# Penman-Monteith approaches for estimating crop evapotranspiration in screenhouses—a case study with table-grape

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## Abstract

In arid and semi-arid regions many crops are grown under screens or in screenhouses to protect them from excessive radiation, strong winds, hailstorms and insects, and to reduce crop water requirements. Screens modify the crop microclimate, which means that it is necessary to accurately estimate crop water use under screens in order to improve the irrigation management and thereby increase water-use efficiency. The goal of the present study was to develop a set of calibrated relationships between inside and outside climatic variables, which would enable growers to predict crop water use under screens, based on standard external meteorological measurements and evapotranspiration (ET) models. Experiments were carried out in the Jordan Valley region of eastern Israel in a table-grape vineyard that was covered with a transparent screen providing 10 % shading. An eddy covariance system was deployed in the middle of the vineyard and meteorological variables were measured inside and outside the screenhouse. Two ET models were evaluated: a classical Penman-Monteith model (PM) and a Penman-Monteith model modified for screenhouse conditions by the inclusion of an additional boundary-layer resistance (PMsc). Energy-balance closure analysis, presented as a linear relation between half-hourly values of available and consumed energy (1,344 data points), yielded the regression Y = 1.05X–9.93 (W m^{−2}), in which Y = sum of latent and sensible heat fluxes, and X = net radiation minus soil heat flux, with *R* ^{2} = 0.81. To compensate for overestimation of the eddy fluxes, ET was corrected by forcing the energy balance closure. Average daily ET under the screen was 5.4 ± 0.54 mm day^{−1}, in general agreement with the model estimates and the applied irrigation. The results showed that measured ET under the screen was, on average, 34 % lower than that estimated outside, indicating significant potential water saving through screening irrigated vineyards. The PM model was somewhat more accurate than the PMsc for estimating ET under the screen. A model sensitivity analysis illustrates how changes in certain climatic conditions or screen properties would affect evapotranspiration.

## Keywords

Energy balance Penman-Monteith Eddy covariance Net radiation Wind Temperature## List of symbols and abbreviations

## Symbol

*B*Bowen ratio (−)

*C*_{p}Specific heat of air (J kg

^{−1}K^{−1})*D*Mean leaf diameter (m)

*d*Canopy zero-plane displacement (m)

*d*_{s}Screenhouse zero-plane displacement (m)

*e*_{s},*e*_{a}Saturated and actual vapour pressure, respectively (kPa)

*G*Soil heat flux density (W m

^{−2})*G*_{l,max}Maximum leaf resistance (s m

^{−1})*G*_{s}Stomatal resistance (μmol s

^{−1}m^{−2})*H*_{s}Screenhouse height (m)

*H*Canopy sensible heat flux (W m

^{−2})*H*_{f}Forced sensible heat flux (W m

^{−2})*h*Canopy height (m)

*LE*Canopy latent heat flux (W m

^{−2})*LE*_{f}Forced latent heat flux (W m

^{−2})*R*Gas constant, 8.3144 (J K

^{−1}mol^{−1})*R*_{G}Global radiation (W m

^{−2})*R*_{N}Net radiation (W m

^{−2})*r*_{a}Aerodynamic resistance (s m

^{−1})*r*_{b}Boundary layer resistance (s m

^{−1})*r*_{c}Canopy resistance (s m

^{−1})*r*_{l}Leaf resistance (s m

^{−1})*S*Sensitivity coefficient (−)

*S*_{photons}Regression constant (μmol s

^{−1}m^{−2})*T*_{a}Air temperature (°C)

*T*_{l}Leaf temperature (K)

*u*Horizontal wind speed (m s

^{−1})*z*_{m},*z*_{h}Height of wind and humidity measurements (m)

*z*_{0m}Roughness length for momentum (m)

*z*_{0h}Roughness length for heat and water-vapour transfer (m)

## Greek letters

- α
Grass albedo = 0.23 (−)

*∆*Slope of saturation vapour pressure- temperature curve (kPa °C

^{−1})*∆****=***∆*(1 + r_{b}/r_{a})*γ*Psychrometric constant (kPa K

^{−1})*γ**=

*γ*(1+(r_{c}+ r_{b})/r_{a})- ν
Air kinematic viscosity (m

^{2}s^{−1})*ρ*_{a}Air density (kg m

^{−3})

## Abbreviations

- EC
Eddy covariance

- ET
Evapotranspiration

- LAI
Leaf area index

- NSE
Nash-Sutcliffe efficiency coefficient (−)

- PAR
Photosynthetically active radiation (μmol s

^{−1}m^{−2})- PM
_{in} Penman-Monteith model inside screenhouse

- PM
_{out} Penman-Monteith model outside screenhouse

- PMsc
Penman-Monteith model modified for screenhouse conditions

- Press
Atmospheric pressure (Pa)

- Re
Reynolds number (−)

- RMSE
Root-mean-square error (units depend on the parameter)

- VPD
Vapor-pressure deficit (kPa)

- WI
Willmott index (−)

## Subscripts

*in out*Inside and outside the screenhouse respectively

*m*Measured parameter

*p*Predicted parameter

## Notes

### Acknowledgments

The authors acknowledge technical support by A. Grava and M. Bahar. The present study was supported by the Chief Scientist of the Israeli Ministry of Agriculture and Rural Development, under grant number 304-0394. The research was also supported by Research Grant Award No. IS-4374-11C from BARD, the United States–Israel Binational Agricultural Research and Development Fund.

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