Type:	Package
Title:	Atmospheric Thermodynamics and Visualization
Version:	1.2.2
Date:	2025-05-05
Author:	Jon Sáenz [aut, cph], Santos J. González-Rojí [aut, cre, cph], Sheila Carreno-Madinabeitia [aut, cph], Gabriel Ibarra-Berastegi [ctb, cph]
Maintainer:	Santos J. González-Rojí <santosjose.gonzalez@ehu.eus>
Description:	Deals with many computations related to the thermodynamics of atmospheric processes. It includes many functions designed to consider the density of air with varying degrees of water vapour in it, saturation pressures and mixing ratios, conversion of moisture indices, computation of atmospheric states of parcels subject to dry or pseudoadiabatic vertical evolutions and atmospheric instability indices that are routinely used for operational weather forecasts or meteorological diagnostics.
Depends:	R (≥ 3.5.0)
License:	GPL-3
Encoding:	UTF-8
Repository:	CRAN
NeedsCompilation:	yes
Packaged:	2025-05-05 12:47:14 UTC; santi
Date/Publication:	2025-05-07 11:30:02 UTC

Atmospheric Thermodynamics and Visualization

Description

Deals with many computations related to the thermodynamics of atmospheric processes. It includes many functions designed to consider the density of air with varying degrees of water vapour in it, saturation pressures and mixing ratios, conversion of moisture indices, computation of atmospheric states of parcels subject to dry or pseudoadiabatic vertical evolutions and atmospheric instability indices that are routinely used for operational weather forecasts or meteorological diagnostics.

Unless otherwise explicitly noted (boltonTLCL and stuve_diagram) all parameters to functions must be provided in the International System of Units: P in Pa, T in K and w in kg/kg.

Author(s)

Jon Sáenz, Santos J. González-Rojí, Sheila Carreno-Madinabeitia and Gabriel Ibarra-Berastegi

Maintainer: Santos J. González-Rojí <santosjose.gonzalez@ehu.eus>

Examples

# CAPE, CIN index
data(RadiosondeA)
aPs<-RadiosondeA[,1]*100
aTs<-C2K(RadiosondeA[,3])
aws<-RadiosondeA[,6]/1000
capeCin<-CAPE_CIN(PlowTop=98000,precoolType="adiabatic",
                  Ps=aPs,Ts=aTs,ws=aws,doLog=0,deltaP=5,
                  getLiftedBack=TRUE,upToTop=TRUE)
print(min(capeCin$CAPE))


#pdf("stuve.pdf")
stuveA<-stuve_diagram(Pres = aPs/100,Temp=aTs-273.15)
lines(capeCin$Tl-273.15,capeCin$Pl/100,col="red",lwd=2)
#dev.off()

# Adiabatic Ascent
P0<-101325
T0<-273.15
w0<-0.0025
adiabEvol<-adiabatic_ascent(P0,T0,w0,50000,5)

Adiabatic Downwards Evolution

Description

Calculation of the state of an air parcel subject to an adiabatic downwards evolution, taking into account the initial conditions of the parcel (Pstart, Tstart, wstart, wcstart).

Usage

AnyAdiabaticDown(Pstart, Tstart, wstart, wcstart, Pend, deltaP)

Arguments

Details

In this case, we start from a parcel at pressure pstart (Pa), temperature tstart (K) and mixing ratio wstart (kg/kg), with potentially some condensates wcstart (kg/kg). The latent heat (L) used during the evolution depends on the Temperature (T). It is computed as described by latent_heat_H2O. As the parcel goes down it could evaporate the condensates or, if no condensates are available anymore, it will go down according to a dry adiabatic evolution by means of a dry adiabatic process until the level Pend. At this point, it will have a temperature Tend, mixing ratio (vapour) Wend and Wcend (may be still some condensates could be left) using steps of pressure dP (always positive).

Value

This function returns a list including the following values:

Examples

AnyAdiabaticDown(50000,227,8.5e-5,0.005,101325,5)
AnyAdiabaticDown(70000,237,4e-4,0.005,101325,5)

From Celsius to Kelvin degrees

Description

This function makes the transformation from Celsius to Kelvin degrees.

Usage

C2K(Tc, consts = export_constants())

Arguments

Value

A vector of temperatures in Kelvin degrees is returned.

See Also

aiRthermoConstants and K2C

Examples

data(RadiosondeD)
dTs<-RadiosondeD[,3]
C2K(dTs)

Calculation of CAPE and CIN

Description

Taking into account the data obtained in a radiosonde, and after defining the initial values of the parcel, this function calculates the values of CAPE and CIN for the sounding.

Usage

CAPE_CIN(Ps, Ts, ws, deltaP = 5, P0 = NA, T0 = NA, w0 = NA, PlowTop = NA, 
precoolType = "none", doLog = 0, getLiftedBack = FALSE, upToTop = TRUE, 
checkBuoyancy = 0)

Arguments

Details

CAPE and CIN (J/kg) are calculated from a sounding given by 1D arrays for pressure Ps (Pa), for temperature Ts (K) and for mixing ratio ws (kg/kg).

If P_0/T_0/w_0 are provided, no low vertical averaging is done and these values are used as initial points for the parcel. Missing value is used by default for these arguments.

This function returns some error codes in field outCode in the return value if the computation of CAPE and CIN failed.

Value

Returns:

Examples

data(RadiosondeA)
aPs<-RadiosondeA[,1]*100
aTs<-C2K(RadiosondeA[,3])
aws<-RadiosondeA[,6]/1000
capeCin<-CAPE_CIN(PlowTop=98000,precoolType="adiabatic",
                  Ps=aPs,Ts=aTs,ws=aws,doLog=0,deltaP=5,
                  getLiftedBack=TRUE,upToTop=TRUE)
print(min(capeCin$Tl))

#pdf("stuve.pdf")
stuveA<-stuve_diagram(Pres = aPs/100,Temp=aTs-273.15)
lines(capeCin$Tl-273.15,capeCin$Pl/100,col="red",lwd=2)
#dev.off()

From Kelvin to Celsius degrees

Description

This function makes the transformation from Kelvin degrees to Celsius.

Usage

K2C(Tk, consts = export_constants())

Arguments

Value

This function returns a vector of temperatures in Celsius degrees.

See Also

aiRthermoConstants and C2K

Examples

data(RadiosondeD)
dTs<-RadiosondeD[,3]
K2C(C2K(dTs))

K Instability Index

Description

This function calculates the K instability index (Celsius) from a sounding given by the measured arrays pressure Ps (Pa) temperature Ts (K) and mixing ratio ws (kg/kg).

Usage

Kindex(Ps, Ts, ws, doLog = 0)

Arguments

Details

If needed levels (850, 700 and 500 hPa) are not found in the input sounding (without extrapolation), the function returns -99999999.

Use/do not use logarithmic interpolation in pressure (if needed because mandatory levels such as 700 hPa or 500 hPa are not given in the sounding) when finding the requested levels.

Value

This function returns the K index.

Examples

data(RadiosondeA)
aPs<-RadiosondeA[,1]*100
aTs<-C2K(RadiosondeA[,3])
aws<-RadiosondeA[,6]/1000
aK<-Kindex(aPs,aTs,aws,0)

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
dws<-RadiosondeD[,6]/1000
dK<-Kindex(dPs,dTs,dws,0)

Lifted index

Description

This function calculates the instability parameter Lifted index (Celsius) from pressure, temperature and mixing ratio values described by a vertical sounding.

Usage

LIindex(Ps, Ts, ws, Psurface, deltaP, PWIDTH, doLog = 0)

Arguments

Details

If the 500 hPa needed level is not exactly found in the input sounding, logarithmic/linear vertical interpolation is run to get the corresponding T/w from the Ps/Ts/ws depending on the value of doLog 0/1.

The evolution of the lifted particle is computed by integrating the dT/dP ordinary differential equation (applying the Runge-Kutta 4th order method), that represents the vertical adiabatic evolution from the initial condition to 500 hPa using a pressure step deltaP (Pa). The vertical adiabatic evolution is either dry (before saturation) or pseudoadiabatic at every vertical step with a correction for moisture in c_p using the value of the mixing ratio (c_{pm} as in Tsonis, eq 7.11).

If the sounding does not enclose the needed level of 500 hPa and the interpolation fails, the function returns -99999999.

Value

This function returns the LI index (Celsius).

References

Tsonis, A. A. (2002). An Introduction to Atmospheric Thermodynamics, Cambridge University Press, Cambridge. Eq. 7.11.

Examples

data(RadiosondeA)
aPs<-RadiosondeA[,1]*100
aTs<-C2K(RadiosondeA[,3])
aws<-RadiosondeA[,6]/1000
LIindex(aPs,aTs,aws,max(aPs),5,2500,0)

Potential Temperature from pressure and temperature

Description

This function calculates the potential temperature from given temperature and pressure.

Usage

PT2Theta(P, Temp, w = 0, consts = export_constants())

Arguments

Value

This function returns a vector with potencial temperature. Mixing ratio is only used to correct the value of c_p, not to calculate a moist adiabatic evolution.

See Also

moistCp

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
dThetas=PT2Theta(dPs,dTs)

Temperature from pressure and potential temperature

Description

This function calculates the temperature from a given pressure and potential temperature.

Usage

PTheta2T(P, Theta, w = 0, consts = export_constants())

Arguments

Value

This function returns a vector with temperatures (K).

See Also

moistCp

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
dThetas=PT2Theta(dPs,dTs)
PTheta2T(dPs,dThetas)

Vertically integrated water vapour column

Description

This function calculates the vertically integrated water vapour column integrating in pressure vertical coordinates.

Usage

PW(w, PRES, Psurf, consts = export_constants())

Arguments

Value

This function returns the vertically integrated water vapour column.

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dws<-RadiosondeD[,6]/1000
PW(dws,dPs,dPs[1])

Radiosonde A

Description

Contains the information measured by a sounding in Santander (Station 08023) in 2010, June 16th at 12:00 UTC. It was not a really unstable day but a great amount of (large scale) precipitation was measured.

Usage

data("RadiosondeA")

Format

A data frame with 74 observations on the following 11 variables.

V1

a vector with pressure values (hPa).

V2

a vector with height (m).

V3

a vector with temperature values (Celsius).

V4

a vector with dew point temperature values (Celsius).

V5

a vector with relative humidity values (%).

V6

a vector with mixing ratio values (g/kg).

V7

a vector with wind direction values (degrees).

V8

a vector with wind speed values (knots).

V9

a vector with potential temperature (K).

V10

a vector with equivalent potential temperature (K).

V11

a vector with virtual potential temperature (K).

See Also

RadiosondeD and RadiosondeDavenport

Examples

data(RadiosondeA)
#Calculate the pressure in Pa
RadiosondeA$V1*100

#Calculate the temperature in K
C2K(RadiosondeA$V3)

Radiosonde D

Description

Contains the information measured by a sounding in Barcelona (station 05190) in 2013, August 7th at 12:00 UTC. According to the university of Wyoming, the CAPE was higher than 3000 J/kg and a great amount of (convective) precipitation was measured.

Usage

data("RadiosondeD")

Format

A data frame with 70 observations on the following 11 variables.

V1

a vector with pressure values (hPa).

V2

a vector with height (m).

V3

a vector with temperature values (Celsius).

V4

a vector with dew point temperature values (Celsius).

V5

a vector with relative humidity values (%).

V6

a vector with mixing ratio values (g/kg).

V7

a vector with wind direction values (degrees).

V8

a vector with wind speed values (knots).

V9

a vector with potential temperature (K).

V10

a vector with equivalent potential temperature (K).

V11

a vector with virtual potential temperature (K).

See Also

RadiosondeA and RadiosondeDavenport

Examples

data(RadiosondeD)
#Calculate the pressure in Pa
RadiosondeD$V1*100

#Calculate the temperature in K
C2K(RadiosondeD$V3)

Radiosonde Davenport

Description

Contains the information measured by a sounding in Davenport (station 74455) in 1997, June 21st at 00:00 UTC. That day was a very unstable situation.

Usage

data("RadiosondeDavenport")

Format

A data frame with 67 observations on the following 11 variables.

V1

a vector with pressure values (hPa).

V2

a vector with height (m).

V3

a vector with temperature values (Celsius).

V4

a vector with dew point temperature values (Celsius).

V5

a vector with relative humidity values (%).

V6

a vector with mixing ratio values (g/kg).

V7

a vector with wind direction values (degrees).

V8

a vector with wind speed values (knots).

V9

a vector with potential temperature (K).

V10

a vector with equivalent potential temperature (K).

V11

a vector with virtual potential temperature (K).

See Also

RadiosondeA and RadiosondeD

Examples

data(RadiosondeDavenport)
#Calculate the pressure in Pa
RadiosondeDavenport$V1*100

#Calculate the temperature in K
C2K(RadiosondeDavenport$V3)

Showalter Instability Index

Description

This function computes Showalter instability index (Celsius) from given parameters from a vertical sounding pressure (Pa), temperature (K) and mixing ratio (kg/kg).

Usage

Sindex(Ps, Ts, ws, deltaP, doLog = 0)

Arguments

Details

If the needed levels (850 hPa or 500 hPa) are not exactly found in the input sounding, logarithmic/linear vertical interpolation is run to get the corresponding T/w from the Ps/Ts/ws depending on the value of doLog (TRUE or FALSE).

The evolution of the lifted particle is computed by integrating the dT/dP ordinary differential equation (applying the Runge Kutta 4th order method) that represents the vertical adiabatic evolution from 850 hPa to 500 hPa using a pressure step dP > 0 (Pa). The vertical adiabatic evolution is either dry (before saturation) or pseudoadiabatic at every vertical step with a correction for moisture in the specific heat at constant pressure c_p during the dry steps (as in Tsonis, eq 7.11).

If the sounding does not enclose the needed levels and the interpolation fails, the function returns -99999999.

Value

This function returns the Showalter instability index (Celsius).

References

Djuric D. (1994). Weather Analysis, Prentice Hall, New Jersey.

See Also

LIindex

Examples

data(RadiosondeA)
aPs<-RadiosondeA[,1]*100
aTs<-C2K(RadiosondeA[,3])
aws<-RadiosondeA[,6]/1000
S<-Sindex(aPs,aTs,aws,5,0)

Relative Humidity from temperature, pressure and dew point temperature

Description

This function calculates the relative humidity from given temperature, dew point temperature and pressure.

Usage

TTdP2rh(Temp, Td, P, consts = export_constants())

Arguments

Value

This function returns a vector with relative humidity values.

See Also

saturation_mixing_ratio

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
dws<-RadiosondeD[,6]/1000
dTds<-w2Td(dPs,dws)
rhs<-TTdP2rh(dTs,dTds,dPs)

Pressure from temperature and potential temperature

Description

This function calculates the pressure from given potential temperature and temperature, assuming a dry adiabatic evolution (mixing ratio is only used to correct the values of c_p).

Usage

TTheta2P(Temp, Theta, w = 0, consts = export_constants())

Arguments

Value

This function returns a vector with pressure values.

Examples

	data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
dws<-RadiosondeD[,6]/1000
dTds<-w2Td(dPs,dws)
dThetas<-PT2Theta(dPs,dTs)
TTheta2P(dTs,dThetas)

Total-Totals Instability Index

Description

Total-Totals instability index (Celsius) from parameters (1D arrays) Ps (pressure, Pa) Ts (temperature, Kelvin) and ws (mixing ratio, kg/kg) obtained from a vertical sounding.

Usage

TTindex(Ps, Ts, ws, doLog = 0)

Arguments

Details

If the needed levels (850 hPa or 500 hPa) are not exactly found in the input sounding, logarithmic/linear vertical interpolation is run depending on the value of doLog (TRUE or FALSE).

If the sounding does not enclose the needed levels and the interpolation fails, the function returns -99999999.

Value

This function returns the Total-Totals instability index (Celsius).

Examples

data(RadiosondeDavenport)
aPs<-RadiosondeDavenport[,1]*100
aTs<-C2K(RadiosondeDavenport[,3])
aws<-RadiosondeDavenport[,6]/1000
aTT<-TTindex(aPs,aTs,aws,0)

Properties of an air parcel after adiabatic ascent

Description

A particle located at Pstart pressure (Pa), Tstart temperature (K) and wstart mixing ratio (kg/kg) ascends (pseudo)adiabatically to Pend (Pa). The evolution is computed by numerically integrating the dT/dP ordinary differential equation (ODE) using a 4th order Runge-Kutta scheme, assuming hydrostatic equilibrium and that the particle is saturated after the Lifted Condensation Level (LCL).

Usage

adiabatic_ascent(Pstart, Tstart, wstart, Pend, deltaP = 1)

Arguments

Value

The function returns a list that includes Tend (final value of temperature) and mixRatioEnd (mixing ratio of the air parcel at the end of the evolution).

Examples

P0<-101325
T0<-273.15
w0<-0.0025
adiabEvov<-adiabatic_ascent(P0,T0,w0,50000,5)

Thermodynamical Constansts

Description

Frecuently used constants in atmospheric thermodynamics and in this package.

Usage

data(aiRthermoConstants)

Format

aiRthermoConstants is a vector that includes the constants used by many of the functions in package.

Details

The constants stored in the vector are (in SI units): the gas constant for dry air R_d and for water vapour R_v (\frac{J}{Kkg}), the temperature T_0 corresponding to 0 degree Celsius, es_0 used to calculate the saturated vapour pressure (Pa), 1000 hPa in Pa (P1000), the specific heat of dry air for constant pressure c_p (\frac{J}{Kkg}) and for constant volume c_v (\frac{J}{Kkg}), acceleration due to gravity at sea level g (\frac{m}{s^2}), our definition of a missing value MISSING_VALUE (-99999999) and epsilon \varepsilon (\frac{R_d}{R_v}).

The values of the constants are taken from Bohren & Albrecht (1998), and they are also consistent with those used in Petty (2008), Erukhimova & North (2009) and Davies-Jones (2009).

References

Bohren, C.F., & Albrecht, B. A. (1998). Atmospheric thermodynamics. Atmospheric thermodynamics. Publisher: New York; Oxford: Oxford University Press, 1998. ISBN: 0195099044.

Petty, G.W. (2008). A First Course in Atmospheric Thermodynamics, Sundog Publishing, Madison.

North, G. R. , Erukhimova,T. L. (2009). Atmospheric Thermodynamics, Cambridge University Press, New York.

Davies-Jones, R. (2009). On formulas for equivalent potential temperature, Monthly Weather Review, 137,3137-3148. doi:10.1175/2009MWR2774.1.

Examples

#Define the Rd
data(aiRthermoConstants)
Rd <- aiRthermoConstants['Rd']

#Define gravity
data(aiRthermoConstants)
g <- aiRthermoConstants['g'] 

Find the Temperature at the Lifting Condensation Level (LCL)

Description

This function is used to calculate the Temperature at the Lifting Condensation Level (LCL) using Bolton's approximation instead of integrating the Ordinary Differential Equation (ODE) upwards.

Usage

boltonTLCL(TempCelsius, rh, consts = export_constants())

Arguments

Value

This function calculates an approximation of the temperature in degrees Celsius corresponding to the LCL.

References

Bolton, D. (1980). The computation of equivalent potential temperature, Monthly Weather Review 108, 1046-1053. doi:10.1175/1520-0493(1980)108<1046:TCOEPT>2.0.CO;2.

Examples

T0=273.15
rh=66.25489
boltonTLCL(T0,rh)

Brunt-Vaisalla (angular) frequency (squared)

Description

Brunt-Vaisalla (angular) frequency (aquared, s^{-2}) considering hydrostatic equilibrium. P is used as a vertical level.

Usage

bruntVaisallaOmegaSquared(Ps, Ts, ws, consts = export_constants())

Arguments

Details

The angular frequency (squared, s^{-2}) is returned in order to avoid complex numbers.

Value

The Brunt-Vaisalla (angular) frequency (squared) is returned.

Note

For stable atmospheres, should be positive at every level. Ps, Ts and ws are 1D arrays.

See Also

PT2Theta and densityMoistAir are used inside bruntVaisallaOmegaSquared function.

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
dws<-RadiosondeD[,6]/1000
bruntVaisallaOmegaSquared(dPs,dTs,dws)

Density of Dry Air

Description

From pressure P (Pa) and temperature Temp (K), this funtion calculates the density of dry air in kg/m^3.

Usage

densityDry(P, Temp, consts = export_constants())

Arguments

Value

A vector with density of dry air values is returned (kg/m^3).

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
densityDry(dPs,dTs)

Density of water vapour

Description

From pressure of water vapour Pw (Pa) and temperature Temp (K), this function calculates density of water vapour (kg/m^3).

Usage

densityH2Ov(Pw, Temp, consts = export_constants())

Arguments

Value

A vector with density of water vapour values is returned (kg/m^3).

See Also

q2e and w2q

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
dws<-RadiosondeD[,6]/1000
h2oe<-q2e(dPs,w2q(dws))
densityH2Ov(h2oe,dTs)

Density of Moist Air

Description

From pressure P (Pa) temperature Temp (K) and mixing ratio (kg/kg), this function calculates the density of moist air (kg/m^3).

Usage

densityMoistAir(P, Temp, w, consts = export_constants())

Arguments

Value

A vector with density of moist air values is returned (kg/m^3).

See Also

virtual_temperature

Examples

data(RadiosondeA)
aPs<-RadiosondeA[,1]*100
aTs<-C2K(RadiosondeA[,3])
aws<-RadiosondeA[,6]/1000
densityMoistAir(aPs,aTs,aws)

Relative Humidity from the dew point depression

Description

This function calculates the relative humidity (%) from the dew point depression (K).

Usage

dewpointdepression2rh(P, Temp, dpd, consts = export_constants())

Arguments

Value

A vector with relative humidity (%).

See Also

saturation_mixing_ratio and saturation_pressure_H2O

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
dws<-RadiosondeD[,6]/1000
dTds=w2Td(dPs,dws)
dDPDs=dTs-dTds
dewpointdepression2rh(dPs,dTs,dDPDs)

Compute Mixing Ratio from partial pressure of water vapour

Description

This function calculates the mixing ratio (kg/kg) from the partial vapour pressure of water vapour (Pa).

Usage

e2w(eh2o, P, consts = export_constants())

Arguments

Value

A vector with mixing ratio values.

Examples

	
	
#Partial pressure of water vapour
data(RadiosondeA)
dPs<-RadiosondeA[,1]*100
dws<-RadiosondeA[,6]/1000
eh2o<-q2e(dPs,w2q(dws))
#Pressure
e2w(eh2o,dPs)

Equivalent Potential Temperature

Description

This function calculates the equivalent potential temperature (K), following the techniques used in Davies-Jones (2009).

Usage

equivalentPotentialTemperature(P, Temp, w, TLCL, consts = export_constants())

Arguments

Value

This function returns the value of the equivalent potential temp (K).

References

Davies-Jones, R. (2009). On formulas for equivalent potential temperature. Monthly Weather Review, 137(9), 3137-3148.

See Also

PT2Theta and moistCp

Examples

data(RadiosondeA)
aPs<-RadiosondeA[,1]*100
aP0<-aPs[1]
aT0<-C2K(RadiosondeA[1,3])
aw0<-RadiosondeA[1,6]/1000
deltaP=1
Na=length(aPs)
Ptop=aPs[Na]
fndlcl=find_lcl(Ptop,aP0,aT0,aw0,deltaP)
TLCL=fndlcl$Tlcl
equivalentPotentialTemperature(aP0,aT0,aw0,TLCL)

Export the constants

Description

This function exports to R the constants frecuently used in the C part of aiRthermo for consistency.

Usage

export_constants()

Details

The constants stored in the vector are (in SI units): the gas constant for dry air R_d and for water vapour R_v (\frac{J}{Kkg}), the temperature T_0 corresponding to 0 degree Celsius, es_0 used to calculate the saturated vapour pressure (Pa), 1000 hPa in Pa (P1000), the specific heat of dry air for constant pressure c_p (\frac{J}{Kkg}) and for constant volume c_v (\frac{J}{Kkg}), acceleration due to gravity at sea level g (\frac{m}{s^2}), our definition of a missing value MISSING_VALUE (-99999999) and epsilon \varepsilon (\frac{R_d}{R_v}).

Constants are taken from Bohren & Albrecht (1998), and they are also consistent with those used in Petty (2008), Erukhimova & North (2009) and Davies-Jones (2009).

References

Bohren, C.F., & Albrecht, B. A. (1998). Atmospheric thermodynamics. Atmospheric thermodynamics. Publisher: New York; Oxford: Oxford University Press, 1998. ISBN: 0195099044.

Petty, G.W. (2008). A First Course in Atmospheric Thermodynamics, Sundog Publishing, Madison.

North, G. R. , Erukhimova,T. L. (2009). Atmospheric Thermodynamics, Cambridge University Press, New York.

Davies-Jones, R. (2009). On formulas for equivalent potential temperature, Monthly Weather Review, 137,3137-3148. doi:10.1175/2009MWR2774.1.

See Also

aiRthermoConstants

Examples

aiRthermoConstants<-export_constants()

Export the lines for the thermodynamic diagram

Description

This function exports the fixedlines for Stüve Diagram. It includes the data for plotting the pseudoadiabatic (adiabat_*_T), dry adiabatic (theta_*_T) and constant mixing ratio lines (wsat_*_T).

Usage

export_lines()

See Also

fixedlines

Examples

data(RadiosondeA)
aPs<-RadiosondeA[,1]*100
aTs<-C2K(RadiosondeA[,3])
stuveA<-stuve_diagram(Pres = aPs/100,Temp=aTs-273.15)

Calculation of the Lifted Condensation Level (LCL)

Description

For a particle with initial conditions P_0, T_0 and w_0, this function performs an adiabatic vertical evolution until it gets saturated at most when Ptop is reached.

Usage

find_lcl(Ptop, P0, T0, w0, deltaP)

Arguments

Value

Returns a list including the following values:

Examples

Ptop=50000
P0=101325
T0=273.15
w0=0.0025
deltaP=5
rh=100*w0/saturation_mixing_ratio(P0,T0,export_constants())
fndlcl=find_lcl(Ptop,P0,T0,w0,deltaP)

Data for plotting the lines of the thermodynamic (STUVE) diagram

Description

The vectors included in the list are: both components of the pseudoadiabatic lines (adiabatic_x_T, and adiabatic_y_T), labels of the pseudoadiabatic lines (adiabatic_z_T), both components of the dry adiabatic lines (theta_x_T and theta_y_T), both components of the constant mixing ratio lines (wsat_x_T and wsat_y_T) and their labels (wsat_z_T). The X components are provided in Celsius and the Y components in hPa.

Usage

data(fixedlines)

Details

The pseudoadiabatic lines were calculated by the authors for this R-package following pseudoadiabatic evolutions from 1050 hPa.

The dry adiabatic lines were obtained using the functions in aiRthermo for different initial conditions and for a fixed set of initial potential temperatures. A similar procedure was applied on the calculation of the constant mixing ratio lines, starting from different values of saturation mixing ratio.

Source

The data were calculated by the authors for this R-package.

See Also

export_lines

Examples

data(fixedlines)

Saturated Adiabat Gamma

Description

Saturated adiabat at the points of the sounding as computed internally, considering hydrostatic balance and as \frac{dT}{dP} (in pressure levels) (K/Pa).

Usage

gamma_saturated(Ps, Temps)

Arguments

Value

This function returns the vertical derivate \Gamma _s= \frac{dT}{dP} \Big|_s for a saturated adiabatic evolution.

Examples

data(RadiosondeA)
aPs<-RadiosondeA[,1]*100
aTs<-C2K(RadiosondeA[,3])
gamma_saturated(aPs,aTs)

Latent heat of vaporization or sublimation of water

Description

This function calculates the latent heat of vaporization or sublimation of water depending as a function of temperature. It uses a polynomial approximation over water or ice.

Usage

latent_heat_H2O(Temps)

Arguments

Details

Taking into account the observed values in tables from Rogers and Yau (1989) and Feistel and Wagner (2006), a polynomial model is used to calculate the latent heat at different temperatures.

Value

This function returns the latent heat of vaporization or sublimation of water.

References

Rogers, R. R., and Yau, M. K. (1989). A Short Course in Cloud Physics, 3rd Edition, Pergamon Press, Oxford.

Feistel, R. and Wagner, W. (2006). A new equation of state for H2O ice Ih, Journal of Physical and Chemical Reference Data 35 1021-1047. doi:10.1063/1.2183324.

Examples

data(RadiosondeA)
aTs<-C2K(RadiosondeA[,3])
latent_heat_H2O(aTs) 

Moist Adiabatic Lapse Rate

Description

This function calculates the moist adiabatic lapse rate according to a provided mixing ratio (kg/kg) (Tsonis, eq 7.29).

Usage

moistAdiabaticLapseRate(w, consts = export_constants())

Arguments

Value

This function returns a vector with the moist adiabatic lapse rate (dry adiabatic lapse rate with correction of c_p due to the water vapour in moist air).

References

Tsonis, A. A. (2002). An Introduction to Atmospheric Thermodynamics, Cambridge University Press, Cambridge. Eq. 7.29.

Examples

data(RadiosondeA)
aws<-RadiosondeA[,6]/1000
moistAdiabaticLapseRate(aws)

Moist Cp

Description

This function corrects the value of dry c_p due to the existence of water vapour acording to equation 7.11 from Tsonis (2002).

Usage

moistCp(w, consts = export_constants())

Arguments

Value

This function returns the value of dry c_p corrected by the mixing ratio.

References

Tsonis, A. A. (2002). An Introduction to Atmospheric Thermodynamics, Cambridge University Press, Cambridge. Eq. 7.11.

See Also

w2q and moistCv

Examples

data(RadiosondeD)
dws<-RadiosondeD[,6]/1000
moistCp(dws)

Moist cv value

Description

This function is similar to moistCp but for c_v. In this case, it is the value of c_v corrected due to the existence of water vapour (equation 7.12) from Tsonis (2002).

Usage

moistCv(w, consts = export_constants())

Arguments

Value

This function returns the value of c_v corrected due to the existence of water vapour.

References

Tsonis, A. A. (2002). An Introduction to Atmospheric Thermodynamics, Cambridge University Press, Cambridge. Eq. 7.12.

See Also

w2q and moistCp

Examples

data(RadiosondeD)
dws<-RadiosondeD[,6]/1000
moistCv(dws)

State of a parcel

Description

The function calculates the state of a parcel for easier computations.

Usage

parcelState(Press, Temp, w = 0, consts = export_constants())

Arguments

Value

This function returns a list including the following values:

See Also

PT2Theta, virtual_temperature and saturation_mixing_ratio

Examples

parcelState(101325,273.15,0.2)

Partial Vapour Pressure

Description

This function calculates the partial vapour pressure from specific humidity.

Usage

q2e(P, q, consts = export_constants())

Arguments

Value

This function returns the value of the partial vapour pressure (Pa).

Examples

# Get partial pressure of water vapour
data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dws<-RadiosondeD[,6]/1000
h2oe<-q2e(dPs,w2q(dws))

Water vapour mixing Ratio to specific humidity

Description

This function calculates the water vapour mixing ratio (kg/kg) from specific humidity (kg/kg).

Usage

q2w(q)

Arguments

Value

This function returns a vector with mixing ratio values in kg/kg.

Examples

data(RadiosondeD)
dws<-RadiosondeD[,6]/1000
q2w(w2q(dws))

Specific Humidity from relative humidity

Description

This function calculates the specific humidity from a given relative humidity.

Usage

rh2shum(P, Temp, rh, consts = export_constants())

Arguments

Value

This function returns a vector with specific humidity (kg/kg).

See Also

rh2shum

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
dws<-RadiosondeD[,6]/1000
dTds<-w2Td(dPs,dws)
rhs<-TTdP2rh(dTs,dTds,dPs)
rh2shum(dPs,dTs,rhs)

Mixing Ratio from relative humidity

Description

This function gets the mixing ratio (kg/kg) from a given relative humidity (%), pressure (Pa) and temperature (K).

Usage

rh2w(P, Temp, rh, consts = export_constants())

Arguments

Value

This function returns a vector with mixing ratio values (kg/kg).

See Also

saturation_mixing_ratio

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
dws<-RadiosondeD[,6]/1000
dTds<-w2Td(dPs,dws)
rhs<-TTdP2rh(dTs,dTds,dPs)
wfromrh<-rh2w(dPs,dTs,rhs)

Saturation Mixing Ratio

Description

This function calculates the saturation mixing ratio from a given temperature and pressure.

Usage

saturation_mixing_ratio(P, Temp, consts = export_constants())

Arguments

Value

This function returns a vector with saturation mixing ratio values (kg/kg).

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
saturation_mixing_ratio(dPs,dTs)

Saturation Pressure

Description

This function returns the saturation pressure (Pa) from a given array of temperatures (K). It uses approximate equations 5.67 and 5.70 in Bohren Albrecht, 1998.

Usage

saturation_pressure_H2O(Temps)

Arguments

Details

Saturation pressure of water vapour e_s is computed over ice/water depending whether the temperature is over/under 273.15 K (0 degree Celsius) at every element of the array.

Value

This function returns a vector with saturation pressure values (Pa).

References

Bohren, C.F., & Albrecht, B. A. (1998). Atmospheric thermodynamics. Atmospheric thermodynamics. Publisher: New York; Oxford: Oxford University Press, 1998. ISBN: 0195099044. Equations 5.67 and 5.70.

Examples

data(RadiosondeA)
aTs<-C2K(RadiosondeA[,3])
esats<-saturation_pressure_H2O(aTs)

Thermodynamic (STUVE) Diagram

Description

This function generates an Stüve diagram.

Usage

stuve_diagram(Pres, Temp, TempD = NA, XLIM = c(-80, 45), YLIM = c(1050, 100), 
col.lines = NULL, lty.lines = NULL, lwd.lines = NULL)

Arguments

Details

It is possible to add extra lines and to save as a pdf, jpeg or png (see examples).

Value

The result is a plot object.

Examples

data(RadiosondeA)
aPs<-RadiosondeA[,1]*100
aTs<-C2K(RadiosondeA[,3])
aws<-RadiosondeA[,6]/1000
capeCin<-CAPE_CIN(PlowTop=98000,precoolType="adiabatic",
                  Ps=aPs,Ts=aTs,ws=aws,doLog=0,deltaP=5,
                  getLiftedBack=TRUE,upToTop=TRUE)

#How to add a line to the plot
stuveA<-stuve_diagram(Pres = aPs/100,Temp=aTs-273.15)
lines(capeCin$Tl-273.15,capeCin$Pl/100,col="blue",lwd=2)

Virtual Temperature

Description

This function calculates the virtual temperature from given pressure and mixing ratio.

Usage

virtual_temperature(P, Temp, w, consts = export_constants())

Arguments

Value

This function returns a vector with virtual temperature values.

See Also

q2e

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dTs<-C2K(RadiosondeD[,3])
dws<-RadiosondeD[,6]/1000
virtual_temperature(dPs,dTs,dws)

Dew point temperature from mixing ratio

Description

This function calculates the dew point temperature from given mixing ratio and pressure, following the APPROXIMATE expression 5.68 in Bohren and Albrech (1998).

Usage

w2Td(P, w, consts = export_constants())

Arguments

Value

This function returns a vector with the dew point temperature.

References

Bohren, C.F., & Albrecht, B. A. (1998). Atmospheric thermodynamics. Atmospheric thermodynamics. Publisher: New York; Oxford: Oxford University Press, 1998. ISBN: 0195099044. Equation 5.68.

Examples

data(RadiosondeD)
dPs<-RadiosondeD[,1]*100
dws<-RadiosondeD[,6]/1000
w2Td(dPs,dws)

Specific Humidity from mixing ratio

Description

This function calculates the specific humidity from a given Water mixing ratio.

Usage

w2q(w)

Arguments

Value

The function returns a vector with the specific humidity.

Examples

data(RadiosondeD)
dws<-RadiosondeD[,6]/1000
w2q(dws)