1:2.3 Water Vapor

Relative humidity is required by SWAT+ if the Penman-Monteith or Priestley-Taylor equation is used to estimate potential evapotranspiration. It is also used to calculate the vapor pressure deficit on plant growth. The Penman-Monteith equation includes terms that quantify the effect of the amount of water vapor in the air near the evaporative surface on evaporation. Both Penman-Monteith and Priestley-Taylor require the actual vapor pressure, which is calculated from the relative humidity.

Relative humidity is the ratio of an air volume’s actual vapor pressure to its saturation vapor pressure:

$R_h=\frac{e}{e^o}$ 1:2.3.1

where $R_h$ is the relative humidity on a given day, $e^o$ is the actual vapor pressure on a given day ($kPa$), and is the saturation vapor pressure on a given day ($kPa$).

The saturation vapor pressure is the maximum vapor pressure that is thermodynamically stable and is a function of the air temperature. SWAT+ calculates saturation vapor pressure using an equation presented by Tetens (1930) and Murray (1967):

$e^o=exp[\frac{16.78*\overline T_{av}-116.9}{\overline T_{av}+237.3}]$ 1:2.3.2

where $e^o$ is the saturation vapor pressure on a given day ($kPa$) and $\overline T_{av}$ is the mean daily air temperature ($\degree C$). When relative humidity is known, the actual vapor pressure can be calculated by rearranging equation 1:2.3.1:

$e=R_h*e^o$ 1:2.3.3

The saturation vapor pressure curve is obtained by plotting equation 1:2.3.2. The slope of the saturation vapor pressure curve can be calculated by differentiating equation 1:2.3.2:

$\Delta=\frac{4098*e^o}{(\overline T_{av}+237.3)^2}$ 1:2.3.4

where is the slope of the saturation vapor pressure curve ($kPa\degree C^{-1}$$^{-1}$), $e^o$ is the saturation vapor pressure on a given day ($kPa$) and $\overline T_{av}$ is the mean daily air temperature ($\degree C$).

The rate of evaporation is proportional to the difference between the vapor pressure of the surface layer and the vapor pressure of the overlying air. This difference is termed the vapor pressure deficit:

$vpd=e^o-e$ 1:2.3.5

where $vpd$ is the vapor pressure deficit ($kPa$), $e^o$ is the saturation vapor pressure on a given day ($kPa$), and $e$ is the actual vapor pressure on a given day ($kPa$). The greater the value of $vpd$ the higher the rate of evaporation.

The latent heat of vaporization, $\lambda$, is the quantity of heat energy that must be absorbed to break the hydrogen bonds between water molecules in the liquid state to convert them to gas. The latent heat of vaporization is a function of temperature and can be calculated with the equation (Harrison, 1963):

$\lambda=2.501-2.361*10^{-3}*\overline T_{av}$ 1:2.3.6

where is the latent heat of vaporization ($MJ\space kg^{-1}$) and $\overline T_{av}$ is the mean daily air temperature ($\degree C$).

Evaporation involves the exchange of both latent heat and sensible heat between the evaporating body and the air. The psychrometric constant, $\gamma$, represents a balance between the sensible heat gained from air flowing past a wet bulb thermometer and the sensible heat converted to latent heat (Brunt, 1952) and is calculated:

$\gamma=\frac{c_p*P}{0.622*\lambda}$ 1:2.3.7

where is the psychrometric constant ($kPa\degree C^{-1}$$^{-1}$), $c_p$ is the specific heat of moist air at constant pressure (1.013 x 10$^{-3}$ $MJ\space kg^{-1}\degree C^{-1}$$^{-1}$), P is the atmospheric pressure ($kPa$), and is the latent heat of vaporization ($MJ\space kg^{-1}$).

Calculation of the psychrometric constant requires a value for atmospheric pressure. SWAT+ estimates atmospheric pressure using an equation developed by Doorenbos and Pruitt (1977) from mean barometric pressure data at a number of East African sites:

$P=101.3-0.01152*EL+0.544*10^{-6}*EL^2$ 1:2.3.8

where $P$ is the atmospheric pressure ($kPa$) and $EL$ is the elevation ($m$).

The daily relative humidity data required by SWAT+ may be read from an input file or generated by the model. The variable RHSIM in the master watershed (file.cio) file identifies the method used to obtain relative humidity data. To read in daily relative humidity data, the variable is set to 1 and the name of the relative humidity data file and the number of different records stored in the file are set. To generate daily relative humidity values, RHSIM is set to 2. The equations used to generate relative humidity data in SWAT+ are reviewed in Chapter 1:3.

Table 1:2-2: SWAT+ input variables used in relative humidity calculations.

Variable Name	Definition	File Name
RHD	$R_h$: daily average relative humidity	.hmd
TMP_MX	$T_{mx}$: maximum temperature for day ($\degree C$)	.tmp
TMP_MN	$T_{mn}$: minimum temperature for day ($\degree C$)	.tmp
SUB_ELEV	$EL$: elevation ($m$)	.sub
RHSIM	Relative humidity input code: 1-measured, 2-generated	file.cio
NHTOT	Number of relative humidity records within the .hmd file (required if RHSIM = 1)	file.cio
RHFILE	Name of measured relative humidity input file (.hmd) (required if RHSIM = 1)	file.cio
IHGAGE	Number of relative humidity record used within the subbasin (required if RHSIM = 1)	.sub

See description of .hmd file in the User’s Manual for input and format requirements if measured relative humidity data is being used.