# 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

• 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.
• 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