This article describes the implementation of the Hargreaves-Samani evapotranspiration method within GoldSim, adhering to the standards defined in FAO Irrigation and Drainage Paper No. 56 (FAO-56). This specific implementation utilizes the temperature-based solar radiation estimation described in Equation 50 of the manual.
Reference Evapotranspiration (ETo) is a critical parameter for water balance modeling, irrigation scheduling, and hydrological studies. While the Penman-Monteith method is the industry standard, it requires extensive meteorological data (wind speed, humidity, radiation) that is often unavailable. The Hargreaves-Samani (HS) method provides a reliable alternative by using only air temperature and solar geometry.
Model Implementation
This GoldSim implementation follows a three-step approach. This allows users to view intermediate values like solar radiation and easily swap them for measured data if it becomes available.
Step 1: Extraterrestrial Radiation (Ra) The model calculates Ra based on the site's latitude and the day of the year. This represents the solar energy reaching the top of the atmosphere. To ensure stability across all geographies, the logic includes a conditional switch: for standard latitudes, it employs geometric equations, but it switches to a lookup table if the latitude angle is less than 67 degrees (or exceeds the extreme latitude threshold). This ensures the model remains accurate even in polar regions where the sunset hour angle logic can encounter mathematical limitations during 24-hour daylight or darkness.
Step 2: Estimated Solar Radiation (Rs) Using the daily temperature range (Tmax - Tmin), the model estimates Rs at the surface. This is based on the principle that the temperature difference is a proxy for cloud cover.
Equation: Rs = KT * sqrt(max(0, Tmax - Tmin)) * Ra
Calibration: An adjustment coefficient (KT) (0.15 - 0.2). Note: KT (or kRs) is an empirical coefficient that accounts for the 'aridity' or 'coastal influence' of the site."
Step 3: Reference Evapotranspiration (ETo) The ETo value is calculated as a depth per time (mm/day), by converting energy flux into water depth using the standard latent heat conversion factor.
Equation: 0.0135 * (Tavg|C| + 17.8) * Rs * 0.408 mm/(MJ/m2)
Note: The factor 0.408 represents the latent heat conversion.
Results
The model operates on a daily time step to calculate Reference Evapotranspiration (ETo). To estimate the actual water requirements of a specific crop (ETc), users can adjust the Kc factor located at the root level of the model. The Time History Result element provides a direct comparison between these calculated outputs and the historical measured benchmarks.
Test Case Study: Logan, Utah
To verify the model, a comparison was performed using a 22-year historical dataset (2000–2022) from the Utah State University (USU) Experimental Farm in Logan, Utah.
While seasonal trends match closely, the simulated results for Logan are slightly lower than the USU benchmarks. This is an expected physical outcome. The USU data uses the Penman-Monteith method, which includes a dedicated 'Aerodynamic Term' to account for wind speed. Because Logan is a windy, high-altitude valley, the wind would result in a drying effect that temperature-based models like Hargreaves-Samani cannot explicitly 'see.'
Conclusion
The Hargreaves-Samani GoldSim model provides a useful approximation of atmospheric water demand. Its reliance on minimal data makes it an helpful tool for sites lacking sophisticated weather stations.
For the full methodology, please refer to: Allen, R.G., Pereira, L.S., Raes, D. and Smith, M. (1998). FAO Irrigation and Drainage Paper 56. Official FAO Link
Contact:
Jason Lillywhite (Lillywhite Water Solutions)
Comments
4 comments
Hello Jason,
Thanks for your lesson today regarding evaporation which is one of the Water Management webinars series. I just wanted to follow up with you on Daily extraterrestrial radiation ('RadEx' element in model) especially when Latitude is greater than 67 degree (I was not a questioner). Such so, arccos(x) in Omega element could not be calculated when Lat is greater than 67 degree because of the limitation of x range which is between -1 and +1. In order to get daily extraterrestrial radiation where Lat is greater than 67 degree, I prefer to use the 15th day of the month value instead of using 'DayofYear' in 'Delta' element and GoldSim could interpolate/estimate daily 'RadEx'.
Here is the reference table and see Table 2.6 and there are some comments above and below the table regarding Ra. For example, 'For the winter months in latitudes greater than 55° (N or S), the equations for Ra have limited validity. Reference should be made to the Smithsonian Tables to assess possible deviations'
http://www.fao.org/3/X0490E/x0490e0j.htm#annex%202.%20meteorological%20tables
As well as it could be implemented in 'Reference ET model' or other models. I think it's only for very high latitude situations and just wanted to let you know my thoughts.
Thanks in advance for your taking your time to consider this.
Regards,
Homin Kim
Homin Kim,
Thank you for the reference to that table. I incorporated this into the model so it will be used when the latitude is out of range.
-Jason
Hi, the pdf link is no longer active. Is it possible to get a copy? Thank you.
Ashley,
I changed the link to the FAO 56 Guidelines, which includes the equation on page 60 of the document I link at the top of the article now. Please have a look and let me know if you have other questions.
Note: I updated the model to include a validation test for data measured at Logan Utah, USA.
-Jason
Please sign in to leave a comment.