def calcTvDiff(press, thetae0, interpTenv, interpTdEnv):
"""
Calculates the virtual temperature difference between the thetae0
moist adiabat and a given sounding at some pressure.
Parameters
- - - - - -
press: pressure (Pa)
thetae0: equivalent potential temperature of the adiabat (K)
interpTenv: interpolator for environmental temperature (deg C)
interpTdEnv: interpolator for environmental dew point temperature (deg C)
Returns
- - - - - -
TvDiff: the virtual temperature difference at pressure press
between the thetae0 moist adiabat and the given sounding (K).
"""
c = constants()
Tcloud=findTmoist(thetae0,press)
wvcloud=wsat(Tcloud,press)
Tvcloud=Tcloud*(1. + c.eps*wvcloud)
Tenv=interpTenv(press*1.e-2) + c.Tc
Tdenv=interpTdEnv(press*1.e-2) + c.Tc
wvenv=wsat(Tdenv,press)
Tvenv=Tenv*(1. + c.eps*wvenv)
return Tvcloud - Tvenv
def calcBuoy(height, thetae0, interpTenv, interpTdEnv, interpPress):
#input: height (m), thetae0 (K), plus function handles for
#T,Td, press soundings
#output: Bout = buoyant acceleration in m/s^2
#neglect liquid water loading in the virtual temperature
press=interpPress(height)*100.#%Pa
Tcloud=findTmoist(thetae0,press) #K
wvcloud=wsat(Tcloud,press); #kg/kg
Tvcloud=Tcloud*(1. + c.eps*wvcloud)
Tenv=interpTenv(height) + c.Tc
Tdenv=interpTdEnv(height) + c.Tc
wvenv=wsat(Tdenv,press); #kg/kg
Tvenv=Tenv*(1. + c.eps*wvenv)
TvDiff=Tvcloud - Tvenv
#print '%10.3f %10.3f %10.3f\n' %(press*0.01,height,TvDiff)
return c.g0*(TvDiff/Tvenv)
def F(t, y, entrain_rate, interpTenv, interpTdEnv, interpPress):
yp = np.zeros((4,1))
velocity = y[0]
height = y[1]
thetae_cloud = y[2]
wT_cloud = y[3]
#yp[0] is the acceleration, in this case the buoyancy
yp[0] = calcBuoy(height, thetae_cloud, interpTenv, interpTdEnv, interpPress)
press = interpPress(height)*100. #Pa
Tdenv = interpTdEnv(height) + c.Tc #K
Tenv = interpTenv(height) + c.Tc #K
wTenv = wsat(Tdenv, press) #kg/kg
thetaeEnv = thetaep(Tdenv, Tenv, press)
#yp[1] is the rate of change of height
yp[1] = velocity
#yp[2] is the rate of change of thetae_cloud
yp[2] = entrain_rate*(thetaeEnv - thetae_cloud)
#yp[3] is the rate of change of wT_cloud
yp[3] = entrain_rate*(wTenv - wT_cloud)
return yp
def answer_entrain():
filename = 'littlerock.nc'
print 'reading file: %s\n' %(filename)
nc_file = Dataset(filename)
var_names = nc_file.variables.keys()
print nc_file.ncattrs()
print nc_file.units
print nc_file.col_names
sound_var = nc_file.variables[var_names[3]]
press = sound_var[:,0]
height = sound_var[:,1]
temp = sound_var[:,2]
dewpoint = sound_var[:,3]
#height must have unique values
envHeight= nudge(height)
#Tenv and TdEnv interpolators return temp. in deg C, given height in m
#Press interpolator returns pressure in hPa given height in m
interpTenv = lambda zVals: np.interp(zVals, envHeight, temp)
interpTdEnv = lambda zVals: np.interp(zVals, envHeight, dewpoint)
interpPress = lambda zVals: np.interp(zVals, envHeight, press)
p900_level = np.where(abs(900 - press) < 2.)
p800_level = np.where(abs(800 - press) < 7.)
thetaeVal=thetaep(dewpoint[p900_level] + c.Tc,temp[p900_level] + c.Tc,press[p900_level]*100.)
height_800=height[p800_level]
wTcloud = wsat(dewpoint[p900_level] + c.Tc, press[p900_level]*100.)
entrain_rate = 2.e-4
winit = 0.5 #initial velocity (m/s)
yinit = [winit, height_800, thetaeVal, wTcloud]
tinit = 0
tfin = 2500
dt = 10
#want to integrate F using ode45 (from MATLAB) equivalent integrator
r = ode(F).set_integrator('dopri5')
r.set_f_params(entrain_rate, interpTenv, interpTdEnv, interpPress)
r.set_initial_value(yinit, tinit)
y = np.array(yinit)
t = np.array(tinit)
#stop tracking the parcel when the time runs out, or if the parcel stops moving/is desecnding
while r.successful() and r.t < tfin and r.y[0] > 0:
#find y at the next time step
#(r.integrate(t) updates the fields r.y and r.t so that r.y = F(t) and r.t = t
#where F is the function being integrated)
r.integrate(r.t+dt)
if r.y[0] <= 0:
break
#keep track of y at each time step
y = np.vstack((y, r.y))
t = np.vstack((t, r.t))
wvel = y[:,0]
cloud_height = y[:,1]
thetae_cloud = y[:,2]
wT_cloud = y[:,3]
plt.figure(1)
plt.plot(wvel, cloud_height)
plt.xlabel('vertical velocity (m/s)')
plt.ylabel('height above surface (m)')
plt.gca().set_title('vertical velocity of a cloud parcel vs height,\
entrainment rate of %4.1e $s^{-1}$' %entrain_rate)
Tcloud = np.zeros(cloud_height.size)
wvCloud = np.zeros(cloud_height.size)
wlCloud = np.zeros(cloud_height.size)
for i in range(0, len(cloud_height)):
the_press = interpPress(cloud_height[i])*100.
Tcloud[i], wvCloud[i], wlCloud[i] = tinvert_thetae(thetae_cloud[i],
wT_cloud[i], the_press)
Tadia= np.zeros(cloud_height.size)
wvAdia = np.zeros(cloud_height.size)
wlAdia = np.zeros(cloud_height.size)
for i in range(0, len(cloud_height)):
the_press = interpPress(cloud_height[i])*100.
Tadia[i], wvAdia[i], wlAdia[i] = tinvert_thetae(thetae_cloud[0],
wT_cloud[0], the_press)
plt.figure(2)
TcloudHandle, = plt.plot(Tcloud - c.Tc, cloud_height, 'r-')
TenvHandle, = plt.plot(temp, envHeight, 'g-')
TadiaHandle, = plt.plot(Tadia - c.Tc, cloud_height, 'b-')
plt.xlabel('temperature (deg C)')
plt.ylabel('height above surface (m)')
plt.gca().set_title('temp. of rising cloud parcel vs height,\
entrainment rate of %4.1e $s^{-1}$' %entrain_rate)
plt.gca().legend([TcloudHandle, TenvHandle, TadiaHandle],['cloud', 'environment', 'moist adiabat'])
plt.show()
def convecSkew(figNum):
"""
Usage: convecSkew(figNum)
Input: figNum = integer
Takes any integer, creates figure(figNum), and plots a
skewT logp thermodiagram.
Output: skew=30 and the handle for the plot
"""
fig=plt.figure(figNum)
fig.clf()
ax1=fig.add_subplot(111)
yplot = range(1000,190,-10)
xplot = range(-300,-139)
pvals = np.size(yplot)
tvals = np.size(xplot)
temp = np.zeros([pvals, tvals])
theTheta = np.zeros([pvals, tvals])
ws = np.zeros([pvals, tvals])
theThetae = np.zeros([pvals, tvals])
skew = 30 #skewness factor (deg C)
# lay down a reference grid that labels xplot,yplot points
# in the new (skewT-lnP) coordinate system .
# Each value of the temp matrix holds the actual (data)
# temperature label (in deg C) of the xplot, yplot coordinate.
# pairs. The transformation is given by W&H 3.56, p. 78. Note
# that there is a sign difference, because rather than
# taking y= -log(P) like W&H, I take y= +log(P) and
# then reverse the y axis
for i in yplot:
for j in xplot:
# Note that we don't have to transform the y
# coordinate, as it is still pressure.
iInd = yplot.index(i)
jInd = xplot.index(j)
temp[iInd, jInd] = convertSkewToTemp(j, i, skew)
Tk = c.Tc + temp[iInd, jInd]
pressPa = i * 100.
theTheta[iInd, jInd] = theta(Tk, pressPa)
ws[iInd, jInd] = wsat(Tk, pressPa)
theThetae[iInd, jInd] = thetaes(Tk, pressPa)
#
# Contour the temperature matrix.
#
# First, make sure that all plotted lines are solid.
mpl.rcParams['contour.negative_linestyle'] = 'solid'
tempLabels = range(-40, 50, 10)
tempLevs = ax1.contour(xplot, yplot, temp, tempLabels, \
colors='k')
#
# Customize the plot
#
ax1.set_yscale('log')
locs = np.array(range(100, 1100, 100))
labels = locs
ax1.set_yticks(locs)
ax1.set_yticklabels(labels) # Conventionally labels semilog graph.
ax1.set_ybound((200, 1000))
plt.setp(ax1.get_xticklabels(), weight='bold')
plt.setp(ax1.get_yticklabels(), weight='bold')
ax1.yaxis.grid(True)
thetaLabels = range(200, 390, 10)
thetaLevs = ax1.contour(xplot, yplot, theTheta, thetaLabels, \
colors='b')
wsLabels =[0.1,0.25,0.5,1,2,3] + range(4, 20, 2) + [20,24,28]
wsLevs = ax1.contour(xplot, yplot, (ws * 1.e3), wsLabels, \
colors='g')
thetaeLabels = np.arange(250, 410, 10)
thetaeLevs = ax1.contour(xplot, yplot, theThetae, thetaeLabels, \
colors='r')
# Transform the temperature,dewpoint from data coords to
# plotting coords.
ax1.set_title('skew T - lnp chart')
ax1.set_ylabel('pressure (hPa)')
ax1.set_xlabel('temperature (deg C)')
#
# Crop image to a more usable size
#
TempTickLabels = range(-15, 40, 5)
TempTickCoords = TempTickLabels
skewTickCoords = convertTempToSkew(TempTickCoords, 1.e3, skew)
ax1.set_xticks(skewTickCoords)
ax1.set_xticklabels(TempTickLabels)
skewLimits = convertTempToSkew([-15, 35], 1.e3, skew)
ax1.axis([skewLimits[0], skewLimits[1], 300, 1.e3])
#
# Create line labels
#
fntsz = 9 # Handle for 'fontsize' of the line label.
ovrlp = True # Handle for 'inline'. Any integer other than 0
# creates a white space around the label.
thetaeLevs.clabel(thetaeLabels, inline=ovrlp, fmt='%5d', fontsize=fntsz,use_clabeltext=True)
tempLevs.clabel(inline=ovrlp, fmt='%2d', fontsize=fntsz,use_clabeltext=True)
thetaLevs.clabel(inline=ovrlp, fmt='%5d', fontsize=fntsz,use_clabeltext=True)
wsLevs.clabel(inline=ovrlp, fmt='%2d', fontsize=fntsz,use_clabeltext=True)
#print thetaeLabels
#
# Flip the y axis
#
ax1.invert_yaxis()
ax1.figure.canvas.draw()
return skew, ax1
xplot2=convertTempToSkew(Tdew,press,skew)
TdHandle, = plt.plot(xplot2,press,'b--', linewidth=2.5)
plt.title('convectively unstable sounding: base at 900 hPa')
plt.show()
#print -dpdf initial_sound.pdf
#put on the top and bottom LCLs and the thetae sounding
Tlcl=np.zeros(numPoints)
pLCL=np.zeros(numPoints)
theTheta=np.zeros(numPoints)
theThetae=np.zeros(numPoints)
Tpseudo=np.zeros(numPoints)
wtotal=np.zeros(numPoints)
for i in range(0, numPoints):
wtotal[i]=wsat(Tdew[i] + c.Tc,press[i]*100.);
Tlcl[i],pLCL[i]=LCLfind(Tdew[i] + c.Tc,Temp[i]+c.Tc,press[i]*100.)
theThetae[i]=thetaep(Tdew[i] + c.Tc,Temp[i] + c.Tc,press[i]*100.)
#find the temperature along the pseudo adiabat at press[i]
Tpseudo[i]=findTmoist(theThetae[i],press[i]*100.)
#no liquid water in sounding
xplot=convertTempToSkew(Tlcl[0] - c.Tc,pLCL[0]*0.01,skew);
bot,=plt.plot(xplot,pLCL[0]*0.01,'ro',markersize=12, markerfacecolor ='r')
xplot=convertTempToSkew(Tlcl[-1] - c.Tc,pLCL[-1]*0.01,skew)
top,=plt.plot(xplot,pLCL[-1]*0.01,'bd',markersize=12,markerfacecolor='b')
#print -dpdf initial_lcls.pdf
xplot=convertTempToSkew(Tpseudo - c.Tc,press,skew)
thetaEhandle,=plt.plot(xplot,press,'c-', linewidth=2.5)
ax.legend([Thandle, TdHandle, bot, top, thetaEhandle], ['Temp (deg C)','Dewpoint (deg C)',
'LCL bot (835 hPa)','LCL top (768 hPa)','$\\theta_e$'])
plt.title('convectively unstable sounding: base at 900 hPa')
def convecSkew(figNum):
"""
Skew-T diagram for the level of free convection.
Take any integer, creates figure(figNum), and plots a
skewT logp thermodiagram.
"""
fig = plt.figure(figNum)
fig.clf()
ax1 = fig.add_subplot(111)
yplot = range(1000, 190, -10)
xplot = range(-300, -139)
pvals = np.size(yplot)
tvals = np.size(xplot)
temp = np.zeros([pvals, tvals])
theTheta = np.zeros([pvals, tvals])
ws = np.zeros([pvals, tvals])
theThetae = np.zeros([pvals, tvals])
skew = 30 #skewness factor (deg C)
"""
lay down a reference grid that labels xplot,yplot points
in the new (skewT-lnP) coordinate system .
Each value of the temp matrix holds the actual (data)
temperature label (in deg C) of the xplot, yplot coordinate.
pairs. The transformation is given by W&H 3.56, p. 78. Note
that there is a sign difference, because rather than
taking y= -log(P) like W&H, I take y= +log(P) and
then reverse the y axis
"""
for i in yplot:
for j in xplot:
# We don't have to transform the y
# coordinate, as it is still pressure.
iInd = yplot.index(i)
jInd = xplot.index(j)
temp[iInd, jInd] = convertSkewToTemp(j, i, skew)
Tk = c.Tc + temp[iInd, jInd]
pressPa = i * 100.
theTheta[iInd, jInd] = theta(Tk, pressPa)
ws[iInd, jInd] = wsat(Tk, pressPa)
theThetae[iInd, jInd] = thetaes(Tk, pressPa)
# Contour the temperature matrix.
# First, make sure that all plotted lines are solid.
mpl.rcParams["contour.negative_linestyle"] = "solid"
tempLabels = range(-40, 50, 10)
tempLevs = ax1.contour(xplot, yplot, temp, tempLabels, \
colors="k")
# Customize the plot
ax1.set_yscale("log")
locs = np.array(range(100, 1100, 100))
labels = locs
ax1.set_yticks(locs)
ax1.set_yticklabels(labels) # Conventionally labels semilog graph.
ax1.set_ybound((200, 1000))
plt.setp(ax1.get_xticklabels(), weight="bold")
plt.setp(ax1.get_yticklabels(), weight="bold")
ax1.yaxis.grid(True)
thetaLabels = range(200, 390, 10)
thetaLevs = ax1.contour(xplot, yplot, theTheta, thetaLabels, \
colors="b")
wsLabels = [0.1, 0.25, 0.5, 1, 2, 3] + range(4, 20, 2) + [20, 24, 28]
wsLevs = ax1.contour(xplot, yplot, (ws * 1.e3), wsLabels, \
colors="g")
thetaeLabels = np.arange(250, 410, 10)
thetaeLevs = ax1.contour(xplot, yplot, theThetae, thetaeLabels, \
colors="r")
# Transform the temperature,dewpoint from data coords to
# plotting coords.
ax1.set_title("skew T - lnp chart")
ax1.set_ylabel("pressure (hPa)")
ax1.set_xlabel("temperature (deg C)")
#
# Crop image to a more usable size
#
TempTickLabels = range(-15, 40, 5)
TempTickCoords = TempTickLabels
skewTickCoords = convertTempToSkew(TempTickCoords, 1.e3, skew)
ax1.set_xticks(skewTickCoords)
ax1.set_xticklabels(TempTickLabels)
skewLimits = convertTempToSkew([-15, 35], 1.e3, skew)
ax1.axis([skewLimits[0], skewLimits[1], 300, 1.e3])
#
# Create line labels
#
fntsz = 9 # Handle for fontsize of the line label.
ovrlp = True # Handle for inline. Any integer other than 0
# creates a white space around the label.
thetaeLevs.clabel(thetaeLabels,
inline=ovrlp,
fmt="%5d",
fontsize=fntsz,
use_clabeltext=True)
tempLevs.clabel(inline=ovrlp,
fmt="%2d",
fontsize=fntsz,
use_clabeltext=True)
thetaLevs.clabel(inline=ovrlp,
fmt="%5d",
fontsize=fntsz,
use_clabeltext=True)
wsLevs.clabel(inline=ovrlp, fmt="%2d", fontsize=fntsz, use_clabeltext=True)
#print thetaeLabels
#
# Flip the y axis
#
ax1.invert_yaxis()
ax1.figure.canvas.draw()
return skew, ax1
for i in range(0, len(pvec)):
Tvec_eq[i], wv[i], wl[i] = tinvert_thetae(thetae_eq, eqwv_bot, pvec[i])
xcoord_eq[i] = convertTempToSkew(Tvec_eq[i] - c.Tc, pvec[i]*0.01, skew)
Tvec_sf[i], wv[i], wl[i] = tinvert_thetae(thetae_sf, sfwv_bot, pvec[i])
xcoord_sf[i] = convertTempToSkew(Tvec_sf[i] - c.Tc, pvec[i]*0.01, skew)
tempA=Tvec_sf[len(Tvec_sf)-1]
pressA=pbot
tempB=Tvec_eq[len(Tvec_eq)-1]
pressB=pbot
tempC=Tvec_eq[0]
pressC=ptop
tempD=Tvec_sf[0]
pressD=ptop;
wvD=wsat(tempD,ptop)
wvC=wsat(tempC,ptop)
hot_adiabat=plt.plot(xcoord_eq,pvec*0.01,'r-',linewidth=3)
cold_adiabat=plt.plot(xcoord_sf,pvec*0.01,'b-', linewidth=3)
plt.axis([convertTempToSkew(-15.,1000.,skew),
convertTempToSkew(35.,1000.,skew), 1020, 350])
xtempA=convertTempToSkew(tempA - c.Tc,pressA*0.01,skew);
xtempB=convertTempToSkew(tempB - c.Tc,pressB*0.01,skew);
xtempC=convertTempToSkew(tempC - c.Tc,pressC*0.01,skew);
xtempD=convertTempToSkew(tempD - c.Tc,pressD*0.01,skew);
plt.text(xtempA,pressA*0.01,'A', fontweight='bold',fontsize= 22, color='b');
plt.text(xtempB,pressB*0.01,'B', fontweight='bold',fontsize= 22,color='b');
#equate kinetic and potential energy to get maximum
#updraft speed
plt.figure(5)
maxvel=np.sqrt(2*cumCAPE);
plt.plot(maxvel, presslevs[1:]*0.01,'k-');
plt.title('maximum updraft (m/s) vs. pressure (hPa)');
plt.gca().invert_yaxis()
plt.show()
#
# find storm indices
#
# lifted index
thetaeVal=thetaep(dewpoint[0] + c.Tc,temp[0] + c.Tc,press[0]*100.)
wT=wsat(dewpoint[0] + c.Tc,press[0]*100.)
Tadia_500,wv,wl=tinvert_thetae(thetaeVal,wT,500.e2)
Temp_500=interpTenv(500.) + c.Tc
lifted_index= Temp_500 - Tadia_500
# total totals = vertical totals plus cross totals
Temp_850=interpTenv(850.) + c.Tc
dew_850 = interpTdenv(850.) + c.Tc
TT_index=Temp_850 + dew_850 - 2*Temp_500
# Sholwater
thetaeVal=thetaep(dew_850,Temp_850,850.*100.)
wT=wsat(dew_850,850*100.)
Tadia_500,wv,wl=tinvert_thetae(thetaeVal,wT,500.e2)
sholwater=Temp_500 - Tadia_500
# SWEAT
speed_850=interpSpeed(850.)
speed_500=interpSpeed(500.)
for i in range(0, len(pvec)):
Tvec_eq[i], wv[i], wl[i] = tinvert_thetae(thetae_eq, eqwv_bot, pvec[i])
xcoord_eq[i] = convertTempToSkew(Tvec_eq[i] - c.Tc, pvec[i]*0.01, skew)
Tvec_sf[i], wv[i], wl[i] = tinvert_thetae(thetae_sf, sfwv_bot, pvec[i])
xcoord_sf[i] = convertTempToSkew(Tvec_sf[i] - c.Tc, pvec[i]*0.01, skew)
tempA = Tvec_sf[len(Tvec_sf)-1]
pressA = pbot
tempB = Tvec_eq[len(Tvec_eq)-1]
pressB = pbot
tempC = Tvec_eq[0]
pressC = ptop
tempD = Tvec_sf[0]
pressD = ptop
wvD = wsat(tempD, ptop)
wvC = wsat(tempC, ptop)
hot_adiabat = plt.plot(xcoord_eq,pvec*0.01, "r-", linewidth=3)
cold_adiabat = plt.plot(xcoord_sf,pvec*0.01, "b-", linewidth=3)
plt.axis([convertTempToSkew(-15.,1000.,skew), convertTempToSkew(35.,1000.,skew), 1020, 350])
# transform along the coordinates
xtempA = convertTempToSkew(tempA - c.Tc,pressA*0.01, skew)
xtempB = convertTempToSkew(tempB - c.Tc,pressB*0.01, skew)
xtempC = convertTempToSkew(tempC - c.Tc,pressC*0.01, skew)
xtempD = convertTempToSkew(tempD - c.Tc,pressD*0.01, skew)
# plot
plt.text(xtempA,pressA*0.01, "A", fontweight="bold", fontsize= 22, color="b")
# during this rise?
import site
site.addsitedir('C:\Users\Den\mya405\python\\thermlib')
from constants import constants as c
from new_thermo import wsat, thetaep, tinvert_thetae
from findLCL0 import findLCL0
from findTmoist import findTmoist
press0=1.e5
Temp0=15 + c.Tc
Td0=2 + c.Tc
#
#step 1: find the lcl
#
wv0=wsat(Td0,press0)
plcl, Tlcl =findLCL0(wv0,press0,Temp0)
print 'found Plcl=%8.2f (hPa) and Tlcl=%8.2f (deg C)\n' %(plcl*1.e-2, Tlcl - c.Tc)
the_thetae=thetaep(Tlcl,Tlcl,plcl)
# step 2 raise air 200 hPa above plcl along pseudo adiabat,
# find wsat at that temperature, compare to wv0 to find the amount
# of liquid water condensed
pnew = plcl - 200.e2
newTemp, newWv, newWl = tinvert_thetae(the_thetae, wv0, pnew)
#check: