def ode_littlerock():
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
newHeight= 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, newHeight, temp)
interpTdEnv = lambda zVals: np.interp(zVals, newHeight, dewpoint)
interpPress = lambda zVals: np.interp(zVals, newHeight, 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]
yinit = [0.5, height_800] #(intial velocity = 0.5 m/s, initial height in m)
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(thetaeVal, interpTenv, interpTdEnv, interpPress)
r.set_initial_value(yinit, tinit)
y = np.array(yinit)
t = np.array(tinit)
#stop integration when the parcel changes direction, or time runs 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 = F(t) and r.t = t
#where F is the function being integrated)
r.integrate(r.t+dt)
#keep track of y at each time step
y = np.vstack((y, r.y))
t = np.vstack((t, r.t))
wvel = y[:,0]
height = y[:,1]
plt.figure(1)
plt.plot(wvel, height)
plt.xlabel('vertical velocity (m/s)')
plt.ylabel('height about surface (m)')
plt.show()
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()
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')
plt.show()
#print -dpdf base900_thetae.pdf
c = constants(); eqT_bot=30 + c.Tc eqwv_bot=14*1.e-3 sfT_bot=21 + c.Tc sfwv_bot=3.e-3 eqwv_top=3.e-3 sfwv_top=3.e-3 ptop=410.e2 pbot=1000.e2 eqTd_bot=findTdwv(eqwv_bot,pbot) sfTd_bot=findTdwv(sfwv_bot,pbot) thetae_eq=thetaep(eqTd_bot,eqT_bot,pbot) thetae_sf=thetaep(sfTd_bot,sfT_bot,pbot) fig1 = plt.figure(1) skew, ax1 = convecSkew(1) pvec=np.arange(ptop, pbot, 1000) #initialize vectors Tvec_eq = np.zeros(pvec.size) Tvec_sf = np.zeros(pvec.size) wv = np.zeros(pvec.size) wl = np.zeros(pvec.size) xcoord_eq = np.zeros(pvec.size) xcoord_sf = np.zeros(pvec.size)
plt.ylabel('pressure (hPa)')
plt.xlabel('temperature (deg C)')
plt.show()
plt.figure(2)
skew, ax2 = convecSkew(2)
xtemp=convertTempToSkew(temp,press,skew)
xdew=convertTempToSkew(dewpoint,press,skew)
plt.semilogy(xtemp,press,'g-',linewidth=4)
plt.semilogy(xdew,press,'b-',linewidth=4)
#use 900 hPa sounding level for adiabat
#array.argmin() finds the index of the min. value of array
p900_level = np.abs(900 - press).argmin()
thetaeVal=thetaep(dewpoint[p900_level] + c.Tc,temp[p900_level] + c.Tc,press[p900_level]*100.)
pressVals,tempVals =calcAdiabat(press[p900_level]*100.,thetaeVal,200.e2)
xTemp=convertTempToSkew(tempVals - c.Tc,pressVals*1.e-2,skew)
p900_adiabat = plt.semilogy(xTemp,pressVals*1.e-2,'r-',linewidth=4)
xleft=convertTempToSkew(-20,1.e3,skew)
xright=convertTempToSkew(25.,1.e3,skew)
#
#interpolator fails if two pressure values are the same
#
newPress = nudge(press)
#independent variable used to interpolate must be in increasing order
#pVals must be in hPa
interpTenv = lambda pVals: np.interp(pVals, newPress[::-1], temp[::-1])
interpTdenv = lambda pVals: np.interp(pVals, newPress[::-1], dewpoint[::-1])
interpDirec = lambda pVals: np.interp(pVals, newPress[::-1], direct[::-1])
c = constants() eqT_bot = 30 + c.Tc eqwv_bot = 14*1.e-3 sfT_bot = 21 + c.Tc sfwv_bot = 3.e-3 eqwv_top = 3.e-3 sfwv_top = 3.e-3 ptop = 4e2 pbot = 1000.e2 # Perform the functions as the heat expands eqTd_bot = findTdwv(eqwv_bot,pbot) sfTd_bot = findTdwv(sfwv_bot,pbot) thetae_eq = thetaep(eqTd_bot,eqT_bot,pbot) thetae_sf = thetaep(sfTd_bot,sfT_bot,pbot) # plot fig1 = plt.figure(1) skew, ax1 = convecSkew(1) # Initialize vector arrays. pvec = np.arange(ptop, pbot, 1000) Tvec_eq = np.zeros(pvec.size) Tvec_sf = np.zeros(pvec.size) wv = np.zeros(pvec.size) wl = np.zeros(pvec.size) xcoord_eq = np.zeros(pvec.size) xcoord_sf = np.zeros(pvec.size)
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:
#ws = wsat(newTemp, pnew)
#wl = wv0 - ws
out_msg = '\nat new pressure level %8.2f hPa\n\
the temperature is %8.2f deg C\n\