# Atmospheric thermodynamics calculators and LCL calculator.
import math
# Function to calculate the saturation vapor pressure over water in mb for temperature T in C.
# Relationship is from Bolton as quoted in Grant Petty's Atmospheric Thermo book.
def esatWater(T):
return 6.112*math.exp(17.67*T/(243.5+T))
# Function to calculate relative humidity, RH, in %, from T and Tdew in C.
# This function calls the esatWater function.
def RelativeHumidity(Tdew,T):
return 100.0*esatWater(Tdew)/esatWater(T)
# Function to calculate the approximate water vapor mixing ratio in g/kg
# Inputs are water vapor pressure, e, in mb and total pressure, P, in mb.
def mixingRatio(e,P):
Ro = 8314.3 # Universal gas constant in Joules/K kmole
RD = Ro/28.97 # Dry air gas constant in Joules/K kg
Rv = Ro/18.02 # Water vapor gas constant in Joules/K kg
epsilon=RD/Rv
return epsilon*e*1000.0/(P-e)
# Potential temperature calculator, returning in Celsius.
# T is entered in Celsius, P in mb.
def PotTemp(T,P):
theta=(T+273.15)*((1000.0/P)**(2.0/7.0))
return theta-273.15
# Pressure altitude calcutor, returning in meters.
# Inputs:
# To, Po, starting temperature in Kelvin and mb.
# Pz pressure in mb where the pressure altitude is desired.
def PressureAltitude(To,Po,Pz):
gamma=9.8/1000.0 # Lapse rate in Kelvin / meter
Ro = 8314.3 # Universal gas constant in Joules/K kmole
RD = Ro/28.97 # Dry air gas constant in Joules/K kg
g = 9.81 # Acceleration due to gravity in N/kg.
expon=RD*gamma/g
PressureRatio=Pz/Po
z=(To/gamma)*(1-PressureRatio**expon)
return z
# Function to calculate the Lifting condensation level properties, LCL.
# LCL P and T calculator given Tdew, To, and Po at the level o.
# Theory: mixing ratio and potential temperature are constant (conserved) below the LCL.
# Solve the equations for mixing ratio and potential temperature for pressure.
# Set these equations for pressure equal to each other and solve for temperature.
# INPUTS:
# Po in mb
# To in Celsius
# Tdew in Celsius.
# OUTPUTS:
# P in mb, pressure at the LCL.
# Tc in Celsius, temperature at the LCL.
# zo in meters, the height of the starting level o as a pressure altitude.
# z in meters, the height of the LCL level pressure altitude.
# thetaK in Kelvin, the potential temperature below the LCL (constant value).
# wo in kg/kg, the water vapor mixing ratio below the LCL (constant value)
# Tw in Celsius, wet bulb temperature at Po.
# ThetaW in Kelvin, wet bulb temperature at 1000 mb.
def LCL(Po,To,Tdew):
epsilon=0.622
e0=esatWater(0.0) # Saturation vapor pressure at T=0 C.
zo=PressureAltitude(285.0,1013.25,Po) # Pressure altitude at the initial point.
esatTdew=esatWater(Tdew) # Saturation vapor pressure at the dew point temp.
wo=mixingRatio(esatTdew,Po)/1000.0 # kg/kg value.
beta=epsilon*e0/(wo*1000.0) # Intermediate value.
thetaK=PotTemp(To,Po) + 273.15 # Potential temperature in Kelvin.
thetaE_K=thetaK+3000.0*wo
Tguess=-10.0 + 273.15 # Initial guess in Kelvin.
#print " Itterating to get the LCL temperature"
for i in range(100):
T=273.15+(3.5*math.log(Tguess/thetaK)-math.log(beta))*(243.5+Tguess-273.15)/17.67
# print "Tguess={0:1.3f}".format(Tguess),"K"," T={0:1.3f}".format(T),"K"
Tguess=T
Tc=T-273.15 # temperature at the LCL in Celsius.
P=1000.0*((T/thetaK)**3.5) # Pressure at the LCL in mb.
z=PressureAltitude(To+273.15,Po,P)+zo # Pressure altitude at the LCL in meters.
# Get the wetbulb temperature and the wetbulb potential temperature.
PressureValues=[Po,1000.0] # Pressure values for wet bulb and wetbulb potential temp are needed.
nudge = 0.5 # Used for itterating towards a solution, use the new value with the old value.
for pref in PressureValues: # Loop over pressure values
Tguess=(Tdew+To)/2.0 + 273.15 # Initial estimate for wetbulb
for i in range(100):
Tw=nudge*(thetaE_K-3.0*mixingRatio(esatWater(Tguess-273.15),pref))*((pref/1000.0)**(2./7.)) + (1.0-nudge)*Tguess
Tguess=Tw
if pref == Po:
Twvalue=Tw-273.15
elif pref == 1000.0:
thetaW=Tw
return P,Tc,zo,z,thetaK,wo,thetaE_K,Twvalue,thetaW
# Demonstrate saturation water vapor partial pressure calculator.
print "SATURATON VAPOR PRESSURE CALCULATOR RESULTS"
esat20C=esatWater(20.0)
print "esatWater(T=20C)={0:1.2f}".format(esat20C),"mb\n"
# Demonstrate relative humidity calculator.
print "RELATIVE HUMIDITY CALCULATOR RESULTS"
Tdew=-1.0 # Celsius
T =20.0 # Celsius
RH = RelativeHumidity(Tdew,T)
print "RH(Tdew={0:1.1f}".format(Tdew),"C, T={0:1.1f}".format(T),"C) = {0:1.2f}".format(RH),"%\n"
# Demonstrate water vapor mixing ratio calculator.
print "SATURATION WATER VAPOR MIXING RATIO CALCULATOR RESULTS"
P=1000.0 # total pressure in mb.
T=20.0 # temperature in Celsius.
Wsat20C=mixingRatio(esatWater(T),P)
print "INPUT VALUES:"
print " P={0:1.1f}".format(P),"mb"
print " T={0:1.2f}".format(T),"C"
print "Calculated Wsat={0:1.2f}".format(Wsat20C),"g/kg\n"
# Demonstrate water vapor mixing ratio calculator.
print "SATURATION WATER VAPOR MIXING RATIO CALCULATOR RESULTS"
P=1000.0 # total pressure in mb.
T=-1.0 # temperature in Celsius.
Wsat20C=mixingRatio(esatWater(T),P)
print "INPUT VALUES:"
print " P={0:1.1f}".format(P),"mb"
print " T={0:1.2f}".format(T),"C"
print "Calculated Wsat={0:1.2f}".format(Wsat20C),"g/kg\n"
# Demonstrate the pressure altitude calculator.
To=290.0 # Kelvin Assumed temperature value at the surface.
Po=1013.25 # mb Taken to be sea level pressure.
Pz=400.0 # mb Pressure at the unknown altitude.
z=PressureAltitude(To,Po,Pz)
print "PRESSURE ALTITUDE CALCULATOR RESULTS"
print "INPUT VALUES:"
print " Po={0:1.1f}".format(Po),"mb"
print " To={0:1.2f}".format(To),"C"
print " Pz={0:1.1f}".format(Pz),"mb"
print "Calculated Pressure Altitude={0:1.1f}".format(z),"meters\n"
# Demonstrate the LCL calculator.
# Input values
Po=876.0 # Pressure at the measurement level.
To=21.0 # Temperature at the measurement level.
Tdew=9.59 # Dewpoint temperature at the measurement level.
# Call the function
P,Tc,zo,z,thetaK,wo,thetaE_K,Tw,thetaW = LCL(Po,To,Tdew)
# Summary the LCL calculation output.
print "LCL CALCULATOR RESULTS"
print "INPUT VALUES:"
print " Po={0:1.1f}".format(Po),"mb"
print " To={0:1.2f}".format(To),"C"
print " Tdew={0:1.2f}".format(Tdew),"C"
print " Calculated Pressure Altitude={0:1.1f}".format(zo),"meters"
print "CONSTANT VALUES BELOW THE LCL:"
print " Potential Temperature={0:1.1f}".format(thetaK),"K ={0:1.1f}".format(thetaK-273.15),"C"
print " Water vapor mixing ratio={0:1.2e}".format(wo),"kg/kg ={0:1.2f}".format(wo*1000.0),"g/kg"
print "CONSTANT VALUE EVERYWHERE ON THE PARCEL TRAJECTORY:"
print " Equivalent Potential Temperature={0:1.1f}".format(thetaE_K),"K ={0:1.1f}".format(thetaE_K-273.15),"C"
print "WET BULB RELATED VALUES:"
print " Wetbulb Temperature={0:1.1f}".format(Tw+273.15),"K ={0:1.1f}".format(Tw),"C"
print " Wetbulb Potential Temperature={0:1.1f}".format(thetaW),"K ={0:1.1f}".format(thetaW-273.15),"C"
print "LCL VALUES:"
print " P={0:1.1f}".format(P),"mb"
print " T={0:1.1f}".format(Tc+273.15),"K ={0:1.2f}".format(Tc),"C"
print " Calculated Pressure Altitude={0:1.1f}".format(z),"meters"
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