PE_Oudin {airGR}  R Documentation 
Computation of series of potential evapotranspiration at the daily or hourly time steps with Oudin's formula
Description
Function which computes PE using the formula from Oudin et al. (2005). PE can be computed at the daily time step from hourly or daily temperature and at the hourly time step with hourly or daily temperature through a disaggregation of daily PE . See details.
Usage
PE_Oudin(JD, Temp, Lat, LatUnit = c("rad", "deg"),
TimeStepIn = "daily", TimeStepOut = "daily",
RunFortran = FALSE)
Arguments
JD 
[numeric] time series of Julian day of the year []; see details 
Temp 
[numeric] time series of daily (or hourly) mean air temperature [°C] 
Lat 
[numeric] latitude of measurement for the temperature series [radians or degrees]. Atomic vector, except if 
LatUnit 
[character] latitude unit (default = 
TimeStepIn 
[character] time step of inputs (e.g. 
TimeStepOut 
[character] time step of outputs (e.g. 
RunFortran 
[boolean] to run the code in the Fortran mode or in the R mode (default) 
Details
To calculate basinwide Oudin potential evapotranspiration, it is advised, when possible, to use either station temperature or gridded temperature data to calculate PE and then average these PE values at the basin scale.
In the JD
argument, the Julian day of the year of the 1st of January is equal to 1 and the 31st of December to 365 (366 in leap years). If the Julian day of the year is computed on an object of the POSIXlt
class, the user has to add 1 to the returned value (e.g. as.POSIXlt("20161231")$yday + 1
).
When hourly temperature is provided, all the values of the same day have to be set to the same Julian day of the year (e.g. as.POSIXlt("20161231 00:00:00")$yday + 1
and as.POSIXlt("20161231 00:01:00")$yday + 1
). Each single day must be provided 24 identical Julian day values (one for each hour).
Four cases are possible:

TimeStepIn = "daily"
andTimeStepOut = "daily"
: this is the classical application of the Oudin et al. (2005) formula 
TimeStepIn = "daily"
andTimeStepOut = "hourly"
: the daily temperature is used inside thePE_Oudin
function to calculate daily PE, which is then disaggregated at the hourly time step with use of a sinusoidal function (see Lobligeois, 2014, p. 78) 
TimeStepIn = "hourly"
andTimeStepOut = "daily"
: the hourly temperature is aggregated at the daily time step and the daily PE is calculated normally withinPE_Oudin

TimeStepIn = "hourly"
andTimeStepOut = "hourly"
: the hourly temperature is aggregated at the daily time step, the daily PE is then calculated normally withinPE_Oudin
, which is finally disaggregated at the hourly time step with use of a sinusoidal function (see Lobligeois, 2014, p. 78)
The use of the PEdaily_Oudin
corresponds to the first case of the use of PE_Oudin
.
Value
[numeric] time series of daily potential evapotranspiration [mm/time step]
Author(s)
Laurent Coron, Ludovic Oudin, Olivier Delaigue, Guillaume Thirel, François Bourgin
References
Oudin, L., Hervieu, F., Michel, C., Perrin, C., Andréassian, V., Anctil, F. and Loumagne, C. (2005).
Which potential evapotranspiration input for a lumped rainfallrunoff model?
Part 2  Towards a simple and efficient potential evapotranspiration model for rainfallrunoff modelling.
Journal of Hydrology, 303(14), 290306, doi:10.1016/j.jhydrol.2004.08.026.
Lobligeois, F. (2014).
Mieux connaitre la distribution spatiale des pluies amélioretil la modélisation des crues ? Diagnostic sur 181 bassins versants français.
PhD thesis (in French), AgroParisTech  Irstea Antony, Paris, France.
Examples
library(airGR)
data(L0123001)
PotEvap < PE_Oudin(JD = as.POSIXlt(BasinObs$DatesR)$yday + 1,
Temp = BasinObs$T,
Lat = 0.8, LatUnit = "rad")