Water Yield: Evapotranspiration calculation methods

I have a question about which evapotranspiration layer I should use in the Water Yield model.
I’m working on a study that projects future land use in the future. Since evapotranspiration (ET) is directly related to temperature, I’d prefer to create my own layers to account for the effects of climate change.
To do so, I’m using the equation provided by the InVEST manual:
REFERENCE ET: ET0=0.0013×0.408×RA×(Tav+17)×(TD−0.0123P)^0.76

The problem is that when I compare values yielded by this equation (e.g. 40mm per year - REFERENCE ET) to values from the literature (e.g. 1,300mm per year - WorldClim: POTENTIAL ET) they have different magnitude. The manual says the potential ET “…may be used for reference ET”. However, these two layers yield completely different results. Hardly comparable. I believe the potential ET layer yields a more realistic output, even though the input data for this model should be the reference ET.
The study area is in the northern portion of Georgia, USA. Which value of ET you believe is more realistic?
Please, see both water yield outputs below (All other parameters constant, except by ET).

Thank you!

1 Like

Hi @fabiosecanho -

It looks like you’re using the Modified Hargreaves method for calculating Reference ET, which I often use, so a few things come to mind. This equation is used to calculate a value for each month of the year, then the monthly values must be added together to get the annual value used in the model. Is the 40mm you mention the total over all 12 months?

Also be sure to verify the units for temperature and precipitation that go into the ET equation. I’ve been caught off guard when it turned out that my precip units were in cm, or temperature values were (real values * 10).

~ Stacie

@swolny Thank you very much for your contribution! I’m sorry I didn’t answer earlier, but just now I noticed your comment! My bad!

This value (40mm) is per year already and I double-checked all units, they are correct.


Hi Fabiosecanho,

As I am encountering the same issue with calculating Et0 using ET0=0.0013×0.408×RA×(Tav+17)×(TD−0.0123P)^0.76–my result are considerably less than the real values–I was wondering if you could manage to find the problem.


Hi to everyone. I am wondering about these issues as well. I am currently using the Sun radiation tool in ArcGis to calculate RA, which provides rediation results in a monthly basis. Should I divide the RAD value thus obtained by the number of days in the month to apply it in the Hargreaves equation correctly? Or just keep it as it is if I want to have the ETo monthly value?

Hello @evselem and welcome to the forums!

I’m not personally familiar with the ArcGIS Sun Radiation tool, but I think as long as you can convert the units of the tool’s output raster to the units needed by the Modified Hargreaves equation, then you should be fine. According to the InVEST User’s Guide, the RA parameter should be in megajoules per square meter per day of extraterrestrial radiation. Reference evapotranspiration is discussed here in the InVEST user’s guide, for your reference.


I think this is not an uncommon issue, however I am still inside the confusion. The Hargreaves model asks for climate data in a monthly basis (maximum and minimum temperatures, average rain) but the imput of solar radiation data should be a daily average for the month? Thanks for your help

Hi @evselem -

The Modified Hargreaves equation is a bit confusing. It does require daily average values of temperature and radiation, but monthly average values for precipitation. I’m just noticing that some of the references are missing in the User Guide, but check out Droogers and Allen 2002, where the Modified Hargreaves equation is described:

Droogers, P. & Allen, R.G. 2002. “Estimating reference evapotranspiration under inaccurate data conditions.” Irrigation and Drainage Systems, vol. 16, Issue 1, February 2002, pp. 33–45

~ Stacie

Hi Swolny, thanks for your reply. As exhaustively as I can do, I’ve checked every factor in the Modified Hargreaves equation, and in the end I always get quite low values for ETo. Ranging between 0.0106 to 2.415 for a given month. As a comparison, I lookes for the values in the Reference_ET layer in the Gura model example, and values range from 910.25 to 1170.59. What is wrong or missing in my calculations? Should I assume that the values I get represent average daily ETo for a given month? Thanks for your assistance

The Modified Hargreaves equation gives daily values, so you need to multiply them by the number of days in each month to get a final monthly value.

I’m not sure where your area of study is, but still, the values you get, even summed on a monthly basis, do seem very low. Assuming that the equation itself is being input correctly, the main thing I would double-check are the units of all of the inputs (temperature, precipitation and radiation).

~ Stacie

Hello Stacey, thanks for your reply. I’ve got to conclude the calculations of monthly and yearly evapotranspiration (my study area is in subtropical Mexico), the ETo range for a whole year is 157 to 1070 mm. I’ve checked temperature units in Celsius degrees and rain in mm. Sun radiation input comes from a raster obtained with the “Area Solar Radiation” tool in ArcGis. The reference radiation values I get for every month are consistently lower than the values from the “Table for monthly average solar radiation”. For instance, my raster’s range for the month of July is 9 to 29 MJ/m2/day, and the constant value from the Table at 20ºN latitude is 38.86 MJ. Using this raster derived from a DEM does make a significant difference as compared to a constant value. What is your advise in this regard?


I haven’t used Area Solar Radiation in a while, and am not sure which version you’re using, or how you’re configuring it, but the documentation for ArcPro says "The output radiation rasters will always be floating-point type and have units of watt hours per square meter (WH/m2). " This is different than the MJ/m2/day that the equation requires, so perhaps you’ve already converted the units?

In general, my inclination would be to use a GIS-generated raster that’s created for your area of interest instead of a monthly average value from the very generic table. Otherwise, I haven’t had these issues, so don’t have the experience to provide additional advice.

~ Stacie

Thanks for your reply Stacie. It is correct, ArcGis delivers sun radiation in WH/m2. What I am doing is calculate an average value for the whole month, or either configure the tool to calculate the radiation for the 15th day of the month (results are almost the same), then convert WH to MJ, which is a simple multiplication in the raster calculator. Now I wonder if an ET range of 157 to 1070 is a coherent value, when there are spots in the area where rain is close to 3000 mm