**Latent Heat of Vaporization (l)**^{1}

^{1}Reference: Harrison (1963)

l = 2.501 - (2.361 x 10^{-3}) T (3-1)

where:

l latent heat of vaporization [MJ kg^{-1}]

T air temperature [°C]

The value of the latent heat varies only slightly over normal temperature ranges. A single value may be taken (for T = 20 °C): l = 2.45 MJ kg^{-1}.

**Atmospheric Pressure (P)**^{2}

^{2}Reference: Burmanet al.(1987)

_{}(3-2)

where:

P atmospheric pressure at elevation z [kPa]

P_{o}atmospheric pressure at sea level = 101.3 [kPa]

z elevation [m]

z_{o}elevation at reference level [m]

g gravitational acceleration = 9.807 [m s^{-2}]

R specific gas constant == 287 [J kg^{-1}K^{-1}]

a_{1}constant lapse rate moist air = 0.0065 [K m^{-1}]

T_{Ko }reference temperature [K] at elevation z_{o}given byT

_{Ko}= 273.16 + T (3-3)

where:

T mean air temperature for the time period of calculation [°C]

When assuming P_{o} = 101.3 [kPa] at z_{o} = 0, and T_{Ko} = 293 [K] for T = 20 [°C], equation (3-3) becomes:

_{}(3-4)

**Atmospheric Density (r)**^{3}

^{3}Reference: Smithet al.(1991)

_{}(3-5)

where:

r atmospheric density [kg m^{-3}]

R specific gas constant = 287 [J kg^{-1}K^{-1}]

T_{Kv}virtual temperature [K]

_{}(3-6)

where:

T_{K}absolute temperature [K]: T_{K}= 273.16 + T [°C]

e_{a}actual vapour pressure [kPa]

For average conditions (e_{a} in the range 1 - 5 [kPa] and P between 80 - 100 [kPa]), equation (3-6) may be substituted by:

T_{Kv}» 1.01 (T + 273) (3-7)

T is set equal to mean daily temperature for 24-hour calculation time steps.

**Saturation Vapour Pressure (e**_{s}**)**^{4}

^{4}Reference: Tetens (1930)

_{}(3-8)

where:

e°(T) saturation vapour pressure function [kPa]

T air temperature [°C]

**Slope Vapour Pressure Curve (D)**^{5}

^{5}References: Tetens (1930), Murray (1967)

_{}(3-9)

where:

D slope vapour pressure curve [kPa C^{-1}]

T air temperature [°C]

e°(T) saturation vapour pressure at temperature T [kPa]

In 24-hour calculations, D is calculated using mean daily air temperature. In hourly calculations T refers to the hourly mean, T_{hr}.

**Psychrometric Constant (g)**^{6}

^{6}Reference: Brunt (1952)

_{}(3-10)

where:

g psychrometric constant [kPa C^{-1}]

c_{p}specific heat of moist air = 1.013 [kJ kg^{-1}°C^{-1}]

P atmospheric pressure [kPa]: equations 2 or 4

e ratio molecular weight of water vapour/dry air = 0.622

l latent heat of vaporization [MJ kg^{-1}]

**Dew Point Temperature (T**_{dew}**)**^{7}

^{7}Reference: Bosen (1958); Jensenet al.(1990)

When it is not observed, T_{dew} can be computed from e_{a} by:

_{}(3-11)

where:

T_{dew}dew point temperature [°C]

e_{a}actual vapour pressure [kPa]

For the case of measurements with the Assmann psychrometer, T_{dew} can be calculated from

_{}(3-12)

**Short Wave Radiation on a Clear-Sky Day (R**_{so}**)**^{8}

^{8}Reference: Allen (1996)

The calculation of R_{so} is required for computing net long wave radiation and for checking calibration of pyranometers and integrity of R_{so} data. Q good approximation for R_{so} for daily and hourly periods is:

R_{so}= (0.75 + 2 x 10^{-5}z)R_{a}(3-13)

where:

z station elevation [m]

R_{a}extraterrestrial radiation [MJ m^{-2}d^{-1}]

Equation (3-13) is valid for station elevations less than 6000 m having low air turbidity. The equation was developed by linearizing Beer's radiation extinction law as a function of station elevation and assuming that the average angle of the sun above the horizon is about 50°.

For areas of high turbidity caused by pollution or airborne dust or for regions where the sun angle is significantly less than 50° so that the path length of radiation through the atmosphere is increased, an adaption of Beer's law can be employed where P is used to represent atmospheric mass:

_{}(3-14)

where:

K_{t}turbidity coefficient [], 0 < K_{t}£ 1.0 where K_{t}= 1.0 for clean air and K_{t}= 1.0 for extremely trubid, dusty or polluted air.P atmospheric pressure [kPa]

f angle of the sun above the horizon [rad]

R

_{a}extraterrestrial radiation [MJ m^{-2}d^{-1}]

For hourly or shorter periods f is calculated as:

sin f = sin j sin d + cos j cos d cos w (3-15)

where:

j latitude [rad]

d solar declination [rad] (Equation 24 in Chapter 3)

w solar time angle at midpoint of hourly or shorter period [rad] (Equation (31) in chapter 3)

For 24-hour periods, the mean daily sun angle, weighted according to R_{a}, can be approximated as:

_{}(3-16)

where:

f_{24}average f during the daylight period, weighted according to R_{a}[rad]

j latitude [rad]

J day in the year []

The f _{24} variable is used in Equation (3-14) or (3-18) to represent the average sun angle during daylight hours and has been weighted to represent integrated 24-hour transmission effects on 24-hour R_{so} by the atmosphere. f _{24} in Equation (3-16) should be limited to ³ 0.

In some situations, the estimation for R_{so} can be improved by modifying Equation (3-14) to consider the effects of water vapour on short wave absorption, so that:

R_{so}= (K_{B}+ K_{D}) R_{a}(3-17)

where:

K_{B}the clearness index for direct beam radiation []

K_{D}the corresponding index for diffuse beam radiation []

R_{a}extraterrestrial radiation [MJ m^{-2}d^{-1}]

_{}(3-18)

where:

K_{t}turbidity coefficient [], 0 < K_{t}£ 1.0 where K_{t}= 1.0 for clean air and K_{t}= 1.0 for extremely trubid, dusty or polluted air.P atmospheric pressure [kPa]

f angle of the sun above the horizon [rad]

W precipitable water in the atmosphere [mm]

W = 0.14 e

_{a}P + 2.1 (3-19)

where:

W precipitable water in the atmosphere [mm]

e_{a}actual vapour pressure [kPa]

P atmospheric pressure [kPa]

The diffuse radiation index is estimated from K_{B}:

K_{D}= 0.35 - 0.33 K_{B}for K_{B}³ 0.15

K_{D}= 0.18 + 0.82 K_{B}for K_{B}< 0.15 (3-20)

As with Equation (3-14), the f _{24} variable from Equation (16) is used for f in Equation (3-18) for 24-hour estimates of R_{so}.

Ordinarily, R_{so} computed using Equations (3-13), (3-14) or (3-16) should plot as an upper envelope of measured R_{s} and is useful for checking calibration of instruments. This is illustrated in Annex 5.