Determining Reference Evapotranspiration in Greenhouses from External Climate

The AUB campus in Beirut includes a 10-ha area of green vegetation cover stretching along the northern coast of Beirut. The climate at the location is subhumid to humid and Mediterranean, with average annual precipitation of 850 mm and a grass-reference ${\mathrm{ET}}_{\mathrm{oPM}}$ of 1,150 mm (El-Asmar et al. 2017). The monthly maximum, mean, and minimum air temperatures are 27.2°C, 13°C, and 10.5°C in winter and 31.8°C, 28°C, and 14.7°C in summer, respectively. Average relative humidity in Beirut is 70%. The experiment was conducted in a steel frame prism-shaped greenhouse with an area of $72{\mathrm{m}}^2$ ($5.25\times 13.7\mathrm{m}$). Transparent double plastic polycarbonate films covered the top of the pilot greenhouse and its sidewalls. The roof slopes were east–west oriented. The greenhouse was side-ventilated using an electric suction fan (at a rate of $1.0{\mathrm{m}}^3/{\mathrm{m}}^2/\mathrm{s}$ for a period of $4–5\mathrm{h}/\mathrm{day}$) located at the edge of the southern wall during three periods: from March to April 2015, from May to November 2015, and from May to December 2016. Indoor data for the period from June 18 to July 3, 2015, were missing due to data file corruption. No artificial heating was used within the greenhouse for the duration of the experiment. Based on measurements, a constant wind speed of $0.16\mathrm{m}/\mathrm{s}$ was assumed to dominate within the greenhouse during ventilation. During the unventilated periods, air was allowed to enter the greenhouse, and wind speed was measured periodically using a portable anemometer. Average wind speed varied between 0 and $0.02\mathrm{m}/\mathrm{s}$, and an average of $0.01\mathrm{m}/\mathrm{s}$ was assumed. A drip-irrigated Origanum Syriacum crop (a perennial herb) was planted in the Beirut greenhouse at a density of 6 plants per ${\mathrm{m}}^2$ for the course of the experiment. The crop was planted in November 2014. Origanum has crop growth coefficients that are similar to grass when planted at this density (Jaafar et al. 2017).

Mean annual rainfall at the AREC site is 521 mm. The climate is semiarid, with an average annual grass reference evapotranspiration of 1,300 mm, 70% of which occurs between April and September (Jaafar et al. 2017). The experiment at AREC was conducted from August 11 to October 15, 2017.

The AREC greenhouse was a double-span greenhouse (with an area of $\sim 500{\mathrm{m}}^2$) planted with cucumber at a density of $2.5\mathrm{plants}/{\mathrm{m}}^2$ and having a similar height (4.2 m) and orientation (south–north) to the greenhouse at Beirut but a new plastic cover. The greenhouse was force-ventilated with four large fans (at a rate of $1.0{\mathrm{m}}^3/{\mathrm{m}}^2/\mathrm{s}$) located at the northern side walls (two on each side of the greenhouse door) during the period from August 11 to September 26, 2017. No roof vents were located in either of the two greenhouses. A cucumber crop was planted in the AREC greenhouse in June 2017 (at a farmer-practice density of $2.5\mathrm{plants}/{\mathrm{m}}^2$) and harvested in late October 2017.

The Penman-Monteith equation (${\mathrm{ET}}_{\mathrm{oPM}}$) was used to calculate daily ${\mathrm{ET}}_{\mathrm{o}}$ for a grass reference surface (Monteith and Unsworth 2007). The equation was considered the baseline for the comparative assessment of the Hargreaves-Samani ${\mathrm{ET}}_{\mathrm{o}}$ equation. The equation for ${\mathrm{ET}}_{\mathrm{oPM}}$ is written aswhere ${\mathrm{ET}}_{\mathrm{oPM}}$ = reference evapotranspiration for grass ($\mathrm{mm}/\mathrm{day}$); $\mathrm{\Delta }$ = saturation slope vapor pressure curve ($\mathrm{kPa}/°\mathrm{C}$); $R_n$ = net radiation at the grass surface ($\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{day}$); $G$ = soil heat flux ($\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{day}$) (assumed to be small compared to $R_n$ and considered negligible for the daily time step used herein); $\rho$ = air density ($\mathrm{kg}/{\mathrm{m}}^3$); $C_p$ = specific heat of dry air at a constant temperature; $e_s$ = air saturation vapor pressure (kPa); $e_a$ = actual vapor pressure (kPa); $\gamma$ = psychrometric constant ($\mathrm{kPa}/°\mathrm{C}$); $r_s$ = surface resistance, assumed to be $70\mathrm{s}/\mathrm{m}$ (Allen et al. 1998); and $r_a$ = aerodynamic resistance ($\mathrm{s}/\mathrm{m}$); $r_a$ was calculated using Perrier (1975):where $k$ = Karman constant (0.4); $u$ = wind speed at reference height ($\mathrm{m}/\mathrm{s}$); $x$ = reference height (2 m); $d$ = zero plane displacement (m) (Brenner and Incoll 1997); $h_c$ = mean crop height (m), estimated as for grass herein at 0.12 m; and ${\mathrm{z}}_0$ = roughness length of the crop relative to momentum transfer (m) (Brenner and Incoll 1997) estimated usingwhere $z_0^{\prime }$ = roughness length of bare soil surface (0.01 m); $c_d$ = mean drag coefficient, taken as 0.07; and LAI = leaf area index as estimated for grass ($24h_c$) (Allen et al. 1998).

The zero plane displacement $d$ was estimated according to Brenner and Incoll (1997):

The surface resistance $r_s$ was estimated usingwhere $r_s^c$ = canopy resistance, estimated as the ratio between the stomatal resistance $r_{sT}$ and the effective leaf area index ${\mathrm{LAI}}_e$; $r_{sT}$ was obtained from an exponential relationship with the solar radiation $R_s$ (Yang et al. 1990); $r_s^s$ = soil resistance ($\mathrm{s}/\mathrm{m}$); and $a$ and $b$ = empirical coefficients taken as 1.52 and 0.05, respectively (Gong et al. 2017). ${\mathrm{LAI}}_e$ was calculated as a function of LAI:

The $r_s^s$ was calculated usingwhere $r_{s\min }^s$ = minimum soil resistance when the soil water content is at field capacity, assumed to be $10\mathrm{s}/\mathrm{m}$ (Griend and Owe 1994); ${\theta }_s$ = soil water content within the top 10 cm of the soil; and ${\theta }_{\mathrm{FC}}$ = field capacity for the top 10 cm of the soil, assumed to be 80% of ${\theta }_s$ (which was the irrigation threshold used in the experiment). The soil of the AUB site was silty loam with a field capacity of 32.1% by volume, while the soils at AREC were clay with a field capacity of 42%.

The recorded data were time integrated to a daily time step for input into the ET calculator. Solar radiation measurements $R_s$ were used to estimate the net radiation $R_n$ used in the ${\mathrm{ET}}_{\mathrm{oPM}}$ calculations for the respective conditions (greenhouse and outdoors); $R_n$ was calculated as the difference between the net short-wave radiation $R_{ns}$ and the net outgoing long-wave radiation $R_{nl}$, calculated as per Brutsaert (1982):

The radiation balance inside the greenhouse was treated differently than that outside the greenhouse by accounting for the greenhouse transmissivity. Inside the greenhouse, $R_{ns}$ was calculated usingwhere $R_s$ = solar radiation measured using the pyranometer, which recorded the solar radiation that passed through the greenhouse roof material; and $\alpha$ = grass albedo, the fraction of the incident sunlight that a surface reflects (taken as 0.23 for grass).

$R_{nl}$ inside the greenhouse was estimated usingwhere $\sigma$ = Stefan-Boltzmann constant ($4.901\times {10}^{-9}\mathrm{MJ}/{\mathrm{K}}^4/{\mathrm{m}}^2/\mathrm{day}$); $e_a$ = measured actual vapor pressure in kPa (from relative humidity); $T_{k\max }$, $T_{k\min }$ = maximum and minimum absolute temperature in Kelvin (as measured outdoors for outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ and inside the greenhouse for GH ${\mathrm{ET}}_{\mathrm{oPM}}$) during the 24-h period; and $f_{cd}$ = cloudiness function (dimensionless) (limited to $0.05\le f_{cd}\le 1.0$), calculated aswhere $R_{so}$ = incoming clear-sky solar radiation ($\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{day}$), calculated aswhere $z$ = elevation at the measurement location (m), equal to 15 m for the AUB site and 997 m for the AREC site; $R_a$ = extraterrestrial radiation ($\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{day}$); and the constant 0.75 is unit-less.

The application of ${\mathrm{ET}}_{\mathrm{oPM}}$ is usually limited to cases in which temperature, vapor pressure, wind speed, and solar radiation measurements are available. To account for cases in which this data is lacking or unreliable, the Hargreaves and Samani (1985) empirical equation (${\mathrm{ET}}_{\mathrm{oH}}$, in $\mathrm{mm}/\mathrm{day}$) was used to evaluate ${\mathrm{ET}}_{\mathrm{o}}$ inside and outside the greenhouse:where $R_s$ = solar radiation (in equivalent $\mathrm{mm}/\mathrm{day}$), either measured or calculated based on latitude; and $T_{\mathrm{mean}}$ = daily mean air temperature (°C). When measured, $R_s$ must be converted to $\mathrm{mm}/\mathrm{day}$ (Allen et al. 1998):where ${\rho }_w$ = density of water ($\mathrm{1,000}\mathrm{kg}/{\mathrm{m}}^3$); and $\lambda$ = latent heat of vaporization, calculated using Harrison (1963) ($\mathrm{MJ}/{\mathrm{kg}}^1$):

Greenhouse ${\mathrm{ET}}_{\mathrm{oH}}$ was calculated using two approaches. The first approach used measured solar radiation, denoted hereinafter by a subscript $m$ ($R_{sm}$); ${\mathrm{ET}}_{\mathrm{oHm}}$ denotes ET calculated using this approach. In the second approach, ${\mathrm{ET}}_{\mathrm{oH}}$ was calculated using estimates of solar radiation [as proposed by Hargreaves and Samani (1985)], denoted hereinafter by a subscript $c$ ($R_{sc}$); ${\mathrm{ET}}_{\mathrm{oHc}}$ denotes ET calculated using this approach. Estimated solar radiation $R_{sc}$ is usually used when no solar radiation measurements are available or when measurements are not reliable:where $R_{sc}$ = modeled (calculated) solar radiation ($\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{day}$); $K_{RS}$ = adjustment factor (0.16 for interior regions and 0.19 for coastal zones, accounting for climatological cloud cover conditions); $R_a$ = extraterrestrial radiation, which is a function of a location’s latitude and the time of the year ($\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{day}$); and $\mathrm{\Delta }T$ = daily temperature range calculated as the difference between the daily maximum and minimum air temperatures ($T_{\max }-T_{\min }$) (°C). ${\mathrm{ET}}_{\mathrm{oHc}}$ inside the greenhouse was calculated by using the indoor temperature range in Eqs. (13) and (16), as proposed by Fernández et al. (2010), and reducing the outdoor solar radiation by an estimate of the greenhouse transmissivity $\tau$. Greenhouse transmissivity $\tau$ was calculated as the ratio of daily solar radiation measured inside the greenhouse to daily solar radiation measured outside the greenhouse for the period of the experiment. The integrity of the outdoor solar radiation calculations was checked against the incoming clear-sky solar radiation ($R_{so}$) ($\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{day}$), estimated by a cloudiness function proposed by Allen et al. (1998) using Eq. (12).

The relationships between outdoor and greenhouse ${\mathrm{ET}}_{\mathrm{o}}$ were derived from data collected during the calibration period. The calibration periods for ventilated conditions were from March 7 to April 3, 2015, from May 5 to November 6, 2015, and from May 6 to July 24, 2016 (a total of 272 days). For unventilated conditions, calibration was performed on data collected from January 1 to March 6, 2015, from April 4 to May 4, 2015, and from February 16 to April 7, 2016 (a total of 146 days). Using the data collected during the calibration periods, relationships between daily greenhouse ${\mathrm{ET}}_{\mathrm{o}}$ and (1) daily outdoor ${\mathrm{ET}}_{\mathrm{o}}$, (2) daily outdoor solar radiation, and (3) extraterrestrial solar radiation were derived.

Verification of the developed equations was carried out by comparing the modeled ${\mathrm{ET}}_{\mathrm{o}}$ results to ${\mathrm{ET}}_{\mathrm{o}}$ calculated from the observed weather data. To eliminate bias, the data used in the verification were not included in the calibration process. Data for the verification process were collected during the following periods: from July 24 to December 2, 2016, for ventilated conditions (131 days), and from April 8 to May 5, 2016, and December 3, 2016 to January 15, 2017, for unventilated conditions (72 days). ${\mathrm{ET}}_{\mathrm{oPM}}$ inside the greenhouse was compared to the external meteorological variables in order to identify whether any significant relationships exist between greenhouse ${\mathrm{ET}}_{\mathrm{o}}$ and outdoor weather variables (temperature, relative humidity, and solar radiation). All derived relationships were then verified using data from the outdoor weather station. Error statistics for both the calibration and verification stages were generated for comparison.

To test the representations of the relationships developed between GH and outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ and solar radiation, the relationships between outdoor climate and GH ${\mathrm{ET}}_{\mathrm{oPM}}$ developed from the AUB site were validated using data collected at the AREC site for 2 months. The AREC greenhouse is larger, and the site lies in a semiarid region within the Beqaa Valley in Lebanon, while the AUB site is within a coastal environment characterized by a subhumid climate. Validation of the proposed equations under these different experimental and climatic conditions was important in order to test the applicability of the proposed equations. Average wind speed within the AREC greenhouse was measured at $0.13\mathrm{m}/\mathrm{s}$ (due to ventilation). The outdoor weather station at AREC registered an average wind speed of $1.7\mathrm{m}/\mathrm{s}$ for the duration of the AREC experiment.

Figs. 3(a–c) show GH ${\mathrm{ET}}_{\mathrm{oPM}}$ versus outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$, outdoor ${\mathrm{ET}}_{\mathrm{oHm}}$, and outdoor $R_{sm}$, respectively (for ventilated conditions). Statistical error parameters are presented in Table 2. Mean daily GH ${\mathrm{ET}}_{\mathrm{oPM}}$ at the AUB site was smaller than outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ by 33%. GH ${\mathrm{ET}}_{\mathrm{oPM}}$ and outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ were very similar when the latter was less than $2\mathrm{mm}/\mathrm{day}$. At higher outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$, GH ${\mathrm{ET}}_{\mathrm{oPM}}$ was, on average, 41% less than outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$. At the AREC site, mean daily greenhouse ${\mathrm{ET}}_{\mathrm{oPM}}$ was smaller than outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ by 38% [Fig. 3(a)]. Despite the difference in transmissivity between the greenhouses at AUB and AREC, the ratio of GH ${\mathrm{ET}}_{\mathrm{oPM}}$ to outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ was very close at both sites. The ratio was found to be a function of the extraterrestrial solar radiation at the site (details in the following).

Figs. 3(d–f) show GH ${\mathrm{ET}}_{\mathrm{oPM}}$ versus outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$, outdoor ${\mathrm{ET}}_{\mathrm{oHm}}$, and outdoor $R_{sm}$, respectively (for unventilated conditions). Under unventilated conditions at the AUB site, mean daily GH ${\mathrm{ET}}_{\mathrm{oPM}}$ was 14% less than outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$. At the AREC site, due to the large difference between the windy outdoor conditions and the unventilated conditions inside the greenhouse, mean daily greenhouse ${\mathrm{ET}}_{\mathrm{oPM}}$ was 45% less than outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$. Other weather variables, such as outdoor mean air temperature, were found to be unsuitable for predicting greenhouse ${\mathrm{ET}}_{\mathrm{oPM}}$ with enough certainty ($R^2=0.52$ for all data; $R^2=0.17$ for ventilated conditions; and $R^2=0.62$ for unventilated conditions).

On average, daily greenhouse ${\mathrm{ET}}_{\mathrm{oPM}}$ was less than outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ by 25% at the AUB site and by 40% at the AREC site. These results are comparable with lysimetric ${\mathrm{ET}}_{\mathrm{o}}$ reported by Fernández et al. (2010) for a plastic greenhouse planted with a perennial grass crop; the authors reported a 20% reduction in ${\mathrm{ET}}_{\mathrm{oPM}}$ as compared to outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ within the whitened greenhouse, as well as an ${\mathrm{ET}}_{\mathrm{oPM}}$ range of $0.7–4.1\mathrm{mm}/\mathrm{day}$ in southern Spain. When outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ values were less than $2\mathrm{mm}/\mathrm{day}$, greenhouse ${\mathrm{ET}}_{\mathrm{oPM}}$ was either equal to outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ or greater (this was mainly an air temperature effect during the cold months of December and January). This indicates that greenhouse crop irrigation requirements during these 2 months may exceed those for outdoor crops. Lower ratios of greenhouse to outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ occurred during the spring and summer, when outdoor ${\mathrm{ET}}_{\mathrm{oPM}}$ was higher than $2\mathrm{mm}/\mathrm{day}$. This can be attributed to the dominant effect of solar radiation over other weather variables. Although lower relative humidity and higher mean air temperatures favored a higher theoretical evaporative demand inside the greenhouses (as evidenced by the data during the unventilated period in the spring of both years), greenhouse $R_s$ was much lower than outdoor $R_s$. This sharp gradient in solar radiation between the two settings caused the large difference in ${\mathrm{ET}}_{\mathrm{o}}$ between the outdoors and inside the greenhouse. These findings are in agreement with lysimetric greenhouse evapotranspiration measurements reported by Orgaz et al. (2005), who found that the actual seasonal evapotranspiration of greenhouse crops is lower than that of outdoor crops. This was attributed to a lower reference ${\mathrm{ET}}_{\mathrm{o}}$ rather than to lower crop coefficient values, which agrees with the results reported herein. Fernández et al. (2010) showed that greenhouse ${\mathrm{ET}}_{\mathrm{oPM}}$ can be accurately estimated using radiation methods in humid climates when the aerodynamic term is relatively small (i.e., with high aerodynamic resistance), which is also in general agreement with the results presented herein.

Prediction of greenhouse ET using the Hargreaves equation was better validated in the unventilated case [Fig. 3(f)] than in the ventilated case [Fig. 3(b)]. In the semiarid environment at the AREC site, ventilation brought drier air into the greenhouse, which increased evapotranspiration. This was not the case for the coastal weather in Beirut; hence, the prediction using the Hargreaves equation at the AUB site could not be validated at the AREC site [Fig. 3(b)]. In the unventilated case, the relationship between greenhouse ET and the outdoor Hargreaves equation was valid regardless of the climatic conditions (i.e., the relationship did not differ between arid, semiarid, and humid environments). The same applied to the prediction using the outdoor solar radiation [Figs. 3(c and g)].

Greenhouse transmissivity $\tau$ is another major factor in relating greenhouse ${\mathrm{ET}}_{\mathrm{oPM}}$ to outdoor solar radiation $R_s$. Greenhouse transmissivity $\tau$ is an important factor in determining the energy fraction that reaches the plants in the greenhouse. Greenhouse transmissivity at the AREC site was found to be much higher than at the AUB site. Average $\tau$ was 0.49 for the AUB greenhouse (longer period of measurements) and 0.73 at the AREC greenhouse. This can be attributed to the newer greenhouse material at the AREC site. Transmissivity is usually a function of the type and age of the greenhouse material, the shading, and greenhouse geometry and orientation. Incident solar radiation also affects the daily transmissivity values because of variations in the sun’s azimuth and atmospheric cloudiness (Castilla 2013; Sánchez et al. 2015b; Von Zabeltitz 2011). The orientation of the greenhouse roofs and walls allowed more solar radiation to enter the greenhouses in winter than in summer (due to roof reflection). Also, higher values of $\tau$ were observed in winter due to cloudiness, and this minimized the difference between outdoor and indoor incident solar radiation. Greenhouse transmissivity values for the AUB site were lower than those reported by Fernández et al. (2010), who noted a reduction in solar radiation of 39% for unwhitened greenhouses. This indicates that good estimates of $\tau$ are crucial for calculating evapotranspiration inside greenhouses, and therefore $\tau$ must be taken into account when predicting greenhouse ET from outdoor $R_s$. The difference between $\tau$ at the two sites affected the regression equation parameters that relate greenhouse ET to outdoor $R_s$. GH ${\mathrm{ET}}_{\mathrm{oPM}}$ at both sites was related to the measured outdoor $R_s$ and the square root of the transmissivity (Table 3). The derived relationship was validated with data collected at the AREC site for ventilated conditions (with a relative error of less than 10%):where $R_{sm\_\mathrm{out}}$ = measured outdoor solar radiation in equivalent $\mathrm{mm}/\mathrm{day}$; and the constant 0.42 and the transmissivity $\tau$ are unit-less.

The greenhouse vapor pressure deficit (VPD) was highly correlated with the outdoor VPD under ventilated conditions [Fig. 7(a)], but not under unventilated conditions [Fig. 7(b)]. For unventilated conditions, the vapor pressure deficit in the greenhouse was correlated with the difference between the inside and outside air temperatures [Fig. 7(d)], which was not the case when the greenhouses were ventilated [Fig. 7(c)]. The radiation exchange in unventilated greenhouses is complex due to the longwave net radiation term in the energy balance equation.