def invert_Se(Se, z, r):
# Given Moist Static Energy Se [J], mixing ratio r and height z [m],
# return Temperature T [K]
T0 = (Se - Lv0*r - g*z)/Cpd
def Tfind_Se(T, Se, z, r): return Se - Se_r(T, z, r)
T = rootfinder.fzero(Tfind_Se, T0, Se, z, r)
return T
def invert_theta_l(theta_l, rt, p):
T = thermo.theta_to_T(theta_l, p)
r_star = thermo.r_star(p, T)
if r_star < rt:
T0 = numpy.array([233.15, theta_l])
T = rootfinder.fzero(Tfind, T0, p, theta_l, rt)
return T
def find_Tmoist(thetaE0, press):
"""
Calculates the temperatures along a moist adiabat.
Parameters
----------
thetaE0 : float
Initial equivalent potential temperature (K).
press : float or array_like
Pressure (Pa).
Returns
-------
Temp : float or array_like
Temperature (K) of thetaE0 adiabat at 'press'.
Examples
--------
>>> np.array([find_Tmoist(300., 8.e4)])
array([ 271.0638])
>>> find_Tmoist(330., 8.e4)
283.7226584032411
"""
Tstart = c.Tc
try:
brackets = rf.find_interval(thetaes_diff, Tstart, thetaE0, press)
Temp = rf.fzero(thetaes_diff, brackets, thetaE0, press)
except BracketError as e:
print("couldn't find bracket: debug info: ", e.extra_info)
Temp = np.nan
return Temp
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 invert_theta_l(theta_l, rt, p):
T = thermo.theta_to_T(theta_l, p)
r_star = thermo.r_star(p, T)
if r_star < rt:
T0 = numpy.array([233.15, theta_l])
T = rootfinder.fzero(Tfind, T0, p, theta_l, rt)
return T
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 invert_theta_l(thetal, p, rt):
# Given Liquid Water Potential Temperature thetal [K],
# pressure p [Pa] and total mixing ratio rt,
# return Temperature T [K]
T = theta_to_T(thetal, p)
rstar = r_star(p, T)
if r_star < rt:
T0 = array([230., thetal])
T = rootfinder.fzero(Tfind_thetal, p, T0, thetal, rt)
return T
def tinvert_thetae(thetaeVal, rT, press):
"""
temp,rv,rl=tinvert_thetae(thetaeVal, rT, press)
Uses a rootfinder to determine the temperature for which the
pseudo equivilant potential temperature (thetaepress) is equal to the
equivilant potential temperature (thetae) of the parcel.
Parameters
----------
thetaeVal : float
Thetae of parcel (K).
rT : float
Total water mixing ratio (kg/kg).
press : float
Pressure of parcel in (Pa).
Returns
-------
theTemp : float
Temperature for which thetaep equals the parcel thetae (K).
rv : float
Vapor mixing ratio of the parcel (kg/kg).
rl : float
liquid water mixing ratio of the parcel (kg/kg) at 'press'.
Raises
------
IOError
If 'press' is larger than 100000 Pa.
Examples
--------
>>> tinvert_thetae(300., 0.001, 8.e4)
(278.683729619619, 0.001, 0)
"""
if press > 1.e5:
raise IOError('expecting pressure level less than 100000 Pa')
# The temperature has to be somewhere between thetae
# (T at surface) and -40 deg. C (no ice).
Tstart = c.Tc
brackets = rf.find_interval(find_resid_thetae, Tstart, thetaeVal, rT,
press)
theTemp = rf.fzero(find_resid_thetae, brackets, thetaeVal, rT, press)
rv, rl = find_rvrl(theTemp, rT, press)
return theTemp, rv, rl
def tinvert_rsat(Tstart, rsat, press):
"""
rootfind the temp that produces rsat at press.
Parameters
----------
temp : float
temperature (K)
rsat : float
saturation mixing ratio (kg/kg)
press : float
pressure (hPa)
Returns
-------
Tdew : temperature (K) at with air is saaturated
"""
brackets = rf.find_interval(find_resid_rsat, Tstart, rsat, press)
temp = rf.fzero(find_resid_rsat, brackets, rsat, press)
return temp
