推荐|Python绘制3D动态对流层顶(Tropopause)
作者
Mathew Barlow: Professor of Climate Science University of Massachusetts Lowell
工具
GFS, the nomads server, python, and the python packages numpy, matplotlib, cartopy, scipy, and netcdf4
potential-vorticity: Python code (gfs_pv_1.2.py) for dynamic tropopause (DT) calculations: DT pressure, DT potential temperature (theta), PV on the 330K isentropic surface, and a PV and theta cross-section at the latitude where the tropopause is lowest in the domain. The date and time need to be set in the beginning of the code; the domain can be changed there as well. gfs_pv_1.2_3D.py is the same code but with additional (poor) 3D plots This code has a DOI and is citable: DOI The data source is the online GFS analysis, and the date and time need to be set within the period of available data. The program can take a few minutes to run because it is accessing data over the internet.
代码
https://github.com/mathewbarlow/potential-vorticity
具体参考以上链接
1#
2# run on python 3.7
3#
4# python code for some calculations related to the dynamic tropopause (DT)-
5# DT pressure, DT potential temperature, 330K PV,
6# and a cross-section of PV at the latitude where the tropopause is lowest -
7# all based on the GFS analysis available online.As the data is accessed
8# online, the program can take a while to run.
9#
10# the date and lat-lon range can be set below
11#
12# (poorly) coded by Mathew Barlow
13# initial release: 14 Nov 2017
14# last updated: 10 Oct 2019
15#
16# this code has *not* been extensively tested and has been
17# awkwardly translated from other coding languages, so if you find
18# any errors or have any suggestions or improvements, including for
19# the plotting, please let me know at <a href="mailto:Mathew_Barlow@uml.edu">Mathew_Barlow@uml.edu</a> . Thanks!
20#
21# Support from NSF AGS-1623912 is gratefully acknowledged
22#
23
24import numpy as np
25import netCDF4
26import matplotlib.pyplot as plt
27import matplotlib.ticker as tick
28from mpl_toolkits.mplot3d import axes3d
29import cartopy.crs as ccrs
30from scipy.ndimage import gaussian_filter
31from cartopy.feature import NaturalEarthFeature
32from cartopy.mpl.gridliner import LONGITUDE_FORMATTER, LATITUDE_FORMATTER
33from cartopy.mpl.ticker import LatitudeFormatter, LongitudeFormatter
34
35from datetime import datetime
36
37
38# VALUES TO SET *************************************************
39# set date, lat-lon range, and PV-value definition of tropopause
40mydate='20191016'
41myhour='06'
42(lat1,lat2)=(20,70)
43(lon1,lon2)=(120,240.1)
44tpdef=2 # definition of tropopause in PVU
45#****************************************************************
46
47
48#constants
49re=6.37e6
50g=9.81
51cp=1004.5
52r=2*cp/7
53kap=r/cp
54omega=7.292e-5
55pi=3.14159265
56
57# open dataset, retreive variables, close dataset
58
59url='https://nomads.ncep.noaa.gov/dods/gfs_0p25/gfs'+\
60mydate+'/gfs_0p25_'+myhour+'z_anl'
61
62file = netCDF4.Dataset(url)
63
64lat_in= file.variables['lat'][:]
65lon_in= file.variables['lon'][:]
66lev = file.variables['lev'][:]
67
68pres2pv_in = file.variables['pres2pv']
69pressfc_in = file.variables['pressfc']
70
71nlev = lev.size
72nx = lon_in.size
73ny = lat_in.size
74
75u_in = np.full((nlev, ny, nx), None)
76v_in = np.full((nlev, ny, nx), None)
77t_in = np.full((nlev, ny, nx), None)
78hgt_in = np.full((nlev, ny, nx), None)
79
80ilev = 0
81while ilev < nlev:
82 print(ilev)
83 u_in = file.variables['ugrdprs']
84 ilev = ilev + 1
85
86ilev = 0
87while ilev < nlev:
88 v_in = file.variables['vgrdprs']
89 ilev = ilev + 1
90
91ilev = 0
92while ilev < nlev:
93 t_in = file.variables['tmpprs']
94 ilev = ilev + 1
95
96ilev = 0
97while ilev < nlev:
98 hgt_in = file.variables['hgtprs']
99 ilev = ilev + 1
100
101#t_in = file.variables['tmpprs']
102#u_in = file.variables['ugrdprs']
103#v_in = file.variables['vgrdprs']
104#hgt_in = file.variables['hgtprs']
105
106file.close()
107
108# get array indices for lat-lon range
109# specified above
110iy1 = np.argmin( np.abs( lat_in - lat1 ) )
111iy2 = np.argmin( np.abs( lat_in - lat2 ) )
112ix1 = np.argmin( np.abs( lon_in - lon1 ) )
113ix2 = np.argmin( np.abs( lon_in - lon2 ) )
114
115# select specified lat-lon range
116t=t_in[:,iy1:iy2,ix1:ix2]
117lon=lon_in
118lat=lat_in
119u=u_in[:,iy1:iy2,ix1:ix2]
120v=v_in[:,iy1:iy2,ix1:ix2]
121hgt=hgt_in[:,iy1:iy2,ix1:ix2]
122pres2pv=pres2pv_in
123pressfc=pressfc_in
124
125# some prep work for derivatives
126xlon,ylat=np.meshgrid(lon,lat)
127
128# define potential temperature and Coriolis parameter
129theta=t*(1.E5/(lev[:,np.newaxis,np.newaxis]*100))**kap
130f=2*omega*np.sin(ylat*pi/180)
131
132lon = np.array(lon, dtype='float')
133lat = np.array(lat, dtype='float')
134lev = np.array(lev, dtype='float')
135u = np.array(u, dtype='float')
136v = np.array(v, dtype='float')
137hgt = np.array(hgt, dtype='float')
138pres2pv = np.array(pres2pv, dtype='float')
139pressfc = np.array(pressfc, dtype='float')
140theta = np.array(theta, dtype='float')
141f = np.array(f, dtype='float')
142
143# calculate derivatives
144
145def ddp(f):
146# handle unevenly-spaced levels with 2nd order
147# Lagrange interpolation
148# except for top and bottom, where use forward diff
149 lev3=lev.reshape(lev.size,1,1)*100
150 dpp=lev3-np.roll(lev3,-1,axis=0)
151 dpm=lev3-np.roll(lev3,1,axis=0)
152 fp=np.roll(f,-1,axis=0)
153 fm=np.roll(f,1,axis=0)
154 ddp_f=(
155 fm*dpp/( (dpp-dpm)*(-dpm) ) +
156 f*(dpp+dpm)/( dpm*dpp ) +
157 fp*dpm/( (dpm-dpp)*(-dpp) )
158 )
159 ddp_f=(f-f)/(lev3-lev3)
160 ddp_f[-1,:,:]=(f[-1,:,:]-f[-2,:,:])/(lev3[-2,:,:]-lev3[-1,:,:])
161 return(ddp_f)
162
163def ddx(f):
164# use center-difference, assuming evenly spaced lon
165# except for side-boundaries, where use forward diff
166 x=(re*np.cos(ylat*np.pi/180)*np.pi/180)*lon
167 x3=x.reshape(1,x.shape,x.shape)
168 dx3=np.roll(x3,-1,axis=2)-np.roll(x3,1,axis=2)
169 ddx_f=(np.roll(f,-1,axis=2)-np.roll(f,1,axis=2))/dx3
170 ddx_f[:,:,0]=(f[:,:,1]-f[:,:,0])/(x3[:,:,1]-x3[:,:,0])
171 ddx_f[:,:,-1]=(f[:,:,-2]-f[:,:,-1])/(x3[:,:,-2]-x3[:,:,-1])
172 return(ddx_f)
173
174def ddy(f):
175# use center-difference, assuming evenly spaced lon
176# except for N/S boundaries, where use forward diff
177 y=(re*np.pi/180)*lat
178 y3=y.reshape(1,y.shape,1)
179 dy3=np.roll(y3,-1,axis=1)-np.roll(y3,1,axis=1)
180 ddy_f=(np.roll(f,-1,axis=1)-np.roll(f,1,axis=1))/dy3
181 ddy_f[:,0,:]=(f[:,1,:]-f[:,0,:])/(y3[:,1,:]-y3[:,0,:])
182 ddy_f[:,-1,:]=(f[:,-2,:]-f[:,-1,:])/(y3[:,-2,:]-y3[:,-1,:])
183 return(ddy_f)
184
185
186#lev3=lev.reshape(lev.size,1,1)
187#ddp_theta=np.gradient(theta,lev3*100,axis=0)
188#ddx_theta=np.gradient(theta,axis=2)/dx
189#ddy_theta=np.gradient(theta,axis=1)/dy
190
191gf=1
192
193ddp_theta=ddp(theta)
194ddp_u=ddp(gaussian_filter(u,sigma=gf))
195ddp_v=ddp(gaussian_filter(v,sigma=gf))
196
197ddx_theta=ddx(theta)
198ddy_theta=ddy(theta)
199ddx_v=ddx(gaussian_filter(v,sigma=gf))
200ddy_ucos=ddy(gaussian_filter(u,sigma=gf)*np.cos(ylat*pi/180))
201
202# calculate contributions to PV and PV
203absvort=ddx_v-(1/np.cos(ylat*pi/180))*ddy_ucos+f
204pv_one=g*absvort*(-ddp_theta)
205pv_two=g*(ddp_v*ddx_theta-ddp_u*ddy_theta)
206pv=pv_one+pv_two
207
208# calculate pressure of tropopause, Fortran-style (alas!)
209# as well as potential temperature (theta) and height
210#
211# starting from 10hPa and working down, to avoid
212# more complicated vertical structure higher up
213#
214nx=ix2-ix1+1
215ny=iy2-iy1+1
216nz=lev.size
217nzs=np.argwhere(lev==50.0)
218tp=np.empty((ny-1,nx-1))*np.nan # initialize as undef
219tp_theta=np.empty((ny-1,nx-1))*np.nan # initialize as undef
220tp_hgt=np.empty((ny-1,nx-1))*np.nan # initialize as undef
221
222for ix in range(0,nx-1):
223 for iy in range(0,ny-1):
224 for iz in range(nzs,0,-1):
225 if pv/1e-6<=tpdef:
226 if np.isnan(tp):
227 tp=(
228 (lev*(pv-tpdef*1e-6)
229 -lev*(pv-tpdef*1e-6))/
230 (pv-pv)
231 )
232
233 tp_theta=(
234 ((lev-tp)*theta+
235 (tp-lev)*theta)/
236 (lev-lev)
237 )
238
239 tp_hgt=(
240 ((lev-tp)*hgt+
241 (tp-lev)*hgt)/
242 (lev-lev)
243 )
244
245# calculate PV on the 330K isentropic surface
246# (also not in a pythonic way)
247nx=ix2-ix1+1
248ny=iy2-iy1+1
249nz=lev.size
250pv330=np.empty((ny-1,nx-1))*np.nan # initialize as undef
251for ix in range(0,nx-1):
252 for iy in range(0,ny-1):
253 for iz in range(nz-2,0,-1):
254 if theta>=330:
255 if theta<=330:
256 if np.isnan(pv330):
257 pv330=(
258 ((330-theta)*pv+
259 (theta-330)*pv)/
260 (theta-theta)
261 )
262
263
264# slight smoothing of result
265# (appears to work better than smoothing u,v,t first)
266tp=gaussian_filter(tp,sigma=1)
267tp_theta=gaussian_filter(tp_theta,sigma=1)
268pv330=gaussian_filter(pv330,sigma=1)
269
270# define spatial correlation function for testing results
271def scorr(a,b):
272 abar=np.mean(a)
273 bbar=np.mean(b)
274 covar=sum((a-abar)*(b-bbar))
275 avar=sum((a-abar)**2)
276 bvar=sum((b-bbar)**2)
277 r=covar/np.sqrt(avar*bvar)
278 return(r)
279
280# identify latitude of lowest tropopause
281maxloc=np.argwhere(tp==np.amax(tp))
282latmax=lat]
283
284
285# now make some plots - these badly need to be improved
286
287states = NaturalEarthFeature(category='cultural',
288 scale='50m', facecolor='none',
289 name='admin_1_states_provinces_shp')
290
291# get date for plotting
292fdate=datetime.strptime(mydate, '%Y%m%d').strftime('%d %b %Y')
293
294plt.close(fig='all')
295
296print('got here')
297
298nframe=30
299iframe=0
300while iframe<=nframe:
301 plt.figure(iframe,figsize=plt.figaspect(0.5))
302
303 pressfc_smooth=gaussian_filter(pressfc,sigma=1)
304 ax=plt.gca(projection='3d')
305
306 surf=ax.plot_surface(xlon,ylat,tp,cmap="coolwarm",alpha=1,
307 rstride=1,cstride=1,
308 linewidth=0, antialiased=False)
309
310 ax.plot_surface(xlon,ylat,pressfc_smooth/100,color="lightgray",
311 rstride=1,cstride=1,
312 linewidth=0, antialiased=False)
313
314 ax.set_zlim(1000,100)
315 ax.set_xlim(lon1,lon2)
316 ax.set_ylim(lat1,lat2)
317 ax.view_init(elev=90 - iframe*90/nframe,azim=-90)
318
319 plt.title('2PVU Dynamic Tropopause over topography\n'+myhour+'Z '+fdate)
320 plt.colorbar(surf)
321
322 plt.savefig('goo'+ '{:04d}'.format(iframe)+'.png', bbox_inches='tight',
323 dpi=300)
324
325 iframe=iframe+1
彩蛋
1.thorpe_tropopause
https://github.com/mathewbarlow/thorpe_tropopause
2.stratospheric-polar-vortex
https://github.com/mathewbarlow/stratospheric-polar-vortex
文章来源于微信公众号：气象学家
你的代码实现很有启发性，学习了！
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