:) - energy_deact) / (ref_temp * RR ))) &
2712	/ (1. + EXP( (temp(:) * entropy(:) - energy_deact) / ( RR*temp(:))))
2713
2714	END FUNCTION Arrhenius_modified_1d
2715
2716	FUNCTION Arrhenius_modified_0d (kjpindex,temp,ref_temp,energy_act,energy_deact,entropy) RESULT ( val_arrhenius )
2717	!! 0.1 Input variables
2718
2719	INTEGER(i_std),INTENT(in) :: kjpindex !! Domain size (-)
2720	REAL(r_std),DIMENSION(kjpindex),INTENT(in) :: temp !! Temperature (K)
2721	REAL(r_std), INTENT(in) :: ref_temp !! Temperature of reference (K)
2722	REAL(r_std),INTENT(in) :: energy_act !! Activation Energy (J mol-1)
2723	REAL(r_std),INTENT(in) :: energy_deact !! Deactivation Energy (J mol-1)
2724	REAL(r_std),INTENT(in) :: entropy !! Entropy term (J K-1 mol-1)
2725
2726	!! 0.2 Result
2727
2728	REAL(r_std), DIMENSION(kjpindex) :: val_arrhenius !! Temperature dependance based on
2729	!! a Arrhenius function (-)
2730
2731	val_arrhenius(:)=EXP(((temp(:)-ref_temp)energy_act)/(ref_tempRR*(temp(:)))) &
2732	* (1. + EXP( (ref_temp * entropy - energy_deact) / (ref_temp * RR ))) &
2733	/ (1. + EXP( (temp(:) * entropy - energy_deact) / ( RR*temp(:))))
2734
2735	END FUNCTION Arrhenius_modified_0d
2736
2737
2738	END MODULE diffuco

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