def findLCL0(wv, press0, temp0):
"""
findLCL0(wv, press0, temp0)
Finds the temperature and pressure at the lifting condensation
level (LCL) of an air parcel (using a rootfinder).
Parameters
- - - - - -
wv : float
Mixing ratio (K).
temp0 : float
Temperature (K).
press0: float
pressure (Pa)
Returns
- - - - -
plcl : float
Pressure at the LCL (Pa).
Tlcl : float
Temperature at the LCL (K).
Raises
- - - -
NameError
If the air is saturated at a given wv, temp0 and press0 (i.e. Tdew(wv, press0) >= temp0)
Tests
- - - - -
>>> Td = Tdfind(5., 9.e4)
>>> Td > 280.
True
>>> findLCL0(5., 9.e4, 280.)
Traceback (most recent call last):
...
NameError: parcel is saturated at this pressure
>>> p1, T1 = findLCL0(0.001, 9.e4, 280.)
>>> print T1, p1
250.226034799 60692.0428535
"""
Td = Tdfind(wv, press0)
if (Td >= temp0):
raise NameError('parcel is saturated at this pressure')
theta0 = theta(temp0, press0, wv)
#evalzero = lambda pguess: lclzero(pguess, wv, theta0)
#will return plcl, Tlcl when Tchange returns approx. 0
#(i.e. when the parcel temperature = Td)
plcl = fzero(Tchange, [1000*100, 200*100], (wv, theta0))
Tlcl = invtheta(theta0, plcl, wv)
return plcl, Tlcl
def findLCL0(wv, press0, temp0):
"""
findLCL0(wv, press0, temp0)
Finds the temperature and pressure at the lifting condensation
level (LCL) of an air parcel (using a rootfinder).
Parameters
- - - - - -
wv : float
Mixing ratio (K).
temp0 : float
Temperature (K).
press0: float
pressure (Pa)
Returns
- - - - -
plcl : float
Pressure at the LCL (Pa).
Tlcl : float
Temperature at the LCL (K).
Raises
- - - -
NameError
If the air is saturated at a given wv, temp0 and press0 (i.e. Tdew(wv, press0) >= temp0)
Tests
- - - - -
>>> Td = Tdfind(5., 9.e4)
>>> Td > 280.
True
>>> findLCL0(5., 9.e4, 280.)
Traceback (most recent call last):
...
NameError: parcel is saturated at this pressure
>>> p1, T1 = findLCL0(0.001, 9.e4, 280.)
>>> print T1, p1
250.226034799 60692.0428535
"""
Td = Tdfind(wv, press0)
if (Td >= temp0):
#raise NameError('parcel is saturated at this pressure')
return press0, temp0
theta0 = theta(temp0, press0, wv)
#evalzero = lambda pguess: lclzero(pguess, wv, theta0)
#will return plcl, Tlcl when Tchange returns approx. 0
#(i.e. when the parcel temperature = Td)
plcl = fzero(Tchange, [1000 * 100, 200 * 100], (wv, theta0))
Tlcl = invtheta(theta0, plcl, wv)
return plcl, Tlcl
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
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
""" Carnot heat engine: 0. Isothermal expansion from A to B 1. Dry adiabatic expansion from B to C 2. Isothermal compression from C to D (heat flow, Qout, out of the system) 3. Dry adiabatic compression from D to C note that Qin > Qout so that work done by the system in the carnot cycle = Qin - Qout > 0 """ pressA = 1.e5 tempA = 15 + c.Tc pressC = 0.7e5 tempC = 5 + c.Tc thetaA = theta(tempA, pressA) thetaC = theta(tempC, pressC) thetaB = thetaC 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.figure(1) skew, ax1 = convecSkew(1) xtempA = convertTempToSkew(tempA - c.Tc, pressA * 0.01, skew)
c=constants() #Carnot heat engine: # #dry adiabatic expansion from B to C #isothermal compression from C to D (heat flow, Qout, out of the system) #dry adiabatic compression from D to C #note that Qin > Qout so that work done by the system in the carnot cycle = Qin - Qout > 0 pressA=1.e5 tempA=15 + c.Tc pressC=0.7e5 tempC=5 + c.Tc; thetaA=theta(tempA,pressA) thetaC=theta(tempC,pressC) thetaB=thetaC 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.figure(1) skew, ax1 =convecSkew(1) xtempA=convertTempToSkew(tempA - c.Tc,pressA*0.01,skew)