# ET.Penman

##### Penman Formulation

Implementing the Penman formulation for estimating open-water evaporation or potential evapotranspiration

##### Usage

```
# S3 method for Penman
ET(data, constants, ts="daily", solar="sunshine hours",
wind="yes", windfunction_ver=1948, alpha = 0.08, z0 = 0.001,
…)
```

##### Arguments

- data
A list which contains the following items (climate variables) required by Penman formulation:

*Tmax*,*Tmin*,*RHmax*,*RHmin*,*Rs*or*n*or*Cd*,*u2*or*uz*- constants
A list named

`constants`

consists of constants required for the calculation of Penman formulation which must contain the following items:*Elev*- ground elevation above mean sea level in m,*lambda*- latent heat of vaporisation = 2.45 MJ.kg^-1,*lat_rad*- latitude in radians,*Gsc*- solar constant = 0.0820 MJ.m^-2.min^-1,*z*- height of wind instrument in m,*sigma*- Stefan-Boltzmann constant = 4.903*10^-9 MJ.K^-4.m^-2.day^-1. The following constants are also required when argument`solar`

has value of`sunshine hours`

:*as*- fraction of extraterrestrial radiation reaching earth on sunless days,*bs*- difference between fracion of extraterrestrial radiation reaching full-sun days and that on sunless days.- ts
Must be either

`daily`

,`monthly`

or`annual`

, which indicates the disired time step that the output ET estimates should be on. Default is`daily`

.- solar
Must be either

`data`

,`sunshine hours`

,`cloud`

or`monthly precipitation`

:`data`

indicates that solar radiation data is to be used directly for calculating evapotranspiration;`sunshine hours`

indicates that solar radiation is to be calculated using the real data of sunshine hours;`cloud`

sunshine hours is to be estimated from cloud data;`monthly precipitation`

indicates that solar radiation is to be calculated directly from monthly precipitation. Default is`sunshine hours`

.- wind
Must be either

`yes`

or`no`

.`yes`

indicates that the calculation will use real data of wind speed;`no`

indicates that the alternative calculation without using wind data will be used in Penman formulation (Valiantzas 2006, Equation33). Default is`yes`

.- windfunction_ver
The version of Penman wind function that will be used within the Penman formulation. Must be either

`1948`

or`1956`

.`1948`

is for applying the Penman's 1948 wind function (Penman, 1948);`1956`

is for applying the Penman's 1956 wind function (Penman, 1956) Default is`1948`

.- alpha
Any numeric value between 0 and 1 (dimensionless), albedo of evaporative surface representing the portion of the incident radiation that is reflected back at the surface. Default is 0.08 for open-water surface which is for the calculation of Penman open-water evaporation, all other values will trigger the calculation of Penman potential evapotranspriation.

- z0
Any value (metres), roughness height of the evaporative surface. Default is 0.001 for open-water surface which is for the calculation of Penman open-water evaporation, all other values will trigger the calculation of Penman potential evapotranspriation.

- …
Dummy for generic function, no need to define.

##### Details

The alternative calculation options can be selected through arguments `solar`

, `wind`

and `windfunction_ver`

, please see `Arguments`

for details.
User-defined evaporative surface is allowed through arguments `alpha`

and `z0`

, please see `Arguments`

for details.

##### Value

The function prints a calculation summary to the screen containing the following elements:
- ET model name and ET quantity estimated
- Evaporative surface with values of albedo and roughness height
- Option for calculating solar radiation (i.e. the value of argument `solar`

)
- If actual wind data has been used for calculation (i.e. the value of argument `wind`

) and which version of Penman wind function has been used (i.e. the value of argument `windfunction_ver`

)
- Time step of the output ET estimates (i.e. the value of argument `ts`

)
- Units of the output ET estimates
- Time duration of the ET estimation
- Number of ET estimates obtained in the entire time-series
- Basic statistics of the estimated ET time-series including *mean*, *max* and *min* values.

The function also generates a list containing the following components, which is saved into a `csv`

file named as *ET_Penman.csv* in the working directory:

Daily aggregated estimations of Penman open-water evaporation or potential evapotranspiration.

Monthly aggregated estimations of Penman open-water evaporation or potential evapotranspiration.

Annually aggregated estimations of Penman open-water evaporation or potential evapotranspiration.

Monthly averaged estimations of daily Penman open-water evaporation or potential evapotranspiration.

Annually averaged estimations of daily Penman open-water evaporation or potential evapotranspiration.

Name of the formulation used which equals to `Penman`

.

Type of the estimation obtained which is either `Open-water Evaporation`

or `Potential Evapotranspiration`

.

A message to inform the users about how solar radiation has been calculated by using which data.

A message to inform the users about if actual wind data has been used in the calculations or alternative calculations has been performed without wind data, and which version of the Penman wind function has been used.

##### References

McMahon, T., Peel, M., Lowe, L., Srikanthan, R. & McVicar, T. 2012. *Estimating actual, potential, reference crop and pan evaporation using standard meteorological data: a pragmatic synthesis*. Hydrology and Earth System Sciences Discussions, 9, 11829-11910.

Penman, H. L. 1948. *Natural evaporation from open water, bare soil and grass*. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 193, 120-145.

Valiantzas, J. D. 2006. *Simplified versions for the Penman evaporation equation using routine weather data*. Journal of Hydrology, 331, 690-702.

Penman, H. L. 1956. *Evaporation: An introductory survey*. Netherlands Journal of Agricultural Science, 4, 9-29.

##### See Also

##### Examples

```
# NOT RUN {
# Use processed existing data set and constants from
# kent Town, Adelaide
data("processeddata")
data("constants")
# Call ET.Penman under the generic function ET
results <- ET.Penman(data, constants, ts="daily",
solar="sunshine hours", wind="yes",
windfunction_ver = "1948", alpha = 0.08, z0 = 0.001)
# }
```

*Documentation reproduced from package Evapotranspiration, version 1.10, License: GPL (>= 2)*