def dels_tropfn(p_out):
T_BLtop = findTmoist(thetae0, p_BL) #temperature of boundary layer top
T_out = findTmoist(thetae0, p_out)
thickness = lambda p: (c.Rd/(p*g))*findTmoist(thetae0, p)
delz_trop = integrate.quad(thickness, p_out, p_BL)[0]
delz_trop = np.zeros(len(p_out))
for i,p_oute in enumerate(p_out):
delz_trop[i] = integrate.quad(thickness, p_oute, p_BL)[0]
dels_trop = c.cpd*np.subtract(T_BLtop, T_out) + g*(-delz_trop) #difference in dry static energy between boundary layer top and tropopause (J)
return dels_trop
def calcAdiabat(press0, thetae0, topPress):
"""
Calculates the temperature-pressure coordinates of a moist adiabat.
Parameters
- - - - - -
press0: the initial pressure (Pa)
thetae0: the equivalent potential temperature (K) of the adiabat
topPress: the final pressure (Pa)
Returns
- - - - - -
(pressVals, tempVals): pressVals (Pa) and tempVals (K) are type ndarray
and are the coordinates of the thetae0 adiabat
Tests
- - - - -
>>> p,T = calcAdiabat(800*100, 300, 1000*100)
>>> len(p)
50
>>> len(T)
50
"""
pressVals = np.linspace(press0, topPress, 50)
tempVals = findTmoist(thetae0, pressVals)
return pressVals, np.asarray(tempVals)
def calcTvDiff(press, thetae0, interpTenv, interpTdEnv):
"""
Calculates the virtual temperature difference between the thetae0
moist adiabat and a given sounding at some pressure.
Parameters
- - - - - -
press: pressure (Pa)
thetae0: equivalent potential temperature of the adiabat (K)
interpTenv: interpolator for environmental temperature (deg C)
interpTdEnv: interpolator for environmental dew point temperature (deg C)
Returns
- - - - - -
TvDiff: the virtual temperature difference at pressure press
between the thetae0 moist adiabat and the given sounding (K).
"""
Tcloud=findTmoist(thetae0,press)
wvcloud=wsat(Tcloud,press)
Tvcloud=Tcloud*(1. + c.eps*wvcloud)
Tenv=interpTenv(press*1.e-2) + c.Tc
Tdenv=interpTdEnv(press*1.e-2) + c.Tc
wvenv=wsat(Tdenv,press)
Tvenv=Tenv*(1. + c.eps*wvenv)
return Tvcloud - Tvenv
def dels_BLfn(p_BL):
T_BLtop = findTmoist(thetae0, p_BL) #temperature of boundary layer top
delz_BL = np.subtract(p_s, p_BL)/(g*rho_BL)
s_BLtop = c.cpd*np.array(T_BLtop) + g*np.array(delz_BL) #dry static energy at top of boundary layer
s_BL = np.add(s_BLtop,s_surf)/2. #dry static energy of BL (well-mixed)
dels_BL = np.subtract(s_BL, s_BLtop) #difference in dry static energy between BL and right above BL
return dels_BL
def equations(p):
l_m, f = p
p_LCL, T_LCL = findLCL0(f*q_sat, p_s, T_BL)
T_LCL = findTmoist(thetae0, p_LCL)
delz_LCL = integrate.quad(thickness, p_t, p_LCL)[0]
dels_LCL = c.cpd*(T_LCL-T_t) + g*(-delz_LCL)
return (l_m - ((omega_BL*l_d**2)/(omega_BL - (g*Q_mtrop)/(dels_LCL + L_v*(f*q_sat - q_FA))))**(0.5), \
(f-1)*q_sat - (2*zhat*(q_FAd - q_sat))/(l_d**2 - l_m**2)*(l_m + zhat - (zhat + l_d)*np.exp((l_m - l_d)/zhat)))
def calcBuoy(height, thetae0, interpTenv, interpTdEnv, interpPress):
#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=findTmoist(thetae0,press) #K
wvcloud=wsat(Tcloud,press); #kg/kg
Tvcloud=Tcloud*(1. + c.eps*wvcloud)
Tenv=interpTenv(height) + c.Tc
Tdenv=interpTdEnv(height) + c.Tc
wvenv=wsat(Tdenv,press); #kg/kg
Tvenv=Tenv*(1. + c.eps*wvenv)
TvDiff=Tvcloud - Tvenv
#print '%10.3f %10.3f %10.3f\n' %(press*0.01,height,TvDiff)
return c.g0*(TvDiff/Tvenv)
def T_afn(p_out):
T_a = np.mean(findTmoist(thetae0, np.linspace(p_BL, p_out)))
return T_a
eps_BLs = np.linspace(0.1, 0.8, 10)
eps_as = np.linspace(0.1, 0.8, 10)
eps_BLss, eps_ass = np.meshgrid(eps_BLs, eps_as)
p_outs = np.zeros(eps_BLss.shape)
#p_BLs = np.zeros(eps_BLss.shape)
#T_as = np.zeros(eps_BLss.shape)
q_sat = wsat(T_s, p_s) #mixing ratio above sea surface (100% saturated)
thetae0 = thermo.theta_e(T_s, p_s, q_sat, 0) #theta_e in moist region
#use surface temperature to get moist adiabat
plevs = np.linspace(50e2, p_s, 1000)
Tadb = findTmoist(thetae0, plevs)
for i, eps_BL in enumerate(eps_BLs):
print 'eps_BL', eps_BL
for j, eps_a in enumerate(eps_as):
print 'eps_a', eps_a
#T_a = np.mean(Tadb)
#T_out = findTmoist(thetae0, p_out)
#T_strat = T_out
#rho_BL = p_s/(c.Rd*T_BL)
s_surf = c.cpd*T_s #dry static energy at surface
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
zeta_levs = -h * np.log(plevs / p_s)
zeta_T = 16
for i, zeta in enumerate(zeta_levs):
if (zeta < zeta_T):
Tphumb[i] = T_s - gamma_ph * zeta
else:
Tphumb[i] = T_s - gamma_ph * zeta_T
Told = np.zeros(plevs.shape)
Tnew = np.zeros(plevs.shape)
for i, p in enumerate(plevs[:-1]):
Tgm[i + 1] = Tgm[i] * (1 + gamma_m * c.Rd * delp / p)
Tgd[i + 1] = Tgd[i] * (1 + gamma_d * c.Rd * delp / p)
Told[i] = findTmoist.findTmoist(thetae0, p)
Tnew[i] = findTmoist_new.findTmoist(thetae0, p, q_sat, 0)
plt.figure(1)
plt.plot(Told[:-1],
plevs[:-1] / 100.,
color='r',
label='Told - root finder moist adiabat')
plt.plot(Tnew[:-1],
plevs[:-1] / 100.,
color='b',
label='Tnew - root finder moist adiabat')
plt.plot(Tgm[:-1], plevs[:-1] / 100., 'g--', label='constant gamma_m')
plt.plot(Tgd[:-1], plevs[:-1] / 100., 'k--', label='constant gamma_d')
plt.plot(Tphumb, plevs / 100., color='y', label='pierre humbert profile')
plt.legend()
def T_BLfn(p_BL):
T_BLtop = findTmoist(thetae0, p_BL) #temperature of boundary layer top
T_BL = np.add(T_s,T_BLtop)/2. #temperature of boundary layer, consistent with well-mixed assumption (linear mixing)
return T_BL
RH_ms = np.zeros(eps_BLss.shape)
delhs = np.zeros(eps_BLss.shape)
massbalance = np.zeros(eps_BLss.shape)
p_LCLs = np.zeros(eps_BLss.shape)
q_sat = wsat(T_s, p_s) #mixing ratio above sea surface (100% saturated)
thetae0 = thermo.theta_e(T_s, p_s, q_sat, 0) #theta_e in moist region
#use surface temperature to get moist adiabat
plevs = np.linspace(50e2, p_s, 1000)
#Tadb = findTmoist(thetae0, plevs)
omega_BLs = np.zeros(eps_BLss.shape)
w_BLs = np.zeros(eps_BLss.shape)
#T_out = findT(T_s, p_out)
T_out = findTmoist(thetae0, p_out)
T_strat = T_out
#T_strat = np.mean(findTmoist(thetae0, np.linspace(95,p_out,50)))
#rho_BL = p_s/(c.Rd*T_BL)
s_surf = c.cpd*T_s #dry static energy at surface
q_FA = wsat(T_out, p_out)
l_d = 3000e3
for i, eps_BL in enumerate(eps_BLs):
print 'eps_BL', eps_BL
for j, eps_a in enumerate(eps_as):
d = 100000e3 #
p_s = 1000e2 #surface pressure (Pa)
p_t = 200e2 #tropopause (Pa)
p_BL = 900e2 #boundary layer top (Pa)
T_s = 302
delz_BL = z[BLi]
c_E = 0.001
l_d = domsize*1e3*(1./np.sqrt(2))
#r = np.linspace(0, l_d, 1e6)
q_sat = wsat(T_s, p_s) #mixing ratio above sea surface (100% saturated)
q_sat = wsat(T_s, p_s) #mixing ratio above sea surface (100% saturated)
thetae0 = thermo.theta_e(T_s, p_s, q_sat, 0) #theta_e in moist region
T_BLtop = findTmoist(thetae0, p_BL) #temperature of boundary layer top
T_t = findTmoist(thetae0, p_t) #temperature of tropopause (outflow region)
T_BL = (T_s + T_BLtop)/2. #temperature of boundary layer, consistent with well-mixed assumption (linear mixing)
q_FA = wsat(T_t, p_t) #free troposphere water vapor mixing ratio
zhat = delz_BL/c_E
q_BL = q_sat + 2*zhat*(q_FA - q_sat)/(l_d**2 - rbin_centers**2)*(rbin_centers + zhat - (zhat + l_d)*np.exp((rbin_centers - l_d)/zhat))
RH_c = q_BL/q_sat
if varname == 'QV':
titlename = r'$q_v$'
if varname == 'RH':
titlename = 'RH'
w_ms = np.zeros(len(domsizes))
l_ms = np.zeros(len(domsizes))
l_ds = np.zeros(len(domsizes))
massbalance = np.zeros(len(domsizes))
waterbalance = np.zeros(len(domsizes))
Ebalance = np.zeros(len(domsizes))
RHs = np.zeros(len(domsizes))
Ps = np.zeros(len(domsizes))
delhs = np.zeros(len(domsizes))
p_LCLs = np.zeros(len(domsizes))
q_sat = wsat(T_s, p_s) #mixing ratio above sea surface (100% saturated)
thetae0 = thermo.theta_e(T_s, p_s, q_sat, 0) #theta_e in moist region
#use surface temperature to get moist adiabat
T_a = np.mean(findTmoist(thetae0, np.linspace(p_s, p_t)))
T_out = findTmoist(thetae0, p_out)
T_BL = T_s
M_BL = (p_s - p_BL)/g #mass of boundary layer in kg m^-2
rho_BL = p_s/(c.Rd*T_BL)
s_surf = c.cpd*T_s #dry static energy at surface
#def T_BLfn(p_BL):
# T_BLtop = findTmoist(thetae0, p_BL) #temperature of boundary layer top
# T_BL = np.add(T_s,T_BLtop)/2. #temperature of boundary layer, consistent with well-mixed assumption (linear mixing)
# return T_BL
#def T_afn(p_BL):
# T_a = np.mean(findTmoist(thetae0, np.linspace(p_BL, p_out)))
for i, zeta in enumerate(zeta_levs):
if (zeta < zeta_T):
Tphumb[i] = T_s - gamma_ph*zeta
else:
Tphumb[i] = T_s - gamma_ph*zeta_T
Told = np.zeros(plevs.shape)
Tnew = np.zeros(plevs.shape)
for i, p in enumerate(plevs[:-1]):
Tgm[i+1] = Tgm[i]*(1 + gamma_m*c.Rd*delp/p)
Tgd[i+1] = Tgd[i]*(1+ gamma_d*c.Rd*delp/p)
Told[i] = findTmoist.findTmoist(thetae0, p)
Tnew[i] = findTmoist_new.findTmoist(thetae0, p, q_sat, 0)
plt.figure(1)
plt.plot(Told[:-1], plevs[:-1]/100., color='r', label='Told - root finder moist adiabat')
plt.plot(Tnew[:-1], plevs[:-1]/100., color='b', label='Tnew - root finder moist adiabat')
plt.plot(Tgm[:-1], plevs[:-1]/100., 'g--', label='constant gamma_m')
plt.plot(Tgd[:-1], plevs[:-1]/100., 'k--', label='constant gamma_d')
plt.plot(Tphumb, plevs/100., color ='y', label='pierre humbert profile')
plt.legend()
#plt.gca().invert_yaxis()
def T_stratfn(p_out):
return findTmoist(thetae0, p_out)
q_BLms = np.zeros(len(domsizes))
omega_ms = np.zeros(len(domsizes))
for j, domsize in enumerate(domsizes):
l_d = domsize * 1000
print l_d / 1e3
r = np.linspace(0, l_d, 1e6)
q_sat = wsat(T_s,
p_s) #mixing ratio above sea surface (100% saturated)
thetae0 = thermo.theta_e(T_s, p_s, q_sat, 0) #theta_e in moist region
#use surface temperature to get moist adiaba
T_BLtop = findTmoist(thetae0, p_BL) #temperature of boundary layer top
T_t = findTmoist(thetae0,
p_t) #temperature of tropopause (outflow region)
#T_BL = (T_s + T_BLtop)/2. #temperature of boundary layer, consistent with well-mixed assumption (linear mixing)
T_BL = T_s
q_BLsat = wsat(T_BL, (p_s + p_BL) / 2.)
q_BLtopsat = wsat(T_BLtop, p_BL)
q_FA = wsat(T_t, p_t) #free troposphere water vapor mixing ratio
#q_FA = 0.01
q_FAd = q_FA
#q_FA = 0.001
M_trop = (p_BL - p_t) / g #mass of troposphere in kg m^-2
for j, domsize in enumerate(domsizes):
l_d = domsize*1000
print l_d/1e3
r = np.linspace(0, l_d, 1e6)
q_sat = wsat(T_s, p_s) #mixing ratio above sea surface (100% saturated)
thetae0 = thermo.theta_e(T_s, p_s, q_sat, 0) #theta_e in moist region
#use surface temperature to get moist adiaba
T_BLtop = findTmoist(thetae0, p_BL) #temperature of boundary layer top
T_t = findTmoist(thetae0, p_t) #temperature of tropopause (outflow region)
#T_BL = (T_s + T_BLtop)/2. #temperature of boundary layer, consistent with well-mixed assumption (linear mixing)
T_BL = T_s
q_BLsat = wsat(T_BL, (p_s + p_BL)/2.)
q_BLtopsat = wsat(T_BLtop, p_BL)
q_FA = wsat(T_t, p_t) #free troposphere water vapor mixing ratio
#q_FA = 0.01
q_FAd = q_FA
#q_FA = 0.001
M_trop = (p_BL - p_t)/g #mass of troposphere in kg m^-2
d = 100000e3 #
p_s = 1000e2 #surface pressure (Pa)
p_t = 200e2 #tropopause (Pa)
p_BL = 900e2 #boundary layer top (Pa)
T_s = 302
delz_BL = zBL
c_E = 0.001
l_d = domsize*(1./np.sqrt(2))
#r = np.linspace(0, l_d, 1e6)
q_sat = wsat(T_s, p_s) #mixing ratio above sea surface (100% saturated)
q_sat = wsat(T_s, p_s) #mixing ratio above sea surface (100% saturated)
thetae0 = thermo.theta_e(T_s, p_s, q_sat, 0) #theta_e in moist region
T_BLtop = findTmoist(thetae0, p_BL) #temperature of boundary layer top
T_t = findTmoist(thetae0, p_t) #temperature of tropopause (outflow region)
T_BL = (T_s + T_BLtop)/2. #temperature of boundary layer, consistent with well-mixed assumption (linear mixing)
q_FA = wsat(T_t, p_t) #free troposphere water vapor mixing ratio
zhat = delz_BL/c_E
q_BL = q_sat + 2*zhat*(q_FA - q_sat)/(l_d**2 - rbin_centers**2)*(rbin_centers + zhat - (zhat + l_d)*np.exp((rbin_centers - l_d)/zhat))
#plot vertical means
plt.figure(1)
fieldmeanbar = np.mean(fieldmeans, axis=0)
fieldaverage = np.mean(fieldmeanbar)
