in which E = total evaporation rate; E_n = evaporation rate due to net radiation; E_a = evaporation rate due to mass transfer; Δ = saturation vapor pressure gradient, a function of air temperature; and γ = psychrometric constant, which may be shown to vary slightly with temperature. The mass-transfer evaporation rate E_a is calculated with an empirical mass-transfer formula (Ponce, 2014a: Mass-Transfer Approach).

In the Penman-Monteith method, the mass-transfer evaporation rate E_a is calculated based on physical principles. The original form of the Penman-Monteith equation, in dimensionally consistent units, is the following (Ponce, 2014b):

in which

• ρλE = total evaporative energy flux, in cal/(cm²-s);

• ρ = density of water, in gr/cm³;

• λ = heat of vaporization, in cal/gr;

• E = evaporation rate, in cm/s;

• Δ = saturation vapor pressure gradient, in mb/°C;

• H = energy flux supplied externally, by net radiation, in cal/(cm²-s);

• ρ_a = density of moist air, in gr/cm³;

• c_p = specific heat of moist air, in cal/(gr-°C);

• (e_s  -  e_a) = vapor pressure deficit, in mb;

• r_a = external (aerodynamic) resistance, in s/cm; and

• γ * = modified psychrometric constant, in mb/°C, equal to:

  rs γ *  =   γ   ( 1  +  _____ )                              ra

  (3)

  in which:

• γ = psychrometric constant, in mb/°C, which varies slightly with temperature (Ponce, 2014c), and

• r_s = internal (stomatal or surface) resistance, in s/cm.

The quantity r_a^-1 is the external conductance, in cm³ of air per cm² of surface per second (cm/s).

In evaporation rate units, Eq. 2 is expressed as follows:

in which

• E = total evaporation rate, in cm/s;

• E_n = evaporation rate due to net radiation, in cm/s;

• ρ = density of water, in gr/cm³;

• λ = heat of vaporization, in cal/gr;

  and

• Δ, γ *, ρ_a, c_p, (e_s  -  e_a), and r_a  are in the same units as in Eq. 2.

Equation 4 is the equation of the Penman-Monteith method used in the online calculator presented here.

3.  USE OF THE ONLINE CALCULATOR

We run the calculator ONLINE_PENMAN_MONTEITH with the following input data:

Month [Select one]:       April Air temperature Ta (C°):       20 Net radiation Qn (cal cm-2 d-1):       550 Relative humidity φ (%):       70 Wind velocity v2 (km d-1):       200 Atmospheric pressure pa (mb):       1013.25

Output from the calculator is shown below.

The reference crop potential evapotranspiration for the month of April is:  19.32 cm. ANSWER.