def mixr(t,p):
"""mx = mixr(t,p)
Computes the saturation mixing ratio given ambient temperature(s) (t) and
pressure(s) (p).
Inputs:
t = dry bulb temperature(s) (deg C or K) (vector of length N)
p = pressure(s) (hPa) (vector of length N)
Outputs:
mixr = saturation mixing ratio for the given temperature and pressure
RLT, 010607
"""
es = esat(t)
mx = 621.97*(es/(p-es))
return mx
def mixr(t, p):
"""mx = mixr(t,p)
Computes the saturation mixing ratio given ambient temperature(s) (t) and
pressure(s) (p).
Inputs:
t = dry bulb temperature(s) (deg C or K) (vector of length N)
p = pressure(s) (hPa) (vector of length N)
Outputs:
mixr = saturation mixing ratio for the given temperature and pressure
RLT, 010607
"""
es = esat(t)
mx = 621.97 * (es / (p - es))
return mx
def LCLfind(Td, T, p):
"""
LCLfind(Td, T, p)
Finds the temperature and pressure at the lifting condensation
level (LCL) of an air parcel.
Parameters
- - - - - -
Td : float
Dewpoint temperature (K).
T : float
Temperature (K).
p : float
Pressure (Pa)
Returns
- - - -
Tlcl : float
Temperature at the LCL (K).
plcl : float
Pressure at the LCL (Pa).
Raises
- - - -
NameError
If the air is saturated at a given Td and T (ie. Td >= T)
Examples
- - - - -
>>> [Tlcl, plcl] = LCLfind(280., 300., 8.e4)
>>> print [Tlcl, plcl]
[275.76250387361404, 59518.928699453245]
>>> LCLfind(300., 280., 8.e4)
Traceback (most recent call last):
...
NameError: parcel is saturated at this pressure
References
- - - - - -
Emanuel 4.6.24 p. 130 and 4.6.22 p. 129
"""
c = constants()
hit = Td >= T
if hit is True:
raise NameError('parcel is saturated at this pressure')
e = esat(Td)
ehPa = e * 0.01
#Bolton's formula requires hPa.
# This is is an empircal fit from for LCL temp from Bolton, 1980 MWR.
Tlcl = (2840. / (3.5 * np.log(T) - np.log(ehPa) - 4.805)) + 55.
r = c.eps * e / (p - e)
#disp(sprintf('r=%0.5g',r'))
cp = c.cpd + r * c.cpv
logplcl = np.log(p) + cp / (c.Rd * (1 + r / c.eps)) * \
np.log(Tlcl / T)
plcl = np.exp(logplcl)
#disp(sprintf('plcl=%0.5g',plcl))
return Tlcl, plcl
def wsat(Temp, press):
"""
wsat(Temp, press)
Calculates the saturation vapor mixing ratio of an air parcel.
Parameters
- - - - - -
Temp : float or array_like
Temperature in Kelvin.
press : float or array_like
Pressure in Pa.
Returns
- - - -
theWs : float or array_like
Saturation water vapor mixing ratio in (kg/kg).
Raises
- - - -
IOError
If both 'Temp' and 'press' are array_like.
Examples
- - - - -
>>> wsat(300, 8e4)
0.028751159650442507
>>> wsat([300,310], 8e4)
[0.028751159650442507, 0.052579529573838296]
>>> wsat(300, [8e4, 7e4])
[0.028751159650442507, 0.033076887758679716]
>>> wsat([300, 310], [8e4, 7e4])
Traceback (most recent call last):
...
IOError: Can't have two vector inputs.
"""
c = constants()
es = esat(Temp)
# We need to test for all possible cases of (Temp,press)
# combinations (ie. (vector,vector), (vector,scalar),
# (scalar,vector), or (scalar,scalar).
try:
len(es)
except:
esIsVect = False
else:
esIsVect = True
try:
len(press)
except:
pressIsVect = False
else:
pressIsVect = True
if esIsVect and pressIsVect:
raise IOError, "Can't have two vector inputs."
elif esIsVect:
theWs = c.eps * es / (press - es)
#theWs = [(c.eps * i/ (press - i)) for i in es]
# Limit ws values so rootfinder doesn't blow up.
#theWs = list(replaceelem(theWs,0,0.060))
elif pressIsVect:
theWs = c.eps * es / (press - es)
#theWs = [(c.eps * es/ (i - es)) for i in press]
# Limit ws values so rootfinder doesn't blow up.
#theWs = list(replaceelem(theWs,0,0.060))
else: # Neither 'es' nor 'press' in a vector.
theWs = (c.eps * es / (press - es))
# Limit ws value so rootfinder doesn't blow up.
if theWs > 0.060: theWs = 0.060
elif theWs < 0: theWs = 0
# Set minimum and maximum acceptable values for theWs.
try:
len(theWs)
except:
if theWs > 0.060: theWs = 0.060
elif theWs < 0: theWs = 0
else:
theWs[theWs < 0] = 0
theWs[theWs > 0.060] = 0.060
# theWs = list(replaceelem(theWs, 0, 0.060))
return theWs
def LCLfind(Td, T, p):
"""
LCLfind(Td, T, p)
Finds the temperature and pressure at the lifting condensation
level (LCL) of an air parcel.
Parameters
- - - - - -
Td : float
Dewpoint temperature (K).
T : float
Temperature (K).
p : float
Pressure (Pa)
Returns
- - - -
Tlcl : float
Temperature at the LCL (K).
plcl : float
Pressure at the LCL (Pa).
Raises
- - - -
NameError
If the air is saturated at a given Td and T (ie. Td >= T)
Examples
- - - - -
>>> [Tlcl, plcl] = LCLfind(280., 300., 8.e4)
>>> print [Tlcl, plcl]
[275.76250387361404, 59518.928699453245]
>>> LCLfind(300., 280., 8.e4)
Traceback (most recent call last):
...
NameError: parcel is saturated at this pressure
References
- - - - - -
Emanuel 4.6.24 p. 130 and 4.6.22 p. 129
"""
c = constants();
hit = Td >= T;
if hit is True:
raise NameError('parcel is saturated at this pressure');
e = esat(Td);
ehPa = e * 0.01; #Bolton's formula requires hPa.
# This is is an empircal fit from for LCL temp from Bolton, 1980 MWR.
Tlcl = (2840. / (3.5 * np.log(T) - np.log(ehPa) - 4.805)) + 55.;
r = c.eps * e / (p - e);
#disp(sprintf('r=%0.5g',r'))
cp = c.cpd + r * c.cpv;
logplcl = np.log(p) + cp / (c.Rd * (1 + r / c.eps)) * \
np.log(Tlcl / T);
plcl = np.exp(logplcl);
#disp(sprintf('plcl=%0.5g',plcl))
return Tlcl, plcl
def wsat(Temp, press):
"""
wsat(Temp, press)
Calculates the saturation vapor mixing ratio of an air parcel.
Parameters
- - - - - -
Temp : float or array_like
Temperature in Kelvin.
press : float or array_like
Pressure in Pa.
Returns
- - - -
theWs : float or array_like
Saturation water vapor mixing ratio in (kg/kg).
Raises
- - - -
IOError
If both 'Temp' and 'press' are array_like.
Examples
- - - - -
>>> wsat(300, 8e4)
0.028751159650442507
>>> wsat([300,310], 8e4)
[0.028751159650442507, 0.052579529573838296]
>>> wsat(300, [8e4, 7e4])
[0.028751159650442507, 0.033076887758679716]
>>> wsat([300, 310], [8e4, 7e4])
Traceback (most recent call last):
...
IOError: Can't have two vector inputs.
"""
c = constants();
es = esat(Temp);
# We need to test for all possible cases of (Temp,press)
# combinations (ie. (vector,vector), (vector,scalar),
# (scalar,vector), or (scalar,scalar).
try:
len(es)
except:
esIsVect = False
else:
esIsVect = True
try:
len(press)
except:
pressIsVect = False
else:
pressIsVect = True
if esIsVect and pressIsVect:
raise IOError, "Can't have two vector inputs."
elif esIsVect:
theWs = c.eps*es/(press - es)
#theWs = [(c.eps * i/ (press - i)) for i in es]
# Limit ws values so rootfinder doesn't blow up.
#theWs = list(replaceelem(theWs,0,0.060))
elif pressIsVect:
theWs = c.eps*es/(press - es)
#theWs = [(c.eps * es/ (i - es)) for i in press]
# Limit ws values so rootfinder doesn't blow up.
#theWs = list(replaceelem(theWs,0,0.060))
else: # Neither 'es' nor 'press' in a vector.
theWs = (c.eps * es/ (press - es))
# Limit ws value so rootfinder doesn't blow up.
if theWs > 0.060: theWs = 0.060
elif theWs < 0: theWs = 0
# Set minimum and maximum acceptable values for theWs.
try:
len(theWs)
except:
if theWs > 0.060: theWs = 0.060
elif theWs < 0: theWs = 0
else:
theWs[theWs < 0] = 0
theWs[theWs > 0.060] = 0.060
# theWs = list(replaceelem(theWs, 0, 0.060))
return theWs
def humidity(x, t=288.15, p=101325, in_type='specific humidity', out_type='water vapor', nounits=False,
method='Murphy_Koop'):
"""
Convert Humidity data into other humidity data
humidity:
- partial pressure of water vapor in Pa (not hPa nor mbar)
- specific humidity in kg/kg (not g/kg)
- mixing ratio in kg/kg (not g/kg)
- relative humidity in percent
- dew point temperature in K (not degree Celsius)
- virtual temperature in K (not degree Celsius)
"""
in_unit = None
out_unit = None
ispandas = False
inputs = ['water vapor', 'specific humidity', 'relative humidity', 'virtual temperature', 'ppmv']
outputs = ['water vapor', 'specific humidity', 'relative humidity', 'mixing ratio', 'ppmv', 'virtual temperature',
'dewpoint']
if in_type not in inputs:
print "Unkown: %s" % in_type
print inputs
if out_type not in outputs:
print "Unkown: %s" % out_type
print outputs
# retain time information
if isinstance(x, pd.DataFrame) | isinstance(x, pd.Series):
# convert to numpy
time = x.index
if isinstance(x, pd.DataFrame):
columns = x.columns
x = np.ma.asarray(x)
ispandas = True
if isinstance(p, pd.DataFrame) | isinstance(p, pd.Series):
p = np.ma.asarray(p)
# Vectorize funktion or not?
x = np.ma.asarray(x)
c = 0.622 # Constant (Mv / Md)
if in_type in ('partial pressure', 'partial pressure of water vapor', 'water vapor'):
e = x
in_unit = 'Pa'
elif in_type == 'specific humidity':
q = x
e = (q * p) / (c + (1 - c) * q)
in_unit = 'kg/kg + Pa (p)'
elif in_type == 'mixing ratio':
r = x
e = (r * p) / (r + c)
in_unit = '1 + Pa (p)'
elif in_type == 'relative humidity':
RH = x
es = esat(t, method=method, info=False)
e = (RH / 100.) * es
in_unit = '% + K (t)'
elif in_type == 'virtual temperature':
Tv = x
e = p * (1 - t / Tv) / (1 - c)
in_unit = 'K + K (t)'
elif in_type == 'ppmv':
x = (x / 1e6)
e = x * p / (1 + x)
in_unit = 'ppmv + Pa (p)'
else:
print "[INPUT] Unknown Conversion"
return
if out_type in ('partial pressure', 'partial pressure of water vapor', 'water vapor'):
out = e
out_unit = 'Pa'
elif out_type == 'specific humidity':
Pd = p - e
out = (e * c) / (e * c + Pd)
out_unit = '+ Pa (p) = kg/kg '
elif out_type == 'mixing ratio':
Pd = p - e
out = (e / Pd) * c
out_unit = '+ Pa (p) = 1 '
elif out_type == 'ppmv':
Pd = p - e
out = (e / Pd) * 1e6
out_unit = '+ Pa (p) = ppmv'
elif out_type == 'relative humidity':
es = esat(t, method=method)
out = 100. * e / es
out_unit = '+ K (t) = %'
elif out_type == 'virtual temperature':
out = t / (1 - (e / p) * (1 - c))
out_unit = '+K (t) + Pa (p) = K'
elif out_type == 'dew point':
out = dewpoint(e, method=method)
out_unit = 'K'
else:
print "[OUTPUT] Unknown Conversion"
return
if ispandas:
if len(out.shape) > 1:
out = pd.DataFrame(out, index=time, columns=columns)
else:
out = pd.Series(out, index=time)
if nounits:
return out
else:
print "Conversion: %s => %s" % (in_unit, out_unit)
print in_type, ' => ', out_type
return out
