Water Cycles - Hydrogeology: Objectives, Methods, Applications - page 26

b) Thornthwaite's equation

PET = 16 (10 t/I) a f(λ)

Where:

• PET: monthly potential evapotranspiration (in mm)
• I: heat index for a given year = Σ i of the 12 previous months (thermal
memory)
• with the monthly index i = (t/5) 1.514
• t: average monthly temperature (°C)
• a (coeffi cient dependent on I) = 6.75·10 -7 I 3 - 7.71·10 -5 I 2 + 1.79·10 -2 I +
0.4923
• f(λ): factor dependent on the latitude and season, given by reference
tables

This equation is well-adapted to climates with regular precipitation
(oceanic, equatorial), but does not work well in climates with a distinct
dry season.

c) Turc's equation (1961)

This equation works over any time period (month, decade, day). Unlike
the previous equation, this one takes into account solar radiation, which
can be measured with a pyranometer or reconstructed from the duration
of insolation measured by a heliograph.
PET = 0.013 n [t/(t + 15)] (Rg + 50) [1 + (50 - hr)/70]
[The last term is necessary only when the relative humidity (hr in %) drops
below 50% (Mediterranean climate or drier).]

Where:

• PET (in mm);

• n: length of the period under consideration in days (1 day, 10, 30,…);

• hr: relative humidity in %;

• t: average temperature over the period (°C);

• Rg: global solar radiation (cal·cm -2 . day), measured with a pyranometer.
If only a heliograph is available, one can estimate with Rga: incoming
extraterrestrial radiation (cal·cm -2 . day) given by the Angot tables, based
on Angstrom's equation, dependent on latitude and season
Rg = Rga (0.18 + 0.62 . h/H)