| 3 |
michaesp |
1 |
c -------------------------------------------------------------------------
|
|
|
2 |
c Potential temperature (TH)
|
|
|
3 |
c -------------------------------------------------------------------------
|
|
|
4 |
|
|
|
5 |
subroutine calc_TH (pt,t,p)
|
|
|
6 |
|
|
|
7 |
implicit none
|
|
|
8 |
|
|
|
9 |
c Argument declaration
|
|
|
10 |
real pt ! Potential temperature [K]
|
|
|
11 |
real t ! Temperature [either in C or in K]
|
|
|
12 |
real p ! Pressure [hPa]
|
|
|
13 |
|
|
|
14 |
c Physical parameters
|
|
|
15 |
real rdcp,tzero
|
|
|
16 |
data rdcp,tzero /0.286,273.15/
|
|
|
17 |
|
|
|
18 |
c Calculation - distinction between temperature in C or in K
|
|
|
19 |
if (t.lt.100.) then
|
|
|
20 |
pt = (t+tzero) * ( (1000./p)**rdcp )
|
|
|
21 |
else
|
|
|
22 |
pt = t * ( (1000./p)**rdcp )
|
|
|
23 |
endif
|
|
|
24 |
|
|
|
25 |
end
|
|
|
26 |
|
|
|
27 |
c -------------------------------------------------------------------------
|
|
|
28 |
c Density (RHO)
|
|
|
29 |
c -------------------------------------------------------------------------
|
|
|
30 |
|
|
|
31 |
subroutine calc_RHO (rho,t,p)
|
|
|
32 |
|
|
|
33 |
implicit none
|
|
|
34 |
|
|
|
35 |
c Argument declaration
|
|
|
36 |
real rho ! Density [kg/m^3]
|
|
|
37 |
real t ! Temperature [either in C or in K]
|
|
|
38 |
real p ! Pressure [hPa]
|
|
|
39 |
|
|
|
40 |
c Physical parameters
|
|
|
41 |
real rd,tzero
|
|
|
42 |
data rd,tzero /287.05,273.15/
|
|
|
43 |
|
|
|
44 |
c Auxiliary variables
|
|
|
45 |
real tk
|
|
|
46 |
|
|
|
47 |
c Calculation - distinction between temperature in C or in K
|
|
|
48 |
if (t.lt.100.) then
|
|
|
49 |
tk = t + tzero
|
|
|
50 |
else
|
|
|
51 |
tk = t
|
|
|
52 |
endif
|
|
|
53 |
|
|
|
54 |
rho = 100.*p/( tk * rd )
|
|
|
55 |
|
|
|
56 |
end
|
|
|
57 |
|
|
|
58 |
c -------------------------------------------------------------------------
|
|
|
59 |
c Relative humidity (RH)
|
|
|
60 |
c -------------------------------------------------------------------------
|
|
|
61 |
|
|
|
62 |
subroutine calc_RH (rh,t,p,q)
|
|
|
63 |
|
|
|
64 |
implicit none
|
|
|
65 |
|
|
|
66 |
c Argument declaration
|
|
|
67 |
real rh ! Relative humidity [%]
|
|
|
68 |
real t ! Temperature [either in C or in K]
|
|
|
69 |
real p ! Pressure [hPa]
|
|
|
70 |
real q ! Specific humidity [g/kg]
|
|
|
71 |
|
|
|
72 |
c Physical parameters
|
|
|
73 |
real rdcp,tzero
|
|
|
74 |
data rdcp,tzero /0.286,273.15/
|
|
|
75 |
real b1,b2w,b3,b4w,r,rd
|
|
|
76 |
data b1,b2w,b3,b4w,r,rd /6.1078, 17.2693882, 273.16, 35.86,
|
|
|
77 |
& 287.05, 461.51/
|
|
|
78 |
|
|
|
79 |
c Auxiliary variables
|
|
|
80 |
real ge
|
|
|
81 |
real gqd
|
|
|
82 |
real tc
|
|
|
83 |
real pp,qk
|
|
|
84 |
|
|
|
85 |
c Calculation - distinction between temperature in C or in K
|
|
|
86 |
if (t.gt.100.) then
|
|
|
87 |
tc = t - tzero
|
|
|
88 |
else
|
|
|
89 |
tc = t
|
|
|
90 |
endif
|
|
|
91 |
qk = 0.001 * q
|
|
|
92 |
|
|
|
93 |
ge = b1*exp(b2w*tc/(tc+b3-b4w))
|
|
|
94 |
gqd = r/rd*ge/(p-(1.-r/rd)*ge)
|
|
|
95 |
rh = 100.*qk/gqd
|
|
|
96 |
|
|
|
97 |
end
|
|
|
98 |
|
|
|
99 |
c -------------------------------------------------------------------------
|
|
|
100 |
c Equivalent potential temperature (THE)
|
|
|
101 |
c -------------------------------------------------------------------------
|
|
|
102 |
|
|
|
103 |
subroutine calc_THE (the,t,p,q)
|
|
|
104 |
|
|
|
105 |
implicit none
|
|
|
106 |
|
|
|
107 |
c Argument declaration
|
|
|
108 |
real the ! Equivalent potential temperature [K]
|
|
|
109 |
real t ! Temperature [either in C or in K]
|
|
|
110 |
real p ! Pressure [hPa]
|
|
|
111 |
real q ! Specific humidity [g/kg]
|
|
|
112 |
|
|
|
113 |
c Physical parameters
|
|
|
114 |
real rdcp,tzero
|
|
|
115 |
data rdcp,tzero /0.286,273.15/
|
|
|
116 |
|
|
|
117 |
c Auxiliary variables
|
|
|
118 |
real tk,qk
|
|
|
119 |
|
|
|
120 |
c Calculation - distinction between temperature in C or in K
|
|
|
121 |
if (t.lt.100.) then
|
|
|
122 |
tk = t + tzero
|
|
|
123 |
else
|
|
|
124 |
tk = t
|
|
|
125 |
endif
|
|
|
126 |
qk = 0.001 * q
|
|
|
127 |
|
|
|
128 |
the = tk*(1000./p)
|
|
|
129 |
+ **(0.2854*(1.0-0.28*qk))*exp(
|
|
|
130 |
+ (3.376/(2840.0/(3.5*alog(tk)-alog(
|
|
|
131 |
+ 100.*p*max(1.0E-10,qk)/(0.622+0.378*
|
|
|
132 |
+ q))-0.1998)+55.0)-0.00254)*1.0E3*
|
|
|
133 |
+ max(1.0E-10,qk)*(1.0+0.81*qk))
|
|
|
134 |
|
|
|
135 |
end
|
|
|
136 |
|
|
|
137 |
c -------------------------------------------------------------------------
|
|
|
138 |
c Latent heating rate (LHR)
|
|
|
139 |
c -------------------------------------------------------------------------
|
|
|
140 |
|
|
|
141 |
subroutine calc_LHR (lhr,t,p,q,w,rh)
|
|
|
142 |
|
|
|
143 |
implicit none
|
|
|
144 |
|
|
|
145 |
c Argument declaration
|
|
|
146 |
real lhr ! Latent heating rate [K/h]
|
|
|
147 |
real t ! Temperature [either in C or in K]
|
|
|
148 |
real p ! Pressure [hPa]
|
|
|
149 |
real q ! Specific humidity [kg/kg]
|
|
|
150 |
real w ! Vertical velocity [m/s]
|
|
|
151 |
real rh ! Relative humidity [%]
|
|
|
152 |
|
|
|
153 |
c Physical parameters
|
|
|
154 |
real p0,kappa,tzero,g
|
|
|
155 |
data p0,kappa,tzero,g /1000.,0.286,273.15,9.81/
|
|
|
156 |
real blog10,cp,r,lw,eps
|
|
|
157 |
data blog10,cp,r,lw,eps /.08006,1004.,287.,2.5e+6,0.622/
|
|
|
158 |
|
|
|
159 |
c Auxiliary variables
|
|
|
160 |
real tk
|
|
|
161 |
real qk
|
|
|
162 |
real tt
|
|
|
163 |
real esat,c
|
|
|
164 |
real omega
|
|
|
165 |
|
|
|
166 |
c Calculation - distinction between temperature in C or in K
|
|
|
167 |
if (t.lt.100.) then
|
|
|
168 |
tk = t + tzero
|
|
|
169 |
else
|
|
|
170 |
tk = t
|
|
|
171 |
endif
|
|
|
172 |
qk = 0.001 * q
|
|
|
173 |
|
|
|
174 |
omega = -p/(r*tk) * g * w
|
|
|
175 |
|
|
|
176 |
if (rh.lt.80.) then
|
|
|
177 |
lhr = 0.
|
|
|
178 |
else if (omega.gt.0.) then
|
|
|
179 |
lhr = 0.
|
|
|
180 |
else
|
|
|
181 |
c = lw/cp*eps*blog10*esat(tk)/p
|
|
|
182 |
tt = (tk*(p0/p)**kappa)
|
|
|
183 |
lhr = 3600.*
|
|
|
184 |
> (1.-exp(.2*(80.-rh)))
|
|
|
185 |
> *(-c*kappa*tt*omega/(100.*p))/(1.+c)
|
|
|
186 |
|
|
|
187 |
endif
|
|
|
188 |
|
|
|
189 |
end
|
|
|
190 |
|
|
|
191 |
c -------------------------------------------------------------------------
|
|
|
192 |
c Wind speed (VEL)
|
|
|
193 |
c -------------------------------------------------------------------------
|
|
|
194 |
|
|
|
195 |
subroutine calc_VEL (vel,u,v)
|
|
|
196 |
|
|
|
197 |
implicit none
|
|
|
198 |
|
|
|
199 |
c Argument declaration
|
|
|
200 |
real vel ! Wind speed [m/s]
|
|
|
201 |
real u ! Zonal wind component [m/s]
|
|
|
202 |
real v ! Meridional wind component [m/s]
|
|
|
203 |
|
|
|
204 |
vel = sqrt ( u*u + v*v )
|
|
|
205 |
|
|
|
206 |
end
|
|
|
207 |
|
|
|
208 |
c -------------------------------------------------------------------------
|
|
|
209 |
c Wind direction (DIR)
|
|
|
210 |
c -------------------------------------------------------------------------
|
|
|
211 |
|
|
|
212 |
subroutine calc_DIR (dir,u,v)
|
|
|
213 |
|
|
|
214 |
implicit none
|
|
|
215 |
|
|
|
216 |
c Argument declaration
|
|
|
217 |
real dir ! Wind direction [deg]
|
|
|
218 |
real u ! Zonal wind component [m/s]
|
|
|
219 |
real v ! Meridional wind component [m/s]
|
|
|
220 |
|
|
|
221 |
call getangle(1.,0.,u,v,dir)
|
|
|
222 |
|
|
|
223 |
end
|
|
|
224 |
|
|
|
225 |
c -------------------------------------------------------------------------
|
|
|
226 |
c Zonal derivative of U (DUDX)
|
|
|
227 |
c -------------------------------------------------------------------------
|
|
|
228 |
|
|
|
229 |
subroutine calc_DUDX (dudx,u1,u0,lat)
|
|
|
230 |
|
|
|
231 |
implicit none
|
|
|
232 |
|
|
|
233 |
c Argument declaration
|
|
|
234 |
real dudx ! Derivative of U in zonal direction [s^-1]
|
|
|
235 |
real u1 ! U @ LON + 1 DLON [m/s]
|
|
|
236 |
real u0 ! U @ LON - 1 DLON [m/s]
|
|
|
237 |
real lat ! Latitude [deg]
|
|
|
238 |
|
|
|
239 |
c Physical parameters
|
|
|
240 |
real pi180
|
|
|
241 |
parameter (pi180=31.14159/180.)
|
|
|
242 |
real deltay
|
|
|
243 |
parameter (deltay =1.11e5)
|
|
|
244 |
|
|
|
245 |
dudx = (u1-u0) / ( 2. * deltay * cos(pi180 * lat) )
|
|
|
246 |
|
|
|
247 |
end
|
|
|
248 |
|
|
|
249 |
c -------------------------------------------------------------------------
|
|
|
250 |
c Zonal derivative of V (DVDX)
|
|
|
251 |
c -------------------------------------------------------------------------
|
|
|
252 |
|
|
|
253 |
subroutine calc_DVDX (dvdx,v1,v0,lat)
|
|
|
254 |
|
|
|
255 |
c Argument declaration
|
|
|
256 |
real dvdx ! Derivative of V in zonal direction [s^-1]
|
|
|
257 |
real v1 ! V @ LON + 1 DLON [m/s]
|
|
|
258 |
real v0 ! V @ LON - 1 DLON [m/s]
|
|
|
259 |
real lat ! Latitude [deg]
|
|
|
260 |
|
|
|
261 |
c Physical parameters
|
|
|
262 |
real pi180
|
|
|
263 |
parameter (pi180=3.14159/180.)
|
|
|
264 |
real deltay
|
|
|
265 |
parameter (deltay =1.11e5)
|
|
|
266 |
|
|
|
267 |
dvdx = (v1-v0) / ( 2. * deltay * cos(pi180 * lat) )
|
|
|
268 |
|
|
|
269 |
end
|
|
|
270 |
|
|
|
271 |
c -------------------------------------------------------------------------
|
|
|
272 |
c Zonal derivative of T (DTDX)
|
|
|
273 |
c -------------------------------------------------------------------------
|
|
|
274 |
|
|
|
275 |
subroutine calc_DTDX (dtdx,t1,t0,lat)
|
|
|
276 |
|
|
|
277 |
implicit none
|
|
|
278 |
|
|
|
279 |
c Argument declaration
|
|
|
280 |
real dtdx ! Derivative of T in zonal direction [K/m]
|
|
|
281 |
real t1 ! T @ LON + 1 DLON [K]
|
|
|
282 |
real t0 ! T @ LON - 1 DLON [K]
|
|
|
283 |
real lat ! Latitude [deg]
|
|
|
284 |
|
|
|
285 |
c Physical parameters
|
|
|
286 |
real pi180
|
|
|
287 |
parameter (pi180=3.14159/180.)
|
|
|
288 |
real deltay
|
|
|
289 |
parameter (deltay =1.11e5)
|
|
|
290 |
|
|
|
291 |
dtdx = (t1-t0) / ( 2. * deltay * cos(pi180 * lat) )
|
|
|
292 |
|
|
|
293 |
end
|
|
|
294 |
|
|
|
295 |
c -------------------------------------------------------------------------
|
|
|
296 |
c Zonal derivative of TH (DTHDX)
|
|
|
297 |
c -------------------------------------------------------------------------
|
|
|
298 |
|
|
|
299 |
subroutine calc_DTHDX (dthdx,t1,t0,p,lat)
|
|
|
300 |
|
|
|
301 |
implicit none
|
|
|
302 |
|
|
|
303 |
c Argument declaration
|
|
|
304 |
real dthdx ! Derivative of TH in zonal direction [K/m]
|
|
|
305 |
real t1 ! T @ LON + 1 DLON [K]
|
|
|
306 |
real t0 ! T @ LON - 1 DLON [K]
|
|
|
307 |
real p ! P [hPa]
|
|
|
308 |
real lat ! Latitude [deg]
|
|
|
309 |
|
|
|
310 |
c Physical parameters
|
|
|
311 |
real pi180
|
|
|
312 |
parameter (pi180=3.14159/180.)
|
|
|
313 |
real deltay
|
|
|
314 |
parameter (deltay =1.11e5)
|
|
|
315 |
real rdcp,pref
|
|
|
316 |
data rdcp,pref /0.286,1000./
|
|
|
317 |
|
|
|
318 |
dthdx = (pref/p)**rdcp *
|
|
|
319 |
> (t1-t0) / ( 2. * deltay * cos(pi180 * lat) )
|
|
|
320 |
|
|
|
321 |
end
|
|
|
322 |
|
|
|
323 |
c -------------------------------------------------------------------------
|
|
|
324 |
c Meridional derivative of U (DUDY)
|
|
|
325 |
c -------------------------------------------------------------------------
|
|
|
326 |
|
|
|
327 |
subroutine calc_DUDY (dudy,u1,u0)
|
|
|
328 |
|
|
|
329 |
implicit none
|
|
|
330 |
|
|
|
331 |
c Argument declaration
|
|
|
332 |
real dudy ! Derivative of U in meridional direction [s^-1]
|
|
|
333 |
real u1 ! U @ LAT + 1 DLAT [m/s]
|
|
|
334 |
real u0 ! U @ LAT - 1 DLAT [m/s]
|
|
|
335 |
|
|
|
336 |
c Physical parameters
|
|
|
337 |
real deltay
|
|
|
338 |
parameter (deltay =1.11e5)
|
|
|
339 |
|
|
|
340 |
dudy = (u1-u0) / ( 2. * deltay )
|
|
|
341 |
|
|
|
342 |
end
|
|
|
343 |
|
|
|
344 |
c -------------------------------------------------------------------------
|
|
|
345 |
c Meridional derivative of V (DVDY)
|
|
|
346 |
c -------------------------------------------------------------------------
|
|
|
347 |
|
|
|
348 |
subroutine calc_DVDY (dvdy,v1,v0)
|
|
|
349 |
|
|
|
350 |
implicit none
|
|
|
351 |
|
|
|
352 |
c Argument declaration
|
|
|
353 |
real dvdy ! Derivative of V in meridional direction [s^-1]
|
|
|
354 |
real v1 ! V @ LAT + 1 DLAT [m/s]
|
|
|
355 |
real v0 ! V @ LAT - 1 DLAT [m/s]
|
|
|
356 |
|
|
|
357 |
c Physical parameters
|
|
|
358 |
real deltay
|
|
|
359 |
parameter (deltay =1.11e5)
|
|
|
360 |
|
|
|
361 |
dvdy = (v1-v0) / ( 2. * deltay )
|
|
|
362 |
|
|
|
363 |
end
|
|
|
364 |
|
|
|
365 |
c -------------------------------------------------------------------------
|
|
|
366 |
c Meridional derivative of T (DTDY)
|
|
|
367 |
c -------------------------------------------------------------------------
|
|
|
368 |
|
|
|
369 |
subroutine calc_DTDY (dtdy,t1,t0)
|
|
|
370 |
|
|
|
371 |
implicit none
|
|
|
372 |
|
|
|
373 |
c Argument declaration
|
|
|
374 |
real dtdy ! Derivative of T in meridional direction [K/m]
|
|
|
375 |
real t1 ! T @ LAT + 1 DLAT [K]
|
|
|
376 |
real t0 ! T @ LAT - 1 DLAT [K]
|
|
|
377 |
|
|
|
378 |
c Physical parameters
|
|
|
379 |
real deltay
|
|
|
380 |
parameter (deltay =1.11e5)
|
|
|
381 |
|
|
|
382 |
dtdy = (t1-t0) / ( 2. * deltay )
|
|
|
383 |
|
|
|
384 |
end
|
|
|
385 |
|
|
|
386 |
c -------------------------------------------------------------------------
|
|
|
387 |
c Meridional derivative of TH (DTHDY)
|
|
|
388 |
c -------------------------------------------------------------------------
|
|
|
389 |
|
|
|
390 |
subroutine calc_DTHDY (dthdy,t1,t0,p)
|
|
|
391 |
|
|
|
392 |
implicit none
|
|
|
393 |
|
|
|
394 |
c Argument declaration
|
|
|
395 |
real dthdy ! Derivative of TH in meridional direction [K/m]
|
|
|
396 |
real t1 ! TH @ LAT + 1 DLAT [K]
|
|
|
397 |
real t0 ! TH @ LAT - 1 DLAT [K]
|
|
|
398 |
real p ! P [hPa]
|
|
|
399 |
|
|
|
400 |
c Physical parameters
|
|
|
401 |
real deltay
|
|
|
402 |
parameter (deltay =1.11e5)
|
|
|
403 |
real rdcp,pref
|
|
|
404 |
data rdcp,pref /0.286,1000./
|
|
|
405 |
|
|
|
406 |
dthdy = (pref/p)**rdcp * (t1-t0) / ( 2. * deltay )
|
|
|
407 |
|
|
|
408 |
end
|
|
|
409 |
|
|
|
410 |
c -------------------------------------------------------------------------
|
|
|
411 |
c Wind shear of U (DUDZ)
|
|
|
412 |
c -------------------------------------------------------------------------
|
|
|
413 |
|
|
|
414 |
subroutine calc_DUDZ (dudz,u1,u0,z1,z0)
|
|
|
415 |
|
|
|
416 |
implicit none
|
|
|
417 |
|
|
|
418 |
c Argument declaration
|
|
|
419 |
real dudz ! Wind shear [m/s per m = 1/m]
|
|
|
420 |
real u1 ! U @ Z + 1 DZ [m/s]
|
|
|
421 |
real u0 ! U @ Z - 1 DZ [m/s]
|
|
|
422 |
real z1 ! Z + 1 DZ [m]
|
|
|
423 |
real z0 ! Z - 1 DZ [m]
|
|
|
424 |
|
|
|
425 |
dudz = (u1-u0) / (z1-z0)
|
|
|
426 |
|
|
|
427 |
end
|
|
|
428 |
|
|
|
429 |
c -------------------------------------------------------------------------
|
|
|
430 |
c Wind shear of V (DVDZ)
|
|
|
431 |
c -------------------------------------------------------------------------
|
|
|
432 |
|
|
|
433 |
subroutine calc_DVDZ (dvdz,v1,v0,z1,z0)
|
|
|
434 |
|
|
|
435 |
implicit none
|
|
|
436 |
|
|
|
437 |
c Argument declaration
|
|
|
438 |
real dvdz ! Wind shear [m/s per m = 1/m]
|
|
|
439 |
real v1 ! V @ Z + 1 DZ [m/s]
|
|
|
440 |
real v0 ! V @ Z - 1 DZ [m/s]
|
|
|
441 |
real z1 ! Z + 1 DZ [m]
|
|
|
442 |
real z0 ! Z - 1 DZ [m]
|
|
|
443 |
|
|
|
444 |
dvdz = (v1-v0) / (z1-z0)
|
|
|
445 |
|
|
|
446 |
end
|
|
|
447 |
|
|
|
448 |
c -------------------------------------------------------------------------
|
|
|
449 |
c Vertical derivative of T (DTDZ)
|
|
|
450 |
c -------------------------------------------------------------------------
|
|
|
451 |
|
|
|
452 |
subroutine calc_DTDZ (dtdz,t1,t0,z1,z0)
|
|
|
453 |
|
|
|
454 |
implicit none
|
|
|
455 |
|
|
|
456 |
c Argument declaration
|
|
|
457 |
real dtdz ! Vertical derivative of T [K/m]
|
|
|
458 |
real t1 ! T @ Z + 1 DZ [K]
|
|
|
459 |
real t0 ! T @ Z - 1 DZ [K]
|
|
|
460 |
real z1 ! Z + 1 DZ [m]
|
|
|
461 |
real z0 ! Z - 1 DZ [m]
|
|
|
462 |
|
|
|
463 |
dtdz = (t1-t0) / (z1-z0)
|
|
|
464 |
|
|
|
465 |
end
|
|
|
466 |
|
|
|
467 |
c -------------------------------------------------------------------------
|
|
|
468 |
c Vertical derivative of TH (DTHDẐ)
|
|
|
469 |
c -------------------------------------------------------------------------
|
|
|
470 |
|
|
|
471 |
subroutine calc_DTHDZ (dthdz,t1,t0,z1,z0,p,t)
|
|
|
472 |
|
|
|
473 |
implicit none
|
|
|
474 |
|
|
|
475 |
c Argument declaration
|
|
|
476 |
real dthdz ! Vertical derivative of TH [K/m]
|
|
|
477 |
real t1 ! T @ Z + 1 DZ [K]
|
|
|
478 |
real t0 ! T @ Z - 1 DZ [K]
|
|
|
479 |
real t ! T [K]
|
|
|
480 |
real z1 ! Z + 1 DZ [m]
|
|
|
481 |
real z0 ! Z - 1 DZ [m]
|
|
|
482 |
real p ! P [hPa]
|
|
|
483 |
|
|
|
484 |
c Physical parameters
|
|
|
485 |
real rdcp,tzero,pref,g,r
|
|
|
486 |
data rdcp,tzero,pref,g,r /0.286,273.15,1000.,287.,9.81/
|
|
|
487 |
|
|
|
488 |
c Auxiliary variables
|
|
|
489 |
real tk1,tk0,tk
|
|
|
490 |
|
|
|
491 |
if (t0.lt.100.) then
|
|
|
492 |
tk0 = t0 + tzero
|
|
|
493 |
endif
|
|
|
494 |
if (t1.lt.100.) then
|
|
|
495 |
tk1 = t1 + tzero
|
|
|
496 |
endif
|
|
|
497 |
if (t.lt.100.) then
|
|
|
498 |
tk = t + tzero
|
|
|
499 |
endif
|
|
|
500 |
|
|
|
501 |
dthdz = (pref/p)**rdcp *
|
|
|
502 |
> ( (tk1-tk0)/(z1-z0) + rdcp * tk * g / r )
|
|
|
503 |
|
|
|
504 |
end
|
|
|
505 |
|
|
|
506 |
c -------------------------------------------------------------------------
|
|
|
507 |
c Squared Brunt-Vaisäla frequency (NSQ)
|
|
|
508 |
c -------------------------------------------------------------------------
|
|
|
509 |
|
|
|
510 |
subroutine calc_NSQ (nsq,dthdz,th)
|
|
|
511 |
|
|
|
512 |
implicit none
|
|
|
513 |
|
|
|
514 |
c Argument declaration
|
|
|
515 |
real nsq ! Squared Brunt-Vaisäla frequency [s^-1]
|
|
|
516 |
real dthdz ! D(TH)/DZ [K/m]
|
|
|
517 |
real th ! K
|
|
|
518 |
|
|
|
519 |
c Physical parameters
|
|
|
520 |
real g
|
|
|
521 |
parameter (g=9.81)
|
|
|
522 |
|
|
|
523 |
nsq = g/th * dthdz
|
|
|
524 |
|
|
|
525 |
end
|
|
|
526 |
|
|
|
527 |
c -------------------------------------------------------------------------
|
|
|
528 |
c Relative vorticity (RELVORT)
|
|
|
529 |
c -------------------------------------------------------------------------
|
|
|
530 |
|
|
|
531 |
subroutine calc_RELVORT (relvort,dudy,dvdx,u,lat)
|
|
|
532 |
|
|
|
533 |
implicit none
|
|
|
534 |
|
|
|
535 |
c Argument declaration
|
|
|
536 |
real relvort ! Relative vorticity [s^-1]
|
|
|
537 |
real u ! Zonal wind component [m/s]
|
|
|
538 |
real dudy ! du/dy [s^-1]
|
|
|
539 |
real dvdx ! dv/dx [s^-1]
|
|
|
540 |
real lat ! Latitude [deg]
|
|
|
541 |
|
|
|
542 |
c Physical parameters
|
|
|
543 |
real pi180
|
|
|
544 |
parameter (pi180=3.14159/180.)
|
|
|
545 |
real deltay
|
|
|
546 |
parameter (deltay =1.11e5)
|
|
|
547 |
|
|
|
548 |
relvort = dvdx - dudy + u * pi180/deltay * tan(pi180 * lat)
|
|
|
549 |
|
|
|
550 |
end
|
|
|
551 |
|
|
|
552 |
c -------------------------------------------------------------------------
|
|
|
553 |
c Absolute vorticity (ABSVORT)
|
|
|
554 |
c -------------------------------------------------------------------------
|
|
|
555 |
|
|
|
556 |
subroutine calc_ABSVORT (absvort,dudy,dvdx,u,lat,lon,
|
|
|
557 |
> pollon,pollat)
|
|
|
558 |
|
|
|
559 |
implicit none
|
|
|
560 |
|
|
|
561 |
c Argument declaration
|
|
|
562 |
real absvort ! Absolute vorticity [s^-1]
|
|
|
563 |
real u ! Zonal wind component [m/s]
|
|
|
564 |
real dudy ! du/dy [s^-1]
|
|
|
565 |
real dvdx ! dv/dx [s^-1]
|
|
|
566 |
real lat ! Latitude [deg]
|
|
|
567 |
real lon ! Longitude [deg]
|
|
|
568 |
real pollon,pollat ! Rotated north pole [deg]
|
|
|
569 |
|
|
|
570 |
c Physical parameters
|
|
|
571 |
real pi180
|
|
|
572 |
parameter (pi180=3.14159/180.)
|
|
|
573 |
real deltay
|
|
|
574 |
parameter (deltay =1.11e5)
|
|
|
575 |
real omega
|
|
|
576 |
parameter (omega=7.292e-5)
|
|
|
577 |
|
|
|
578 |
c Externals
|
|
|
579 |
real lmtolms
|
|
|
580 |
real phtophs
|
|
|
581 |
real lmstolm
|
|
|
582 |
real phstoph
|
|
|
583 |
external lmtolms,phtophs
|
|
|
584 |
external lmstolm,phstoph
|
|
|
585 |
|
|
|
586 |
c Auxiliary varaibles
|
|
|
587 |
real truelat
|
|
|
588 |
|
|
|
589 |
truelat = phstoph(lat,lon,pollat,pollon)
|
|
|
590 |
|
|
|
591 |
absvort = dvdx - dudy + u * pi180/deltay * tan(pi180 * lat) +
|
|
|
592 |
> 2. * omega * sin(pi180 * truelat)
|
|
|
593 |
|
|
|
594 |
end
|
|
|
595 |
|
|
|
596 |
c -------------------------------------------------------------------------
|
|
|
597 |
c Divergence (DIV)
|
|
|
598 |
c -------------------------------------------------------------------------
|
|
|
599 |
|
|
|
600 |
subroutine calc_DIV (div,dudx,dvdy,v,lat)
|
|
|
601 |
|
|
|
602 |
implicit none
|
|
|
603 |
|
|
|
604 |
c Argument declaration
|
|
|
605 |
real div ! Divergence [s^-1]
|
|
|
606 |
real v ! Meridional wind component [m/s]
|
|
|
607 |
real dudx ! du/dx [s^-1]
|
|
|
608 |
real dvdy ! dv/dy [s^-1]
|
|
|
609 |
real lat ! Latitude [deg]
|
|
|
610 |
|
|
|
611 |
c Physical parameters
|
|
|
612 |
real pi180
|
|
|
613 |
parameter (pi180=3.14159/180.)
|
|
|
614 |
real deltay
|
|
|
615 |
parameter (deltay =1.11e5)
|
|
|
616 |
|
|
|
617 |
div = dudx + dvdy - v * pi180/deltay * tan(pi180 * lat)
|
|
|
618 |
|
|
|
619 |
end
|
|
|
620 |
|
|
|
621 |
c -------------------------------------------------------------------------
|
|
|
622 |
c Deformation (DEF)
|
|
|
623 |
c -------------------------------------------------------------------------
|
|
|
624 |
|
|
|
625 |
subroutine calc_DEF (def,dudx,dvdx,dudy,dvdy)
|
|
|
626 |
|
|
|
627 |
implicit none
|
|
|
628 |
|
|
|
629 |
c Argument declaration
|
|
|
630 |
real def ! Deformation [s^-1]
|
|
|
631 |
real dudx ! du/dx [s^-1]
|
|
|
632 |
real dvdx ! dv/dy [s^-1]
|
|
|
633 |
real dudy ! du/dx [s^-1]
|
|
|
634 |
real dvdy ! dv/dy [s^-1]
|
|
|
635 |
|
|
|
636 |
c Physical parameters
|
|
|
637 |
real pi180
|
|
|
638 |
parameter (pi180=3.14159/180.)
|
|
|
639 |
|
|
|
640 |
def = sqrt( (dvdx+dudy)**2 + (dudx-dvdy)**2 )
|
|
|
641 |
|
|
|
642 |
end
|
|
|
643 |
|
|
|
644 |
c -------------------------------------------------------------------------
|
|
|
645 |
c Potential Vorticity (PV)
|
|
|
646 |
c -------------------------------------------------------------------------
|
|
|
647 |
|
|
|
648 |
subroutine calc_PV (pv,absvort,dthdz,dudz,dvdz,dthdx,dthdy,rho)
|
|
|
649 |
|
|
|
650 |
implicit none
|
|
|
651 |
|
|
|
652 |
c Argument declaration
|
|
|
653 |
real pv ! Ertel-PV [PVU]
|
|
|
654 |
real absvort ! Absolute vorticity [s^-1]
|
|
|
655 |
real dthdz ! dth/dz [K/m]
|
|
|
656 |
real dudz ! du/dz [m/s per m = 1/s]
|
|
|
657 |
real dvdz ! dv/dz [m/s per m = 1/s]
|
|
|
658 |
real dthdx ! dth/dx [K/m]
|
|
|
659 |
real dthdy ! dth/dy [K/m]
|
|
|
660 |
real rho ! Density [kg/m^3]
|
|
|
661 |
|
|
|
662 |
c Physical and numerical parameters
|
|
|
663 |
real scale
|
|
|
664 |
parameter (scale=1.E6)
|
|
|
665 |
real g
|
|
|
666 |
parameter (g=9.80665)
|
|
|
667 |
|
|
|
668 |
pv = scale * 1./rho *
|
|
|
669 |
> ( absvort * dthdz + dudz * dthdy - dvdz * dthdx)
|
|
|
670 |
|
|
|
671 |
end
|
|
|
672 |
|
|
|
673 |
c -------------------------------------------------------------------------
|
|
|
674 |
c Richardson number (RI)
|
|
|
675 |
c -------------------------------------------------------------------------
|
|
|
676 |
|
|
|
677 |
subroutine calc_RI (ri,dudz,dvdz,nsq)
|
|
|
678 |
|
|
|
679 |
implicit none
|
|
|
680 |
|
|
|
681 |
c Argument declaration
|
|
|
682 |
real ri ! Richardson number
|
|
|
683 |
real dudz ! Du/Dp [m/s per m = 1/s]
|
|
|
684 |
real dvdz ! Dv/Dp [m/s per m = 1/s]
|
|
|
685 |
real nsq ! Squared Brunt-Vailälä frequency [s^-1]
|
|
|
686 |
real rho ! Density [kg/m^3]
|
|
|
687 |
|
|
|
688 |
c Physical and numerical parameters
|
|
|
689 |
real g
|
|
|
690 |
parameter (g=9.80665)
|
|
|
691 |
|
|
|
692 |
ri = nsq / ( dudz**2 + dvdz**2 )
|
|
|
693 |
|
|
|
694 |
end
|
|
|
695 |
|
|
|
696 |
c -------------------------------------------------------------------------
|
|
|
697 |
c Ellrod and Knapp's turbulence indicator (TI)
|
|
|
698 |
c -------------------------------------------------------------------------
|
|
|
699 |
|
|
|
700 |
subroutine calc_TI (ti,def,dudz,dvdz)
|
|
|
701 |
|
|
|
702 |
implicit none
|
|
|
703 |
|
|
|
704 |
c Argument declaration
|
|
|
705 |
real ti ! Turbulence idicator
|
|
|
706 |
real def ! Deformation [s^-1]
|
|
|
707 |
real dudz ! Du/Dp [m/s per m = 1/s]
|
|
|
708 |
real dvdz ! Dv/Dp [m/s per m = 1/s]
|
|
|
709 |
|
|
|
710 |
ti = def * sqrt ( dudz**2 + dvdz**2 )
|
|
|
711 |
|
|
|
712 |
end
|
|
|
713 |
|
|
|
714 |
c -------------------------------------------------------------------------
|
|
|
715 |
c Distance from starting position
|
|
|
716 |
c -------------------------------------------------------------------------
|
|
|
717 |
|
|
|
718 |
subroutine calc_DIST0 (dist0,lon0,lat0,lon1,lat1)
|
|
|
719 |
|
|
|
720 |
implicit none
|
|
|
721 |
|
|
|
722 |
c Argument declaration
|
|
|
723 |
real dist0 ! Distance from starting position [km]
|
|
|
724 |
real lon0,lat0 ! Starting position
|
|
|
725 |
real lon1,lat1 ! New position
|
|
|
726 |
|
|
|
727 |
c Externals
|
|
|
728 |
real sdis
|
|
|
729 |
external sdis
|
|
|
730 |
|
|
|
731 |
dist0 = sdis(lon0,lat0,lon1,lat1)
|
|
|
732 |
|
|
|
733 |
end
|
|
|
734 |
|
|
|
735 |
c -------------------------------------------------------------------------
|
|
|
736 |
c Heading of the trajectory (HEAD)
|
|
|
737 |
c -------------------------------------------------------------------------
|
|
|
738 |
|
|
|
739 |
subroutine calc_HEAD (head,lon0,lat0,lon1,lat1)
|
|
|
740 |
|
|
|
741 |
implicit none
|
|
|
742 |
|
|
|
743 |
c Argument declaration
|
|
|
744 |
real head ! Heading angle (in deg) relativ to zonal direction
|
|
|
745 |
real lon0,lat0 ! Starting position
|
|
|
746 |
real lon1,lat1 ! New position
|
|
|
747 |
|
|
|
748 |
c Physical parameters
|
|
|
749 |
real pi180
|
|
|
750 |
parameter (pi180=3.14159/180.)
|
|
|
751 |
|
|
|
752 |
c Auixiliary variables
|
|
|
753 |
real dx,dy
|
|
|
754 |
|
|
|
755 |
dx = (lon1-lon0) * cos(pi180*0.5*(lat0+lat1))
|
|
|
756 |
dy = lat1-lat0
|
|
|
757 |
|
|
|
758 |
call getangle(1.,0.,dx,dy,head)
|
|
|
759 |
|
|
|
760 |
end
|
|
|
761 |
|
|
|
762 |
c
|
|
|
763 |
c *************************************************************************
|
|
|
764 |
c Auxiliary subroutines and functions
|
|
|
765 |
c *************************************************************************
|
|
|
766 |
|
|
|
767 |
c -------------------------------------------------------------------------
|
|
|
768 |
c Saturation vapor pressure over water
|
|
|
769 |
c -------------------------------------------------------------------------
|
|
|
770 |
|
|
|
771 |
real function esat(t)
|
|
|
772 |
|
|
|
773 |
C This function returns the saturation vapor pressure over water
|
|
|
774 |
c (mb) given the temperature (Kelvin).
|
|
|
775 |
C The algorithm is due to Nordquist, W. S. ,1973: "Numerical
|
|
|
776 |
C Approximations of Selected Meteorological Parameters for Cloud
|
|
|
777 |
C Physics Problems" ECOM-5475, Atmospheric Sciences Laboratory,
|
|
|
778 |
c U. S. Army Electronics Command, White Sands Missile Range,
|
|
|
779 |
c New Mexico 88002.
|
|
|
780 |
|
|
|
781 |
real p1,p2,c1,t
|
|
|
782 |
|
|
|
783 |
p1=11.344-0.0303998*t
|
|
|
784 |
p2=3.49149-1302.8844/t
|
|
|
785 |
c1=23.832241-5.02808*log10(t)
|
|
|
786 |
esat=10.**(c1-1.3816e-7*10.**p1+8.1328e-3*10.**p2-2949.076/t)
|
|
|
787 |
|
|
|
788 |
end
|
|
|
789 |
|
|
|
790 |
c --------------------------------------------------------------------------
|
|
|
791 |
c Angle between two vectors
|
|
|
792 |
c --------------------------------------------------------------------------
|
|
|
793 |
|
|
|
794 |
SUBROUTINE getangle (ux1,uy1,ux2,uy2,angle)
|
|
|
795 |
|
|
|
796 |
c Given two vectors <ux1,uy1> and <ux2,uy2>, determine the angle (in deg)
|
|
|
797 |
c between the two vectors.
|
|
|
798 |
|
|
|
799 |
implicit none
|
|
|
800 |
|
|
|
801 |
c Declaration of subroutine parameters
|
|
|
802 |
real ux1,uy1
|
|
|
803 |
real ux2,uy2
|
|
|
804 |
real angle
|
|
|
805 |
|
|
|
806 |
c Auxiliary variables and parameters
|
|
|
807 |
real len1,len2,len3
|
|
|
808 |
real val1,val2,val3
|
|
|
809 |
real vx1,vy1
|
|
|
810 |
real vx2,vy2
|
|
|
811 |
real pi
|
|
|
812 |
parameter (pi=3.14159265359)
|
|
|
813 |
|
|
|
814 |
vx1 = ux1
|
|
|
815 |
vx2 = ux2
|
|
|
816 |
vy1 = uy1
|
|
|
817 |
vy2 = uy2
|
|
|
818 |
|
|
|
819 |
len1=sqrt(vx1*vx1+vy1*vy1)
|
|
|
820 |
len2=sqrt(vx2*vx2+vy2*vy2)
|
|
|
821 |
|
|
|
822 |
if ((len1.gt.0.).and.(len2.gt.0.)) then
|
|
|
823 |
vx1=vx1/len1
|
|
|
824 |
vy1=vy1/len1
|
|
|
825 |
vx2=vx2/len2
|
|
|
826 |
vy2=vy2/len2
|
|
|
827 |
|
|
|
828 |
val1=vx1*vx2+vy1*vy2
|
|
|
829 |
val2=-vy1*vx2+vx1*vy2
|
|
|
830 |
|
|
|
831 |
len3=sqrt(val1*val1+val2*val2)
|
|
|
832 |
|
|
|
833 |
if ( (val1.ge.0.).and.(val2.ge.0.) ) then
|
|
|
834 |
val3=acos(val1/len3)
|
|
|
835 |
else if ( (val1.lt.0.).and.(val2.ge.0.) ) then
|
|
|
836 |
val3=pi-acos(abs(val1)/len3)
|
|
|
837 |
else if ( (val1.ge.0.).and.(val2.le.0.) ) then
|
|
|
838 |
val3=-acos(val1/len3)
|
|
|
839 |
else if ( (val1.lt.0.).and.(val2.le.0.) ) then
|
|
|
840 |
val3=-pi+acos(abs(val1)/len3)
|
|
|
841 |
endif
|
|
|
842 |
else
|
|
|
843 |
val3=0.
|
|
|
844 |
endif
|
|
|
845 |
|
|
|
846 |
angle=180./pi*val3
|
|
|
847 |
|
|
|
848 |
END
|
|
|
849 |
|
|
|
850 |
|
|
|
851 |
c --------------------------------------------------------------------------
|
|
|
852 |
c Spherical distance between lat/lon points
|
|
|
853 |
c --------------------------------------------------------------------------
|
|
|
854 |
|
|
|
855 |
real function sdis(xp,yp,xq,yq)
|
|
|
856 |
c
|
|
|
857 |
c calculates spherical distance (in km) between two points given
|
|
|
858 |
c by their spherical coordinates (xp,yp) and (xq,yq), respectively.
|
|
|
859 |
c
|
|
|
860 |
real re
|
|
|
861 |
parameter (re=6370.)
|
|
|
862 |
real pi180
|
|
|
863 |
parameter (pi180=3.14159/180.)
|
|
|
864 |
real xp,yp,xq,yq,arg
|
|
|
865 |
|
|
|
866 |
arg=sin(pi180*yp)*sin(pi180*yq)+
|
|
|
867 |
> cos(pi180*yp)*cos(pi180*yq)*cos(pi180*(xp-xq))
|
|
|
868 |
if (arg.lt.-1.) arg=-1.
|
|
|
869 |
if (arg.gt.1.) arg=1.
|
|
|
870 |
|
|
|
871 |
sdis=re*acos(arg)
|
|
|
872 |
|
|
|
873 |
end
|
|
|
874 |
|