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.

Summary of the Paper "Crop evapotranspiration estimation with FAO56: Past and future”

Water management is a very well discussed topic in the field of agriculture. And evapotranspiration (ET) represents the key variable in agricultural management and water resources. (Fisher, et al., 2017). Pereira, L.S., et al. introduced in 2014 the paper “Crop evapotranspiration estimation with FAO56: Past and future”, which reflects on the publication “FAO irrigation and drainage Paper No. 56 – crop evapotranspiration” of the food and agriculture organization (FAO) of the united nations, which was introduced in 1998. I am going to explain what Pereira, et al. (2014) had published.

Reference evapotranspiration

In the first place, it is important to know that the FAO56 paper (FAO56) by Allen et al. (1998) provides pursuing guidelines on the FAO paper No 24 (FAO24) by Doorenbos and Pruitt (1977), which had then introduced the two-step crop coefficient-reference ET (K_c-ET_ref) procedure, to estimate crop ET. ET_ref is defined by Doorenbos and Pruitt (1977) as “the rate of evapotranspiration from an extensive surface of 8 to 15 cm tall, green grass cover of uniform height, actively growing, completely shading the ground and not short of water”. The FAO56 used this definition as the basic for their own one. And K_c is a standardized crop coefficient to consider crop specific influences on the ET. (Pereira, et al., 2014)

FAO56 standardized the method of estimating the ET_ref to the Penman–Monteith (PM) method and parameterized it, so that the standardized grass crop reference (ET₀) also referred to PM-ET₀ can be calculated. Regarding to Pereira (2014), this approach is highly accepted around scientist and was cited more than 11’500 times, in research articles. However, an accurate estimation of ET₀ can only be achieved with weather datasets of good quality. (Pereira, et al., 2014)

Crop evapotranspiration

Since the crop coefficients-reference ET concept was widely used around the globe, there was no need to change a lot. Adjustment of the FAO24 Kc coefficients on the new PM-ET₀ was required and new coefficients for more crop species and diverse conditions were added.
Furthermore, FAO56 had worked out a dual crop coefficient concept, i.e., K_c = K_cb + K_e, because “the single K_c only represents typical conditions that can vary with wetting frequency […] and with the type of irrigation practised” (Pereira et al.,2014).  K_cb, represents as the basal crop coefficient mainly plant transpiration. The other newly introduced coefficient K_e, is primarily for soil evaporation. An improvement with the dual approach, is that, the estimation of the evaporation is more accurate. (Pereira et al., 2014)

Water balance model tree nursery

Last but not least, some of the guidelines of the FAO56 also influenced the business of modelling. The dual crop approach per example, is used in several models. Pereira predicts not only an increase in the usage of K_c-ET_ref in gridded weather data, but also an increasing trend of the dual approach over the single crop approach.
Several parameters, such as weather data for precise estimation of ET₀, or all coefficients for the different species in the area, are relevant for modelling the water balance at the tree nursery in Schinzach.

In conclusion, for the “Remote sensing, GIS, and water balance”-Project in Schinznach, it is certainly necessary to estimate the evapotranspiration for modelling the water balance at the tree nursery. Therefore, the K_c-ET_ref approach from FAO56 seems to be a solid method to estimate the potential ET, as it is now and also will be used worldwide in the future.

References

Doorenbos J., und W.O. Pruitt. 1977. „FAO Irrigation and Drainage Paper No. 24.“

Fisher, Joshua B. u. a. 2017. „The Future of Evapotranspiration: Global Requirements for Ecosystem Functioning, Carbon and Climate Feedbacks, Agricultural Management, and Water Resources: THE FUTURE OF EVAPOTRANSPIRATION“. Water Resources Research 53(4): 2618–26.

Pereira, Luis S., Richard G. Allen, Martin Smith, und Dirk Raes. 2015. „Crop evapotranspiration estimation with FAO56: Past and future“. Agricultural Water Management 147: 4–20.

Richard G. ALLEN, Luis S. PEREIRA, Dirk RAES, und Martin SMITH. 1998. „FAO Irrigation and Drainage Paper“. : 333.