# 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"

Water Vapor Calculator (Python v2.7.13)

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