FUNDAMENTALS OF AGROMETEOROLOGY

Appendix to Theme 9: Additional equations needed for FAO
Penman-Monteith ETo calculations


900
0.408( Rn  G )   u 2 (e s  e a )
ETo  T  273
   (1  0.34u 2 )
where: ETo is the reference evapotranspiration [mm d-1]
Rn is the net radiation at the crop surface [MJ m -2 d-1]
G is the soil heat flux density [MJ m-2 d-1]
T is the average air temperature at 2 m height [ºC]
u2 is the wind speed at 2 m height [m s-1]
es is the saturation vapour pressure [kPa]
ea is the actual vapour pressure [kPa]
es – ea is the saturation vapour pressure deficit [kPa]
 is the slope of the vapour pressure curve [kPa ºC-1]
 is the psychrometric constant [kPa ºC-1]
RH max RH min
eº (Tmin )  eº (Tmax )
100 100 eº (Tmax )  eº (Tmin ) ea
ea  es  RH   100
2 2 es
Rn  Rns  Rnl where: Rn is net radiation [MJ m-2 d-1]

Rns is net incoming shortwave radiation [MJ m-2 d-1]
Rnl is net outgoing long-wave radiation [MJ m-2 d-1]

Rns  (1   ) Rs is the albedo, which is 0.23 for the hypothetical grass

reference crop [dimensionless]
Rs is solar or shortwave radiation [MJ m-2 d-1]

 n
Rs   a s  bs  Ra Ra is extraterrestrial radiation [MJ m-2 d-1]
 N
as + bs is the fraction of Ra reaching the earth on clear days
Where no calibrated values are available, the values a s = 0.25 and bs = 0.50 are recommended.

Rso  (0.75  2  10 5 z ) Ra Rso is clear-sky solar radiation [MJ m-2 d-1]

z is altitude [m]

T  Tmin 
Rnl   max    R
 
0.34  0.14 ea 1.35 s  0.35 
 2   Rso 
G  0 for day and 10-day periods


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