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preProcess.py
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preProcess.py
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'''
Take input data and write mesh+metr info to our format.
mesh: lat,lon,areaCell
metr: u,v,theta,verticalVorticity,inRegion on DT
'''
import numpy as np
import netCDF4
import matplotlib.pyplot as plt
from mpl_toolkits.basemap import Basemap
import helpers
import llMesh
import mpasMesh
import wrfUniformMesh as wrfMesh
def get_missingCells_file(data):
"""Return mask of missing values, coded for GFS netCDF4 object"""
#if search vertical column down from top, there can be no 2pvu value if:
#-entire column is above 2pvu: DT below sfc
#-entire column is below 2pvu: wrong hemisphere or low pv column (tropics, anticyclonic,...)
pvInd = 1
isMissing = data.variables['TMP_P0_L109_GLL0'][pvInd,:,:].mask
return isMissing
def fill_missingVals_region(valsIn, nLat, nLon, isMissing, inRegion):
"""For missing values in region that is used, fill value is average of non-missing neighbors"""
vals = np.copy(valsIn)
needFill = isMissing*inRegion;
nNeedFill = np.sum(needFill); print "Filling {0} values".format(nNeedFill)
while (np.sum(needFill)>0):
for iLat in xrange(nLat):
for iLon in xrange(nLon):
if (needFill[iLat,iLon]>0): #True>0 is True, False==0 is True
nbrInds_lat, nbrInds_lon = nbrInds_ll(iLat, iLon, nLat, nLon)
nbrsNeedFill = needFill[nbrInds_lat, nbrInds_lon]
if (False in nbrsNeedFill): #have neighbor with value
#fill value is average of valid nbrs
validNbrs = nbrsNeedFill==False;
valsNbrs = vals[nbrInds_lat, nbrInds_lon]
vals[iLat, iLon] = np.mean(valsNbrs[validNbrs])+1.e-10 #so don't have same value
needFill[iLat,iLon]=False
return vals
def get_segmentVars_file(data):
"""Return data of variables needed from file, with no time index, in SI units. Coded for GFS"""
#fname = '/data02/cases/2014/gfs_4_20140101_0000_123.nc'
#data = netCDF4.Dataset(fname,'r')
lat = data.variables['lat_0'][:] * np.pi/180. #deg 2 radians
lon = data.variables['lon_0'][:] * np.pi/180.
#for pvu levels, lv_PVL4 = [-2, 2]*E-6
pvInd = 1
tmp = data.variables['TMP_P0_L109_GLL0'][pvInd,:,:].data #K
press = data.variables['PRES_P0_L109_GLL0'][pvInd,:,:].data #Pa
u = data.variables['UGRD_P0_L109_GLL0'][pvInd,:,:].data #m/s
v = data.variables['VGRD_P0_L109_GLL0'][pvInd,:,:].data
return (lat, lon, u, v, tmp, press)
def calc_vertVorticity_ll(u, v, nLat, nLon, lat, r):
'''
Calculate vertical vorticity on a latitude/longitude mesh
Arguments:
u - zonal wind
v - meridional wind
nLat - number of latitude points
nLon - number of longitude points
lat - latitudes
r - radius of sphere
Pulled from: http://www.ncl.ucar.edu/Document/Functions/Built-in/uv2vr_cfd.shtml :
According to H.B. Bluestein [Synoptic-Dynamic Meteorology in Midlatitudes, 1992,
Oxford Univ. Press p113-114],
let D represent the partial derivative, a the radius of the earth,
phi the latitude and dx2/dy2 the appropriate longitudinal and latitudinal spacing,
respectively. Then, letting j be the latitude y-subscript, and i be the longitude x-subscript:
rv = Dv/Dx - Du/Dy + (u/a)*tan(phi)
rv(j,i) = (v(j,i+1)-v(j,i-1))/dx2(j)
- (u(j+1,i)-u(j-1,i))/dy2(j)
+ (u(j,i)/a)*tan(phi(j)) #since meridians aren't parallel
The last terms accounts for the convergence of the meridians on a sphere.
'''
#we'll do the above centered finite differencing for the non-pole latitudes.
#for the poles, we'll do a finite volume \int gradxu dA = \int u.n dS since
#trying to finite difference it confuses me. remember that the poles are really
#nLon copies of the same point
vort = np.empty((nLat, nLon), dtype=float)
dRadLat = np.pi/(nLat-1) #[-pi/2, pi/2], ie with values at both poles
dRadLon = 2.*np.pi/nLon #[0,2pi)
dy = r*dRadLat; dy2 = 2.*dy #arc length on a sphere
#calc values for non poles
for iLat in xrange(1,nLat-1):
tanphi = np.tan(lat[iLat])/r
dx = r*np.cos(lat[iLat])*dRadLon; dx2 = 2.*dx
for iLon in xrange(nLon):
iWest = (iLon-1)%nLon # -1%4=3 so don't worry about negatives
iEast = (iLon+1)%nLon
iSouth = iLat+1; iNorth = iLat-1
dv_dx = (v[iLat, iEast]-v[iLat, iWest])/dx2
du_dy = (u[iNorth, iLon]-u[iSouth, iLon])/dy2
meridTerm = u[iLat, iLon]*tanphi
vort[iLat, iLon] = dv_dx-du_dy+meridTerm
#calc values for north and south poles with finite volume approach
#around next latitude equatorward of pole
iLat = nLat-1;
dx = r*np.cos(lat[iLat-1])*dRadLon #for evenly spaced lats, same dx for south and north
#for area of the cap, http://mathworld.wolfram.com/SphericalCap.html
a = dx/dRadLon
h = r-np.sqrt(r*r-a*a)
areaCap = 2.*np.pi*r*h
#around south pole, remember integrate with domain on left
undS = np.sum(u[iLat-1,:])*-dx #since +dx has domain on right
vort[iLat,:] = undS/areaCap
iLat = 0
undS = np.sum(u[iLat+1,:])*dx
vort[iLat,:] = undS/areaCap
return vort
def calc_vorticity_wrfTrop_uniform(u, v, dx, dy, mapFac=1.0):
"""Calculate vertical vorticity on a uniformly spaced WRF domain"""
#Steven's files have variables already processed to cell centers.
#u,v come in ordered [south_north=y, west_east=x]
#we'll use numpy.gradient for the finite difference,
#e.g., http://stackoverflow.com/questions/17901363/gradient-calculation-with-python
du_dy, du_dx = np.gradient(u, dy, dx)
dv_dy, dv_dx = np.gradient(v, dy, dx)
#In physical space, dx and dy are not constants.
#If we act like we were finite differencing across the faces of each cell,
#grid stretching gets lumped into O(approx) and we just scale the d/dDirection
dv_dx *= mapFac # d/dxEarth = d/(dxGrid/mapFac)
du_dy *= mapFac
return dv_dx-du_dy
def calc_potentialTemperature(tmp, press):
"""
Return potential temperature
Arguments:
tmp - temperature (K)
press - pressure (Pa)
"""
Cp = 1004.5; Rd = 287.04;
Rd_cp = Rd/Cp; p0 = 1.e5
theta = tmp*((p0/press)**Rd_cp)
return theta
def eraTimeToCalendarTime(hrs):
"""
In the ERA file, time is stored as "hours since 1900-01-01 00:00:0.0"
we'll convert that to a datetime object and return a nice looking string
"""
tBase = dt.datetime(1900, 1, 1, 0)
#note that TypeError: unsupported type for timedelta hours component: numpy.int32
tNew = tBase + dt.timedelta(hours=hrs)
tTuple = dt.datetime.timetuple(tNew);
s = time.strftime('%Y-%m-%d_%H', tTuple)
return s
def demo_eraI(fMesh, filesDataIn, fNameOut, r, dRegion, latThresh, iTimeStart_fData, iTimeEnd_fData, info='eraI case'):
"""
Pre-process ERA-Interim data into tpvTrack format
Arguments:
fMesh - path to file with mesh inforamtion
filesDataIn - Input ERA-I filepaths
fNameOut - filepath for output file
r - radius of sphere
dRegion - radius of neighborhood
latThresh - latitude cutoff for subset of domain used for segmentation, tracking,...
iTimeStart_fData - integer index for start time of each file
iTimeEnd_fData - integer index for end time of each file (can use -1 for last time in file)
"""
#mesh ---------------------
data = netCDF4.Dataset(fMesh,'r')
d2r = np.pi/180.;
lat = data.variables['latitude'][:]*d2r; lon = data.variables['longitude'][:]*d2r
#want latitudes to be in [-pi/2, pi/2] and longitudes in [0, 2pi)
lon = lon%(2.*np.pi)
data.close()
mesh = llMesh.Mesh(lat,lon, r, dRegion)
#mesh.fill_latCellArea()
mesh.fill_inDisk()
mesh.fill_inRegion(latThresh)
cell0 = llMesh.Cell(mesh,-1)
#metr fields -----------------
nFiles = len(filesDataIn)
if (nFiles<1):
return mesh, cell0
dataOut = write_netcdf_header_metr(fNameOut, info, mesh)
iTimeGlobal = 0
for iFile in xrange(nFiles):
fPath = filesDataIn[iFile]
data = netCDF4.Dataset(fPath,'r')
#loop over individual times ------------------------------
#times = data.variables['time'][:]; nTimes = len(times); nTimes = 20
#for iTime in xrange(nTimes):
iTimeStart = iTimeStart_fData[iFile]; iTimeEnd = iTimeEnd_fData[iFile]
if (iTimeEnd<0): #use all times in file
times = data.variables['time'][:]; nTimes = len(times);
iTimeEnd = nTimes-1
for iTime in xrange(iTimeStart,iTimeEnd+1):
#read from file
theta = data.variables['pt'][iTime,:,:]
u = data.variables['u'][iTime,:,:]; v = data.variables['v'][iTime,:,:]
#fill in missing values w/in region
#ERA-I doesn't appear to have any missing values...I don't know how their interpolation works.
#Some old documentation described PP2DINT that extrapolates using constant values.
#This rando site: https://badc.nerc.ac.uk/data/ecmwf-op/levels.html
#says
#"The ECMWF Operational and ERA-40 datasets also provide data on a "PV=+/-2" surface on which the potential vorticity takes the value 2PVU in the northern hemisphere and -2PVU in the southern hemisphere (1PVU = 10-6 m2 s-1 K kg-1), provided such a surface can be found searching downwards from the Model level close to 96hPa. Values at this model level are used where the search is unsuccessful."
#compute additional fields
vort = calc_vertVorticity_ll(u, v, mesh.nLat, mesh.nLon, mesh.lat, r)
#write to file
u = helpers.flatten_2dTo1d(u, mesh.nLat, mesh.nLon)
v = helpers.flatten_2dTo1d(v, mesh.nLat, mesh.nLon)
theta = helpers.flatten_2dTo1d(theta, mesh.nLat, mesh.nLon)
vort = helpers.flatten_2dTo1d(vort, mesh.nLat, mesh.nLon)
write_netcdf_iTime_metr(dataOut, iTimeGlobal, u,v,theta,vort)
iTimeGlobal = iTimeGlobal+1
#end iTime
#end iFile
dataOut.close()
return mesh, cell0
def demo_mpas(fMesh, filesDataIn, fNameOut, r, dRegion, latThresh, iTimeStart_fData, iTimeEnd_fData, info='mpas case'):
"""
Pre-process MPAS data into tpvTrack format
Arguments:
fMesh - path to file with mesh inforamtion
filesDataIn - Input MPAS output filepaths
fNameOut - filepath for output file
r - radius of sphere
dRegion - radius of neighborhood
latThresh - latitude cutoff for subset of domain used for segmentation, tracking,...
iTimeStart_fData - integer index for start time of each file
iTimeEnd_fData - integer index for end time of each file (can use -1 for last time in file)
"""
#mesh ---------------------
data = netCDF4.Dataset(fMesh,'r')
lat = data.variables['latCell'][:]; lon = data.variables['lonCell'][:]
lon = lon%(2.*np.pi) #want latitudes to be in [-pi/2, pi/2] and longitudes in [0, 2pi)
nEdgesOnCell = data.variables['nEdgesOnCell'][:];
cellsOnCell = data.variables['cellsOnCell'][:]-1;
areaCell = data.variables['areaCell'][:]
data.close()
mesh = mpasMesh.Mesh(lat,lon, areaCell, cellsOnCell, nEdgesOnCell, r, dRegion)
mesh.fill_inRegion(latThresh)
cell0 = mpasMesh.Cell(mesh,-1)
#metr fields -----------------
nFiles = len(filesDataIn)
if (nFiles<1):
return mesh, cell0
dataOut = write_netcdf_header_metr(fNameOut, info, mesh)
iTimeGlobal = 0
for iFile in xrange(nFiles):
fPath = filesDataIn[iFile]
data = netCDF4.Dataset(fPath,'r')
#loop over individual times ------------------------------
#times = data.variables['time'][:]; nTimes = len(times); nTimes = 20
#for iTime in xrange(nTimes):
iTimeStart = iTimeStart_fData[iFile]; iTimeEnd = iTimeEnd_fData[iFile]
if (iTimeEnd<0): #use all times in file
nTimes = len(data.dimensions['Time'])
iTimeEnd = nTimes-1
for iTime in xrange(iTimeStart,iTimeEnd+1):
#read from file
theta = data.variables['theta_pv'][iTime,:]
u = data.variables['u_pv'][iTime,:]; v = data.variables['v_pv'][iTime,:]
vort = data.variables['vort_pv'][iTime,:]
#fill in missing values w/in region
#MPAS will have surface values if whole column is above 2pvu.
#Unclear what to do if whole column is below 2pvu (like near equator)
#compute additional fields
#write to file
write_netcdf_iTime_metr(dataOut, iTimeGlobal, u,v,theta,vort)
iTimeGlobal = iTimeGlobal+1
#end iTime
#end iFile
dataOut.close()
return mesh, cell0
def demo_wrf_trop(fMesh, filesDataIn, fNameOut, r, dRegion, latThresh, iTimeStart_fData, iTimeEnd_fData, fMapProj, info='wrf case', pvIndex=3):
"""
Pre-process WRF diagnosed tropopause data into tpvTrack format
Arguments:
fMesh - path to file with mesh inforamtion
filesDataIn - Input ERA-I filepaths
fNameOut - filepath for output file
r - radius of sphere
dRegion - radius of neighborhood
latThresh - latitude cutoff for subset of domain used for segmentation, tracking,...
iTimeStart_fData - integer index for start time of each file
iTimeEnd_fData - integer index for end time of each file (can use -1 for last time in file)
fMapProj - filepath with information about domain's map projection
"""
#For Steven's wrfout_trop files that have already been processed in a particular way.
#I think the grid is oriented such that u,v are both grid and global zonal,meridional velocities.
#If this isn't true, there's some figuring out to do.
#mesh ---------------------
data = netCDF4.Dataset(fMesh,'r')
dataProj = netCDF4.Dataset(fMapProj,'r')
d2r = np.pi/180.;
lat = data.variables['XLAT'][0,:,:]*d2r; lon = data.variables['XLONG'][0,:,:]*d2r
dx = data.DX
dy = data.DY
#want latitudes to be in [-pi/2, pi/2] and longitudes in [0, 2pi)
lon = lon%(2.*np.pi)
data.close()
mesh = wrfMesh.Mesh(lat,lon, dx, dy, r, dRegion)
mesh.fill_inRegion(latThresh)
mapFac = dataProj.variables['MAPFAC_M'][0,:,:]
#mapFac = 1.0
mesh.fill_cellArea(mapFac)
cell0 = wrfMesh.Cell(mesh,-1)
#metr fields -----------------
nFiles = len(filesDataIn)
if (nFiles<1):
return mesh, cell0
cosalpha = dataProj.variables['COSALPHA'][0,:,:]
sinalpha = dataProj.variables['SINALPHA'][0,:,:]
dataProj.close()
dataOut = write_netcdf_header_metr(fNameOut, info, mesh)
iTimeGlobal = 0
for iFile in xrange(nFiles):
fPath = filesDataIn[iFile]
data = netCDF4.Dataset(fPath,'r')
#loop over individual times ------------------------------
#times = data.variables['time'][:]; nTimes = len(times); nTimes = 20
#for iTime in xrange(nTimes):
iTimeStart = iTimeStart_fData[iFile]; iTimeEnd = iTimeEnd_fData[iFile]
if (iTimeEnd<0): #use all times in file
nTimes = len(data.dimensions['time']);
iTimeEnd = nTimes-1
for iTime in xrange(iTimeStart,iTimeEnd+1):
#read from file
theta = data.variables['THETA'][iTime,pvIndex,:,:]
u = data.variables['U'][iTime,pvIndex,:,:]
v = data.variables['V'][iTime,pvIndex,:,:]
#fill in missing values w/in region
#apparently netCDF4 doesn't return a masked array if all masks are False
try:
print "Time {0}, number of missing values: {1}".format(iTimeGlobal, np.sum(theta.mask))
for var in (theta, u, v):
#we'll just replace missing values with global mean
meanVal = np.mean(var); print "Replacing values with: ",meanVal
var[var.mask==True] = meanVal
#print "Missing values still in theta? ", True in theta.mask
theta = theta.data;
u = u.data
v = v.data
except AttributeError:
print "Time {0}, number of missing values: {1}".format(iTimeGlobal,0)
#compute additional fields
vort = calc_vorticity_wrfTrop_uniform(u, v, dx, dy, mapFac=mapFac)
#rotate grid-relative wind to global (apparently the stored rotation is for earth->grid)
uGlobal = u*cosalpha-v*sinalpha
vGlobal = u*sinalpha+v*cosalpha
u = uGlobal; v = vGlobal
#write to file
u = helpers.flatten_2dTo1d(u, mesh.ny, mesh.nx)
v = helpers.flatten_2dTo1d(v, mesh.ny, mesh.nx)
theta = helpers.flatten_2dTo1d(theta, mesh.ny, mesh.nx)
vort = helpers.flatten_2dTo1d(vort, mesh.ny, mesh.nx)
write_netcdf_iTime_metr(dataOut, iTimeGlobal, u,v,theta,vort)
iTimeGlobal = iTimeGlobal+1
#end iTime
#end iFile
dataOut.close()
return mesh, cell0
def write_netcdf_header_metr(fName, info, mesh):
"""Create file and write header for tpvTrack preprocess netcdf file"""
data = netCDF4.Dataset(fName, 'w', format='NETCDF4')
data.description = info
# dimensions
nCells = mesh.nCells
data.createDimension('time', None)
data.createDimension('nCells', nCells)
# variables
latCell_data = data.createVariable('latCell', 'f8', ('nCells',))
lonCell_data = data.createVariable('lonCell', 'f8', ('nCells',))
u_data = data.createVariable('u', 'f8', ('time','nCells',))
v_data = data.createVariable('v', 'f8', ('time','nCells',))
theta_data = data.createVariable('theta', 'f8', ('time','nCells',))
vort_data = data.createVariable('vort', 'f8', ('time','nCells',))
#units and descriptions
latCell_data.units = 'radians'; latCell_data.long_name='Latitude'
lonCell_data.units = 'radians'; lonCell_data.long_name='Longitude'
u_data.units = 'm/s'; u_data.long_name='Zonal velocity'
v_data.units = 'm/s'; v_data.long_name='Meridional velocity'
theta_data.units = 'K'; theta_data.long_name='Potential temperature'
vort_data.units = '1/s'; vort_data.long_name='Vertical vorticity'
#fill lat/lon
allCells = np.arange(nCells)
lat, lon = mesh.get_latLon_inds(allCells)
data.variables['latCell'][:] = lat[:]
data.variables['lonCell'][:] = lon[:]
return data
def write_netcdf_iTime_metr(data, iTime, u,v,theta,vort):
"""Write one time into tpvTrack preprocess netcdf file"""
# fill file. with time as unlimited, dimension will just keep growing
data.variables['u'][iTime,:] = u[:]
data.variables['v'][iTime,:] = v[:]
data.variables['theta'][iTime,:] = theta[:]
data.variables['vort'][iTime,:] = vort[:]
#
def plot_metr(fMetr):
"""Example of plotting preprocess variables on map"""
data = netCDF4.Dataset(fMetr,'r')
nTimes = len(data.dimensions['time'])
lat = data.variables['latCell'][:]*180./np.pi
lon = data.variables['lonCell'][:]*180./np.pi
m = Basemap(projection='ortho',lon_0=0,lat_0=90., resolution='l')
x,y = m(lon, lat)
keys = ['u','v','theta','vort']
bounds = [[-50.,50.], [-50.,50.], [270.,360.], [-1.e-4,1.e-4]]
for iTime in xrange(nTimes):
for iKey in xrange(len(keys)):
key = keys[iKey]
keyRange = bounds[iKey]; keyMin = keyRange[0]; keyMax = keyRange[1]
plt.figure()
vals = data.variables[key][iTime,:]
m.drawcoastlines()
m.pcolor(x,y,vals,tri=True, shading='flat',edgecolors='none',cmap=plt.cm.RdBu_r, vmin=keyMin, vmax=keyMax)
plt.colorbar()
plt.title(key)
s = '{0}_t{1}.png'.format(key, iTime)
plt.savefig(s, bbox_inches='tight'); plt.close()
if __name__ == '__main__':
fMetr = '/data01/tracks/wrf/algo/fields_debug.nc'
plot_metr(fMetr)
# ------------------------- Untested code --------------------------------
def calc_vertVorticity_wrf(U,V,MSFU,MSFV,MSFT,DX,DY,NX,NY):
print "Uhoh. calc_vertVorticity_wrf function is untested!!!"
'''
Adapted from DCOMPUTEABSVORT(AV,U,V,MSFU,MSFV,MSFT,COR,DX,DY,NX,NY,
+ NZ,NXP1,NYP1)
from NCL source code (https://github.com/yyr/ncl/blob/master/ni/src/lib/nfpfort/wrf_pvo.f)
u,v: unstaggered grid-relative winds
msf{u,v,t}: map-scale factors
d{x,y}: computational grid spacing
N{x,y}: # of cells in each direction
2D arrays are indexed on the grid (S_N=v, W_E=u)
For a uniform grid, could just do:
du_dy, du_dx = np.gradient(u, dy, dx)
dv_dy, dv_dx = np.gradient(v, dy, dx)
return dv_dx-du_dy
'''
#for interior cells, do finite difference between neighboring cells, e.g., (valNorth-valSouth)/2dy.
#to get u at midpt of horizontal cell, average left and right boundaries.
vort = np.empty((NX,NY),dtype=float)
for J in xrange(NY):
JP1 = min(J+1,NY-1)
JM1 = max(J-1,0)
for I in xrange(NX):
IP1 = min(I+1,NX-1)
IM1 = max(I-1,0)
DSX = (IP1-IM1)*DX
DSY = (JP1-JM1)*DY
MM = MSFT[j,i]*MSFT[j,i]
du_dy = .5* (U[JP1,I]/MSFU[JP1,I]+ U[JP1,I+1]/MSFU[JP1,I+1] -
U[JM1,I]/MSFU[JM1,I]- U[JM1,I+1]/MSFU[JM1,I+1])/(DSY/MM)
#
dv_dx = .5*(V[J,IP1]/MSFV[J,IP1]+ V[J+1,IP1]/MSFV[J+1,IP1] -
V[J,IM1]/MSFV[J,IM1]+ V[J+1,IM1]/MSFV[J+1,IM1])/(DSX/MM)
#
vort[I,J] = dv_dx-du_dy
return vort
def demo_wrfUntested(fMesh, filesDataIn, fNameOut, r, dRegion, latThresh, iTimeStart_fData, iTimeEnd_fData, info='wrf case'):
#mesh ---------------------
data = netCDF4.Dataset(fMesh,'r')
d2r = np.pi/180.;
lat = data.variables['XLAT'][0,:,:]*d2r; lon = data.variables['XLONG'][0,:,:]*d2r
dx = data.variables['RDX'][0]; dx = 1./dx;
dy = data.variables['RDY'][0]; dy = 1./dy;
#want latitudes to be in [-pi/2, pi/2] and longitudes in [0, 2pi)
lon = lon%(2.*np.pi)
data.close()
mesh = wrfMesh.Mesh(lat,lon, r, dRegion)
mesh.fill_inRegion(latThresh)
cell0 = wrfMesh.Cell(mesh,-1)
#metr fields -----------------
nFiles = len(filesDataIn)
if (nFiles<1):
return mesh, cell0
dataOut = write_netcdf_header_metr(fNameOut, info, mesh)
iTimeGlobal = 0
for iFile in xrange(nFiles):
fPath = filesDataIn[iFile]
data = netCDF4.Dataset(fPath,'r')
#loop over individual times ------------------------------
#times = data.variables['time'][:]; nTimes = len(times); nTimes = 20
#for iTime in xrange(nTimes):
iTimeStart = iTimeStart_fData[iFile]; iTimeEnd = iTimeEnd_fData[iFile]
if (iTimeEnd<0): #use all times in file
nTimes = len(data.dimensions['Time']);
iTimeEnd = nTimes-1
for iTime in xrange(iTimeStart,iTimeEnd+1):
#read from file
theta = data.variables['pt'][iTime,:,:]
ug = data.variables['U'][iTime,:,:]; #south-north, west-east-stagger
vg = data.variables['V'][iTime,:,:]; #south-north-stagger, west-east
mapfac = data.variables['MAPFAC_M'][iTime,:,:]
sinalpha = data.variables['SINALPHA'][iTime,:,:]
cosalpha = data.variables['COSALPHA'][iTime,:,:]
#fill in missing values w/in region
#ERA-I doesn't appear to have any missing values...I don't know how their interpolation works.
#Some old documentation described PP2DINT that extrapolates using constant values.
#This rando site: https://badc.nerc.ac.uk/data/ecmwf-op/levels.html
#says
#"The ECMWF Operational and ERA-40 datasets also provide data on a "PV=+/-2" surface on which the potential vorticity takes the value 2PVU in the northern hemisphere and -2PVU in the southern hemisphere (1PVU = 10-6 m2 s-1 K kg-1), provided such a surface can be found searching downwards from the Model level close to 96hPa. Values at this model level are used where the search is unsuccessful."
#compute additional fields
vort = calc_vertVorticity_ll(u, v, mesh.nLat, mesh.nLon, mesh.lat, r)
#write to file
u = helpers.flatten_2dTo1d(u, mesh.nLat, mesh.nLon)
v = helpers.flatten_2dTo1d(v, mesh.nLat, mesh.nLon)
theta = helpers.flatten_2dTo1d(theta, mesh.nLat, mesh.nLon)
vort = helpers.flatten_2dTo1d(vort, mesh.nLat, mesh.nLon)
write_netcdf_iTime_metr(dataOut, iTimeGlobal, u,v,theta,vort)
iTimeGlobal = iTimeGlobal+1
#end iTime
#end iFile
dataOut.close()
return mesh, cell0