def find_corners(temps, press=1.e3, skew=30.):
"""
convert a pair of temperatures into skew plotting coordinates at a constant pressure level
Parameters
----------
temps : [float]
xaxis corner temperatures (degC)
press : float
pressure level for skew conversion
skew : float
coefficient to use in the tempToSkew conversion
Returns
-------
corners : [float]
x axis corners in plotting coordinates
"""
corners = convertTempToSkew(temps, press, skew)
return list(corners)
def find_corners(temps, press=1.e3, skew=30.):
"""
convert a pair of temperatures into skew plotting coordinates at a constant pressure level
Parameters
----------
temps : [float]
xaxis corner temperatures (degC)
press : float
pressure level for skew conversion
skew : float
coefficient to use in the tempToSkew conversion
Returns
-------
corners : [float]
x axis corners in plotting coordinates
"""
corners = convertTempToSkew(temps, press, skew)
return list(corners)
def makePlot(ax,Temp=None,Tdew=None,Tpseudo=None,press=None,Tlcl=None,pLCL=None,botLabel='LCL bot (835 hPa)',topLabel='LCL top (768 hPa)'):
"""
Draw a tephigram of a convectively unstable layer with Temp, Tdew, Tpseudo soundings, as well as the LCL of the top and the bottom of
the layer
"""
xplot = convertTempToSkew(Tlcl[0] - c.Tc, pLCL[0] * pa2hPa, skew)
bot, = ax.plot(xplot, pLCL[0] * pa2hPa, 'ro', markersize=12, markerfacecolor='r',label=botLabel)
xplot = convertTempToSkew(Tlcl[-1] - c.Tc, pLCL[-1] * pa2hPa, skew)
top, = ax.plot(xplot, pLCL[-1] * pa2hPa,'bd', markersize=12,
markerfacecolor='b',label = topLabel)
xplot = convertTempToSkew(Tpseudo - c.Tc, press, skew)
thetaEhandle, = ax.plot(xplot, press, 'c-', linewidth=2.5,label=r'$\theta_e$')
xplot1 = convertTempToSkew(Temp - c.Tc, press, skew)
Thandle, = ax.plot(xplot1, press, 'k-', linewidth=2.5,label='Temp (deg C)')
xplot2 = convertTempToSkew(Tdew - c.Tc, press, skew)
TdHandle, = ax.plot(xplot2, press, 'b--', linewidth=2.5,label='Dewpoint (deg C)')
ax.legend(loc='best',numpoints=1)
base=press[0]
title_string = 'convectively unstable sounding: base at {} hPa'.format(base)
ax.set_title(title_string)
return ax
title='{} at {}'.format(location,times[0][2:])
print('title: :',title)
units=attributes['units'].split(';')
units_dict={}
for count,var in enumerate(sounding.columns):
units_dict[var]=units[count]
# In[7]:
skew=30.
triplets=zip(sounding['temp'],sounding['dwpt'],sounding['pres'])
xcoord_T=[]
xcoord_Td=[]
for a_temp,a_dew,a_pres in triplets:
xcoord_T.append(convertTempToSkew(a_temp,a_pres,skew))
xcoord_Td.append(convertTempToSkew(a_dew,a_pres,skew))
# In[8]:
get_ipython().magic('matplotlib inline')
skew=30
plt.close('all')
fig,ax =plt.subplots(1,1,figsize=(8,8))
corners=[-15,35]
ax,skew = makeSkewWet(ax,corners=corners,skew=skew)
ax.plot(xcoord_T,sounding['pres'],color='k',label='temp')
ax.plot(xcoord_Td,sounding['pres'],color='g',label='dew')
[line.set(linewidth=3) for line in ax.lines[-2:]]
out=ax.set(title=title)
def makeSkewDry(ax, skew=30):
"""
draw a skew-T lnP diagram on an axis
Parameters
----------
ax : matplotlib.axes
matplotlib figure axis
skew : float
adjustable coefficient to make isotherms slope
compared to adiabats
Returns
-------
ax : matplotlib.axes
the modified figure axis
skew : float
skew coefficient (K)
"""
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])
# 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] = find_theta(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 = ax.contour(xplot, yplot, temp, tempLabels, \
colors='k')
#
# Customize the plot
#
ax.set_yscale('log')
locs = np.array(range(100, 1100, 100))
labels = locs
ax.set_yticks(locs)
ax.set_yticklabels(labels) # Conventionally labels semilog graph.
ax.set_ybound((200, 1000))
plt.setp(ax.get_xticklabels(), weight='bold')
plt.setp(ax.get_yticklabels(), weight='bold')
ax.yaxis.grid(True)
thetaLabels = list(range(200, 390, 10))
thetaLevs = ax.contour(xplot, yplot, theTheta, thetaLabels, \
colors='b')
# Transform the temperature,dewpoint from data coords to
# plotting coords.
ax.set_title('skew T - lnp chart')
ax.set_ylabel('pressure (hPa)')
ax.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)
ax.set_xticks(skewTickCoords)
ax.set_xticklabels(TempTickLabels)
skewLimits = convertTempToSkew([-15, 35], 1.e3, skew)
ax.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.
tempLevs.clabel(inline=ovrlp,
inline_spacing=0,
fmt='%2d',
fontsize=fntsz,
use_clabeltext=True)
thetaLevs.clabel(inline=ovrlp,
inline_spacing=0,
fmt='%5d',
fontsize=fntsz,
use_clabeltext=True)
ax.invert_yaxis()
ax.figure.canvas.draw()
return ax, skew
def makeSkewWet(ax, corners=[-30, 25], skew=30):
"""
draw a skew-T lnP diagram on an axis
Parameters
----------
ax : matplotlib.axes
matplotlib figure axis
corners : [float]
x axis temperature limits (degC)
skew : float
adjustable coefficient to make isotherms slope
compared to adiabats
Returns
-------
ax : matplotlib.axes
the modified figure axis
"""
yplot = range(1000, 190, -6) #
xcorners = find_corners(corners, skew=skew)
xplot = list(np.linspace(xcorners[0], xcorners[1], 45))
pvals = np.size(yplot)
tvals = np.size(xplot)
temp = np.zeros([pvals, tvals])
theTheta = np.zeros_like(temp)
the_rsat = np.zeros_like(temp)
theThetae = np.zeros([pvals, tvals])
# 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 presshPa in yplot: #loop over pressures
for skewed in xplot: #loop over skewed xcoords
# Note that we don't have to transform the y
# coordinate, as it is still pressure.
iInd = yplot.index(presshPa)
jInd = xplot.index(skewed)
temp[iInd, jInd] = convertSkewToTemp(skewed, presshPa, skew)
Tk = c.Tc + temp[iInd, jInd]
pressPa = presshPa * 100.
theTheta[iInd, jInd] = find_theta(Tk, pressPa)
rs = find_rsat(Tk, pressPa)
the_rsat[iInd, jInd] = rs
theThetae[iInd, jInd] = find_thetaet(Tk,rs,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, 5)
ax.contour(xplot, yplot, temp, tempLabels, \
colors='k')
#
# contour theta
#
thetaLabels = list(range(200, 390, 10))
thetaLevs = ax.contour(xplot, yplot, theTheta, thetaLabels, \
colors='b')
#
# contour rsat
#
rsLabels = [0.1, 0.25, 0.5, 1, 2, 3] + list(range(4, 28, 2)) #+ [26, 28]
rsLevs = ax.contour(xplot,
yplot,
the_rsat * 1.e3,
levels=rsLabels,
colors='g',
linewidths=.5)
thetaeLabels = np.arange(250, 410, 10)
thetaeLevs = ax.contour(xplot, yplot, theThetae, thetaeLabels, \
colors='r')
#
# Customize the plot
#
ax.set_yscale('log')
locs = np.array(range(100, 1100, 100))
labels = locs
ax.set_yticks(locs)
ax.set_yticklabels(labels) # Conventionally labels semilog graph.
ax.set_ybound((200, 1000))
plt.setp(ax.get_xticklabels(), weight='bold')
plt.setp(ax.get_yticklabels(), weight='bold')
ax.yaxis.grid(True)
ax.set_title('skew T - lnp chart')
ax.set_ylabel('pressure (hPa)')
ax.set_xlabel('temperature (deg C)')
#
# Crop image to a more usable size
#
TempTickLabels = range(-30, 40, 5)
TempTickCoords = TempTickLabels
skewTickCoords = convertTempToSkew(TempTickCoords, 1.e3, skew)
ax.set_xticks(skewTickCoords)
ax.set_xticklabels(TempTickLabels)
skewLimits = convertTempToSkew([-15, 35], 1.e3, skew)
ax.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.
#tempLevs.clabel(inline=ovrlp, inline_spacing=0,fmt='%2d', fontsize=fntsz,use_clabeltext=True)
thetaLevs.clabel(inline=ovrlp,
inline_spacing=0,
fmt='%3d',
fontsize=fntsz,
use_clabeltext=True)
rsLevs.clabel(inline=ovrlp,
inline_spacing=0,
fmt='%3.2g',
fontsize=fntsz,
use_clabeltext=True)
thetaeLevs.clabel(thetaeLabels,
inline_spacing=0,
inline=ovrlp,
fmt='%5g',
fontsize=fntsz,
use_clabeltext=True)
ax.invert_yaxis()
#ax.figure.canvas.draw()
xcorners = find_corners(corners, skew=skew)
ax.set(ylim=(1000, 300), xlim=xcorners)
return ax, skew
def makeSkewWet(ax, corners=[-30, 25], skew=30):
"""
draw a skew-T lnP diagram on an axis
Parameters
----------
ax : matplotlib.axes
matplotlib figure axis
corners : [float]
x axis temperature limits (degC)
skew : float
adjustable coefficient to make isotherms slope
compared to adiabats
Returns
-------
ax : matplotlib.axes
the modified figure axis
"""
yplot = range(1000, 190, -6) #
xcorners = find_corners(corners, skew=skew)
xplot = list(np.linspace(xcorners[0], xcorners[1], 45))
pvals = np.size(yplot)
tvals = np.size(xplot)
temp = np.zeros([pvals, tvals])
theTheta = np.zeros_like(temp)
the_rsat = np.zeros_like(temp)
theThetae = np.zeros([pvals, tvals])
# 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 presshPa in yplot: #loop over pressures
for skewed in xplot: #loop over skewed xcoords
# Note that we don't have to transform the y
# coordinate, as it is still pressure.
iInd = yplot.index(presshPa)
jInd = xplot.index(skewed)
temp[iInd, jInd] = convertSkewToTemp(skewed, presshPa, skew)
Tk = c.Tc + temp[iInd, jInd]
pressPa = presshPa * 100.
theTheta[iInd, jInd] = find_theta(Tk, pressPa)
rs = find_rsat(Tk, pressPa)
the_rsat[iInd, jInd] = rs
theThetae[iInd, jInd] = find_thetaet(Tk, rs, 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)
ax.contour(xplot, yplot, temp, tempLabels, \
colors='k')
#
# contour theta
#
thetaLabels = list(range(200, 390, 10))
thetaLevs = ax.contour(xplot, yplot, theTheta, thetaLabels, \
colors='b')
#
# contour rsat
#
rsLabels = [0.1, 0.25, 0.5, 1, 2, 3] + list(range(4, 28, 2)) #+ [26, 28]
rsLevs = ax.contour(xplot,
yplot,
the_rsat * 1.e3,
levels=rsLabels,
colors='g',
linewidths=.5)
thetaeLabels = np.arange(250, 410, 10)
thetaeLevs = ax.contour(xplot, yplot, theThetae, thetaeLabels, \
colors='r')
#
# Customize the plot
#
ax.set_yscale('log')
locs = np.array(range(100, 1100, 100))
labels = locs
ax.set_yticks(locs)
ax.set_yticklabels(labels) # Conventionally labels semilog graph.
ax.set_ybound((200, 1000))
plt.setp(ax.get_xticklabels(), weight='bold')
plt.setp(ax.get_yticklabels(), weight='bold')
ax.yaxis.grid(True)
ax.set_title('skew T - lnp chart')
ax.set_ylabel('pressure (hPa)')
ax.set_xlabel('temperature (deg C)')
#
# Crop image to a more usable size
#
TempTickLabels = range(-30, 40, 5)
TempTickCoords = TempTickLabels
skewTickCoords = convertTempToSkew(TempTickCoords, 1.e3, skew)
ax.set_xticks(skewTickCoords)
ax.set_xticklabels(TempTickLabels)
skewLimits = convertTempToSkew([-15, 35], 1.e3, skew)
ax.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.
#tempLevs.clabel(inline=ovrlp, inline_spacing=0,fmt='%2d', fontsize=fntsz,use_clabeltext=True)
thetaLevs.clabel(inline=ovrlp,
inline_spacing=0,
fmt='%3d',
fontsize=fntsz,
use_clabeltext=True)
rsLevs.clabel(inline=ovrlp,
inline_spacing=0,
fmt='%3.2g',
fontsize=fntsz,
use_clabeltext=True)
thetaeLevs.clabel(thetaeLabels,
inline_spacing=0,
inline=ovrlp,
fmt='%5g',
fontsize=fntsz,
use_clabeltext=True)
ax.invert_yaxis()
#ax.figure.canvas.draw()
xcorners = find_corners(corners, skew=skew)
ax.set(ylim=(1000, 300), xlim=xcorners)
return ax, skew
press = np.arange(Pbot, Ptop - 10, -10)
Temp = (Tbot + slope * (press - Pbot))
slope = (Tdewtop - Tdewbot) / (Ptop - Pbot)
Tdew = (Tdewbot + slope * (press - Pbot))
#
#figure 1: plot the T,Tdew profile only
#
plt.close('all')
fig, ax = plt.subplots(1, 1, figsize=(10, 10))
ax, skew = makeSkewWet(ax,corners=[5,25])
#zoom the axis to focus on layer
skewLimits = convertTempToSkew([5, 25], 1.e3, skew)
ax.axis([skewLimits[0], skewLimits[1], 1000, 600])
xplot1 = convertTempToSkew(Temp, press, skew)
#plot() returns a list of handles for each line plotted
Thandle, = ax.plot(xplot1, press, 'k-', linewidth=2.5,label='Temp (deg C)')
xplot2 = convertTempToSkew(Tdew, press, skew)
TdHandle, = ax.plot(xplot2, press, 'b--', linewidth=2.5,label='Dewpoint (deg C)')
ax.set_title('convectively unstable sounding: base at 900 hPa')
ax.legend(numpoints=1,loc='best')
fig.savefig('initial_sound.png')
fig.savefig('initial_sound.pdf')
#
# figure 2, add thetae sounding and LCL for layer top and bottom
#
tempB=tempA
term1=(thetaB/tempB)**(c.cpd/c.Rd)
term1=1./term1
pressB=term1*1.e5
tempD=tempC
thetaD=thetaA
term1=(thetaD/tempD)**(c.cpd/c.Rd)
term1=1./term1
pressD=term1*1.e5
plt.close('all')
fig,ax = plt.subplots(1,1)
corners = [5,30]
ax, skew = makeSkewWet(ax,corners=corners)
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)
ax.text(xtempA,pressA*0.01,'A', fontweight='bold',fontsize= 22, color='b')
ax.text(xtempB,pressB*0.01,'B', fontweight='bold',fontsize= 22,color='b')
ax.text(xtempC,pressC*0.01,'C', fontweight='bold',fontsize= 22,color='b')
ax.text(xtempD,pressD*0.01,'D', fontweight='bold',fontsize= 22, color='b')
xmin = convertTempToSkew(corners[0],pressA*0.01,skew)
xmax = convertTempToSkew(corners[1],pressA*0.01,skew)
ax.axis([xmin, xmax, 1000, 600])
ax.set_title('forward carnot cycle')
plt.show()
fields=['id','temp','rv','rl','press']
A_dict = dict(zip(fields,('A',A_temp,A_rv,A_rl,A_press)))
A_tup = calc_enthalpy(A_dict)
print(format_tup(A_tup))
# ### B. Lift to 400 hPa and remove 80% of the liquied water
# In[201]:
plt.close('all')
fig,ax = plt.subplots(1,1,figsize=[10,8])
ax,skew = makeSkewWet(ax,corners=[-15,35])
lcl_temp, lcl_press = find_lcl(A_Td,A_tup.temp,A_tup.press)
xplot=convertTempToSkew(A_tup.temp - c.Tc,A_tup.press*pa2hPa,skew)
bot=ax.plot(xplot, A_tup.press*pa2hPa-10., 'ko', markersize=14, markerfacecolor='k')
ax.text(xplot,A_tup.press*pa2hPa-20.,'A',fontsize=30)
pressrange=np.arange(1000,395.,-10.)
trop_adiabat=[]
for press in pressrange:
temp,rv,rl = tinvert_thetae(A_thetae,A_tup.rt,press*1.e2)
xtemp = convertTempToSkew(temp - c.Tc,press,skew)
trop_adiabat.append(xtemp)
ax.plot(trop_adiabat,pressrange,'r-',lw=10)
B_press=400.e2 #Pa
temp,rv,rl = tinvert_thetae(thetae_trop,A_tup.rt,B_press)
rl = 0.2*rl #rain out 80% of liquid
B_dict = dict(zip(fields,('B',temp,rv,rl,B_press)))
ax.text(trop_adiabat[-1],B_press*pa2hPa,'B',fontsize=30)
B_tup = calc_enthalpy(B_dict)
Temp_860=find_Tmoist(thetae_900,press)
rv_860=find_rsat(Temp_860,press)
rv_900 = rv_860 #vapor is conserved
Tdew_860=Temp_860
print("temp,Tdew,rv at LCL press: {} hPa {} C {} C {} kg/kg" .format(n(press*1.e-2),e(k2c(Temp_860)),e(k2c(Tdew_860)),e(rv_900)))
#
# now descend adiabatically to 900 hPa
#
press=900.e2
Temp_900,rv_900,rl_900=tinvert_thetae(thetae_900,rv_900,press)
Tdew_900=find_Td(rv_900,press)
print("temperature and dewpoint at {} hPa hPa = {} C {} C".format(n(press*1.e-2),e(k2c(Temp_900)), e(k2c(Tdew_900))))
#
# draw these on the sounding at 900 hPa as a red circle and blue diamond
#
xplot=convertTempToSkew(Temp_900 - c.Tc,press*pa2hPa,skew)
bot=ax.plot(xplot, press*pa2hPa, 'ro', markersize=14, markerfacecolor='r')
xplot=convertTempToSkew(Tdew_900 - c.Tc,press*pa2hPa,skew)
bot=ax.plot(xplot, press*pa2hPa, 'bd', markersize=14, markerfacecolor='b')
#
#now look at an LCL of 700 hPa -- with thetae = 332 K
#
press=700.e2
thetae_800=332. #K
Temp_700=find_Tmoist(thetae_800,press)
Tdew_700 = Temp_700
rv_700=find_rsat(Temp_700,press)
print("temp,Tdew, rv at LCL press: {} hPa: {} C {} C {} kg/kg" .format(n(press*1.e-2),e(k2c(Temp_700)),e(k2c(Tdew_700)),e(rv_700)))
# get the temperature and dewpoint at 800 hPa
#
