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PV.py
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PV.py
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#!/usr/bin/python3.8
import sys,math,random
import warnings
import numpy as np
from numpy import newaxis
import warnings
import time
from netCDF4 import Dataset
import scipy.ndimage as ndimage
from windspharm.standard import VectorWind
from windspharm.tools import prep_data, recover_data, order_latdim
from decimal import *
import traceback
class potential_vorticity:
def ddx(self,s,lat,lon,missingData):
lonLen = len(lon)
latLen = len(lat)
dsdx = np.empty((latLen,lonLen))
rearth = 6371221.3
di = abs(np.cos(np.radians(0.0))*rearth*(np.radians(lon[1]-lon[0])))
# GRIB order - S-N(OUTER)
# W-E(INNER)
has_left = s[:,:-2] > -999.99
has_right = s[:,2:] > -999.99
has_value = s[:,1:-1] > -999.99
dsdx = np.zeros((73,144))
dsdx[:, 1:-1] = -999.99
dsdx[:, 1:-1] = np.where(has_right & has_value, (s[:,2:] - s[:,1:-1]) / di, dsdx[:, 1:-1])
dsdx[:, 1:-1] = np.where(has_left & has_value, (s[:,1:-1] - s[:,:-2]) / di, dsdx[:, 1:-1])
dsdx[:, 1:-1] = np.where(has_left & has_right, (s[:,2:] - s[:,:-2]) / (2. * di), dsdx[:, 1:-1])
hasValue = s[1:-1,0] > -999.99
hasRight = s[1:-1,-1] > -999.99
hasLeft = s[1:-1,1] > -999.99
hasRight2 = s[1:-1,-2] > -999.99
if (np.allclose(2*lon[0]-lon[-1],lon[1],1e-3) or np.allclose(2*lon[0]-lon[-1],lon[1] + 360.0,1e-3)):
dsdx[1:-1,0] = -999.99
dsdx[1:-1,-1] = -999.99
dsdx[1:-1,0] = np.where(hasRight & hasValue,(s[1:-1,-1] - s[1:-1,0]) / di, dsdx[1:-1, 0])
dsdx[1:-1,0] = np.where(hasLeft & hasValue,(s[1:-1,1] - s[1:-1,0]) / di, dsdx[1:-1, 0])
dsdx[1:-1,0] = np.where(hasLeft & hasRight,(s[1:-1,1] - s[1:-1,-1]) /2. * di, dsdx[1:-1, 0])
dsdx[1:-1,-1] = np.where(hasRight & hasRight2,(s[1:-1,-1] - s[1:-1,-2]) / di, dsdx[1:-1, -1])
dsdx[1:-1,-1] = np.where(hasLeft & hasRight,(s[1:-1,1] - s[1:-1,-1]) / di, dsdx[1:-1, -1])
dsdx[1:-1,-1] = np.where(hasValue & hasRight2,(s[1:-1,0] - s[1:-1,-2]) /2. * di, dsdx[1:-1, -1])
elif (np.allclose(lon[0],lon[-1],1e-3)):
dsdx[1:-1,0] = -999.99
dsdx[1:-1,-1] = -999.99
dsdx[1:-1,0] = np.where(hasLeft & hasRight2,(s[1:-1,1] - s[1:-1,-2]) / 2. *di, dsdx[1:-1, 0])
dsdx[1:-1,0] = np.where(hasValue & hasRight2,(s[1:-1,0] - s[1:-1,-2]) /di, dsdx[1:-1, 0])
dsdx[1:-1,0] = np.where(hasLeft & hasValue,(s[1:-1,1] - s[1:-1,0]) / di, dsdx[1:-1, 0])
else:
dsdx[1:-1,0] = -999.99
dsdx[1:-1,-1] = -999.99
dsdx[1:-1,0] = np.where(hasLeft & hasValue,(s[1:-1,1] - s[1:-1,0]) / di, dsdx[1:-1, 0])
dsdx[1:-1,-1] = np.where(hasRight & hasRight2,(s[1:-1,-1] - s[1:-1,-2]) / di, dsdx[1:-1, -1])
return dsdx
def ddy(self,s,lat,lon):
lonLen = len(lon)
latLen = len(lat)
dsdy = np.empty((latLen,lonLen))
rearth = 6371221.3
dj = abs(np.radians((lat[0]-lat[1])) * rearth)
# North Pole
hasNValue = s[0,:] > -999.99
hasNLeft = s[1,:] > -999.99
dsdy[0,:] = -999.99
dsdy[0,:] = np.where(hasNValue & hasNLeft, (s[0,:]-s[1,:])/dj,dsdy[0,:])
#South Pole
hasSRValue = s[-1,:] > -999.99
hasSR2Value = s[-2,:] > -999.99
dsdy[-1,:] = -999.99
dsdy[-1,:] = np.where(hasSRValue & hasSR2Value,(s[-2,:]-s[-1,:])/dj,dsdy[-1,:])
#Regular coordinates
has_value = s[1:-1, :] > -999.99
has_right = s[2:,:] > -999.99
has_left = s[:-2,:] > -999.99
dsdy[1:-1,:] = -999.99
dsdy[1:-1,:] = np.where(has_left & has_value,(s[2,:] - s[1:-1,:]) / dj, dsdy[1:-1,:])
dsdy[1:-1,:] = np.where(has_right & has_value,(s[1:-1,:] - s[:-2,:]) / dj, dsdy[1:-1,:])
dsdy[1:-1,:] = np.where(has_left & has_right,(s[2:,:] - s[:-2,:])/(2.*dj),dsdy[1:-1,:])
return dsdy
def relvor(self):
uSouth = u[1,:]
uSouthMissing = (u[1,:] < -999.99).sum()
relv[0,:] = uSouth[uSouth > -999.99].sum()
sphericalCapFactor = math.cos(math.radians(lat[1]))/(1.-math.sin (math.radians(lat[1])))/rearth /float(lonLen-uSouthMissing)
relv[0,:] = relv[0,:]*sphericalCapFactor
uNorth = u[-2,:]
uNorthMissing = (u[-2,:] < -999.99).sum()
relv[-1,:] = uNorth[uNorth > -999.99].sum()
sphericalCapFactor = math.cos(math.radians(lat[-2]))/(1.-math.sin (math.radians(lat[-2])))/rearth /float(lonLen-uNorthMissing)
relv[-1,:] = relv[-1,:]*sphericalCapFactor
hasNoU = u[1:-1,:] < -999.99
hasNoDvDx = dvdx[1:-1,:] < -999.99
hasNoDuDy = dudy[1:-1,:] < -999.99
relv[1:-1,:] = np.where(hasNoU| hasNoDvDx |hasNoDuDy,-999.99,relv[1:-1,:])
relv[1:-1,:] = dvdx[1:-1,:]-dudy[1:-1,:]+(u[1:-1,:]*np.tan(np.radians(lat[1:-1,None])))/rearth
def absvor(self,relv):
corl = np.empty((latLen))
corl = 2.0 * omega * np.sin(np.radians(lat))
corl = corl[:,None]
hasNoRelv = relv[:,:] < -999.99
absv = np.empty((latLen,lonLen))
absv = np.where(hasNoRelv,-999.99,absv[:,:])
absv = relv + corl
return absv
def pot(self,tmp,pres):
cp = 1004.0
md = 28.9644
R = 8314.41
Rd = R/md
pottemp = np.zeros_like(tmp)
pottemp = tmp * (100000./pres[:,None,None]) ** (Rd/cp)
return pottemp
def potsfc(self,tsfc,psfc):
cp = 1004.0
md = 28.9644
R = 8314.41
Rd = R/md
pottemp = np.zeros_like(tsfc)
pottemp = tsfc * (100000./psfc) ** (Rd/cp)
return pottemp
def pvonp(self,ni,nj,lat,lon,pres,pres1,pres2,tmp,tmp1,tmp2,u,u1,u2,v,v1,v2,missingData):
cp = 1004.
gravity = 9.80665
md = 28.9644
R = 8314.41
Rd = R/md
kappa = Rd/cp
#print(v)
dvdx = self.ddx(v,lat,lon,missingData)
dudy = self.ddy(u,lat,lon,missingData)
#print(dudy)
relv = self.relvor(lat,lon,u,v,dvdx,dudy)
absv = self.absvor(lat,lon,relv)
theta = np.empty_like(tmp,dtype=object)
theta1 = np.empty_like(tmp1,dtype=object)
theta2 = np.empty_like(tmp2,dtype=object)
pres = float(pres)
pres1 = float(pres1)
pres2 = float(pres2)
theta[:,:] = self.pot(tmp[:,:],pres1)
theta1[:,:] = self.pot(tmp1[:,:],pres1)
theta2[:,:] = self.pot(tmp2[:,:],pres2)
dpotdx = self.ddx(theta,lat,lon,missingData)
dpotdy = self.ddy(theta,lat,lon,missingData)
lnp1p2 = np.log(pres1/pres2)
dpi = -1. /(pres1 - pres2)
pv = np.empty((nj,ni))
for j in range(0,nj):
for i in range(0,ni):
stabl = (theta[j,i]/pres) *(np.log(tmp1[j,i]/tmp2[j,i])/lnp1p2 - kappa)
du = u1[j,i] - u2[j,i]
dv = v1[j,i] - v2[j,i]
dth = theta1[j,i] - theta2[j,i]
vorcor = (du * dpotdy[j,i] - dv * dpotdx[j,i])/dth
pv[j,i] = gravity * (absv[j,i] +vorcor) * dth *dpi *1e6
for j in range(0,nj):
if (abs(lat[j] - 90.) < 0.001):
for i in range(1,ni-1):
pv[j,0] = pv[j,0]+pv[j,i]
if (abs(lon[1] - lon[ni-1]) < 0.001):
pv[j,0] = pv[j,0]/float(ni-1)
else:
pv[j,0] = pv[j,0]+pv[j,-1]
pv[j,0] = pv[j,0]/float(ni-1)
k = 0
m = 0
for j in range(0,nj):
for i in range(0,ni):
print(lon[i],lat[j],pv[j,i])
#if (lat[j] > 0.0 and pv[j,i] <= 0.):
# print(lon[i],lat[j],pv[j,i])
# k += 1
#elif (lat[j] < 0.0 and pv[j,i] >= 0.):
# print(lon[i],lat[j],pv[j,i])
# m += 1
#print(k,m)
return pv
def pvlayr(self,ni,nj,lat,lon,pres,pres1,pres2,tmp1,tmp2,u1,u2,v1,v2):
cp = 1004.
gravity = 9.80665
md = 28.9644
R = 8314.41
Rd = R/md
kappa = Rd/cp
pres1 = float(pres1)
pres2 = float(pres2)
lnp1 = np.log(pres1)
lnp2 = np.log(pres2)
pav = (pres1*lnp1+pres2*lnp2)/(lnp1+lnp2)
uav = np.empty((nj,ni))
vav = np.empty((nj,ni))
tav = np.empty((nj,ni))
potav = np.empty((nj,ni))
uav[:,:] = (lnp2*u2[:,:] + lnp1*u1[:,:])/(lnp1+lnp2)
vav[:,:] = (lnp2*v2[:,:] + lnp1*v1[:,:])/(lnp1+lnp2)
tav[:,:] = np.exp((lnp2*np.log(tmp2[:,:]) + lnp1*np.log(tmp1[:,:]))/(lnp1+lnp2))
potav[:,:] = self.pot(tav,pav)
missingData = float(-999.99)
dvdx = self.ddx(vav,lat,lon,missingData)
dudy = self.ddy(uav,lat,lon,missingData)
relv = self.relvor(lat,lon,uav,vav,dvdx,dudy)
absv = self.absvor(lat,lon,relv)
dpotdx = self.ddx(potav,lat,lon,missingData)
dpotdy = self.ddy(potav,lat,lon,missingData)
pv = np.empty((nj,ni))
stabl = np.empty((nj,ni))
vorcor = np.empty((nj,ni))
for j in range(0,nj):
for i in range(0,ni):
stabl[j,i] = potav[j,i]/pav * (np.log(tmp1[j,i]/tmp2[j,i])/(lnp1-lnp2)-kappa)
vorcor[j,i] = ((v1[j,i] - v2[j,i])*dpotdx[j,i]-(u1[j,i] - u2[j,i])*dpotdy[j,i])/(self.pot(tmp1[j,i],pres1)-self.pot(tmp2[j,i],pres2))
pv[j,i] = -gravity * (absv[j,i]+vorcor[j,i]) * stabl[j,i] * 1e6
for j in range(0,nj):
if (abs(lat[j] - 90.) < 0.001):
for i in range(1,ni-1):
pv[j,0] = pv[j,0]+pv[j,i]
if (abs(lon[1] - lon[ni-1]) < 0.001):
pv[j,0] = pv[j,0]/float(ni-1)
else:
pv[j,0] = pv[j,0]+pv[j,-1]
pv[j,0] = pv[j,0]/float(ni-1)
k = 0
m = 0
#for j in range(0,nj):
# for i in range(0,ni):
#if (lat[j] > 0.0 and pv[i,j] <= 0.):
# print(lat[j])
# k += 1
#elif (lat[j] < 0.0 and pv[i,j] >= 0.):
# print(lat[j])
# m += 1
#print(k,m)
return pv
def pv_isobaric_bluestein(self,ni,nj,lat,lon,pres,pres1,pres2,tmp,tmp1,tmp2,u,u1,u2,v,v1,v2,missingData):
gravity = 9.80665
pres = float(pres)
pres1 = float(pres1)
pres2 = float(pres2)
missingData = float(-999.99)
dvdx = self.ddx(v,lat,lon,missingData)
dudy = self.ddy(u,lat,lon,missingData)
relv = self.relvor(ni,nj,lat,lon,u,v,dvdx,dudy)
absv = self.absvor(lat,lon,relv)
dtdx = self.ddx(tmp,lat,lon,missingData)
dtdy = self.ddy(tmp,lat,lon,missingData)
theta = np.empty_like(tmp,dtype=object)
theta1 = np.empty_like(tmp1,dtype=object)
theta2 = np.empty_like(tmp2,dtype=object)
theta[:,:] = self.pot(tmp[:,:],pres)
theta1[:,:] = self.pot(tmp1[:,:],pres1)
theta2[:,:] = self.pot(tmp2[:,:],pres2)
dpi = pres1 - pres2
pv = np.empty((nj,ni))
for j in range(0,nj):
for i in range(0,ni):
dudp = (u1[j,i] - u2[j,i])/dpi
dvdp = (v1[j,i] - v2[j,i])/dpi
dth = theta1[j,i] - theta2[j,i]
static_stability =-(tmp[j,i]/theta[j,i])*dth/dpi
vorcor = (dvdp * dtdx[j,i]) - (dudp * dtdy[j,i])*static_stability
stability = dth/dpi
pv[j,i] = -gravity *(absv[j,i] +vorcor) * dth/dpi *10**6
for j in range(0,nj):
if (abs(lat[j] - 90.) < 0.001):
for i in range(1,ni-1):
pv[j,0] = pv[j,0]+pv[j,i]
if (abs(lon[1] - lon[ni-1]) < 0.001):
pv[j,0] = pv[j,0]/float(ni-1)
else:
pv[j,0] = pv[j,0]+pv[j,-1]
pv[j,0] = pv[j,0]/float(ni-1)
#xx = pv[np.where(pv > 0.0)]
#yy = lat[np.where(lat <0.0)]
#lats = np.reshape(lat,(nj,ni))
#pv = np.where((pv > 0.0) & (lat < 0.0))
#print(len(pv))
#sys.exit()
return pv
def pv_rossby(self,ni,nj,lat,lon,pres,pres1,pres2,tmp,tmp1,tmp2,u,u1,u2,v,v1,v2,missingData):
gravity = 9.80665
pres = float(pres)
pres1 = float(pres1)
pres2 = float(pres2)
missingData = float(-999.99)
dvdx = self.ddx(v,lat,lon,missingData)
dudy = self.ddy(u,lat,lon,missingData)
relv = self.relvor(ni,nj,lat,lon,u,v,dvdx,dudy)
absv = self.absvor(lat,lon,relv)
theta = np.empty_like(tmp,dtype=object)
theta1 = np.empty_like(tmp1,dtype=object)
theta2 = np.empty_like(tmp2,dtype=object)
theta[:,:] = self.pot(tmp[:,:],pres1)
theta1[:,:] = self.pot(tmp1[:,:],pres1)
theta2[:,:] = self.pot(tmp2[:,:],pres2)
dpotdx = self.ddx(theta,lat,lon,missingData)
dpotdy = self.ddy(theta,lat,lon,missingData)
dpi = pres1 - pres2
pv = np.empty((nj,ni))
for j in range(0,nj):
for i in range(0,ni):
dudp = (u1[j,i] - u2[j,i])/dpi
dvdp = (v1[j,i] - v2[j,i])/dpi
dth = theta1[j,i] - theta2[j,i]
stability = dth/dpi
vorcor = (dvdp*dpotdx[j,i])-(dudp*dpotdy[j,i])
pv[j,i] = -gravity* (absv[j,i]*stability-vorcor)*10**6
#print(pv[j,i])
for j in range(0,nj):
if (abs(lat[j] - 90.) < 0.001):
for i in range(1,ni-1):
pv[j,0] = pv[j,0]+pv[j,i]
if (abs(lon[1] - lon[ni-1]) < 0.001):
pv[j,0] = pv[j,0]/float(ni-1)
else:
pv[j,0] = pv[j,0]+pv[j,-1]
pv[j,0] = pv[j,0]/float(ni-1)
k = 0
m = 0
for j in range(0,nj):
for i in range(0,ni):
#print(lon[i],lat[j],pv[j,i])
if (lat[j] > 0.0 and pv[j,i] <= 0.):
#print(lon[i],lat[j],pv[j,i])
k += 1
elif (lat[j] < 0.0 and pv[j,i] >= 0.):
#print(lon[i],lat[j],pv[j,i])
m += 1
print(k,m)
#sys.exit()
return pv
def testsipv(self,lats,lons,kthta,thta,pthta,uthta,vthta,missingData):
latLen = len(lats)
lonLen = len(lons)
t1 = time.time()
ipvRef = self.sipv(lats,lons,kthta,thta,pthta,uthta,vthta,missingData)
t2 = time.time()
print(t2-t1)
t3 = time.time()
ipv = self.sipv2(lats,lons,kthta,thta,pthta,uthta,vthta,missingData)
t4 = time.time()
print(t4-t3)
for k in range(0,16):
for j in range(0,latLen):
for i in range(0,lonLen):
if (ipvRef[k,j,i]-ipv[k,j,i] != 0.):
print(ipvRef[k,j,i]-ipv[k,j,i])
sys.exit()
return ipv
def tests2thta(self,lats,lons,plevs,kthta,uwndI,psfc,uins,thta,pthta):
latLen = len(lats)
lonLen = len(lons)
t1 = time.time()
uRef = self.s2thta(lats,lons,plevs,kthta,uwndI,psfc,uins,thta,pthta)
sys.exit()
t2 = time.time()
print(t2-t1)
t3 = time.time()
u = self.s2thtaref(lats,lons,plevs,kthta,uwndI,psfc,uins,thta,pthta)
t4 = time.time()
print(t4-t3)
for k in range(0,1):
for j in range(0,latLen):
for i in range(0,lonLen):
print(uRef[k,j,i],u[k,j,i])
sys.exit()
return ipv
def sipv2(self,lats,lons,kthta,thta,pthta,uthta,vthta,missingData):
latLen = len(lats)
lonLen = len(lons)
ipv = np.zeros((kthta,latLen,lonLen))
dltdlp = np.empty((kthta,latLen,lonLen))
stabl = np.zeros((kthta,latLen,lonLen))
tdwn = np.zeros((kthta,latLen,lonLen))
tdwn_ref = np.zeros((kthta,latLen,lonLen))
tup = np.zeros((kthta,latLen,lonLen))
dlt = np.empty((kthta,latLen,lonLen))
dlp = np.empty((kthta,latLen,lonLen))
absVor = np.zeros((kthta,latLen,lonLen))
p0 = 100000.
kappa = 2./7.
gravity = 9.80665
args = []
for uthta2d,vthta2d in zip(uthta,vthta):
w = VectorWind(uthta2d,vthta2d)
absVorLevel=w.absolutevorticity()
b = absVorLevel[newaxis,:,:]
args.append(b)
absVor = np.concatenate(args,axis=0)
# For internal levels
ipv[1:-1,:,:] = -999.99
hasPthta = pthta[1:-1,:,:] > 0
hasPthta0 = pthta[0:-2,:,:] > 0
hasAbsVor = absVor[1:-1,:,:] > 0
tdwn[1:-1,:,:] = thta[0:-3,None,None]*(pthta[0:-2,:,:]/p0)**kappa
tup[1:-1,:,:] = thta[2:-1,None,None]*(pthta[2:,:,:]/p0)**kappa
dlt[1:-1,:,:] = np.log(tup[1:-1,:,:]/tdwn[1:-1,:,:])
dlp[1:-1,:,:] = np.log(pthta[2:,:,:]/pthta[0:-2,:,:])
dltdlp[1:-1,:,:] = dlt[1:-1,:,:]/dlp[1:-1,:,:]
stabl[1:-1,:,:] = (thta[1:-2,None,None]/pthta[1:-1,:,:]) *(dltdlp[1:-1,:,:]-kappa)
ipv[1:-1,:,:] = -gravity*absVor[1:-1,:,:]*stabl[1:-1,:,:]
# Boundary Layer
hasNoPthta = pthta[0,:,:] <= 0.
hasNoPthta0 = pthta[1,:,:] <= 0.
hasNoAbsVor = absVor[0,:,:] < -999.99
ipv[0,:,:] = np.where(hasNoPthta|hasNoPthta0|hasNoAbsVor,-999.99,ipv[0,:,:])
tdwn[0,:,:] = thta[0,None,None] * (pthta[0,:,:]/p0)**kappa
tup[0,:,:] = thta[1,None,None] * (pthta[1,:,:]/p0)**kappa
dlt[0,:,:] = np.log(tup[0,:,:]) - np.log(tdwn[0,:,:])
dlp[0,:,:] = np.log(pthta[1,:,:])-np.log(pthta[0,:,:])
dltdlp[0,:,:] = dlt[0,:,:]/dlp[0,:,:]
stabl[0,:,:] = (thta[0,None,None]/pthta[0,:,:]) *(dltdlp[0,:,:]-kappa)
ipv[0,:,:] = -gravity * absVor[0,:,:] * stabl[0,:,:]
# Topmost Layer
hasNoPthta = pthta[-1,:,:] <= 0.
hasNoPthta0 = pthta[-2,:,:] <= 0.
hasNoAbsVor = absVor[-1,:,:] < -999.99
ipv[-1,:,:] = np.where(hasNoPthta|hasNoPthta0|hasNoAbsVor,-999.99,ipv[-1,:,:])
tdwn[-1,:,:] = thta[-3,None,None]*(pthta[-2,:,:]/p0)**kappa
tup[-1,:,:] = thta[-2,None,None]*(pthta[-1,:,:]/p0)**kappa
dlt[-1,:,:] = np.log(tup[-1,:,:]/tdwn[-1,:,:])
dlp[-1,:,:] = np.log(pthta[-1,:,:]/pthta[-2,:,:])
dltdlp[-1,:,:] = dlt[-1,:,:]/dlp[-1,:,:]
stabl[-1,:,:] = (thta[-2,None,None]/pthta[-1,:,:]) *(dltdlp[-1,:,:]-kappa)
ipv[-1,:,:] = -gravity * absVor[-1,:,:] * stabl[-1,:,:]
smoothedIPV = ndimage.gaussian_filter(ipv*1e6,sigma=(0,2,2),order=0)
return smoothedIPV
def sipv(self,lats,lons,kthta,thta,pthta,uthta,vthta,missingData):
latLen = len(lats)
lonLen = len(lons)
ipv = np.empty((kthta,latLen,lonLen))
p0 = 100000.
kappa = 2./7.
gravity = 9.80665
rearth = 6371221.3
ntrunc = int(lonLen/2)
np.seterr(all='warn')
warnings.filterwarnings('error')
tdwn_ref = np.empty((kthta,latLen,lonLen))
tup_ref = np.empty((kthta,latLen,lonLen))
dlt_ref = np.empty((kthta,latLen,lonLen))
dlp_ref = np.empty((kthta,latLen,lonLen))
dltdlp_ref = np.empty((kthta,latLen,lonLen))
stabl_ref = np.empty((kthta,latLen,lonLen))
ipv_ref = np.empty((kthta,latLen,lonLen))
t1 = time.time()
for k in range(0,kthta):
uthta2d = uthta[k,:,:]
vthta2d = vthta[k,:,:]
w = VectorWind(uthta2d,vthta2d)
absv=w.absolutevorticity()
for j in range(0,latLen):
for i in range(0,lonLen):
if (k == 0):
if (pthta[k,j,i] <= 0. or pthta[k+1,j,i] <= 0. or absv[j,i] < missingData):
ipv_ref[k,j,i] = missingData
else:
tdwn_ref[k,j,i] = thta[k] * (pthta[k,j,i]/p0)**kappa
tup_ref[k,j,i] = thta[k+1] * (pthta[k+1,j,i]/p0)**kappa
dlt_ref[k,j,i] = np.log(tup_ref[k,j,i]) - np.log(tdwn_ref[k,j,i])
if (pthta[k+1,j,i] == pthta[k,j,i]):
pthta[k+1,j,i] +=10
dlp_ref[k,j,i] = np.log(pthta[k+1,j,i])-np.log(pthta[k,j,i])
try:
dltdlp_ref[k,j,i] = dlt_ref[k,j,i]/dlp_ref[k,j,i]
except Warning:
print(pthta[k+1,j,i],pthta[k,j,i])
print(sys.exc_info())
sys.exit()
stabl_ref[k,j,i] = (thta[k]/pthta[k,j,i]) *(dltdlp_ref[k,j,i]-kappa)
ipv_ref[k,j,i] = -gravity * absv[j,i] * stabl_ref[k,j,i]
elif (k == kthta-1):
if (pthta[k,j,i] <= 0. or pthta[k-1,j,i] <= 0. or absv[j,i] < missingData):
ipv_ref[k,j,i] = missingData
else:
tdwn_ref[k,j,i] = thta[k-1] * (pthta[k-1,j,i]/p0)**kappa
tup_ref[k,j,i] = thta[k] * (pthta[k,j,i]/p0)**kappa
dlt_ref[k,j,i] = np.log(tup_ref[k,j,i]/tdwn_ref[k,j,i])
dlp_ref[k,j,i] = np.log(pthta[k,j,i]/pthta[k-1,j,i])
dltdlp_ref[k,j,i] = dlt_ref[k,j,i]/dlp_ref[k,j,i]
stabl_ref[k,j,i] = (thta[k]/pthta[k,j,i]) *(dltdlp_ref[k,j,i]-kappa)
ipv_ref[k,j,i] = -gravity * absv[j,i] * stabl_ref[k,j,i]
else:
if (pthta[k+1,j,i] > 0. and pthta[k-1,j,i] > 0. and absv[j,i] > missingData):
tdwn_ref[k,j,i] = thta[k-1] * (pthta[k-1,j,i]/p0)**kappa
tup_ref[k,j,i] = thta[k+1] * (pthta[k+1,j,i]/p0)**kappa
dlt_ref[k,j,i] = np.log(tup_ref[k,j,i]/tdwn_ref[k,j,i])
if (pthta[k+1,j,i] == pthta[k-1,j,i]):
pthta[k+1,j,i] +=10
dlp_ref[k,j,i] = np.log(pthta[k+1,j,i]/pthta[k-1,j,i])
try:
dltdlp_ref[k,j,i] = dlt_ref[k,j,i]/dlp_ref[k,j,i]
except Warning:
print(dlt,dlp)
stabl_ref[k,j,i] = (thta[k]/pthta[k,j,i]) *(dltdlp_ref[k,j,i]-kappa)
ipv_ref[k,j,i] = -gravity * absv[j,i] * stabl_ref[k,j,i]
#print(absv[j,i])
elif (pthta[k+1,j,i] <= 0. and pthta[k-1,j,i] > 0. and pthta[k,j,i] > 0. and absv[j,i] > missingData):
tdwn_ref[k,j,i] = thta[k-1]*(pthta[k-1,j,i]/p0)**kappa
tup_ref[k,j,i] = thta[k]*(pthta[k,j,i]/p0)**kappa
dlt_ref[k,j,i] = np.log(tup_ref[k,j,i]/tdwn_ref[k,j,i])
dlp_ref[k,j,i] = np.log(pthta[k,j,i]/pthta[k-1,j,i])
dltdlp_ref[k,j,i] = dlt_ref[k,j,i]/dlp_ref[k,j,i]
stabl = (thta[k]/pthta[k,j,i]) *(dltdlp-kappa)
ipv_ref[k,j,i] = -gravity * absv[j,i] * stabl_ref[k,j,i]
elif (pthta[k+1,j,i] > 0. and pthta[k-1,j,i] <= 0. and pthta[k,j,i] > 0. and absv[j,i] > missingData):
tdwn_ref[k,j,i] = thta[k] * (pthta[k,j,i]/p0)**kappa
tup_ref[k,j,i] = thta[k+1] * (pthta[k+1,j,i]/p0)**kappa
dlt_ref[k,j,i] = np.log(tup_ref[k,j,i]/tdwn_ref[k,j,i])
dlp_ref[k,j,i] = np.log(pthta[k+1,j,i]/pthta[k,j,i])
dltdlp_ref[k,j,i] = dlt_ref[k,j,i]/dlp_ref[k,j,i]
stabl_ref[k,j,i] = (thta[k]/pthta[k,j,i]) *(dltdlp_ref[k,j,i]-kappa)
ipv_ref[k,j,i] = -gravity * absv[j,i] * stabl_ref[k,j,i]
else:
ipv_ref[k,j,i] = missingData
ipv_ref[k,:,:] = ndimage.gaussian_filter(ipv_ref[k,:,:]*1e6,sigma=2,order=0)
return ipv_ref
def ipv(self,lats,lons,kthta,thta,pthta,uthta,vthta,missingData):
latLen = len(lats)
lonLen = len(lons)
ipv = np.empty((kthta,latLen,lonLen))
p0 = 100000.
kappa = 2./7.
gravity = 9.80665
for k in range(0,kthta):
dvdx = self.ddx(vthta[k,:,:],lats,lons,missingData)
dudy = self.ddy(uthta[k,:,:],lats,lons,missingData)
relv = self.relvor(lats,lons,uthta[k,:,:],vthta[k,:,:],dvdx,dudy)
absv = self.absvor(lats,lons,relv)
#print(absv.shape)
for j in range(0,latLen):
for i in range(0,lonLen):
if (k == 0):
if (pthta[k,j,i] <= 0. or pthta[k+1,j,i] <= 0. or absv[j,i] < missingData):
ipv[k,j,i] = missingData
else:
tdwn = thta[k] * (pthta[k,j,i]/p0)**kappa
tup = thta[k+1] * (pthta[k+1,j,i]/p0)**kappa
dlt = np.log(tup/tdwn)
dlp = np.log(pthta[k+1,j,i]/pthta[k,j,i])
dltdlp = dlt/dlp
stabl = (thta[k]/pthta[k,j,i]) *(dltdlp-kappa)
ipv[k,j,i] = -gravity * absv[j,i] * stabl
elif (k == kthta-1):
if (pthta[k,j,i] <= 0. or pthta[k-1,j,i] <= 0. or absv[j,i] < missingData):
ipv[k,j,i] = missingData
else:
tdwn = thta[k-1] * (pthta[k-1,j,i]/p0)**kappa
tup = thta[k] * (pthta[k,j,i]/p0)**kappa
dlt = np.log(tup/tdwn)
dlp = np.log(pthta[k,j,i]/pthta[k-1,j,i])
dltdlp = dlt/dlp
stabl = (thta[k]/pthta[k,j,i]) *(dltdlp-kappa)
ipv[k,j,i] = -gravity * absv[j,i] * stabl
else:
if (pthta[k+1,j,i] > 0. and pthta[k-1,j,i] > 0. and absv[j,i] > missingData):
tdwn = thta[k-1] * (pthta[k-1,j,i]/p0)**kappa
tup = thta[k+1] * (pthta[k+1,j,i]/p0)**kappa
dlt = np.log(tup/tdwn)
dlp = np.log(pthta[k+1,j,i]/pthta[k-1,j,i])
dltdlp = dlt/dlp
stabl = (thta[k]/pthta[k,j,i]) *(dltdlp-kappa)
ipv[k,j,i] = -gravity * absv[j,i] * stabl
#print(absv[j,i])
elif (pthta[k+1,j,i] <= 0. and pthta[k-1,j,i] > 0. and pthta[k,j,i] > 0. and absv[j,i] > missingData):
tdwn = thta[k-1]*(pthta[k-1,j,i]/p0)**kappa
tup = thta[k]*(pthta[k,j,i]/p0)**kappa
dlt = np.log(tup/tdwn)
dlp = np.log(pthta[k,j,i]/pthta[k-1,j,i])
dltdlp = dlt/dlp
stabl = (thta[k]/pthta[k,j,i]) *(dltdlp-kappa)
ipv[k,j,i] = -gravity * absv[j,i] * stabl
elif (pthta[k+1,j,i] > 0. and pthta[k-1,j,i] <= 0. and pthta[k,j,i] > 0. and absv[j,i] > missingData):
tdwn = thta[k] * (pthta[k,j,i]/p0)**kappa
tup = thta[k+1] * (pthta[k+1,j,i]/p0)**kappa
dlt = np.log(tup/tdwn)
dlp = np.log(pthta[k+1,j,i]/pthta[k,j,i])
dltdlp = dlt/dlp
stabl = (thta[k]/pthta[k,j,i]) *(dltdlp-kappa)
ipv[k,j,i] = -gravity * absv[j,i] * stabl
else:
ipv[k,j,i] = missingData
ipv[k,:,:] = ndimage.gaussian_filter(ipv[k,:,:]*1e6,sigma=2,order=0)
return ipv
def ipv2(self,lats,lons,kthta,thta,pthta,uthta,vthta,missingData):
latLen = len(lats)
lonLen = len(lons)
ipv = np.empty((kthta,latLen,lonLen))
p0 = 100000.
kappa = 2./7.
gravity = 9.80665
for k in range(0,kthta):
dvdx = self.ddx(vthta[k,:,:],lats,lons,missingData)
dudy = self.ddy(uthta[k,:,:],lats,lons,missingData)
relv = self.relvor(lats,lons,uthta[k,:,:],vthta[k,:,:],dvdx,dudy)
absv = self.absvor(lats,lons,relv)
for j in range(0,latLen):
for i in range(0,lonLen):
if (k == 0):
if (pthta[k,j,i] <= 0. or pthta[k+1,j,i] <= 0. or absv[j,i] < missingData):
ipv[k,j,i] = missingData
else:
tdwn = thta[k]
tup = thta[k+1]
deltaTheta = tup - tdwn
deltaP = pthta[k+1,j,i]-pthta[k,j,i]
stabl = deltaTheta/deltaP
ipv[k,j,i] = -gravity * absv[j,i] * stabl
elif (k == kthta-1):
if (pthta[k,j,i] <= 0. or pthta[k-1,j,i] <= 0. or absv[j,i] < missingData):
ipv[k,j,i] = missingData
else:
tdwn = thta[k-1]
tup = thta[k]
deltaTheta = tup - tdwn
deltaP = pthta[k,j,i] - pthta[k-1,j,i]
stabl = deltaTheta/deltaP
ipv[k,j,i] = -gravity * absv[j,i] * stabl
else:
if (pthta[k+1,j,i] > 0. and pthta[k-1,j,i] > 0. and absv[j,i] > missingData):
tdwn = thta[k-1]
tup = thta[k+1]
deltaTheta = tup - tdwn
deltaP = pthta[k+1,j,i] - pthta[k-1,j,i]
stabl = deltaTheta/deltaP
ipv[k,j,i] = -gravity * absv[j,i] * stabl
#print(absv[j,i])
elif (pthta[k+1,j,i] <= 0. and pthta[k-1,j,i] > 0. and pthta[k,j,i] > 0. and absv[j,i] > missingData):
tdwn = thta[k-1]
tup = thta[k]
deltaTheta = tup - tdwn
deltaP = pthta[k,j,i] - pthta[k-1,j,i]
stabl = deltaTheta/deltaP
ipv[k,j,i] = -gravity * absv[j,i] * stabl
elif (pthta[k+1,j,i] > 0. and pthta[k-1,j,i] <= 0. and pthta[k,j,i] > 0. and absv[j,i] > missingData):
tdwn = thta[k]
tup = thta[k+1]
deltaTheta = tup - tdwn
deltaP = pthta[k+1,j,i] - pthta[k,j,i]
stabl = deltaTheta/deltaP
ipv[k,j,i] = -gravity * absv[j,i] * stabl
else:
ipv[k,j,i] = missingData
return ipv
def p2thta(self,lats,lons,plevs,tsfc,psfc,tpres):
maxlvl = 17
plvls = len(plevs)
cp = float(1004)
md = 28.9644
R = 8314.41
Rd = R/md
kappa = 2./7.
dthta = 10.
epsln = 0.001
kmax = 10
p0 = 100000.
latLen = len(lats)
lonLen = len(lons)
thtap = np.zeros((plvls,latLen,lonLen))
potsfc = np.zeros((latLen,lonLen))
alogp = np.zeros((plvls))
thta = np.zeros(maxlvl)
# Calculate potential temperature at the surface. Keep track of lowest value.
# Calculate potential temperature at the surface. Keep track of lowest value.
potsfc = self.potsfc(tsfc,psfc)
thtalo = np.min(potsfc)
# Compute potential temperature for each isobaric level eliminating superadiabatic or neutral layer
thtap = self.pot(tpres,plevs)
thtahi = thtap[9,0,0]
for k in range(0,len(plevs)):
for j in range(0,latLen):
for i in range(0,lonLen):
if (psfc[j,i] > plevs[k]) :
if (k > 0):
if (psfc[j,i] < plevs[k-1]):
if (thtap[k,j,i] <= potsfc[j,i]):
thtap[k,j,i] = potsfc[j,i]+0.01
elif (thtap[k,j,i] <= thtap[k-1,j,i]):
thtap[k,j,i] = thtap[k-1,j,i]+0.01
else:
if (thtap[0,j,i] <= potsfc[j,i]):
thtap[0,j,i] = potsfc[j,i]+0.01
if (k >= 9 and thtap[k,j,i] > thtahi):
thtahi = thtap[k,j,i]
# Identify isentropic levels to interpolate to
kout = 0
while (True):
kout += 1
thta[0] = 200. + float(kout-1)*dthta
if (thta[0] + dthta >= thtalo):
break
looping = True
while(looping):
thta[0] += dthta
npts = 0
j = 0
while (looping and j < latLen):
i = 0
while (looping and i < lonLen):
if (potsfc[j,i] <= thta[0]):
npts +=1
if (npts >= (latLen*lonLen)/10.):
looping = False
i += 1
j +=1
print('first entropic level is ',thta[0])
kthta = 1
while (kthta < maxlvl):
if (thta[kthta] <= thtahi):
thta[kthta] = thta[kthta-1]+dthta
kthta += 1
looping = True
while (looping):
kthta -=1
npts = 0
j = 0
while (looping and j < latLen):
i = 0
while (looping and i < lonLen):
if (thtap[-1,j,i] >= thta[kthta]):
npts += 1
if (float(npts) >= float(latLen*lonLen)/10.):
looping = False
i +=1
j = +1
if (kthta >= maxlvl):
print('P2THTA: ONLY THE FIRST')
else:
print('TOP ISENTROPIC LEVEL', thta[kthta])
print(thta)
alogp[:] = np.log(plevs[:])
maxit = 0
resmax = 1.
pthta = np.zeros((kthta,latLen,lonLen),dtype='float64')
for kout in range(0,kthta):
for j in range(0,latLen):
for i in range(0,lonLen):
# Begin IF
if (thta[kout] < potsfc[j,i]):
pthta[kout,j,i] = psfc[j,i] + random.uniform(0,0.01)
elif (thta[kout] > thtap[-1,j,i]):
pthta[kout,j,i] = 1.
elif (abs(thta[kout]-potsfc[j,i]) < 0.001):
pthta[kout,j,i] = psfc[j,i]
else:
looping = True
kin = 0
while (looping and kin < plvls):
if (thta[kout] < thtap[kin,j,i]):
#Begin IF
if (kin == 0):
potdwn = potsfc[j,i]
pdwn = psfc[j,i]
alogpd = np.log(psfc[j,i])
# # Begin If
if (abs(psfc[j,i]-plevs[kin]) < 0.001):
potup = thtap[kin+1,j,i]
pup = plevs[kin+1]
alogpu = alogp[kin+1]
else:
potup = thtap[kin,j,i]
pup = plevs[kin]
alogpu = alogp[kin]
# End if
elif (potsfc[j,i] > thtap[kin+1,j,i]):
potdwn = potsfc[j,i]
pdwn = psfc[j,i]
alogpd = np.log(psfc[j,i])
if (abs(psfc[j,i]-plevs[kin]) < 0.001):
potup =thtap[kin+1,j,i]
pup = plevs[kin+1]
alogpu = alogp[kin+1]
else:
potup = thtap[kin,j,i]
pup = plevs[kin]
alogpu = alogp[kin]
#End if
else:
potup = thtap[kin,j,i]
pup = plevs[kin]
alogpu = alogp[kin]
potdwn = thtap[kin-1,j,i]
pdwn = plevs[kin-1]
alogpd = alogp[kin-1]
# End if
looping = False
kin +=1
# While loop end
# End if Matches line 625
tdwn = potdwn * (pdwn/100000.)** kappa
tup = potup *(pup/100000.)** kappa
a = (tup - tdwn)/(alogpu - alogpd)
b = tup - a *alogpu
if (alogpu-alogpd == 0.):
diffpupd = 0.0001
try:
dltdlp = (np.log(tup/tdwn))/(diffpupd)
except Warning:
print(dltdlp)
print("divide by zero")
else:
try:
dltdlp = (np.log(tup/tdwn))/(alogpu-alogpd)
except Warning:
print("divide by zero")
interc = np.log(tup) - dltdlp*alogpu
pln = (np.log(thta[kout]) - interc - kappa*alogp[0])/(dltdlp-kappa)
#pln = alogpd + 0.5 * (alogpu - alogpd)
resid = 1
#k = 0
#pok = (p0)**kappa
kmax = 10
while (resid > epsln and k < kmax) :
#ekp = np.exp(-kappa * pln)
#t = a * pln + b
#f = thta[kout] - pok * t * ekp
#fp = pok * ekp * (kappa * t -a)
#pin = pln - f/fp
#res = abs(pln -pin)
#pln = pin
#k = k+1
t1 = dltdlp * pln+interc
thta1 = t1 + kappa *(np.log(p0 / pln))
f= np.log(thta[kout]) - thta1
dfdp = dltdlp/np.exp(pln) + kappa/np.exp(-pln)
pin = pln - f/dfdp
resid = abs(pln - pin)
pln = pin
k += 1
pthta[kout,j,i] = np.exp(pln)
#print(pthta[kout,j,i])
if (pthta[kout-1,j,i] > 0.):
if (pthta[kout,j,i] > pthta[kout-1,j,i]):
pthta[kout,j,i] = pthta[kout-1,j,i] + 0.01
print(pthta.shape)
ret = []
ret.append(kthta)
ret.append(pthta)
ret.append(thta)
return ret
def s2thta(self,lats,lons,pres,kthta,ssfc,psfc,spres,thta,pthta):
plvls = len(pres)
latLen = len(lats)