Hargreaves equation¶

The Hargreaves equation (Hargreaves and Samani, 1985) is a simple evapotranspiration model that only requires a few easily accessible parameters: mininimum, maximum and mean temperature, and extraterrestrial radiation.

The Hargreaves method is recommended by the FAO (Allen et al, 1998) as an alternative method for estimating ETo if insufficient meteorological data are available for the Penman-Monteith method. However, the FAO suggest that using the Penman-Monteith method with estimated solar radiation, vapor pressure and wind speed generally provides more accurate estimates than the Hargreaves equation. This is due to the ability of the estimation equations to incorporate general climatic characteristics such as high or low wind speed or high or low relative humidity into the ET_o estimate made using the FAO Penman-Monteith method.

The Hargreaves equation has a tendency to under-estimate ET_ounder high wind conditions(u2 > 3m/s) and to over-estimate under conditions of high relative humidity.

The following example uses the Hargreaves model to estimate monthly PET for the 1st of February, 2014, for Aberdeen, Scotland (latitude 57.1526 degrees N).

First, convert latitude to radians and the date to day of the year (Julian day):

>>> import datetime, pyeto
>>> lat = pyeto.deg2rad(57.1526)  # Convert latitude to radians
>>> day_of_year = datetime.date(2014, 2, 1).timetuple().tm_yday

To estimate extraterrestrial radiation we first need to calculate solar declination, sunset hour angle and inverse relative distance Earth-Sun:

>>> sol_dec = pyeto.sol_dec(day_of_year)            # Solar declination
>>> sha = pyeto.sunset_hour_angle(lat, sol_dec)
>>> ird = pyeto.inv_rel_dist_earth_sun(day_of_year)
>>> et_rad = pyeto.et_rad(lat, sol_dec, sha, ird)   # Extraterrestrial radiation

Finally, we can estimate ET_o, assuming a minimum temperature of 1.3, maximum temperature of 5.6 and mean temperature of 3.8:

>>> hargreaves(1.3, 5.6, 3.8, et_rad)