Predicting the Microclimate in a Naturally Ventilated Plastic House in a Mediterranean Climate

J. agric. Engng Res. (2000) 75, 27}38 Article No. jaer.1999.0482, available online at http://www.idealibrary.com on

Predicting the Microclimate in a Naturally Ventilated Plastic House in a Mediterranean Climate S. Wang; T. Boulard Unite& de Bioclimatologie, INRA, Site Agroparc, 84914 Avignon Cedex 9, France; e-mail: [email protected] (Received 24 December 1998; accepted in revised form 11 August 1999)

The microclimate of a naturally ventilated plastic house was simulated for 23 days using the Gembloux Greenhouse Dynamic Model (GGDM). Improved calculations of natural ventilation #ux and stomatal resistance of vegetation were introduced, based on experimental equations from previous research. A linear non-dimensional ventilation function was developed and compared with those obtained by other authors. Experimental microclimate parameters were used to validate the dynamic performance of the model. Good agreement was obtained between prediction and measurement. For the period from 7 April to 18 April 1992, the standard deviations between the predicted and experimental soil temperature, interior air temperature, relative humidity and crop transpiration were 0)53C, 0)83C, 4)3% and 17)8 W/m2, respectively. Sensitivity analysis showed that the external wind speed and the opening angle of the vents were the most important factors in#uencing the ventilation #ux, and that the in#uence of internal global solar radiation on crop transpiration was much more important than inside air saturation de"cit. ( 2000 Silsoe Research Institute

comes comparable with the rates of time change of the boundary conditions. Thus, a number of dynamic climate models have been developed (Takakura et al., 1971; Kindelan, 1980; van Bavel et al., 1981; Bot, 1983; de Halleux, 1989; Zhang et al., 1997). Despite improvement in the estimation of the greenhouse climate, very few of the models can be used to predict the microclimate over a long period in a full-scale greenhouse under Mediterranean conditions. Prediction is especially di$cult when both ventilation and heating are activated and when the well-developed crop transpiration represents the biggest contribution to the energy balance of the greenhouse (Seginer, 1997). The present study applied the Gembloux Greenhouse Dynamic Model (GGDM) (Deltour et al., 1985) to predict the microclimate in a naturally ventilated plastic house under Mediterranean climatic conditions. A new natural ventilation model, based on the recent contributions to natural ventilation (Boulard & Baille, 1995; Boulard et al., 1996), is included in GGDM. The transpiration process can utilize up to 70% of the solar radiation absorbed by the greenhouse-crop system in summer period (Boulard et al., 1991). The modelling of

1. Introduction Predicting the microclimate inside a greenhouse can help growers to manage crop production and designers to improve the ventilation and heating systems. The internal microclimate can be investigated by experiment and simulation. As compared with experiments, simulation methods may be performed quicker in less expensive, more #exible and repeatable ways. The in#uences of natural ventilation and crop transpiration on the indoor microclimate, should be involved in a more realistic way than in most of the existing models, and would make important contributions to the energy and mass balances of a greenhouse. Early studies of the greenhouse microclimate concentrated on determining the thermal behaviour of the greenhouse (Whittle & Lawrence, 1960; Businger, 1963; Walker, 1965). In order to characterize the mean behaviour of particular elements in the greenhouse, several basic static energy balance models were used (Morris, 1964; Bailey, 1977; Nijskens et al., 1984; Breuer & Short, 1985; Jolliet, 1991). The usefulness of static models decreases when the time response of the greenhouse be0021-8634/00/010027#12 $35.00/0

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Notation A window area, m2 0 C heat capacity per unit volume of the air, a J/m3 K C discharge coe$cient d C speci"c heat of air at constant pressure, p J/kg K C wind e!ect coe$cient w d characteristic length of the vegetation, m D conductive heat #ux density, W/m2 D air saturation de"cit, Pa a e water vapour content of the air, kg/m3 F cloud factor of the sky cn f translation factor s g gravity constant, m/s2 G(a) non-dimensional ventilation function Gr Grashof number h vertical height of vent openings, m h convective heat transfer coe$cient, Vvi W/m2 K I leaf area index l ¸ latent heat #ux density, W/m2 ¸ length of vents, m 0 ¸e non-dimensional Lewis number ¸ crop transpiration, W/m2 vi Nu Nusselt number Pr Prandtl number P shading factor of the vegetation v Q air heating #ux density, W/m2 in r psychometric constant, Pa/K r aerodynamic resistance of the leaf, s/m a R thermal radiant heat #ux density, W/m2

transpiration has been improved by considering the climatic dependence of the crop stomatal resistance. Two main approaches of crop transpiration, based on the direct physical formula or on the Penman}Monteith equation, are considered. Soil temperature, interior air temperature and relative humidity, and crop transpiration estimated using the improved model, are "rstly compared with the measured ones. Then the validated model is used in a sensitivity analysis to quantify the impact of input parameters on the heat balance, with special attention paid to the ventilation and transpiration #uxes.

2. Experimental set-up 2.1. Site and greenhouse description Experiments were carried out in a 416 m2 two-span plastic house, located in Avignon in the south of France. Natural ventilation was controlled by continuous roof vents situated near the gutters (Fig. 1). The measurements

R2 R a Re r f RH s S S g ¹ ; < < g a j o c D¹ / v c e i r s s1}s3 ss v *

coe$cient of determination ventilation rate, h~1 Reynolds number stomatal resistance of the leaf, s/m relative humidity, % slope of saturation vapour pressure to temperature, Pa/K solar radiant heat #ux density, W/m2 global solar radiation, W/m2 temperature, K wind speed, m/s convective heat #ux density, W/m2 volume of the greenhouse, m3 opening angle, deg thermal conductivity of the air, W/mK air density, kg/m3 latent heat of water vaporization, J/kg interior}exterior air temperature di!erence, K ventilation #ux, m3/s cover exterior air interior air sky soil surface "rst to third soil layer subsoil vegetation saturated value

} mean value

were performed over two periods (16}26 March and 7}18 April 1992) when both heating and ventilation were needed. A tomato crop was grown on a substrate consisting of rockwool slabs. Physical characteristics of the greenhouse cover, vegetation and soil are listed in Table 1.

2.2. Instrumentation A meteorological station was installed just above the greenhouse. This measured global solar radiation (pyranometer), wet and dry-bulb temperatures (ventilated platinum resistance thermometer), wind speed and direction (cup anemometer and wind vane). Sensors for internal microclimate variables within the centre of the greenhouse were installed at a height of 1)5 m. The variables included global solar radiation (above the canopy), wet and dry-bulb air temperatures and "rst soil layer temperature. The opening angle of the vents was monitored by a potentiometer. The amount of

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system of irrigation and drainage. The accuracy of the balance was $10 g and was equivalent to $5 g/m2 of transpiration. All the variables were measured every minute, then averaged and recorded hourly using a data logger (Solartron, Schlumberger).

3. Greenhouse dynamic energy balance model 3.1. Structure of the model

Fig. 1. Schematic plan of the greenhouse with the measurement locations (U , external wind speed; T , interior air temperature; e i a, vent opening angle; h, vertical height of the opening; L , 0 vent length)

greenhouse heating was deduced from the measurements of the water temperature at the inlet and outlet of the heating pipe and from the water #ow rate measurements. The leaf area index was estimated each week from measurements of leaf dimensions (non-destructive measurements) and from the correlation between the width and length of the leaves and their surface area (destructive measurements). Crop transpiration was determined by means of a weighting lysimeter, supporting four plants with their rockwool slabs and an independent

The GGDM has been validated in large multi-span glasshouses by Deltour et al. (1985), de Halleux (1989) and Nijskens et al. (1991). It is a classical one-dimensional thermodynamic model that calculates the dynamic energy balance of each greenhouse component (Fig. 2) denoted by subscripts for the cover c, the interior air i, the vegetation v and three soil layers s1, s2 and s3. The interactions between the six layers include heat transfers by conduction D, convection <, solar radiation S and thermal radiation R, as well as the latent heat exchanges ¸. The sensible and latent heat #uxes are calculated for each layer and used to generate the energy and mass balance equations. Detailed descriptions of the equations in the model are given by de Halleux (1989) and Wang et al. (1990). The energy and mass balance equations were solved for given boundary conditions, using an iterative procedure with a simulation time step 1 min, to obtain the unknown temperatures and

Table 1 Characteristics of the cover, the vegetation and soil

Cover Material Transmissivity, % Re#ectivity, %
Solar radiation

Thermal radiation

62 13

28 11

17 22 61

} 5 95

70 30

15 85

Second layer 0)15 2)00 1450 1250

¹hird layer 0)70 2)00 1600 1350

PVC "lm

Tomato

75 4180 White plastic "lm 16 First layer 0)01 2)50 1300 1200

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Fig. 2. Diagram of the heat transfers in Gembloux Greenhouse Dynamic Model where Q is air heating yux density in

humidity of the di!erent layers. The input parameters were subsoil temperature, external air temperature and relative humidity, equivalent radiant sky temperature, global solar radiant #ux density, wind speed, ventilation rate and air heating #ux.

3.2. Improvements of the model 3.2.1. Natural ventilation -ux Under Mediterranean conditions, particularly in spring and summer, natural ventilation plays an important role in the energy and water vapour balances of greenhouses. Several equations for air exchange in greenhouses have been derived with respect to the two main driving forces: buoyancy and wind. It was found that both e!ects were of the same order of magnitude when the wind speed was lower than 2 m/s. Therefore, a relationship which accounted for the combination of thermal and wind e!ects was taken from Boulard & Baille (1995):

CA

¸ C¹ /" 0 d e v 3g*¹

B

D

g*¹ h#C ;2 3@2!(C ;2)3@2 w e w e ¹ e

(1)

where C and C are empirical discharge and wind e!ect d w coe$cients, estimated for this greenhouse as 0)644 and 0)09, respectively (Boulard & Baille, 1995); g is gravity constant in m/s2; h is the vertical height of the vent

opening in m; ¸ is the length of the continuous vents in 0 m; ¹ and D¹ are the exterior air temperature and the e interior}exterior air temperature di!erence respectively in K; ; is the external wind speed in m/s; and / is the e v ventilation #ux in m3/s. The ventilation rate R in h~1 for the model input can a also be deduced from the above ventilation #ux: 3600/ v R" a < g

(2)

where < is the volume of the greenhouse in m3. g 3.2.2. ¸atent heat exchange from the vegetation 3.2.2.1. Stomatal resistance Transpiration greatly in#uences the energy and mass balances inside a greenhouse. Water vapour exchange has to overcome the stomatal resistance and the aerodynamic resistance of the boundary layer around the leaf. The measurement and modelling of the stomatal resistance of tomato crops under greenhouse conditions have been done by Stanghellini (1987), Boulard et al. (1991) and Jolliet and Bailey (1994). Stomatal resistance varied mainly as a function of internal global solar radiation and partly as a function of the greenhouse air temperature above 303C and of saturation de"cit above 1 kPa. In spring, when the model was tested, the air temperature

PRE D I C TIN G T H E M ICR O CL I M A TE IN A M ED I T ER RA N EA N C LI M AT E

and the saturation de"cit sometimes exceeded those threshold values. Thus, a simple empirical relationship between stomatal resistance r in s/m, internal global solar f radiation S in W/m2 and air saturation de"cit D in Pa, gi a taken from Boulard et al. (1991), was used:

A A

B

1 r "200 1# f exp (0)05(S !50)) gi

A A

] 1#0)11exp 0)34

3.2.2.3. Crop transpiration Crop transpiration ¸ in W/m2 is deduced from r and vi a r using either the direct physical formula f ¸ "¸e1@3P I c(r #r )~1(e*!e ) v i vi v l a f

(6)

or the Penman}Monteith approach,

BBB

D a !10 100

sS r 2I oC D gi a l p a ¸ " # vi (s#r)r #2rr (s#r)r #2rr a f a f

(3)

The second factor on the right-hand side of Eqn (3) shows that stomatal resistance decreases with the solar radiation S . When S is greater than 100 W/m2, gi gi r maintains a constant value 200 s/m. The third factor f on the right-hand side of Eqn (3) shows that stomatal resistance increases with inside air saturation de"cit above 10 kPa. 3.2.2.2. Aerodynamic resistance The aerodynamic resistance r in s/m is linked to the a convective heat #ux < in W/m2 between the vegetation vi and the interior air: C (¹ !¹ ) i < "h (¹ !¹ )" a v vi Vvi v i r a

(4)

where h is the convective heat transfer coe$cient in Vvi W/m2 K; C is the heat capacity per unit volume of air in a J/m3 K; and ¹ and ¹ are the interior air and vegetation i v temperatures in K. The aerodynamic resistance is needed to "nd the solution of the convective heat transfer coe$cient C /h . This coe$cient was calculated on the basis of a Vvi an empirical approach of Monteith (1973): j h "Nu Vvi d

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where C is the speci"c heat of air at constant pressure in p J/kg K; e is the water vapour content of the interior air in i kg/m3 and e* is the saturated water vapour content of air v at the vegetation temperature in kg/m3; I is leaf area l index expressed as leaf area per unit ground area; ¸e is the non-dimensional Lewis number, equivalent to the ratio of the thermal di!usivity of air to the molecular di!usivity of the water vapour; P is a shading factor of v the vegetation which refers to the proportion of greenhouse ground area covered by the vegetation; r is the psychometric constant in Pa/K; s is the slope of saturated vapour pressure to temperature in Pa/K; c is the latent heat of water vaporization in J/kg; and o is air density in kg/m3. 3.2.3. Radiant sky temperature The thermal radiant exchange with the sky in#uences the heat balances of the soil surface, the vegetation and the cladding material (partly transparent to the thermal radiation). It is therefore necessary to determine the radiant sky temperature ¹ in K. As the latter is highly r dependent on the cloud cover, an empirical formula proposed by Swinbank (1963) was used:

(5)

where: j is thermal conductivity of the air in W/m K; d is characteristic length of the vegetation in m; and Nu is the Nusselt number expressed in Table 2, according to the #uid dynamic theory described by Monteith (1973). A detailed description of the calculation of h can be found Vvi in de Halleux (1989) and Pieters et al. (1994).

(7)

¹ "F ¹ #0)0552(1!F )¹1>5 r cn e cn e

(8)

where F is the cloud cover factor (1, overcast and 0, cn clear). The cloud cover was estimated from the ratio of di!use and global solar radiation during the day, and from the external air temperature modi"cation during the night (a detailed calculation for F can be found in cn de Halleux et al., 1991).

Table 2 Nusselt number Nu for laminar and turbulent 6ow in natural and forced convective mode past a 6at plate (Monteith, 1973); Gr, Grashof number; Pr, Prandtl number; Re, Reynolds number Laminar yow

Turbulent yow

Natural convection (Gr/Re2*16)

Nu"0)54 (Gr Pr)1@4(Re(5]104)

Nu"0)14 (Gr Pr)1@3(Re'5]104)

Forced convection (Gr/Re2)0.1)

Nu"0)67Re1@2Pr1@3 (Gr(108)

Nu"0)36Re4@5Pr1@3(Gr'108)

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4. Results and analysis 4.1. Global solar radiation Solar radiation provides the photosynthetic energy for the plant growth. Internal global solar radiation depends on greenhouse shape and orientation and cover radiometric properties. A greenhouse transmits di!erent amounts of solar energy to di!erent positions (Critten, 1983). The values at these positions were extensively simpli"ed based on the sun position, transmittance of the cover and experimental direct and di!use solar radiative #ux densities, at the meteorological station. The comparison between simulation and measurement of the internal global solar radiation is shown in Fig. 3, for 264 observations. Linear regression analysis had an R2 of 0)99 with a slope of 1)0 and an intercept of 1)8 W/m2 (the standard deviation between measured and calculated solar radiation was 12)4 W/m2). This high accuracy was a prerequisite to allow a precise simulation of the other climatic variables and crop transpiration.

4.2.
Fig. 4. Computed ventilation yux (~), measured wind speed (---) and opening angle ( ) ) ) ) during the test period (16}26 March)

later (about 0)5}2 m3/s) for the rest of the time when the vents were nearly closed. A non-dimensional ventilation function G(a) is widely used to compare the ventilation performances from different greenhouse types (Fernandez & Bailey, 1992; Kittas et al., 1995; Wang & Deltour, 1996): / G(a)" v (9) UA e 0 where A is the window area in m2 and a is the opening 0 angle in degree. On the basis of the measurement data during the period of 16}26 March, the non-dimensional ventilation function from the ventilation #ux computed by Eqn (1) and the experimental wind speed can be plotted as a function of the window opening angle (Fig. 5). The straight line corresponding to this study was "tted to the measured values (264 data; coe$cient of determination R2"0)99) with the following expression: G(a)"1)758]10~3a

Fig. 3. Comparison between simulated indoor global solar radiation and the measured value

(10)

Fig. 5. Four diwerent non-dimensional ventilation functions as a function of the opening angle; , Fernandez and Bailey (1992); , Kittas et al. (1995); , Wang and Deltour (1996); , this study

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the geometry of the window is of minor importance. The function of Fernandez & Bailey (1992) is a little below that of this study, probably because it was only validated for small ((163) opening angles. The overestimation of the function by Kittas et al. (1995) is due to the external wind speed being measured at 4 m above the ground while in this case it was measured at a height 5)5 m.

4.3. First soil layer temperature, interior air temperature and relative humidity

Fig. 6. Comparison of the xrst soil layer temperature T , interior sl air temperature and relative humidity between simulation and measurement (16}26 March); , external; ~~, measured; ) ) ) ) ) , simulated

The other three existing non-dimensional ventilation functions, are also presented in Fig. 5. The good agreement between this study and other studies whose function were derived from small (Fernandez & Bailey, 1992) or large (Wang & Deltour, 1996) greenhouses with noncontinuous (Fernandez & Bailey, 1992) or continuous (Kittas et al., 1995) roof vents, seems to indicate that

The comparative analysis between simulation and measurement can determine the suitability and reliability of the GGDM when applied to Mediterranean conditions. Figure 6 shows the simulated and measured values of "rst soil layer temperature, interior air temperature and relative humidity, for the period of 16}26 March. Larger residuals between measurement and simulation for these parameters were found during sunrise and sunset periods. This error was probably caused by the larger capacity given in the simulation system. The relative humidity during the "rst three and a half days was lost because the cotton mesh used for the wet-bulb temperature measurement was dry. The values of mean, maximum and standard deviation of the absolute errors of the test variables are listed in Table 3. The standard deviation of the "rst soil layer temperature, interior air temperature and relative humidity between simulation and measurement were 0)53C, 0)83C and 3)8%, respectively. The experimental data were plotted as a function of the simulated ones for "rst soil layer temperature, interior air temperature and relative humidity for the period of 7}18 April. The linear regression for 288 observations (Fig. 7) had R2 values of 0)87, 0)90 and 0)67 for ¹ , ¹ and RH , respectively. s1 i i

Table 3 Comparison results between measurement and simulation Date

Parameters

Mean absolute error

Maximum absolute error

Standard deviation

16}26 March (N"264)

First soil layer temperature, 3C Air temperature, 3C Relative humidity, % Global solar radiation, W/m2

0)8 1)0 5)3 6)5

2)7 4)3 17)1 58)6

0)5 0)8 3)8 12)4

7}18 April (N"288)

First soil layer temperature, 3C Air temperature, 3C Relative humidity, % Crop transpiration, W/m2*

0)7 0)9 5)6 14)5

2)4 3)7 19)0 68)7

0)5 0)8 4)3 17)8

N, observation number. * Simulated by Eqn (6).

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transpiration in the middle of the day and at night. This discrepancy was probably the result of a poor estimation of the sky radiant temperature during this period. However, the present model was generally satisfactory for predicting the crop transpiration both during day and night. This was illustrated by the good agreement between estimated and measured values of the crop transpiration for 288 observations (R2 of 0)96, standard deviation of 17)8 W/m2, slope of 0)94, intercept of !8)5 W/m2). A similar and good result was also obtained by the Penman}Monteith equation (R2 of 0)96, standard deviation of 17)9 W/m2, slope of 0)99, intercept of !8)2 W/m2). A perceptive improvement in estimation of crop transpiration was observed during the day when air saturation de"cit was low as shown in Fig. 9, especially for the two last days of the series.

4.5. Sensitivity analysis Sensitivity analysis can help to quantify the impact of the input parameters on the ventilation #ux. According to a previous study (Wang et al., 1990), the sensitivity of the ventilation #ux / to the external wind speed can be v de"ned as

Fig. 7. Simulated (sim) xrst soil layer temperature T , interior air sl temperature T and relative humidity RH plotted against the i experimental (exp) data (7}18 April)

4.4. Crop transpiration The transpiration #ux was measured by the lysimeter and was calculated by Eqns (6) and (7) where the relevant parameters were simulated by GGDM. Figure 8 shows the simulated and experimental hourly crop transpiration versus time for 12 successive sunny days (7}18 April). The direct physical model slightly underestimated crop

; d/ f" e v (11) s /M d; v e where f is the translation factor of the external modi"cas tion on the ventilation #ux and /1 is the mean ventilation v #ux during the simulation. The larger the translation factor, the more e!ect the parameter ; has on the value e of / . As an example, the analytical form of the translav tion factor of the ventilation #ux to the external wind speed is given in Appendix A. A sensitivity analysis for ventilation was carried out by the evaluation of the translation factors concerning external wind speed, interior}exterior air temperature di!erence, vertical height of the opening and exterior air temperature for the period of 16}26 March. It was found (Fig. 10) that the translation factors were nearly zero during the night since the greenhouse vent was almost closed. During the day, the external wind speed and the vertical height of the vent opening were the largest in#uences on the ventilation #ux with similar e!ects. The temperature di!erence has a small and positive e!ect, whereas the external air temperature has a negative in#uence on the ventilation #ux because / decreases when ¹ increases. v e It is clear, from Eqn (7), that the two main parameters in#uencing crop transpiration are internal solar radiation and air saturation de"cit. The sensitivity study can help to quantify the relative importance of both parameters and the consequences of stomatal regulation on transpiration, with respect to high saturation de"cits.

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Fig. 8. Comparison between simulated crop transpiration using direct physical formula (~) and the Penman}Monteith equation (---) and experimental ( ) value as a function of time for 12 successive sunny days (7}18 April)

The analytical forms of the translation factor of crop transpiration to internal global solar radiation and air saturation de"cit, are also given in Appendix A.

A sensitivity analysis for crop transpiration was carried out based on the evaluation of the translation factor for the period of 7}18 April. It was found (Fig. 11) that

Fig. 9. Indoor global solar radiation S (=) and air saturation dexcit D (}) as a function of time for 7}18 April gi a

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S . W AN G ; T . BO U LA RD

Fig. 10. Translation factors of the ventilation yux to relevant parameters for 16}26 March; ~h*, external wind speed; ~~, interiorexterior air temperature diwerence; , vertical height of the opening; , exterior air temperature

the radiative e!ect was much more important than the convective one, particularly during the periods when the saturation de"cit was low (17}18 April) in Fig. 9. During sunny days, it was clear (Fig. 11) that the relative importance of radiative and convective e!ects on crop transpiration was not symmetrical with respect to solar noon: the radiative e!ect predominated in the morning, though the convective e!ect became important in the afternoon. A very sharp decrease of the translation factor was clearly observed concerning saturation de"cit at the beginning of the afternoon when D became greater than a 1 kPa. Above 1 kPa the e!ect of an increase of saturation de"cit, on the limitation of stomatal conductance, was much more important than the e!ect of a direct increase of the gradient of water vapour between leaf and air.

5. Conclusions Availability of the improved Gembloux Greenhouse Dynamic Model allows the prediction of the micro-

climate inside an experimental plastic greenhouse, which is a!ected in various ways by natural ventilation, air heating and crop growth. Air exchange rates reach high values during diurnal periods under a Mediterranean climate due to greenhouse natural ventilation using continuous roof vents. The selected equation was used successfully to predict the ventilation #ux from previous work, with experimentally identi"ed discharge and wind e!ect coe$cients. The derived non-dimensional ventilation function matched well with those of other authors. It was shown that empirical coe$cients of this function had similar values for continuous or non-continuous ventilation vents and for di!erent types of greenhouse structures. The sensitivity analysis showed that the external wind speed and the opening angle of the vents were the most important factors that in#uence the ventilation #ux. Comparison between simulated crop transpiration using the Penman}Monteith equation or a direct physical formula and measured values showed that, in protected conditions, both approaches gave similar results. However, the Penman}Monteith approach gave better

PRE D I C TIN G T H E M ICR O CL I M A TE IN A M ED I T ER RA N EA N C LI M AT E

Fig. 11. Translation factors of crop transpiration to indoor solar radiation (

estimations when air saturation de"cit was low. This good agreement proved that the choice of the models of stomatal and aerodynamic resistances was appropriate. The sensitivity analysis also showed that in greenhouse conditions, the contribution of solar radiation to transpiration was much more important than that of convection. After the validation under Mediterranean climatic conditions, this model and the attached sensitivity analysis could be applied to develop a better understanding of the dynamic behaviour of the greenhouse and of crop transpiration. In particular, this study could be used to maintain a better balance between irrigation and greenhouse crop transpiration and to prevent extreme air temperatures and humidity.

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) and air saturation dexcit (~~) for 7}18 April

Boulard T; Baille A; Mermier M; Villette F (1991). Mesures et modeH lisation de la reH sistance stomatique foliaire et la transpiration d'un couvert de tomates de serre [Measurement and modelling of stomatal resistance and transpiration in a greenhouse tomato canopy]. Agronomie, 11, 259}274 Boulard T; Meneses J F; Mermier M; Papadakis G (1996). The mechanisms involved in the natural ventilation of greenhouses. Agricultural and Forest Meteorology, 79, 61}77 Breuer J J G; Short T H (1985). Greenhouse energy demand comparisons for the Netherlands and Ohio, USA. Acta Horticulture, 174, 145}153 Businger J A (1963). The glasshouse (greenhouse) climate. In Physics of Plant Environment, pp. 277}318. North}Holland, Amsterdam Critten D L (1983). A computer model to calculate the daily light integral and transmissivity of a greenhouse. Journal of Agricultural Engineering Research 28, 61}76 de Halleux D (1989). Dynamic model of heat and mass transfer in greenhouses: theoretical and experimental study. PhD Thesis, Gembloux, Belgium, 278pp de Halleux D; Nijskens J; Deltour J (1991). Adjustment and validation of a greenhouse climate dynamic model. Bulletin des Recherches Agronomiques de Gembloux, 26, 429}453 Deltour J; de Halleux D; Nijskens J; Coutisse S; Nisen A (1985). Dynamic modelling of heat and mass transfer in greenhouses. Acta Horticulture, 174, 119}126 Fernandez J E; Bailey B J (1992). Measurement and prediction of greenhouse ventilation rates. Agricultural and Forest Meteorology, 58, 229}245 Jolliet O (1991). HORTITRANS, a model for predicting and optimizing humidity and transpiration in greenhouses. Journal of Agricultural Engineering Research, 57, 23}37

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Appendix A: analytical form of the translation factors
CS

¸ C C ¹ ;2 g*T f" 0 d w e e h#C ;2!JC ; w e w e s ¹ gD¹/1 e v Crop transpiration to indoor solar radiation:

D

(A1)

S f " gi s ¸ vi

C

A A

BBD

D a !10 20r¸ 1#0)11 exp 0)34 vi 100 sr a # (s#r)r #2rr [(s#r)r #2rr ] exp [0)05(S !50)] a f a f gi

G

H

(A2)

Crop transpiration to indoor air saturation de,cit:

G C

D 2I oC 0)15r¸ l p vi f" a ! s ¸ (s#r)r #2rr (s#r)r #2rr a f a f vi

D A A

BBH

1 D a !10 ] 1# exp 0)34 100 exp [0)05(S !50)] gi

(A3)