Description Usage Arguments Details Value Note Author(s) References Examples
FAO PenmanMonteith equations to compute grass reference evapotranspiration from weather data for daily, monthly, hourly or shorter periods.
1 2 3 4 
x 
datetime object or day of the year (must be datetime object if calculation period is shorter than a day) 
Tmax 
maximum temperature [degreeC] during 24hour period (for daily values) 
Tmin 
minimum temperature [degreeC] during 24hour period (for daily values) 
Rhmax 
maximum of air humidity [percent] during 24hour period (for daily values) 
Rhmin 
minimum of air humidity [percent] during 24hour period(for daily values) 
Tmean 
mean air temperature [degreeC]. For periods shorter 1 day. 
Rhmean 
mean relative air humidity [percent]. For periods shorter 1 day or if Rhmax and Rhmin are missing. 
u 
wind speed [m/s] at 2 meter height. If measurement height is not 2 m, define height with control < list(uz = 2) 
Rs 
solar radiation [MJ/(m2 time)] 
n 
actual hours of sunshine. Used to calculate Rs if Rs messurements are not available (see 
P 
air pressure [kPa]. Estimated with 
elev 
station elevation above sea level [m] 
lat.rad 
latitude [rad]. Use either lat.rad or lat.deg. Latitude is positive for the northern hemisphere and negative for the southern hemisphere 
lat.deg 
latitude [degree]. Use either lat.deg or lat.rad. Latitude is positive for the northern hemisphere and negative for the southern hemisphere 
long.deg 
longitude [degree] east of Greenwich (for periods < 1 day) 
tl 
length of calculation period [hour] (1 for hourly, 0.5 for 30minute and 24 for daily period). Only needed if x is datetime object with length of 1. 
G 
soil heat flux (Assumed to be 0 for daily calculations) (for calculation periods shorter than a day estimated with 
actVP 
Actual vapor pressure [kPa]. If Rhmax, Rhmin and Rhmean are NULL 
control 
list for control parameters and empirical factors (see details, 
must be provided as.numeric (1366) or as a common datetime object (e.g, POSIXct, POSIXlt or Date objects). All formats for which is.timepoint from the lubridate package returns TRUE can be used
controlDefaults
and constDefaults
)Lz:
longitude of the centre of the local time zone (degrees west of Greenwich)
 0 for Greenwich
 345 for Germany
 330 for Cairo (Egypt)
 255 for Bangkok (Thailand)
 75, 90, 105 and 120 for Eastern, Central, Rocky Mountain and Pacific time zones (United States)
Lz is only needed if calculation period is shorter than 1 day.
uz: height of wind measurements (m)
albedo: default 0.23 for the hypothetical grass and alfalfa reference crops used in
the FAO56 PM equations
as: regression constant, expressing fraction of extraterrestrial radiation reaching earth on overcast days (n = 0) (default = 0.25)
bs: as + bs fraction of extraterrestrial radiation reaching earth on clear days (n = N) (default = 0.5)
Tko: reference temperature [degreeC] at elevation z0. Only needed if atmospheric pressure is missing. Often assumed to be 20 degreeC.
z0: elevation at reference level (fefault = 0 [m])
est.ratio.Rs.Rso:
Rs/Rso is used to represent cloud cover. For hourly or shorter periods during the nighttime,
the ratio Rs/Rso is set equal to the Rs/Rso calculated for a time period occurring 23 hours before sunset.
If single values during nighttime are calculated Rs/Rso ration 23 hours before sunset can not be calculated
and an approximation is needed. Following Allen (1999) one can assume Rs/Rso = 0.4 to 0.6 during nighttime periods
in humid and subhumid climates and Rs/Rso = 0.7 to 0.8 in arid and semiarid climates. A value of Rs/Rso = 0.3 presumes
total cloud cover.
grass reference evapotranspiration [mm]
eq. 6 from reference for daily and eq. 53 for hourly or shorter periods
Ullrich Dettmann
Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. (1998). Crop evapotranspirationGuidelines for computing crop water requirementsFAO Irrigation and drainage paper 56. FAO, Rome, 300(9).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39  # 
# Daily Evapotranspiration
# 
ETref(x = 187, Rs = 22.07, elev = 100, lat.deg = 50.8, Tmax = 21.5, Tmin = 12.3,
Rhmax = 84, Rhmin = 63,
u = 2.78, control = list(uz = 10), P = 100.1)
# Calculation with sunshine hour (n) instead of
# global radiation (Rs) (Rs ist estimated from n with estRs):
ETref(x = 187, n = 9.25, elev = 100, lat.deg = 50.8, Tmax = 21.5, Tmin = 12.3,
Rhmax = 84, Rhmin = 63,
u = 2.78, control = list(uz = 10), P = 100.1)
# 
# Hourly Evapotranspiration
# 
ETref(x = as.POSIXct(c('20181001 14:30', '20181001 15:30')),
Tmean = c(38, 37.8), Rhmean = c(52, 52.3), u = c(3.3, 3.2), Rs = c(2.450, 2.5), elev = 8,
lat.deg = 16.22, long.deg = 343.75, G = c(0.175, 0.178) , P = c(101.21, 101.21) ,
control = list(Lz = 15))
# If only one time step is calculated tl must be provided (1 for hourly, 0.5 for 30 minute periods):
ETref(x = as.POSIXct('20181001 14:30'), tl = 1,
Tmean = 38, Rhmean = 52, u = 3.3, Rs = 2.450, elev = 8,
lat.deg = 16.22, long.deg = 343.75, G = 0.1749218, P = 101.2056,
control = list(Lz = 15))
# Calculation with missing soil heat flux (G) and atmospheric pressure (P) (G is estimated with estG
# and P with estP)
ETref(x = as.POSIXct('20181001 14:30'), tl = 1,
Tmean = 38, Rhmean = 52, u = 3.3, Rs = 2.450, elev = 8,
lat.deg = 16.22, long.deg = 343.75,
control = list(Lz = 15))
# 

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