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.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) adia_rls = sfc_rvap - adia_rvaps
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])
fig_dict=dict(press=press,Tpseudo=Tpseudo,Temp=Temp,Tdew=Tdew,Tlcl=Tlcl,pLCL=pLCL,botLabel='LCL bot (835 hPa)',
topLabel='LCL top (768 hPa)')
ax = makePlot(ax,**fig_dict)
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[5]: 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_Td,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 100 hPa thetae goes bananas, so # so trim so we only have # toplim=len(press) - np.searchsorted(press[::-1],1.5e4) clipped_press=press[:toplim] # # find temps along that adiabat # adia_temps= np.array([find_Tmoist(sfc_thetae,the_press) for the_press in clipped_press]) adia_rvaps = find_rsat(adia_temps,clipped_press) adia_rls = sfc_rvap - adia_rvaps
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
