As input, the Penman formula uses both time-related climatic data and time-independent data which have usually a geographic reference.
Calculation-wise, the evapotranspiration is calculated by a sequence of queries.
The first query, Q_Station_data, calculates certain parameters out of the time-independent station data.
Lat_rad: [Latitude_decimal]*3.14159/180
AeroDyn_Res: Log(([Instr_height_wind_cm]-0.667*[Cropheight_cm])/(0.123*[Cropheight_cm])) *Log(([Instr_height_tempr_cm]-0.667*[Cropheight_cm])/(0.0123*[Cropheight_cm]))/0.41^2
AeroT_Cff: 0.622*3.486*86400/[Aerodyn_res]/1.01
Canopy_resistance_Grass: 200/(0.24*[Cropheight_cm])
Canopy_resistance_Alfalfa: 200/(1.5*Log([Cropheight_cm])-1.4)
Gamma_Cff_Grass: [Canopy_resistance_Grass]/[AeroDyn_Res]
Gamma_Cff_Alfalfa: [Canopy_resistance_Alfalfa]/[AeroDyn_Res]
The second query, Q_Penman is used to process the time-related (monthly) meteorological records.
Ea_Tmax: 0.6108*Exp((17.27*[Tmax])/([Tmax]+237.3))
Ea_Tmin: 0.6108*Exp((17.27*[Tmin])/([Tmin]+237.3))
Ea_mean: ([Ea_Tmax]+[Ea_Tmin])/2
Edew: [RHmean]/(50/[Ea_Tmin]+50/[Ea_Tmax])
RH_delta: [Edew]/[Ea_Tmin]/2+[Edew]/[Ea_Tmax]/2
Etx_Etn: 2049*[Ea_Tmax]/([Tmax]+237.3)^2+2049*[Ea_Tmin]/([Tmin]+237.3)^2
P_atm: 101.3*((293-0.0065*[Altitude_m])/293)^5.253
lambda: 2.501-(0.002361*([Avg_Temp]))
gamma: 0.0016286*[P_atm]/[lambda]
rc: Canopy_resistance_Grass
ra: Q_Station_data.AeroDyn_Res/[Wind_m_s]
gamma_S: [gamma]*(1+[rc]/[ra])
dl_dl_qm: [Etx_Etn]/([Etx_Etn]+[gamma_S])
gm_dl_qm: [gamma]/([Etx_Etn]+[gamma_S])
Aeroterm: ([gm_dl_qm])*([AeroT_Cff])/([Avg_Temp]+273)*[Wind_m_s]*([Ea_mean]-[Edew])
dayno: (30.5*[Mon]-14.6)
soldeclin: Sin(2*3.14159/365*[dayno]-1.39)*0.4093
xx: Sin([soldeclin])*Sin(Q_Station_data.Lat_rad)
yy: Cos([soldeclin])*Cos([Q_Station_data].[Lat_rad])
o: -Tan([soldeclin])*Tan([Q_Station_data].[Lat_rad])
omega: ArcTan(-[o]/Sqr(-[o]*[o]+1))+2*ArcTan(1)
dr: 1+(0.033*Cos((2*3.14159/365)*[dayno]))
Ra_: 37.586*[dr]*([omega]*[xx]+Sin([omega])*[yy])
N: 24/3.14159*[omega]
n_N: [Sunhours]/[N]
Rns: (1-[StData_db].[Albedo_alpha])*[Ra_]*([StData_db].[S_wave_a]+[StData_db].[S_wave_b]*[n_N])
LWR: 0.00000000245*([StData_db].[L_wave_al]+[StData_db].[L_wave_bl]*Sqr([Edew]))*([StData_db].[L_wave_Rad_b]+[StData_db].[L_wave_a]*[n_N])*((([Tmax]+273.16)^4)+(([Tmin]+273.16)^4))
Rn_Rns_Rl: [Rns]-[LWR]
Rad_Term: [dl_dl_qm]*[Rn_Rns_Rl]/[lambda]
E_comb: [Rad_Term]+[Aeroterm]