How can I calculate Vapor Pressure Deficit from Temperature and Relative Humidity?

Question

I have a series of measurements of temperature and relative humidity (RH), together with mosquito capture data. Because mosquitoes are sensitive to desiccation, it's reasonable that RH may be useful in predicting their activity. But I recently heard of a value called saturation deficit or vapor pressure deficit which has been well correlated with evapotranspiration in plant leaves.

Is it accurate to say saturation deficit is the "perceived dryness" or "drying power" of the air?

Can saturation deficit be calculated directly from temperature and RH? Is it dependent on elevation, air pressure or anything else (all measurements are <600m above sea level).

How do we calculate it? I have found two methods online which give wildly different results.

Answer 1

From [The ASCE Standardized Reference Evapotranspiration Equation]1

Given T is temperature in degrees Celsius, and RH is relative humidity:

Saturation Vapor Pressure (es) =

0.6108 * exp(17.27 * T / (T + 237.3))

Actual Vapor Pressure (ea) =

RH / 100 * es 

Vapor Pressure Deficit =

ea - es

Why this is a meaningful measurement: "The strain under which an organism is placed in maintaining a water balance during temperature changes is much more clearly shown by noting the vapor pressure deficit than by recording the relative humidity." Anderson, D. B. 1936. Relative humidity or vapor pressure deficit. Ecology 17, no. 2: 277–282.

Answer 2

From Dennis Hartman "Global Physical Climatology" (p 350)

---

Given relative humidity in percent ($RH$) and temperature in Kelvin ($K$):

First, calculate saturation vapor pressure, $e_s$ in millibars (mb):

$$e_s= 6.11*exp\left( \frac{L}{R_v}\left(\frac{1}{273} - \frac{1}{T}\right) \right)$$

Where $L$ is the latent heat of vaporization, $2.5\times10^6\text{ J kg}^{-1}$, $R_v$ is the gas constant for water vapor ($461 \text{ J K}^{-1}\text{kg}^{-1}$.

Then calculate vapor pressure deficit, $vpd$, which is the difference between the saturation vapor pressure and the actual vapor pressure:

$$vpd = e_s*(100-RH)/100$$

Here are two functions written in R that will do this:

get.es <- function(temp){
  es <- 6.11 * exp((2.5e6 / 461) * (1 / 273 - 1 / (273 + temp)))
  return(es)
}

get.vpd <- function(rh, temp){
  ## calculate saturation vapor pressure
  es <- get.es(temp)
  ## calculate vapor pressure deficit
  vpd <- ((100 - rh) / 100) * es
  return(vpd)
}

And to test them out, you can plot the relationship between temperature and es (black) and at 50% RH, for example (in red):

temp <- -30:30
plot(temp, get.es(temp), type = "l", xlab = "T", ylab = "es or vpd")
lines(temp, get.vpd(50, temp), col = "red")

Answer 3

After checking the reference James suggested:

Allen, RG, Pereira, LS, Raes, D, Smith, M (1998) Meteorological data, Chapter 3. In: Crop evapotranspiration - Guidelines for computing crop water requirements. Food and Agricuture Organization (FAO) Irrigation and Drainage Paper 56. United Nations, FAO, Rome, Italy. Available from http://www.fao.org/docrep/x0490e/x0490e07.htm#calculation%20procedures

I found that, in the reference, it is less recommended to calculate Actual vapour pressure (ea) using mean relative humidity (as the get.ea function)

# function suggested by James 
# Calculate actual vapor pressure (ea)
get.ea <- function(rh, tmin, tmax){
  esm <- get.esm(tmin, tmax)
  ea <- (rh/100) * esm
  return(ea)
}

according to the reference http://www.fao.org/docrep/x0490e/x0490e07.htm#calculation%20procedures, Eq. 17, ea = [e°(Tmin) RHmax/100 + e°(Tmax) RHmin/100]/2, it is recommended to derive ea from maximum and minimum relative humidity rather than from the mean relative humidity.

therefore, the function get.ea can be modified as follows.

# reference http://www.fao.org/docrep/x0490e/x0490e07.htm#calculation%20procedures, Eq. 17 
# Calculate actual vapor pressure (ea)
# based on maximum and minimum relative humidity

get.ea <- function(rhmin, rhmax, tmin, tmax){
  esmn <- get.esmn(tmin) # other fun same as James suggested
  esmx <- get.esmx(tmax) 
  ea <- (esmn * rhmax/100 + esmx * rhmin/100) / 2
  return(ea)
}

Except for the modification of get.ea, the other functions are same as James suggested.

Answer 4

By the name I think it is simply the difference between vapor pressure at saturation and the actual vapor pressure. The later should simply be the relative humidity times the vapor pressure at saturation. You should be able to find some tables (or formulas for vapor pressure as a function of temperature). You can look up vapor pressure in Wikipedia. They give a formula they call the Antoine equation. Also more theoretically you could look at the Clausius-Clapeyron equation, but I think it would be easier just to plug in the Antoine equation instead.

Answer 5

R Code for calculating Vapor Pressure Deficit (kPa) from temperature and relative humidity using equations from Allen et al. (1998)

Vapor Pressure Deficit (VPD) = Saturation Vapor Pressure (ES) – Actual Vapor Pressure (EA). Below is R code for estimating VPD using mean minimum and maximum monthly temperatures and mean monthly relative humidity according to Allen et al. (1998). I have used a VPD index for calculating the Growing Season Index of Jolly et al. (1995) for a variable in ecological niche modeling.

Allen, RG, Pereira, LS, Raes, D, Smith, M (1998) Meteorological data, Chapter 3. In: Crop evapotranspiration - Guidelines for computing crop water requirements. Food and Agricuture Organization (FAO) Irrigation and Drainage Paper 56. United Nations, FAO, Rome, Italy. Available from http://www.fao.org/docrep/x0490e/x0490e00.htm#Contents (Accessed 11 June 2014)

Jolly, WM, Nemani, R, Running, SW (2005) A generalized, bioclimatic index to predict foliar phenology in response to climate. Glob Chang Biol 11:619–632

Calculate Vapor Pressure Deficit (in KPa, Kilopaschals) in R according to equations of Allen et al. (1998) for Example 5 using mean monthly minimum (tmin) and maximum (tmax) temperatures (Celsius) and mean monthly pecent relative humidity (rh, 100 = 100%): [http://www.fao.org/docrep/x0490e/x0490e07.htm#chapter 3 meteorological data]

Declare in R values of three required environmental variables from Example 5 of Allen et al. (1998)

tmin <- 18 tmax <- 25 rh <- 68

Using rh = 68 as mean of 82% and 54% rh in example; so, final vpd value will not exactly match example

Calculate saturation vapor pressure for mean minimum monthly temperature (esmn)

get.esmn <- function(tmin){ esmn <- .6108 * exp((17.27 * tmin) / (tmin + 237.3)) return(esmn) }

Calculate saturation vapor pressure for mean maximum monthly temperature (esmx)

get.esmx <- function(tmax){ esmx <- .6108 * exp((17.27 * tmax) / (tmax + 237.3)) return(esmx) }

Calculate mean saturation vapor pressure (esm)

get.esm <- function(tmin, tmax){ esmn <- get.esmn(tmin) esmx <- get.esmx(tmax) esm <- (esmn + esmx)/2 return(esm) }

Calculate actual vapor pressure (ea)

get.ea <- function(rh, tmin, tmax){ esm <- get.esm(tmin, tmax) ea <- (rh/100) * esm return(ea) }

Calculate vapor pressure deficit (vpd = esm - ea; getting esm and ea functions)

get.vpd <- function(rh, tmin, tmax){ esm <- get.esm(tmin, tmax) ea <- get.ea(rh, tmin, tmax) vpd <- esm - ea return(vpd) }

Check variable values and results

esmn <- get.esmn(tmin) esmx <- get.esmx(tmax) esm <- get.esm(tmin, tmax) ea <- get.ea(rh) vpd <- get.vpd(rh, tmin, tmax)

Define temp (mean temperature), tmin and tmax for plotting relationship of esm and vpd

get.temp <- function(tmin, tmax){ temp <- (tmin + tmax)/2 return(temp) } tmin <- -40:20 tmax <- -20:40

Plot relationship of esm and vpd to mean temperature

plot(get.temp(tmin,tmax), get.esm(tmin, tmax), type = "l", xlab = "Temp (C)", ylab = "esm (black) or vpd (red) (kPa)") lines(temp, get.vpd(50, tmin, tmax), col = "red")