# Derive Reference Potential Evapotranspiration from Potential Evapotranspiration

I'm working on a project in Rajasthan, India involving modelling water supply and demand in a catchment. For this, I am working with WEAP which has modules for estimating groundwater recharge using a simple bucket model.

This model needs daily temperature and reference (potential) evapotranspiration values. The reference evapotranspiration is calculated according to the modified Penman-Monteith equation as described in the FAO56-Paper. As part of the project, I'd like to use climate models. One with a sufficient resolution is the HAR model, which has values for potential evapotranspiration. Is there a way to get from potential evapotranspiration to the reference evapotranspiration?

EDIT: I am not sure whether the model Potential Evapotranspiration values implicitly contain information about the surface, or if they are a spatially comparable, independent of the surface. Since I am modeling the catchment disaggregated by landuse types with a uniform climate, I need a value that is independent of the surface properties and can be transferred to the landuse types via the surface coefficients as described in the FAO paper.

I agree that terminology about evapotranspiration is confusing especially when using the expression "potential evapotranspiration", as stated in the FAO-56 paper:

The use of other denominations such as potential ET is strongly discouraged due to ambiguities in their definitions

# Definition

So let's refer to the FAO terminology:

1. Reference evapotranspiration ($ET_0$) refers to the evapotranspiration observed on well watered grass for given meteorological conditions (radiation, temperature, humidity, and wind speed).

2. Crop evapotranspiration under standard conditions ($ET_c$) refers to the evapotranspiration observed on well watered specific crop for given meteorological conditions. The relationship between $ET_c$ and $ET_0$ is given by:

$$ET_c = K_C\times ET_0 \tag{1}$$

1. Crop evapotranspiration under non-standard conditions ($ET_{c,adj}$) refers to the evapotranspiration observed on a specific crop under water and environmental stress for given meteorological conditions. The relationship to $ET_0$ is either defined using a stress coefficient $K_s$: $$ET_{c,adj} = K_s \times K_c \times ET_0 \tag{2}$$ Or using an adjusted crop coefficient $K_{c,adj}$: $$ET_{c,adj} = K_{c,adj} \times ET_0 \tag{3}$$

# Confusions

Now, you may find different common usage for the terms potential or actual evapotranspiration that leads to your confusion.

Potential evapotranspiration is sometimes referred to $ET_0$ or $ET_c$ or even less strict definition such as atmospheric demand for water.

Actual evapotranspiration is referred either to $ET_c$, $ET_{c,adj}$ or less strict definition such as the amount of water evaporated.

# Pragmatism

Regarding your issue, pick one:

• Read to find out what are the definitions involved in WEAP and HAR
• Look at the data and find out if potential evapotranspiration refers to grass (definition 1) or to specific crop with a given coefficient (definition 2, eq.1)
• Use the other HAR data (everything is available) to compute $ET_0$ using FAO-56 method.
• Last but not least, do not bother that much as evapotranspiration is full of uncertainties and you could not proove which of $ET_0$, $ET_c$ or $ET_{c,adj}$ best represent your actual evapotranspiration. You are interested in the relative dynamics of $ET$, choose realistic ranges of landcover coefficient and calibration will do the mass balance.
• I have trouble with the term 'Actual evapotranspiration' referring to those calculated values since 'Actual' implies true (or at least measured) and the crop ET values are at best estimates. This is especially true for the non-adjusted value. – haresfur Nov 22 '17 at 1:08
• @haresfur In my opinion, potential and real evaporation are abstract notions of evapotranspirative demand and the ability of a plant cover to respond to it. These are abstract because of not being measurable except very locally with invasive experiments. So, on a larger scale, they are always estimated but the terminology often persists to refer to the underlying concept for the sake of simplicity, I guess. It is a common (and troubling) laziness to refrain from the distinction between a conceptual value and its estimator. I agree, rigorous don't. – Delforge Nov 22 '17 at 11:05
• Eddy-covariance does provide an areal measurement of evapotranspiration, although you can argue about the precision and accuracy. Water balance can provide an indirect measurement of ET at the catchment scale but obviously has its own issues. That's why I agree that it is important to be clear in the terminology. People often neglect the evaporation component, too. – haresfur Nov 22 '17 at 23:05
• Thanks for the clarification! Is the whole notion of a crop coefficient actually transferable to non-irrigated areas such as shrubland? There is a method to calculate K_c from NDVI (e.g. Landsat). Are the values I get from that method (in the non-irrigated case) something like a footprint of the environmental "circumstances"? In other words, would these K_c values yield a rough approximation of the actual evapotranspiration if multiplied by ET_0? I need to get a rough estimate of groundwater recharge in theses areas using a soil moisture model model that employs ET_0 and K_c. – telegott Dec 5 '17 at 19:54