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source: palm/trunk/SOURCE/land_surface_model.f90 @ 1496

Last change on this file since 1496 was 1496, checked in by maronga, 9 years ago
added beta version of a land surface model and a simple radiation model for clear sky conditions
Property svn:keywords set to `Id`
File size: 51.4 KB

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1	MODULE land_surface_model_mod
2
3	!--------------------------------------------------------------------------------!
4	! This file is part of PALM.
5	!
6	! PALM is free software: you can redistribute it and/or modify it under the terms
7	! of the GNU General Public License as published by the Free Software Foundation,
8	! either version 3 of the License, or (at your option) any later version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 1997-2014 Leibniz Universitaet Hannover
18	!--------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	! Initial revision
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: land_surface_model.f90 1496 2014-12-02 17:25:50Z maronga $
27	!
28	!
29	! Description:
30	! ------------
31	! Land surface model, consisting of a solver for the energy balance at the
32	! surface and a four layer soil scheme. The scheme is similar to the TESSEL
33	! scheme implemented in the ECMWF IFS model, with modifications according to
34	! H-TESSEL. The implementation is based on the formulation implemented in the
35	! DALES model.
36	!------------------------------------------------------------------------------!
37	USE arrays_3d, &
38	ONLY: pt, pt_p, q, q_p, qsws, rif, shf, ts, us, z0, z0h
39
40	USE cloud_parameters, &
41	ONLY: cp, l_d_r, l_v, rho_l, r_d, r_v
42
43	USE control_parameters, &
44	ONLY: dt_3d, humidity, intermediate_timestep_count, &
45	intermediate_timestep_count_max, pt_surface, rho_surface, &
46	surface_pressure, timestep_scheme, tsc
47
48	USE indices, &
49	ONLY: nxlg, nxrg, nyng, nysg, nzb_s_inner
50
51	USE kinds
52
53	USE radiation_model_mod, &
54	ONLY: Rn, SW_in, sigma_SB
55
56
57	IMPLICIT NONE
58
59	!
60	!-- LSM model constants
61	INTEGER(iwp), PARAMETER :: soil_layers = 4 !: number of soil layers (fixed for now)
62
63	REAL(wp), PARAMETER :: &
64	b_CH = 6.04_wp, & ! Clapp & Hornberger exponent
65	lambda_h_dry = 0.19_wp, & ! heat conductivity for dry soil
66	lambda_h_sm = 3.44_wp, & ! heat conductivity of the soil matrix
67	lambda_h_water = 0.57_wp, & ! heat conductivity of water
68	psi_sat = -0.388_wp, & ! soil matrix potential at saturation
69	rhoC_soil = 2.19E6_wp, & ! volumetric heat capacity of soil
70	rhoC_water = 4.20E6_wp, & ! volumetric heat capacity of water
71	m_max_depth = 0.0002_wp ! Maximum capacity of the water reservoir (m)
72
73
74	!
75	!-- LSM variables
76	INTEGER(iwp) :: veg_type = 2, & !: vegetation type, 0: user-defined, 1-19: generic (see list)
77	soil_type = 3 !: soil type, 0: user-defined, 1-6: generic (see list)
78
79	LOGICAL :: conserve_water_content = .TRUE., & !: open or closed bottom surface for the soil model
80	land_surface = .FALSE. !: flag parameter indicating wheather the lsm is used
81
82	! value 9999999.9_wp -> generic available or user-defined value must be set
83	! otherwise -> no generic variable and user setting is optional
84	REAL(wp) :: alpha_VanGenuchten = 0.0_wp, & !: NAMELIST alpha_VG
85	canopy_resistance_coefficient = 0.0_wp, & !: NAMELIST gD
86	C_skin = 20000.0_wp, & !: Skin heat capacity
87	drho_l_lv, & !: (rho_l * l_v)**-1
88	exn, & !: value of the Exner function
89	e_s = 0.0_wp, & !: saturation water vapour pressure
90	field_capacity = 0.0_wp, & !: NAMELIST m_fc
91	f_shortwave_incoming = 9999999.9_wp, & !: NAMELIST f_SW_in
92	hydraulic_conductivity = 0.0_wp, & !: NAMELIST gamma_w_sat
93	Ke = 0.0_wp, & !: Kersten number
94	lambda_skin_stable = 9999999.9_wp, & !: NAMELIST lambda_skin_s
95	lambda_skin_unstable = 9999999.9_wp, & !: NAMELIST lambda_skin_u
96	leaf_area_index = 9999999.9_wp, & !: NAMELIST LAI
97	l_VanGenuchten = 0.0_WP, & !: NAMELIST l_VG
98	min_canopy_resistance = 110.0_wp, & !: NAMELIST r_s_min
99	m_total = 0.0_wp, & !: weighed total water content of the soil (m3/m3)
100	n_VanGenuchten = 0.0_WP, & !: NAMELIST n_VG
101	q_s = 0.0_wp, & !: saturation specific humidity
102	residual_moisture = 0.0_wp, & !: NAMELIST m_res
103	rho_cp, & !: rho_surface * cp
104	rho_lv, & !: rho * l_v
105	rd_d_rv, & !: r_d / r_v
106	saturation_moisture = 0.0_wp, & !: NAMELIST m_sat
107	vegetation_coverage = 9999999.9_wp, & !: NAMELIST c_veg
108	wilting_point = 0.0_wp !: NAMELIST m_wilt
109
110	REAL(wp), DIMENSION(0:soil_layers-1) :: &
111	ddz_soil, & !: 1/dz_soil
112	ddz_soil_stag, & !: 1/dz_soil_stag
113	dz_soil, & !: soil grid spacing (center-center)
114	dz_soil_stag, & !: soil grid spacing (edge-edge)
115	root_extr = 0.0_wp, & !: root extraction
116	root_fraction = (/0.35_wp, 0.38_wp, 0.23_wp, 0.04_wp/), & !: distribution of root surface area to the individual soil layers
117	soil_level = (/0.07_wp, 0.28_wp, 1.00_wp, 2.89_wp/), & !: soil layer depths (m)
118	soil_moisture = 0.0_wp !: soil moisture content (m3/m3)
119
120	REAL(wp), DIMENSION(0:soil_layers) :: &
121	soil_temperature = 9999999.9_wp !: soil temperature (K)
122
123	#if defined( __nopointer )
124	REAL(wp), DIMENSION(:,:), ALLOCATABLE, TARGET :: T_0, & !: skin temperature (K)
125	T_0_p, & !: progn. skin temperature (K)
126	m_liq, & !: liquid water reservoir (m)
127	m_liq_p !: progn. liquid water reservoir (m)
128	#else
129	REAL(wp), DIMENSION(:,:), POINTER :: T_0, &
130	T_0_p, &
131	m_liq, &
132	m_liq_p
133
134	REAL(wp), DIMENSION(:,:), ALLOCATABLE, TARGET :: T_0_1, T_0_2, &
135	m_liq_1, m_liq_2
136	#endif
137
138	!
139	!-- Temporal tendencies for time stepping
140	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: tT_0_m, & !: skin temperature tendency (K)
141	tm_liq_m !: liquid water reservoir tendency (m)
142
143	!
144	!-- Energy balance variables
145	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: &
146	alpha_VG, & !: coef. of Van Genuchten
147	c_liq, & !: liquid water coverage (of vegetated area)
148	c_veg, & !: vegetation coverage
149	f_SW_in, & !: ?
150	G, & !: surface soil heat flux
151	H, & !: surface flux of sensible heat
152	gamma_w_sat, & !: hydraulic conductivity at saturation
153	gD, & !: coefficient for dependence of r_canopy on water vapour pressure deficit
154	LAI, & !: leaf area index
155	LE, & !: surface flux of latent heat (total)
156	LE_veg, & !: surface flux of latent heat (vegetation portion)
157	LE_soil, & !: surface flux of latent heat (soil portion)
158	LE_liq, & !: surface flux of latent heat (liquid water portion)
159	lambda_h_sat, & !: heat conductivity for dry soil
160	lambda_skin_s, & !: coupling between skin and soil (depends on vegetation type)
161	lambda_skin_u, & !: coupling between skin and soil (depends on vegetation type)
162	l_VG, & !: coef. of Van Genuchten
163	m_fc, & !: soil moisture at field capacity (m3/m3)
164	m_res, & !: residual soil moisture
165	m_sat, & !: saturation soil moisture (m3/m3)
166	m_wilt, & !: soil moisture at permanent wilting point (m3/m3)
167	n_VG, & !: coef. Van Genuchten
168	r_a, & !: aerodynamic resistance
169	r_canopy, & !: canopy resistance
170	r_soil, & !: soil resitance
171	r_soil_min, & !: minimum soil resistance
172	r_s, & !: total surface resistance (combination of r_soil and r_canopy)
173	r_s_min !: minimum canopy resistance
174
175	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
176	lambda_h, & !: heat conductivity of soil (?)
177	lambda_w, & !: hydraulic diffusivity of soil (?)
178	gamma_w, & !: hydraulic conductivity of soil (?)
179	rhoC_total !: volumetric heat capacity of the actual soil matrix (?)
180
181	#if defined( __nopointer )
182	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE, TARGET :: &
183	T_soil, & !: Soil temperature (K)
184	T_soil_p, & !: Prog. soil temperature (K)
185	m_soil, & !: Soil moisture (m3/m3)
186	m_soil_p !: Prog. soil moisture (m3/m3)
187	#else
188	REAL(wp), DIMENSION(:,:,:), POINTER :: &
189	T_soil, T_soil_p, &
190	m_soil, m_soil_p
191
192	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE, TARGET :: &
193	T_soil_1, T_soil_2, &
194	m_soil_1, m_soil_2
195
196
197	#endif
198
199
200	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
201	tT_soil_m, & !: T_soil storage array
202	tm_soil_m, & !: m_soil storage array
203	root_fr !: root fraction (sum=1)
204
205	!
206	!-- Land surface parameters according to the following classes (veg_type)
207	!-- (0 user defined)
208	!-- 1 crops, mixed farming
209	!-- 2 short grass
210	!-- 3 evergreen needleleaf trees
211	!-- 4 deciduous needleleaf trees
212	!-- 5 evergreen broadleaf trees
213	!-- 6 deciduous broadleaf trees
214	!-- 7 tall grass
215	!-- 8 desert
216	!-- 9 tundra
217	!-- 10 irrigated crops
218	!-- 11 semidesert
219	!-- 12 ice caps and glaciers
220	!-- 13 bogs and marshes
221	!-- 14 inland water
222	!-- 15 ocean
223	!-- 16 evergreen shrubs
224	!-- 17 deciduous shrubs
225	!-- 18 mixed forest/woodland
226	!-- 19 interrupted forest
227
228	!
229	!-- Land surface parameters I r_s_min, LAI, c_veg, gD
230	REAL(wp), DIMENSION(0:3,1:19) :: veg_pars = RESHAPE( (/ &
231	180.0_wp, 3.00_wp, 0.90_wp, 0.00_wp, & ! 1
232	110.0_wp, 2.00_wp, 0.85_wp, 0.00_wp, & ! 2
233	500.0_wp, 5.00_wp, 0.90_wp, 0.03_wp, & ! 3
234	500.0_wp, 5.00_wp, 0.90_wp, 0.03_wp, & ! 4
235	175.0_wp, 5.00_wp, 0.90_wp, 0.03_wp, & ! 5
236	240.0_wp, 6.00_wp, 0.99_wp, 0.13_wp, & ! 6
237	100.0_wp, 2.00_wp, 0.70_wp, 0.00_wp, & ! 7
238	250.0_wp, 0.50_wp, 0.00_wp, 0.00_wp, & ! 8
239	80.0_wp, 1.00_wp, 0.50_wp, 0.00_wp, & ! 9
240	180.0_wp, 3.00_wp, 0.90_wp, 0.00_wp, & ! 10
241	150.0_wp, 0.50_wp, 0.10_wp, 0.00_wp, & ! 11
242	0.0_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 12
243	240.0_wp, 4.00_wp, 0.60_wp, 0.00_wp, & ! 13
244	0.0_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 14
245	0.0_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 15
246	225.0_wp, 3.00_wp, 0.50_wp, 0.00_wp, & ! 16
247	225.0_wp, 1.50_wp, 0.50_wp, 0.00_wp, & ! 17
248	250.0_wp, 5.00_wp, 0.90_wp, 0.03_wp, & ! 18
249	175.0_wp, 2.50_wp, 0.90_wp, 0.03_wp & ! 19
250	/), (/ 4, 19 /) )
251
252	!
253	!-- Land surface parameters II z0, z0h
254	REAL(wp), DIMENSION(0:1,1:19) :: roughness_par = RESHAPE( (/ &
255	0.25_wp, 0.25E-2_wp, & ! 1
256	0.20_wp, 0.20E-2_wp, & ! 2
257	2.00_wp, 2.00_wp, & ! 3
258	2.00_wp, 2.00_wp, & ! 4
259	2.00_wp, 2.00_wp, & ! 5
260	2.00_wp, 2.00_wp, & ! 6
261	0.47_wp, 0.47E-2_wp, & ! 7
262	0.013_wp, 0.013E-2_wp, & ! 8
263	0.034_wp, 0.034E-2_wp, & ! 9
264	0.5_wp, 0.50E-2_wp, & ! 10
265	0.17_wp, 0.17E-2_wp, & ! 11
266	1.3E-3_wp, 1.3E-4_wp, & ! 12
267	0.83_wp, 0.83E-2_wp, & ! 13
268	0.00_wp, 0.00E-2_wp, & ! 14
269	0.00_wp, 0.00E-2_wp, & ! 15
270	0.10_wp, 0.10E-2_wp, & ! 16
271	0.25_wp, 0.25E-2_wp, & ! 17
272	2.00_wp, 2.00E-2_wp, & ! 18
273	1.10_wp, 1.10E-2_wp & ! 19
274	/), (/ 2, 19 /) )
275
276	!
277	!-- Land surface parameters III lambda_skin_s, lambda_skin_u, f_SW_in
278	REAL(wp), DIMENSION(0:2,1:19) :: skin_pars = RESHAPE( (/ &
279	10.0_wp, 10.0_wp, 0.05_wp, & ! 1
280	10.0_wp, 10.0_wp, 0.05_wp, & ! 2
281	20.0_wp, 15.0_wp, 0.03_wp, & ! 3
282	20.0_wp, 15.0_wp, 0.03_wp, & ! 4
283	20.0_wp, 15.0_wp, 0.03_wp, & ! 5
284	20.0_wp, 15.0_wp, 0.03_wp, & ! 6
285	10.0_wp, 10.0_wp, 0.05_wp, & ! 7
286	15.0_wp, 15.0_wp, 0.00_wp, & ! 8
287	10.0_wp, 10.0_wp, 0.05_wp, & ! 9
288	10.0_wp, 10.0_wp, 0.05_wp, & ! 10
289	10.0_wp, 10.0_wp, 0.05_wp, & ! 11
290	58.0_wp, 58.0_wp, 0.00_wp, & ! 12
291	10.0_wp, 10.0_wp, 0.05_wp, & ! 13
292	1.0E20_wp, 1.0E20_wp, 0.00_wp, & ! 14
293	1.0E20_wp, 1.0E20_wp, 0.00_wp, & ! 15
294	10.0_wp, 10.0_wp, 0.05_wp, & ! 16
295	10.0_wp, 10.0_wp, 0.05_wp, & ! 17
296	20.0_wp, 15.0_wp, 0.03_wp, & ! 18
297	20.0_wp, 15.0_wp, 0.03_wp & ! 19
298	/), (/ 3, 19 /) )
299
300	!
301	!-- Root distribution (sum = 1) level 1, level 2, level 3, level 4,
302	REAL(wp), DIMENSION(0:3,1:19) :: root_distribution = RESHAPE( (/ &
303	0.24_wp, 0.41_wp, 0.31_wp, 0.04_wp, & ! 1
304	0.35_wp, 0.38_wp, 0.23_wp, 0.04_wp, & ! 2
305	0.26_wp, 0.39_wp, 0.29_wp, 0.06_wp, & ! 3
306	0.26_wp, 0.38_wp, 0.29_wp, 0.07_wp, & ! 4
307	0.24_wp, 0.38_wp, 0.31_wp, 0.07_wp, & ! 5
308	0.25_wp, 0.34_wp, 0.27_wp, 0.14_wp, & ! 6
309	0.27_wp, 0.27_wp, 0.27_wp, 0.09_wp, & ! 7
310	1.00_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 8
311	0.47_wp, 0.45_wp, 0.08_wp, 0.00_wp, & ! 9
312	0.24_wp, 0.41_wp, 0.31_wp, 0.04_wp, & ! 10
313	0.17_wp, 0.31_wp, 0.33_wp, 0.19_wp, & ! 11
314	0.00_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 12
315	0.25_wp, 0.34_wp, 0.27_wp, 0.11_wp, & ! 13
316	0.00_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 14
317	0.00_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 15
318	0.23_wp, 0.36_wp, 0.30_wp, 0.11_wp, & ! 16
319	0.23_wp, 0.36_wp, 0.30_wp, 0.11_wp, & ! 17
320	0.19_wp, 0.35_wp, 0.36_wp, 0.10_wp, & ! 18
321	0.19_wp, 0.35_wp, 0.36_wp, 0.10_wp & ! 19
322	/), (/ 4, 19 /) )
323
324	!
325	!-- Soil parameters according to the following porosity classes (soil_type)
326	!-- (0 user defined)
327	!-- 1 coarse
328	!-- 2 medium
329	!-- 3 medium-fine
330	!-- 4 fine
331	!-- 5 very fine
332	!-- 6 organic
333	!
334	!-- Soil parameters I alpha_VG, l_VG, n_VG, gamma_w_sat
335	REAL(wp), DIMENSION(0:3,1:6) :: soil_pars = RESHAPE( (/ &
336	3.83_wp, 1.250_wp, 1.38_wp, 6.94E-6_wp, & ! 1
337	3.14_wp, -2.342_wp, 1.28_wp, 1.16E-6_wp, & ! 2
338	0.83_wp, -0.588_wp, 1.25_wp, 0.26E-6_wp, & ! 3
339	3.67_wp, -1.977_wp, 1.10_wp, 2.87E-6_wp, & ! 4
340	2.65_wp, 2.500_wp, 1.10_wp, 1.74E-6_wp, & ! 5
341	1.30_wp, 0.400_wp, 1.20_wp, 0.93E-6_wp & ! 6
342	/), (/ 4, 6 /) )
343
344	!
345	!-- Soil parameters II m_sat, m_fc, m_wilt, m_res
346	REAL(wp), DIMENSION(0:3,1:6) :: m_soil_pars = RESHAPE( (/ &
347	0.403_wp, 0.244_wp, 0.059_wp, 0.025_wp, & ! 1
348	0.439_wp, 0.347_wp, 0.151_wp, 0.010_wp, & ! 2
349	0.430_wp, 0.383_wp, 0.133_wp, 0.010_wp, & ! 3
350	0.520_wp, 0.448_wp, 0.279_wp, 0.010_wp, & ! 4
351	0.614_wp, 0.541_wp, 0.335_wp, 0.010_wp, & ! 5
352	0.766_wp, 0.663_wp, 0.267_wp, 0.010_wp & ! 6
353	/), (/ 4, 6 /) )
354
355
356	SAVE
357
358
359	PRIVATE
360
361
362	PUBLIC alpha_VanGenuchten, C_skin, canopy_resistance_coefficient, &
363	conserve_water_content, field_capacity, f_shortwave_incoming, &
364	hydraulic_conductivity, init_lsm, lambda_skin_stable, &
365	lambda_skin_unstable, land_surface, leaf_area_index, &
366	lsm_energy_balance, lsm_soil_model, l_VanGenuchten, &
367	min_canopy_resistance, n_VanGenuchten, residual_moisture, &
368	root_fraction, saturation_moisture, soil_level, soil_moisture, &
369	soil_temperature, soil_type, vegetation_coverage, veg_type, &
370	wilting_point
371
372	#if defined( __nopointer )
373	PUBLIC m_liq, m_liq_p, m_soil, m_soil_p, T_0, T_0_p, T_soil, T_soil_p
374	#else
375	PUBLIC m_liq, m_liq_1, m_liq_2, m_liq_p, m_soil, m_soil_1, m_soil_2, &
376	m_soil_p, T_0, T_0_1, T_0_2, T_0_p, T_soil, T_soil_1, T_soil_2, &
377	T_soil_p
378	#endif
379
380
381	INTERFACE init_lsm
382	MODULE PROCEDURE init_lsm
383	END INTERFACE init_lsm
384
385	INTERFACE lsm_energy_balance
386	MODULE PROCEDURE lsm_energy_balance
387	END INTERFACE lsm_energy_balance
388
389	INTERFACE lsm_soil_model
390	MODULE PROCEDURE lsm_soil_model
391	END INTERFACE lsm_soil_model
392
393
394	CONTAINS
395
396
397	!------------------------------------------------------------------------------!
398	! Description:
399	! ------------
400	!-- Initialization of the land surface model
401	!------------------------------------------------------------------------------!
402	SUBROUTINE init_lsm
403
404
405	IMPLICIT NONE
406
407	INTEGER(iwp) :: i !: running index
408	INTEGER(iwp) :: j !: running index
409	INTEGER(iwp) :: k !: running index
410
411
412	!
413	!-- Calculate frequently used parameters
414	rho_cp = cp * rho_surface
415	rd_d_rv = r_d / r_v
416	rho_lv = rho_surface * l_v
417	drho_l_lv = 1.0 / (rho_l * l_v)
418
419	!
420	!-- Allocate skin and soil temperature / humidity
421	#if defined( __nopointer )
422	ALLOCATE ( T_0(nysg:nyng,nxlg:nxrg) )
423	ALLOCATE ( T_0_p(nysg:nyng,nxlg:nxrg) )
424	#else
425	ALLOCATE ( T_0_1(nysg:nyng,nxlg:nxrg) )
426	ALLOCATE ( T_0_2(nysg:nyng,nxlg:nxrg) )
427	#endif
428
429	ALLOCATE ( tT_0_m(nysg:nyng,nxlg:nxrg) )
430
431	#if defined( __nopointer )
432	ALLOCATE ( T_soil(0:soil_layers,nysg:nyng,nxlg:nxrg) )
433	ALLOCATE ( T_soil_p(0:soil_layers,nysg:nyng,nxlg:nxrg) )
434	#else
435	ALLOCATE ( T_soil_1(0:soil_layers,nysg:nyng,nxlg:nxrg) )
436	ALLOCATE ( T_soil_2(0:soil_layers,nysg:nyng,nxlg:nxrg) )
437	#endif
438
439	ALLOCATE ( tT_soil_m(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
440
441	#if defined( __nopointer )
442	ALLOCATE ( m_liq(nysg:nyng,nxlg:nxrg) )
443	ALLOCATE ( m_liq_p(nysg:nyng,nxlg:nxrg) )
444	#else
445	ALLOCATE ( m_liq_1(nysg:nyng,nxlg:nxrg) )
446	ALLOCATE ( m_liq_2(nysg:nyng,nxlg:nxrg) )
447	#endif
448
449	ALLOCATE ( tm_liq_m(nysg:nyng,nxlg:nxrg) )
450
451	#if defined( __nopointer )
452	ALLOCATE ( m_soil(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
453	ALLOCATE ( m_soil_p(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
454	#else
455	ALLOCATE ( m_soil_1(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
456	ALLOCATE ( m_soil_2(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
457	#endif
458
459	ALLOCATE ( tm_soil_m(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
460
461
462	#if ! defined( __nopointer )
463	!
464	!-- Initial assignment of the pointers
465	T_soil => T_soil_1; T_soil_p => T_soil_2
466	T_0 => T_0_1; T_0_p => T_0_2
467	m_soil => m_soil_1; m_soil_p => m_soil_2
468	m_liq => m_liq_1; m_liq_p => m_liq_2
469	#endif
470
471	T_0 = 0.0_wp
472	T_0_p = 0.0_wp
473	tT_0_m = 0.0_wp
474
475	T_soil = 0.0_wp
476	T_soil_p = 0.0_wp
477	tT_soil_m = 0.0_wp
478
479	m_liq = 0.0_wp
480	m_liq_p = 0.0_wp
481	tm_liq_m = 0.0_wp
482
483	m_soil = 0.0_wp
484	m_soil_p = 0.0_wp
485	tm_soil_m = 0.0_wp
486
487	!
488	!-- Allocate 2D vegetation model arrays
489	ALLOCATE ( alpha_VG(nysg:nyng,nxlg:nxrg) )
490	ALLOCATE ( c_liq(nysg:nyng,nxlg:nxrg) )
491	ALLOCATE ( c_veg(nysg:nyng,nxlg:nxrg) )
492	ALLOCATE ( f_SW_in(nysg:nyng,nxlg:nxrg) )
493	ALLOCATE ( G(nysg:nyng,nxlg:nxrg) )
494	ALLOCATE ( H(nysg:nyng,nxlg:nxrg) )
495	ALLOCATE ( gamma_w_sat(nysg:nyng,nxlg:nxrg) )
496	ALLOCATE ( gD(nysg:nyng,nxlg:nxrg) )
497	ALLOCATE ( LAI(nysg:nyng,nxlg:nxrg) )
498	ALLOCATE ( LE(nysg:nyng,nxlg:nxrg) )
499	ALLOCATE ( LE_veg(nysg:nyng,nxlg:nxrg) )
500	ALLOCATE ( LE_soil(nysg:nyng,nxlg:nxrg) )
501	ALLOCATE ( LE_liq(nysg:nyng,nxlg:nxrg) )
502	ALLOCATE ( l_VG(nysg:nyng,nxlg:nxrg) )
503	ALLOCATE ( lambda_h_sat(nysg:nyng,nxlg:nxrg) )
504	ALLOCATE ( lambda_skin_u(nysg:nyng,nxlg:nxrg) )
505	ALLOCATE ( lambda_skin_s(nysg:nyng,nxlg:nxrg) )
506	ALLOCATE ( m_fc(nysg:nyng,nxlg:nxrg) )
507	ALLOCATE ( m_res(nysg:nyng,nxlg:nxrg) )
508	ALLOCATE ( m_sat(nysg:nyng,nxlg:nxrg) )
509	ALLOCATE ( m_wilt(nysg:nyng,nxlg:nxrg) )
510	ALLOCATE ( n_VG(nysg:nyng,nxlg:nxrg) )
511	ALLOCATE ( r_a(nysg:nyng,nxlg:nxrg) )
512	ALLOCATE ( r_canopy(nysg:nyng,nxlg:nxrg) )
513	ALLOCATE ( r_soil(nysg:nyng,nxlg:nxrg) )
514	ALLOCATE ( r_soil_min(nysg:nyng,nxlg:nxrg) )
515	ALLOCATE ( r_s(nysg:nyng,nxlg:nxrg) )
516	ALLOCATE ( r_s_min(nysg:nyng,nxlg:nxrg) )
517
518	!
519	!-- Set initial and default values
520	c_liq = 0.0_wp
521	c_veg = 0.0_wp
522	f_SW_in = 0.05_wp
523	gD = 0.0_wp
524	LAI = 0.0_wp
525	lambda_skin_u = 10.0_wp
526	lambda_skin_s = 10.0_wp
527
528
529	G = 0.0_wp
530	H = rho_cp * shf
531	LE = rho_l * l_v * qsws
532	LE_veg = 0.0_wp
533	LE_soil = LE
534	LE_liq = 0.0_wp
535
536	r_a = 50.0_wp
537	r_canopy = 0.0_wp
538	r_soil = 0.0_wp
539	r_soil_min = 50.0_wp
540	r_s = 110.0_wp
541	r_s_min = min_canopy_resistance
542
543	!
544	!-- Allocate 3D soil model arrays
545	ALLOCATE ( root_fr(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
546	ALLOCATE ( lambda_h(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
547	ALLOCATE ( rhoC_total(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
548
549	lambda_h = 0.0_wp
550	!
551	!-- If required, allocate humidity-related variables for the soil model
552	IF ( humidity ) THEN
553	ALLOCATE ( lambda_w(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
554	ALLOCATE ( gamma_w(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
555
556	lambda_w = 0.0_wp
557	ENDIF
558
559	!
560	!-- Calculate grid spacings. Temperature and moisture are defined at
561	!-- the center of the soil layers, whereas gradients/fluxes are defined
562	!-- at the edges (_stag)
563	dz_soil_stag(0) = soil_level(0)
564
565	DO k = 1, soil_layers-1
566	dz_soil_stag(k) = soil_level(k) - soil_level(k-1)
567	ENDDO
568
569	DO k = 0, soil_layers-2
570	dz_soil(k) = 0.5 * (dz_soil_stag(k+1) + dz_soil_stag(k))
571	ENDDO
572	dz_soil(soil_layers-1) = dz_soil_stag(soil_layers-1)
573
574	ddz_soil = 1.0 / dz_soil
575	ddz_soil_stag = 1.0 / dz_soil_stag
576	!
577	!-- Initialize soil
578	IF ( soil_type .NE. 0 ) THEN
579	alpha_VG = soil_pars(0,soil_type)
580	l_VG = soil_pars(1,soil_type)
581	n_VG = soil_pars(2,soil_type)
582	gamma_w_sat = soil_pars(3,soil_type)
583	m_sat = m_soil_pars(0,soil_type)
584	m_fc = m_soil_pars(1,soil_type)
585	m_wilt = m_soil_pars(2,soil_type)
586	m_res = m_soil_pars(3,soil_type)
587	ELSE
588	alpha_VG = alpha_VanGenuchten
589	l_VG = l_VanGenuchten
590	n_VG = n_VanGenuchten
591	gamma_w_sat = hydraulic_conductivity
592	m_sat = saturation_moisture
593	m_fc = field_capacity
594	m_wilt = wilting_point
595	m_res = residual_moisture
596	ENDIF
597
598	!
599	!-- Map user settings of T and q for each soil layer
600	!-- (make sure that the soil moisture does not drop below the permanent
601	!-- wilting point) -> problems with devision by zero)
602	DO k = 0, soil_layers-1
603	T_soil(k,:,:) = soil_temperature(k)
604	m_soil(k,:,:) = MAX(soil_moisture(k),m_wilt(:,:))
605	ENDDO
606	T_soil(soil_layers,:,:) = soil_temperature(soil_layers)
607
608
609	exn = ( surface_pressure / 1000.0_wp )**0.286_wp
610	T_0 = pt_surface * exn
611
612	T_soil_p = T_soil
613	m_soil_p = m_soil
614
615	!
616	!-- Calculate saturation soil heat conductivity
617	lambda_h_sat(:,:) = lambda_h_sm ** (1.0_wp - m_sat(:,:)) * &
618	lambda_h_water ** m_sat(:,:)
619
620	!
621	!-- Initialize vegetation
622	IF ( veg_type .NE. 0 ) THEN
623
624	r_s_min = veg_pars(0,veg_type)
625	LAI = veg_pars(1,veg_type)
626	c_veg = veg_pars(2,veg_type)
627	gD = veg_pars(3,veg_type)
628	lambda_skin_s = skin_pars(0,veg_type)
629	lambda_skin_u = skin_pars(1,veg_type)
630	f_SW_in = skin_pars(2,veg_type)
631	z0 = roughness_par(0,veg_type)
632	z0h = roughness_par(1,veg_type)
633
634
635	DO k = 0, soil_layers-1
636	root_fr(k,:,:) = root_distribution(k,veg_type)
637	ENDDO
638
639	ELSE
640
641	DO k = 0, soil_layers-1
642	root_fr(k,:,:) = root_fraction(k)
643	ENDDO
644
645	ENDIF
646
647	!
648	!-- Possibly do user-defined actions (e.g. define heterogeneous land surface)
649	CALL user_init_land_surface
650
651	!
652	!-- Set artifical values for ts and us so that r_a has its initial value for
653	!-- the first time step
654	DO i = nxlg, nxrg
655	DO j = nysg, nyng
656	k = nzb_s_inner(j,i)
657	us(j,i) = 0.1_wp
658	ts(j,i) = (pt(k+1,j,i) - pt(k,j,i)) / r_a(j,i)
659	shf(j,i) = - us(j,i) * ts(j,i)
660	ENDDO
661	ENDDO
662
663	!
664	!-- Calculate humidity at the surface
665	IF ( humidity ) THEN
666	CALL calc_q0
667	ENDIF
668
669	RETURN
670
671	END SUBROUTINE init_lsm
672
673
674
675	!------------------------------------------------------------------------------!
676	! Description:
677	! ------------
678	!
679	!------------------------------------------------------------------------------!
680	SUBROUTINE lsm_energy_balance
681
682
683	IMPLICIT NONE
684
685	INTEGER(iwp) :: i !: running index
686	INTEGER(iwp) :: j !: running index
687	INTEGER(iwp) :: k, ks !: running index
688
689	REAL(wp) :: f1, & !: resistance correction term 1
690	f2, & !: resistance correction term 2
691	f3, & !: resistance correction term 3
692	m_min, & !: minimum soil moisture
693	T_1, & !: actual temperature at first grid point
694	e, & !: water vapour pressure
695	e_s, & !: water vapour saturation pressure
696	e_s_dT, & !: derivate of e_s with respect to T
697	tend, & !: tendency
698	dq_s_dT, & !: derivate of q_s with respect to T
699	coef_1, & !: coef. for prognostic equation
700	coef_2, & !: coef. for prognostic equation
701	f_LE, & !: factor for LE
702	f_LE_veg, & !: factor for LE_veg
703	f_LE_soil, & !: factor for LE_soil
704	f_LE_liq, & !: factor for LE_liq
705	f_H, & !: factor for H
706	lambda_skin, & !: Current value of lambda_skin
707	m_liq_max !: maxmimum value of the liquid water reservoir
708
709	!
710	!-- Calculate the exner function for the current time step
711	exn = ( surface_pressure / 1000.0_wp )**0.286_wp
712
713
714	DO i = nxlg, nxrg
715	DO j = nysg, nyng
716
717
718	!
719	!-- Set lambda_skin according to stratification
720	IF ( rif(j,i) >= 0.0_wp ) THEN
721	lambda_skin = lambda_skin_s(j,i)
722	ELSE
723	lambda_skin = lambda_skin_u(j,i)
724	ENDIF
725	!
726	!-- First step: calculate aerodyamic resistance. As pt(0), us, ts
727	!-- are not available for the current time step, data from the last
728	!-- time step is used here.
729	k = nzb_s_inner(j,i)
730
731	! r_a(j,i) = (pt(k+1,j,i) - pt(k,j,i)) / (ts(j,i) * us(j,i) + 1.0E-20)
732	r_a(j,i) = (pt(k+1,j,i) - pt(k,j,i)) / - (shf(j,i) + 1.0E-20)
733
734	!
735	!-- Second step: calculate canopy resistance r_canopy
736	!-- f1-f3 here are defined as 1/f1-f3 as in ECMWF documentation
737
738	!-- f1: correction for incoming shortwave radiation
739	f1 = MIN(1.0_wp, ( 0.004_wp * SW_in(j,i) + 0.05_wp ) / &
740	(0.81_wp * (0.004_wp * SW_in(j,i) + 1.0_wp) ) )
741
742	!
743	!-- f2: correction for soil moisture f2=0 for very dry soil
744	m_total = 0.0_wp
745	DO ks = 0, soil_layers-1
746	m_total = m_total + root_fr(ks,j,i) * m_soil(ks,j,i)
747	ENDDO
748
749	IF ( m_total .GT. m_wilt(j,i) .AND. m_total .LE. m_fc(j,i) ) THEN
750	f2 = ( m_total - m_wilt(j,i) ) / (m_fc(j,i) - m_wilt(j,i) )
751	ELSE
752	f2 = 1.0E-20_wp
753	ENDIF
754
755	!
756	!-- Calculate water vapour pressure at saturation
757	!-- (T_0 should be replaced by liquid water temp?!)
758	e_s = 0.01 * 610.78_wp * EXP( 17.269_wp * ( T_0(j,i) - 273.16_wp )&
759	/ ( T_0(j,i) - 35.86_wp ) )
760
761	!
762	!-- f3: correction for vapour pressure deficit
763	IF ( gD(j,i) .NE. 0.0_wp ) THEN
764	!
765	!-- Calculate vapour pressure
766	e = q_p(k+1,j,i) * surface_pressure / 0.622
767	f3 = EXP ( -gD(j,i) * (e_s - e) )
768	ELSE
769	f3 = 1.0_wp
770	ENDIF
771
772	!
773	!-- To do: check for very dry soil -> r_canopy goes to infinity
774	r_canopy(j,i) = r_s_min(j,i) / (LAI(j,i) * f1 * f2 * f3 + 1.0E-20)
775
776	!
777	!-- Third step: calculate bare soil resistance r_soil
778	m_min = c_veg(j,i) * m_wilt(j,i) + (1.0_wp - c_veg(j,i)) * &
779	m_res(j,i)
780
781	f2 = ( m_soil(0,j,i) - m_min ) / ( m_fc(j,i) - m_min )
782	f2 = MAX(f2,1.0E-20)
783
784	r_soil(j,i) = r_soil_min(j,i) / f2
785
786	!
787	!-- Calculate fraction of liquid water reservoir
788	m_liq_max = m_max_depth * LAI(j,i)
789	c_liq(j,i) = MIN(1.0, m_liq(j,i)/m_liq_max)
790
791	q_s = 0.622_wp * e_s / surface_pressure
792	IF ( q_s .LE. q_p(k+1,j,i)) THEN
793	! PRINT*, "dew fall at (before)", time_since_reference_point
794	r_canopy(j,i) = 0.0_wp
795	r_soil(j,i) = 0.0_wp
796	ENDIF
797
798
799	!
800	!-- Calculate coefficients for the total evapotranspiration
801	f_LE_veg = rho_lv * c_veg(j,i) * (1.0 - c_liq(j,i)) / (r_a(j,i) &
802	+ r_canopy(j,i))
803	f_LE_soil = rho_lv * (1.0 - c_veg(j,i)) / (r_a(j,i) + r_soil(j,i))
804	f_LE_liq = rho_lv * c_veg(j,i) * c_liq(j,i) / r_a(j,i)
805
806
807	! Plant cannot transpirate below wilting point. here, r_canopy
808	! should go to infinity
809	! IF ( m_soil(k,j,i) .LT. m_wilt(j,i) ) THEN
810	! f_LE_veg(j,i) = 0.0
811	! ENDIF
812
813	f_H = rho_cp / r_a(j,i)
814	f_LE = f_LE_veg + f_LE_soil + f_LE_liq
815
816	!
817	!-- Calculate derivative of q_s for Taylor series expansion
818	e_s_dT = e_s * ( 17.269_wp / (T_0(j,i) - 35.86_wp) - &
819	17.269_wp*(T_0(j,i) - 273.16_wp) / (T_0(j,i) &
820	- 35.86_wp)**2 )
821
822	dq_s_dT = 0.622_wp * e_s_dT / surface_pressure
823
824	T_1 = pt_p(k+1,j,i) * exn
825
826	!
827	!-- Add LW up so that it can be removed in prognostic equation
828	Rn(j,i) = Rn(j,i) + sigma_SB * T_0(j,i) ** 4
829
830	!
831	!-- Numerator of the prognostic equation
832	coef_1 = Rn(j,i) + 3.0_wp * sigma_SB * T_0(j,i) ** 4 + f_H / exn &
833	* T_1 + f_LE * ( q_p(k+1,j,i) - q_s + dq_s_dT * T_0(j,i) &
834	) + lambda_skin * T_soil(0,j,i)
835
836	!
837	!-- Denominator of the prognostic equation
838	coef_2 = 4.0_wp * sigma_SB * T_0(j,i) ** 3 + f_LE * dq_s_dT + &
839	lambda_skin + f_H / exn
840
841	tend = 0.0_wp
842
843	!
844	!-- Implicit solution when the skin layer has no heat capacity,
845	!-- otherwise use RK3 scheme.
846	T_0_p(j,i) = ( coef_1 * dt_3d * tsc(2) + C_skin * T_0(j,i) ) / &
847	( C_skin + coef_2 * dt_3d * tsc(2) )
848
849	!
850	!-- Add RK3 term
851	T_0_p(j,i) = T_0_p(j,i) + dt_3d * tsc(3) * tT_soil_m(0,j,i)
852
853	!
854	!-- Calculate true tendency
855	tend = (T_0_p(j,i) - T_0(j,i) - tsc(3) * tT_0_m(j,i)) / (dt_3d &
856	* tsc(2))
857
858	!
859	!-- Calculate T_0 tendencies for the next Runge-Kutta step
860	IF ( timestep_scheme(1:5) == 'runge' ) THEN
861	IF ( intermediate_timestep_count == 1 ) THEN
862	tT_0_m(j,i) = tend
863	ELSEIF ( intermediate_timestep_count < &
864	intermediate_timestep_count_max ) THEN
865	tT_0_m(j,i) = -9.5625_wp * tend + 5.3125_wp * tT_0_m(j,i)
866	ENDIF
867	ENDIF
868
869	pt_p(k,j,i) = T_0_p(j,i) / exn
870	!
871	!-- Calculate fluxes
872	Rn(j,i) = Rn(j,i) + 3.0_wp * sigma_SB * T_0(j,i)**4 &
873	- 4.0_wp * sigma_SB * T_0(j,i)*3 T_0_p(j,i)
874	G(j,i) = lambda_skin * (T_0_p(j,i) - T_soil(0,j,i))
875	H(j,i) = - f_H * ( pt_p(k+1,j,i) - pt_p(k,j,i) )
876	LE(j,i) = - f_LE * ( q_p(k+1,j,i) - q_s + dq_s_dT * &
877	T_0(j,i) - dq_s_dT * T_0_p(j,i) )
878
879	LE_veg(j,i) = - f_LE_veg * ( q_p(k+1,j,i) - q_s + dq_s_dT * &
880	T_0(j,i) - dq_s_dT * T_0_p(j,i) )
881	LE_soil(j,i) = - f_LE_soil * ( q_p(k+1,j,i) - q_s + dq_s_dT * &
882	T_0(j,i) - dq_s_dT * T_0_p(j,i) )
883	LE_liq(j,i) = - f_LE_liq * ( q_p(k+1,j,i) - q_s + dq_s_dT * &
884	T_0(j,i) - dq_s_dT * T_0_p(j,i) )
885
886
887	! IF ( i == 1 .AND. j == 1 ) THEN
888	! PRINT*, "Rn", Rn(j,i)
889	! PRINT*, "H", H(j,i)
890	! PRINT*, "LE", LE(j,i)
891	! PRINT*, "LE_liq", LE_liq(j,i)
892	! PRINT*, "LE_veg", LE_veg(j,i)
893	! PRINT*, "LE_soil", LE_soil(j,i)
894	! PRINT*, "G", G(j,i)
895	! ENDIF
896
897
898	IF ( LE(j,i) .EQ. 0.0 ) THEN
899	! PRINT*, "+++ Evapotranspiration -> 0"
900	r_s(j,i) = 1.0E10
901	ELSE
902	r_s(j,i) = - rho_lv * ( q_p(k+1,j,i) - q_s + dq_s_dT * T_0(j,i)&
903	- dq_s_dT * T_0_p(j,i) ) / LE(j,i) - r_a(j,i)
904	ENDIF
905
906	!
907	!-- Calculate change in liquid water reservoir due to dew fall or
908	!-- evaporation of liquid water (to do: add interception from rainfall)
909	IF ( q_s .LE. q_p(k+1,j,i)) THEN
910	!
911	!-- Check if reservoir is full (avoid values > m_liq_max)
912	!-- In that case, LE_liq goes to LE_soil. In this case
913	!-- LE_veg is zero anyway (because c_liq = 1), so that tend is
914	!-- zero and no further check is needed
915	IF ( m_liq(j,i) .EQ. m_liq_max ) THEN
916	LE_soil(j,i) = LE_soil(j,i) + LE_liq(j,i)
917	LE_liq(j,i) = 0.0_wp
918	ENDIF
919
920	!
921	!-- In case LE_veg becomes negative (unphysical behavior), let
922	!-- the water enter the liquid water reservoir as dew on the
923	!-- plant
924	IF ( LE_veg(j,i) .LT. 0.0_wp ) THEN
925	LE_liq(j,i) = LE_liq(j,i) + LE_veg(j,i)
926	LE_veg(j,i) = 0.0_wp
927	ENDIF
928	ENDIF
929
930	tend = - LE_liq(j,i) * drho_l_lv
931
932
933	m_liq_p(j,i) = m_liq(j,i) + dt_3d * ( tsc(2) * tend &
934	+ tsc(3) * tm_liq_m(j,i) )
935
936	!
937	!-- Check if reservoir is overfull -> reduce to maximum
938	!-- (conservation of water is violated here)
939	m_liq_p(j,i) = MIN(m_liq_p(j,i),m_liq_max)
940
941	!
942	!-- Check if reservoir is empty (avoid values < 0.0)
943	!-- (conservation of water is violated here)
944	m_liq_p(j,i) = MAX(m_liq_p(j,i),0.0_wp)
945
946
947	!
948	!-- Calculate m_liq tendencies for the next Runge-Kutta step
949	IF ( timestep_scheme(1:5) == 'runge' ) THEN
950	IF ( intermediate_timestep_count == 1 ) THEN
951	tm_liq_m(j,i) = tend
952	ELSEIF ( intermediate_timestep_count < &
953	intermediate_timestep_count_max ) THEN
954	tm_liq_m(j,i) = -9.5625_wp * tend + 5.3125_wp * tm_liq_m(j,i)
955	ENDIF
956	ENDIF
957
958	!
959	!-- Calculate fluxes in the atmosphere
960	shf(j,i) = H(j,i) / rho_cp
961	qsws(j,i) = LE(j,i) / rho_lv
962
963	ENDDO
964	ENDDO
965
966
967
968	END SUBROUTINE lsm_energy_balance
969
970
971	!------------------------------------------------------------------------------!
972	! Description:
973	! ------------
974	!
975	!------------------------------------------------------------------------------!
976	SUBROUTINE lsm_soil_model
977
978
979	IMPLICIT NONE
980
981	INTEGER(iwp) :: i !: running index
982	INTEGER(iwp) :: j !: running index
983	INTEGER(iwp) :: k !: running index
984
985	REAL(wp) :: h_VG !: Van Genuchten coef. h
986
987	REAL(wp), DIMENSION(0:soil_layers-1) :: gamma_temp, & !: temp. gamma
988	lambda_temp, & !: temp. lambda
989	tend !: tendency
990
991	DO i = nxlg, nxrg
992	DO j = nysg, nyng
993	DO k = 0, soil_layers-1
994	!
995	!-- Calculate volumetric heat capacity of the soil, taking into
996	!-- account water content
997	rhoC_total(k,j,i) = (rhoC_soil * (1.0 - m_sat(j,i)) &
998	+ rhoC_water * m_soil(k,j,i))
999
1000	!
1001	!-- Calculate soil heat conductivity at the center of the soil
1002	!-- layers
1003	Ke = 1.0 + LOG10(MAX(0.1,m_soil(k,j,i) / m_sat(j,i)))
1004	lambda_temp(k) = Ke * (lambda_h_sat(j,i) + lambda_h_dry) + &
1005	lambda_h_dry
1006
1007	ENDDO
1008
1009	!
1010	!-- Calculate soil heat conductivity (lambda_h) at the _stag level
1011	!-- using linear interpolation
1012	DO k = 0, soil_layers-2
1013
1014	lambda_h(k,j,i) = lambda_temp(k) + &
1015	( lambda_temp(k+1) - lambda_temp(k) ) &
1016	* 0.5 * dz_soil_stag(k) * ddz_soil(k+1)
1017
1018	ENDDO
1019	lambda_h(soil_layers-1,j,i) = lambda_temp(soil_layers-1)
1020
1021	!
1022	!-- Prognostic equation for soil temperature T_soil
1023	tend(:) = 0.0_wp
1024	tend(0) = (1.0/rhoC_total(0,j,i)) * &
1025	( lambda_h(0,j,i) * ( T_soil(1,j,i) - T_soil(0,j,i) ) &
1026	* ddz_soil(0) + G(j,i) ) * ddz_soil_stag(0)
1027
1028	DO k = 1, soil_layers-1
1029	tend(k) = (1.0/rhoC_total(k,j,i)) &
1030	* ( lambda_h(k,j,i) &
1031	* ( T_soil(k+1,j,i) - T_soil(k,j,i) ) &
1032	* ddz_soil(k) &
1033	- lambda_h(k-1,j,i) &
1034	* ( T_soil(k,j,i) - T_soil(k-1,j,i) ) &
1035	* ddz_soil(k-1) &
1036	) * ddz_soil_stag(k)
1037	ENDDO
1038
1039	T_soil_p(0:soil_layers-1,j,i) = T_soil(0:soil_layers-1,j,i) &
1040	+ dt_3d * ( tsc(2) &
1041	* tend(:) + tsc(3) &
1042	* tT_soil_m(:,j,i) )
1043
1044	!
1045	!-- Calculate T_soil tendencies for the next Runge-Kutta step
1046	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1047	IF ( intermediate_timestep_count == 1 ) THEN
1048	DO k = 0, soil_layers-1
1049	tT_soil_m(k,j,i) = tend(k)
1050	ENDDO
1051	ELSEIF ( intermediate_timestep_count < &
1052	intermediate_timestep_count_max ) THEN
1053	DO k = 0, soil_layers-1
1054	tT_soil_m(k,j,i) = -9.5625_wp * tend(k) + 5.3125_wp &
1055	* tT_soil_m(k,j,i)
1056	ENDDO
1057	ENDIF
1058	ENDIF
1059
1060
1061	DO k = 0, soil_layers-1
1062	!
1063	!-- Calculate soil diffusivity at the center of the soil layers
1064	lambda_temp(k) = (- b_CH * gamma_w_sat(j,i) * psi_sat &
1065	/ m_sat(j,i) ) * ( MAX(m_soil(k,j,i), &
1066	m_wilt(j,i)) / m_sat(j,i) )**(b_CH + 2.0_wp)
1067
1068	!
1069	!-- Calculate the hydraulic conductivity after Van Genuchten (1980)
1070	h_VG = ( ( (m_res(j,i) - m_sat(j,i)) / ( m_res(j,i) - &
1071	MAX(m_soil(k,j,i),m_wilt(j,i)) ) )**(n_VG(j,i) &
1072	/ (n_VG(j,i)-1.0_wp)) - 1.0_wp &
1073	)**(1.0_wp/n_VG(j,i)) / alpha_VG(j,i)
1074
1075	gamma_temp(k) = gamma_w_sat(j,i) * ( ( (1.0_wp + &
1076	(alpha_VG(j,i)h_VG)n_VG(j,i))*(1.0_wp &
1077	-1.0_wp/n_VG(j,i)) - (alpha_VG(j,i)*h_VG &
1078	)(n_VG(j,i)-1.0_wp))2 ) &
1079	/ ( (1.0_wp + (alpha_VG(j,i)h_VG)*n_VG(j,i) &
1080	)*((1.0_wp - 1.0_wp/n_VG(j,i))(l_VG(j,i) &
1081	+ 2.0)) )
1082
1083	ENDDO
1084
1085
1086	IF ( humidity ) THEN
1087	!
1088	!-- Calculate soil diffusivity (lambda_w) at the _stag level
1089	!-- using linear interpolation
1090	DO k = 0, soil_layers-2
1091
1092	lambda_w(k,j,i) = lambda_temp(k) + &
1093	( lambda_temp(k+1) - lambda_temp(k) ) &
1094	* 0.5 * dz_soil_stag(k) * ddz_soil(k+1)
1095	gamma_w(k,j,i) = gamma_temp(k) + &
1096	( gamma_temp(k+1) - gamma_temp(k) ) &
1097	* 0.5 * dz_soil_stag(k) * ddz_soil(k+1)
1098
1099	ENDDO
1100
1101	!
1102	!
1103	!-- In case of a closed bottom (= water content is conserved), set
1104	!-- hydraulic conductivity to zero to that no water will be lost
1105	!-- in the bottom layer.
1106	IF ( conserve_water_content ) THEN
1107	gamma_w(soil_layers-1,j,i) = 0.0_wp
1108	ELSE
1109	gamma_w(soil_layers-1,j,i) = lambda_temp(soil_layers-1)
1110	ENDIF
1111
1112	!-- The root extraction (= root_extr * LE_veg / (rho_l * l_v))
1113	!-- ensures the mass conservation for water. The transpiration of
1114	!-- plants equals the cumulative withdrawals by the roots in the
1115	!-- soil. The scheme takes into account the availability of water
1116	!-- in the soil layers as well as the root fraction in the
1117	!-- respective layer
1118
1119	!
1120	!-- Calculate the root extraction (ECMWF 7.69, with some
1121	!-- modifications)
1122	m_total = 0.0_wp
1123	DO k = 0, soil_layers-1
1124	m_total = m_total + root_fr(k,j,i) * m_soil(k,j,i) * &
1125	dz_soil_stag(k)
1126
1127	ENDDO
1128
1129	!
1130	!-- For conservation of mass, the sum of root_extr must be 1
1131	DO k = 0, soil_layers-1
1132	root_extr(k) = root_fr(k,j,i) * m_soil(k,j,i) &
1133	* dz_soil_stag(k) / m_total
1134	ENDDO
1135
1136
1137	!
1138	!-- Prognostic equation for soil water content m_soil
1139	tend(:) = 0.0_wp
1140	tend(0) = ( lambda_w(0,j,i) * ( m_soil(1,j,i) - m_soil(0,j,i) )&
1141	* ddz_soil(0) - gamma_w(0,j,i) - ( root_extr(0) &
1142	* LE_veg(j,i) + LE_soil(j,i) ) * drho_l_lv &
1143	) * ddz_soil_stag(0)
1144
1145	DO k = 1, soil_layers-2
1146	tend(k) = ( lambda_w(k,j,i) * ( m_soil(k+1,j,i) &
1147	- m_soil(k,j,i) ) * ddz_soil(k) - gamma_w(k,j,i)&
1148	- lambda_w(k-1,j,i) * (m_soil(k,j,i) - &
1149	m_soil(k-1,j,i)) * ddz_soil(k-1) &
1150	+ gamma_w(k-1,j,i) - (root_extr(k) * LE_veg(j,i)&
1151	* drho_l_lv) &
1152	) * ddz_soil_stag(k)
1153
1154	ENDDO
1155	tend(soil_layers-1) = ( - gamma_w(soil_layers-1,j,i) &
1156	- lambda_w(soil_layers-2,j,i) &
1157	* (m_soil(soil_layers-1,j,i) &
1158	- m_soil(soil_layers-2,j,i)) &
1159	* ddz_soil(soil_layers-2) &
1160	+ gamma_w(soil_layers-2,j,i) - ( &
1161	root_extr(soil_layers-1) &
1162	* LE_veg(j,i) * drho_l_lv ) &
1163	) * ddz_soil_stag(soil_layers-1)
1164
1165	m_soil_p(0:soil_layers-1,j,i) = m_soil(0:soil_layers-1,j,i) &
1166	+ dt_3d * ( tsc(2) * tend(:) &
1167	+ tsc(3) * tm_soil_m(:,j,i) )
1168
1169	!
1170	!-- Account for dry soils (find a better solution here!)
1171	m_soil_p(:,j,i) = MAX(m_soil_p(:,j,i),0.0_wp)
1172
1173	!
1174	!-- Calculate m_soil tendencies for the next Runge-Kutta step
1175	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1176	IF ( intermediate_timestep_count == 1 ) THEN
1177	DO k = 0, soil_layers-1
1178	tm_soil_m(k,j,i) = tend(k)
1179	ENDDO
1180	ELSEIF ( intermediate_timestep_count < &
1181	intermediate_timestep_count_max ) THEN
1182	DO k = 0, soil_layers-1
1183	tm_soil_m(k,j,i) = -9.5625_wp * tend(k) + 5.3125_wp &
1184	* tm_soil_m(k,j,i)
1185	ENDDO
1186	ENDIF
1187	ENDIF
1188
1189	ENDIF
1190
1191	ENDDO
1192	ENDDO
1193
1194	!
1195	!-- Calculate surface specific humidity
1196	IF ( humidity ) THEN
1197	CALL calc_q0
1198	ENDIF
1199
1200
1201	END SUBROUTINE lsm_soil_model
1202
1203
1204	!------------------------------------------------------------------------------!
1205	! Description:
1206	! ------------
1207	!
1208	!------------------------------------------------------------------------------!
1209	SUBROUTINE calc_q0
1210
1211	IMPLICIT NONE
1212
1213	INTEGER :: i !: running index
1214	INTEGER :: j !: running index
1215	INTEGER :: k !: running index
1216	REAL(wp) :: resistance !: aerodynamic and soil resistance term
1217
1218	DO i = nxlg, nxrg
1219	DO j = nysg, nyng
1220
1221	k = nzb_s_inner(j,i)
1222	!
1223	!-- Temporary solution as long as T_0 is prescribed
1224
1225	pt_p(k,j,i) = T_0(j,i) / exn
1226	!
1227	!-- Calculate water vapour pressure at saturation
1228	e_s = 0.01_wp * 610.78_wp * EXP( 17.269_wp * ( T_0(j,i) - &
1229	273.16_wp ) / ( T_0(j,i) - &
1230	35.86_wp ) )
1231
1232	!
1233	!-- Calculate specific humidity at saturation
1234	q_s = 0.622_wp * e_s / surface_pressure
1235
1236
1237	resistance = r_a(j,i) / (r_a(j,i) + r_s(j,i))
1238
1239	!
1240	!-- Calculate specific humidity at surface
1241	q_p(k,j,i) = resistance * q_s + (1.0_wp - resistance) &
1242	* q_p(k+1,j,i)
1243
1244	ENDDO
1245	ENDDO
1246
1247	END SUBROUTINE calc_q0
1248
1249
1250	END MODULE land_surface_model_mod

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