Question

What is the Penman Combination equation and what does each term mean in the equation. What unit should each term be in?

Answer 1

The penman combination is a semi-empirical equation combining mass transfer (Ea) and energy budget (H) methods.
It is used for calculating the potential evaporation using synoptic meteorological data.

According to Penman the potential evaporation Eo (in mm/day) can be calculated as:

where
:-
?∆/γ is an empirical parameter depending on temperature.

♦️Table for weighting factor ∆/γ and temperature:-

?H is calculated as H = (1-r)Rin - Ro

where :-
▪️Ro is the outgoing radiation,
▪️r is the albedo (0.05 for water) and
▪️Rin is the incoming radiation

?Rin is calculated by:-

▫️ (1-r)Rin = 0.95Ra(0.18 + 0.55n/N)

where :-
▪️Ra is the solar radiation and
▪️n/N is the ration between actual sunshine hours and possible sunshine hours.

The term n/N can also be estimated using the cloudiness.
Example a cloudiness of 60 % gives an n/N of 40 %
(= 100 -60).

♦️Table for Ra( solar radiation), Ra is expressed in equivalent evaporation (mm/day)

?Ro is calculated by:-

▫️σTa⁴(0.56-0.09√ed )(0.10+0.90n/N)

where :-
▪️ed is the actual vapor pressure, and
▪️σTa⁴ is the theoretical black body radiation

♦️Table for value of σTa⁴:-

?Ea is calculated by:-

▫️ Ea = 0.35(0.5 + u2/100)(ea – ed)

where:-
▪️ u2 is the wind speed in miles/day (1 mile = 1609 m)
▪️ ea is the saturation vapor pressure

♦️Table for air temperature and saturation vapour pressure(mm)

Remember that the relative humidity RH = ed/ea