International Journal of Agronomy

Volume 2018, Article ID 7935140, 13 pages

https://doi.org/10.1155/2018/7935140

## Application of the Flux-Variance Technique for Evapotranspiration Estimates in Three Types of Agricultural Structures

^{1}Institute of Soil, Water and Environmental Sciences, Agricultural Research Organization, The Volcani Center, P.O. Box 15159, Rishon LeZion 7528809, Israel^{2}HIT-Holon Institute of Technology, P.O. Box 305, Holon 58102, Israel

Correspondence should be addressed to Josef Tanny; li.vog.irga.inaclov@ianat

Received 21 December 2017; Revised 27 March 2018; Accepted 4 April 2018; Published 11 June 2018

Academic Editor: Paolo Inglese

Copyright © 2018 Ori Ahiman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Irrigation of protected crops requires sound knowledge of evapotranspiration. Previous studies have established that the eddy-covariance (EC) technique is suitable for whole canopy evapotranspiration measurements in large agricultural screenhouses. Nevertheless, the eddy-covariance technique remains difficult to apply in the farm due to costs, operational complexity, and postprocessing of data, thereby inviting alternative techniques to be developed. The subject of this paper is the evaluation of a turbulent transport technique, the flux variance (FV), whose instrumentation needs and operational demands are not as elaborate as the EC, to estimate evapotranspiration within large agricultural structures. Measurements were carried out in three types of agricultural structures: (i) a banana plantation in a light-shading (8%) screenhouse (S1), (ii) a pepper crop in an insect-proof (50-mesh) screenhouse (S2), and (iii) a tomato crop in a naturally ventilated greenhouse with a plastic roof and 50-mesh screened sidewalls (S3). Quality control analysis of the EC data showed that turbulence development and flow stationarity conditions in the three structures were suitable for flux measurements. However, within the insect-proof screenhouse (below the screen) and the plastic-covered greenhouse, of the energy balance closure was poor; hence, the alternative simple method could not be used. Results showed that the FV technique was suitable for reliable estimates of ET in shading and insect-proof screenhouses with of the regressions between FV latent heat flux and latent heat flux deduced from energy balance closure of 0.99 and 0.92 during validation for S1 and S2, respectively.

#### 1. Introduction

In recent years, the area of vegetables and orchards grown in protected cultivation systems is constantly increasing. These include, among other structures, naturally ventilated greenhouses [1], insect-proof screenhouses [2], and shading screenhouses [3]. These structures are naturally ventilated and hence have significant interaction with the external environment. The advantages and limitations of such protected cultivation systems are well documented in the literature [4, 5].

Protected crops are exposed to microclimatic conditions that are significantly different from those in the open field. Hence, the interaction between protected crops and their microenvironment has been the topic of much research during the past years (e.g., [6–8]). One effect of covering the crops is in modifying the exchange of energy, mass, and momentum between the plants and their environment. This modification may affect the evapotranspiration; that is, the water vapor flux from the canopy to the atmosphere, which, in turn, will affect the irrigation demands. The possibility of water saving through reduced transpiration and irrigation demands initiated a number of research studies focused on evapotranspiration measurements and estimates, mainly in screenhouses [3, 9–13].

The most common method for direct measurements of evapotranspiration and other scalar fluxes is the eddy covariance [14]. The method was originally developed and mostly used for flux measurements over open surfaces like forests, natural, or agricultural fields and open water bodies. Due to its high capabilities in reliable measurements of whole canopy evapotranspiration, in recent years, its performance was also examined in protected environments like screenhouses.

Results obtained in various screenhouses [2, 3, 9, 12, 13] illustrated the reliability of the eddy-covariance technique within such protected environments. In all these studies, the EC system was deployed above the plants and below the screen, at a height which is smaller than twice the canopy height. Although conditions at such a height apparently do not meet the common requirements for flux measurements [15], turbulence analysis and flux results supported the use of the EC method at such heights within screenhouses. For example, Tanny et al. [3] evaluated the suitability of the eddy-covariance technique to directly measure evapotranspiration in a large banana screenhouse with almost mature plants. Results were promising: they found 94% closure of the energy balance and daily evapotranspiration values, in agreement with the irrigation applied by the grower. Even though their EC system was deployed relatively close to the canopy top, the spectral energy density decayed with the frequency in a rate close to −5/3, suggesting that turbulence properties resembled the flow in the inertial subrange of steady-boundary layers. Tanny et al. [12] extended these results by measuring turbulent fluxes simultaneously with two EC systems installed at two heights above the crop and below the screen within a large banana screenhouse. Similar friction velocities were measured at the two levels, validating the constant-flux layer assumption within the air gap between the canopy top and the horizontal screen.

Due to the high cost of sensors and complex operation and data analysis, the EC method is inaccessible for day-to-day use by growers as a tool for irrigation management. To assist growers in improving irrigation management, a family of simplified methods was developed in recent years that are capable of indirectly estimating the canopy sensible heat flux and extracting evapotranspiration as a residual of the energy balance closure. One method of this family is the flux-variance (FV) method, which is derived from the MOST principle that any scalar variance normalized by the scalar flux depends on atmospheric stability only. Using this theory, it can be shown that, under unstable conditions, the sensible heat flux is proportional to , where is the standard deviation of air temperature measured at high frequency (∼10 Hz) above the canopy. Hence, the method can be applied using fast response single-point measurement of air temperature [16] and auxiliary, relatively simple measurements of net radiation and soil heat flux.

The flux-variance (FV) method, which is the topic of the present paper, has been applied in several studies in open fields. There are three technical aspects involved with applying the FV method: measurement height, sampling frequency, and the available fetch. *Measurement height*: no study in the literature identified the optimal height where the measurement of sensible heat flux, *H*, is in best agreement with a reference value. Most literature studies show measurements that were done at a single height in the surface layer, larger than (e.g., [16]), that is, within and above the roughness sublayer which is about . *Measurement frequency*: most studies reported sampling frequencies between 0.1 and 20 Hz [17–19]; however, no report compared the method’s performance at different frequencies to identify the optimal one. *Fetch*: literature studies were conducted under height/fetch ratio in the range 1 : 90–1 : 200 [17, 18, 20].

Several studies examined the value of , the similarity constant associated with the FV method (see Section 2) and the correlation between EC and FV sensible heat fluxes. The value of was in the range 0.9–1.1, and the coefficient of correlation with EC sensible heat flux was in the range 0.72–0.98 [17–20].

The main goal of the present study was to examine the FV technique for crops cultivated in three modified environments that are very common in regions of mild winter climates like the Mediterranean basin [4]. The structures examined are a tomato greenhouse with impermeable plastic roof and screened sidewall openings for natural ventilation, an insect-proof screenhouses with dense net that blocks insect invasion, in which pepper was grown, and a banana screenhouse that protects the crop from hail, high wind speed, and supraoptimal solar radiation. The ultimate goal is to provide guidelines on the optimal use of the FV technique in estimating ET for irrigation management in such structures. Hence, sensible heat flux estimates using FV are used for extracting evapotranspiration from the energy balance closure, and results are compared with ET measurements.

#### 2. Theory

The detailed theory of the flux-variance method is given by Wesson et al. [16]. This section provides only a brief outline with major equations.

The Monin-Obukhov similarity theory (MOST) implies that any nondimensional turbulence statistics depends on the atmospheric stability only, , where is the measurement height, is the zero-plane displacement height, and is the Obukhov length defined as follows:where is the friction velocity, , , and are fluctuations in longitudinal, transversal, and vertical velocity components, respectively, is air temperature, is von-Karman’s constant, is the gravitational acceleration, and is the covariance between vertical velocity and temperature fluctuations which represents the mean kinematic sensible heat flux. Based on MOST, the air temperature standard deviation can be expressed as follows:where is the temperature scaling parameter given by . As shown by Albertson et al. [21] and Wesson et al. [16] under unstable conditions, the temperature standard deviation, , can be approximated by the following equation:where is a similarity constant [22]. From (2) and (3), it can be shown thatwhere is the air density and is the air specific heat at constant pressure. Hence, the sensible heat flux can be estimated by calculating the temperature standard deviation obtained from a single-point measurement of air temperature at high-sampling frequency. Note that (4) can only predict positive sensible heat fluxes under unstable conditions since . An approximate expression for stable conditions was also suggested [16], but analysis of such conditions was outside the scope of the present study.

To estimate evapotranspiration, the energy balance closure equation is used as , where is the latent heat flux (evapotranspiration), is the sensible heat flux, is the net radiation, and is the soil heat flux. The latent heat flux is extracted by , where is the flux variance sensible heat flux calculated by (4). Since in the present study, the measured energy balance was not perfectly closed (see Section 4), a “closed” was estimated, derived by forcing the energy balance closure [23] using the eddy-covariance sensible heat flux, . Finally, the flux-variance latent heat flux, , is validated against the “closed” latent heat flux, .

#### 3. Materials and Methods

##### 3.1. Sites, Crops, and Structures

The study is based on three comprehensive field campaigns carried out in three different agricultural structures each with a different crop. Details on each of the campaigns are given below (see also [24] for details on S1 and S2).

###### 3.1.1. Campaign S1: Banana, 8% Shading Screen

The screenhouse was located at 32°42′N; 34°57′E, 20 m AMSL, on the Mediterranean coastline in western Israel near the Carmel mountain. The calibration period was 7.08.2011–29.08.2011 (DOY 219–241), during which 21 days were analyzed. Screenhouse dimensions were 250 × 450 m^{2} and 5.5 ± 0.1 m high, with the longer side oriented nearly east-west (Figure 1). Screenhouse cover was a woven screen, with nominal shading of 8% (manufacturer’s data), and a rectangular hole of 2.3 mm × 3 mm, made of clear, round polyethylene monofilaments 0.3 mm in diameter (Polysack Plastic Industries Inc., Israel). Banana, *Grand Nain* AAA, was planted during May 2011, in groups of four, separated 4.5 m between rows and 3.5 m between plants in a row. During the experiment, plant height was 4.3 m and Leaf area index (LAI) was 1.4. Plants were irrigated following regional recommendations for screenhouse banana. Soil comprised 44% clay, 26% sand, and 30% silt. Dry and volumetric soil heat capacities were and [25].