# Questions about the use of RA data and Reference Evapotranspiration

Hi, I’m Xiao. During the pandemic, I hope everyone is well.
I had a problem calculating reference evapotranspiration using RA data( Daily extraterrestrial radiation) and others.
(1) In the Annex Table 2.6 Annex2, values of RA at different latitudes are provided, but singular latitudes, such as 33 degrees north latitude, cannot be determined. How should this be solved? Just like this post described? Value for extraterrestrial radiation of Water Yield Model
(2)I would like to ask if The unit of ET0 calculated by using The ‘Modified Hargreaves’ Method formula (𝐸𝑇0=0.0013×0.408×𝑅𝐴×(𝑇𝑎𝑣+17)×(𝑇𝐷−0.0123𝑃)0.76) is mm/day?. According to the inVEST documentation Reference Evapotranspiration, the ‘modified Hargreaves’ method uses the average of the mean daily maximum and mean daily minimum temperatures for each month (Tavg in degrees Celsius), the difference between mean daily maximum and mean daily minimums for each month (TD), extraterrestrial radiation (RA in MJ/m-2 d-1) and precipitation ( in mm per month), all of which can be relatively easily obtained. As for temperature, does “mean daily maximum” mean the average of all the highest temperatures in a month, “mean daily minimums” mean the average of all the lowest temperatures in a month? Does Tavg mean the average of the two mean values obtained from the front?
(3)The temperature and precipitation input in the formula are counted by month, while the RA input is counted by day. What unit should the final output ET0 be? I found two posts. https://community.naturalcapitalproject.org/t/the-modified-hargreaves-method/1842, https://community.naturalcapitalproject.org/t/water-yield-evapotranspiration/413 and their description puzzled me.
(4) Can I understand the equation as described below: If I input the daily maximum temperature, minimum temperature, daily precipitation, and RA data into the formula, I can get the daily reference evapotranspiration. If I input the mean value of all the maximum temperatures, the mean value of all the minimum temperatures, and monthly precipitation of the current month, I can get the monthly reference evapotranspiration? Finally, the monthly values must be added together to get the annual value used in the model? OR if I input the mean value of all the maximum temperatures, the mean value of all the minimum temperatures, and monthly precipitation of the current month, I can get the daily reference evapotranspiration? Then multiply the daily by the number of days of each month to get the monthly evapotranspiration? I don’t know which understanding is correct. Please tell me what the correct understanding is.

These questions have puzzled me for a long time. I hope they can be answered.

Hi @Xiao_Zhang,

Thanks for writing in to the Forum with your thorough and detailed questions. We hope you and yours are faring well during the pandemic too.

@swolny, NatCap’s Senior GIS Analyst, plans to provide you with a detailed response about using the modified Hargreaves method to calculate ET₀ and to answer your other questions. She has experience with this approach. She is out of the office today but will be back to reply on Monday, January 10, 2022.

Jesse

OK! Thank you very much. Best wishes to you!

Hi @Xiao_Zhang -

While I am not an expert in the Modified Hargreaves theory, I have used this method for calculating ET for many years, so can address some of your questions (and agree that it’s very confusing). It looks like you did a good search on this forum for ideas, and you might also want to do a more general web search for Modified Hargreaves, where you’ll surely find more information about its implementation.

(1) The forum post you refer to does list my recommendations. As I said, given the coarseness of the model (and the fact that RA is already a monthly average), it is not critical to use exactly the right RA. If you do really want to get specific, you can use a different source of RA data, or a GIS tool to make a map for your area of interest, and derive the RA value that way.

(2) You’re correct that the formula calculates mm/day. Then you need to sum the daily values by month, then sum the monthly values to get the final map with annual average values. (This might also address your questions (3) and (4).

As for temperature, does “mean daily maximum” mean the average of all the highest temperatures in a month, “mean daily minimums” mean the average of all the lowest temperatures in a month? Yes.

Does Tavg mean the average of the two mean values obtained from the front? Yes. ((Tmin + Tmax) / 2.0)

~ Stacie

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I understand what you mean. Thank you very much for your kind help. Best wishes to you!

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