Hi Maftuna,

Good question and while I don’t know what the most common formula of PET used is I do have some thoughts on what the most appropriate form of PET is. As evaporation is both a radiative and aerodynamic process it is best to use a fully physical form of PET such as Penman, and if you don’t have all input met vars needed to drive Penman then Priestley Taylor is worth considering. Please see papers 61 and 51 below. If interested in PET over long temporal extents then CO2 concentration also comes into play; please see paper 126. Ultimately, it does depend on your application and it’s a balance with data availability too.

126. Yang, Y.T., Roderick, M.L., Zhang, S.L., McVicar, T.R. and Donohue, R.J. (2019) Hydrologic implications of vegetation response to elevated CO2in climate projections. Nature Climate Change. 9(1), 44-48, doi:10.1038/s41558-018-0361-0

61 McVicar, T.R., Roderick, M.L., Donohue, R.J., Li, L.T., Van Niel, T.G., Thomas, A., Grieser, J., Jhajharia, D., Himri, Y., Mahowald, N.M., Mescherskaya, A.V., Kruger, A.C., Rehman, S., and Dinpashoh, Y. (2012) Global review and synthesis of trends in observed terrestrial near-surface wind speeds: Implications for evaporation. Journal of Hydrology. 416-417, 182-205. doi:10.1016/j.jhydrol.2011.10.024

51. Donohue, R.J., McVicar, T.R. and Roderick, M.L. (2010) Assessing the ability of potential evaporation formulations to capture the dynamics in evaporative demand within a changing climate. Journal of Hydrology. 386(1-4), 186-197. doi:10.1016/j.jhydrol.2010.03.020

Good luck and I hope this reply helps.

See you

Tim

---------------------------------------------------------- Dr Tim R. McVicar CSIRO Environment

GPO Box 1700, CANBERRA ACT 2601, AUSTRALIA

Associate Investigator of the Australian Research Council (ARC) Centre of Excellence for Climate Extremes

Adjunct Professor: Department of Hydraulic Engineering, Tsinghua University, Beijing

Associate Editor : Remote Sensing of Environment (August 2014 – March 2021)

Editor-in-Chief: Journal of Hydrology (July 2015 - June 2018)

Phone: (02) 6246-5741 / e-mail: [email protected] Web sites: Researcher ID: D-8614-2011

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Dear Maftuna

The answer to your question, as the colleague before me mentioned in his answer, is very complex and very voluminous

There is no one best method for calculating potential evapotranspiration.

This is because potential evapotranspiration is due to many factors, and they are highly variable.

There is no one model for determining evapotranspiration that is universal.

But we still have to answer the question, right? :)

The basic models for calculating evapotranspiration are divided depending on which of the environmental factors they consider to be the most important

We can briefly and roughly divide them as follows:

• Energy models (Turc)

• Temperature models (Blaney-Criddle)

• Mass balance models (Penman)

• Mixed models (Penman-Monteith)

and many others

The Penman-Monteith model is considered the basic one. It is also included in the FAO methodology, which is available in the famous publication, FAO 56. I am sending a link to this in Researchgate. It is free for download here.

However, more precise models require more data to work correctly. This data is not always available. Then we resort to using simpler models. It is better to determine evapotranspiration using a more elementary model, but to feed it with correct data, than to work with complex models if the data is not representative enough

The other important problem is that the models for determining evapotranspiration, which I mentioned above, have a good representation for climate and soils that are not typical for your country. In my opinion, if your experiments are in Uzbekistan, they will not give very good results. The reason is that you have a much more continental climate, compared to the climate for which the models I mentioned were developed.

It is good to familiarize yourself with the Alpatev model, it is very simple to calculate, but use it as a check on other models, especially if you have difficulty finding a sufficiently long series of climate data. In the former Soviet Union, a lot of work was done on evapotranspiration models specifically for Uzbekistan. I even think that there were different models developed for different regions of the Fergana Valley, because the climate there is very different in terms of precipitation and temperature extremes. You of course know this better than I do.

Finally, I am sending you a link to the FAO methodology

Article FAO Irrigation and drainage paper No. 56

The most common methods for determining PET are:

a) Penman-Monteith equation (FAO-56):

• Considered the most accurate and widely accepted method
• Combines both energy balance and aerodynamic principles
• Requires multiple climatic parameters (temperature, humidity, wind speed, solar radiation)
• Recommended by FAO (Food and Agriculture Organization)

b) Other methods (less common but still important):

1.Thornthwaite method:

• Based mainly on temperature data
• Simpler but less accurate
• Mainly used for historical studies

2.Hargreaves method:

• Uses temperature and solar radiation data
• Simpler than Penman-Monteith
• Good for areas with limited data

3.Blaney-Criddle method:

• Based on temperature and day length
• Used primarily for agricultural purposes
• Less accurate than Penman-Monteith

3.Conclusion: The Penman-Monteith equation (FAO-56) is the most common and recommended method for determining potential evapotranspiration@

Use regular method, it simple.

Hi Amel and All,

Good to hear from you.

Strictly speaking FAO-56 is not a form of potential evapotranspiration. In the FAO-56 method, reference conditions are prescribed for the crop including a surface resistance (rs) of 70 s/m, whereas the term ‘potential evapotranspiration (PET)’ implies that there is no resistance from the land to the atmosphere. That is, for potential evapotranspiration conceptually rs = 0 s/m. FAO-56 is a measure of atmospheric evaporative demand and potential evapotranspiration is a subset of this. The conceptual difference between atmospheric evaporative demand and potential evapotranspiration is tricky and I’ll explain this using precipitation as an example.

Precipitation is the generic / umbrella (pardon the pun) term covering rainfall, snow, sleet, hail and other forms of water that falls from the atmosphere to the Earth’s surface. We all know what precipitation means and can agree on that. Similar to ‘precipitation’, the term ‘atmospheric evaporative demand’ is a generic / umbrella term covering potential evapotranspiration, crop reference evapotranspiration and pan evaporation. Atmospheric evaporative demand is any estimate or measurement of the amount of water, where the phase changes from liquid to gas and moves from the Earth’s surface to the atmosphere, that is, the calculation of atmospheric evaporative demand is independent on land conditions, or in other words atmospheric evaporative demand calculation is driven by atmospheric variables only. Note: I am not saying that atmospheric evaporative demand is not influenced by land conditions, the feedbacks / connection from the Earth’s surface influence the atmospheric variables, but when calculating atmospheric evaporative demand only consider atmospheric variables change. So, while potential evapotranspiration and crop reference evapotranspiration are both forms of atmospheric evaporative demand, they are not equivalent. I hope this is clear to you.

If you want to learn how FAO-56 is derived from Penman then see Section 2 of https://doi.org/10.4225/08/585ac38172fb7

If wanting to assess how climate change (not just global warming) impacts potential evapotranspiration then I would strongly recommend not using the Thornthwaite formulation. As you say it is based mainly air temperature only and potential evapotranspiration is driven by more than just air temperature changes. It is best to use a fully physical based model of potential evapotranspiration (if you have the data).

See you and I hope this helps (it’s a nuanced topic)

Tim

I looked into the various evapotranspiration calculation methods when I developed ETCalc (https://etcalc.hydrotools.tech). I would say that the most popular method is Penman-Monteith. Of note, Penman-Monteith is also more data intensive, or much more complex than the other methods I used.

ETCalc (https://etcalc.hydrotools.tech) is a tool that integrates several customizable methods for calculating daily Potential Evapotranspiration (PET), Reference Evapotranspiration (ETR) and Actual Evapotranspiration (ET) based on user provided meteorological data and crop coefficients. The tool currently integrates Penman-Monteith, Thornthwaite, Blaney-Criddle, Turc, Priestley-Taylor, Hargreaves, Jensen-Haise and Abtew empirical equations.

You can check the data requirements in the User Guide using the link provided above. A few of the methods available in ETCalc require only one parameter.

Please note that ETCalc is part of the Hydrology Tool Set (HTS; https://www.hydrotools.tech), which includes several other tools for the analysis of various hydrological processes (e.g.; hydrograph separation, precipitation partitioning, crop water deficit, irrigation requirements, water budget, groundwater recharge).

Dear Serban Danielescu

I have familiarized myself with the ETCalc you recommended. Can I use monthly data for the required requirements?

Thank you for trying ETCalc. The model operates with daily input datasets and produces daily output (which can can be averaged over monthly, yearly, etc. periods). Some of the evapotranspiration methods might work with monthly data (and some specifically require daily data), but am not sure if using a monthly dataset might trip some of the coding / averaging algorithms. The information available in the online ETCalc manual might be of help https://etcalc.hydrotools.tech/pageMain.php

Dear Serban Danielescu

Thank you for your recommendation. You know, I am conducting research in the dry Aral Sea basin. The climate of this area is dry. My research requires calculating the aridity index of that area. I need PET to calculate this. For this, there is not enough climate data for the dry areas of the Aral Sea (for example, for the Muynak district).