Empirical estimation of evapotranspiration for a water balance at a tree nursery in Switzerland

Evapotranspiration is the key component to model the water balance of a certain place. The task of our project is to model the water balance in a  tree nursery in the central Switzerland. The are many ways existing to distinguish the potential evapotranspiration (ET). The focus in this blog is set on different empirical estimation of ET and mainly on the method I described in my previous blog post.

The Penman-Montieth Method (PMM) was recommended in the FAO 56 paper (Allen et al., 1998) and enjoys an excellent reputation for estimating the reference crop Evapotranspiration (ET₀). However, this physically based method requires a load of data of different weather parameters and several equation solving. Because of that I would like to introduce three other methods, that, corresponding to (Kamasani et al., 2012) correlate the best to complex PMM.

1. Hargreaves Method a temperature-based method (HRM)
2. Priestley and Taylor a radiation-based method (PTM) (a simplified version of the Penman-Monteith method)
3. FAO-24 Modified Penman Method a physically-based method (MPM)

1. Hargreaves Method (HRM)

Hargreaves and Samani (1982, 1985) publicated several improvements on their former studies, for estimating grass-related reference ET (mm d⁻¹) one of them is:

ET = aR_aTD^1/2 (T_a + 17.8)

As a is a constant, and R_a (the extraterrestrial radiation expressed in equivalent evaporation units) can be found in tables, the only variable is TD (Temperature difference). Therefore, you need to estimate the daily maximum and minimum temperature. (Xu and Singh 2002)

2. Priestley and Taylor method (PTM) a simplified version of Penman (1948)

A simplified version of the PMM, was introduced by Priestley and Taylor (1972). It is good for estimation of ET (mm d⁻¹) of generally wet or humid areas.

ET = α (Δ / + γ) (R_n/ λ)

For this equation α and γ are constants. λ is the latent heat (in calories per gram), given in tables. The net radiation (R_n) is the difference between the incoming net shortwave radiation (R_ns) and the outgoing net longwave radiation (R_nl). And Δ is the slope of saturation vapour pressure curve (in mb/◦C), estimation through  Local measurements of solar radiation, minimum and maximum temperature and humidity are the requirements to solve the equation above. (Xu and Singh 2002)

3. FAO-24 Modified Penman Method (MPM)

In 1977 a modified method of the Penman method was introduced in the FAO 24 paper. It is a mass transfer and energy balance method for estimation of ET₀ (mm d⁻¹).

ET0 = C ((Δ/ (Δ+γ)) R_n + (γ/(Δ +γ)) (0.27)(1.0+0.01 U2)(e_s-e_a))

Where c = 0.68 + 0.0028 (RH_max) + 0.018 (R_s) – 0.068 (u_d) + 0.013 (u_d / u_n) + 0.0097 (u_d)(u_d/u_n) +0.000043 (RH_max) (Rs) (u_d). γ is the psychrometric constant (in mb/◦C) and Δ is also the same as in the formula above. (Xu and Singh 2002; Kamasani et al., 2012)

For this method measurements of temperature, relative humidity (RH_max, RH_min), windspeed (U2, u_d, u_n) are required to solve the equation. Saturation vapour pressure e_s and e_a can be calculated with temperature.

Method	Formula	Required inputs: Primary                               Secondary
Hargreaves Method (HRM)	ET = aRaTD^1/2 (Ta + 17.8)	Tmax, Tmin,
Priestley and Taylor method (PTM)	ET = α (Δ / + γ) (Rn/ λ)	Rn, Δ	Rns and Rnl for Rn, Tmax and Tmin for Δ
FAO-24 Modified Penman Method (MPM)	ET0 = C ((Δ/ (Δ+γ)) Rn + (γ/(Δ +γ)) (0.27)(1.0+0.01 U2)(es-ea)) c = 0.68 + 0.0028 (RHmax) + 0.018 (Rs) – 0.068 (ud) + 0.013 (ud / un) + 0.0097 (ud)(ud/un)+ 0.000043 (RHmax) (Rs) (ud)	Tmax, Tmin, RHmax, RHmin, u2, ud/un, es, ea, Δ

Comparison

First of all, these methods are all recommended methods to estimate Evapotranspiration. As the HRM method is very simply estimated with only maximum and minimum temperature, is it useful when less meteorological data is available.
Additional to temperature, short and longwave radiation must be measured, and all the constants must be found for the conditions in the local area, to solve the Priestley and Taylor equation. The calculation of the slope of saturation vapour pressure curve is not a big deal. And radiation can be measured with pyranometers, radiometers or solarimeters.
The MPM comes along with two other parameters like windspeed and humidity. The relative humidity can be measured directly with hygrometers and the windspeed is measured with anemometers at 2 meters height.(Allan et al., 1998)

I got all the background information out of the FAO 56 online book on the FAO webpage (fao.org). This helped me a lot to create this post and will help our group for the project later.

Addressing to our project in Schinzach, it is more a matter of the equipment and meteorological data available than the usefulness of different ways of estimating ET. With the FAO 56 paper it is may possible to apply the most recommended Penman-Montieth Method.

References:

G. Allan, Richard, L Pereira, Dirk Raes, and Martin Smith. 1998. Crop Evapotranspiration-Guidelines for Computing Crop Water Requirements-FAO Irrigation and Drainage Paper 56. Vol. 56.

Kamasani, Chandrasekhar Reddy, S Aruna Jyothy, and P Mallikarjuna. 2012. “Evaluation of Evapotranspiration Estimation Methods and Development of Crop Coefficients for Groundnut Crop.” IOSR Journal of Engineering 2 (June)

Xu, C.-Y., and V. P. Singh. 2002. “Cross Comparison of Empirical Equations for Calculating Potential Evapotranspiration with Data from Switzerland.” Water Resources Management 16 (3): 197–219.