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source: branches/ORCHIDEE_3_CMIP6/ORCHIDEE/src_sechiba/diffuco.f90 @ 7599

Last change on this file since 7599 was 7245, checked in by nicolas.vuichard, 3 years ago
improve Carbon mass balance closure. See ticket #785
Property svn:keywords set to `Revision Date HeadURL Date Author Revision`
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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, &
237	& frac_nobio, snow_nobio, totfrac_nobio, &
238	& swnet, swdown, coszang, ccanopy, humrel, veget, veget_max, lai, qsintveg, qsintmax, assim_param, &
239	& vbeta , vbeta1, vbeta2, vbeta3, vbeta3pot, vbeta4, vbeta5, gsmean, rveget, rstruct, cimean, gpp, &
240	& lalo, neighbours, resolution, ptnlev1, precip_rain, frac_age, tot_bare_soil, frac_snow_veg, frac_snow_nobio, &
241	& hist_id, hist2_id)
242
243	!! 0. Variable and parameter declaration
244
245	!! 0.1 Input variables
246
247	INTEGER(i_std), INTENT(in) :: kjit !! Time step number (-)
248	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
249	INTEGER(i_std),INTENT (in) :: hist_id !! _History_ file identifier (-)
250	INTEGER(i_std),INTENT (in) :: hist2_id !! _History_ file 2 identifier (-)
251	INTEGER(i_std),DIMENSION (kjpindex), INTENT (in) :: index !! Indeces of the points on the map (-)
252	INTEGER(i_std),DIMENSION (kjpindex*(nlai+1)), INTENT (in) :: indexlai !! Indeces of the points on the 3D map
253	INTEGER(i_std),DIMENSION (kjpindex*nvm), INTENT (in) :: indexveg !! Indeces of the points on the 3D map (-)
254	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind speed (m s^{-1})
255	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Northward Lowest level wind speed (m s^{-1})
256	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: zlev !! Height of first layer (m)
257	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: z0m !! Surface roughness Length for momentum (m)
258	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: z0h !! Surface roughness Length for heat (m)
259	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: roughheight !! Effective height for roughness (m)
260	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_sol !! Skin temperature (K)
261	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_air !! Lowest level temperature (K)
262	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_growth !! Growth temperature (Â°C) - Is equal to t2m_month
263	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! Air Density (kg m^{-3})
264	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsurf !! Near surface air specific humidity (kg kg^{-1})
265	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level air specific humidity (kg kg^{-1})
266	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: snow !! Snow mass (kg)
267	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: flood_frac !! Fraction of floodplains
268	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: flood_res !! Reservoir in floodplains (estimation to avoid over-evaporation)
269	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: pb !! Surface level pressure (hPa)
270	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: evap_bare_lim !! Limit to the bare soil evaporation when the
271	!! 11-layer hydrology is used (-)
272	REAL(r_std),DIMENSION (kjpindex,nstm), INTENT (inout) :: evap_bare_lim_ns !! Limit to the bare soil evaporation when the
273	!! 11-layer hydrology is used (-)
274	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: evapot !! Soil Potential Evaporation (mm day^{-1})
275	!! NdN This variable does not seem to be used at
276	!! all in diffuco
277	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: evapot_corr !! Soil Potential Evaporation
278	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT (in) :: frac_nobio !! Fraction of ice,lakes,cities,... (-)
279	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT (in) :: snow_nobio !! Snow on ice,lakes,cities,... (kg m^{-2})
280	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: totfrac_nobio !! Total fraction of ice+lakes+cities+... (-)
281	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: swnet !! Net surface short-wave flux (W m^{-2})
282	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: swdown !! Down-welling surface short-wave flux (W m^{-2})
283	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: coszang !! Cosine of the solar zenith angle (unitless)
284	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: ccanopy !! CO2 concentration inside the canopy (ppm)
285	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget !! Fraction of vegetation type (-)
286	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget_max !! Max. fraction of vegetation type (LAI->infty)
287	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: lai !! Leaf area index (m^2 m^{-2})
288	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintveg !! Water on vegetation due to interception (kg m^{-2})
289	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintmax !! Maximum water on vegetation for interception
290	!! (kg m^{-2})
291	REAL(r_std),DIMENSION (kjpindex,nvm,npco2), INTENT (in) :: assim_param !! referenced vcmax, nue, leaf N for photosynthesis
292	REAL(r_std),DIMENSION (kjpindex,2), INTENT (in) :: lalo !! Geographical coordinates
293	INTEGER(i_std),DIMENSION (kjpindex,NbNeighb),INTENT (in):: neighbours !! Vector of neighbours for each
294	!! grid point (1=N, 2=E, 3=S, 4=W)
295	REAL(r_std),DIMENSION (kjpindex,2), INTENT(in) :: resolution !! The size in km of each grid-box in X and Y
296	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: ptnlev1 !! 1st level of soil temperature (Kelvin)
297	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: precip_rain !! Rain precipitation expressed in mm/tstep
298	REAL(r_std),DIMENSION (kjpindex,nvm,nleafages), INTENT (in) :: frac_age !! Age efficiency for isoprene emissions (from STOMATE)
299	REAL(r_std),DIMENSION (kjpindex), INTENT(in) :: tot_bare_soil !! Total evaporating bare soil fraction
300	REAL(r_std),DIMENSION (kjpindex), INTENT(in) :: frac_snow_veg !! Snow cover fraction on vegeted area
301	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT(in):: frac_snow_nobio !! Snow cover fraction on non-vegeted area
302
303	!! 0.2 Output variables
304
305	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta !! Total beta coefficient (-)
306	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta1 !! Beta for sublimation (-)
307	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta4 !! Beta for bare soil evaporation (-)
308	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta5 !! Beta for floodplains
309	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: gsmean !! Mean stomatal conductance to CO2 (mol m-2 s-1)
310	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta2 !! Beta for interception loss (-)
311	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta3 !! Beta for transpiration (-)
312	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta3pot !! Beta for potential transpiration
313	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: rveget !! Stomatal resistance for the whole canopy (s m^{-1})
314	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: rstruct !! Structural resistance for the vegetation
315	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: cimean !! Mean leaf Ci (ppm)
316	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT(out) :: gpp !! Assimilation ((gC m^{-2} dt_sechiba^{-1}), total area)
317
318	!! 0.3 Modified variables
319
320	REAL(r_std),DIMENSION (kjpindex, nvm), INTENT (inout) :: humrel !! Soil moisture stress (within range 0 to 1)
321	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: q_cdrag !! Surface drag coefficient (-)
322
323	!! 0.4 Local variables
324
325	REAL(r_std),DIMENSION (kjpindex,nvm) :: vbeta23 !! Beta for fraction of wetted foliage that will
326	!! transpire once intercepted water has evaporated (-)
327	REAL(r_std),DIMENSION (kjpindex) :: raero !! Aerodynamic resistance (s m^{-1})
328	INTEGER(i_std) :: ilai
329	CHARACTER(LEN=4) :: laistring
330	CHARACTER(LEN=80) :: var_name !! To store variables names for I/O
331	REAL(r_std),DIMENSION(kjpindex) :: qsatt !! Surface saturated humidity (kg kg^{-1})
332	REAL(r_std),DIMENSION (kjpindex,nvm) :: cim !! Intercellular CO2 over nlai
333
334	!_ ================================================================================================================================
335
336	wind(:) = SQRT (u(:)u(:) + v(:)v(:))
337
338	!! 1. Calculate the different coefficients
339
340	IF (.NOT.ldq_cdrag_from_gcm) THEN
341	! Case 1a)
342	CALL diffuco_aero (kjpindex, kjit, u, v, zlev, z0h, z0m, roughheight, temp_sol, temp_air, &
343	qsurf, qair, snow, q_cdrag)
344	ENDIF
345
346	! Case 1b)
347	CALL diffuco_raerod (kjpindex, u, v, q_cdrag, raero)
348
349	!! 2. Make an estimation of the saturated humidity at the surface
350
351	CALL qsatcalc (kjpindex, temp_sol, pb, qsatt)
352
353	!! 3. Calculate the beta coefficient for sublimation
354
355	CALL diffuco_snow (kjpindex, qair, qsatt, rau, u, v, q_cdrag, &
356	snow, frac_nobio, totfrac_nobio, snow_nobio, frac_snow_veg, frac_snow_nobio, &
357	vbeta1)
358
359
360	CALL diffuco_flood (kjpindex, qair, qsatt, rau, u, v, q_cdrag, evapot, evapot_corr, &
361	& flood_frac, flood_res, vbeta5)
362
363	!! 4. Calculate the beta coefficient for interception
364
365	CALL diffuco_inter (kjpindex, qair, qsatt, rau, u, v, q_cdrag, humrel, veget, &
366	& qsintveg, qsintmax, rstruct, vbeta2, vbeta23)
367
368
369	!! 5. Calculate the beta coefficient for transpiration
370
371	CALL diffuco_trans_co2 (kjpindex, swdown, pb, qsurf, qair, temp_air, temp_growth, rau, u, v, q_cdrag, humrel, &
372	assim_param, ccanopy, &
373	veget, veget_max, lai, qsintveg, qsintmax, vbeta3, vbeta3pot, &
374	rveget, rstruct, cimean, gsmean, gpp, &
375	vbeta23, hist_id, indexveg, indexlai, index, kjit, cim)
376
377	!
378	!biogenic emissions
379	!
380	IF ( ok_bvoc ) THEN
381	CALL chemistry_bvoc (kjpindex, swdown, coszang, temp_air, &
382	temp_sol, ptnlev1, precip_rain, humrel, veget_max, &
383	lai, frac_age, lalo, ccanopy, cim, wind, snow, &
384	veget, hist_id, hist2_id, kjit, index, &
385	indexlai, indexveg)
386	ENDIF
387	!
388	! combination of coefficient : alpha and beta coefficient
389	! beta coefficient for bare soil
390	!
391
392	CALL diffuco_bare (kjpindex, tot_bare_soil, veget_max, evap_bare_lim, evap_bare_lim_ns, vbeta2, vbeta3, vbeta4)
393
394	!! 6. Combine the alpha and beta coefficients
395
396	! Ajout qsintmax dans les arguments de la routine.... Nathalie / le 13-03-2006
397	CALL diffuco_comb (kjpindex, humrel, rau, u, v, q_cdrag, pb, qair, temp_sol, temp_air, snow, &
398	& veget, lai, tot_bare_soil, vbeta1, vbeta2, vbeta3, vbeta4, &
399	& evap_bare_lim, evap_bare_lim_ns, veget_max, vbeta, qsintmax)
400
401	CALL xios_orchidee_send_field("q_cdrag",q_cdrag)
402	CALL xios_orchidee_send_field("raero",raero)
403	CALL xios_orchidee_send_field("wind",wind)
404	CALL xios_orchidee_send_field("qsatt",qsatt)
405	CALL xios_orchidee_send_field("coszang",coszang)
406	CALL xios_orchidee_send_field('cim', cim)
407
408	IF ( .NOT. almaoutput ) THEN
409	CALL histwrite_p(hist_id, 'raero', kjit, raero, kjpindex, index)
410	CALL histwrite_p(hist_id, 'cdrag', kjit, q_cdrag, kjpindex, index)
411	CALL histwrite_p(hist_id, 'Wind', kjit, wind, kjpindex, index)
412	CALL histwrite_p(hist_id, 'qsatt', kjit, qsatt, kjpindex, index)
413	CALL histwrite_p(hist_id, 'cim', kjit, cim, kjpindex*nvm, indexveg)
414
415	IF ( hist2_id > 0 ) THEN
416	CALL histwrite_p(hist2_id, 'raero', kjit, raero, kjpindex, index)
417	CALL histwrite_p(hist2_id, 'cdrag', kjit, q_cdrag, kjpindex, index)
418	CALL histwrite_p(hist2_id, 'Wind', kjit, wind, kjpindex, index)
419	CALL histwrite_p(hist2_id, 'qsatt', kjit, qsatt, kjpindex, index)
420	ENDIF
421	ELSE
422	CALL histwrite_p(hist_id, 'cim', kjit, cim, kjpindex*nvm, indexveg)
423	ENDIF
424
425	IF (printlev>=3) WRITE (numout,*) ' diffuco_main done '
426
427	END SUBROUTINE diffuco_main
428
429	!! =============================================================================================================================
430	!! SUBROUTINE: diffuco_finalize
431	!!
432	!>\BRIEF Write to restart file
433	!!
434	!! DESCRIPTION: This subroutine writes the module variables and variables calculated in diffuco
435	!! to restart file
436	!!
437	!! RECENT CHANGE(S): None
438	!! REFERENCE(S): None
439	!! FLOWCHART: None
440	!! \n
441	!_ ==============================================================================================================================
442	SUBROUTINE diffuco_finalize (kjit, kjpindex, rest_id, rstruct )
443
444	!! 0. Variable and parameter declaration
445	!! 0.1 Input variables
446	INTEGER(i_std), INTENT(in) :: kjit !! Time step number (-)
447	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
448	INTEGER(i_std),INTENT (in) :: rest_id !! _Restart_ file identifier (-)
449	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: rstruct !! Structural resistance for the vegetation
450
451	!! 0.4 Local variables
452	INTEGER :: ilai
453	CHARACTER(LEN=4) :: laistring
454	CHARACTER(LEN=80) :: var_name
455
456	!_ ================================================================================================================================
457
458	!! 1. Prepare the restart file for the next simulation
459	IF (printlev>=3) WRITE (numout,*) 'Complete restart file with DIFFUCO variables '
460
461	CALL restput_p (rest_id, 'rstruct', nbp_glo, nvm, 1, kjit, rstruct, 'scatter', nbp_glo, index_g)
462
463	END SUBROUTINE diffuco_finalize
464
465
466	!! ================================================================================================================================
467	!! SUBROUTINE : diffuco_clear
468	!!
469	!>\BRIEF Housekeeping module to deallocate the variables
470	!! rstruct and raero
471	!!
472	!! DESCRIPTION : Housekeeping module to deallocate the variables
473	!! rstruct and raero
474	!!
475	!! RECENT CHANGE(S) : None
476	!!
477	!! MAIN OUTPUT VARIABLE(S) : None
478	!!
479	!! REFERENCE(S) : None
480	!!
481	!! FLOWCHART : None
482	!! \n
483	!_ ================================================================================================================================
484
485	SUBROUTINE diffuco_clear()
486
487	! Deallocate and reset variables in chemistry module
488	CALL chemistry_clear
489
490	END SUBROUTINE diffuco_clear
491
492
493	!! ================================================================================================================================
494	!! SUBROUTINE : diffuco_aero
495	!!
496	!>\BRIEF This module first calculates the surface drag
497	!! coefficient, for cases in which the surface drag coefficient is NOT provided by the coupled
498	!! atmospheric model LMDZ or when the flag ldq_cdrag_from_gcm is set to FALSE
499	!!
500	!! DESCRIPTION : Computes the surface drag coefficient, for cases
501	!! in which it is NOT provided by the coupled atmospheric model LMDZ. The module first uses the
502	!! meteorolgical input to calculate the Richardson Number, which is an indicator of atmospheric
503	!! stability in the surface layer. The formulation used to find this surface drag coefficient is
504	!! dependent on the stability determined. \n
505	!!
506	!! Designation of wind speed
507	!! \latexonly
508	!! \input{diffucoaero1.tex}
509	!! \endlatexonly
510	!!
511	!! Calculation of geopotential. This is the definition of Geopotential height (e.g. Jacobson
512	!! eqn.4.47, 2005). (required for calculation of the Richardson Number)
513	!! \latexonly
514	!! \input{diffucoaero2.tex}
515	!! \endlatexonly
516	!!
517	!! \latexonly
518	!! \input{diffucoaero3.tex}
519	!! \endlatexonly
520	!!
521	!! Calculation of the virtual air temperature at the surface (required for calculation
522	!! of the Richardson Number)
523	!! \latexonly
524	!! \input{diffucoaero4.tex}
525	!! \endlatexonly
526	!!
527	!! Calculation of the virtual surface temperature (required for calculation of th
528	!! Richardson Number)
529	!! \latexonly
530	!! \input{diffucoaero5.tex}
531	!! \endlatexonly
532	!!
533	!! Calculation of the squared wind shear (required for calculation of the Richardson
534	!! Number)
535	!! \latexonly
536	!! \input{diffucoaero6.tex}
537	!! \endlatexonly
538	!!
539	!! Calculation of the Richardson Number. The Richardson Number is defined as the ratio
540	!! of potential to kinetic energy, or, in the context of atmospheric science, of the
541	!! generation of energy by wind shear against consumption
542	!! by static stability and is an indicator of flow stability (i.e. for when laminar flow
543	!! becomes turbulent and vise versa). It is approximated using the expression below:
544	!! \latexonly
545	!! \input{diffucoaero7.tex}
546	!! \endlatexonly
547	!!
548	!! The Richardson Number hence calculated is subject to a minimum value:
549	!! \latexonly
550	!! \input{diffucoaero8.tex}
551	!! \endlatexonly
552	!!
553	!! Computing the drag coefficient. We add the add the height of the vegetation to the
554	!! level height to take into account that the level 'seen' by the vegetation is actually
555	!! the top of the vegetation. Then we we can subtract the displacement height.
556	!! \latexonly
557	!! \input{diffucoaero9.tex}
558	!! \endlatexonly
559	!!
560	!! For the stable case (i.e $R_i$ $\geq$ 0)
561	!! \latexonly
562	!! \input{diffucoaero10.tex}
563	!! \endlatexonly
564	!!
565	!! \latexonly
566	!! \input{diffucoaero11.tex}
567	!! \endlatexonly
568	!!
569	!! For the unstable case (i.e. $R_i$ < 0)
570	!! \latexonly
571	!! \input{diffucoaero12.tex}
572	!! \endlatexonly
573	!!
574	!! \latexonly
575	!! \input{diffucoaero13.tex}
576	!! \endlatexonly
577	!!
578	!! If the Drag Coefficient becomes too small than the surface may uncouple from the atmosphere.
579	!! To prevent this, a minimum limit to the drag coefficient is defined as:
580	!!
581	!! \latexonly
582	!! \input{diffucoaero14.tex}
583	!! \endlatexonly
584	!!
585	!! RECENT CHANGE(S): None
586	!!
587	!! MAIN OUTPUT VARIABLE(S): q_cdrag
588	!!
589	!! REFERENCE(S) :
590	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
591	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
592	!! Circulation Model. Journal of Climate, 6, pp.248-273
593	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influences de l'irrigation
594	!! sur le cycle de l'eau, PhD Thesis, available from:
595	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
596	!! - Jacobson M.Z., Fundamentals of Atmospheric Modeling (2nd Edition), published Cambridge
597	!! University Press, ISBN 0-521-54865-9
598	!!
599	!! FLOWCHART :
600	!! \latexonly
601	!! \includegraphics[scale=0.5]{diffuco_aero_flowchart.png}
602	!! \endlatexonly
603	!! \n
604	!_ ================================================================================================================================
605
606	SUBROUTINE diffuco_aero (kjpindex, kjit, u, v, zlev, z0h, z0m, roughheight, temp_sol, temp_air, &
607	qsurf, qair, snow, q_cdrag)
608
609	!! 0. Variable and parameter declaration
610
611	!! 0.1 Input variables
612
613	INTEGER(i_std), INTENT(in) :: kjpindex, kjit !! Domain size
614	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind speed (m s^{-1})
615	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Northward Lowest level wind speed (m s^{-1})
616	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: zlev !! Height of first atmospheric layer (m)
617	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: z0h !! Surface roughness Length for heat (m)
618	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: z0m !! Surface roughness Length for momentum (m)
619	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: roughheight !! Effective roughness height (m)
620	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_sol !! Ground temperature (K)
621	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_air !! Lowest level temperature (K)
622	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsurf !! near surface specific air humidity (kg kg^{-1})
623	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level specific air humidity (kg kg^{-1})
624	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: snow !! Snow mass (kg)
625
626	!! 0.2 Output variables
627
628	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: q_cdrag !! Surface drag coefficient (-)
629
630	!! 0.3 Modified variables
631
632	!! 0.4 Local variables
633
634	INTEGER(i_std) :: ji, jv
635	REAL(r_std) :: speed, zg, zdphi, ztvd, ztvs, zdu2
636	REAL(r_std) :: zri, cd_neut, zscf, cd_tmp
637	!_ ================================================================================================================================
638
639	!! 1. Initialisation
640
641	! test if we have to work with q_cdrag or to calcul it
642	DO ji=1,kjpindex
643
644	!! 1a).1 Designation of wind speed
645	!! \latexonly
646	!! \input{diffucoaero1.tex}
647	!! \endlatexonly
648	speed = wind(ji)
649
650	!! 1a).2 Calculation of geopotentiel
651	!! This is the definition of Geopotential height (e.g. Jacobson eqn.4.47, 2005). (required
652	!! for calculation of the Richardson Number)
653	!! \latexonly
654	!! \input{diffucoaero2.tex}
655	!! \endlatexonly
656	zg = zlev(ji) * cte_grav
657
658	!! \latexonly
659	!! \input{diffucoaero3.tex}
660	!! \endlatexonly
661	zdphi = zg/cp_air
662
663	!! 1a).3 Calculation of the virtual air temperature at the surface
664	!! required for calculation of the Richardson Number
665	!! \latexonly
666	!! \input{diffucoaero4.tex}
667	!! \endlatexonly
668	ztvd = (temp_air(ji) + zdphi / (un + rvtmp2 * qair(ji))) * (un + retv * qair(ji))
669
670	!! 1a).4 Calculation of the virtual surface temperature
671	!! required for calculation of the Richardson Number
672	!! \latexonly
673	!! \input{diffucoaero5.tex}
674	!! \endlatexonly
675	ztvs = temp_sol(ji) * (un + retv * qsurf(ji))
676
677	!! 1a).5 Calculation of the squared wind shear
678	!! required for calculation of the Richardson Number
679	!! \latexonly
680	!! \input{diffucoaero6.tex}
681	!! \endlatexonly
682	zdu2 = MAX(cepdu2,speed**2)
683
684	!! 1a).6 Calculation of the Richardson Number
685	!! The Richardson Number is defined as the ratio of potential to kinetic energy, or, in the
686	!! context of atmospheric science, of the generation of energy by wind shear against consumption
687	!! by static stability and is an indicator of flow stability (i.e. for when laminar flow
688	!! becomes turbulent and vise versa).\n
689	!! It is approximated using the expression below:
690	!! \latexonly
691	!! \input{diffucoaero7.tex}
692	!! \endlatexonly
693	zri = zg * (ztvd - ztvs) / (zdu2 * ztvd)
694
695	!! The Richardson Number hence calculated is subject to a minimum value:
696	!! \latexonly
697	!! \input{diffucoaero8.tex}
698	!! \endlatexonly
699	zri = MAX(MIN(zri,5.),-5.)
700
701	!! 1a).7 Computing the drag coefficient
702	!! We add the add the height of the vegetation to the level height to take into account
703	!! that the level 'seen' by the vegetation is actually the top of the vegetation. Then we
704	!! we can subtract the displacement height.
705	!! \latexonly
706	!! \input{diffucoaero9.tex}
707	!! \endlatexonly
708
709	!! 7.0 Snow smoothering
710	!! Snow induces low levels of turbulence.
711	!! Sensible heat fluxes can therefore be reduced of ~1/3. Pomeroy et al., 1998
712	cd_neut = ct_karman ** 2. / ( LOG( (zlev(ji) + roughheight(ji)) / z0m(ji) ) * LOG( (zlev(ji) + roughheight(ji)) / z0h(ji) ) )
713
714	!! 1a).7.1 - for the stable case (i.e $R_i$ $\geq$ 0)
715	IF (zri .GE. zero) THEN
716
717	!! \latexonly
718	!! \input{diffucoaero10.tex}
719	!! \endlatexonly
720	zscf = SQRT(un + cd * ABS(zri))
721
722	!! \latexonly
723	!! \input{diffucoaero11.tex}
724	!! \endlatexonly
725	cd_tmp=cd_neut/(un + trois * cb * zri * zscf)
726	ELSE
727
728	!! 1a).7.2 - for the unstable case (i.e. $R_i$ < 0)
729	!! \latexonly
730	!! \input{diffucoaero12.tex}
731	!! \endlatexonly
732	zscf = un / (un + trois * cb * cc * cd_neut * SQRT(ABS(zri) * &
733	& ((zlev(ji) + roughheight(ji)) / z0m(ji))))
734
735	!! \latexonly
736	!! \input{diffucoaero13.tex}
737	!! \endlatexonly
738	cd_tmp=cd_neut * (un - trois * cb * zri * zscf)
739	ENDIF
740
741	!! If the Drag Coefficient becomes too small than the surface may uncouple from the atmosphere.
742	!! To prevent this, a minimum limit to the drag coefficient is defined as:
743
744	!! \latexonly
745	!! \input{diffucoaero14.tex}
746	!! \endlatexonly
747	!!
748	q_cdrag(ji) = MAX(cd_tmp, min_qc/MAX(speed,min_wind))
749
750	! In some situations it might be useful to give an upper limit on the cdrag as well.
751	! The line here should then be uncommented.
752	!q_cdrag(ji) = MIN(q_cdrag(ji), 0.5/MAX(speed,min_wind))
753
754	END DO
755
756	IF (printlev>=3) WRITE (numout,*) ' not ldqcdrag_from_gcm : diffuco_aero done '
757
758	END SUBROUTINE diffuco_aero
759
760
761	!! ================================================================================================================================
762	!! SUBROUTINE : diffuco_snow
763	!!
764	!>\BRIEF This subroutine computes the beta coefficient for snow sublimation.
765	!!
766	!! DESCRIPTION : This routine computes beta coefficient for snow sublimation, which
767	!! integrates the snow on both vegetation and other surface types (e.g. ice, lakes,
768	!! cities etc.) \n
769	!!
770	!! A critical depth of snow (snowcri) is defined to calculate the fraction of each grid-cell
771	!! that is covered with snow (snow/snowcri) while the remaining part is snow-free.
772	!! We also carry out a first calculation of sublimation (subtest) to lower down the beta
773	!! coefficient if necessary (if subtest > snow). This is a predictor-corrector test.
774	!!
775	!! RECENT CHANGE(S): None
776	!!
777	!! MAIN OUTPUT VARIABLE(S): ::vbeta1
778	!!
779	!! REFERENCE(S) :
780	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
781	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
782	!! Circulation Model. Journal of Climate, 6, pp. 248-273
783	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influences de l'irrigation
784	!! sur le cycle de l'eau, PhD Thesis, available from:
785	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
786	!!
787	!! FLOWCHART : None
788	!! \n
789	!_ ================================================================================================================================
790
791	SUBROUTINE diffuco_snow (kjpindex, qair, qsatt, rau, u, v,q_cdrag, &
792	& snow, frac_nobio, totfrac_nobio, snow_nobio, frac_snow_veg, frac_snow_nobio, &
793	vbeta1)
794
795	!! 0. Variable and parameter declaration
796
797	!! 0.1 Input variables
798
799	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
800	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level specific air humidity (kg kg^{-1})
801	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsatt !! Surface saturated humidity (kg kg^{-1})
802	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! Air density (kg m^{-3})
803	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind speed (m s^{-1})
804	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Northward Lowest level wind speed (m s^{-1})
805	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
806	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: snow !! Snow mass (kg m^{-2})
807	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT (in) :: frac_nobio !! Fraction of ice, lakes, cities etc. (-)
808	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT (in) :: snow_nobio !! Snow on ice, lakes, cities etc. (-)
809	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: totfrac_nobio !! Total fraction of ice, lakes, cities etc. (-)
810	REAL(r_std),DIMENSION (kjpindex), INTENT(in) :: frac_snow_veg !! Snow cover fraction on vegeted area
811	REAL(r_std),DIMENSION (kjpindex,nnobio), INTENT(in) :: frac_snow_nobio!! Snow cover fraction on non-vegeted area
812
813	!! 0.2 Output variables
814
815	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta1 !! Beta for sublimation (dimensionless ratio)
816
817	!! 0.3 Modified variables
818
819	!! 0.4 Local variables
820
821	REAL(r_std) :: subtest !! Sublimation for test (kg m^{-2})
822	REAL(r_std) :: zrapp !! Modified factor (ratio)
823	REAL(r_std) :: speed !! Wind speed (m s^{-1})
824	REAL(r_std) :: vbeta1_add !! Beta for sublimation (ratio)
825	INTEGER(i_std) :: ji, jv !! Indices (-)
826	!_ ================================================================================================================================
827
828	!! 1. Calculate beta coefficient for snow sublimation on the vegetation\n
829
830	DO ji=1,kjpindex ! Loop over # pixels - domain size
831
832	! Fraction of mesh that can sublimate snow
833	vbeta1(ji) = (un - totfrac_nobio(ji)) * frac_snow_veg(ji)
834
835	! Limitation of sublimation in case of snow amounts smaller than the atmospheric demand.
836	speed = MAX(min_wind, wind(ji))
837
838	subtest = dt_sechiba * vbeta1(ji) * speed * q_cdrag(ji) * rau(ji) * &
839	& ( qsatt(ji) - qair(ji) )
840
841	IF ( subtest .GT. min_sechiba ) THEN
842	zrapp = snow(ji) / subtest
843	IF ( zrapp .LT. un ) THEN
844	vbeta1(ji) = vbeta1(ji) * zrapp
845	ENDIF
846	ENDIF
847
848	END DO ! Loop over # pixels - domain size
849
850	!! 2. Add the beta coefficients calculated from other surfaces types (snow on ice,lakes, cities...)
851
852	DO jv = 1, nnobio ! Loop over # other surface types
853	!!$ !
854	!!$ IF ( jv .EQ. iice ) THEN
855	!!$ !
856	!!$ ! Land ice is of course a particular case
857	!!$ !
858	!!$ DO ji=1,kjpindex
859	!!$ vbeta1(ji) = vbeta1(ji) + frac_nobio(ji,jv)
860	!!$ ENDDO
861	!!$ !
862	!!$ ELSE
863	!
864	DO ji=1,kjpindex ! Loop over # pixels - domain size
865
866	vbeta1_add = frac_nobio(ji,jv) * frac_snow_nobio(ji, jv)
867
868	! Limitation of sublimation in case of snow amounts smaller than
869	! the atmospheric demand.
870	speed = MAX(min_wind, wind(ji))
871
872	!! Limitation of sublimation by the snow accumulated on the ground
873	!! A first approximation is obtained with the old values of
874	!! qair and qsol_sat: function of temp-sol and pb. (see call of qsatcalc)
875	subtest = dt_sechiba * vbeta1_add * speed * q_cdrag(ji) * rau(ji) * &
876	& ( qsatt(ji) - qair(ji) )
877
878	IF ( subtest .GT. min_sechiba ) THEN
879	zrapp = snow_nobio(ji,jv) / subtest
880	IF ( zrapp .LT. un ) THEN
881	vbeta1_add = vbeta1_add * zrapp
882	ENDIF
883	ENDIF
884
885	vbeta1(ji) = vbeta1(ji) + vbeta1_add
886
887	ENDDO ! Loop over # pixels - domain size
888
889	!!$ ENDIF
890
891	ENDDO ! Loop over # other surface types
892
893	IF (printlev>=3) WRITE (numout,*) ' diffuco_snow done '
894
895	END SUBROUTINE diffuco_snow
896
897
898	!! ================================================================================================================================
899	!! SUBROUTINE : diffuco_flood
900	!!
901	!>\BRIEF This routine computes partial beta coefficient : floodplains
902	!!
903	!! DESCRIPTION :
904	!!
905	!! RECENT CHANGE(S): None
906	!!
907	!! MAIN OUTPUT VARIABLE(S) : vbeta5
908	!!
909	!! REFERENCE(S) : None
910	!!
911	!! FLOWCHART : None
912	!! \n
913	!_ ================================================================================================================================
914
915	SUBROUTINE diffuco_flood (kjpindex, qair, qsatt, rau, u, v, q_cdrag, evapot, evapot_corr, &
916	& flood_frac, flood_res, vbeta5)
917
918	! interface description
919	! input scalar
920	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size
921	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level specific humidity
922	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsatt !! Surface saturated humidity
923	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! Density
924	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Lowest level wind speed
925	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Lowest level wind speed
926	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
927	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: flood_res !! water mass in flood reservoir
928	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: flood_frac !! fraction of floodplains
929	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: evapot !! Potential evaporation
930	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: evapot_corr!! Potential evaporation2
931	! output fields
932	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta5 !! Beta for floodplains
933
934	! local declaration
935	REAL(r_std) :: subtest, zrapp, speed
936	INTEGER(i_std) :: ji, jv
937
938	!_ ================================================================================================================================
939	!
940	! beta coefficient for sublimation for floodplains
941	!
942	DO ji=1,kjpindex
943	!
944	IF (evapot(ji) .GT. min_sechiba) THEN
945	vbeta5(ji) = flood_frac(ji) *evapot_corr(ji)/evapot(ji)
946	ELSE
947	vbeta5(ji) = flood_frac(ji)
948	ENDIF
949	!
950	! -- Limitation of evaporation in case of water amounts smaller than
951	! the atmospheric demand.
952
953	!
954	speed = MAX(min_wind, SQRT (u(ji)u(ji) + v(ji)v(ji)))
955	!
956	subtest = dt_sechiba * vbeta5(ji) * speed * q_cdrag(ji) * rau(ji) * &
957	& ( qsatt(ji) - qair(ji) )
958	!
959	IF ( subtest .GT. min_sechiba ) THEN
960	zrapp = flood_res(ji) / subtest
961	IF ( zrapp .LT. un ) THEN
962	vbeta5(ji) = vbeta5(ji) * zrapp
963	ENDIF
964	ENDIF
965	!
966	END DO
967
968	IF (printlev>=3) WRITE (numout,*) ' diffuco_flood done '
969
970	END SUBROUTINE diffuco_flood
971
972
973	!! ================================================================================================================================
974	!! SUBROUTINE : diffuco_inter
975	!!
976	!>\BRIEF This routine computes the partial beta coefficient
977	!! for the interception for each type of vegetation
978	!!
979	!! DESCRIPTION : We first calculate the dry and wet parts of each PFT (wet part = qsintveg/qsintmax).
980	!! The former is submitted to transpiration only (vbeta3 coefficient, calculated in
981	!! diffuco_trans_co2), while the latter is first submitted to interception loss
982	!! (vbeta2 coefficient) and then to transpiration once all the intercepted water has been evaporated
983	!! (vbeta23 coefficient). Interception loss is also submitted to a predictor-corrector test,
984	!! as for snow sublimation. \n
985	!!
986	!! \latexonly
987	!! \input{diffucointer1.tex}
988	!! \endlatexonly
989	!! Calculate the wet fraction of vegetation as the ration between the intercepted water and the maximum water
990	!! on the vegetation. This ratio defines the wet portion of vegetation that will be submitted to interception loss.
991	!!
992	!! \latexonly
993	!! \input{diffucointer2.tex}
994	!! \endlatexonly
995	!!
996	!! Calculation of $\beta_3$, the canopy transpiration resistance
997	!! \latexonly
998	!! \input{diffucointer3.tex}
999	!! \endlatexonly
1000	!!
1001	!! We here determine the limitation of interception loss by the water stored on the leaf.
1002	!! A first approximation of interception loss is obtained using the old values of
1003	!! qair and qsol_sat, which are functions of temp-sol and pb. (see call of 'qsatcalc')
1004	!! \latexonly
1005	!! \input{diffucointer4.tex}
1006	!! \endlatexonly
1007	!!
1008	!! \latexonly
1009	!! \input{diffucointer5.tex}
1010	!! \endlatexonly
1011	!!
1012	!! \latexonly
1013	!! \input{diffucointer6.tex}
1014	!! \endlatexonly
1015	!!
1016	!! Once the whole water stored on foliage has evaporated, transpiration can take place on the fraction
1017	!! 'zqsvegrap'.
1018	!! \latexonly
1019	!! \input{diffucointer7.tex}
1020	!! \endlatexonly
1021	!!
1022	!! RECENT CHANGE(S): None
1023	!!
1024	!! MAIN OUTPUT VARIABLE(S): ::vbeta2, ::vbeta23
1025	!!
1026	!! REFERENCE(S) :
1027	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
1028	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
1029	!! Circulation Model. Journal of Climate, 6, pp. 248-273
1030	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influences de l'irrigation
1031	!! sur le cycle de l'eau, PhD Thesis, available from:
1032	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
1033	!! - Perrier, A, 1975. Etude physique de l'Ã©vaporation dans les conditions naturelles. Annales
1034	!! Agronomiques, 26(1-18): pp. 105-123, pp. 229-243
1035	!!
1036	!! FLOWCHART : None
1037	!! \n
1038	!_ ================================================================================================================================
1039
1040	SUBROUTINE diffuco_inter (kjpindex, qair, qsatt, rau, u, v, q_cdrag, humrel, veget, &
1041	& qsintveg, qsintmax, rstruct, vbeta2, vbeta23)
1042
1043	!! 0 Variable and parameter declaration
1044
1045	!! 0.1 Input variables
1046
1047	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
1048	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level specific air humidity (kg kg^{-1})
1049	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsatt !! Surface saturated humidity (kg kg^{-1})
1050	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! Air Density (kg m^{-3})
1051	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind speed (m s^{-1})
1052	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Northward Lowest level wind speed (m s^{-1})
1053	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
1054	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: humrel !! Soil moisture stress (within range 0 to 1)
1055	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget !! vegetation fraction for each type (fraction)
1056	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintveg !! Water on vegetation due to interception (kg m^{-2})
1057	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintmax !! Maximum water on vegetation (kg m^{-2})
1058	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: rstruct !! architectural resistance (s m^{-1})
1059
1060	!! 0.2 Output variables
1061
1062	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta2 !! Beta for interception loss (-)
1063	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta23 !! Beta for fraction of wetted foliage that will
1064	!! transpire (-)
1065
1066	!! 0.4 Local variables
1067
1068	INTEGER(i_std) :: ji, jv !! (-), (-)
1069	REAL(r_std) :: zqsvegrap, ziltest, zrapp, speed !!
1070	!_ ================================================================================================================================
1071
1072	!! 1. Initialize
1073
1074	vbeta2(:,:) = zero
1075	vbeta23(:,:) = zero
1076
1077	!! 2. The beta coefficient for interception by vegetation.
1078
1079	DO jv = 2,nvm
1080
1081	DO ji=1,kjpindex
1082
1083	IF (veget(ji,jv) .GT. min_sechiba .AND. qsintveg(ji,jv) .GT. zero ) THEN
1084
1085	zqsvegrap = zero
1086	IF (qsintmax(ji,jv) .GT. min_sechiba ) THEN
1087
1088	!! \latexonly
1089	!! \input{diffucointer1.tex}
1090	!! \endlatexonly
1091	!!
1092	!! We calculate the wet fraction of vegetation as the ration between the intercepted water and the maximum water
1093	!! on the vegetation. This ratio defines the wet portion of vegetation that will be submitted to interception loss.
1094	!!
1095	zqsvegrap = MAX(zero, qsintveg(ji,jv) / qsintmax(ji,jv))
1096	END IF
1097
1098	!! \latexonly
1099	!! \input{diffucointer2.tex}
1100	!! \endlatexonly
1101	speed = MAX(min_wind, wind(ji))
1102
1103	!! Calculation of $\beta_3$, the canopy transpiration resistance
1104	!! \latexonly
1105	!! \input{diffucointer3.tex}
1106	!! \endlatexonly
1107	vbeta2(ji,jv) = veget(ji,jv) * zqsvegrap * (un / (un + speed * q_cdrag(ji) * rstruct(ji,jv)))
1108
1109	!! We here determine the limitation of interception loss by the water stored on the leaf.
1110	!! A first approximation of interception loss is obtained using the old values of
1111	!! qair and qsol_sat, which are functions of temp-sol and pb. (see call of 'qsatcalc')
1112	!! \latexonly
1113	!! \input{diffucointer4.tex}
1114	!! \endlatexonly
1115	ziltest = dt_sechiba * vbeta2(ji,jv) * speed * q_cdrag(ji) * rau(ji) * &
1116	& ( qsatt(ji) - qair(ji) )
1117
1118	IF ( ziltest .GT. min_sechiba ) THEN
1119
1120	!! \latexonly
1121	!! \input{diffucointer5.tex}
1122	!! \endlatexonly
1123	zrapp = qsintveg(ji,jv) / ziltest
1124	IF ( zrapp .LT. un ) THEN
1125
1126	!! \latexonly
1127	!! \input{diffucointer6.tex}
1128	!! \endlatexonly
1129	!!
1130	!! Once the whole water stored on foliage has evaporated, transpiration can take place on the fraction
1131	!! 'zqsvegrap'.
1132	IF ( humrel(ji,jv) >= min_sechiba ) THEN
1133	vbeta23(ji,jv) = MAX(vbeta2(ji,jv) - vbeta2(ji,jv) * zrapp, zero)
1134	ELSE
1135	! We don't want transpiration when the soil cannot deliver it
1136	vbeta23(ji,jv) = zero
1137	ENDIF
1138
1139	!! \latexonly
1140	!! \input{diffucointer7.tex}
1141	!! \endlatexonly
1142	vbeta2(ji,jv) = vbeta2(ji,jv) * zrapp
1143	ENDIF
1144	ENDIF
1145	END IF
1146	! ! Autre formulation possible pour l'evaporation permettant une transpiration sur tout le feuillage
1147	! !commenter si formulation Nathalie sinon Tristan
1148	! speed = MAX(min_wind, wind(ji))
1149	!
1150	! vbeta23(ji,jv) = MAX(zero, veget(ji,jv) * (un / (un + speed * q_cdrag(ji) * rstruct(ji,jv))) - vbeta2(ji,jv))
1151
1152	END DO
1153
1154	END DO
1155
1156	IF (printlev>=3) WRITE (numout,*) ' diffuco_inter done '
1157
1158	END SUBROUTINE diffuco_inter
1159
1160
1161	!! ==============================================================================================================================
1162	!! SUBROUTINE : diffuco_bare
1163	!!
1164	!>\BRIEF This routine computes the partial beta coefficient corresponding to
1165	!! bare soil
1166	!!
1167	!! DESCRIPTION : Bare soil evaporation is submitted to a maximum possible flow (evap_bare_lim)
1168	!!
1169	!! Calculation of wind speed
1170	!! \latexonly
1171	!! \input{diffucobare1.tex}
1172	!! \endlatexonly
1173	!!
1174	!! The calculation of $\beta_4$
1175	!! \latexonly
1176	!! \input{diffucobare2.tex}
1177	!! \endlatexonly
1178	!!
1179	!! RECENT CHANGE(S): None
1180	!!
1181	!! MAIN OUTPUT VARIABLE(S): ::vbeta4
1182	!!
1183	!! REFERENCE(S) :
1184	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
1185	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
1186	!! Circulation Model. Journal of Climate, 6, pp.248-273
1187	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influences de l'irrigation
1188	!! sur le cycle de l'eau, PhD Thesis, available from:
1189	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
1190	!!
1191	!! FLOWCHART : None
1192	!! \n
1193	!_ ================================================================================================================================
1194
1195	SUBROUTINE diffuco_bare (kjpindex, tot_bare_soil, veget_max, evap_bare_lim, evap_bare_lim_ns, vbeta2, vbeta3, vbeta4)
1196
1197	!! 0. Variable and parameter declaration
1198
1199	!! 0.1 Input variables
1200	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
1201	REAL(r_std),DIMENSION (kjpindex), INTENT(in) :: tot_bare_soil !! Total evaporating bare soil fraction
1202	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget_max !! Max. fraction of vegetation type (LAI->infty)
1203	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: vbeta2 !! Beta for Interception
1204	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: vbeta3 !! Beta for Transpiration
1205
1206	!! 0.2 Output variables
1207	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta4 !! Beta for bare soil evaporation (-)
1208
1209	!! 0.3 Modified variables
1210	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: evap_bare_lim !! limiting factor for bare soil evaporation
1211	!! when the 11-layer hydrology is used (-)
1212	REAL(r_std),DIMENSION (kjpindex,nstm), INTENT (inout) :: evap_bare_lim_ns !! limiting factor for bare soil evaporation
1213	!! when the 11-layer hydrology is used (-)
1214	!! 0.4 Local variables
1215	INTEGER(i_std) :: ji
1216	REAL(r_std), DIMENSION(kjpindex) :: vegtot
1217	!_ ================================================================================================================================
1218
1219	!! 1. Calculation of the soil resistance and the beta (beta_4) for bare soil
1220
1221	! To use the new version of hydrol_split_soil and ensure the water conservation, we must have throughout sechiba at all time:
1222	! a) evap_bare_lim(ji) = SUM(evap_bare_lim_ns(ji,:)soiltile(ji,:)vegtot(ji))
1223	! b) all the terms (vbeta4, evap_bare_lim, evap_bare_lim_ns) =0 if evap_bare_lim(ji) LE min_sechiba
1224	! This must also be kept true in diffuco_comb
1225
1226	DO ji = 1, kjpindex
1227
1228	! The limitation by 1-beta2-beta3 is due to the fact that evaporation under vegetation is possible
1229	!! \latexonly
1230	!! \input{diffucobare3.tex}
1231	!! \endlatexonly
1232
1233	IF ( (evap_bare_lim(ji) .GT. min_sechiba) .AND. &
1234	! in this case we can't have vegtot LE min_sechina, cf hydrol_soil
1235	(un - SUM(vbeta2(ji,:)+vbeta3(ji,:)) .GT. min_sechiba) ) THEN
1236	! eventually, none of the left-hand term is close to zero
1237
1238	vegtot(ji) = SUM(veget_max(ji,:))
1239	IF (evap_bare_lim(ji) < (un - SUM(vbeta2(ji,:)+vbeta3(ji,:)))) THEN
1240	! Standard case
1241	vbeta4(ji) = evap_bare_lim(ji)
1242	ELSE
1243	vbeta4(ji) = un - SUM(vbeta2(ji,:)+vbeta3(ji,:))
1244
1245	! We now have to redefine evap_bare_lim & evap_bare_lim_ns
1246	IF (evap_bare_lim(ji) .GT. min_sechiba) THEN
1247	evap_bare_lim_ns(ji,:) = evap_bare_lim_ns(ji,:) * vbeta4(ji) / evap_bare_lim(ji)
1248	ELSE ! we must re-invent evap_bare_lim_ns => uniform across soiltiles
1249	evap_bare_lim_ns(ji,:) = tot_bare_soil(ji)/vegtot(ji)
1250	ENDIF
1251
1252	evap_bare_lim(ji) = vbeta4(ji)
1253	! consistent with evap_bare_lim(ji) =
1254	! SUM(evap_bare_lim_ns(ji,:)soiltile(ji,:)vegtot(ji))
1255	! as SUM(soiltile(ji,:)) = 1
1256	END IF
1257
1258	ELSE ! instead of having very small vbeta4, we set everything to zero
1259	vbeta4(ji) = zero
1260	evap_bare_lim(ji) = zero
1261	evap_bare_lim_ns(ji,:) = zero
1262	ENDIF
1263
1264	END DO
1265
1266	IF (printlev>=3) WRITE (numout,*) ' diffuco_bare done '
1267
1268	END SUBROUTINE diffuco_bare
1269
1270
1271	!! ==============================================================================================================================
1272	!! SUBROUTINE : diffuco_trans_co2
1273	!!
1274	!>\BRIEF This subroutine computes carbon assimilation and stomatal
1275	!! conductance, following respectively Farqhuar et al. (1980) and Ball et al. (1987).
1276	!!
1277	!! DESCRIPTION :\n
1278	!! *** General:\n
1279	!! The equations are different depending on the photosynthesis mode (C3 versus C4).\n
1280	!! Assimilation and conductance are computed over 20 levels of LAI and then
1281	!! integrated at the canopy level.\n
1282	!! This routine also computes partial beta coefficient: transpiration for each
1283	!! type of vegetation.\n
1284	!! There is a main loop on the PFTs, then inner loops on the points where
1285	!! assimilation has to be calculated.\n
1286	!! This subroutine is called at each sechiba time step by sechiba_main.\n
1287	!! *** Details:
1288	!! - Integration at the canopy level\n
1289	!! \latexonly
1290	!! \input{diffuco_trans_co2_1.1.tex}
1291	!! \endlatexonly
1292	!! - Light''s extinction \n
1293	!! The available light follows a simple Beer extinction law.
1294	!! The extinction coefficients (ext_coef) are PFT-dependant constants and are defined in constant_co2.f90.\n
1295	!! \latexonly
1296	!! \input{diffuco_trans_co2_1.2.tex}
1297	!! \endlatexonly
1298	!! - Estimation of relative humidity of air (for calculation of the stomatal conductance)\n
1299	!! \latexonly
1300	!! \input{diffuco_trans_co2_1.3.tex}
1301	!! \endlatexonly
1302	!! - Calculation of the water limitation factor\n
1303	!! \latexonly
1304	!! \input{diffuco_trans_co2_2.1.tex}
1305	!! \endlatexonly
1306	!! - Calculation of temperature dependent parameters for C4 plants\n
1307	!! \latexonly
1308	!! \input{diffuco_trans_co2_2.2.tex}
1309	!! \endlatexonly
1310	!! - Calculation of temperature dependent parameters for C3 plants\n
1311	!! \latexonly
1312	!! \input{diffuco_trans_co2_2.3.tex}
1313	!! \endlatexonly
1314	!! - Vmax scaling\n
1315	!! Vmax is scaled into the canopy due to reduction of nitrogen
1316	!! (Johnson and Thornley,1984).\n
1317	!! \latexonly
1318	!! \input{diffuco_trans_co2_2.4.1.tex}
1319	!! \endlatexonly
1320	!! - Assimilation for C4 plants (Collatz et al., 1992)\n
1321	!! \latexonly
1322	!! \input{diffuco_trans_co2_2.4.2.tex}
1323	!! \endlatexonly
1324	!! - Assimilation for C3 plants (Farqhuar et al., 1980)\n
1325	!! \latexonly
1326	!! \input{diffuco_trans_co2_2.4.3.tex}
1327	!! \endlatexonly
1328	!! - Estimation of the stomatal conductance (Ball et al., 1987)\n
1329	!! \latexonly
1330	!! \input{diffuco_trans_co2_2.4.4.tex}
1331	!! \endlatexonly
1332	!!
1333	!! RECENT CHANGE(S):
1334	!!
1335	!! 2018/12 added a nitrogen use efficiency constraint on maximum rate of carboxylation
1336	!!
1337	!! 2018/11 replaced t2m and q2m by temp_air and qair; prognostic variables on first atmospheric model layer
1338	!!
1339	!! 2006/06 N. de Noblet
1340	!! - addition of q2m and t2m as input parameters for the
1341	!! calculation of Rveget
1342	!! - introduction of vbeta23
1343	!!
1344	!! MAIN OUTPUT VARIABLE(S): beta coefficients, resistances, CO2 intercellular
1345	!! concentration
1346	!!
1347	!! REFERENCE(S) :
1348	!! - Ball, J., T. Woodrow, and J. Berry (1987), A model predicting stomatal
1349	!! conductance and its contribution to the control of photosynthesis under
1350	!! different environmental conditions, Prog. Photosynthesis, 4, 221â 224.
1351	!! - Collatz, G., M. Ribas-Carbo, and J. Berry (1992), Coupled photosynthesis
1352	!! stomatal conductance model for leaves of C4 plants, Aust. J. Plant Physiol.,
1353	!! 19, 519â538.
1354	!! - Farquhar, G., S. von Caemmener, and J. Berry (1980), A biochemical model of
1355	!! photosynthesis CO2 fixation in leaves of C3 species, Planta, 149, 78â90.
1356	!! - Johnson, I. R., and J. Thornley (1984), A model of instantaneous and daily
1357	!! canopy photosynthesis, J Theor. Biol., 107, 531 545
1358	!! - McMurtrie, R.E., Rook, D.A. and Kelliher, F.M., 1990. Modelling the yield of Pinus radiata on a
1359	!! site limited by water and nitrogen. For. Ecol. Manage., 30: 381-413
1360	!! - Bounoua, L., Hall, F. G., Sellers, P. J., Kumar, A., Collatz, G. J., Tucker, C. J., and Imhoff, M. L. (2010), Quantifying the
1361	!! negative feedback of vegetation to greenhouse warming: A modeling approach, Geophysical Research Letters, 37, Artn L23701,
1362	!! Doi 10.1029/2010gl045338
1363	!! - Bounoua, L., Collatz, G. J., Sellers, P. J., Randall, D. A., Dazlich, D. A., Los, S. O., Berry, J. A., Fung, I.,
1364	!! Tucker, C. J., Field, C. B., and Jensen, T. G. (1999), Interactions between vegetation and climate: Radiative and physiological
1365	!! effects of doubled atmospheric co2, Journal of Climate, 12, 309-324, Doi 10.1175/1520-0442(1999)012<0309:Ibvacr>2.0.Co;2
1366	!! - Sellers, P. J., Bounoua, L., Collatz, G. J., Randall, D. A., Dazlich, D. A., Los, S. O., Berry, J. A., Fung, I.,
1367	!! Tucker, C. J., Field, C. B., and Jensen, T. G. (1996), Comparison of radiative and physiological effects of doubled atmospheric
1368	!! co2 on climate, Science, 271, 1402-1406, DOI 10.1126/science.271.5254.1402
1369	!! - Lewis, J. D., Ward, J. K., and Tissue, D. T. (2010), Phosphorus supply drives nonlinear responses of cottonwood
1370	!! (populus deltoides) to increases in co2 concentration from glacial to future concentrations, New Phytologist, 187, 438-448,
1371	!! DOI 10.1111/j.1469-8137.2010.03307.x
1372	!! - Kattge, J., Knorr, W., Raddatz, T., and Wirth, C. (2009), Quantifying photosynthetic capacity and its relationship to leaf
1373	!! nitrogen content for global-scale terrestrial biosphere models, Global Change Biology, 15, 976-991,
1374	!! DOI 10.1111/j.1365-2486.2008.01744.x
1375	!!
1376	!! FLOWCHART : None
1377	!! \n
1378	!_ ================================================================================================================================
1379
1380	SUBROUTINE diffuco_trans_co2 (kjpindex, swdown, pb, qsurf, qair, temp_air, temp_growth, rau, u, v, q_cdrag, humrel, &
1381	assim_param, Ca, &
1382	veget, veget_max, lai, qsintveg, qsintmax, vbeta3, vbeta3pot, rveget, rstruct, &
1383	cimean, gsmean, gpp, &
1384	vbeta23, hist_id, indexveg, indexlai, index, kjit, cim)
1385
1386	!
1387	!! 0. Variable and parameter declaration
1388	!
1389
1390	!
1391	!! 0.1 Input variables
1392	!
1393	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (unitless)
1394	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: swdown !! Downwelling short wave flux
1395	!! @tex ($W m^{-2}$) @endtex
1396	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: pb !! Lowest level pressure (hPa)
1397	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qsurf !! Near surface specific humidity
1398	!! @tex ($kg kg^{-1}$) @endtex
1399	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Specific humidity at first atmospheric model layer
1400	!! @tex ($kg kg^{-1}$) @endtex
1401	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_air !! Air temperature at first atmospheric model layer (K)
1402	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_growth !! Growth temperature (Â°C) - Is equal to t2m_month
1403	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! air density @tex ($kg m^{-3}$) @endtex
1404	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Lowest level wind speed
1405	!! @tex ($m s^{-1}$) @endtex
1406	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Lowest level wind speed
1407	!! @tex ($m s^{-1}$) @endtex
1408	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
1409	REAL(r_std),DIMENSION (kjpindex,nvm,npco2), INTENT (in) :: assim_param !! referenced vcmax, nue, leaf N
1410	!! for photosynthesis
1411	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: Ca !! CO2 concentration inside the canopy
1412	!! @tex ($\mu mol mol^{-1}$) @endtex
1413	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: humrel !! Soil moisture stress (0-1,unitless)
1414	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget !! Coverage fraction of vegetation for each PFT
1415	!! depending on LAI (0-1, unitless)
1416	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget_max !! Maximum vegetation fraction of each PFT inside
1417	!! the grid box (0-1, unitless)
1418	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: lai !! Leaf area index @tex ($m^2 m^{-2}$) @endtex
1419	!! @tex ($m s^{-1}$) @endtex
1420	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintveg !! Water on vegetation due to interception
1421	!! @tex ($kg m^{-2}$) @endte
1422	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintmax !! Maximum water on vegetation
1423	!! @tex ($kg m^{-2}$) @endtex
1424	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: vbeta23 !! Beta for fraction of wetted foliage that will
1425	!! transpire (unitless)
1426	INTEGER(i_std),INTENT (in) :: hist_id !! _History_ file identifier (-)
1427	INTEGER(i_std),DIMENSION (kjpindex*nvm), INTENT (in) :: indexveg !! Indeces of the points on the 3D map (-)
1428	INTEGER(i_std),DIMENSION (kjpindex*(nlai+1)), INTENT (in) :: indexlai !! Indeces of the points on the 3D map
1429	INTEGER(i_std),DIMENSION (kjpindex), INTENT (in) :: index !! Indeces of the points on the map (-)
1430	INTEGER(i_std), INTENT(in) :: kjit !! Time step number (-)
1431	!
1432	!! 0.2 Output variables
1433	!
1434	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta3 !! Beta for Transpiration (unitless)
1435	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: vbeta3pot !! Beta for Potential Transpiration
1436	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: rveget !! stomatal resistance of vegetation
1437	!! @tex ($s m^{-1}$) @endtex
1438	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: rstruct !! structural resistance @tex ($s m^{-1}$) @endtex
1439	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: cimean !! mean intercellular CO2 concentration
1440	!! @tex ($\mu mol mol^{-1}$) @endtex
1441	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: gsmean !! mean stomatal conductance to CO2 (umol m-2 s-1)
1442	REAL(r_Std),DIMENSION (kjpindex,nvm), INTENT (out) :: gpp !! Assimilation ((gC m^{-2} dt_sechiba^{-1}), total area)
1443	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (out) :: cim !! Intercellular CO2 over nlai
1444	!
1445	!! 0.3 Modified variables
1446	!
1447
1448	!
1449	!! 0.4 Local variables
1450	!
1451	REAL(r_std),DIMENSION (kjpindex) :: vcmax !! maximum rate of carboxylation. Notice that,
1452	!! as it is currently written, this is only
1453	!! a function of nue and leafN_top
1454	!! @tex ($\mu mol CO2 m^{-2} s^{-1}$) @endtex
1455	REAL(r_std),DIMENSION (kjpindex,nvm) :: nue !! Nitrogen use Efficiency with impact of leaf age (umol CO2 (gN)-1 s-1)
1456	REAL(r_std),DIMENSION (kjpindex,nvm) :: ntot !! Total canopy (eg leaf) N (gN m-2[ground])
1457	REAL(r_std) :: N_profile !! N-content reduction factor for a specific canopy depth (unitless)
1458	REAL(r_std),DIMENSION (kjpindex) :: leafN_top !! Leaf N content - top of canopy (gN m-2[leaf])
1459	INTEGER(i_std) :: ji, jv, jl, limit_photo !! indices (unitless)
1460	REAL(r_std), DIMENSION(kjpindex,nlai+1) :: info_limitphoto
1461	REAL(r_std), DIMENSION(kjpindex,nvm,nlai) :: leaf_ci !! intercellular CO2 concentration (ppm)
1462	REAL(r_std), DIMENSION(kjpindex) :: leaf_ci_lowest !! intercellular CO2 concentration at the lowest
1463	!! LAI level
1464	!! @tex ($\mu mol mol^{-1}$) @endtex
1465	INTEGER(i_std), DIMENSION(kjpindex) :: ilai !! counter for loops on LAI levels (unitless)
1466	REAL(r_std), DIMENSION(kjpindex) :: zqsvegrap !! relative water quantity in the water
1467	!! interception reservoir (0-1,unitless)
1468	REAL(r_std) :: speed !! wind speed @tex ($m s^{-1}$) @endtex
1469	! Assimilation
1470	LOGICAL, DIMENSION(kjpindex) :: assimilate !! where assimilation is to be calculated
1471	!! (unitless)
1472	LOGICAL, DIMENSION(kjpindex) :: calculate !! where assimilation is to be calculated for
1473	!! in the PFTs loop (unitless)
1474	INTEGER(i_std) :: nic,inic,icinic !! counter/indices (unitless)
1475	INTEGER(i_std), DIMENSION(kjpindex) :: index_calc !! index (unitless)
1476	INTEGER(i_std) :: nia,inia,nina,inina,iainia !! counter/indices (unitless)
1477	INTEGER(i_std), DIMENSION(kjpindex) :: index_assi,index_non_assi !! indices (unitless)
1478	REAL(r_std), DIMENSION(kjpindex, nlai+1) :: vc2 !! rate of carboxylation (at a specific LAI level)
1479	!! @tex ($\mu mol CO2 m^{-2} s^{-1}$) @endtex
1480	REAL(r_std), DIMENSION(kjpindex, nlai+1) :: vj2 !! rate of Rubisco regeneration (at a specific LAI
1481	!! level) @tex ($\mu mol e- m^{-2} s^{-1}$) @endtex
1482	REAL(r_std), DIMENSION(kjpindex, nlai+1) :: assimi !! assimilation (at a specific LAI level)
1483	!! @tex ($\mu mol m^{-2} s^{-1}$) @endtex
1484	!! (temporary variables)
1485	REAL(r_std), DIMENSION(kjpindex) :: gstop !! stomatal conductance to H2O at topmost level
1486	!! @tex ($m s^{-1}$) @endtex
1487	REAL(r_std), DIMENSION(kjpindex,nlai+1) :: gs !! stomatal conductance to CO2
1488	!! @tex ($\mol m^{-2} s^{-1}$) @endtex
1489	REAL(r_std), DIMENSION(kjpindex) :: gamma_star !! CO2 compensation point (ppm)
1490	!! @tex ($\mu mol mol^{-1}$) @endtex
1491
1492	REAL(r_std), DIMENSION(kjpindex) :: air_relhum !! air relative humidity at 2m
1493	!! @tex ($kg kg^{-1}$) @endtex
1494	REAL(r_std), DIMENSION(kjpindex) :: VPD !! Vapor Pressure Deficit (kPa)
1495	REAL(r_std), DIMENSION(kjpindex) :: water_lim !! water limitation factor (0-1,unitless)
1496
1497	REAL(r_std), DIMENSION(kjpindex) :: gstot !! total stomatal conductance to H2O
1498	!! Final unit is
1499	!! @tex ($m s^{-1}$) @endtex
1500	REAL(r_std), DIMENSION(kjpindex) :: assimtot !! total assimilation
1501	!! @tex ($\mu mol CO2 m^{-2} s^{-1}$) @endtex
1502	REAL(r_std), DIMENSION(kjpindex) :: Rdtot !! Total Day respiration (respiratory CO2 release other than by photorespiration) (mumol CO2 mâ2 sâ1)
1503	REAL(r_std), DIMENSION(kjpindex) :: leaf_gs_top !! leaf stomatal conductance to H2O at topmost level
1504	!! @tex ($\mol H2O m^{-2} s^{-1}$) @endtex
1505	REAL(r_std), DIMENSION(nlai+1) :: laitab !! tabulated LAI steps @tex ($m^2 m^{-2}$) @endtex
1506	REAL(r_std), DIMENSION(kjpindex) :: qsatt !! surface saturated humidity at 2m (??)
1507	!! @tex ($g g^{-1}$) @endtex
1508	REAL(r_std), DIMENSION(nvm,nlai) :: light !! fraction of light that gets through upper LAI
1509	!! levels (0-1,unitless)
1510	REAL(r_std), DIMENSION(kjpindex) :: T_Vcmax !! Temperature dependance of Vcmax (unitless)
1511	REAL(r_std), DIMENSION(kjpindex) :: S_Vcmax_acclim_temp !! Entropy term for Vcmax
1512	!! accounting for acclimation to temperature (J K-1 mol-1)
1513	REAL(r_std), DIMENSION(kjpindex) :: T_Jmax !! Temperature dependance of Jmax
1514	REAL(r_std), DIMENSION(kjpindex) :: S_Jmax_acclim_temp !! Entropy term for Jmax
1515	!! accounting for acclimation toxs temperature (J K-1 mol-1)
1516	REAL(r_std), DIMENSION(kjpindex) :: T_gm !! Temperature dependance of gmw
1517	REAL(r_std), DIMENSION(kjpindex) :: T_Rd !! Temperature dependance of Rd (unitless)
1518	REAL(r_std), DIMENSION(kjpindex) :: T_Kmc !! Temperature dependance of KmC (unitless)
1519	REAL(r_std), DIMENSION(kjpindex) :: T_KmO !! Temperature dependance of KmO (unitless)
1520	REAL(r_std), DIMENSION(kjpindex) :: T_Sco !! Temperature dependance of Sco
1521	REAL(r_std), DIMENSION(kjpindex) :: T_gamma_star !! Temperature dependance of gamma_star (unitless)
1522	REAL(r_std), DIMENSION(kjpindex) :: vc !! Maximum rate of Rubisco activity-limited carboxylation (mumol CO2 mâ2 sâ1)
1523	REAL(r_std), DIMENSION(kjpindex) :: vj !! Maximum rate of e- transport under saturated light (mumol CO2 mâ2 sâ1)
1524	REAL(r_std), DIMENSION(kjpindex) :: gm !! Mesophyll diffusion conductance (molCO2 mâ2 sâ1 barâ1)
1525	REAL(r_std), DIMENSION(kjpindex) :: g0var
1526	REAL(r_std), DIMENSION(kjpindex,nlai+1) :: Rd !! Day respiration (respiratory CO2 release other than by photorespiration) (mumol CO2 mâ2 sâ1)
1527	REAL(r_std), DIMENSION(kjpindex) :: Kmc !! MichaelisâMenten constant of Rubisco for CO2 (mubar)
1528	REAL(r_std), DIMENSION(kjpindex) :: KmO !! MichaelisâMenten constant of Rubisco for O2 (mubar)
1529	REAL(r_std), DIMENSION(kjpindex) :: Sco !! Relative CO2 /O2 specificity factor for Rubisco (bar bar-1)
1530	REAL(r_std), DIMENSION(kjpindex) :: gb_co2 !! Boundary-layer conductance (molCO2 mâ2 sâ1 barâ1)
1531	REAL(r_std), DIMENSION(kjpindex) :: gb_h2o !! Boundary-layer conductance (molH2O mâ2 sâ1 barâ1)
1532	REAL(r_std), DIMENSION(kjpindex) :: fvpd !! Factor for describing the effect of leaf-to-air vapour difference on gs (-)
1533	REAL(r_std), DIMENSION(kjpindex) :: low_gamma_star !! Half of the reciprocal of Sc/o (bar bar-1)
1534	REAL(r_std) :: fcyc !! Fraction of electrons at PSI that follow cyclic transport around PSI (-)
1535	REAL(r_std) :: z !! A lumped parameter (see Yin et al. 2009) ( mol mol-1)
1536	REAL(r_std) :: Rm !! Day respiration in the mesophyll (umol CO2 mâ2 sâ1)
1537	REAL(r_std) :: Cs_star !! Cs -based CO2 compensation point in the absence of Rd (ubar)
1538	REAL(r_std), DIMENSION(kjpindex) :: Iabs !! Photon flux density absorbed by leaf photosynthetic pigments (umol photon mâ2 sâ1)
1539	REAL(r_std), DIMENSION(kjpindex) :: Jmax !! Maximum value of J under saturated light (umol eâ mâ2 sâ1)
1540	REAL(r_std), DIMENSION(kjpindex, nlai+1) :: JJ !! Rate of eâ transport (umol eâ mâ2 sâ1)
1541	REAL(r_std) :: J2 !! Rate of all eâ transport through PSII (umol eâ mâ2 sâ1)
1542	REAL(r_std) :: VpJ2 !! eâ transport-limited PEP carboxylation rate (umol CO2 mâ2 sâ1)
1543	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)
1544	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)
1545	REAL(r_std) :: Obs !! Bundle-sheath oxygen partial pressure (ubar)
1546	REAL(r_std), DIMENSION(kjpindex, nlai+1) :: Cc !! Chloroplast CO2 partial pressure (ubar)
1547	REAL(r_std) :: ci_star !! Ci -based CO2 compensation point in the absence of Rd (ubar)
1548	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))
1549	REAL(r_std) :: QQ,UU,PSI,x1,x2,x3 !! Variables used for solving the cubic equation (see Yin et al. (2009))
1550
1551	REAL(r_std) :: cresist !! coefficient for resistances (??)
1552	REAL(r_std), DIMENSION(kjpindex) :: laisum !! when calculating cim over nlai
1553
1554	! @defgroup Photosynthesis Photosynthesis
1555	! @{
1556	! 1. Preliminary calculations\n
1557	!_ ================================================================================================================================
1558
1559	cim(:,:)=zero
1560	leaf_ci(:,:,:) = zero
1561
1562	!
1563	! 1.1 Calculate LAI steps\n
1564	! The integration at the canopy level is done over nlai fixed levels.
1565	!! \latexonly
1566	!! \input{diffuco_trans_co2_1.1.tex}
1567	!! \endlatexonly
1568	! @}
1569	! @codeinc
1570	DO jl = 1, nlai+1
1571	laitab(jl) = laimax(EXP(lai_level_depthREAL(jl-1,r_std))-1.)/(EXP(lai_level_depth*REAL(nlai,r_std))-un)
1572	ENDDO
1573	! @endcodeinc
1574
1575	! @addtogroup Photosynthesis
1576	! @{
1577	!
1578	! 1.2 Calculate light fraction for each LAI step\n
1579	! The available light follows a simple Beer extinction law.
1580	! The extinction coefficients (ext_coef) are PFT-dependant constants and are defined in constant_co2.f90.
1581	!! \latexonly
1582	!! \input{diffuco_trans_co2_1.2.tex}
1583	!! \endlatexonly
1584	! @}
1585	! @codeinc
1586	DO jl = 1, nlai
1587	DO jv = 1, nvm
1588	light(jv,jl) = exp( -ext_coeff(jv)*laitab(jl) )
1589	ENDDO
1590	ENDDO
1591	! @endcodeinc
1592	!
1593	! Photosynthesis parameters
1594	!
1595
1596	! IF (downregulation_co2) THEN
1597	! DO jv= 1, nvm
1598	! vcmax(:,jv) = assim_param(:,jv,ivcmax)(un-downregulation_co2_coeff(jv)log(Ca(:)/downregulation_co2_baselevel))
1599	! ENDDO
1600	! ELSE
1601	! vcmax(:,:) = assim_param(:,:,ivcmax)
1602	! ENDIF
1603
1604
1605	nue(:,:) = assim_param(:,:,inue)
1606	ntot(:,:) = assim_param(:,:,ileafn)
1607
1608
1609
1610	! DO jv = 1, nvm
1611	! vcmax(:,:) = Vcmax25(jv)
1612	! ENDDO
1613
1614	! @addtogroup Photosynthesis
1615	! @{
1616	!
1617	! 1.3 Estimate relative humidity of air (for calculation of the stomatal conductance).\n
1618	!! \latexonly
1619	!! \input{diffuco_trans_co2_1.3.tex}
1620	!! \endlatexonly
1621	! @}
1622	!
1623
1624	CALL qsatcalc (kjpindex, temp_air, pb, qsatt)
1625	air_relhum(:) = &
1626	( qair(:) * pb(:) / (Tetens_1+qair(:)* Tetens_2) ) / &
1627	( qsatt(:)pb(:) / (Tetens_1+qsatt(:)Tetens_2 ) )
1628
1629
1630	VPD(:) = ( qsatt(:)pb(:) / (Tetens_1+qsatt(:)Tetens_2 ) ) &
1631	- ( qair(:) * pb(:) / (Tetens_1+qair(:)* Tetens_2) )
1632	! VPD is needed in kPa
1633	VPD(:) = VPD(:)/10.
1634
1635	!
1636	! 2. beta coefficient for vegetation transpiration
1637	!
1638	rstruct(:,1) = rstruct_const(1)
1639	rveget(:,:) = undef_sechiba
1640	!
1641	vbeta3(:,:) = zero
1642	vbeta3pot(:,:) = zero
1643	gsmean(:,:) = zero
1644	gpp(:,:) = zero
1645	!
1646	cimean(:,1) = Ca(:)
1647	!
1648	! @addtogroup Photosynthesis
1649	! @{
1650	! 2. Loop over vegetation types\n
1651	! @}
1652	!
1653	DO jv = 2,nvm
1654	gamma_star(:)=zero
1655	Kmo(:)=zero
1656	Kmc(:)=zero
1657	gm(:)=zero
1658	g0var(:) =zero
1659
1660	Cc(:,:)=zero
1661	Vc2(:,:)=zero
1662	JJ(:,:)=zero
1663	info_limitphoto(:,:)=zero
1664	gs(:,:)=zero
1665	assimi(:,:)=zero
1666	Rd(:,:)=zero
1667
1668	!
1669	! @addtogroup Photosynthesis
1670	! @{
1671	!
1672	! 2.1 Initializations\n
1673	!! \latexonly
1674	!! \input{diffuco_trans_co2_2.1.tex}
1675	!! \endlatexonly
1676	! @}
1677	!
1678	! beta coefficient for vegetation transpiration
1679	!
1680	rstruct(:,jv) = rstruct_const(jv)
1681	cimean(:,jv) = Ca(:)
1682
1683	WHERE (lai(:,jv) .GT. min_sechiba)
1684	leafN_top(:) = ntot(:,jv) * ext_coeff_N(jv) / ( 1. - exp(-ext_coeff_N(jv) * lai(:,jv)) )
1685	ELSEWHERE
1686	leafN_top(:) = zero
1687	ENDWHERE
1688
1689	vcmax(:) = nue(:,jv)*leafN_top(:)
1690
1691	!
1692	!! mask that contains points where there is photosynthesis
1693	!! For the sake of vectorisation [DISPENSABLE], computations are done only for convenient points.
1694	!! nia is the number of points where the assimilation is calculated and nina the number of points where photosynthesis is not
1695	!! calculated (based on criteria on minimum or maximum values on LAI, vegetation fraction, shortwave incoming radiation,
1696	!! temperature and relative humidity).
1697	!! For the points where assimilation is not calculated, variables are initialized to specific values.
1698	!! The assimilate(kjpindex) array contains the logical value (TRUE/FALSE) relative to this photosynthesis calculation.
1699	!! The index_assi(kjpindex) array indexes the nia points with assimilation, whereas the index_no_assi(kjpindex) array indexes
1700	!! the nina points with no assimilation.
1701	nia=0
1702	nina=0
1703	!
1704	DO ji=1,kjpindex
1705	!
1706	IF ( ( lai(ji,jv) .GT. 0.01 ) .AND. &
1707	( veget_max(ji,jv) .GT. min_sechiba ) ) THEN
1708
1709	IF ( ( veget(ji,jv) .GT. min_sechiba ) .AND. &
1710	( swdown(ji) .GT. min_sechiba ) .AND. &
1711	( humrel(ji,jv) .GT. min_sechiba) .AND. &
1712	( temp_growth(ji) .GT. tphoto_min(jv) ) .AND. &
1713	( temp_growth(ji) .LT. tphoto_max(jv) ) ) THEN
1714	!
1715	assimilate(ji) = .TRUE.
1716	nia=nia+1
1717	index_assi(nia)=ji
1718	!
1719	ELSE
1720	!
1721	assimilate(ji) = .FALSE.
1722	nina=nina+1
1723	index_non_assi(nina)=ji
1724	!
1725	ENDIF
1726	ELSE
1727	!
1728	assimilate(ji) = .FALSE.
1729	nina=nina+1
1730	index_non_assi(nina)=ji
1731	!
1732	ENDIF
1733	!
1734
1735	ENDDO
1736	!
1737
1738	gstot(:) = zero
1739	gstop(:) = zero
1740	assimtot(:) = zero
1741	Rdtot(:)=zero
1742	leaf_gs_top(:) = zero
1743	!
1744	zqsvegrap(:) = zero
1745	WHERE (qsintmax(:,jv) .GT. min_sechiba)
1746	!! relative water quantity in the water interception reservoir
1747	zqsvegrap(:) = MAX(zero, qsintveg(:,jv) / qsintmax(:,jv))
1748	ENDWHERE
1749	!
1750	!! Calculates the water limitation factor.
1751	water_lim(:) = humrel(:,jv)
1752
1753	! give a default value of ci for all pixel that do not assimilate
1754	DO jl=1,nlai
1755	DO inina=1,nina
1756	leaf_ci(index_non_assi(inina),jv,jl) = Ca(index_non_assi(inina))
1757	ENDDO
1758	ENDDO
1759	!
1760	ilai(:) = 1
1761	!
1762	! Here is the calculation of assimilation and stomatal conductance
1763	! based on the work of Farquahr, von Caemmerer and Berry (FvCB model)
1764	! as described in Yin et al. 2009
1765	! Yin et al. developed a extended version of the FvCB model for C4 plants
1766	! and proposed an analytical solution for both photosynthesis pathways (C3 and C4)
1767	! Photosynthetic parameters used are those reported in Yin et al.
1768	! Except For Vcmax25, relationships between Vcmax25 and Jmax25 for which we use
1769	! Medlyn et al. (2002) and Kattge & Knorr (2007)
1770	! Because these 2 references do not consider mesophyll conductance, we neglect this term
1771	! in the formulations developed by Yin et al.
1772	! Consequently, gm (the mesophyll conductance) tends to the infinite
1773	! This is of importance because as stated by Kattge & Knorr and Medlyn et al.,
1774	! values of Vcmax and Jmax derived with different model parametrizations are not
1775	! directly comparable and the published values of Vcmax and Jmax had to be standardized
1776	! to one consistent formulation and parametrization
1777
1778	! See eq. 6 of Yin et al. (2009)
1779	! Parametrization of Medlyn et al. (2002) - from Bernacchi et al. (2001)
1780	T_KmC(:) = Arrhenius(kjpindex,temp_air,298.,E_KmC(jv))
1781	T_KmO(:) = Arrhenius(kjpindex,temp_air,298.,E_KmO(jv))
1782	T_Sco(:) = Arrhenius(kjpindex,temp_air,298.,E_Sco(jv))
1783	T_gamma_star(:) = Arrhenius(kjpindex,temp_air,298.,E_gamma_star(jv))
1784
1785
1786	! Parametrization of Yin et al. (2009) - from Bernacchi et al. (2001)
1787	T_Rd(:) = Arrhenius(kjpindex,temp_air,298.,E_Rd(jv))
1788
1789
1790	! For C3 plants, we assume that the Entropy term for Vcmax and Jmax
1791	! acclimates to temperature as shown by Kattge & Knorr (2007) - Eq. 9 and 10
1792	! and that Jmax and Vcmax respond to temperature following a modified Arrhenius function
1793	! (with a decrease of these parameters for high temperature) as in Medlyn et al. (2002)
1794	! and Kattge & Knorr (2007).
1795	! In Yin et al. (2009), temperature dependance to Vcmax is based only on a Arrhenius function
1796	! Concerning this apparent unconsistency, have a look to the section 'Limitation of
1797	! Photosynthesis by gm' of Bernacchi (2002) that may provide an explanation
1798
1799	! Growth temperature tested by Kattge & Knorr range from 11 to 35Â°C
1800	! So, we limit the relationship between these lower and upper limits
1801	S_Jmax_acclim_temp(:) = aSJ(jv) + bSJ(jv) * MAX(11., MIN(temp_growth(:),35.))
1802	T_Jmax(:) = Arrhenius_modified(kjpindex,temp_air,298.,E_Jmax(jv),D_Jmax(jv),S_Jmax_acclim_temp)
1803
1804	S_Vcmax_acclim_temp(:) = aSV(jv) + bSV(jv) * MAX(11., MIN(temp_growth(:),35.))
1805	T_Vcmax(:) = Arrhenius_modified(kjpindex,temp_air,298.,E_Vcmax(jv),D_Vcmax(jv),S_Vcmax_acclim_temp)
1806
1807
1808
1809	vc(:) = vcmax(:) * T_Vcmax(:)
1810	! As shown by Kattge & Knorr (2007), we make use
1811	! of Jmax25/Vcmax25 ratio (rJV) that acclimates to temperature for C3 plants
1812	! rJV is written as a function of the growth temperature
1813	! rJV = arJV + brJV * T_month
1814	! See eq. 10 of Kattge & Knorr (2007)
1815	! and Table 3 for Values of arJV anf brJV
1816	! Growth temperature is monthly temperature (expressed in Â°C) - See first paragraph of
1817	! section Methods/Data of Kattge & Knorr
1818	vj(:) = ( arJV(jv) + brJV(jv) * MAX(11., MIN(temp_growth(:),35.)) ) * vcmax(:) * T_Jmax(:)
1819
1820	T_gm(:) = Arrhenius_modified(kjpindex,temp_air,298.,E_gm(jv),D_gm(jv),S_gm(jv))
1821	gm(:) = gm25(jv) * T_gm(:) * MAX(1-stress_gm(jv), water_lim(:))
1822
1823	g0var(:) = g0(jv)* MAX(1-stress_gs(jv), water_lim(:))
1824	! @endcodeinc
1825	!
1826	KmC(:)=KmC25(jv)*T_KmC(:)
1827	KmO(:)=KmO25(jv)*T_KmO(:)
1828	Sco(:)=Sco25(jv)*T_sco(:)
1829	gamma_star(:) = gamma_star25(jv)*T_gamma_star(:)
1830
1831
1832
1833	! low_gamma_star is defined by Yin et al. (2009)
1834	! as the half of the reciprocal of Sco - See Table 2
1835	low_gamma_star(:) = 0.5 / Sco(:)
1836
1837	! VPD expressed in kPa
1838	! Note : MIN(1.-min_sechiba,MAX(min_sechiba,(a1(jv) - b1(jv) * VPD(:)))) is always between 0-1 not including 0 and 1
1839	fvpd(:) = 1. / ( 1. / MIN(1.-min_sechiba,MAX(min_sechiba,(a1(jv) - b1(jv) * VPD(:)))) - 1. ) &
1840	* MAX(1-stress_gs(jv), water_lim(:))
1841
1842	! leaf boundary layer conductance
1843	! conversion from a conductance in (m s-1) to (mol H2O m-2 s-1)
1844	! from Pearcy et al. (1991, see below)
1845	gb_h2o(:) = gb_ref * 44.6 * (tp_00/temp_air(:)) * (pb(:)/pb_std)
1846
1847	! conversion from (mol H2O m-2 s-1) to (mol CO2 m-2 s-1)
1848	gb_co2(:) = gb_h2o(:) / ratio_H2O_to_CO2
1849
1850	!
1851	! @addtogroup Photosynthesis
1852	! @{
1853	!
1854	! 2.4 Loop over LAI discretized levels to estimate assimilation and conductance\n
1855	! @}
1856	!
1857	!! The calculate(kjpindex) array is of type logical to indicate wether we have to sum over this LAI fixed level (the LAI of
1858	!! 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
1859	!! corresponding point is indexed in the index_calc array.
1860	JJ(:,:)=zero
1861	vc2(:,:)=zero
1862	vj2(:,:)=zero
1863	Cc(:,:)=zero
1864	gs(:,:)=zero
1865	assimi(:,:)=zero
1866	Rd(:,:)=zero
1867
1868	DO jl = 1, nlai
1869	!
1870	nic=0
1871	calculate(:) = .FALSE.
1872	!
1873	IF (nia .GT. 0) then
1874	DO inia=1,nia
1875	calculate(index_assi(inia)) = (laitab(jl) .LE. lai(index_assi(inia),jv) )
1876	IF ( calculate(index_assi(inia)) ) THEN
1877	nic=nic+1
1878	index_calc(nic)=index_assi(inia)
1879	ENDIF
1880	ENDDO
1881	ENDIF
1882	!
1883	! @addtogroup Photosynthesis
1884	! @{
1885	!
1886	! 2.4.1 Vmax is scaled into the canopy due to reduction of nitrogen
1887	!! (Johnson and Thornley,1984).\n
1888	!! \latexonly
1889	!! \input{diffuco_trans_co2_2.4.1.tex}
1890	!! \endlatexonly
1891	! @}
1892	!
1893	N_profile = exp( -ext_coeff_N(jv)*laitab(jl) )
1894	!
1895
1896	vc2(:,jl) = vc(:) * N_profile * MAX(1-stress_vcmax(jv),water_lim(:))
1897	vj2(:,jl) = vj(:) * N_profile * MAX(1-stress_vcmax(jv),water_lim(:))
1898
1899	! see Comment in legend of Fig. 6 of Yin et al. (2009)
1900	! Rd25 is assumed to equal 0.01 Vcmax25
1901	Rd(:,jl) = vcmax(:) * N_profile * 0.01 * T_Rd(:) * MAX(1-stress_vcmax(jv), water_lim(:))
1902
1903	Iabs(:)=swdown(:)W_to_molRG_to_PARext_coeff(jv)light(jv,jl)
1904
1905	! eq. 4 of Yin et al (2009)
1906	Jmax(:)=vj2(:,jl)
1907	JJ(:,jl) = ( alpha_LL(jv) * Iabs(:) + Jmax(:) - sqrt((alpha_LL(jv) * Iabs(:) + Jmax(:) )**2. &
1908	- 4 * theta(jv) * Jmax(:) * alpha_LL(jv) * Iabs(:)) ) &
1909	/ ( 2 * theta(jv))
1910
1911	!
1912	IF ( is_c4(jv) ) THEN
1913	!
1914	! @addtogroup Photosynthesis
1915	! @{
1916	!
1917	! 2.4.2 Assimilation for C4 plants (Collatz et al., 1992)\n
1918	!! \latexonly
1919	!! \input{diffuco_trans_co2_2.4.2.tex}
1920	!! \endlatexonly
1921	! @}
1922	!
1923	!
1924	!
1925	IF (nic .GT. 0) THEN
1926	DO inic=1,nic
1927
1928	! Analytical resolution of the Assimilation based Yin et al. (2009)
1929	icinic=index_calc(inic)
1930
1931	! Eq. 28 of Yin et al. (2009)
1932	fcyc= 1. - ( 4.(1.-fpsir(jv))(1.+fQ(jv)) + 3.h_protons(jv)fpseudo(jv) ) / &
1933	( 3.h_protons(jv) - 4.(1.-fpsir(jv)))
1934
1935	! See paragraph after eq. (20b) of Yin et al.
1936	Rm=Rd(icinic,jl)/2.
1937
1938	! We assume that cs_star equals ci_star (see Comment in legend of Fig. 6 of Yin et al. (2009)
1939	! Equation 26 of Yin et al. (2009)
1940	Cs_star = (gbs(jv) * low_gamma_star(icinic) * Oi - &
1941	( 1. + low_gamma_star(icinic) * alpha(jv) / 0.047) * Rd(icinic,jl) + Rm ) &
1942	/ ( gbs(jv) + kp(jv) )
1943
1944	! eq. 11 of Yin et al (2009)
1945	J2 = JJ(icinic,jl) / ( 1. - fpseudo(jv) / ( 1. - fcyc ) )
1946
1947	! Equation right after eq. (20d) of Yin et al. (2009)
1948	z = ( 2. + fQ(jv) - fcyc ) / ( h_protons(jv) * (1. - fcyc ))
1949
1950	VpJ2 = fpsir(jv) * J2 * z / 2.
1951
1952	A_3=9999.
1953
1954	! See eq. right after eq. 18 of Yin et al. (2009)
1955	DO limit_photo=1,2
1956	! Is Vc limiting the Assimilation
1957	IF ( limit_photo .EQ. 1 ) THEN
1958	a = 1. + kp(jv) / gbs(jv)
1959	b = 0.
1960	x1 = Vc2(icinic,jl)
1961	x2 = KmC(icinic)/KmO(icinic)
1962	x3 = KmC(icinic)
1963	! Is J limiting the Assimilation
1964	ELSE
1965	a = 1.
1966	b = VpJ2
1967	x1 = (1.- fpsir(jv)) * J2 * z / 3.
1968	x2 = 7. * low_gamma_star(icinic) / 3.
1969	x3 = 0.
1970	ENDIF
1971
1972	m=fvpd(icinic)-g0var(icinic)/gb_co2(icinic)
1973	d=g0var(icinic)(Ca(icinic)-Cs_star) + fvpd(icinic)Rd(icinic,jl)
1974	f=(b-Rm-low_gamma_star(icinic)Oigbs(jv))x1d + agbs(jv)x1Ca(icinic)d
1975	j=(b-Rm+gbs(jv)x3 + x2gbs(jv)Oi)m + (alpha(jv)x2/0.047-1.)d &
1976	+ agbs(jv)(Ca(icinic)*m - d/gb_co2(icinic) - (Ca(icinic) - Cs_star ))
1977
1978	g=(b-Rm-low_gamma_star(icinic)Oigbs(jv))x1m - (alpha(jv)low_gamma_star(icinic)/0.047+1.)x1*d &
1979	+ agbs(jv)x1(Ca(icinic)m - d/gb_co2(icinic) - (Ca(icinic)-Cs_star ))
1980
1981	h=-((alpha(jv)low_gamma_star(icinic)/0.047+1.)x1m + (agbs(jv)x1(m-1.))/gb_co2(icinic) )
1982	i= ( b-Rm + gbs(jv)x3 + x2gbs(jv)Oi )d + agbs(jv)Ca(icinic)*d
1983	l= ( alpha(jv)x2/0.047 - 1.)m - (agbs(jv)(m-1.))/gb_co2(icinic)
1984
1985	p = (j-(h-l*Rd(icinic,jl))) / l
1986	q = (i+j*Rd(icinic,jl)-g) / l
1987	r = -(f-i*Rd(icinic,jl)) / l
1988
1989	! See Yin et al. (2009) and Baldocchi (1994)
1990	QQ = ( (p*2._r_std) - 3._r_std q) / 9._r_std
1991	UU = ( 2._r_std* (p*3._r_std) - 9._r_std pq + 27._r_std r) /54._r_std
1992
1993	IF ( (QQ .GE. 0._r_std) .AND. (ABS(UU/(QQ**1.5_r_std) ) .LE. 1._r_std) ) THEN
1994	PSI = ACOS(UU/(QQ**1.5_r_std))
1995	A_3_tmp = -2._r_std * SQRT(QQ) * COS(( PSI + 4._r_std * PI)/3._r_std ) - p / 3._r_std
1996	IF (( A_3_tmp .LT. A_3 )) THEN
1997	A_3 = A_3_tmp
1998	info_limitphoto(icinic,jl)=2.
1999	ELSE
2000	! In case, J is not limiting the assimilation
2001	! we have to re-initialise a, b, x1, x2 and x3 values
2002	! in agreement with a Vc-limited assimilation
2003	a = 1. + kp(jv) / gbs(jv)
2004	b = 0.
2005	x1 = Vc2(icinic,jl)
2006	x2 = KmC(icinic)/KmO(icinic)
2007	x3 = KmC(icinic)
2008	info_limitphoto(icinic,jl)=1.
2009	ENDIF
2010	ENDIF
2011
2012	IF ( ( A_3 .EQ. 9999. ) .OR. ( A_3 .LT. (-Rd(icinic,jl)) ) ) THEN
2013	IF ( printlev>=4 ) THEN
2014	WRITE(numout,*) 'We have a problem in diffuco_trans_co2 for A_3'
2015	WRITE(numout,*) 'no real positive solution found for pft:',jv
2016	WRITE(numout,*) 'temp_air:',temp_air(icinic)
2017	WRITE(numout,*) 'vpd:',vpd(icinic)
2018	END IF
2019	A_3 = -Rd(icinic,jl)
2020	ENDIF
2021	assimi(icinic,jl) = A_3
2022
2023	IF ( ABS( assimi(icinic,jl) + Rd(icinic,jl) ) .LT. min_sechiba ) THEN
2024	gs(icinic,jl) = g0var(icinic)
2025	!leaf_ci keeps its initial value (Ca).
2026	ELSE
2027	! Eq. 24 of Yin et al. (2009)
2028	Obs = ( alpha(jv) * assimi(icinic,jl) ) / ( 0.047 * gbs(jv) ) + Oi
2029	! Eq. 23 of Yin et al. (2009)
2030	Cc(icinic,jl) = ( ( assimi(icinic,jl) + Rd(icinic,jl) ) * ( x2 * Obs + x3 ) + low_gamma_star(icinic) &
2031	* Obs * x1 ) &
2032	/ MAX(min_sechiba, x1 - ( assimi(icinic,jl) + Rd(icinic,jl) ))
2033	! Eq. 22 of Yin et al. (2009)
2034	leaf_ci(icinic,jv,jl) = ( Cc(icinic,jl) - ( b - assimi(icinic,jl) - Rm ) / gbs(jv) ) / a
2035	! Eq. 25 of Yin et al. (2009)
2036	! It should be Cs instead of Ca but it seems that
2037	! other equations in Appendix C make use of Ca
2038	gs(icinic,jl) = g0var(icinic) + ( assimi(icinic,jl) + Rd(icinic,jl) ) / &
2039	( Ca(icinic) - Cs_star ) * fvpd(icinic)
2040	ENDIF
2041	ENDDO
2042	ENDDO
2043	ENDIF
2044	ELSE
2045	!
2046	! @addtogroup Photosynthesis
2047	! @{
2048	!
2049	! 2.4.3 Assimilation for C3 plants (Farqhuar et al., 1980)\n
2050	!! \latexonly
2051	!! \input{diffuco_trans_co2_2.4.3.tex}
2052	!! \endlatexonly
2053	! @}
2054	!
2055	!
2056	IF (nic .GT. 0) THEN
2057	DO inic=1,nic
2058	icinic=index_calc(inic)
2059
2060	A_1=9999.
2061
2062	! See eq. right after eq. 18 of Yin et al. (2009)
2063	DO limit_photo=1,2
2064	! Is Vc limiting the Assimilation
2065	IF ( limit_photo .EQ. 1 ) THEN
2066	x1 = vc2(icinic,jl)
2067	! It should be O not Oi (comment from Vuichard)
2068	x2 = KmC(icinic) * ( 1. + 2gamma_star(icinic)Sco(icinic) / KmO(icinic) )
2069	! Is J limiting the Assimilation
2070	ELSE
2071	x1 = JJ(icinic,jl)/4.
2072	x2 = 2. * gamma_star(icinic)
2073	ENDIF
2074
2075
2076	! See Appendix B of Yin et al. (2009)
2077	a = g0var(icinic) * ( x2 + gamma_star(icinic) ) + &
2078	( g0var(icinic) / gm(icinic) + fvpd(icinic) ) * ( x1 - Rd(icinic,jl) )
2079	b = Ca(icinic) * ( x1 - Rd(icinic,jl) ) - gamma_star(icinic) * x1 - Rd(icinic,jl) * x2
2080	c = Ca(icinic) + x2 + ( 1./gm(icinic) + 1./gb_co2(icinic) ) * ( x1 - Rd(icinic,jl) )
2081	d = x2 + gamma_star(icinic) + ( x1 - Rd(icinic,jl) ) / gm(icinic)
2082	m = 1./gm(icinic) + ( g0var(icinic)/gm(icinic) + fvpd(icinic) ) * ( 1./gm(icinic) + 1./gb_co2(icinic) )
2083
2084	p = - ( d + (x1 - Rd(icinic,jl) ) / gm(icinic) + a * ( 1./gm(icinic) + 1./gb_co2(icinic) ) + &
2085	( g0var(icinic)/gm(icinic) + fvpd(icinic) ) * c ) / m
2086
2087	q = ( d * ( x1 - Rd(icinic,jl) ) + ac + ( g0var(icinic)/gm(icinic) + fvpd(icinic) ) b ) / m
2088	r = - a * b / m
2089
2090	! See Yin et al. (2009)
2091	QQ = ( (p*2._r_std) - 3._r_std q) / 9._r_std
2092	UU = ( 2._r_std* (p*3._r_std) - 9._r_std pq + 27._r_std r) /54._r_std
2093
2094	IF ( (QQ .GE. 0._r_std) .AND. (ABS(UU/(QQ**1.5_r_std) ) .LE. 1._r_std) ) THEN
2095	PSI = ACOS(UU/(QQ**1.5_r_std))
2096	A_1_tmp = -2._r_std * SQRT(QQ) * COS( PSI / 3._r_std ) - p / 3._r_std
2097	IF (( A_1_tmp .LT. A_1 )) THEN
2098	A_1 = A_1_tmp
2099	info_limitphoto(icinic,jl)=2.
2100	ELSE
2101	! In case, J is not limiting the assimilation
2102	! we have to re-initialise x1 and x2 values
2103	! in agreement with a Vc-limited assimilation
2104	x1 = vc2(icinic,jl)
2105	! It should be O not Oi (comment from Vuichard)
2106	x2 = KmC(icinic) * ( 1. + 2gamma_star(icinic)Sco(icinic) / KmO(icinic) )
2107	info_limitphoto(icinic,jl)=1.
2108	ENDIF
2109	ENDIF
2110	ENDDO
2111	IF ( (A_1 .EQ. 9999.) .OR. ( A_1 .LT. (-Rd(icinic,jl)) ) ) THEN
2112	IF ( printlev>=4 ) THEN
2113	WRITE(numout,*) 'We have a problem in diffuco_trans_co2 for A_1'
2114	WRITE(numout,*) 'no real positive solution found for pft:',jv
2115	WRITE(numout,*) 'temp_air:',temp_air(icinic)
2116	WRITE(numout,*) 'vpd:',vpd(icinic)
2117	END IF
2118	A_1 = -Rd(icinic,jl)
2119	ENDIF
2120	assimi(icinic,jl) = A_1
2121
2122	IF ( ABS( assimi(icinic,jl) + Rd(icinic,jl) ) .LT. min_sechiba ) THEN
2123	gs(icinic,jl) = g0var(icinic)
2124	ELSE
2125	! Eq. 18 of Yin et al. (2009)
2126	Cc(icinic,jl) = ( gamma_star(icinic) * x1 + ( assimi(icinic,jl) + Rd(icinic,jl) ) * x2 ) &
2127	/ MAX( min_sechiba, x1 - ( assimi(icinic,jl) + Rd(icinic,jl) ) )
2128	! Eq. 17 of Yin et al. (2009)
2129	leaf_ci(icinic,jv,jl) = Cc(icinic,jl) + assimi(icinic,jl) / gm(icinic)
2130	! See eq. right after eq. 15 of Yin et al. (2009)
2131	ci_star = gamma_star(icinic) - Rd(icinic,jl) / gm(icinic)
2132	!
2133	! Eq. 15 of Yin et al. (2009)
2134	gs(icinic,jl) = g0var(icinic) + ( assimi(icinic,jl) + Rd(icinic,jl) ) / ( leaf_ci(icinic,jv,jl) &
2135	- ci_star ) * fvpd(icinic)
2136	ENDIF
2137	ENDDO
2138	ENDIF
2139	ENDIF
2140	!
2141	IF (nic .GT. 0) THEN
2142	!
2143	DO inic=1,nic
2144	!
2145	! @addtogroup Photosynthesis
2146	! @{
2147	!
2148	!! 2.4.4 Estimatation of the stomatal conductance (Ball et al., 1987).\n
2149	!! \latexonly
2150	!! \input{diffuco_trans_co2_2.4.4.tex}
2151	!! \endlatexonly
2152	! @}
2153	!
2154	icinic=index_calc(inic)
2155	!
2156	! keep stomatal conductance of topmost level
2157	!
2158	IF ( jl .EQ. 1 ) THEN
2159	leaf_gs_top(icinic) = gs(icinic,jl)
2160	!
2161	ENDIF
2162	!
2163	! @addtogroup Photosynthesis
2164	! @{
2165	!
2166	!! 2.4.5 Integration at the canopy level\n
2167	!! \latexonly
2168	!! \input{diffuco_trans_co2_2.4.5.tex}
2169	!! \endlatexonly
2170	! @}
2171	! total assimilation and conductance
2172	assimtot(icinic) = assimtot(icinic) + &
2173	assimi(icinic,jl) * (laitab(jl+1)-laitab(jl))
2174	Rdtot(icinic) = Rdtot(icinic) + &
2175	Rd(icinic,jl) * (laitab(jl+1)-laitab(jl))
2176	gstot(icinic) = gstot(icinic) + &
2177	gs(icinic,jl) * (laitab(jl+1)-laitab(jl))
2178	!
2179	ilai(icinic) = jl
2180	!
2181	ENDDO
2182	!
2183	ENDIF
2184	ENDDO ! loop over LAI steps
2185
2186	IF(jv==testpft) THEN
2187	CALL histwrite_p(hist_id, 'Cc', kjit, Cc, kjpindex*(nlai+1), indexlai)
2188	CALL histwrite_p(hist_id, 'Vc', kjit, Vc2, kjpindex*(nlai+1), indexlai)
2189	CALL histwrite_p(hist_id, 'Vj', kjit, JJ, kjpindex*(nlai+1), indexlai)
2190	CALL histwrite_p(hist_id, 'limitphoto', kjit, info_limitphoto, kjpindex*(nlai+1), indexlai)
2191	CALL histwrite_p(hist_id, 'gammastar', kjit, gamma_star, kjpindex,index)
2192	CALL histwrite_p(hist_id, 'Kmo', kjit, Kmo, kjpindex,index)
2193	CALL histwrite_p(hist_id, 'Kmc', kjit, Kmc, kjpindex,index)
2194	CALL histwrite_p(hist_id, 'gm', kjit, gm, kjpindex, index)
2195	CALL histwrite_p(hist_id, 'gs', kjit, gs, kjpindex*(nlai+1), indexlai)
2196	CALL histwrite_p(hist_id, 'assimi', kjit, assimi, kjpindex*(nlai+1), indexlai)
2197	CALL histwrite_p(hist_id, 'Rd', kjit, Rd, kjpindex*(nlai+1), indexlai)
2198	ENDIF
2199	!! Calculated intercellular CO2 over nlai needed for the chemistry module
2200	cim(:,jv)=0.
2201	laisum(:)=0
2202	DO jl=1,nlai
2203	WHERE (laitab(jl) .LE. lai(:,jv) )
2204	cim(:,jv)= cim(:,jv)+leaf_ci(:,jv,jl)*(laitab(jl+1)-laitab(jl))
2205	laisum(:)=laisum(:)+ (laitab(jl+1)-laitab(jl))
2206	ENDWHERE
2207	ENDDO
2208	WHERE (laisum(:)>0)
2209	cim(:,jv)= cim(:,jv)/laisum(:)
2210	ENDWHERE
2211
2212
2213	!
2214	!! 2.5 Calculate resistances
2215	!
2216	IF (nia .GT. 0) THEN
2217	!
2218	DO inia=1,nia
2219	!
2220	iainia=index_assi(inia)
2221
2222	!! Mean stomatal conductance for CO2 (mol m-2 s-1)
2223	gsmean(iainia,jv) = gstot(iainia)
2224	!
2225	! cimean is the "mean ci" calculated in such a way that assimilation
2226	! calculated in enerbil is equivalent to assimtot
2227	!
2228	IF ( ABS(gsmean(iainia,jv)-g0var(iainia)*laisum(iainia)) .GT. min_sechiba) THEN
2229	cimean(iainia,jv) = (fvpd(iainia)*(assimtot(iainia)+Rdtot(iainia))) /&
2230	(gsmean(iainia,jv)-g0var(iainia)*laisum(iainia)) + gamma_star(iainia)
2231	ELSE
2232	cimean(iainia,jv) = gamma_star(iainia)
2233	ENDIF
2234
2235	! conversion from umol m-2 (PFT) s-1 to gC m-2 (mesh area) tstep-1
2236	gpp(iainia,jv) = assimtot(iainia)12e-6veget_max(iainia,jv)*dt_sechiba
2237
2238	!
2239	! conversion from mol/m^2/s to m/s
2240	!
2241	! As in Pearcy, Schulze and Zimmermann
2242	! Measurement of transpiration and leaf conductance
2243	! Chapter 8 of Plant Physiological Ecology
2244	! Field methods and instrumentation, 1991
2245	! Editors:
2246	!
2247	! Robert W. Pearcy,
2248	! James R. Ehleringer,
2249	! Harold A. Mooney,
2250	! Philip W. Rundel
2251	!
2252	! ISBN: 978-0-412-40730-7 (Print) 978-94-010-9013-1 (Online)
2253
2254	gstot(iainia) = mol_to_m_1 (temp_air(iainia)/tp_00)&
2255	(pb_std/pb(iainia))gstot(iainia)ratio_H2O_to_CO2
2256	gstop(iainia) = mol_to_m_1 * (temp_air(iainia)/tp_00)*&
2257	(pb_std/pb(iainia))leaf_gs_top(iainia)ratio_H2O_to_CO2*&
2258	laitab(ilai(iainia)+1)
2259	!
2260	rveget(iainia,jv) = un/gstop(iainia)
2261
2262	!
2263	!
2264	! rstruct is the difference between rtot (=1./gstot) and rveget
2265	!
2266	! Correction Nathalie - le 27 Mars 2006 - Interdire a rstruct d'etre negatif
2267	!rstruct(iainia,jv) = un/gstot(iainia) - &
2268	! rveget(iainia,jv)
2269	rstruct(iainia,jv) = MAX( un/gstot(iainia) - &
2270	rveget(iainia,jv), min_sechiba)
2271	!
2272	!
2273	!! wind is a global variable of the diffuco module.
2274	speed = MAX(min_wind, wind(iainia))
2275	!
2276	! beta for transpiration
2277	!
2278	! Corrections Nathalie - 28 March 2006 - on advices of Fred Hourdin
2279	!! Introduction of a potentiometer rveg_pft to settle the rveg+rstruct sum problem in the coupled mode.
2280	!! rveg_pft=1 in the offline mode. rveg_pft is a global variable declared in the diffuco module.
2281	!vbeta3(iainia,jv) = veget_max(iainia,jv) * &
2282	! (un - zqsvegrap(iainia)) * &
2283	! (un / (un + speed * q_cdrag(iainia) * (rveget(iainia,jv) + &
2284	! rstruct(iainia,jv))))
2285	!! Global resistance of the canopy to evaporation
2286	cresist=(un / (un + speed * q_cdrag(iainia) * &
2287	veget(iainia,jv)/veget_max(iainia,jv) * &
2288	(rveg_pft(jv)*(rveget(iainia,jv) + rstruct(iainia,jv)))))
2289
2290	IF ( humrel(iainia,jv) >= min_sechiba ) THEN
2291	vbeta3(iainia,jv) = veget(iainia,jv) * &
2292	(un - zqsvegrap(iainia)) * cresist + &
2293	MIN( vbeta23(iainia,jv), veget(iainia,jv) * &
2294	zqsvegrap(iainia) * cresist )
2295	ELSE
2296	! Because of a minimum conductance g0, vbeta3 cannot be zero even if humrel=0
2297	! in the above equation.
2298	! Here, we force transpiration to be zero when the soil cannot deliver it
2299	vbeta3(iainia,jv) = zero
2300	END IF
2301
2302	! vbeta3pot for computation of potential transpiration (needed for irrigation)
2303	vbeta3pot(iainia,jv) = MAX(zero, veget(iainia,jv) * cresist)
2304	!
2305	!
2306	ENDDO
2307	!
2308	ENDIF
2309	!
2310	END DO ! loop over vegetation types
2311	!
2312
2313
2314	IF (printlev>=3) WRITE (numout,*) ' diffuco_trans_co2 done '
2315
2316
2317	END SUBROUTINE diffuco_trans_co2
2318
2319
2320	!! ================================================================================================================================
2321	!! SUBROUTINE : diffuco_comb
2322	!!
2323	!>\BRIEF This routine combines the previous partial beta
2324	!! coefficients and calculates the total alpha and complete beta coefficients.
2325	!!
2326	!! DESCRIPTION : Those integrated coefficients are used to calculate (in enerbil.f90) the total evapotranspiration
2327	!! from the grid-cell. \n
2328	!!
2329	!! In the case that air is more humid than surface, dew deposition can occur (negative latent heat flux).
2330	!! In this instance, for temperature above zero, all of the beta coefficients are set to 0, except for
2331	!! interception (vbeta2) and bare soil (vbeta4 with zero soil resistance). The amount of water that is
2332	!! intercepted by leaves is calculated based on the value of LAI of the surface. In the case of freezing
2333	!! temperatures, water is added to the snow reservoir, and so vbeta4 and vbeta2 are set to 0, and the
2334	!! total vbeta is set to 1.\n
2335	!!
2336	!! \latexonly
2337	!! \input{diffucocomb1.tex}
2338	!! \endlatexonly
2339	!!
2340	!! The beta and alpha coefficients are initially set to 1.
2341	!! \latexonly
2342	!! \input{diffucocomb2.tex}
2343	!! \endlatexonly
2344	!!
2345	!! If snow is lower than the critical value:
2346	!! \latexonly
2347	!! \input{diffucocomb3.tex}
2348	!! \endlatexonly
2349	!! If in the presence of dew:
2350	!! \latexonly
2351	!! \input{diffucocomb4.tex}
2352	!! \endlatexonly
2353	!!
2354	!! Determine where the water goes (soil, vegetation, or snow)
2355	!! when air moisture exceeds saturation.
2356	!! \latexonly
2357	!! \input{diffucocomb5.tex}
2358	!! \endlatexonly
2359	!!
2360	!! If it is not freezing dew is put into the interception reservoir and onto the bare soil. If it is freezing,
2361	!! water is put into the snow reservoir.
2362	!! Now modify vbetas where necessary: for soil and snow
2363	!! \latexonly
2364	!! \input{diffucocomb6.tex}
2365	!! \endlatexonly
2366	!!
2367	!! and for vegetation
2368	!! \latexonly
2369	!! \input{diffucocomb7.tex}
2370	!! \endlatexonly
2371	!!
2372	!! Then compute part of dew that can be intercepted by leafs.
2373	!!
2374	!! There will be no transpiration when air moisture is too high, under any circumstance
2375	!! \latexonly
2376	!! \input{diffucocomb8.tex}
2377	!! \endlatexonly
2378	!!
2379	!! There will also be no interception loss on bare soil, under any circumstance.
2380	!! \latexonly
2381	!! \input{diffucocomb9.tex}
2382	!! \endlatexonly
2383	!!
2384	!! The flowchart details the 'decision tree' which underlies the module.
2385	!!
2386	!! RECENT CHANGE(S): None
2387	!!
2388	!! MAIN OUTPUT VARIABLE(S): vbeta1, vbeta4, humrel, vbeta2, vbeta3, vbeta
2389	!!
2390	!! REFERENCE(S) :
2391	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
2392	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
2393	!! Circulation Model. Journal of Climate, 6, pp.248-273
2394	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influences de l'irrigation
2395	!! sur le cycle de l'eau, PhD Thesis, available from:
2396	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
2397	!!
2398	!! FLOWCHART :
2399	!! \latexonly
2400	!! \includegraphics[scale=0.25]{diffuco_comb_flowchart.png}
2401	!! \endlatexonly
2402	!! \n
2403	!_ ================================================================================================================================
2404
2405	SUBROUTINE diffuco_comb (kjpindex, humrel, rau, u, v, q_cdrag, pb, qair, temp_sol, temp_air, &
2406	& snow, veget, lai, tot_bare_soil, vbeta1, vbeta2, vbeta3 , vbeta4, &
2407	& evap_bare_lim, evap_bare_lim_ns, veget_max, vbeta, qsintmax)
2408
2409	! Ajout qsintmax dans les arguments de la routine Nathalie / le 13-03-2006
2410
2411	!! 0. Variable and parameter declaration
2412
2413	!! 0.1 Input variables
2414
2415	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
2416	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: rau !! Air Density (kg m^{-3})
2417	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind speed (m s^{-1})
2418	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Nortward Lowest level wind speed (m s^{-1})
2419	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
2420	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: pb !! Lowest level pressure (hPa)
2421	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: qair !! Lowest level specific air humidity (kg kg^{-1})
2422	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_sol !! Skin temperature (K)
2423	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: temp_air !! Lower air temperature (K)
2424	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: snow !! Snow mass (kg)
2425	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget !! Fraction of vegetation type (fraction)
2426	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: lai !! Leaf area index (m^2 m^{-2})
2427	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: qsintmax !! Maximum water on vegetation (kg m^{-2})
2428	REAL(r_std), DIMENSION (kjpindex), INTENT(in) :: tot_bare_soil!! Total evaporating bare soil fraction
2429	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (in) :: veget_max !! Max. fraction of vegetation type (LAI->infty)
2430
2431	!! 0.2 Output variables
2432
2433	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: vbeta !! Total beta coefficient (-)
2434
2435	!! 0.3 Modified variables
2436
2437	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: vbeta1 !! Beta for sublimation (-)
2438	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: vbeta4 !! Beta for Bare soil evaporation (-)
2439	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (inout) :: humrel !! Soil moisture stress (within range 0 to 1)
2440	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (inout) :: vbeta2 !! Beta for interception loss (-)
2441	REAL(r_std),DIMENSION (kjpindex,nvm), INTENT (inout) :: vbeta3 !! Beta for Transpiration (-)
2442	REAL(r_std),DIMENSION (kjpindex), INTENT (inout) :: evap_bare_lim !! limiting factor for bare soil evaporation
2443	!! when the 11-layer hydrology is used (-)
2444	REAL(r_std),DIMENSION (kjpindex,nstm), INTENT (inout):: evap_bare_lim_ns !! limiting factor for bare soil evaporation
2445	!! when the 11-layer hydrology is used (-)
2446	!! 0.4 Local variables
2447
2448	INTEGER(i_std) :: ji, jv
2449	REAL(r_std) :: zevtest, zsoil_moist, zrapp
2450	REAL(r_std), DIMENSION(kjpindex) :: qsatt
2451	LOGICAL, DIMENSION(kjpindex) :: toveg, tosnow
2452	REAL(r_std) :: coeff_dew_veg
2453	REAL(r_std), DIMENSION(kjpindex) :: vegtot
2454	!_ ================================================================================================================================
2455
2456	!! 1 If we are in presence of dew
2457
2458	CALL qsatcalc (kjpindex, temp_sol, pb, qsatt)
2459
2460
2461	!! 1.1 Determine where the water goes
2462	!! Determine where the water goes (soil, vegetation, or snow)
2463	!! when air moisture exceeds saturation.
2464	!! \latexonly
2465	!! \input{diffucocomb5.tex}
2466	!! \endlatexonly
2467	toveg(:) = .FALSE.
2468	tosnow(:) = .FALSE.
2469	DO ji = 1, kjpindex
2470	IF ( qsatt(ji) .LT. qair(ji) ) THEN
2471	IF (temp_air(ji) .GT. tp_00) THEN
2472	!! If it is not freezing dew is put into the
2473	!! interception reservoir and onto the bare soil.
2474	toveg(ji) = .TRUE.
2475	ELSE
2476	!! If it is freezing water is put into the
2477	!! snow reservoir.
2478	tosnow(ji) = .TRUE.
2479	ENDIF
2480	ENDIF
2481	END DO
2482
2483	!! 1.2 Now modify vbetas where necessary.
2484
2485	!! 1.2.1 Soil and snow
2486	!! \latexonly
2487	!! \input{diffucocomb6.tex}
2488	!! \endlatexonly
2489
2490	! We need to keep consistency between evap_bare_lim, evap_bare_lim_ns and vbeta4 (thus vevapnu)
2491	! or we have a water conservation issue in hydrol_split_soil
2492
2493	DO ji = 1, kjpindex
2494
2495	IF ( toveg(ji) ) THEN
2496
2497	vbeta1(ji) = zero
2498	vegtot(ji) = SUM(veget_max(ji,:))
2499
2500	IF ( (tot_bare_soil(ji) .GT. min_sechiba) .AND. (vegtot(ji).GT. min_sechiba) ) THEN
2501
2502	vbeta4(ji) = tot_bare_soil(ji)
2503
2504	evap_bare_lim_ns(ji,:) = tot_bare_soil(ji)/vegtot(ji)
2505
2506	evap_bare_lim(ji) = vbeta4(ji)
2507	! consistent with evap_bare_lim(ji) = SUM(evap_bare_lim_ns(ji,:)soiltile(ji,:)vegtot(ji))
2508	! as SUM(soiltile(ji,:)) = 1
2509
2510	ELSE
2511	vbeta4(ji) = zero
2512	evap_bare_lim_ns(ji,:) = zero
2513	evap_bare_lim(ji) = zero
2514	ENDIF
2515	ENDIF
2516
2517	IF ( tosnow(ji) ) THEN
2518	vbeta1(ji) = un
2519	vbeta4(ji) = zero
2520	evap_bare_lim_ns(ji,:) = zero
2521	evap_bare_lim(ji) = zero
2522	ENDIF
2523
2524	ENDDO
2525
2526	!! 1.2.2 Vegetation and interception loss
2527	!! \latexonly
2528	!! \input{diffucocomb7.tex}
2529	!! \endlatexonly
2530	DO jv = 1, nvm
2531
2532	DO ji = 1, kjpindex
2533
2534	IF ( toveg(ji) ) THEN
2535	IF (qsintmax(ji,jv) .GT. min_sechiba) THEN
2536
2537	! Compute part of dew that can be intercepted by leafs.
2538	IF ( lai(ji,jv) .GT. min_sechiba) THEN
2539	IF (lai(ji,jv) .GT. 1.5) THEN
2540	coeff_dew_veg= &
2541	& dew_veg_poly_coeff(6)lai(ji,jv)*5 &
2542	& - dew_veg_poly_coeff(5)lai(ji,jv)*4 &
2543	& + dew_veg_poly_coeff(4)lai(ji,jv)*3 &
2544	& - dew_veg_poly_coeff(3)lai(ji,jv)*2 &
2545	& + dew_veg_poly_coeff(2)*lai(ji,jv) &
2546	& + dew_veg_poly_coeff(1)
2547	ELSE
2548	coeff_dew_veg=un
2549	ENDIF
2550	ELSE
2551	coeff_dew_veg=zero
2552	ENDIF
2553	IF (jv .EQ. 1) THEN
2554	! This line may not work with CWRR when frac_bare is distributed among three soiltiles
2555	! Fortunately, qsintmax(ji,1)=0 (LAI=0 in PFT1) so we never pass here
2556	vbeta2(ji,jv) = coeff_dew_veg*tot_bare_soil(ji)
2557	ELSE
2558	vbeta2(ji,jv) = coeff_dew_veg*veget(ji,jv)
2559	ENDIF
2560	ELSE
2561	vbeta2(ji,jv) = zero ! if qsintmax=0, vbeta2=0
2562	ENDIF
2563	ENDIF
2564	IF ( tosnow(ji) ) vbeta2(ji,jv) = zero
2565
2566	ENDDO
2567
2568	ENDDO
2569
2570	!! 1.2.3 Vegetation and transpiration
2571	!! There will be no transpiration when air moisture is too high, under any circumstance
2572	!! \latexonly
2573	!! \input{diffucocomb8.tex}
2574	!! \endlatexonly
2575	DO jv = 1, nvm
2576	DO ji = 1, kjpindex
2577	IF ( qsatt(ji) .LT. qair(ji) ) THEN
2578	vbeta3(ji,jv) = zero
2579	humrel(ji,jv) = zero
2580	ENDIF
2581	ENDDO
2582	ENDDO
2583
2584
2585	!! 1.2.4 Overrules 1.2.2
2586	!! There will also be no interception loss on bare soil, under any circumstance.
2587	!! \latexonly
2588	!! \input{diffucocomb9.tex}
2589	!! \endlatexonly
2590	DO ji = 1, kjpindex
2591	IF ( qsatt(ji) .LT. qair(ji) ) THEN
2592	vbeta2(ji,1) = zero
2593	ENDIF
2594	ENDDO
2595
2596	!! 2 Now calculate vbeta in all cases (the equality needs to hold for enerbil to be consistent)
2597
2598	DO ji = 1, kjpindex
2599	vbeta(ji) = vbeta4(ji) + SUM(vbeta2(ji,:)) + SUM(vbeta3(ji,:))
2600
2601	IF (vbeta(ji) .LT. min_sechiba) THEN
2602	vbeta(ji) = zero
2603	vbeta4(ji) = zero
2604	vbeta2(ji,:)= zero
2605	vbeta3(ji,:)= zero
2606	evap_bare_lim_ns(ji,:) = zero
2607	evap_bare_lim(ji) = zero
2608	END IF
2609	ENDDO
2610
2611	CALL xios_orchidee_send_field("evap_bare_lim",evap_bare_lim)
2612	CALL xios_orchidee_send_field("evap_bare_lim_ns",evap_bare_lim_ns)
2613
2614	IF (printlev>=3) WRITE (numout,*) ' diffuco_comb done '
2615
2616	END SUBROUTINE diffuco_comb
2617
2618
2619	!! ================================================================================================================================
2620	!! SUBROUTINE : diffuco_raerod
2621	!!
2622	!>\BRIEF Computes the aerodynamic resistance, for cases in which the
2623	!! surface drag coefficient is provided by the coupled atmospheric model LMDZ and when the flag
2624	!! 'ldq_cdrag_from_gcm' is set to TRUE
2625	!!
2626	!! DESCRIPTION : Simply computes the aerodynamic resistance, for cases in which the
2627	!! surface drag coefficient is provided by the coupled atmospheric model LMDZ. If the surface drag coefficient
2628	!! is not provided by the LMDZ or signalled by the flag 'ldq_cdrag_from_gcm' set to FALSE, then the subroutine
2629	!! diffuco_aero is called instead of this one.
2630	!!
2631	!! Calculation of the aerodynamic resistance, for diganostic purposes. First calculate wind speed:
2632	!! \latexonly
2633	!! \input{diffucoaerod1.tex}
2634	!! \endlatexonly
2635	!!
2636	!! next calculate ::raero
2637	!! \latexonly
2638	!! \input{diffucoaerod2.tex}
2639	!! \endlatexonly
2640	!!
2641	!! RECENT CHANGE(S): None
2642	!!
2643	!! MAIN OUTPUT VARIABLE(S): ::raero
2644	!!
2645	!! REFERENCE(S) :
2646	!! - de Noblet-DucoudrÃ©, N, Laval, K & Perrier, A, 1993. SECHIBA, a new set of parameterisations
2647	!! of the hydrologic exchanges at the land-atmosphere interface within the LMD Atmospheric General
2648	!! Circulation Model. Journal of Climate, 6, pp.248-273
2649	!! - Guimberteau, M, 2010. ModÃ©lisation de l'hydrologie continentale et influence de l'irrigation
2650	!! sur le cycle de l'eau, PhD Thesis, available from:
2651	!! http://www.sisyphe.upmc.fr/~guimberteau/docs/manuscrit_these.pdf
2652	!!
2653	!! FLOWCHART : None
2654	!! \n
2655	!_ ================================================================================================================================
2656
2657	SUBROUTINE diffuco_raerod (kjpindex, u, v, q_cdrag, raero)
2658
2659	IMPLICIT NONE
2660
2661	!! 0. Variable and parameter declaration
2662
2663	!! 0.1 Input variables
2664
2665	INTEGER(i_std), INTENT(in) :: kjpindex !! Domain size (-)
2666	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: u !! Eastward Lowest level wind velocity (m s^{-1})
2667	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: v !! Northward Lowest level wind velocity (m s^{-1})
2668	REAL(r_std),DIMENSION (kjpindex), INTENT (in) :: q_cdrag !! Surface drag coefficient (-)
2669
2670	!! 0.2 Output variables
2671
2672	REAL(r_std),DIMENSION (kjpindex), INTENT (out) :: raero !! Aerodynamic resistance (s m^{-1})
2673
2674	!! 0.3 Modified variables
2675
2676	!! 0.4 Local variables
2677
2678	INTEGER(i_std) :: ji !! (-)
2679	REAL(r_std) :: speed !! (m s^{-1})
2680	!_ ================================================================================================================================
2681
2682	!! 1. Simple calculation of the aerodynamic resistance, for diganostic purposes.
2683
2684	DO ji=1,kjpindex
2685
2686	!! \latexonly
2687	!! \input{diffucoaerod1.tex}
2688	!! \endlatexonly
2689	speed = MAX(min_wind, wind(ji))
2690
2691	!! \latexonly
2692	!! \input{diffucoaerod2.tex}
2693	!! \endlatexonly
2694	raero(ji) = un / (q_cdrag(ji)*speed)
2695
2696	ENDDO
2697
2698	END SUBROUTINE diffuco_raerod
2699
2700
2701	FUNCTION Arrhenius (kjpindex,temp,ref_temp,energy_act) RESULT ( val_arrhenius )
2702	!! 0.1 Input variables
2703
2704	INTEGER(i_std),INTENT(in) :: kjpindex !! Domain size (-)
2705	REAL(r_std),DIMENSION(kjpindex),INTENT(in) :: temp !! Temperature (K)
2706	REAL(r_std), INTENT(in) :: ref_temp !! Temperature of reference (K)
2707	REAL(r_std),INTENT(in) :: energy_act !! Activation Energy (J mol-1)
2708
2709	!! 0.2 Result
2710
2711	REAL(r_std), DIMENSION(kjpindex) :: val_arrhenius !! Temperature dependance based on
2712	!! a Arrhenius function (-)
2713
2714	val_arrhenius(:)=EXP(((temp(:)-ref_temp)energy_act)/(ref_tempRR*(temp(:))))
2715	END FUNCTION Arrhenius
2716
2717	FUNCTION Arrhenius_modified_1d (kjpindex,temp,ref_temp,energy_act,energy_deact,entropy) RESULT ( val_arrhenius )
2718	!! 0.1 Input variables
2719
2720	INTEGER(i_std),INTENT(in) :: kjpindex !! Domain size (-)
2721	REAL(r_std),DIMENSION(kjpindex),INTENT(in) :: temp !! Temperature (K)
2722	REAL(r_std), INTENT(in) :: ref_temp !! Temperature of reference (K)
2723	REAL(r_std),INTENT(in) :: energy_act !! Activation Energy (J mol-1)
2724	REAL(r_std),INTENT(in) :: energy_deact !! Deactivation Energy (J mol-1)
2725	REAL(r_std),DIMENSION(kjpindex),INTENT(in) :: entropy !! Entropy term (J K-1 mol-1)
2726
2727	!! 0.2 Result
2728
2729	REAL(r_std), DIMENSION(kjpindex) :: val_arrhenius !! Temperature dependance based on
2730	!! a Arrhenius function (-)
2731
2732	val_arrhenius(:)=EXP(((temp(:)-ref_temp)energy_act)/(ref_tempRR*(temp(:)))) &
2733	* (1. + EXP( (ref_temp * entropy(:) - energy_deact) / (ref_temp * RR ))) &
2734	/ (1. + EXP( (temp(:) * entropy(:) - energy_deact) / ( RR*temp(:))))
2735
2736	END FUNCTION Arrhenius_modified_1d
2737
2738	FUNCTION Arrhenius_modified_0d (kjpindex,temp,ref_temp,energy_act,energy_deact,entropy) RESULT ( val_arrhenius )
2739	!! 0.1 Input variables
2740
2741	INTEGER(i_std),INTENT(in) :: kjpindex !! Domain size (-)
2742	REAL(r_std),DIMENSION(kjpindex),INTENT(in) :: temp !! Temperature (K)
2743	REAL(r_std), INTENT(in) :: ref_temp !! Temperature of reference (K)
2744	REAL(r_std),INTENT(in) :: energy_act !! Activation Energy (J mol-1)
2745	REAL(r_std),INTENT(in) :: energy_deact !! Deactivation Energy (J mol-1)
2746	REAL(r_std),INTENT(in) :: entropy !! Entropy term (J K-1 mol-1)
2747
2748	!! 0.2 Result
2749
2750	REAL(r_std), DIMENSION(kjpindex) :: val_arrhenius !! Temperature dependance based on
2751	!! a Arrhenius function (-)
2752
2753	val_arrhenius(:)=EXP(((temp(:)-ref_temp)energy_act)/(ref_tempRR*(temp(:)))) &
2754	* (1. + EXP( (ref_temp * entropy - energy_deact) / (ref_temp * RR ))) &
2755	/ (1. + EXP( (temp(:) * entropy - energy_deact) / ( RR*temp(:))))
2756
2757	END FUNCTION Arrhenius_modified_0d
2758
2759
2760	END MODULE diffuco

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