2.2. The Greenhouse Energy Balance
The physical properties of the glass covering strongly affects the greenhouse radiation balance. In fact, the glass covering transmittance (GCT) is about 70% in the visible (VIS) and near infrared (NIR) wavelengths, but only 3% in the far infrared (IR). As a result, while a relevant part of the global solar radiation (GSR) enters the greenhouse, the sky long waver radiation (SKLR) cannot enter and is discarded from the radiation balance. In the same way, Albedo (A – the fraction of GSR reflected by surfaces inside the greenhouse) can exit without interference, while the long wave radiation emitted inside cannot exit from the greenhouse. Therefore, used in place of the SKLR, is the greenhouse cladding long wave radiation (GCLR) emitted toward the ground from the upper and sidewalls of the greenhouse (cladding surface). Cladding surface emits in function of its temperature, according to the Stefan–Boltzmann law. The latter will be partly balanced by the radiation emitted upward from the surface (SULR), which is also estimated with the Stefan–Boltzmann law.
The greenhouse energy balance model applied in this work is based on the former work of Mariani et al. [14
]. The model works with an hourly time step and all the fluxes are expressed in Wm−2
. The fluxes directed towards the greenhouse ground surface are assumed positive.
The greenhouse net radiation (GNR) at the ground surface inside the greenhouse is expressed as:
GNR = CTGSR GSR (1 − A) − CTLR SULR + GCLR
GNR is the greenhouse net radiation and is used in place of the standard radiation budget of earth’s surface suitable for field crops.
CTGSR is the transmittance for global solar radiation
CTLR is the transmittance for far infra-red radiation.
The term GNR is used both for the energy balance of the greenhouse and as a term of net radiation equation of the Penman–Monteith model, for the simulation of the reference crop evapotranspiration (ET0).
More specifically, the energy balance equation (all terms are in W m−2) is expressed as:
GNR + G + LE + FV + FW = ΔQS + ΔQP
where G is the ground heat flux, LE is the latent heat evapotranspiration flux, FV is the flux through the vent-holes (term of flow by convection—chimney effect—and advection through the openings in a closed greenhouse), and FW is the flux through the windows (heat flow through the cladding surface of the greenhouse). Finally, ΔQS is the accumulation of heat in the greenhouse and ΔQP is the accumulation term of photosynthesis.
The convention adopted is that fluxes directed towards the greenhouse ground surface are positive while the others are negative. To moderate the excessive summer heat, the aeration (term Qvent) is adopted, while shading is avoided.
The equations adopted to simulate the different terms of the energy balance are hereafter described.
G is expressed as function of GNR:
G = − 0.05 × GNR for GNR > 0 while G = − 0.5 × GNR for GNR < 0.
FW = Kr Sc (t2 − t1) /S [W m−2]
Sc is the greenhouse cover area,
S is the greenhouse floor area,
Kr is the coefficient of heat transmission [W m−2 °C−1],
t1 and t2 are the temperatures, respectively, inside and outside the greenhouse [°C] (being the working hypothesis, outer surface with t = t2 while inner surface t = t1).
FV = (R V (t2 − t1) Cs/3600)/S [W m−2]
V is the greenhouse volume [m−3],
R is the number of air volumes exchanged per hour
Cs is the specific heat of the humid air [J kg−1 °C−1] and is calculated with the equation Cs = cpm rom where cpm is the enthalpy of the humid air (cpm = 1005 + 1820 rms), rms is the mixing ratio [kg of water vapor per kg of air], and rom is the density of the humid air [kg m−3] (rom: = ro × (1 + rms(1013,t1)/1000)/(1 + 1.609 × rms(1013,t1)/1000).
The latent heat flux equation is:
LE0 = − ET0 kc ((2450 1000)/3600)
ET0 is the Penman–Monteith reference crop evapotranspiration [mm h−1
kc is the crop coefficient for rose.
The terms of the balance described above are used for the following equations
Ie_min = GNRTLn + FWTLn + FVTLn + GTLn + LETLn + AW
Ie_max:= GNRTLx + FWTLx + FVTLx + GTLx + LETLx + AC
where TLn and TLx are equal to 21 and 23 °C during day (period between sunrise and sunset) and to 15 and 17 °C during night. AW and AC [W m−2] are air heating and air conditioning of the previous hour. The operational rule adopted is that if Ie_min < 0 the negative value is compensated by heating, while if Ie_max is >0 the positive value is compensated by air conditioning.
In the present work, only the heating needs will be considered. The model works with an hourly step due to the fact that the variability of rate variables is strong enough to request an hourly approach.
The scheme described was already calibrated and validated by Mariani et al. [14
] in order to obtain the heating requirements for tomato production.