source: CONFIG_DEVT/LMDZOR_V6.2_work_ENSEMBLES/modeles/ORCHIDEE/DOC/ORCHIDEE/src_sechiba/enerbil/equations_collated.tex @ 5477

Last change on this file since 5477 was 5477, checked in by aclsce, 4 years ago
  • Created CONFIG_DEVT directory
  • First import of LMDZOR_V6.2_work_ENSEMBLES working configuration
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1\documentclass{article}
2\begin{document}
3
4
5{ \bf enerbil.f90 equations }
6
7\vspace {10mm}
8{ \bf enerbil\_begin }
9
10\vspace {10mm}
11enerbilbegin1.tex
12
13\begin{equation}
14    ps^{t} = T_S C_p
15\end{equation}
16
17\vspace {10mm}
18enerbilbegin2.tex
19
20\begin{equation}
21    \frac{\delta q_s^{t}}{\delta t} = \delta q_s \frac{(p_l)^\kappa}{C_p^{air}}
22\end{equation}
23
24\vspace {10mm}
25enerbilbegin3.tex
26
27\begin{equation}
28    R^{LW}_{abs} = \epsilon R^{LW}_{\downarrow}
29\end{equation}
30
31\vspace {10mm}
32enerbilbegin4.tex
33
34\begin{equation}
35    R_{net} = R^{LW}_{\downarrow} + S^{SW}_{net} - \epsilon \sigma T^4 (1-\epsilon) R^{LW}_{\downarrow}
36\end{equation}
37
38\vspace {10mm}
39{ \bf enerbil\_surftemp }
40
41\vspace {10mm}
42enerbilsurftemp1.tex
43
44\begin{equation}
45    U = max \{ U_{min}, \sqrt{u^2 + v^2} \}
46\end{equation}
47
48\vspace {10mm}
49enerbilsurftemp2.tex
50
51\begin{equation}
52    z_{ikt}=\frac{1}{\rho_{air} U q_{c}}; \quad z_{ikq}=\frac{1}{\rho_{air} U q_{c}}
53\end{equation}
54
55\vspace {10mm}
56enerbilsurftemp3.tex
57
58\begin{equation}
59    H^{t} = \frac{B_T^{orc} - ps^{t}}{z_{ikt} - A_T^{orc}}
60\end{equation}
61
62\vspace {10mm}
63enerbilsurftemp4.tex
64
65\begin{equation}
66    \lambda E _{sub}^{t} = \lambda E_{sub}^0 \frac{B_q^{orc} - q_{s, sat}}{z_{ikq}-A_q^{orc}}
67\end{equation}
68
69\vspace {10mm}
70enerbilsurftemp5.tex
71
72\begin{equation}
73    \lambda E _{evap}^{t} = \lambda E_{evap}^0  \left( 1-\beta_{v1} \beta_v \left( \frac {  B_q^{orc} - \alpha_v q_{s, sat}  }{  z_{ikq} - A_q^{orc}  }  \right) \right)
74\end{equation}
75
76\vspace {10mm}
77enerbilsurftemp6.tex
78
79\begin{equation}
80    R^{net}_{sns} = \left( \frac{1}{C_p} \right) 4 \epsilon \sigma \left( \left( \frac{1}{C_p} \right) ps_{t} ^3 \right)
81\end{equation}
82
83\vspace {10mm}
84enerbilsurftemp7.tex
85
86\begin{equation}
87    H_{sns} = \frac{1} { \left( \frac{1}{\rho_{air} S q_{c}} - A_T^{orc} \right)}
88\end{equation}
89
90\vspace {10mm}
91enerbilsurftemp8.tex
92
93\begin{equation}
94    \lambda E_{sns}^{sub} = \lambda E_{sub}^0 \beta_{v1} \frac{1}{C_p} \left( \frac{ ({\delta q_s^{t}}/{\delta t}) } {z_{ikq} - A_q^{orc} } \right)
95\end{equation}
96
97\vspace {10mm}
98enerbilsurftemp9.tex
99
100\begin{equation}
101    \lambda E_{sns}^{evap} = \lambda E_{evap}^0 (1-\beta_{v1}) \beta_v \alpha_v \frac{1}{C_p} \left( \frac{ ({\delta q_s^{t}}/{\delta t}) } {z_{ikq} - A_q^{orc} } \right)
102\end{equation}
103
104\vspace {10mm}
105enerbilsurftemp10.tex
106
107\begin{equation}
108    \Sigma E^{t} = R_{net} + H^{t} + {\lambda E}_{sub}^{t} + {\lambda E}_{evap}^{t} + G
109\end{equation}
110
111\vspace {10mm}
112enerbilsurftemp11.tex
113
114\begin{equation}
115    \Sigma E^{sns} = R^{sns} + H^{sns} + {\lambda E}_{sub}^{sns} + {\lambda E}_{evap}^{sns} + G
116\end{equation}
117
118\vspace {10mm}
119enerbilsurftemp12.tex
120
121\begin{equation}
122    \Delta \theta = \frac {\Delta t (\Sigma E^{t})} {\left( \frac {1}{C_p^{air}} (C_p^{soil} + \Delta T) (\Sigma E^{sns}) \right)}
123\end{equation}
124
125\vspace {10mm}
126enerbilsurftemp13.tex
127
128\begin{equation}
129    ps_{t+\Delta t} = ps_{t} + \Delta \theta
130\end{equation}
131
132\vspace {10mm}
133enerbilsurftemp14.tex
134
135\begin{equation}
136    q_{s,sat}^{t+\Delta t} = q_{s,sat} + \left( \left( \frac{1}{C_p^{air}} \right) \left( \frac{\delta q_s^{t}}{\delta t} \right) \delta\theta \right)
137\end{equation}
138
139\vspace {10mm}
140enerbilsurftemp15.tex
141
142\begin{equation}
143    T_{s}^{t+\Delta t} = \frac {ps^{t+\Delta t}}{C_p^{air}}
144\end{equation}
145
146\vspace {10mm}
147enerbilsurftemp16.tex
148
149\begin{equation}
150    E_{pot}^{air,t+\Delta t} = z_{ikt} (H^{t} - H^{sns} \Delta \theta) + ps^{t+\Delta t}
151\end{equation}
152
153\vspace {10mm}
154enerbilsurftemp17.tex
155
156\begin{equation}
157    {\lambda E} ^{evap} = ({\lambda E}_{evap}^{t} - {\lambda E} _{evap} ^{sns} \Delta \theta) + ({\lambda E}_{sub}^{t} - {\lambda E}_{sub}^{sns} \Delta \theta)
158\end{equation}
159
160\vspace {10mm}
161enerbilsurftemp18.tex
162
163\begin{equation}
164    q_{air}^{t+\Delta t}(ji) = q_{air}(ji)
165\end{equation}
166
167\vspace {10mm}
168enerbilsurftemp19.tex
169
170\begin{equation}
171   q_{air}^{t+\Delta t} = z_{ikq} \frac {1} {(\lambda E^{evap}_0  (1 - \beta_{v1}) \beta_1 \alpha_v + \lambda E^{sub}_0 \beta_{v1})} {\lambda E} ^{evap} + q_{s,sat}^{t+\Delta t} 
172\end{equation}
173
174\vspace {10mm}
175{ \bf surf\_land\_orchidee (links from LMDZ to ORCHIDEE)} 
176
177\vspace {10mm}
178surflandLMDZ1.tex
179
180\begin{equation}
181    A_T^{orc} = B_T^{lmdz} \Delta t
182\end{equation}
183
184\vspace {10mm}
185surflandLMDZ2.tex
186
187\begin{equation}
188    B_T^{orc} = A_T^{lmdz}
189\end{equation}
190
191\vspace {10mm}
192surflandLMDZ3.tex
193
194\begin{equation}
195    A_q^{orc} = B_q^{lmdz} \Delta t
196\end{equation}
197
198\vspace {10mm}
199surflandLMDZ4.tex
200
201\begin{equation}
202    B_q^{orc} = A_q^{lmdz}
203\end{equation}
204
205\vspace {10mm}
206{ \bf enerbil\_flux} 
207
208\vspace {10mm}
209enerbilflux1.tex
210
211\begin{equation}
212    U=max\{U_{min}, \sqrt{u^2+v^2} \}
213\end{equation}
214
215\vspace {10mm}
216enerbilflux2.tex
217
218\begin{equation}
219    q_c=|v|q_{c, drag}
220\end{equation}
221
222\vspace {10mm}
223enerbilflux3.tex
224
225\begin{equation}
226    R^{LW}_{\uparrow}=\epsilon \sigma T_{sol}^4+\epsilon 4 \sigma T_{sol}^3(T_{s}^{t+\Delta t}-T_{s})
227\end{equation}
228
229\vspace {10mm}
230enerbilflux4.tex
231
232\begin{equation}
233    R^{LW}_{\uparrow}=R^{LW}_{\uparrow}+(1-\epsilon)R^{LW}_{\downarrow}
234\end{equation}
235
236\vspace {10mm}
237enerbilflux5.tex
238
239\begin{equation}
240    T_{s}^{rad}=\epsilon \sigma T_{s}^4 + R^{LW}_{\uparrow}
241\end{equation}
242
243\vspace {10mm}
244enerbilflux6.tex
245
246\begin{equation}
247    q_{surf}=\beta_{v,1} (q_{s,sat}^{t+\Delta t})+(1-\beta_{v,1})\beta_v\alpha_v(q_{s,sat}^{t+\Delta t})
248\end{equation}
249
250\vspace {10mm}
251enerbilflux7.tex
252
253\begin{equation}
254    q_s = max \{q_s, q_{air} \}
255\end{equation}
256
257\vspace {10mm}
258enerbilflux8.tex
259
260\begin{equation}
261    R_{net}=R^{LW}_{\downarrow}+R^{SW}_{net}-R^{LW}_{\uparrow}
262\end{equation}
263
264\vspace {10mm}
265enerbilflux9.tex
266
267\begin{equation}
268    vev_{app} = dt(\rho)q_c \beta_{v,1}(q_{s,sat}^{t+\Delta t}-q_{air})+\Delta t(\rho)q_c(1-\beta_{1,v}\beta_v(\alpha_v)q_{s,sat}^{t+\Delta t}-q_{air})
269\end{equation}
270
271\vspace {10mm}
272enerbilflux10.tex
273
274\begin{equation}
275   H=\lambda E_0^{sub}(\rho)q_c(\beta_{v,1})(q_{s,sat}^{t+\Delta t}-q_{air}+\lambda E_0^{evap}(\rho)q_c(1-\beta_{v,1})\beta_v(\alpha_v)q_{s,sat}^{t+\Delta t}-q_{air})
276\end{equation}
277
278\vspace {10mm}
279enerbilflux11.tex
280
281\begin{equation}
282   \lambda E^{sub}=\lambda E_0^{sub} (\rho)q_c\beta_{v,1}(q_{s,sat}^{t+\Delta t}-q_{air})
283\end{equation}
284
285\vspace {10mm}
286enerbilflux12.tex
287
288\begin{equation}
289    H = \rho q_c (ps^{t+\Delta t}- E^{pot}_{air})
290\end{equation}
291
292\vspace {10mm}
293enerbilflux13.tex
294
295\begin{equation}
296   R^{LW}_{net} = R^{LW}_{\downarrow}-R^{LW}_{\uparrow}
297\end{equation}
298
299\vspace {10mm}
300enerbilflux14.tex
301
302\begin{equation}
303   E^{pot}_{air} = max \{0, \Delta t \rho q_c (q_{s,sat}^{t+\Delta t} -q_{air}) \}
304\end{equation}
305
306\vspace {10mm}
307enerbilflux15.tex
308
309\begin{equation}
310   T_{air}= \frac{E^{pot}_{air}}{c_{p, air}}
311\end{equation}
312
313
314
315
316
317
318
319
320
321{\bf enerbil\_evapveg.f90}
322
323\vspace {10mm}
324enerbilevapveg1.tex
325
326\begin{equation}
327    U = max\{U_{min}, \sqrt{u^2 + v^2} \}
328\end{equation}
329
330\vspace {10mm}
331enerbilevapveg2.tex
332
333\begin{equation}
334   E^{snow} = \beta_{v1} \Delta t \rho U q_c^{drag} (q_{sol,s}^{t+\Delta t}- q_{air})
335\end{equation}
336
337\vspace {10mm}
338enerbilevapveg3.tex
339
340\begin{equation}
341   E^{soil} = (1-\beta_{v1})\beta_{v4} \Delta t \rho U q_c^{drag} (q_{sol,s}^{t+\Delta t} - q_{air})
342\end{equation}
343
344\vspace {10mm}
345enerbilevapveg4.tex
346
347\begin{equation}
348    U = max\{U_{min}, \sqrt{u^2 + v^2} \}
349\end{equation}
350
351\vspace {10mm}
352enerbilevapveg5.tex
353
354\begin{equation}
355   xx = \Delta t (1-\beta_{v1}) (q_{s,sat}^{t+\Delta t} - q_{a}) \rho S q_c^{drag}
356\end{equation}
357
358\vspace {10mm}
359enerbilevapveg6.tex
360
361\begin{equation}
362   (Interception) = xx \beta_{v2}
363\end{equation}
364
365\vspace {10mm}
366enerbilevapveg7.tex
367
368\begin{equation}
369   (Transpiration) = xx \beta_{v3}
370\end{equation}
371
372
373\vspace {10mm}
374enerbilevapveg8.tex
375
376\begin{equation}
377   U = max \{U_{min}, \sqrt{u^2 + v^2} \}
378\end{equation}
379
380
381\vspace {10mm}
382enerbilevapveg9.tex
383
384\begin{equation}
385   (Assimilation) = \beta_{v,CO_2} \Delta t \rho S q_c^{drag} (\chi_{CO_2}^{canopy} - \bar{Ci})
386\end{equation}
387
388
389
390
391
392\end{document}
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