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source: palm/trunk/SOURCE/land_surface_model.f90 @ 1502

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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	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: land_surface_model.f90 1501 2014-12-03 17:44:29Z kanani $
27	!
28	! 1500 2014-12-03 17:42:41Z maronga
29	! Corrected calculation of aerodynamic resistance (r_a).
30	! Precipitation is now added to liquid water reservoir using LE_liq.
31	! Added support for dry runs.
32	!
33	! 1496 2014-12-02 17:25:50Z maronga
34	! Initial revision
35	!
36	!
37	! Description:
38	! ------------
39	! Land surface model, consisting of a solver for the energy balance at the
40	! surface and a four layer soil scheme. The scheme is similar to the TESSEL
41	! scheme implemented in the ECMWF IFS model, with modifications according to
42	! H-TESSEL. The implementation is based on the formulation implemented in the
43	! DALES model.
44	!
45	! To do list:
46	! -----------
47	! - Add support for binary I/O support
48	! - Add support for lsm data output
49	! - Check for time step criterion
50	! - Check use with RK-2 and Euler time-stepping
51	! - Adaption for use with cloud physics (liquid water potential temperature)
52	! - Check reaction of plants at wilting point and at atmospheric saturation
53	! - Consider partial absorption of the net shortwave radiation by the skin layer
54	! - Allow for water surfaces, check performance for bare soils
55	!------------------------------------------------------------------------------!
56	USE arrays_3d, &
57	ONLY: pt, pt_p, q, q_p, qsws, rif, shf, ts, us, z0, z0h
58
59	USE cloud_parameters, &
60	ONLY: cp, l_d_r, l_v, precipitation_rate, rho_l, r_d, r_v
61
62	USE control_parameters, &
63	ONLY: dt_3d, humidity, intermediate_timestep_count, &
64	intermediate_timestep_count_max, precipitation, pt_surface, &
65	rho_surface, surface_pressure, timestep_scheme, tsc
66
67	USE indices, &
68	ONLY: nxlg, nxrg, nyng, nysg, nzb_s_inner
69
70	USE kinds
71
72	USE radiation_model_mod, &
73	ONLY: Rn, SW_in, sigma_SB
74
75
76	IMPLICIT NONE
77
78	!
79	!-- LSM model constants
80	INTEGER(iwp), PARAMETER :: soil_layers = 4 !: number of soil layers (fixed for now)
81
82	REAL(wp), PARAMETER :: &
83	b_CH = 6.04_wp, & ! Clapp & Hornberger exponent
84	lambda_h_dry = 0.19_wp, & ! heat conductivity for dry soil
85	lambda_h_sm = 3.44_wp, & ! heat conductivity of the soil matrix
86	lambda_h_water = 0.57_wp, & ! heat conductivity of water
87	psi_sat = -0.388_wp, & ! soil matrix potential at saturation
88	rhoC_soil = 2.19E6_wp, & ! volumetric heat capacity of soil
89	rhoC_water = 4.20E6_wp, & ! volumetric heat capacity of water
90	m_max_depth = 0.0002_wp ! Maximum capacity of the water reservoir (m)
91
92
93	!
94	!-- LSM variables
95	INTEGER(iwp) :: veg_type = 2, & !: vegetation type, 0: user-defined, 1-19: generic (see list)
96	soil_type = 3 !: soil type, 0: user-defined, 1-6: generic (see list)
97
98	LOGICAL :: conserve_water_content = .TRUE., & !: open or closed bottom surface for the soil model
99	land_surface = .FALSE. !: flag parameter indicating wheather the lsm is used
100
101	! value 9999999.9_wp -> generic available or user-defined value must be set
102	! otherwise -> no generic variable and user setting is optional
103	REAL(wp) :: alpha_VanGenuchten = 0.0_wp, & !: NAMELIST alpha_VG
104	canopy_resistance_coefficient = 0.0_wp, & !: NAMELIST gD
105	C_skin = 20000.0_wp, & !: Skin heat capacity
106	drho_l_lv, & !: (rho_l * l_v)**-1
107	exn, & !: value of the Exner function
108	e_s = 0.0_wp, & !: saturation water vapour pressure
109	field_capacity = 0.0_wp, & !: NAMELIST m_fc
110	f_shortwave_incoming = 9999999.9_wp, & !: NAMELIST f_SW_in
111	hydraulic_conductivity = 0.0_wp, & !: NAMELIST gamma_w_sat
112	Ke = 0.0_wp, & !: Kersten number
113	lambda_skin_stable = 9999999.9_wp, & !: NAMELIST lambda_skin_s
114	lambda_skin_unstable = 9999999.9_wp, & !: NAMELIST lambda_skin_u
115	leaf_area_index = 9999999.9_wp, & !: NAMELIST LAI
116	l_VanGenuchten = 0.0_WP, & !: NAMELIST l_VG
117	min_canopy_resistance = 110.0_wp, & !: NAMELIST r_s_min
118	m_total = 0.0_wp, & !: weighed total water content of the soil (m3/m3)
119	n_VanGenuchten = 0.0_WP, & !: NAMELIST n_VG
120	q_s = 0.0_wp, & !: saturation specific humidity
121	residual_moisture = 0.0_wp, & !: NAMELIST m_res
122	rho_cp, & !: rho_surface * cp
123	rho_lv, & !: rho * l_v
124	rd_d_rv, & !: r_d / r_v
125	saturation_moisture = 0.0_wp, & !: NAMELIST m_sat
126	vegetation_coverage = 9999999.9_wp, & !: NAMELIST c_veg
127	wilting_point = 0.0_wp !: NAMELIST m_wilt
128
129	REAL(wp), DIMENSION(0:soil_layers-1) :: &
130	ddz_soil, & !: 1/dz_soil
131	ddz_soil_stag, & !: 1/dz_soil_stag
132	dz_soil, & !: soil grid spacing (center-center)
133	dz_soil_stag, & !: soil grid spacing (edge-edge)
134	root_extr = 0.0_wp, & !: root extraction
135	root_fraction = (/0.35_wp, 0.38_wp, 0.23_wp, 0.04_wp/), & !: distribution of root surface area to the individual soil layers
136	soil_level = (/0.07_wp, 0.28_wp, 1.00_wp, 2.89_wp/), & !: soil layer depths (m)
137	soil_moisture = 0.0_wp !: soil moisture content (m3/m3)
138
139	REAL(wp), DIMENSION(0:soil_layers) :: &
140	soil_temperature = 9999999.9_wp !: soil temperature (K)
141
142	#if defined( __nopointer )
143	REAL(wp), DIMENSION(:,:), ALLOCATABLE, TARGET :: T_0, & !: skin temperature (K)
144	T_0_p, & !: progn. skin temperature (K)
145	m_liq, & !: liquid water reservoir (m)
146	m_liq_p !: progn. liquid water reservoir (m)
147	#else
148	REAL(wp), DIMENSION(:,:), POINTER :: T_0, &
149	T_0_p, &
150	m_liq, &
151	m_liq_p
152
153	REAL(wp), DIMENSION(:,:), ALLOCATABLE, TARGET :: T_0_1, T_0_2, &
154	m_liq_1, m_liq_2
155	#endif
156
157	!
158	!-- Temporal tendencies for time stepping
159	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: tT_0_m, & !: skin temperature tendency (K)
160	tm_liq_m !: liquid water reservoir tendency (m)
161
162	!
163	!-- Energy balance variables
164	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: &
165	alpha_VG, & !: coef. of Van Genuchten
166	c_liq, & !: liquid water coverage (of vegetated area)
167	c_veg, & !: vegetation coverage
168	f_SW_in, & !: ?
169	G, & !: surface soil heat flux
170	H, & !: surface flux of sensible heat
171	gamma_w_sat, & !: hydraulic conductivity at saturation
172	gD, & !: coefficient for dependence of r_canopy on water vapour pressure deficit
173	LAI, & !: leaf area index
174	LE, & !: surface flux of latent heat (total)
175	LE_veg, & !: surface flux of latent heat (vegetation portion)
176	LE_soil, & !: surface flux of latent heat (soil portion)
177	LE_liq, & !: surface flux of latent heat (liquid water portion)
178	lambda_h_sat, & !: heat conductivity for dry soil
179	lambda_skin_s, & !: coupling between skin and soil (depends on vegetation type)
180	lambda_skin_u, & !: coupling between skin and soil (depends on vegetation type)
181	l_VG, & !: coef. of Van Genuchten
182	m_fc, & !: soil moisture at field capacity (m3/m3)
183	m_res, & !: residual soil moisture
184	m_sat, & !: saturation soil moisture (m3/m3)
185	m_wilt, & !: soil moisture at permanent wilting point (m3/m3)
186	n_VG, & !: coef. Van Genuchten
187	r_a, & !: aerodynamic resistance
188	r_canopy, & !: canopy resistance
189	r_soil, & !: soil resitance
190	r_soil_min, & !: minimum soil resistance
191	r_s, & !: total surface resistance (combination of r_soil and r_canopy)
192	r_s_min !: minimum canopy resistance
193
194	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
195	lambda_h, & !: heat conductivity of soil (?)
196	lambda_w, & !: hydraulic diffusivity of soil (?)
197	gamma_w, & !: hydraulic conductivity of soil (?)
198	rhoC_total !: volumetric heat capacity of the actual soil matrix (?)
199
200	#if defined( __nopointer )
201	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE, TARGET :: &
202	T_soil, & !: Soil temperature (K)
203	T_soil_p, & !: Prog. soil temperature (K)
204	m_soil, & !: Soil moisture (m3/m3)
205	m_soil_p !: Prog. soil moisture (m3/m3)
206	#else
207	REAL(wp), DIMENSION(:,:,:), POINTER :: &
208	T_soil, T_soil_p, &
209	m_soil, m_soil_p
210
211	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE, TARGET :: &
212	T_soil_1, T_soil_2, &
213	m_soil_1, m_soil_2
214
215
216	#endif
217
218
219	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
220	tT_soil_m, & !: T_soil storage array
221	tm_soil_m, & !: m_soil storage array
222	root_fr !: root fraction (sum=1)
223
224	!
225	!-- Land surface parameters according to the following classes (veg_type)
226	!-- (0 user defined)
227	!-- 1 crops, mixed farming
228	!-- 2 short grass
229	!-- 3 evergreen needleleaf trees
230	!-- 4 deciduous needleleaf trees
231	!-- 5 evergreen broadleaf trees
232	!-- 6 deciduous broadleaf trees
233	!-- 7 tall grass
234	!-- 8 desert
235	!-- 9 tundra
236	!-- 10 irrigated crops
237	!-- 11 semidesert
238	!-- 12 ice caps and glaciers
239	!-- 13 bogs and marshes
240	!-- 14 inland water
241	!-- 15 ocean
242	!-- 16 evergreen shrubs
243	!-- 17 deciduous shrubs
244	!-- 18 mixed forest/woodland
245	!-- 19 interrupted forest
246
247	!
248	!-- Land surface parameters I r_s_min, LAI, c_veg, gD
249	REAL(wp), DIMENSION(0:3,1:19) :: veg_pars = RESHAPE( (/ &
250	180.0_wp, 3.00_wp, 0.90_wp, 0.00_wp, & ! 1
251	110.0_wp, 2.00_wp, 0.85_wp, 0.00_wp, & ! 2
252	500.0_wp, 5.00_wp, 0.90_wp, 0.03_wp, & ! 3
253	500.0_wp, 5.00_wp, 0.90_wp, 0.03_wp, & ! 4
254	175.0_wp, 5.00_wp, 0.90_wp, 0.03_wp, & ! 5
255	240.0_wp, 6.00_wp, 0.99_wp, 0.13_wp, & ! 6
256	100.0_wp, 2.00_wp, 0.70_wp, 0.00_wp, & ! 7
257	250.0_wp, 0.50_wp, 0.00_wp, 0.00_wp, & ! 8
258	80.0_wp, 1.00_wp, 0.50_wp, 0.00_wp, & ! 9
259	180.0_wp, 3.00_wp, 0.90_wp, 0.00_wp, & ! 10
260	150.0_wp, 0.50_wp, 0.10_wp, 0.00_wp, & ! 11
261	0.0_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 12
262	240.0_wp, 4.00_wp, 0.60_wp, 0.00_wp, & ! 13
263	0.0_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 14
264	0.0_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 15
265	225.0_wp, 3.00_wp, 0.50_wp, 0.00_wp, & ! 16
266	225.0_wp, 1.50_wp, 0.50_wp, 0.00_wp, & ! 17
267	250.0_wp, 5.00_wp, 0.90_wp, 0.03_wp, & ! 18
268	175.0_wp, 2.50_wp, 0.90_wp, 0.03_wp & ! 19
269	/), (/ 4, 19 /) )
270
271	!
272	!-- Land surface parameters II z0, z0h
273	REAL(wp), DIMENSION(0:1,1:19) :: roughness_par = RESHAPE( (/ &
274	0.25_wp, 0.25E-2_wp, & ! 1
275	0.20_wp, 0.20E-2_wp, & ! 2
276	2.00_wp, 2.00_wp, & ! 3
277	2.00_wp, 2.00_wp, & ! 4
278	2.00_wp, 2.00_wp, & ! 5
279	2.00_wp, 2.00_wp, & ! 6
280	0.47_wp, 0.47E-2_wp, & ! 7
281	0.013_wp, 0.013E-2_wp, & ! 8
282	0.034_wp, 0.034E-2_wp, & ! 9
283	0.5_wp, 0.50E-2_wp, & ! 10
284	0.17_wp, 0.17E-2_wp, & ! 11
285	1.3E-3_wp, 1.3E-4_wp, & ! 12
286	0.83_wp, 0.83E-2_wp, & ! 13
287	0.00_wp, 0.00E-2_wp, & ! 14
288	0.00_wp, 0.00E-2_wp, & ! 15
289	0.10_wp, 0.10E-2_wp, & ! 16
290	0.25_wp, 0.25E-2_wp, & ! 17
291	2.00_wp, 2.00E-2_wp, & ! 18
292	1.10_wp, 1.10E-2_wp & ! 19
293	/), (/ 2, 19 /) )
294
295	!
296	!-- Land surface parameters III lambda_skin_s, lambda_skin_u, f_SW_in
297	REAL(wp), DIMENSION(0:2,1:19) :: skin_pars = RESHAPE( (/ &
298	10.0_wp, 10.0_wp, 0.05_wp, & ! 1
299	10.0_wp, 10.0_wp, 0.05_wp, & ! 2
300	20.0_wp, 15.0_wp, 0.03_wp, & ! 3
301	20.0_wp, 15.0_wp, 0.03_wp, & ! 4
302	20.0_wp, 15.0_wp, 0.03_wp, & ! 5
303	20.0_wp, 15.0_wp, 0.03_wp, & ! 6
304	10.0_wp, 10.0_wp, 0.05_wp, & ! 7
305	15.0_wp, 15.0_wp, 0.00_wp, & ! 8
306	10.0_wp, 10.0_wp, 0.05_wp, & ! 9
307	10.0_wp, 10.0_wp, 0.05_wp, & ! 10
308	10.0_wp, 10.0_wp, 0.05_wp, & ! 11
309	58.0_wp, 58.0_wp, 0.00_wp, & ! 12
310	10.0_wp, 10.0_wp, 0.05_wp, & ! 13
311	1.0E20_wp, 1.0E20_wp, 0.00_wp, & ! 14
312	1.0E20_wp, 1.0E20_wp, 0.00_wp, & ! 15
313	10.0_wp, 10.0_wp, 0.05_wp, & ! 16
314	10.0_wp, 10.0_wp, 0.05_wp, & ! 17
315	20.0_wp, 15.0_wp, 0.03_wp, & ! 18
316	20.0_wp, 15.0_wp, 0.03_wp & ! 19
317	/), (/ 3, 19 /) )
318
319	!
320	!-- Root distribution (sum = 1) level 1, level 2, level 3, level 4,
321	REAL(wp), DIMENSION(0:3,1:19) :: root_distribution = RESHAPE( (/ &
322	0.24_wp, 0.41_wp, 0.31_wp, 0.04_wp, & ! 1
323	0.35_wp, 0.38_wp, 0.23_wp, 0.04_wp, & ! 2
324	0.26_wp, 0.39_wp, 0.29_wp, 0.06_wp, & ! 3
325	0.26_wp, 0.38_wp, 0.29_wp, 0.07_wp, & ! 4
326	0.24_wp, 0.38_wp, 0.31_wp, 0.07_wp, & ! 5
327	0.25_wp, 0.34_wp, 0.27_wp, 0.14_wp, & ! 6
328	0.27_wp, 0.27_wp, 0.27_wp, 0.09_wp, & ! 7
329	1.00_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 8
330	0.47_wp, 0.45_wp, 0.08_wp, 0.00_wp, & ! 9
331	0.24_wp, 0.41_wp, 0.31_wp, 0.04_wp, & ! 10
332	0.17_wp, 0.31_wp, 0.33_wp, 0.19_wp, & ! 11
333	0.00_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 12
334	0.25_wp, 0.34_wp, 0.27_wp, 0.11_wp, & ! 13
335	0.00_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 14
336	0.00_wp, 0.00_wp, 0.00_wp, 0.00_wp, & ! 15
337	0.23_wp, 0.36_wp, 0.30_wp, 0.11_wp, & ! 16
338	0.23_wp, 0.36_wp, 0.30_wp, 0.11_wp, & ! 17
339	0.19_wp, 0.35_wp, 0.36_wp, 0.10_wp, & ! 18
340	0.19_wp, 0.35_wp, 0.36_wp, 0.10_wp & ! 19
341	/), (/ 4, 19 /) )
342
343	!
344	!-- Soil parameters according to the following porosity classes (soil_type)
345	!-- (0 user defined)
346	!-- 1 coarse
347	!-- 2 medium
348	!-- 3 medium-fine
349	!-- 4 fine
350	!-- 5 very fine
351	!-- 6 organic
352	!
353	!-- Soil parameters I alpha_VG, l_VG, n_VG, gamma_w_sat
354	REAL(wp), DIMENSION(0:3,1:6) :: soil_pars = RESHAPE( (/ &
355	3.83_wp, 1.250_wp, 1.38_wp, 6.94E-6_wp, & ! 1
356	3.14_wp, -2.342_wp, 1.28_wp, 1.16E-6_wp, & ! 2
357	0.83_wp, -0.588_wp, 1.25_wp, 0.26E-6_wp, & ! 3
358	3.67_wp, -1.977_wp, 1.10_wp, 2.87E-6_wp, & ! 4
359	2.65_wp, 2.500_wp, 1.10_wp, 1.74E-6_wp, & ! 5
360	1.30_wp, 0.400_wp, 1.20_wp, 0.93E-6_wp & ! 6
361	/), (/ 4, 6 /) )
362
363	!
364	!-- Soil parameters II m_sat, m_fc, m_wilt, m_res
365	REAL(wp), DIMENSION(0:3,1:6) :: m_soil_pars = RESHAPE( (/ &
366	0.403_wp, 0.244_wp, 0.059_wp, 0.025_wp, & ! 1
367	0.439_wp, 0.347_wp, 0.151_wp, 0.010_wp, & ! 2
368	0.430_wp, 0.383_wp, 0.133_wp, 0.010_wp, & ! 3
369	0.520_wp, 0.448_wp, 0.279_wp, 0.010_wp, & ! 4
370	0.614_wp, 0.541_wp, 0.335_wp, 0.010_wp, & ! 5
371	0.766_wp, 0.663_wp, 0.267_wp, 0.010_wp & ! 6
372	/), (/ 4, 6 /) )
373
374
375	SAVE
376
377
378	PRIVATE
379
380
381	PUBLIC alpha_VanGenuchten, C_skin, canopy_resistance_coefficient, &
382	conserve_water_content, field_capacity, f_shortwave_incoming, &
383	hydraulic_conductivity, init_lsm, lambda_skin_stable, &
384	lambda_skin_unstable, land_surface, leaf_area_index, &
385	lsm_energy_balance, lsm_soil_model, l_VanGenuchten, &
386	min_canopy_resistance, n_VanGenuchten, residual_moisture, &
387	root_fraction, saturation_moisture, soil_level, soil_moisture, &
388	soil_temperature, soil_type, vegetation_coverage, veg_type, &
389	wilting_point
390
391	#if defined( __nopointer )
392	PUBLIC m_liq, m_liq_p, m_soil, m_soil_p, T_0, T_0_p, T_soil, T_soil_p
393	#else
394	PUBLIC m_liq, m_liq_1, m_liq_2, m_liq_p, m_soil, m_soil_1, m_soil_2, &
395	m_soil_p, T_0, T_0_1, T_0_2, T_0_p, T_soil, T_soil_1, T_soil_2, &
396	T_soil_p
397	#endif
398
399
400	INTERFACE init_lsm
401	MODULE PROCEDURE init_lsm
402	END INTERFACE init_lsm
403
404	INTERFACE lsm_energy_balance
405	MODULE PROCEDURE lsm_energy_balance
406	END INTERFACE lsm_energy_balance
407
408	INTERFACE lsm_soil_model
409	MODULE PROCEDURE lsm_soil_model
410	END INTERFACE lsm_soil_model
411
412
413	CONTAINS
414
415
416	!------------------------------------------------------------------------------!
417	! Description:
418	! ------------
419	!-- Initialization of the land surface model
420	!------------------------------------------------------------------------------!
421	SUBROUTINE init_lsm
422
423
424	IMPLICIT NONE
425
426	INTEGER(iwp) :: i !: running index
427	INTEGER(iwp) :: j !: running index
428	INTEGER(iwp) :: k !: running index
429
430
431	!
432	!-- Calculate frequently used parameters
433	rho_cp = cp * rho_surface
434	rd_d_rv = r_d / r_v
435	rho_lv = rho_surface * l_v
436	drho_l_lv = 1.0 / (rho_l * l_v)
437
438	!
439	!-- Allocate skin and soil temperature / humidity
440	#if defined( __nopointer )
441	ALLOCATE ( T_0(nysg:nyng,nxlg:nxrg) )
442	ALLOCATE ( T_0_p(nysg:nyng,nxlg:nxrg) )
443	#else
444	ALLOCATE ( T_0_1(nysg:nyng,nxlg:nxrg) )
445	ALLOCATE ( T_0_2(nysg:nyng,nxlg:nxrg) )
446	#endif
447
448	ALLOCATE ( tT_0_m(nysg:nyng,nxlg:nxrg) )
449
450	#if defined( __nopointer )
451	ALLOCATE ( T_soil(0:soil_layers,nysg:nyng,nxlg:nxrg) )
452	ALLOCATE ( T_soil_p(0:soil_layers,nysg:nyng,nxlg:nxrg) )
453	#else
454	ALLOCATE ( T_soil_1(0:soil_layers,nysg:nyng,nxlg:nxrg) )
455	ALLOCATE ( T_soil_2(0:soil_layers,nysg:nyng,nxlg:nxrg) )
456	#endif
457
458	ALLOCATE ( tT_soil_m(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
459
460	#if defined( __nopointer )
461	ALLOCATE ( m_liq(nysg:nyng,nxlg:nxrg) )
462	ALLOCATE ( m_liq_p(nysg:nyng,nxlg:nxrg) )
463	#else
464	ALLOCATE ( m_liq_1(nysg:nyng,nxlg:nxrg) )
465	ALLOCATE ( m_liq_2(nysg:nyng,nxlg:nxrg) )
466	#endif
467
468	ALLOCATE ( tm_liq_m(nysg:nyng,nxlg:nxrg) )
469
470	#if defined( __nopointer )
471	ALLOCATE ( m_soil(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
472	ALLOCATE ( m_soil_p(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
473	#else
474	ALLOCATE ( m_soil_1(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
475	ALLOCATE ( m_soil_2(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
476	#endif
477
478	ALLOCATE ( tm_soil_m(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
479
480
481	#if ! defined( __nopointer )
482	!
483	!-- Initial assignment of the pointers
484	T_soil => T_soil_1; T_soil_p => T_soil_2
485	T_0 => T_0_1; T_0_p => T_0_2
486	m_soil => m_soil_1; m_soil_p => m_soil_2
487	m_liq => m_liq_1; m_liq_p => m_liq_2
488	#endif
489
490	T_0 = 0.0_wp
491	T_0_p = 0.0_wp
492	tT_0_m = 0.0_wp
493
494	T_soil = 0.0_wp
495	T_soil_p = 0.0_wp
496	tT_soil_m = 0.0_wp
497
498	m_liq = 0.0_wp
499	m_liq_p = 0.0_wp
500	tm_liq_m = 0.0_wp
501
502	m_soil = 0.0_wp
503	m_soil_p = 0.0_wp
504	tm_soil_m = 0.0_wp
505
506	!
507	!-- Allocate 2D vegetation model arrays
508	ALLOCATE ( alpha_VG(nysg:nyng,nxlg:nxrg) )
509	ALLOCATE ( c_liq(nysg:nyng,nxlg:nxrg) )
510	ALLOCATE ( c_veg(nysg:nyng,nxlg:nxrg) )
511	ALLOCATE ( f_SW_in(nysg:nyng,nxlg:nxrg) )
512	ALLOCATE ( G(nysg:nyng,nxlg:nxrg) )
513	ALLOCATE ( H(nysg:nyng,nxlg:nxrg) )
514	ALLOCATE ( gamma_w_sat(nysg:nyng,nxlg:nxrg) )
515	ALLOCATE ( gD(nysg:nyng,nxlg:nxrg) )
516	ALLOCATE ( LAI(nysg:nyng,nxlg:nxrg) )
517	ALLOCATE ( LE(nysg:nyng,nxlg:nxrg) )
518	ALLOCATE ( LE_veg(nysg:nyng,nxlg:nxrg) )
519	ALLOCATE ( LE_soil(nysg:nyng,nxlg:nxrg) )
520	ALLOCATE ( LE_liq(nysg:nyng,nxlg:nxrg) )
521	ALLOCATE ( l_VG(nysg:nyng,nxlg:nxrg) )
522	ALLOCATE ( lambda_h_sat(nysg:nyng,nxlg:nxrg) )
523	ALLOCATE ( lambda_skin_u(nysg:nyng,nxlg:nxrg) )
524	ALLOCATE ( lambda_skin_s(nysg:nyng,nxlg:nxrg) )
525	ALLOCATE ( m_fc(nysg:nyng,nxlg:nxrg) )
526	ALLOCATE ( m_res(nysg:nyng,nxlg:nxrg) )
527	ALLOCATE ( m_sat(nysg:nyng,nxlg:nxrg) )
528	ALLOCATE ( m_wilt(nysg:nyng,nxlg:nxrg) )
529	ALLOCATE ( n_VG(nysg:nyng,nxlg:nxrg) )
530	ALLOCATE ( r_a(nysg:nyng,nxlg:nxrg) )
531	ALLOCATE ( r_canopy(nysg:nyng,nxlg:nxrg) )
532	ALLOCATE ( r_soil(nysg:nyng,nxlg:nxrg) )
533	ALLOCATE ( r_soil_min(nysg:nyng,nxlg:nxrg) )
534	ALLOCATE ( r_s(nysg:nyng,nxlg:nxrg) )
535	ALLOCATE ( r_s_min(nysg:nyng,nxlg:nxrg) )
536
537	!
538	!-- Set initial and default values
539	c_liq = 0.0_wp
540	c_veg = 0.0_wp
541	f_SW_in = 0.05_wp
542	gD = 0.0_wp
543	LAI = 0.0_wp
544	lambda_skin_u = 10.0_wp
545	lambda_skin_s = 10.0_wp
546
547
548	G = 0.0_wp
549	H = rho_cp * shf
550
551	IF ( humidity ) THEN
552	LE = rho_l * l_v * qsws
553	ELSE
554	LE = 0.0_wp
555	ENDIF
556
557	LE_veg = 0.0_wp
558	LE_soil = LE
559	LE_liq = 0.0_wp
560
561	r_a = 50.0_wp
562	r_canopy = 0.0_wp
563	r_soil = 0.0_wp
564	r_soil_min = 50.0_wp
565	r_s = 110.0_wp
566	r_s_min = min_canopy_resistance
567
568	!
569	!-- Allocate 3D soil model arrays
570	ALLOCATE ( root_fr(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
571	ALLOCATE ( lambda_h(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
572	ALLOCATE ( rhoC_total(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
573
574	lambda_h = 0.0_wp
575	!
576	!-- If required, allocate humidity-related variables for the soil model
577	IF ( humidity ) THEN
578	ALLOCATE ( lambda_w(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
579	ALLOCATE ( gamma_w(0:soil_layers-1,nysg:nyng,nxlg:nxrg) )
580
581	lambda_w = 0.0_wp
582	ENDIF
583
584	!
585	!-- Calculate grid spacings. Temperature and moisture are defined at
586	!-- the center of the soil layers, whereas gradients/fluxes are defined
587	!-- at the edges (_stag)
588	dz_soil_stag(0) = soil_level(0)
589
590	DO k = 1, soil_layers-1
591	dz_soil_stag(k) = soil_level(k) - soil_level(k-1)
592	ENDDO
593
594	DO k = 0, soil_layers-2
595	dz_soil(k) = 0.5 * (dz_soil_stag(k+1) + dz_soil_stag(k))
596	ENDDO
597	dz_soil(soil_layers-1) = dz_soil_stag(soil_layers-1)
598
599	ddz_soil = 1.0 / dz_soil
600	ddz_soil_stag = 1.0 / dz_soil_stag
601	!
602	!-- Initialize soil
603	IF ( soil_type .NE. 0 ) THEN
604	alpha_VG = soil_pars(0,soil_type)
605	l_VG = soil_pars(1,soil_type)
606	n_VG = soil_pars(2,soil_type)
607	gamma_w_sat = soil_pars(3,soil_type)
608	m_sat = m_soil_pars(0,soil_type)
609	m_fc = m_soil_pars(1,soil_type)
610	m_wilt = m_soil_pars(2,soil_type)
611	m_res = m_soil_pars(3,soil_type)
612	ELSE
613	alpha_VG = alpha_VanGenuchten
614	l_VG = l_VanGenuchten
615	n_VG = n_VanGenuchten
616	gamma_w_sat = hydraulic_conductivity
617	m_sat = saturation_moisture
618	m_fc = field_capacity
619	m_wilt = wilting_point
620	m_res = residual_moisture
621	ENDIF
622
623	!
624	!-- Map user settings of T and q for each soil layer
625	!-- (make sure that the soil moisture does not drop below the permanent
626	!-- wilting point) -> problems with devision by zero)
627	DO k = 0, soil_layers-1
628	T_soil(k,:,:) = soil_temperature(k)
629	m_soil(k,:,:) = MAX(soil_moisture(k),m_wilt(:,:))
630	ENDDO
631	T_soil(soil_layers,:,:) = soil_temperature(soil_layers)
632
633
634	exn = ( surface_pressure / 1000.0_wp )**0.286_wp
635	T_0 = pt_surface * exn
636
637	T_soil_p = T_soil
638	m_soil_p = m_soil
639
640	!
641	!-- Calculate saturation soil heat conductivity
642	lambda_h_sat(:,:) = lambda_h_sm ** (1.0_wp - m_sat(:,:)) * &
643	lambda_h_water ** m_sat(:,:)
644
645	!
646	!-- Initialize vegetation
647	IF ( veg_type .NE. 0 ) THEN
648
649	r_s_min = veg_pars(0,veg_type)
650	LAI = veg_pars(1,veg_type)
651	c_veg = veg_pars(2,veg_type)
652	gD = veg_pars(3,veg_type)
653	lambda_skin_s = skin_pars(0,veg_type)
654	lambda_skin_u = skin_pars(1,veg_type)
655	f_SW_in = skin_pars(2,veg_type)
656	z0 = roughness_par(0,veg_type)
657	z0h = roughness_par(1,veg_type)
658
659
660	DO k = 0, soil_layers-1
661	root_fr(k,:,:) = root_distribution(k,veg_type)
662	ENDDO
663
664	ELSE
665
666	DO k = 0, soil_layers-1
667	root_fr(k,:,:) = root_fraction(k)
668	ENDDO
669
670	ENDIF
671
672	!
673	!-- Possibly do user-defined actions (e.g. define heterogeneous land surface)
674	CALL user_init_land_surface
675
676	!
677	!-- Set artifical values for ts and us so that r_a has its initial value for
678	!-- the first time step
679	DO i = nxlg, nxrg
680	DO j = nysg, nyng
681	k = nzb_s_inner(j,i)
682	!
683	!-- Assure that r_a cannot be zero at model start
684	IF ( pt(k+1,j,i) == pt(k,j,i) ) pt(k+1,j,i) = pt(k+1,j,i) + 1.0E-10_wp
685
686	us(j,i) = 0.1_wp
687	ts(j,i) = (pt(k+1,j,i) - pt(k,j,i)) / r_a(j,i)
688	shf(j,i) = - us(j,i) * ts(j,i)
689	ENDDO
690	ENDDO
691
692	!
693	!-- Calculate humidity at the surface
694	IF ( humidity ) THEN
695	CALL calc_q0
696	ENDIF
697
698	RETURN
699
700	END SUBROUTINE init_lsm
701
702
703
704	!------------------------------------------------------------------------------!
705	! Description:
706	! ------------
707	!
708	!------------------------------------------------------------------------------!
709	SUBROUTINE lsm_energy_balance
710
711
712	IMPLICIT NONE
713
714	INTEGER(iwp) :: i !: running index
715	INTEGER(iwp) :: j !: running index
716	INTEGER(iwp) :: k, ks !: running index
717
718	REAL(wp) :: f1, & !: resistance correction term 1
719	f2, & !: resistance correction term 2
720	f3, & !: resistance correction term 3
721	m_min, & !: minimum soil moisture
722	T_1, & !: actual temperature at first grid point
723	e, & !: water vapour pressure
724	e_s, & !: water vapour saturation pressure
725	e_s_dT, & !: derivate of e_s with respect to T
726	tend, & !: tendency
727	dq_s_dT, & !: derivate of q_s with respect to T
728	coef_1, & !: coef. for prognostic equation
729	coef_2, & !: coef. for prognostic equation
730	f_LE, & !: factor for LE
731	f_LE_veg, & !: factor for LE_veg
732	f_LE_soil, & !: factor for LE_soil
733	f_LE_liq, & !: factor for LE_liq
734	f_H, & !: factor for H
735	lambda_skin, & !: Current value of lambda_skin
736	m_liq_max !: maxmimum value of the liquid water reservoir
737
738	!
739	!-- Calculate the exner function for the current time step
740	exn = ( surface_pressure / 1000.0_wp )**0.286_wp
741
742
743	DO i = nxlg, nxrg
744	DO j = nysg, nyng
745	k = nzb_s_inner(j,i)
746
747	!
748	!-- Set lambda_skin according to stratification
749	IF ( rif(j,i) >= 0.0_wp ) THEN
750	lambda_skin = lambda_skin_s(j,i)
751	ELSE
752	lambda_skin = lambda_skin_u(j,i)
753	ENDIF
754
755	!
756	!-- First step: calculate aerodyamic resistance. As pt, us, ts
757	!-- are not available for the prognostic time step, data from the last
758	!-- time step is used here. Note that this formulation is the
759	!-- equivalent to the ECMWF formulation using drag coefficients
760	r_a(j,i) = (pt(k+1,j,i) - pt(k,j,i)) / (ts(j,i) * us(j,i) + 1.0E-20)
761
762	!
763	!-- Second step: calculate canopy resistance r_canopy
764	!-- f1-f3 here are defined as 1/f1-f3 as in ECMWF documentation
765
766	!-- f1: correction for incoming shortwave radiation
767	f1 = MIN(1.0_wp, ( 0.004_wp * SW_in(j,i) + 0.05_wp ) / &
768	(0.81_wp * (0.004_wp * SW_in(j,i) + 1.0_wp) ) )
769
770	!
771	!-- f2: correction for soil moisture f2=0 for very dry soil
772	m_total = 0.0_wp
773	DO ks = 0, soil_layers-1
774	m_total = m_total + root_fr(ks,j,i) * m_soil(ks,j,i)
775	ENDDO
776
777	IF ( m_total .GT. m_wilt(j,i) .AND. m_total .LE. m_fc(j,i) ) THEN
778	f2 = ( m_total - m_wilt(j,i) ) / (m_fc(j,i) - m_wilt(j,i) )
779	ELSE
780	f2 = 1.0E-20_wp
781	ENDIF
782
783	!
784	!-- Calculate water vapour pressure at saturation
785	!-- (T_0 should be replaced by liquid water temp?!)
786	e_s = 0.01 * 610.78_wp * EXP( 17.269_wp * ( T_0(j,i) - 273.16_wp )&
787	/ ( T_0(j,i) - 35.86_wp ) )
788
789	!
790	!-- f3: correction for vapour pressure deficit
791	IF ( gD(j,i) .NE. 0.0_wp ) THEN
792	!
793	!-- Calculate vapour pressure
794	e = q_p(k+1,j,i) * surface_pressure / 0.622
795	f3 = EXP ( -gD(j,i) * (e_s - e) )
796	ELSE
797	f3 = 1.0_wp
798	ENDIF
799
800	!
801	!-- To do: check for very dry soil -> r_canopy goes to infinity
802	r_canopy(j,i) = r_s_min(j,i) / (LAI(j,i) * f1 * f2 * f3 + 1.0E-20)
803
804	!
805	!-- Third step: calculate bare soil resistance r_soil
806	m_min = c_veg(j,i) * m_wilt(j,i) + (1.0_wp - c_veg(j,i)) * &
807	m_res(j,i)
808
809	f2 = ( m_soil(0,j,i) - m_min ) / ( m_fc(j,i) - m_min )
810	f2 = MAX(f2,1.0E-20)
811
812	r_soil(j,i) = r_soil_min(j,i) / f2
813
814	!
815	!-- Calculate fraction of liquid water reservoir
816	m_liq_max = m_max_depth * LAI(j,i)
817	c_liq(j,i) = MIN(1.0, m_liq(j,i)/m_liq_max)
818
819	q_s = 0.622_wp * e_s / surface_pressure
820
821	!
822	!-- In case of dew fall, set resistances to zero.
823	!-- To do: what does that physically reasoning behind this?
824	IF ( humidity ) THEN
825	IF ( q_s .LE. q_p(k+1,j,i) ) THEN
826	r_canopy(j,i) = 0.0_wp
827	r_soil(j,i) = 0.0_wp
828	ENDIF
829	ENDIF
830
831
832	!
833	!-- Calculate coefficients for the total evapotranspiration
834	f_LE_veg = rho_lv * c_veg(j,i) * (1.0 - c_liq(j,i)) / (r_a(j,i) &
835	+ r_canopy(j,i))
836	f_LE_soil = rho_lv * (1.0 - c_veg(j,i)) / (r_a(j,i) + r_soil(j,i))
837	f_LE_liq = rho_lv * c_veg(j,i) * c_liq(j,i) / r_a(j,i)
838
839
840	!
841	!-- If soil moisture is below wilting point, plants do no longer
842	!-- transpirate.
843	IF ( m_soil(k,j,i) .LT. m_wilt(j,i) ) THEN
844	f_LE_veg = 0.0
845	ENDIF
846
847	f_H = rho_cp / r_a(j,i)
848	f_LE = f_LE_veg + f_LE_soil + f_LE_liq
849
850	!
851	!-- Calculate derivative of q_s for Taylor series expansion
852	e_s_dT = e_s * ( 17.269_wp / (T_0(j,i) - 35.86_wp) - &
853	17.269_wp*(T_0(j,i) - 273.16_wp) / (T_0(j,i) &
854	- 35.86_wp)**2 )
855
856	dq_s_dT = 0.622_wp * e_s_dT / surface_pressure
857
858	T_1 = pt_p(k+1,j,i) * exn
859
860	!
861	!-- Add LW up so that it can be removed in prognostic equation
862	Rn(j,i) = Rn(j,i) + sigma_SB * T_0(j,i) ** 4
863
864	IF ( humidity ) THEN
865
866	!
867	!-- Numerator of the prognostic equation
868	coef_1 = Rn(j,i) + 3.0_wp * sigma_SB * T_0(j,i) ** 4 + f_H &
869	/ exn * T_1 + f_LE * ( q_p(k+1,j,i) - q_s + dq_s_dT &
870	* T_0(j,i) ) + lambda_skin * T_soil(0,j,i)
871
872	!
873	!-- Denominator of the prognostic equation
874	coef_2 = 4.0_wp * sigma_SB * T_0(j,i) ** 3 + f_LE * dq_s_dT &
875	+ lambda_skin + f_H / exn
876
877	ELSE
878
879	!
880	!-- Numerator of the prognostic equation
881	coef_1 = Rn(j,i) + 3.0_wp * sigma_SB * T_0(j,i) ** 4 + f_H / &
882	exn * T_1 + lambda_skin * T_soil(0,j,i)
883
884	!
885	!-- Denominator of the prognostic equation
886	coef_2 = 4.0_wp * sigma_SB * T_0(j,i) ** 3 &
887	+ lambda_skin + f_H / exn
888
889	ENDIF
890
891	tend = 0.0_wp
892
893	!
894	!-- Implicit solution when the skin layer has no heat capacity,
895	!-- otherwise use RK3 scheme.
896	T_0_p(j,i) = ( coef_1 * dt_3d * tsc(2) + C_skin * T_0(j,i) ) / &
897	( C_skin + coef_2 * dt_3d * tsc(2) )
898
899	!
900	!-- Add RK3 term
901	T_0_p(j,i) = T_0_p(j,i) + dt_3d * tsc(3) * tT_soil_m(0,j,i)
902
903	!
904	!-- Calculate true tendency
905	tend = (T_0_p(j,i) - T_0(j,i) - tsc(3) * tT_0_m(j,i)) / (dt_3d &
906	* tsc(2))
907
908	!
909	!-- Calculate T_0 tendencies for the next Runge-Kutta step
910	IF ( timestep_scheme(1:5) == 'runge' ) THEN
911	IF ( intermediate_timestep_count == 1 ) THEN
912	tT_0_m(j,i) = tend
913	ELSEIF ( intermediate_timestep_count < &
914	intermediate_timestep_count_max ) THEN
915	tT_0_m(j,i) = -9.5625_wp * tend + 5.3125_wp * tT_0_m(j,i)
916	ENDIF
917	ENDIF
918
919	pt_p(k,j,i) = T_0_p(j,i) / exn
920	!
921	!-- Calculate fluxes
922	Rn(j,i) = Rn(j,i) + 3.0_wp * sigma_SB * T_0(j,i)**4 &
923	- 4.0_wp * sigma_SB * T_0(j,i)*3 T_0_p(j,i)
924	G(j,i) = lambda_skin * (T_0_p(j,i) - T_soil(0,j,i))
925	H(j,i) = - f_H * ( pt_p(k+1,j,i) - pt_p(k,j,i) )
926
927	IF ( humidity ) THEN
928	LE(j,i) = - f_LE * ( q_p(k+1,j,i) - q_s + dq_s_dT &
929	* T_0(j,i) - dq_s_dT * T_0_p(j,i) )
930
931	LE_veg(j,i) = - f_LE_veg * ( q_p(k+1,j,i) - q_s + dq_s_dT &
932	* T_0(j,i) - dq_s_dT * T_0_p(j,i) )
933	LE_soil(j,i) = - f_LE_soil * ( q_p(k+1,j,i) - q_s + dq_s_dT &
934	* T_0(j,i) - dq_s_dT * T_0_p(j,i) )
935	LE_liq(j,i) = - f_LE_liq * ( q_p(k+1,j,i) - q_s + dq_s_dT &
936	* T_0(j,i) - dq_s_dT * T_0_p(j,i) )
937	ENDIF
938
939	! IF ( i == 1 .AND. j == 1 ) THEN
940	! PRINT*, "Rn", Rn(j,i)
941	! PRINT*, "H", H(j,i)
942	! PRINT*, "LE", LE(j,i)
943	! PRINT*, "LE_liq", LE_liq(j,i)
944	! PRINT*, "LE_veg", LE_veg(j,i)
945	! PRINT*, "LE_soil", LE_soil(j,i)
946	! PRINT*, "G", G(j,i)
947	! ENDIF
948
949	!
950	!-- Calculate the true surface resistance
951	IF ( LE(j,i) .EQ. 0.0 ) THEN
952	r_s(j,i) = 1.0E10
953	ELSE
954	r_s(j,i) = - rho_lv * ( q_p(k+1,j,i) - q_s + dq_s_dT * T_0(j,i)&
955	- dq_s_dT * T_0_p(j,i) ) / LE(j,i) - r_a(j,i)
956	ENDIF
957
958	!
959	!-- Calculate fluxes in the atmosphere
960	shf(j,i) = H(j,i) / rho_cp
961
962	!
963	!-- Calculate change in liquid water reservoir due to dew fall or
964	!-- evaporation of liquid water
965	IF ( humidity ) THEN
966	!
967	!-- If precipitation is activated, add rain water to LE_liq.
968	!-- precipitation_rate is given in mm.
969	IF ( precipitation ) THEN
970	LE_liq(j,i) = LE_liq(j,i) + precipitation_rate(j,i) &
971	* 0.001_wp * rho_l * l_v
972	ENDIF
973	!
974	!-- If the air is saturated, check the reservoir water level
975	IF ( q_s .LE. q_p(k+1,j,i)) THEN
976	!
977	!-- Check if reservoir is full (avoid values > m_liq_max)
978	!-- In that case, LE_liq goes to LE_soil. In this case
979	!-- LE_veg is zero anyway (because c_liq = 1), so that tend is
980	!-- zero and no further check is needed
981	IF ( m_liq(j,i) .EQ. m_liq_max ) THEN
982	LE_soil(j,i) = LE_soil(j,i) + LE_liq(j,i)
983	LE_liq(j,i) = 0.0_wp
984	ENDIF
985
986	!
987	!-- In case LE_veg becomes negative (unphysical behavior), let
988	!-- the water enter the liquid water reservoir as dew on the
989	!-- plant
990	IF ( LE_veg(j,i) .LT. 0.0_wp ) THEN
991	LE_liq(j,i) = LE_liq(j,i) + LE_veg(j,i)
992	LE_veg(j,i) = 0.0_wp
993	ENDIF
994	ENDIF
995
996	tend = - LE_liq(j,i) * drho_l_lv
997
998	m_liq_p(j,i) = m_liq(j,i) + dt_3d * ( tsc(2) * tend &
999	+ tsc(3) * tm_liq_m(j,i) )
1000
1001	!
1002	!-- Check if reservoir is overfull -> reduce to maximum
1003	!-- (conservation of water is violated here)
1004	m_liq_p(j,i) = MIN(m_liq_p(j,i),m_liq_max)
1005
1006	!
1007	!-- Check if reservoir is empty (avoid values < 0.0)
1008	!-- (conservation of water is violated here)
1009	m_liq_p(j,i) = MAX(m_liq_p(j,i),0.0_wp)
1010
1011
1012	!
1013	!-- Calculate m_liq tendencies for the next Runge-Kutta step
1014	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1015	IF ( intermediate_timestep_count == 1 ) THEN
1016	tm_liq_m(j,i) = tend
1017	ELSEIF ( intermediate_timestep_count < &
1018	intermediate_timestep_count_max ) THEN
1019	tm_liq_m(j,i) = -9.5625_wp * tend + 5.3125_wp &
1020	* tm_liq_m(j,i)
1021	ENDIF
1022	ENDIF
1023
1024	!
1025	!-- Calculate moisture flux in the atmosphere
1026	qsws(j,i) = LE(j,i) / rho_lv
1027
1028	ENDIF
1029
1030	ENDDO
1031	ENDDO
1032
1033
1034
1035	END SUBROUTINE lsm_energy_balance
1036
1037
1038	!------------------------------------------------------------------------------!
1039	! Description:
1040	! ------------
1041	!
1042	!------------------------------------------------------------------------------!
1043	SUBROUTINE lsm_soil_model
1044
1045
1046	IMPLICIT NONE
1047
1048	INTEGER(iwp) :: i !: running index
1049	INTEGER(iwp) :: j !: running index
1050	INTEGER(iwp) :: k !: running index
1051
1052	REAL(wp) :: h_VG !: Van Genuchten coef. h
1053
1054	REAL(wp), DIMENSION(0:soil_layers-1) :: gamma_temp, & !: temp. gamma
1055	lambda_temp, & !: temp. lambda
1056	tend !: tendency
1057
1058	DO i = nxlg, nxrg
1059	DO j = nysg, nyng
1060	DO k = 0, soil_layers-1
1061	!
1062	!-- Calculate volumetric heat capacity of the soil, taking into
1063	!-- account water content
1064	rhoC_total(k,j,i) = (rhoC_soil * (1.0 - m_sat(j,i)) &
1065	+ rhoC_water * m_soil(k,j,i))
1066
1067	!
1068	!-- Calculate soil heat conductivity at the center of the soil
1069	!-- layers
1070	Ke = 1.0 + LOG10(MAX(0.1,m_soil(k,j,i) / m_sat(j,i)))
1071	lambda_temp(k) = Ke * (lambda_h_sat(j,i) + lambda_h_dry) + &
1072	lambda_h_dry
1073
1074	ENDDO
1075
1076	!
1077	!-- Calculate soil heat conductivity (lambda_h) at the _stag level
1078	!-- using linear interpolation
1079	DO k = 0, soil_layers-2
1080
1081	lambda_h(k,j,i) = lambda_temp(k) + &
1082	( lambda_temp(k+1) - lambda_temp(k) ) &
1083	* 0.5 * dz_soil_stag(k) * ddz_soil(k+1)
1084
1085	ENDDO
1086	lambda_h(soil_layers-1,j,i) = lambda_temp(soil_layers-1)
1087
1088	!
1089	!-- Prognostic equation for soil temperature T_soil
1090	tend(:) = 0.0_wp
1091	tend(0) = (1.0/rhoC_total(0,j,i)) * &
1092	( lambda_h(0,j,i) * ( T_soil(1,j,i) - T_soil(0,j,i) ) &
1093	* ddz_soil(0) + G(j,i) ) * ddz_soil_stag(0)
1094
1095	DO k = 1, soil_layers-1
1096	tend(k) = (1.0/rhoC_total(k,j,i)) &
1097	* ( lambda_h(k,j,i) &
1098	* ( T_soil(k+1,j,i) - T_soil(k,j,i) ) &
1099	* ddz_soil(k) &
1100	- lambda_h(k-1,j,i) &
1101	* ( T_soil(k,j,i) - T_soil(k-1,j,i) ) &
1102	* ddz_soil(k-1) &
1103	) * ddz_soil_stag(k)
1104	ENDDO
1105
1106	T_soil_p(0:soil_layers-1,j,i) = T_soil(0:soil_layers-1,j,i) &
1107	+ dt_3d * ( tsc(2) &
1108	* tend(:) + tsc(3) &
1109	* tT_soil_m(:,j,i) )
1110
1111	!
1112	!-- Calculate T_soil tendencies for the next Runge-Kutta step
1113	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1114	IF ( intermediate_timestep_count == 1 ) THEN
1115	DO k = 0, soil_layers-1
1116	tT_soil_m(k,j,i) = tend(k)
1117	ENDDO
1118	ELSEIF ( intermediate_timestep_count < &
1119	intermediate_timestep_count_max ) THEN
1120	DO k = 0, soil_layers-1
1121	tT_soil_m(k,j,i) = -9.5625_wp * tend(k) + 5.3125_wp &
1122	* tT_soil_m(k,j,i)
1123	ENDDO
1124	ENDIF
1125	ENDIF
1126
1127
1128	DO k = 0, soil_layers-1
1129	!
1130	!-- Calculate soil diffusivity at the center of the soil layers
1131	lambda_temp(k) = (- b_CH * gamma_w_sat(j,i) * psi_sat &
1132	/ m_sat(j,i) ) * ( MAX(m_soil(k,j,i), &
1133	m_wilt(j,i)) / m_sat(j,i) )**(b_CH + 2.0_wp)
1134
1135	!
1136	!-- Calculate the hydraulic conductivity after Van Genuchten (1980)
1137	h_VG = ( ( (m_res(j,i) - m_sat(j,i)) / ( m_res(j,i) - &
1138	MAX(m_soil(k,j,i),m_wilt(j,i)) ) )**(n_VG(j,i) &
1139	/ (n_VG(j,i)-1.0_wp)) - 1.0_wp &
1140	)**(1.0_wp/n_VG(j,i)) / alpha_VG(j,i)
1141
1142	gamma_temp(k) = gamma_w_sat(j,i) * ( ( (1.0_wp + &
1143	(alpha_VG(j,i)h_VG)n_VG(j,i))*(1.0_wp &
1144	-1.0_wp/n_VG(j,i)) - (alpha_VG(j,i)*h_VG &
1145	)(n_VG(j,i)-1.0_wp))2 ) &
1146	/ ( (1.0_wp + (alpha_VG(j,i)h_VG)*n_VG(j,i) &
1147	)*((1.0_wp - 1.0_wp/n_VG(j,i))(l_VG(j,i) &
1148	+ 2.0)) )
1149
1150	ENDDO
1151
1152
1153	IF ( humidity ) THEN
1154	!
1155	!-- Calculate soil diffusivity (lambda_w) at the _stag level
1156	!-- using linear interpolation
1157	DO k = 0, soil_layers-2
1158
1159	lambda_w(k,j,i) = lambda_temp(k) + &
1160	( lambda_temp(k+1) - lambda_temp(k) ) &
1161	* 0.5 * dz_soil_stag(k) * ddz_soil(k+1)
1162	gamma_w(k,j,i) = gamma_temp(k) + &
1163	( gamma_temp(k+1) - gamma_temp(k) ) &
1164	* 0.5 * dz_soil_stag(k) * ddz_soil(k+1)
1165
1166	ENDDO
1167
1168	!
1169	!
1170	!-- In case of a closed bottom (= water content is conserved), set
1171	!-- hydraulic conductivity to zero to that no water will be lost
1172	!-- in the bottom layer.
1173	IF ( conserve_water_content ) THEN
1174	gamma_w(soil_layers-1,j,i) = 0.0_wp
1175	ELSE
1176	gamma_w(soil_layers-1,j,i) = lambda_temp(soil_layers-1)
1177	ENDIF
1178
1179	!-- The root extraction (= root_extr * LE_veg / (rho_l * l_v))
1180	!-- ensures the mass conservation for water. The transpiration of
1181	!-- plants equals the cumulative withdrawals by the roots in the
1182	!-- soil. The scheme takes into account the availability of water
1183	!-- in the soil layers as well as the root fraction in the
1184	!-- respective layer
1185
1186	!
1187	!-- Calculate the root extraction (ECMWF 7.69, with some
1188	!-- modifications)
1189	m_total = 0.0_wp
1190	DO k = 0, soil_layers-1
1191	m_total = m_total + root_fr(k,j,i) * m_soil(k,j,i) * &
1192	dz_soil_stag(k)
1193
1194	ENDDO
1195
1196	!
1197	!-- For conservation of mass, the sum of root_extr must be 1
1198	DO k = 0, soil_layers-1
1199	root_extr(k) = root_fr(k,j,i) * m_soil(k,j,i) &
1200	* dz_soil_stag(k) / m_total
1201	ENDDO
1202
1203
1204	!
1205	!-- Prognostic equation for soil water content m_soil
1206	tend(:) = 0.0_wp
1207	tend(0) = ( lambda_w(0,j,i) * ( m_soil(1,j,i) - m_soil(0,j,i) )&
1208	* ddz_soil(0) - gamma_w(0,j,i) - ( root_extr(0) &
1209	* LE_veg(j,i) + LE_soil(j,i) ) * drho_l_lv &
1210	) * ddz_soil_stag(0)
1211
1212	DO k = 1, soil_layers-2
1213	tend(k) = ( lambda_w(k,j,i) * ( m_soil(k+1,j,i) &
1214	- m_soil(k,j,i) ) * ddz_soil(k) - gamma_w(k,j,i)&
1215	- lambda_w(k-1,j,i) * (m_soil(k,j,i) - &
1216	m_soil(k-1,j,i)) * ddz_soil(k-1) &
1217	+ gamma_w(k-1,j,i) - (root_extr(k) * LE_veg(j,i)&
1218	* drho_l_lv) &
1219	) * ddz_soil_stag(k)
1220
1221	ENDDO
1222	tend(soil_layers-1) = ( - gamma_w(soil_layers-1,j,i) &
1223	- lambda_w(soil_layers-2,j,i) &
1224	* (m_soil(soil_layers-1,j,i) &
1225	- m_soil(soil_layers-2,j,i)) &
1226	* ddz_soil(soil_layers-2) &
1227	+ gamma_w(soil_layers-2,j,i) - ( &
1228	root_extr(soil_layers-1) &
1229	* LE_veg(j,i) * drho_l_lv ) &
1230	) * ddz_soil_stag(soil_layers-1)
1231
1232	m_soil_p(0:soil_layers-1,j,i) = m_soil(0:soil_layers-1,j,i) &
1233	+ dt_3d * ( tsc(2) * tend(:) &
1234	+ tsc(3) * tm_soil_m(:,j,i) )
1235
1236	!
1237	!-- Account for dry soils (find a better solution here!)
1238	m_soil_p(:,j,i) = MAX(m_soil_p(:,j,i),0.0_wp)
1239
1240	!
1241	!-- Calculate m_soil tendencies for the next Runge-Kutta step
1242	IF ( timestep_scheme(1:5) == 'runge' ) THEN
1243	IF ( intermediate_timestep_count == 1 ) THEN
1244	DO k = 0, soil_layers-1
1245	tm_soil_m(k,j,i) = tend(k)
1246	ENDDO
1247	ELSEIF ( intermediate_timestep_count < &
1248	intermediate_timestep_count_max ) THEN
1249	DO k = 0, soil_layers-1
1250	tm_soil_m(k,j,i) = -9.5625_wp * tend(k) + 5.3125_wp &
1251	* tm_soil_m(k,j,i)
1252	ENDDO
1253	ENDIF
1254	ENDIF
1255
1256	ENDIF
1257
1258	ENDDO
1259	ENDDO
1260
1261	!
1262	!-- Calculate surface specific humidity
1263	IF ( humidity ) THEN
1264	CALL calc_q0
1265	ENDIF
1266
1267
1268	END SUBROUTINE lsm_soil_model
1269
1270
1271	!------------------------------------------------------------------------------!
1272	! Description:
1273	! ------------
1274	!
1275	!------------------------------------------------------------------------------!
1276	SUBROUTINE calc_q0
1277
1278	IMPLICIT NONE
1279
1280	INTEGER :: i !: running index
1281	INTEGER :: j !: running index
1282	INTEGER :: k !: running index
1283	REAL(wp) :: resistance !: aerodynamic and soil resistance term
1284
1285	DO i = nxlg, nxrg
1286	DO j = nysg, nyng
1287	k = nzb_s_inner(j,i)
1288	!
1289	!-- Temporary solution as long as T_0 is prescribed
1290
1291	pt_p(k,j,i) = T_0(j,i) / exn
1292	!
1293	!-- Calculate water vapour pressure at saturation
1294	e_s = 0.01_wp * 610.78_wp * EXP( 17.269_wp * ( T_0(j,i) - &
1295	273.16_wp ) / ( T_0(j,i) - &
1296	35.86_wp ) )
1297
1298	!
1299	!-- Calculate specific humidity at saturation
1300	q_s = 0.622_wp * e_s / surface_pressure
1301
1302
1303	resistance = r_a(j,i) / (r_a(j,i) + r_s(j,i))
1304
1305	!
1306	!-- Calculate specific humidity at surface
1307	q_p(k,j,i) = resistance * q_s + (1.0_wp - resistance) &
1308	* q_p(k+1,j,i)
1309
1310	ENDDO
1311	ENDDO
1312
1313	END SUBROUTINE calc_q0
1314
1315
1316	END MODULE land_surface_model_mod

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