def calcBuoy(height, thetae0, interpTenv, interpTdEnv, interpPress):
"""function to calculate buoyant acceleration for an ascending saturated parcel
this version neglects liquid water loading
Parameters
----------
height: float
parcel height (m)
thetae0: float
parcel thetae (K)
interpTenv: func
interp1d function for environmental temperature T(z)
interpTdEnv: func
interp1d function for environmental dewpoint temperature Td(z)
interpPress: func
interp1d function for presusure p(z)
Returns
-------
buoy: float
buoyancy (m/s/s)
"""
#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=find_Tmoist(thetae0,press) #K
rvcloud=find_rsat(Tcloud,press); #kg/kg
Tvcloud=Tcloud*(1. + c.eps*rvcloud)
Tenv=interpTenv(height) + c.Tc
Tdenv=interpTdEnv(height) + c.Tc
rvenv=find_rsat(Tdenv,press); #kg/kg
Tvenv=Tenv*(1. + c.eps*rvenv)
TvDiff=Tvcloud - Tvenv
buoy = c.g0*(TvDiff/Tvenv)
return buoy
def rv_diff(press,thetae_mix,rT_mix):
"""
the lcl is is the pressure where rv=rT_mix
we want a difference that changes sign at cloud base
so below cloud set rv = rsat(temp,press) and
rT_mix - rv will be negative below cloud base and
positive above cloud base
"""
Temp, rv, rl = tinvert_thetae(thetae_mix,rT_mix,press)
#
# below cloud rl ~ 0, so switch to rv=rsat
#
if rl < 1.e-5:
rv=find_rsat(Temp,press)
diff = rT_mix - rv
return diff
def derivs(t, y, entrain_rate, interpTenv, interpTdEnv, interpPress):
"""Function that computes derivative vector for ode integrator
see http://clouds.eos.ubc.ca/~phil/courses/atsc405/docs/entrain.pdf for equations
Parameters
----------
t: float
time (s)
y: vector
4-vector containing wvel (m/s), height (m), thetae (K), rT (kg/kg)
entrain_rate: float
1/m dm/dt (s-1)
interpTenv: func
interp1d function for environmental temperature T(z)
interpTdEnv: func
interp1d function for environmental dewpoint temperature Td(z)
interpPress: func
interp1d function for presusure p(z)
Returns
-------
yp: vector
4-vector containing time derivatives of wvel (m/s^2), height (m/s), thetae (K/s), rT (kg/kg/s)
"""
yp = np.zeros((4,1))
velocity = y[0]
height = y[1]
thetae_cloud = y[2]
rT_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
rTenv = find_rsat(Tdenv, press) #kg/kg
thetaeEnv = find_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 rT_cloud
yp[3] = entrain_rate*(rTenv - rT_cloud)
return yp
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) # In[9]: from a405thermo.thermlib import find_Tmoist,find_thetaep,find_rsat,find_Tv # # find thetae of the surface air # sfc_press,sfc_temp,sfc_td =[sounding[key][0] for key in ['pres','temp','dwpt']] sfc_press,sfc_temp,sfc_td = sfc_press*100.,sfc_temp+c.Tc,sfc_td+c.Tc sfc_rvap = find_rsat(sfc_temp,sfc_press) sfc_thetae=find_thetaep(sfc_td,sfc_temp,sfc_press) press=sounding['pres'].values*100. # # find the index for 200 hPa pressure -- searchsorted requires # the pressure array to be increasing, so flip it for the search, # then flip the index. Above 200 hPa thetae goes bananas, so # so trim so we only have # toplim=len(press) - np.searchsorted(press[::-1],2.e4) press=press[:toplim] # # find temps along that adiabat # adia_temps= np.array([find_Tmoist(sfc_thetae,the_press) for the_press in press]) adia_rvaps = find_rsat(adia_temps,press)
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
#put on the top and bottom LCLs and the thetae sounding
Tlcl = np.zeros_like(press)
pLCL = np.zeros_like(press)
theTheta = np.zeros_like(press)
theThetae = np.zeros_like(press)
Tpseudo = np.zeros_like(press)
rTotal = np.zeros_like(press)
#
# calculate the rTotal,thetae sounding from the original dewpoint and temperture
#
numPoints, = press.shape
for i in range(0, numPoints):
rTotal[i] = find_rsat(Tdew[i] + c.Tc, press[i] * hPa2pa)
Tlcl[i], pLCL[i] = find_lcl(Tdew[i] + c.Tc, Temp[i] + c.Tc,
press[i] * hPa2pa)
theThetae[i] = find_thetaep(Tdew[i] + c.Tc, Temp[i] + c.Tc,
press[i] * hPa2pa)
#find the temperature along the pseudo adiabat at press[i]
Tpseudo[i] = find_Tmoist(theThetae[i], press[i] * hPa2pa)
#
# given the total water and thetae, calcultate temp,dewpoint for pressure vector press
#
Tdew, Temp, Tpseudo = lift_sounding(rTotal,theThetae,press)
fig, ax = plt.subplots(1, 1, figsize=(10, 10))
ax, skew = makeSkewWet(ax,corners=[5,25])
def integ_entrain(df_sounding,entrain_rate):
"""integrate an ascending parcel given a constant entrainment rate
this version hardwired to start parcel at 800 hPa with cloud base
values of environment at 900 hPa
Parameters
----------
df_sounding: pandas dataframe
: cloumns are temperature, dewpoint, height, press
entrain_rate: float
1/m dm/dt (s-1)
Returns
-------
df_out: dataframe
dataframe containing wvel (m/s) ,cloud_height (m) , thetae (K), rT (kg/kg) for assending parcel
interpPress: func
interp1d function for presusure p(z) (used for plotting)
"""
press = df_sounding['pres'].values
height = df_sounding['hght'].values
temp = df_sounding['temp'].values
dewpoint = df_sounding['dwpt'].values
envHeight= nudge(height)
interpTenv = interp1d(envHeight,temp)
interpTdEnv = interp1d(envHeight,dewpoint)
interpPress = interp1d(envHeight,press)
#
# call this cloudbase
#
p900_level = len(press) - np.searchsorted(press[::-1],900.)
thetaeVal=find_thetaep(dewpoint[p900_level] + c.Tc,temp[p900_level] + c.Tc,press[p900_level]*100.)
rTcloud = find_rsat(dewpoint[p900_level] + c.Tc, press[p900_level]*100.)
#
# start parcel here
#
p800_level = len(press) - np.searchsorted(press[::-1],800.)
height_800=height[p800_level]
winit = 0.5 #initial velocity (m/s)
yinit = [winit, height_800, thetaeVal, rTcloud]
tinit = 0 #seconds
tfin = 2500 #seconds
dt = 10 #seconds
#want to integrate derivs using dopr15 runge kutta described at
# http://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.ode.html
#
r = ode(derivs).set_integrator('dopri5')
r.set_f_params(entrain_rate, interpTenv, interpTdEnv, interpPress)
r.set_initial_value(yinit, tinit)
#the while loop below integrates every dt seconds
#we stop tracking the parcel when the time runs out, or if the parcel stops moving/is desecnding
#
var_out = []
time_out =[]
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 = integral of derivs(t) and r.t = time
#where derivs is a vector with the variables to be integrated
#
# move ahead by dt
#
r.integrate(r.t+dt)
#
# stop if there is negative vertical velocity
#
if r.y[0] <= 0:
break
#
#save values for dataframe
#
var_out.append(r.y)
time_out.append(r.t)
#
# convert the output into a datafram
#
colnames=['wvel','cloud_height','thetae_cloud','rT_cloud']
df_out=pd.DataFrame.from_records(var_out,columns=colnames)
df_out['time'] = time_out
return df_out,interpPress
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)
print(format_tup(B_tup))
# In[202]:
top_temp,top_rv,top_rl = tinvert_thetae(A_thetae,B_tup.rt,B_tup.press)
C_temp = top_temp - 20.
C_rt = B_tup.rt #conserve total water from B to C
C_rv = find_rsat(C_temp,B_tup.press)
C_rl = C_rt - C_rv #cool and condense more liquid with constant rt
C_dict = dict(zip(fields,('C',C_temp,C_rv,C_rl,B_tup.press)))
C_tup = calc_enthalpy(C_dict)
C_thetae = find_thetaet(C_tup.temp,C_tup.rt,C_tup.temp,B_tup.press)
xplot=convertTempToSkew(C_tup.temp - c.Tc,C_tup.press*pa2hPa,skew)
top=ax.plot(xplot, C_tup.press*pa2hPa, 'ko', markersize=14, markerfacecolor='g')
ax.text(xplot*0.99, C_tup.press*pa2hPa,'C',fontsize=30)
print(format_tup(C_tup))
display(fig)
# ### D. descend adiabatically to surface
# In[203]:
from importlib import reload
import a405skewT.makeSkewII
reload(a405skewT.makeSkewII)
from a405skewT.makeSkewII import makeSkewWet
fig, ax = plt.subplots(1, 1, figsize=(12, 8))
ax, skew = makeSkewWet(ax,corners=[10,30])
ax.set(ylim=[1000,700])
from a405thermo.thermlib import find_Tmoist,find_rsat,find_Td,tinvert_thetae,convertTempToSkew, find_lcl
import a405thermo.thermlib as tl
#
# set the lcl for 900 hPa to 860 hPa and thetae to 338 K
#
press=860.e2
thetae_900=338. #K
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')
