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Analysis of strategies for reducing calcium deficiencies in glasshouse grown tomatoes: model functions and simulations
Agricultural Systems 76 (2003) 181–205 www.elsevier.com/locate/agsy
Analysis of strategies for reducing calcium deficiencies in glasshouse grown tomatoes: model functions and simulations P.J.C. Hamer* Silsoe Research Institute, Wrest Park, Silsoe, Bedford MK45 4HS, UK Accepted 4 July 2002
Abstract Energy saving measures can result in high levels of humidity in greenhouses which reduces transpiration resulting in calcium deficiency symptoms on tomato leaves with subsequent loss of yield and quality. Transpiration can be increased by lowering the saturation deficit. Control strategies need to be cost-effective so that the benefits are in excess of the costs of carrying out the dehumidification. The HORTITRANS model [Journal of Agricultural Engineering Research, 57 (1994) 23], which predicts the conditions inside a greenhouse, was modified to enable simulations to be carried out for a developing crop and to quantify the effects of high humidity on yield and quality. Saturation deficit set-points were determined so that the transpiration rate was equal to a minimum of 0.65 kg m2 day1, a value derived to be satisfactory from experiments. Simulations were carried out for sample single and double glazed greenhouses with dehumidification by ventilation and heating. The cost of dehumidification was high when the ventilators were widely opened and so ventilation rates were constrained by restricting the maximum angle of opening. For a double glazed house additional profit was greater when the saturation deficit was controlled during the period of daylight compared to continuous control. For the single glazed house, a maximum angle of opening of 3 produced an additional profit of 6 p m2. One year in eight there was a loss. For the double glazed house, a maximum ventilator opening of 10 produced an average additional profit of 90 p m2. The models can be used to study control strategies for other types of greenhouse structures in different climatic regions where short-term (hourly) meteorological data exists using local information on prices and costs. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: Tomato; Calcium deficiency; Transpiration; Simulation control model
* Tel.: +44-1525-864023; fax: +44-1525-860156. E-mail address: [email protected] (P.J.C. Hamer). 0308-521X/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. PII: S0308-521X(02)00101-4
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1. Introduction Energy saving measures in greenhouses can result in high levels of humidity which can lead to yield loss and have detrimental effects on product quality. For example, double glazed greenhouses provide insulation and the tight fitting glass panes result in a low exchange of air with the outside environment. There is a decrease in condensation and moisture introduced transpiration remains in the house resulting in a high relative humidity. Tomato is a crop of major importance to the greenhouse industry and responds to changes in humidity. Tomato leaves which develop under low solar radiation intensities and high humidity are of reduced size and show signs of calcium deficiency (Holder and Cockshull, 1990). The subsequent loss of yield occurs from the trusses adjacent to the leaves that develop under high humidity. Calcium arrives at the leaves along with the transpiration stream since calcium is transported unidirectionally in the xylem and the amount builds up as the leaf grows and transpires (Aikman and Houter, 1990). There is a minimum rate of transpiration relative to leaf growth rate below which calcium deficiency symptoms occur. As well as the loss of yield fruit quality can be reduced, for example the physiological disorder blossom-end rot is associated with low calcium uptake (Adams and Ho, 1993). Experiments to quantify the effects of humidity on yield, control humidity (or saturation deficit) using set-points which are fixed for different periods of the experiment. The set-points, which may be different for the day and night periods, ensure large differences in humidity between treatments so that the crop response is significant. For example, the treatments of Bakker (1991) were ‘high’ or ‘low’ relative humidity by day (from sunrise to sunset) and combined with either a high or low relative humidity by night. The treatments were imposed for about 8 weeks. Holder and Cockshull (1990) maintained four nominal saturation deficits continuously (24 h per day) throughout a 4-week experiment and in another experiment two nominal saturation deficits were maintained either continuously day and night or changed between day and night for a 6-week period. Typically fogging systems are used to raise the humidity and ventilation to reduce it with the same air temperatures maintained at all humidities. However, in commercial greenhouses the relative humidity is constantly varying and the aim of humidity control is to avoid environments which would lead to yield and/or quality reductions. In addition the techniques for control must be cost-effective so that the benefits of control in terms of yield and quality are in excess of the costs of carrying out the dehumidification. In this paper, models are developed to predict the effects of humidity on the growth, yield and quality of fruit and the value of the crop. The environmental conditions inside the greenhouse are simulated using the HORTITRANS model (Jolliet, 1994), which is modified for a developing crop and further modified so that the aerial environment is controlled by saturation deficit set-points. Simulations are carried out to evaluate strategies for control. 2. Model concept In glasshouse-grown crop of indeterminate tomato, the main stem is allowed to develop and lateral shoots removed (unless a shoot is being trained to increase plant
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density by developing another main stem) resulting in the main stem bearing trusses separated by three leaves. The assimilate for the growth of fruit on the truss is mainly supplied by the three subtended leaves (Shishido and Hori, 1977). For the purpose of this model, leaf development is considered in terms of the combined leaf area of two leaves below and one above a truss. These leaves supply the assimilate for the growth of fruit of the associated truss (Bonnemain, 1966). The developmental stages can be defined by the number of the truss and the stages of growth of the associated leaves, flowers and fruit defined by easily determined markers. In this paper, the truss is treated as a whole and the date of anthesis is the date when 50% of the flowers have opened and the harvest date when 50% of the fruits from the truss have been harvested. The marker for leaf development is taken as l/lm=0.5 where l is leaf area and lm is leaf area when the leaves associated with the truss are fully expanded, i.e. when the leaf area is half the final area. Low transpiration rates as a result of high humidity influence leaf growth so that lm is reduced and the yield and quality of fruit from the associated trusses are also reduced. Fig. 1 illustrates how high humidity on 1 day can influence the yield and quality of fruit harvested over a considerable period. A humidity event on day 61, when l/lm=0.5 on truss 6, influences the fruit on this truss which is harvested over about a 3-week period. The humidity event also influences the leaves associated with trusses 5 and 7. At this time the growth rates of these leaves are smaller and therefore likely to have a smaller effect on the fruit production on these trusses. In this illustration the fruit harvested over about a 4–5 week period is influenced by a single short period humidity event.
Fig. 1. Schematic of tomato plant growth where 5, 6, 7 refers to the truss number.
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3. Model functions 3.1. Crop Developmental progress can be described in relation to thermal time (y), the integration of temperature (T) with time (t): ð y ¼ ðT Tb Þdt ð1Þ where Tb is a base temperature at which growth rate is zero. The base temperature for fruit development of 5 C (Aikman, 1996) is used to describe the development of all crop processes. For a tomato leaf growing at its potential, the leaf area (l(y)) relative to the area of the leaf when fully expanded (lm) can be described by a logistic (Hamer, 1996): lðyÞ 1 ¼ lm 1 þ expðbl ðy yl ÞÞ
ð2Þ
where bl=0.0204 Kd1 describes the rate of leaf expansion and yl is the thermal time when l(y)/lm=0.5. The thermal time increment of yl from the leaves of one truss to the next is 89 Kd. The potential leaf growth rate is the first derivative of Eq. (2): ðlðyÞ=lm Þ0 ¼
dðlðyÞ=lm Þ ¼ bl lðyÞ=lm ð1 lðyÞ=lm Þ: dt
ð3Þ
When the crop is grown in an environment leading to low transpiration, leaf growth rate is reduced and can be described as: fe ðlðyÞ=lm Þ0
ð4Þ
where the parameter, fe, limiting leaf growth rate is a function of transpiration: fe ¼ El =Ee when Et < Ec fe ¼ 1 when Et 5 Ec
ð5Þ
and where Et is the leaf transpiration rate and Ec is a minimum ‘critical’ leaf transpiration rate required for adequate leaf growth. If leaf transpiration rate is less than the critical rate, leaf growth rate is reduced. The form of this function is based on the following observations. The flux of calcium is roughly proportional to the transpiration flow since calcium arrives at the leaves along with the transpiration stream and its concentration does not vary much with flow rates (Aikman and Houter, 1990). Herdel et al. (2001) determined the concentrations of nutrients in the xylem sap from intact plants. Similar flux concentrations of calcium were observed during the night (low transpiration) and during the day (high transpiration).
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Concentrations of calcium, relative to leaf dry weight, of 0.39% and less show distinct deficiency symptoms. Holder and Cockshull (1990) showed that humidity treatments that gave calcium levels of 0.6 and 0.7% lead to reduced leaf size and yield and a small effect when the calcium level was 0.9%. Therefore there is a minimum target level for calcium. Since there is a direct relation between the flux of calcium and leaf transpiration there is a minimum transpiration requirement to avoid reductions in leaf size and subsequent effect on yield and quality. The leaf area at the end of leaf expansion (lf) relative to the potential (lm) is derived from the summation of the growth rate over the period of growth: X lf =lm ¼ fe ðlðyÞ=lm Þ0 ð6Þ Transpiration rate is constantly changing during the day in response to fluctuations in irradiance and the saturation deficit, whilst at night the transpiration rate is low. The period over which the crop responds to low calcium uptake is difficult to quantify experimentally. Transpiration (and hence calcium uptake) can be modified by controlling humidity. Bakker (1991) argued that the response of growth and yield to humidity shows a certain similarity with the response to temperature, i.e. a close relationship with the average level of either temperature or humidity. Earlier work demonstrated cumulative growth is not affected by alternating high and low temperatures for several days (de Koning, 1990). However, at the operational level of control, settings need to be adjusted on a daily basis (de Koning, 1994). Therefore, in this paper leaf transpiration is integrated over a 24 h period. The critical leaf transpiration (Ec) and functions relating lf/lm to yield and quality are derived from experiments. 3.2. Critical leaf transpiration, yield and quality functions 3.2.1. Data source The experiments were conducted at HRI Efford in a 16 compartment multi-factorial Venlo-type greenhouses in the 1987/1988, 1990/1991 and 1991/1992 seasons. The main aim of the experiments was to improve the understanding of the effects of humidity on the growth, yield and quality of fruit of a long season tomato crop. The crops were subjected to different humidity regimes by ‘day’ and ‘night’, each period was for 12 h and the change in set-points occurred at 06:00 and at 18:00 h. The water content of the air inside the compartments were controlled according to the saturation deficit. The saturation deficit was decreased by fogging and increased by a combination of heating and ventilation in the first two seasons and by dehumidifiers in the third. The achieved saturation deficits and the dates of establishment and treatment dates are presented in Table 1 for four treatments from combinations of low and high saturation deficits for the day and night periods. Dates of first and sixth anthesis, first and sixth fruit pick and the yield and marketable yield and the percentage of Class 1 fruit from each truss were recorded. Leaf area is taken as the length times breadth of the leaf subtended by a truss. The leaves expanding during the treatment were identified and the yield and quality of fruit on the associated trusses were noted. The treatments did not influence the timing of
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Table 1 The average ‘day’ (d) and ‘night’ (n) saturation deficits achieved in the HRI Efford experiments, the date the plant root made contact with the rockwool slab and the treatment dates. ^, *, ~, & are the symbols in Fig. 1. * Not reported Season
1987/1988 1990/1991 1991/1992
Achieved saturation deficits (kPa)
Slab contact date
d/n (^)
d/n (*)
d/n (~)
d/n (&)
0.19/0.14 0.11/0.10 0.10/0.10
0.20/0.45 0.21/0.17 0.16/0.59
0.48/0.15 0.40/0.37 0.56/0.13
0.56/0.50 0.53/0.50 0.60/0.76
18 December * 23 December
Treatment dates Start
End
20 January 9 December 3 February
2 March 1 March 15 March
development of the crops. The data were analysed by comparing the leaf areas and the yield and quality of the fruit from each treatment relative to the values from the crops grown with the highest saturation deficit (Table 2). The average percentage of Class 1 fruit from the treatments with the highest saturation deficit were 87, 86 and 83% in the first, second and third seasons, respectively. 3.2.2. Leaf transpiration The expanding leaves develop at the top of the crop canopy and are therefore fully exposed to the incoming irradiance and leaf transpiration. The leaf transpiration (El, kg m2 day1) was estimated as a linear function of irradiance (Sc, MJ m2 day1) at the top of the canopy and the saturation deficit (D, kPa) (Jolliet et al., 1993): El ¼ aSc þ bD
ð7Þ
Table 2 The ratio of leaf area (lf), yield (yf) and quality of fruit (qf) as percent in Class 1 relative to the leaf area (lm), yield (ym) and quality of fruit (qm) from the treatment with the highest saturation deficit Season
Saturation deficit (kPa)
lf/lm
yf/ym
qf/qm
Day
Night
1987/1988
0.19 0.20 0.48 0.56
0.14 0.45 0.15 0.50
0.79 0.88 0.90 1.00
0.88 0.94 0.96 1.00
0.95 0.98 0.98 1.00
1990/1991
0.11 0.21 0.40 0.53
0.10 0.17 0.37 0.50
0.71 1.03 0.99 1.00
0.73 0.85 0.99 1.00
0.85 0.97 0.99 1.00
1991/1992
0.10 0.16 0.56 0.60
0.10 0.59 0.13 0.76
0.74 0.89 0.85 1.00
0.69 0.88 0.98 1.00
0.82 0.96 0.96 1.00
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where a=0.121 kg MJ1 and b=b1(1b2exp(Sc/b3)) kg m2 day1 kPa1 where b1=1.04 kg m2 day1 kPa1, b2=0.63 and b3=0.864 MJ m2 day1. The change from the ‘day’ to ‘night’ treatments did not coincide with sunrise and sunset. Each day was divided into three periods: sunrise to sunset (Sc > 0 and D=Dd where Dd is the ‘day’ saturation deficit), sunset to 18.00 and 06:00 to sunrise (Sc=0 and D=Dd) and 18:00 to 06:00 (Sc=0 and D=Dn, where Dn is the ‘night’ saturation deficit). The daytime solar radiation at the top of the canopy was estimated from the daily total global solar radiation measured outside the house (Ss, MJ m2 day1), the transmissivity to short-wave radiation of the glasshouse (t) and the period from sunrise to sunset (ts, h): Sc ¼ tSs ð24=ts Þ
ð8Þ
A transmissivity of t=0.65 was assumed. 3.2.3. Derivation of critical transpiration Leaf transpiration was estimated daily for each treatment (Fig. 2). Leaf transpiration from the high humidity treatments were on occasions as low as 0.1 kg m2 day1 on dull days and increased to 1.6 kg m2 day1 on a day when the irradiance was high. The treatment with the highest saturation deficit increased the leaf transpiration typically by about 0.4 kg m2 day1. A critical transpiration of Ec=0.4 kg m2 day1 was assumed and fe determined from Eq. (5) for each treatment. The mean of fe was determined for the duration of the experiment and a regression analysis, with the intercept forced through the origin, related lf/lm to fe/fm where the subscript m refer to values obtained from the highest saturation deficit treatment. This analysis was repeated for different critical transpirations in the range 0.4–1.0 kg m2 day1 (Table 3). The slope, a1 was fitted to the assumed critical transpiration by a quadratic (R2=99.0%). The critical transpiration Ec=0.65 kg m2 day1 was assumed to be when a1=1.0. 3.2.4. Yield and quality The ratios yf/ym and qf/qm were related to lf/lm by quadratic functions. The parameters were derived by non-linear regression using the statistical package GENSTAT Table 3 The slope (a1) of the regression of lf/lm against fe/fm, with the line constrained through the origin, for different critical leaf transpiration (Ec) Ec (kg m2 day1)
a1
R2 (%)
0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.927 0.972 0.981 1.011 1.030 1.044 1.055
50.5 71.3 67.6 70.0 65.2 59.8 54.6
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Fig. 2. Estimates of leaf transpiration in (a) 1987/1988 (b) 1990/1991 and (c) 1991/1992 for each treatment (see Table 1 for key).
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(Payne et al., 1987). The regressions were constrained so that yf/ym=1 and qf/qm at lf/lm=1 with turning points at yf/ym=1 and qf/qm=1. The yield function [Fig. 3(a)] is: yf =ym ¼ 2:583 þ 7:166ðlf =lm Þ 3:583ðlf =lm Þ2 R 2 ¼ 85:3% ð9Þ and the quality function [Fig. 3(b)] is: qf =qm ¼ 0:984 þ 3:968ðlf =lm Þ 1:984ðlf =lm Þ2 R 2 ¼ 87:8%
ð10Þ
Fig. 3. (a) Yield (yf/ym) and (b) quality (qf/qm) in relation to leaf expansion (lf/lm). The fitted line for yield is Eq. (9) and for quality is Eq. (10).
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3.3. Value The financial return from dehumidification comes from the subsequent sale of the harvested fruit. For determining cost-effective strategies it is necessary to estimate the market prices of fruit so that the crop value of the increase in yield and quality is in excess of the cost of dehumidification. ’Bench-mark’ prices were collected from the Grower trade magazine (published by Nexus), for the years 1992–1994. The bench-mark price is what a competent grower might average over five trading days for Class 1 fruit after commission and marketing charges have been deducted. The bench-mark price is reported every 4 weeks during the harvest period. The average price for the reported week was fitted to a quadratic: v ¼ 161 5:21w þ 0:66w2 R2 ¼ 92:3% ð11Þ where v (p kg1) is the bench-mark price and w is the week number after the start of the year. The average was over the harvest period from weeks 8 to 44. The value of the earliest harvest is about 124 p kg1 and falls to the minimum in week 40 of 58 p kg1. There is considerable variation between seasons. The waste fruit from the Efford experiments was not influenced by treatment and was typically 2%. The fruit that was not Class 1 or waste was assumed to be Class 2 and to have a value of half that of Class 1. Waste is assumed to have no value. 3.4. Environment The HORTITRANS model (Jolliet, 1994) was used to predict the inside saturation deficit as a function of the outside conditions and the characteristics of the greenhouse. HORTITRANS uses a water balance approach to express the variation in the water vapour stored in the inside air as the difference between water vapour sources and sinks. Water sources are crop transpiration and water added by a fogging system and water sinks are condensation on the cladding, ventilation and water extracted by a dehumidification heat pump. All terms in the water balance are linearized. HORTITRANS determines the water and energy to be added to or extracted from the greenhouse air, in order to achieve set-points for humidity and transpiration and thus the cost of achieving set-points can be estimated. The characteristics of the greenhouse are described by parameters to indicate the size of the greenhouse, the ventilator area and angle of opening, an infiltration factor and the type of cladding (Jolliet et al., 1991). HORTITRANS requires hourly values of outside environmental variables of irradiance (global solar radiation), air and ‘sky’ temperature, humidity (or some measure of the water content of the air) and windspeed. A number of modifications to HORTITRANS were made. The leaf area index (L) for a developing crop is required to derive crop transpiration and is estimated from using thermal time (see Appendix). Estimates of sky temperature, procedure for determining set-points for controlling saturation deficit and functions for the cost of dehumidification are determined.
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3.4.1. Sky temperature Sky temperature (Ts), which refers to the equivalent temperature of the long-wave radiation from the sky, Ld=sT4s where s is the Stefan–Boltzmann constant (5.67 108 W m2 K4), is rarely measured. The downward (sky) flux of long-wave radiation was estimated from the Brunt (1932) formula: pffiffiffi Ld ¼ sT 4 0:567:79 103 e ð0:1 þ 0:9n=NÞ ð12Þ where T is air temperature (K), e is vapour pressure (Pa) and n/N is the hours of bright sunshine as a proportion of daylight hours. The meteorological site used for the simulations recorded irradiation hourly rather than hours of bright sunshine in a day. The irradiance was determined daily (S) and n/N derived after Hamer (1992): n=N ¼ ðS=So 0:16Þ=0:65
ð13Þ
where So is the daily irradiance in the absence of atmosphere. So and N were calculated from site latitude and the time of year (Berry, 1964).
3.4.2. Saturation deficit set-points The aim of control is to provide an inside environment so that daily leaf transpiration is at or above the critical level (Ec). This can be achieved by increasing the saturation deficit. In this paper two scenarios are investigated, controlling saturation deficit (1) throughout the ‘day’ and ‘night’ period and (2) during the ‘day’ only. For (1) the saturation deficit set-point (Dsp) can be determined from Eq. (7) when leaf transpiration is the critical transpiration: ð14Þ Ec ¼ aSc þ bd Dsp fd þ bn Dsp ð1 fd Þ where bd is the day time value of b, bn=0.38 kg m2 day1 kPa1 is the night time value of b (when Sc=0 MJ m2 day1) and fd is the fraction of daylight hours in a day (=n/24). By rearranging the terms in Eq. (14) the saturation deficit set-point for scenario (1) is: Dsp ¼
Ec fn aSc bd fn þ bn ð1 fn Þ
ð15Þ
For (2) the night time saturation deficit needs to be known; the value for the previous night (Dn) is used to estimate the daily total leaf transpiration: ð16Þ Ec ¼ aSc þ bd Dsp fn þ bn Dn ð1 fn Þ and by rearranging the terms in Eq. (16) the saturation deficit set-point for scenario (2) is:
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Ec bn Dn ð1 fn Þ Dsp ¼ aSc =bd fn
ð17Þ
3.4.3. Cost of dehumidification A separate study (unreported) showed that the most cost-effective method of dehumidifying for controlling saturation deficit is by simultaneous heating and ventilation. The running costs of a refrigerative dehumidifying was an order of magnitude greater than the cost of burning kerosene to provide the additional heat needed. HORTITRANS calculates the increase in energy consumption (Eh, W m2) when the saturation deficit set-point is reached by ventilation and simultaneous heating to maintain air temperature (referred to as simultaneous heating and ventilation). The heating cost (ch, p m2) of dehumidifying can be calculated from the purchase price of the fuel (pf, p MJ1), the duration of dehumidifying (th, h) and the efficiency of the heating system (eh,%): ch ¼ 3:6 105 Eh pf eh th
ð18Þ
The environmental conditions which lead to symptoms associated with calcium deficiency occur mainly in the winter and spring when the outside temperatures are lower than inside so that the ventilators are closed. During this period the environment is enriched with carbon dioxide (CO2) to improve the yields of tomatoes and other glasshouse crops (Hand, 1982). Additional carbon dioxide is required during ventilation to maintain the same concentration. When fuel gases are used for enrichment, the CO2 is a by-product and there may be sufficient gas produced to maintain the required concentration. The shortfall in gas may be produced by burning fuel at an additional cost. Alternatively, enrichment is by pure CO2. When additional CO2 is required there is an additional cost which depends on the additional ventilation rate for saturation deficit control. The loss of CO2 through leakage and ventilation (Lc, kg m2 h1) is (Chalabi and Fernandez, 1994): Lc ¼ Ve ðC Co Þc
ð19Þ
where Ve (m3 m2 h1) is the ventilation rate, C (ppm, i.e. ml m3) and Co (=350 ppm) are glasshouse CO2 and ambient concentrations, respectively and rc (g ml1) is the density of CO2. HORTITRANS calculates the additional ventilation rate required for saturation deficit control. The cost of the additional CO2 (cc, p m2) is: cc ¼ Lc pc
ð20Þ
where pc (p kg1) is either the additional cost of fuel if CO2 is produced from flue gases or is the purchase price of pure CO2.
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4. Simulations 4.1. Method HORTITRANS predicts from external weather data, the inside environment and estimate energy consumption and ventilation rate required for humidity control. HORTITRANS was modified to enable simulations to be carried out for a developing crop (see Appendix for functions), to quantify the effects of high humidity on yield and quality and to control the aerial environment by saturation deficit setpoints using the model functions presented in this paper. Table 4 presents parameters used for the simulation which includes the greenhouse characteristics, the set-points for temperature control and the commercial prices of fuel and CO2. The fuel is assumed to be natural gas and CO2 for enrichment is produced from the flue gases. If there is insufficient CO2 produced from the heating requirements then the cost of the additional fuel is used (1 MJ of heat produces 0.0512 kg of CO2). The external weather data of irradiance, air temperature, relative humidity and windspeed were hourly values from Cardington, Bedford, UK for the years 1972– 1979. Simulations were carried out for each year with the crop planted on the 1 January and removed on the 15 November, as standard commercial practice in the UK. Simulation were carried out for single glazed (t=0.65) and double glazed (t=0.58) greenhouses. The saturation deficit control was either during the day (i.e. during daylight hours) or continuously (i.e. throughout a 24-h period) and the setpoints determined from the daily value of irradiance (i.e. a pre-knowledge of irradiance is needed). Table 4 Input parameters used in the simulations Parameter
Value
Number of bays Bay width Bay length Gutter height Ridge height Fraction of roof cladding as ventilators Maximum angle of ventilator opening Night temperature control Day temperature control Night vent temperature Day vent temperature Greenhouse CO2 concentration, C Heating efficiency, eh Energy price, pf CO2 price, pc Maximum percentage yield in Class 1, qm
10 3.2 m 100 m 4.0 m 4.8 m 0.20 Variable 16 C 20 C 24 C 24 C 1000 ppm 80% 0.128 p MJ1 2.5 p kg1 85%
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Daily summaries of inside environment and estimates of energy consumption and ventilator rates required for saturation deficit were simulated by HORTITRANS and used as input to estimate tomato crop growth and development (Appendix). The aim of the control is to maximize profit and the term ‘additional profit’ is used which is the difference in the additional income from dehumidifying and the additional cost of control by simultaneous heating and ventilation. 4.2. Results The cost of dehumidification was high and exceeded the additional income through increase in yield and improved quality. Periods of high cost were identified to occur when the difference in the water content of the air inside and outside the greenhouse was small. During these periods the ventilators were widely opened. Ventilation rates were constrained by reducing the maximum angle of ventilator opening. This influences leaf transpiration and therefore the yield and quality of fruit is less than the potential. The maximum angle of ventilator opening was varied in small intervals typically 2 steps for the single glazed house and 5 steps for the double glazed house. Some results of simulation for the single glazed and double glazed house are presented in Tables 5 and 6. The yield potential (the harvested yield accumulated throughout the season when the crop is grown with adequate water and nutrients) was greater in the single glazed house than the double glazed house because of the reduced transmissivity to shortwave radiation. In the single glazed house the yield potential ranged from 42.4 kg m2 in 1972 to 48.3 kg m2 in 1976 when the irradiance during the summer months was exceptionally high. The extra glazed layer reduced yield potential by 10%. For the double glazed house the additional profits were greater when dehumidifying occurred during daylight rather than throughout the 24-h period for each year from 1972 to 1974 (Fig. 4). For the continuous control the maximum profit was achieved when the maximum vent opening was constrained to about 4 but was less Table 5 Single glazed house: simulation outputs with a maximum vent opening of 4 and the saturation deficit controlled during periods of daylight Year
1972 1973 1974 1975 1976 1977 1978 1979
Yield potential (kg m2)
42.4 45.5 45.3 46.7 48.3 44.5 43.6 45.1
Yield increase (kg m2)
0.24 0.27 0.30 0.37 0.19 0.26 0.22 0.14
Additional income (p m2)
28.0 35.5 35.2 45.0 23.9 28.1 23.0 16.9
Additional costs Heating (p m2)
CO2 (p m2)
21.4 21.2 27.1 24.9 18.5 27.0 23.6 19.6
0.0 0.1 0.3 0.2 0.2 0.4 0.1 0.1
Additional profit (p m2)
6.6 14.2 7.8 19.9 5.2 0.7 0.7 2.8
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Table 6 Double glazed house: simulation outputs with the maximum vent opening of 10 and the saturation deficit controlled during periods of daylight Year
1972 1973 1974 1975 1976 1977 1978 1979
Yield potential (kg m2)
38.7 40.9 40.7 42.0 43.5 39.9 39.1 40.5
Yield increase (kg m2)
1.41 1.22 1.50 1.86 1.02 1.47 1.21 1.06
Additional income (p m2)
165.4 153.2 170.7 214.0 123.1 166.2 137.0 129.1
Additional costs Heating (p m2)
CO2 (p m2)
71.0 62.0 79.7 76.9 61.5 80.2 67.6 67.6
0.4 1.0 1.5 0.9 1.4 2.1 0.7 0.6
Additional profit (p m2)
94.0 90.2 89.5 136.2 60.2 83.9 68.7 60.9
than the maximum additional profit achieved by day time control. The subsequent results are for dehumidifying during the day. For the single glazed house the additional profit from dehumidifying was small and considerably variable from year to year (Fig. 5a). In 1979, there was no benefit to dehumidifying and a net loss to the grower whereas in 1975 an additional profit of 20 p m2 was achieved. The differences between the years was due to the yield increase which was 0.5 kg m2 in 1975 compared to 0.2 kg m2 in 1979. Over the 8 years the maximum additional profit was achieved by using a maximum vent opening of 3 . The average additional profit was 6 p m2 (Fig. 5b). One year in eight there was a loss, in another there was no benefit and additional profit achieved in the other 6 years. For the double glazed house the additional profit was considerable in all years of the simulation (Fig. 6a). There was considerable variation in the additional profit between years ranging from 50 to 135 p m2. The maximum vent opening of 10 produced an average additional profit of about 90 p m2 (Fig. 6b). The CO2 from the flue gases, when additional heating was required for control, was sufficient on most occasions to maintain the concentration of CO2 at the required level. The cost of producing extra CO2 was small compared to the cost of heating (Tables 5 and 6).
5. Discussion The model integrates the understanding from biological and physical sciences in order to analysis, by simulation, strategies for cost-effective control. The essential features contained within the crop model functions are that the assimilate for fruit growth is supplied by subtended leaves, the loss of yield and reduced quality are associated with low calcium uptake and that calcium uptake is associated with
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Fig. 4. Double glazed house: simulation of the additional profit in relation to maximum vent opening for saturation deficit controlled during the day (—) and continuously (- - - -).
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Fig. 5. Single glazed house: simulation of the additional profit in relation to the maximum vent opening (a) for the 1972 (^), 1973 (&), 1974 (~), 1975 (&), 1976 (*), 1977 (~), 1978 (^) and 1979 (*) seasons and (b) the average additional profit for the years 1972–1979 (&) seasons with the line fitted to a third order polynomial constrained through the origin.
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Fig. 6. Double glazed house: simulation of the additional profit in relation to the maximum vent opening (a) for the 1972 (^), 1973 (&), 1974 (~), 1975 (&), 1976 (*), 1977 (~), 1978 (^) and 1979 (*) seasons and (b) the average additional profit for the years 1972–1979 (&) seasons with the line fitted to a third order polynomial constrained through the origin.
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transpiration. The assimilate availability assumption is reasonable for undisturbed plants as assimilates follow the easiest path. However, for highly disturbed tomato plants the source leaves can be considered as part of a common source (Heuvelink, 1995). To incorporate a common assimilate source requires an added level of complexity to the distribution of resources from leaves to fruit (see ‘Partitioning dry matter to individual trusses’ in the Appendix) and a method needed to allocate resources to the fruit from different leaves. The functions to describe yield and quality effects [Eqs. (9) and (10)] were in relation to the ratio leaf area of disturbed and undisturbed plants. This approach made use of the data available from the experiments to study the effects of humidity on growth yield and quality of a tomato crop. A better approach would be to consider the reduction in leaf area in relation to the overall radiation interception of the crop expressed in Eq. (25). However, this approach requires data on the time course of leaf area index, information not recorded in the trials. A ‘critical’ leaf transpiration term was introduced to describe limit leaf growth rate. Leaf transpiration was estimated by a simple model involving irradiance and saturation deficit (Jolliet at al., 1993) and the critical leaf transpiration of 0.65 kg m2 day1 derived as the value below which leaf area was reduced due to calcium deficiency. The data from the Efford trials over three seasons were used to derive the model response functions and the critical transpiration value derived by regression. More detailed studies are required to validate the assumptions and the form of the functions used in the model. The HORTITRANS model accurately predicts the environmental conditions inside a greenhouse (Jolliet, 1994). The modifications made to HORTITRANS enabled simulations to be carried out using hourly weather data for a developing tomato crop. The HORTITRANS model can be used for predicting the inside environments for a range of structures including films, which are common in other parts of Europe. Restricting the vent opening to a maximum was a technique used to reduce cost. This was an option available within HORTITRANS to constrain ventilation rates. The angle of vent opening depends to a large extent on the difference between the water content inside and outside the greenhouse. Alternative options such as constraining costs or using the difference in the water content between inside and outside the house is worth investigating. However restricting the angle of opening of the ventilator is an easy option to implement on a computer control system. The fuel prices used in the simulations were current prices for natural gas, which provided heat and CO2 for enrichment. Currently in the UK, natural gas is the cheapest (and cleanest) fuel available to growers. The simulation for a single glazed house showed that humidity control (to avoid the effects of calcium deficiency) was worthwhile 6 years out of eight. It is likely that more expensive fuels and using pure CO2 would not be cost effective for humidity control in single glazed houses. In the sample double glazed house, control was worthwhile in all the years. Humidity is high when the ventilators are closed, due to reduced condensation and low leakage rates in double glazed houses, and therefore transpiration rates are low during dull periods in the winter and early spring. Whether it is cost effective to provide humidity control using fuels other than natural gas for heating and pure CO2 for enrichment is worthy of further investigation.
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It is more cost effective to control humidity (to increase transpiration) during the day than to control humidity continuously. This is not surprising since transpiration rate is low at night. Although the saturation deficit set-point for continuous control is lower than for day time control, the period of control is about three times greater in the winter and early spring. The simulation relied on a prior knowledge of the forthcoming daily irradiance. For real time control an accurate forecast of the irradiance for the coming day is required. Electronic systems for receiving and interpreting weather information are yet to be fully developed. A manual system for entry of forecast irradiance into a control system is required.
6. Conclusions For a double glazed house additional profit was greater when the saturation deficit was controlled during the period of daylight compared to continuous control for the model input used. For the single glazed house, a maximum angle of opening of 3 produced an additional profit of 6 p m2. One year in eight there was a loss. For the double glazed house, a maximum ventilator opening of 10 produced an average additional profit of 90 p m2. The modified version of HORTITRANS can be used subject to validation of the crop response functions, to study control strategies for other types of greenhouse structures in different climatic regions where short-term (hourly) meteorological data exists. Local information on prices and costs are required.
Acknowledgements The project, Management and Control for Quality in greenhouses (MACQU), was funded by the European Union (AIR3-CT93-1603). The author is grateful to Bernard Bailey, Zaid Chalabi and Ken Cockshull for their helpful discussions.
Appendix. Functions and parameters for a developing tomato crop A.1. Functions Tomato yield is related to the amount of radiation intercepted by the crop canopy. This is based on the experimental findings that where water and nutrients are nonlimiting the rate at which crops accumulate dry matter is proportional to the quantity of solar radiation which they intercept (e.g. Biscoe and Gallagher, 1977). The total dry matter DMtot can be considered as the time-integrated product of three factors: ð DMtot ¼ eiSc dt ð21Þ
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where Sc is the daily solar radiation incident at the top of the canopy, i is the fraction of incident radiation intercepted by the canopy (radiation interceptance), e is the amount of dry matter produced per unit of radiation intercepted by a canopy (dry matter: radiation quotient) and t is time measured in days. The total dry matter is partitioned between the leaves, stem, roots and fruit and Kp is the proportion of the total dry matter that is in the fruit. This proportion changes with time since the plant needs to be established before the dry matter partitions to the fruit, and therefore Kp varies with time and can be expressed as: Kp ¼ DMf =DMtot
ð22Þ
where DMf and DMtot are the rates of change of dry matter in fruit and total dry matter, respectively. Once the crop is well established there are about six trusses carrying fruit which are harvested frequently throughout the season. The fruits on a truss are picked over a period of time (typically about 3 weeks) when the fruits change from green to red. The total daily increment of the dry matter partitioned to fruit needs to be distributed to individual trusses: X DMf ¼ dmf ðnÞfðnÞ ð23Þ n
where dmf(n) is the fruit dry matter of truss n and f(n) is the proportion of dry matter that remains on truss n. If none of the fruit on truss n has been picked then f(n)=1 and if all of the fruit has been picked then f(n)=0. The fruit is sold as a fresh weight product and is related to the fruit dry matter by the dry matter content (Kf): Kf ¼ DMf =FWf
ð24Þ
where FWf is the fresh weight of the fruit (yield in the main section of the paper). A.2. Parameters Parameter values describe the seasonal changes in radiation interceptance, the proportion of dry matter in fruits, fruit growth and the dry matter: radiation interception quotient. A constant for the dry matter content is assumed. A.2.1. Dry matter: radiation interception The dry matter: radiation quotient e=2.24 g MJ1 derived by Hamer (1997) closely agreed with a value of 2.01 kg fresh weight of harvested fruit for every 100 MJ of incident solar radiation measured at the top of the canopy reported by Cockshull et al. (1992). The amount of radiation at the top of the crop canopy depends on the transmissivity to short wave radiation of the glasshouse (t) so that Sc=tSs where Ss is solar radiation measured outside and above the greenhouse away from obstructions. The radiation interceptance is the ratio of total solar radiation intercepted by the crop canopy (Si) to Sc and can be described by:
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i ¼ Si Sc ¼ ½1 am ½1 expðKL LÞ
ð25Þ
where KL is the solar radiation extinction coefficient and L is the leaf area index. Tomato crops are grown in rows (usually in pairs) and pathways between the rows provide access for crop management. There is little or no canopy in the interrow spaces and therefore the crop does not intercept all the available radiation even for a very large leaf area index. The term am represents the proportion of the radiation beneath the crop canopy when L is very large. Hamer (1997) derived values of am=0.105, KL=0.686 and L=0.149+0.00502Dl where Dl is the thermal time from planting. At the time of planting L=0.1 is assumed so that L is always positive and L=5.6 is a constant maximum after thermal time 1145 Kd. A.2.2. Proportion of dry matter in fruit (Kp) Hurd et al. (1979) determined the proportion of fresh weight devoted to fruit, vegetative shoots and roots for the indeterminate tomato at weekly intervals. All of the fresh weight gain is devoted to shoots and roots until flowering and thereafter the proportion to fruit increases to a maximum of about 90% about 50–60 days after anthesis and gradually diminishes to about 75–80% at the end of the growing season. Hamer (1997) described the proportion of dry matter in fruit in relation to the thermal time accumulated from the date of first flowering: Kp ¼ 0:978 þ ð0:978 þ 0:263xÞ0:930x
ð26Þ
where x=Dp/100. For the period prior to first flowering there is no fruit and therefore all the dry matter is distributed to leaves, stems and roots. Eq. (26) predicts a maximum for Kp which then continues to decline rather than reach a plateau. The condition Kp=0 for Dp < 0 and a minimum value of Kp=0.65 beyond the maximum was imposed. A.3. Partitioning dry matter to individual trusses Fruit growth can be described by: dmf ðnÞ ¼ cf exp½exp½bf ðt mf Þ
ð27Þ
where dmf(n) is the fruit dry matter on truss n and t is time from anthesis (days) with parameter values for round tomato given by de Koning (1994): cf ¼ 1:082dm mf ¼ 0:396pf ðn; tÞ½1 þ 0:446expð0:219nÞ bf ¼ 1=ð2:44 þ 0:403 mf Þ
ð28Þ
where dmp is the potential fruit dry matter (g) and pf(n,t) is the fruit growth period (the interval of time from flowering to harvest) which varies with temperature and truss number. A method is required to update pf during fruit development. Assum-
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ing the thermal time from anthesis to harvest is Dav when the average temperature is Tav the fruit growth period is: pf ðn; tÞ ¼
Dav Dðn; tÞ þt Tav
ð29Þ
where D(n,t) is thermal time at t accumulated from the date of anthesis on truss n. The amount of dry matter partitioned to fruit is further partitioned to fruits of different ages according to the potential growth rates (Marcelis, 1993). The first derivative of Eq. (27) represents the fruit growth rate: dm0f ¼
dðdmf ðnÞÞ ¼ dmf ðnÞbf exp½bf ðt mf Þ dt
ð30Þ
and the total dry matter partitioned to fruit is allocated to each truss in proportion to the fruit growth rate of that truss and the summation of all the trusses bearing fruit: dmf ðnÞ ¼ DMf
dm0f "dm0f
ð31Þ
The potential dry weight is the parameter cf and is not required since it appears in both the numerator and denominator of Eq. (31). In effect this parameter is replaced by the dry matter radiation quotient. A.4. Period of harvest of each truss The fruit growth model distributes the dry matter to the fruits on each truss. However, the truss consists of fruit of different sizes and maturity since the flowers open and the fruit set at different times. Typically in round tomatoes there are about 10 flowers per truss and they open over a period of about 20 days. Not all the fruit set. Consequently the fruits from a single truss are harvested over a similar period and therefore the model needs to take this into account. The amount of dry matter harvested is assumed to be more or less the same over the period of harvest from a truss (ph(n,t)). Harvesting commences pfph/2 days after anthesis and the last of the fruit is harvested after pf+ph/2 days. When the harvesting of a truss commences, if the quantity of dry matter removed is simply taken as fraction of the number of days in the harvest period, the first fruit would be small and the last large. The dry matter yield harvested dmy(n) is (Hamer, 1997): dmðnÞ 1 þ ay ft ðnÞ dmy ðnÞ ¼ ð32Þ ph ðn; tÞ where ft(n) is the proportion of fruit remaining and the parameter ay=0.15 [Eq. (32)] ensures for a range of trusses the daily rate of fruit harvested is uniform throughout the period the truss was picked. The amount of dry matter harvested is deducted from the total left on the truss. The harvest period is assumed to be temperature dependent and the same technique used to update pf [Eq. (29)] is used to determine the harvest period.
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References Adams, P., Ho, L.C., 1993. Effects of environment on the uptake and distribution of calcium in tomato and on the incidence of blossom-end rot. Plant and Soil 154, 127–132. Aikman, D.P., 1996. A procedure for optimizing carbon dioxide enrichment of a glasshouse tomato crop. Journal of Agricultural Engineering Research 63, 171–184. Aikman, D.P., Houter, G., 1990. Influence of radiation and humidity on transpiration: implications for calcium levels in tomato leaves. Journal of Horticultural Science 65, 245–253. Bakker, J.C., 1991. Analysis of Humidity Effects on Growth and Production of Glasshouse Fruit Vegetables. Thesis, Agricultural University, Wageningen, the Netherlands. Berry, G., 1964. The evaluation of Penman’s natural evaporation formula by electronic computer. Australian Journal of Applied Science 15, 61–64. Biscoe, P.V., Gallagher, J.N., 1977. Weather, dry matter production and yield. In: Landsberg, J.J., Cutting, C.V. (Eds.), Environmental Effects on Crop Physiology. Academic Press, London, pp. 75–100. Bonnemain, J.-L., 1966. Sur les modalite´s de la distribution des assimilates chez la tomate et sur ses me´canismes. Compte rendu de l’Acade´mie des sciences de Paris 262, 1106–1109. Brunt, D., 1932. Notes on radiation in the atmosphere: 1. Quarterly Journal of the Royal Meteorological Society 58, 389–420. Chalabi, Z.S., Fernandez, J.E., 1994. Estimation of net photosynthesis of a greenhouse canopy using a mass balance method and mechanistic models. Agricultural Forest Meteorology 71, 165–182. Cockshull, K.E., Graves, C.J., Cave, R.J., 1992. The influence of shading on yield of glasshouse tomatoes. Journal of Horticultural Science 67, 11–24. de Koning, A.N.M., 1990. Long-term temperature integration of tomato: Growth and development under alternating temperature regimes. Scientia Horticulture 45, 117–127. de Koning, A.N.M., 1994. Development and Dry Matter Distribution in Glasshouse Tomato: A Quantitative Approach. Thesis, Agricultural University, Wageningen, the Netherlands, 240 pp. Hamer, P.J.C., 1992. A semi-mechanistic model of the potential growth and yield of Brussels sprouts. Journal of Horticultural Science 67, 161–169. Hamer, P.J.C., 1996. Optimal control of the aerial environment. In: Sigrimis, N. (Ed.), MACQU 2nd Year Annual Report, Contract No AIR3-CT93-1603. Commission of European Communities, Brussels. Hamer, P.J.C., 1997. Optimal control of the aerial environment. In: Sigrimis, N. (Ed.), MACQU 3rd Year Annual Report, Contract No AIR3-CT93-1603. Commission of European Communities, Brussels. Hand, D.W., 1982. CO2 enrichment, the benefits and problems. Scientia Horticulturae 33, 14–43. Herdel, K., Schmidt, P., Feil, R., Mohr, A., Schurr, U., 2001. Dynamics of concentrations and nutrient fluxes in the xylem of Ricinuc comunis—diurnal course, impact of nutrient availability and nutrient uptake. Plant Cell and Environment 24, 41–52. Heuvelink, E., 1995. Dry matter partitioning in a tomato plant: one common assimilate pool. Journal of Experimental Botany 46, 1025–1033. Holder, R., Cockshull, K.E., 1990. Effects of humidity on the growth and yield of glasshouse tomatoes. Journal of Horticultural Science 65, 31–39. Hurd, R.G., Gay, A.P., Mountifield, A.C., 1979. The effect of partial flower removal on the relation between root, shoot and fruit growth in the indeterminate tomato. Annals of Applied Biology 93, 77– 89. Jolliet, O., 1994. HORTITRANS, a model for predicting and optimizing humidity and transpiration in greenhouses. Journal of Agricultural Engineering Research 57, 23–37. Jolliet, O., Bailey, B.J., Hand, D.J., Cockshull, K., 1993. Tomato yield in greenhouses related to humidity and transpiration. Acta Horticulturae 328, 115–124. Jolliet, O., Danloy, L., Gay, J.-B., Munday, G.L., Reist, A., 1991. HORTICERN: an improved static model for predicting the energy consumption of a greenhouse. Agricultural and Forest Meteorology 55, 265–294. Marcelis, L.F.M., 1993. Simulation of biomass allocation in greenhouse crops—a review. Acta Horticulturae 328, 49–67.
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Payne, R.W., Lane, P.W., Ainsley, A.E., Becknell, K.E., Digby, P.G.N., Harding, S.A., Leech, P.K., Simpson, H.R., Todd, A.D., Verrier, P.J., White, R.G., 1987. GENSTAT 5 Reference Manual. Clarendon Press, Oxford, UK. Shishido, Y., Hori, Y., 1977. Studies on translocation and distribution of photosynthetic assimilates in tomato plants. II. Distribution pattern as affected by phyllotaxis. Toho Journal of Agricultural Research 28, 82–95.
Analysis of strategies for reducing calcium deficiencies in glasshouse grown tomatoes: model functions and simulations P.J.C. Hamer* Silsoe Research Institute, Wrest Park, Silsoe, Bedford MK45 4HS, UK Accepted 4 July 2002
Abstract Energy saving measures can result in high levels of humidity in greenhouses which reduces transpiration resulting in calcium deficiency symptoms on tomato leaves with subsequent loss of yield and quality. Transpiration can be increased by lowering the saturation deficit. Control strategies need to be cost-effective so that the benefits are in excess of the costs of carrying out the dehumidification. The HORTITRANS model [Journal of Agricultural Engineering Research, 57 (1994) 23], which predicts the conditions inside a greenhouse, was modified to enable simulations to be carried out for a developing crop and to quantify the effects of high humidity on yield and quality. Saturation deficit set-points were determined so that the transpiration rate was equal to a minimum of 0.65 kg m2 day1, a value derived to be satisfactory from experiments. Simulations were carried out for sample single and double glazed greenhouses with dehumidification by ventilation and heating. The cost of dehumidification was high when the ventilators were widely opened and so ventilation rates were constrained by restricting the maximum angle of opening. For a double glazed house additional profit was greater when the saturation deficit was controlled during the period of daylight compared to continuous control. For the single glazed house, a maximum angle of opening of 3 produced an additional profit of 6 p m2. One year in eight there was a loss. For the double glazed house, a maximum ventilator opening of 10 produced an average additional profit of 90 p m2. The models can be used to study control strategies for other types of greenhouse structures in different climatic regions where short-term (hourly) meteorological data exists using local information on prices and costs. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: Tomato; Calcium deficiency; Transpiration; Simulation control model
* Tel.: +44-1525-864023; fax: +44-1525-860156. E-mail address: [email protected] (P.J.C. Hamer). 0308-521X/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. PII: S0308-521X(02)00101-4
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1. Introduction Energy saving measures in greenhouses can result in high levels of humidity which can lead to yield loss and have detrimental effects on product quality. For example, double glazed greenhouses provide insulation and the tight fitting glass panes result in a low exchange of air with the outside environment. There is a decrease in condensation and moisture introduced transpiration remains in the house resulting in a high relative humidity. Tomato is a crop of major importance to the greenhouse industry and responds to changes in humidity. Tomato leaves which develop under low solar radiation intensities and high humidity are of reduced size and show signs of calcium deficiency (Holder and Cockshull, 1990). The subsequent loss of yield occurs from the trusses adjacent to the leaves that develop under high humidity. Calcium arrives at the leaves along with the transpiration stream since calcium is transported unidirectionally in the xylem and the amount builds up as the leaf grows and transpires (Aikman and Houter, 1990). There is a minimum rate of transpiration relative to leaf growth rate below which calcium deficiency symptoms occur. As well as the loss of yield fruit quality can be reduced, for example the physiological disorder blossom-end rot is associated with low calcium uptake (Adams and Ho, 1993). Experiments to quantify the effects of humidity on yield, control humidity (or saturation deficit) using set-points which are fixed for different periods of the experiment. The set-points, which may be different for the day and night periods, ensure large differences in humidity between treatments so that the crop response is significant. For example, the treatments of Bakker (1991) were ‘high’ or ‘low’ relative humidity by day (from sunrise to sunset) and combined with either a high or low relative humidity by night. The treatments were imposed for about 8 weeks. Holder and Cockshull (1990) maintained four nominal saturation deficits continuously (24 h per day) throughout a 4-week experiment and in another experiment two nominal saturation deficits were maintained either continuously day and night or changed between day and night for a 6-week period. Typically fogging systems are used to raise the humidity and ventilation to reduce it with the same air temperatures maintained at all humidities. However, in commercial greenhouses the relative humidity is constantly varying and the aim of humidity control is to avoid environments which would lead to yield and/or quality reductions. In addition the techniques for control must be cost-effective so that the benefits of control in terms of yield and quality are in excess of the costs of carrying out the dehumidification. In this paper, models are developed to predict the effects of humidity on the growth, yield and quality of fruit and the value of the crop. The environmental conditions inside the greenhouse are simulated using the HORTITRANS model (Jolliet, 1994), which is modified for a developing crop and further modified so that the aerial environment is controlled by saturation deficit set-points. Simulations are carried out to evaluate strategies for control. 2. Model concept In glasshouse-grown crop of indeterminate tomato, the main stem is allowed to develop and lateral shoots removed (unless a shoot is being trained to increase plant
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density by developing another main stem) resulting in the main stem bearing trusses separated by three leaves. The assimilate for the growth of fruit on the truss is mainly supplied by the three subtended leaves (Shishido and Hori, 1977). For the purpose of this model, leaf development is considered in terms of the combined leaf area of two leaves below and one above a truss. These leaves supply the assimilate for the growth of fruit of the associated truss (Bonnemain, 1966). The developmental stages can be defined by the number of the truss and the stages of growth of the associated leaves, flowers and fruit defined by easily determined markers. In this paper, the truss is treated as a whole and the date of anthesis is the date when 50% of the flowers have opened and the harvest date when 50% of the fruits from the truss have been harvested. The marker for leaf development is taken as l/lm=0.5 where l is leaf area and lm is leaf area when the leaves associated with the truss are fully expanded, i.e. when the leaf area is half the final area. Low transpiration rates as a result of high humidity influence leaf growth so that lm is reduced and the yield and quality of fruit from the associated trusses are also reduced. Fig. 1 illustrates how high humidity on 1 day can influence the yield and quality of fruit harvested over a considerable period. A humidity event on day 61, when l/lm=0.5 on truss 6, influences the fruit on this truss which is harvested over about a 3-week period. The humidity event also influences the leaves associated with trusses 5 and 7. At this time the growth rates of these leaves are smaller and therefore likely to have a smaller effect on the fruit production on these trusses. In this illustration the fruit harvested over about a 4–5 week period is influenced by a single short period humidity event.
Fig. 1. Schematic of tomato plant growth where 5, 6, 7 refers to the truss number.
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3. Model functions 3.1. Crop Developmental progress can be described in relation to thermal time (y), the integration of temperature (T) with time (t): ð y ¼ ðT Tb Þdt ð1Þ where Tb is a base temperature at which growth rate is zero. The base temperature for fruit development of 5 C (Aikman, 1996) is used to describe the development of all crop processes. For a tomato leaf growing at its potential, the leaf area (l(y)) relative to the area of the leaf when fully expanded (lm) can be described by a logistic (Hamer, 1996): lðyÞ 1 ¼ lm 1 þ expðbl ðy yl ÞÞ
ð2Þ
where bl=0.0204 Kd1 describes the rate of leaf expansion and yl is the thermal time when l(y)/lm=0.5. The thermal time increment of yl from the leaves of one truss to the next is 89 Kd. The potential leaf growth rate is the first derivative of Eq. (2): ðlðyÞ=lm Þ0 ¼
dðlðyÞ=lm Þ ¼ bl lðyÞ=lm ð1 lðyÞ=lm Þ: dt
ð3Þ
When the crop is grown in an environment leading to low transpiration, leaf growth rate is reduced and can be described as: fe ðlðyÞ=lm Þ0
ð4Þ
where the parameter, fe, limiting leaf growth rate is a function of transpiration: fe ¼ El =Ee when Et < Ec fe ¼ 1 when Et 5 Ec
ð5Þ
and where Et is the leaf transpiration rate and Ec is a minimum ‘critical’ leaf transpiration rate required for adequate leaf growth. If leaf transpiration rate is less than the critical rate, leaf growth rate is reduced. The form of this function is based on the following observations. The flux of calcium is roughly proportional to the transpiration flow since calcium arrives at the leaves along with the transpiration stream and its concentration does not vary much with flow rates (Aikman and Houter, 1990). Herdel et al. (2001) determined the concentrations of nutrients in the xylem sap from intact plants. Similar flux concentrations of calcium were observed during the night (low transpiration) and during the day (high transpiration).
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Concentrations of calcium, relative to leaf dry weight, of 0.39% and less show distinct deficiency symptoms. Holder and Cockshull (1990) showed that humidity treatments that gave calcium levels of 0.6 and 0.7% lead to reduced leaf size and yield and a small effect when the calcium level was 0.9%. Therefore there is a minimum target level for calcium. Since there is a direct relation between the flux of calcium and leaf transpiration there is a minimum transpiration requirement to avoid reductions in leaf size and subsequent effect on yield and quality. The leaf area at the end of leaf expansion (lf) relative to the potential (lm) is derived from the summation of the growth rate over the period of growth: X lf =lm ¼ fe ðlðyÞ=lm Þ0 ð6Þ Transpiration rate is constantly changing during the day in response to fluctuations in irradiance and the saturation deficit, whilst at night the transpiration rate is low. The period over which the crop responds to low calcium uptake is difficult to quantify experimentally. Transpiration (and hence calcium uptake) can be modified by controlling humidity. Bakker (1991) argued that the response of growth and yield to humidity shows a certain similarity with the response to temperature, i.e. a close relationship with the average level of either temperature or humidity. Earlier work demonstrated cumulative growth is not affected by alternating high and low temperatures for several days (de Koning, 1990). However, at the operational level of control, settings need to be adjusted on a daily basis (de Koning, 1994). Therefore, in this paper leaf transpiration is integrated over a 24 h period. The critical leaf transpiration (Ec) and functions relating lf/lm to yield and quality are derived from experiments. 3.2. Critical leaf transpiration, yield and quality functions 3.2.1. Data source The experiments were conducted at HRI Efford in a 16 compartment multi-factorial Venlo-type greenhouses in the 1987/1988, 1990/1991 and 1991/1992 seasons. The main aim of the experiments was to improve the understanding of the effects of humidity on the growth, yield and quality of fruit of a long season tomato crop. The crops were subjected to different humidity regimes by ‘day’ and ‘night’, each period was for 12 h and the change in set-points occurred at 06:00 and at 18:00 h. The water content of the air inside the compartments were controlled according to the saturation deficit. The saturation deficit was decreased by fogging and increased by a combination of heating and ventilation in the first two seasons and by dehumidifiers in the third. The achieved saturation deficits and the dates of establishment and treatment dates are presented in Table 1 for four treatments from combinations of low and high saturation deficits for the day and night periods. Dates of first and sixth anthesis, first and sixth fruit pick and the yield and marketable yield and the percentage of Class 1 fruit from each truss were recorded. Leaf area is taken as the length times breadth of the leaf subtended by a truss. The leaves expanding during the treatment were identified and the yield and quality of fruit on the associated trusses were noted. The treatments did not influence the timing of
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Table 1 The average ‘day’ (d) and ‘night’ (n) saturation deficits achieved in the HRI Efford experiments, the date the plant root made contact with the rockwool slab and the treatment dates. ^, *, ~, & are the symbols in Fig. 1. * Not reported Season
1987/1988 1990/1991 1991/1992
Achieved saturation deficits (kPa)
Slab contact date
d/n (^)
d/n (*)
d/n (~)
d/n (&)
0.19/0.14 0.11/0.10 0.10/0.10
0.20/0.45 0.21/0.17 0.16/0.59
0.48/0.15 0.40/0.37 0.56/0.13
0.56/0.50 0.53/0.50 0.60/0.76
18 December * 23 December
Treatment dates Start
End
20 January 9 December 3 February
2 March 1 March 15 March
development of the crops. The data were analysed by comparing the leaf areas and the yield and quality of the fruit from each treatment relative to the values from the crops grown with the highest saturation deficit (Table 2). The average percentage of Class 1 fruit from the treatments with the highest saturation deficit were 87, 86 and 83% in the first, second and third seasons, respectively. 3.2.2. Leaf transpiration The expanding leaves develop at the top of the crop canopy and are therefore fully exposed to the incoming irradiance and leaf transpiration. The leaf transpiration (El, kg m2 day1) was estimated as a linear function of irradiance (Sc, MJ m2 day1) at the top of the canopy and the saturation deficit (D, kPa) (Jolliet et al., 1993): El ¼ aSc þ bD
ð7Þ
Table 2 The ratio of leaf area (lf), yield (yf) and quality of fruit (qf) as percent in Class 1 relative to the leaf area (lm), yield (ym) and quality of fruit (qm) from the treatment with the highest saturation deficit Season
Saturation deficit (kPa)
lf/lm
yf/ym
qf/qm
Day
Night
1987/1988
0.19 0.20 0.48 0.56
0.14 0.45 0.15 0.50
0.79 0.88 0.90 1.00
0.88 0.94 0.96 1.00
0.95 0.98 0.98 1.00
1990/1991
0.11 0.21 0.40 0.53
0.10 0.17 0.37 0.50
0.71 1.03 0.99 1.00
0.73 0.85 0.99 1.00
0.85 0.97 0.99 1.00
1991/1992
0.10 0.16 0.56 0.60
0.10 0.59 0.13 0.76
0.74 0.89 0.85 1.00
0.69 0.88 0.98 1.00
0.82 0.96 0.96 1.00
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where a=0.121 kg MJ1 and b=b1(1b2exp(Sc/b3)) kg m2 day1 kPa1 where b1=1.04 kg m2 day1 kPa1, b2=0.63 and b3=0.864 MJ m2 day1. The change from the ‘day’ to ‘night’ treatments did not coincide with sunrise and sunset. Each day was divided into three periods: sunrise to sunset (Sc > 0 and D=Dd where Dd is the ‘day’ saturation deficit), sunset to 18.00 and 06:00 to sunrise (Sc=0 and D=Dd) and 18:00 to 06:00 (Sc=0 and D=Dn, where Dn is the ‘night’ saturation deficit). The daytime solar radiation at the top of the canopy was estimated from the daily total global solar radiation measured outside the house (Ss, MJ m2 day1), the transmissivity to short-wave radiation of the glasshouse (t) and the period from sunrise to sunset (ts, h): Sc ¼ tSs ð24=ts Þ
ð8Þ
A transmissivity of t=0.65 was assumed. 3.2.3. Derivation of critical transpiration Leaf transpiration was estimated daily for each treatment (Fig. 2). Leaf transpiration from the high humidity treatments were on occasions as low as 0.1 kg m2 day1 on dull days and increased to 1.6 kg m2 day1 on a day when the irradiance was high. The treatment with the highest saturation deficit increased the leaf transpiration typically by about 0.4 kg m2 day1. A critical transpiration of Ec=0.4 kg m2 day1 was assumed and fe determined from Eq. (5) for each treatment. The mean of fe was determined for the duration of the experiment and a regression analysis, with the intercept forced through the origin, related lf/lm to fe/fm where the subscript m refer to values obtained from the highest saturation deficit treatment. This analysis was repeated for different critical transpirations in the range 0.4–1.0 kg m2 day1 (Table 3). The slope, a1 was fitted to the assumed critical transpiration by a quadratic (R2=99.0%). The critical transpiration Ec=0.65 kg m2 day1 was assumed to be when a1=1.0. 3.2.4. Yield and quality The ratios yf/ym and qf/qm were related to lf/lm by quadratic functions. The parameters were derived by non-linear regression using the statistical package GENSTAT Table 3 The slope (a1) of the regression of lf/lm against fe/fm, with the line constrained through the origin, for different critical leaf transpiration (Ec) Ec (kg m2 day1)
a1
R2 (%)
0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.927 0.972 0.981 1.011 1.030 1.044 1.055
50.5 71.3 67.6 70.0 65.2 59.8 54.6
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Fig. 2. Estimates of leaf transpiration in (a) 1987/1988 (b) 1990/1991 and (c) 1991/1992 for each treatment (see Table 1 for key).
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(Payne et al., 1987). The regressions were constrained so that yf/ym=1 and qf/qm at lf/lm=1 with turning points at yf/ym=1 and qf/qm=1. The yield function [Fig. 3(a)] is: yf =ym ¼ 2:583 þ 7:166ðlf =lm Þ 3:583ðlf =lm Þ2 R 2 ¼ 85:3% ð9Þ and the quality function [Fig. 3(b)] is: qf =qm ¼ 0:984 þ 3:968ðlf =lm Þ 1:984ðlf =lm Þ2 R 2 ¼ 87:8%
ð10Þ
Fig. 3. (a) Yield (yf/ym) and (b) quality (qf/qm) in relation to leaf expansion (lf/lm). The fitted line for yield is Eq. (9) and for quality is Eq. (10).
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3.3. Value The financial return from dehumidification comes from the subsequent sale of the harvested fruit. For determining cost-effective strategies it is necessary to estimate the market prices of fruit so that the crop value of the increase in yield and quality is in excess of the cost of dehumidification. ’Bench-mark’ prices were collected from the Grower trade magazine (published by Nexus), for the years 1992–1994. The bench-mark price is what a competent grower might average over five trading days for Class 1 fruit after commission and marketing charges have been deducted. The bench-mark price is reported every 4 weeks during the harvest period. The average price for the reported week was fitted to a quadratic: v ¼ 161 5:21w þ 0:66w2 R2 ¼ 92:3% ð11Þ where v (p kg1) is the bench-mark price and w is the week number after the start of the year. The average was over the harvest period from weeks 8 to 44. The value of the earliest harvest is about 124 p kg1 and falls to the minimum in week 40 of 58 p kg1. There is considerable variation between seasons. The waste fruit from the Efford experiments was not influenced by treatment and was typically 2%. The fruit that was not Class 1 or waste was assumed to be Class 2 and to have a value of half that of Class 1. Waste is assumed to have no value. 3.4. Environment The HORTITRANS model (Jolliet, 1994) was used to predict the inside saturation deficit as a function of the outside conditions and the characteristics of the greenhouse. HORTITRANS uses a water balance approach to express the variation in the water vapour stored in the inside air as the difference between water vapour sources and sinks. Water sources are crop transpiration and water added by a fogging system and water sinks are condensation on the cladding, ventilation and water extracted by a dehumidification heat pump. All terms in the water balance are linearized. HORTITRANS determines the water and energy to be added to or extracted from the greenhouse air, in order to achieve set-points for humidity and transpiration and thus the cost of achieving set-points can be estimated. The characteristics of the greenhouse are described by parameters to indicate the size of the greenhouse, the ventilator area and angle of opening, an infiltration factor and the type of cladding (Jolliet et al., 1991). HORTITRANS requires hourly values of outside environmental variables of irradiance (global solar radiation), air and ‘sky’ temperature, humidity (or some measure of the water content of the air) and windspeed. A number of modifications to HORTITRANS were made. The leaf area index (L) for a developing crop is required to derive crop transpiration and is estimated from using thermal time (see Appendix). Estimates of sky temperature, procedure for determining set-points for controlling saturation deficit and functions for the cost of dehumidification are determined.
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3.4.1. Sky temperature Sky temperature (Ts), which refers to the equivalent temperature of the long-wave radiation from the sky, Ld=sT4s where s is the Stefan–Boltzmann constant (5.67 108 W m2 K4), is rarely measured. The downward (sky) flux of long-wave radiation was estimated from the Brunt (1932) formula: pffiffiffi Ld ¼ sT 4 0:567:79 103 e ð0:1 þ 0:9n=NÞ ð12Þ where T is air temperature (K), e is vapour pressure (Pa) and n/N is the hours of bright sunshine as a proportion of daylight hours. The meteorological site used for the simulations recorded irradiation hourly rather than hours of bright sunshine in a day. The irradiance was determined daily (S) and n/N derived after Hamer (1992): n=N ¼ ðS=So 0:16Þ=0:65
ð13Þ
where So is the daily irradiance in the absence of atmosphere. So and N were calculated from site latitude and the time of year (Berry, 1964).
3.4.2. Saturation deficit set-points The aim of control is to provide an inside environment so that daily leaf transpiration is at or above the critical level (Ec). This can be achieved by increasing the saturation deficit. In this paper two scenarios are investigated, controlling saturation deficit (1) throughout the ‘day’ and ‘night’ period and (2) during the ‘day’ only. For (1) the saturation deficit set-point (Dsp) can be determined from Eq. (7) when leaf transpiration is the critical transpiration: ð14Þ Ec ¼ aSc þ bd Dsp fd þ bn Dsp ð1 fd Þ where bd is the day time value of b, bn=0.38 kg m2 day1 kPa1 is the night time value of b (when Sc=0 MJ m2 day1) and fd is the fraction of daylight hours in a day (=n/24). By rearranging the terms in Eq. (14) the saturation deficit set-point for scenario (1) is: Dsp ¼
Ec fn aSc bd fn þ bn ð1 fn Þ
ð15Þ
For (2) the night time saturation deficit needs to be known; the value for the previous night (Dn) is used to estimate the daily total leaf transpiration: ð16Þ Ec ¼ aSc þ bd Dsp fn þ bn Dn ð1 fn Þ and by rearranging the terms in Eq. (16) the saturation deficit set-point for scenario (2) is:
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Ec bn Dn ð1 fn Þ Dsp ¼ aSc =bd fn
ð17Þ
3.4.3. Cost of dehumidification A separate study (unreported) showed that the most cost-effective method of dehumidifying for controlling saturation deficit is by simultaneous heating and ventilation. The running costs of a refrigerative dehumidifying was an order of magnitude greater than the cost of burning kerosene to provide the additional heat needed. HORTITRANS calculates the increase in energy consumption (Eh, W m2) when the saturation deficit set-point is reached by ventilation and simultaneous heating to maintain air temperature (referred to as simultaneous heating and ventilation). The heating cost (ch, p m2) of dehumidifying can be calculated from the purchase price of the fuel (pf, p MJ1), the duration of dehumidifying (th, h) and the efficiency of the heating system (eh,%): ch ¼ 3:6 105 Eh pf eh th
ð18Þ
The environmental conditions which lead to symptoms associated with calcium deficiency occur mainly in the winter and spring when the outside temperatures are lower than inside so that the ventilators are closed. During this period the environment is enriched with carbon dioxide (CO2) to improve the yields of tomatoes and other glasshouse crops (Hand, 1982). Additional carbon dioxide is required during ventilation to maintain the same concentration. When fuel gases are used for enrichment, the CO2 is a by-product and there may be sufficient gas produced to maintain the required concentration. The shortfall in gas may be produced by burning fuel at an additional cost. Alternatively, enrichment is by pure CO2. When additional CO2 is required there is an additional cost which depends on the additional ventilation rate for saturation deficit control. The loss of CO2 through leakage and ventilation (Lc, kg m2 h1) is (Chalabi and Fernandez, 1994): Lc ¼ Ve ðC Co Þc
ð19Þ
where Ve (m3 m2 h1) is the ventilation rate, C (ppm, i.e. ml m3) and Co (=350 ppm) are glasshouse CO2 and ambient concentrations, respectively and rc (g ml1) is the density of CO2. HORTITRANS calculates the additional ventilation rate required for saturation deficit control. The cost of the additional CO2 (cc, p m2) is: cc ¼ Lc pc
ð20Þ
where pc (p kg1) is either the additional cost of fuel if CO2 is produced from flue gases or is the purchase price of pure CO2.
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4. Simulations 4.1. Method HORTITRANS predicts from external weather data, the inside environment and estimate energy consumption and ventilation rate required for humidity control. HORTITRANS was modified to enable simulations to be carried out for a developing crop (see Appendix for functions), to quantify the effects of high humidity on yield and quality and to control the aerial environment by saturation deficit setpoints using the model functions presented in this paper. Table 4 presents parameters used for the simulation which includes the greenhouse characteristics, the set-points for temperature control and the commercial prices of fuel and CO2. The fuel is assumed to be natural gas and CO2 for enrichment is produced from the flue gases. If there is insufficient CO2 produced from the heating requirements then the cost of the additional fuel is used (1 MJ of heat produces 0.0512 kg of CO2). The external weather data of irradiance, air temperature, relative humidity and windspeed were hourly values from Cardington, Bedford, UK for the years 1972– 1979. Simulations were carried out for each year with the crop planted on the 1 January and removed on the 15 November, as standard commercial practice in the UK. Simulation were carried out for single glazed (t=0.65) and double glazed (t=0.58) greenhouses. The saturation deficit control was either during the day (i.e. during daylight hours) or continuously (i.e. throughout a 24-h period) and the setpoints determined from the daily value of irradiance (i.e. a pre-knowledge of irradiance is needed). Table 4 Input parameters used in the simulations Parameter
Value
Number of bays Bay width Bay length Gutter height Ridge height Fraction of roof cladding as ventilators Maximum angle of ventilator opening Night temperature control Day temperature control Night vent temperature Day vent temperature Greenhouse CO2 concentration, C Heating efficiency, eh Energy price, pf CO2 price, pc Maximum percentage yield in Class 1, qm
10 3.2 m 100 m 4.0 m 4.8 m 0.20 Variable 16 C 20 C 24 C 24 C 1000 ppm 80% 0.128 p MJ1 2.5 p kg1 85%
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Daily summaries of inside environment and estimates of energy consumption and ventilator rates required for saturation deficit were simulated by HORTITRANS and used as input to estimate tomato crop growth and development (Appendix). The aim of the control is to maximize profit and the term ‘additional profit’ is used which is the difference in the additional income from dehumidifying and the additional cost of control by simultaneous heating and ventilation. 4.2. Results The cost of dehumidification was high and exceeded the additional income through increase in yield and improved quality. Periods of high cost were identified to occur when the difference in the water content of the air inside and outside the greenhouse was small. During these periods the ventilators were widely opened. Ventilation rates were constrained by reducing the maximum angle of ventilator opening. This influences leaf transpiration and therefore the yield and quality of fruit is less than the potential. The maximum angle of ventilator opening was varied in small intervals typically 2 steps for the single glazed house and 5 steps for the double glazed house. Some results of simulation for the single glazed and double glazed house are presented in Tables 5 and 6. The yield potential (the harvested yield accumulated throughout the season when the crop is grown with adequate water and nutrients) was greater in the single glazed house than the double glazed house because of the reduced transmissivity to shortwave radiation. In the single glazed house the yield potential ranged from 42.4 kg m2 in 1972 to 48.3 kg m2 in 1976 when the irradiance during the summer months was exceptionally high. The extra glazed layer reduced yield potential by 10%. For the double glazed house the additional profits were greater when dehumidifying occurred during daylight rather than throughout the 24-h period for each year from 1972 to 1974 (Fig. 4). For the continuous control the maximum profit was achieved when the maximum vent opening was constrained to about 4 but was less Table 5 Single glazed house: simulation outputs with a maximum vent opening of 4 and the saturation deficit controlled during periods of daylight Year
1972 1973 1974 1975 1976 1977 1978 1979
Yield potential (kg m2)
42.4 45.5 45.3 46.7 48.3 44.5 43.6 45.1
Yield increase (kg m2)
0.24 0.27 0.30 0.37 0.19 0.26 0.22 0.14
Additional income (p m2)
28.0 35.5 35.2 45.0 23.9 28.1 23.0 16.9
Additional costs Heating (p m2)
CO2 (p m2)
21.4 21.2 27.1 24.9 18.5 27.0 23.6 19.6
0.0 0.1 0.3 0.2 0.2 0.4 0.1 0.1
Additional profit (p m2)
6.6 14.2 7.8 19.9 5.2 0.7 0.7 2.8
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Table 6 Double glazed house: simulation outputs with the maximum vent opening of 10 and the saturation deficit controlled during periods of daylight Year
1972 1973 1974 1975 1976 1977 1978 1979
Yield potential (kg m2)
38.7 40.9 40.7 42.0 43.5 39.9 39.1 40.5
Yield increase (kg m2)
1.41 1.22 1.50 1.86 1.02 1.47 1.21 1.06
Additional income (p m2)
165.4 153.2 170.7 214.0 123.1 166.2 137.0 129.1
Additional costs Heating (p m2)
CO2 (p m2)
71.0 62.0 79.7 76.9 61.5 80.2 67.6 67.6
0.4 1.0 1.5 0.9 1.4 2.1 0.7 0.6
Additional profit (p m2)
94.0 90.2 89.5 136.2 60.2 83.9 68.7 60.9
than the maximum additional profit achieved by day time control. The subsequent results are for dehumidifying during the day. For the single glazed house the additional profit from dehumidifying was small and considerably variable from year to year (Fig. 5a). In 1979, there was no benefit to dehumidifying and a net loss to the grower whereas in 1975 an additional profit of 20 p m2 was achieved. The differences between the years was due to the yield increase which was 0.5 kg m2 in 1975 compared to 0.2 kg m2 in 1979. Over the 8 years the maximum additional profit was achieved by using a maximum vent opening of 3 . The average additional profit was 6 p m2 (Fig. 5b). One year in eight there was a loss, in another there was no benefit and additional profit achieved in the other 6 years. For the double glazed house the additional profit was considerable in all years of the simulation (Fig. 6a). There was considerable variation in the additional profit between years ranging from 50 to 135 p m2. The maximum vent opening of 10 produced an average additional profit of about 90 p m2 (Fig. 6b). The CO2 from the flue gases, when additional heating was required for control, was sufficient on most occasions to maintain the concentration of CO2 at the required level. The cost of producing extra CO2 was small compared to the cost of heating (Tables 5 and 6).
5. Discussion The model integrates the understanding from biological and physical sciences in order to analysis, by simulation, strategies for cost-effective control. The essential features contained within the crop model functions are that the assimilate for fruit growth is supplied by subtended leaves, the loss of yield and reduced quality are associated with low calcium uptake and that calcium uptake is associated with
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Fig. 4. Double glazed house: simulation of the additional profit in relation to maximum vent opening for saturation deficit controlled during the day (—) and continuously (- - - -).
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Fig. 5. Single glazed house: simulation of the additional profit in relation to the maximum vent opening (a) for the 1972 (^), 1973 (&), 1974 (~), 1975 (&), 1976 (*), 1977 (~), 1978 (^) and 1979 (*) seasons and (b) the average additional profit for the years 1972–1979 (&) seasons with the line fitted to a third order polynomial constrained through the origin.
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Fig. 6. Double glazed house: simulation of the additional profit in relation to the maximum vent opening (a) for the 1972 (^), 1973 (&), 1974 (~), 1975 (&), 1976 (*), 1977 (~), 1978 (^) and 1979 (*) seasons and (b) the average additional profit for the years 1972–1979 (&) seasons with the line fitted to a third order polynomial constrained through the origin.
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transpiration. The assimilate availability assumption is reasonable for undisturbed plants as assimilates follow the easiest path. However, for highly disturbed tomato plants the source leaves can be considered as part of a common source (Heuvelink, 1995). To incorporate a common assimilate source requires an added level of complexity to the distribution of resources from leaves to fruit (see ‘Partitioning dry matter to individual trusses’ in the Appendix) and a method needed to allocate resources to the fruit from different leaves. The functions to describe yield and quality effects [Eqs. (9) and (10)] were in relation to the ratio leaf area of disturbed and undisturbed plants. This approach made use of the data available from the experiments to study the effects of humidity on growth yield and quality of a tomato crop. A better approach would be to consider the reduction in leaf area in relation to the overall radiation interception of the crop expressed in Eq. (25). However, this approach requires data on the time course of leaf area index, information not recorded in the trials. A ‘critical’ leaf transpiration term was introduced to describe limit leaf growth rate. Leaf transpiration was estimated by a simple model involving irradiance and saturation deficit (Jolliet at al., 1993) and the critical leaf transpiration of 0.65 kg m2 day1 derived as the value below which leaf area was reduced due to calcium deficiency. The data from the Efford trials over three seasons were used to derive the model response functions and the critical transpiration value derived by regression. More detailed studies are required to validate the assumptions and the form of the functions used in the model. The HORTITRANS model accurately predicts the environmental conditions inside a greenhouse (Jolliet, 1994). The modifications made to HORTITRANS enabled simulations to be carried out using hourly weather data for a developing tomato crop. The HORTITRANS model can be used for predicting the inside environments for a range of structures including films, which are common in other parts of Europe. Restricting the vent opening to a maximum was a technique used to reduce cost. This was an option available within HORTITRANS to constrain ventilation rates. The angle of vent opening depends to a large extent on the difference between the water content inside and outside the greenhouse. Alternative options such as constraining costs or using the difference in the water content between inside and outside the house is worth investigating. However restricting the angle of opening of the ventilator is an easy option to implement on a computer control system. The fuel prices used in the simulations were current prices for natural gas, which provided heat and CO2 for enrichment. Currently in the UK, natural gas is the cheapest (and cleanest) fuel available to growers. The simulation for a single glazed house showed that humidity control (to avoid the effects of calcium deficiency) was worthwhile 6 years out of eight. It is likely that more expensive fuels and using pure CO2 would not be cost effective for humidity control in single glazed houses. In the sample double glazed house, control was worthwhile in all the years. Humidity is high when the ventilators are closed, due to reduced condensation and low leakage rates in double glazed houses, and therefore transpiration rates are low during dull periods in the winter and early spring. Whether it is cost effective to provide humidity control using fuels other than natural gas for heating and pure CO2 for enrichment is worthy of further investigation.
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It is more cost effective to control humidity (to increase transpiration) during the day than to control humidity continuously. This is not surprising since transpiration rate is low at night. Although the saturation deficit set-point for continuous control is lower than for day time control, the period of control is about three times greater in the winter and early spring. The simulation relied on a prior knowledge of the forthcoming daily irradiance. For real time control an accurate forecast of the irradiance for the coming day is required. Electronic systems for receiving and interpreting weather information are yet to be fully developed. A manual system for entry of forecast irradiance into a control system is required.
6. Conclusions For a double glazed house additional profit was greater when the saturation deficit was controlled during the period of daylight compared to continuous control for the model input used. For the single glazed house, a maximum angle of opening of 3 produced an additional profit of 6 p m2. One year in eight there was a loss. For the double glazed house, a maximum ventilator opening of 10 produced an average additional profit of 90 p m2. The modified version of HORTITRANS can be used subject to validation of the crop response functions, to study control strategies for other types of greenhouse structures in different climatic regions where short-term (hourly) meteorological data exists. Local information on prices and costs are required.
Acknowledgements The project, Management and Control for Quality in greenhouses (MACQU), was funded by the European Union (AIR3-CT93-1603). The author is grateful to Bernard Bailey, Zaid Chalabi and Ken Cockshull for their helpful discussions.
Appendix. Functions and parameters for a developing tomato crop A.1. Functions Tomato yield is related to the amount of radiation intercepted by the crop canopy. This is based on the experimental findings that where water and nutrients are nonlimiting the rate at which crops accumulate dry matter is proportional to the quantity of solar radiation which they intercept (e.g. Biscoe and Gallagher, 1977). The total dry matter DMtot can be considered as the time-integrated product of three factors: ð DMtot ¼ eiSc dt ð21Þ
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where Sc is the daily solar radiation incident at the top of the canopy, i is the fraction of incident radiation intercepted by the canopy (radiation interceptance), e is the amount of dry matter produced per unit of radiation intercepted by a canopy (dry matter: radiation quotient) and t is time measured in days. The total dry matter is partitioned between the leaves, stem, roots and fruit and Kp is the proportion of the total dry matter that is in the fruit. This proportion changes with time since the plant needs to be established before the dry matter partitions to the fruit, and therefore Kp varies with time and can be expressed as: Kp ¼ DMf =DMtot
ð22Þ
where DMf and DMtot are the rates of change of dry matter in fruit and total dry matter, respectively. Once the crop is well established there are about six trusses carrying fruit which are harvested frequently throughout the season. The fruits on a truss are picked over a period of time (typically about 3 weeks) when the fruits change from green to red. The total daily increment of the dry matter partitioned to fruit needs to be distributed to individual trusses: X DMf ¼ dmf ðnÞfðnÞ ð23Þ n
where dmf(n) is the fruit dry matter of truss n and f(n) is the proportion of dry matter that remains on truss n. If none of the fruit on truss n has been picked then f(n)=1 and if all of the fruit has been picked then f(n)=0. The fruit is sold as a fresh weight product and is related to the fruit dry matter by the dry matter content (Kf): Kf ¼ DMf =FWf
ð24Þ
where FWf is the fresh weight of the fruit (yield in the main section of the paper). A.2. Parameters Parameter values describe the seasonal changes in radiation interceptance, the proportion of dry matter in fruits, fruit growth and the dry matter: radiation interception quotient. A constant for the dry matter content is assumed. A.2.1. Dry matter: radiation interception The dry matter: radiation quotient e=2.24 g MJ1 derived by Hamer (1997) closely agreed with a value of 2.01 kg fresh weight of harvested fruit for every 100 MJ of incident solar radiation measured at the top of the canopy reported by Cockshull et al. (1992). The amount of radiation at the top of the crop canopy depends on the transmissivity to short wave radiation of the glasshouse (t) so that Sc=tSs where Ss is solar radiation measured outside and above the greenhouse away from obstructions. The radiation interceptance is the ratio of total solar radiation intercepted by the crop canopy (Si) to Sc and can be described by:
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i ¼ Si Sc ¼ ½1 am ½1 expðKL LÞ
ð25Þ
where KL is the solar radiation extinction coefficient and L is the leaf area index. Tomato crops are grown in rows (usually in pairs) and pathways between the rows provide access for crop management. There is little or no canopy in the interrow spaces and therefore the crop does not intercept all the available radiation even for a very large leaf area index. The term am represents the proportion of the radiation beneath the crop canopy when L is very large. Hamer (1997) derived values of am=0.105, KL=0.686 and L=0.149+0.00502Dl where Dl is the thermal time from planting. At the time of planting L=0.1 is assumed so that L is always positive and L=5.6 is a constant maximum after thermal time 1145 Kd. A.2.2. Proportion of dry matter in fruit (Kp) Hurd et al. (1979) determined the proportion of fresh weight devoted to fruit, vegetative shoots and roots for the indeterminate tomato at weekly intervals. All of the fresh weight gain is devoted to shoots and roots until flowering and thereafter the proportion to fruit increases to a maximum of about 90% about 50–60 days after anthesis and gradually diminishes to about 75–80% at the end of the growing season. Hamer (1997) described the proportion of dry matter in fruit in relation to the thermal time accumulated from the date of first flowering: Kp ¼ 0:978 þ ð0:978 þ 0:263xÞ0:930x
ð26Þ
where x=Dp/100. For the period prior to first flowering there is no fruit and therefore all the dry matter is distributed to leaves, stems and roots. Eq. (26) predicts a maximum for Kp which then continues to decline rather than reach a plateau. The condition Kp=0 for Dp < 0 and a minimum value of Kp=0.65 beyond the maximum was imposed. A.3. Partitioning dry matter to individual trusses Fruit growth can be described by: dmf ðnÞ ¼ cf exp½exp½bf ðt mf Þ
ð27Þ
where dmf(n) is the fruit dry matter on truss n and t is time from anthesis (days) with parameter values for round tomato given by de Koning (1994): cf ¼ 1:082dm mf ¼ 0:396pf ðn; tÞ½1 þ 0:446expð0:219nÞ bf ¼ 1=ð2:44 þ 0:403 mf Þ
ð28Þ
where dmp is the potential fruit dry matter (g) and pf(n,t) is the fruit growth period (the interval of time from flowering to harvest) which varies with temperature and truss number. A method is required to update pf during fruit development. Assum-
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ing the thermal time from anthesis to harvest is Dav when the average temperature is Tav the fruit growth period is: pf ðn; tÞ ¼
Dav Dðn; tÞ þt Tav
ð29Þ
where D(n,t) is thermal time at t accumulated from the date of anthesis on truss n. The amount of dry matter partitioned to fruit is further partitioned to fruits of different ages according to the potential growth rates (Marcelis, 1993). The first derivative of Eq. (27) represents the fruit growth rate: dm0f ¼
dðdmf ðnÞÞ ¼ dmf ðnÞbf exp½bf ðt mf Þ dt
ð30Þ
and the total dry matter partitioned to fruit is allocated to each truss in proportion to the fruit growth rate of that truss and the summation of all the trusses bearing fruit: dmf ðnÞ ¼ DMf
dm0f "dm0f
ð31Þ
The potential dry weight is the parameter cf and is not required since it appears in both the numerator and denominator of Eq. (31). In effect this parameter is replaced by the dry matter radiation quotient. A.4. Period of harvest of each truss The fruit growth model distributes the dry matter to the fruits on each truss. However, the truss consists of fruit of different sizes and maturity since the flowers open and the fruit set at different times. Typically in round tomatoes there are about 10 flowers per truss and they open over a period of about 20 days. Not all the fruit set. Consequently the fruits from a single truss are harvested over a similar period and therefore the model needs to take this into account. The amount of dry matter harvested is assumed to be more or less the same over the period of harvest from a truss (ph(n,t)). Harvesting commences pfph/2 days after anthesis and the last of the fruit is harvested after pf+ph/2 days. When the harvesting of a truss commences, if the quantity of dry matter removed is simply taken as fraction of the number of days in the harvest period, the first fruit would be small and the last large. The dry matter yield harvested dmy(n) is (Hamer, 1997): dmðnÞ 1 þ ay ft ðnÞ dmy ðnÞ ¼ ð32Þ ph ðn; tÞ where ft(n) is the proportion of fruit remaining and the parameter ay=0.15 [Eq. (32)] ensures for a range of trusses the daily rate of fruit harvested is uniform throughout the period the truss was picked. The amount of dry matter harvested is deducted from the total left on the truss. The harvest period is assumed to be temperature dependent and the same technique used to update pf [Eq. (29)] is used to determine the harvest period.
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