Thermodynamics

Functions related to common atmospheric thermodynamic relationships.

IdealGas(p, t, rho, R = 287.058)

Adiabat(p, t, theta, p0 = 1e+05, kappa = 2/7)

VirtualTemperature(p, t, e, tv, epsilon = 0.622)

MixingRatio(p, e, w, epsilon = 0.622)

ClausiusClapeyron(t, es)

DewPoint(p, ws, td, epsilon = 0.622)

Arguments

p

pressure

t

temperature

rho

density

R

gas constant for air

theta

potential temperature

p0

reference pressure

kappa

ratio of dry air constant and specific heat capacity at constant pressure

e

vapour partial pressure

tv

virtual temperature

epsilon

ratio of dry air constant and vapour constant

w

mixing ratio

es

saturation vapour partial pressure

ws

saturation mixing ratio

td

dewpoint

Value

Each function returns the value of the missing state variable.

Details

IdealGas computes pressure, temperature or density of air according to the ideal gas law \(P=\rho R T\).

Adiabat computes pressure, temperature or potential temperature according to the adiabatic relationship \(\theta = T (P0/P)^\kappa\).

VirtualTemperature computes pressure, temperature, vapour partial pressure or virtual temperature according to the virtual temperature definition \(T(1 - e/P(1 - \epsilon))^{-1}\).

MixingRatio computes pressure, vapour partial temperature, or mixing ratio according to \(w = \epsilon e/(P - e)\).

ClausiusClapeyron computes saturation pressure or temperature according to the August-Roche-Magnus formula \(es = a exp{bT/(T + c)}\) with temperature in Kelvin and saturation pressure in Pa.

DewPoint computes pressure, saturation mixing ration or dew point from the relationship \(ws = \epsilon es(Td)/(p - es(Td))\). Note that the computation of dew point is approximated.

Is important to take note of the units in which each variable is provided. With the default values, pressure should be passed in Pascals, temperature and potential temperature in Kelvins, and density in \(kg/m^3\). ClausiusClayperon and DewPoint require and return values in those units.

The defaults value of the R and kappa parameters are correct for dry air, for the case of moist air, use the virtual temperature instead of the actual temperature.

References

http://www.atmo.arizona.edu/students/courselinks/fall11/atmo551a/ATMO_451a_551a_files/WaterVapor.pdf

See also

Other meteorology functions: Derivate(), EOF(), GeostrophicWind(), WaveFlux(), waves

Examples

IdealGas(1013*100, 20 + 273.15)
#> [1] 1.203788
IdealGas(1013*100, rho = 1.15) - 273.15
#> [1] 33.71118

(theta <- Adiabat(70000, 20 + 273.15))
#> [1] 324.5993
Adiabat(70000, theta = theta) - 273.15
#> [1] 20

# Relative humidity from T and Td
t <- 25 + 273.15
td <- 20 + 273.15
p <- 1000000
(rh <- ClausiusClapeyron(td)/ClausiusClapeyron(t))
#> [1] 0.7380251

# Mixing ratio
ws <- MixingRatio(p, ClausiusClapeyron(t))
w <- ws*rh
DewPoint(p, w) - 273.15    # Recover Td
#> [1] 20.01339