A Procedure for Optimizing Carbon Dioxide Enrichment of a Glasshouse Tomato Crop

J. agric. Engng Res. (1996) 63, 171 – 184

A Procedure for Optimizing Carbon Dioxide Enrichment of a Glasshouse Tomato Crop D. P. Aikman Horticulture Research International, Wellesbourne, Warwick CV35 9EF, UK (Receiy ed 13 March 1995; accepted in rey ised form 10 Noy ember 1995)

The procedure consists of two parts. A Gompertz model for the kinetics of fruit growth is used to predict the time distribution of photosynthate in subsequent harvests. This is combined with predictions of future market prices to compute estimates, one for each day from first anthesis, of a factor to convert CO2 assimilate to expected financial value, based on the worth anticipated from partitioning to fruit. A model of the climate and the crop regime is used to predict temperatures and hence allow for the temperature dependence of fruit growth. The conversion estimates are revised to include the deferred benefit given by additional photosynthesis through increasing early vegetative growth, and hence subsequent photosynthesis and yield. This revision also extends the set of conversion factors to include any period before first anthesis. Given the current environmental variables and conversion factor for that day, a real-time system can use a crop photosynthesis model to predict the cash benefit for any CO2 concentration. The cost of maintaining a concentration can be obtained from a prediction of the ventilation air exchange rate and the unit price of CO2. The CO2 set-point is evaluated as the concentration that maximizes the net profit rate. ÷ 1996 Silsoe Research Institue

1. Introduction

Tomatoes and other glasshouse crops give improved yields with CO2 enrichment.1 An environmental control computer can be used to implement a CO2 set-point and could be used to optimize the profit from CO2 enrichment of the glasshouse tomato crop if a clear cost – benefit analysis can be made. General principles are discussed by Challa and Schapendonk.2 0021-8634 / 96 / 020171 1 13 $18.00 / 0

OPTICO, a model-based real-time expert system,3 assumed a constant economic dry matter index for optimizing CO2 for sweet pepper. With cucumber, individual fruits grow in a relatively short time and Nederhoff et al.4 used a CO2 optimization procedure based on current market prices. Neither of these approaches is appropriate for a tomato crop. The difficulty arises from the contrast in time scales between interacting processes.5 On the one hand, there are the short periods of less than an hour during which the photosynthetic conditions can alter significantly and in which the glasshouse could respond to a change in the set-point for the CO2 concentration, [CO2].6 In contrast, the results of photosynthesis are expressed over periods of time associated with the growth of individual fruits and the duration of the crop, some two and nine months respectively. Over such periods, the market price can vary appreciably and hence neither a constant economic dry matter index, nor the current market price would provide a satisfactory basis. The agronomic results and hence a financially optimal CO2 set-point would depend on several influences: the effect of CO2 on the photosynthetic assimilation rate, the partitioning to fruit and to vegetative structure, the distribution of the photosynthate in subsequent harvests, the fruit worth at such times of harvest, as well as on the cost of CO2 and the ventilation air exchange rate. Crop trials have shown financial benefit from a basic control algorithm for tomato of enrichment to 1000 parts per million by volume (p.p.m.) while vents are closed, and maintenance at the ambient level of 350 p.p.m. when vents are open.7 A strategy for obtaining a more detailed control algorithm would be to compute the CO2 concentration that would maximize the current rate of the predicted net economic benefit. One should note that a set-point equal to the external ambient concentration, like any

171

÷ 1996 Silsoe Research Institute

172

D. P. AIKMAN

other set-point, has cost implications since all of the net assimilation must be met by the supply system. Ideally, a simulation model of the system,8–10 would be used to determine what management strategy over the remainder of the crop period would maximize the expected profit and, within that, what CO2 level should be set now. A simulation model for a glasshouse tomato crop would be based on a mechanistic interpretation of experimental investigations at several levels. It would generally include modules for each of the following plant processes: light interception in a row crop, leaf and canopy photosynthesis, partitioning to fruits and leaves, metabolic and maintenance respiration, crop development and fruit growth. There would also be a module for the rate of loss of CO2 through leakage and ventilation. For economic assessment, there must also be a prediction for future sale prices. However, iterations with even a simple non-linear simulation model may be too slow for use in real time optimization in practice, as one would wish decisions to be made in well under 15 min, the time scale over which [CO2], can change appreciably within a glasshouse.6 A neural network can be trained to fit data generated by a complex system, e.g. the greenhouse climate,11 and reduce the number of state variables required to describe the system satisfactorily. The data set must, of course, contain examples with the relevant information. The procedure developed in this paper is take modules that could be used in a simulation model relevant to the financial implications of the effects of CO2, but to reconfigure their relationships to give a procedure for real time CO2 optimization. The key is that the longer timescale processes will be used to generate a sequence of values, one for each day of the crop, of a scaling factor to convert photosynthetic assimilation of carbon, dependent on [CO2] and the current environment, into estimates of the anticipated financial worth to be obtained from the future sale of produce. The shorter timescale processes, i.e. the crop photosynthesis rate, as a function of the [CO2] in the glasshouse, and the ventilation exchange rate, can use the current value of this factor for the unit worth of photosynthate, together with the unit cost of CO2, in a real-time management system. Given the values of the relevant environmental variables, e.g. radiation, temperature, external [CO2], etc., the management system could determine the net profit rate for any internal [CO2]: the concentration that maximizes the net profit is an estimate of the current optimal [CO2]. This estimate could then be transferred, as a set-point value, to an associated computer that is dedicated to the control of the glasshouse environment. The algo-

rithms could, of course, be incorporated into the control computer system.

2. Background information and description of modules Relevant observations will be described in this section, as will the associated program modules. Their relationships for use in CO2 control are shown in Fig. 1 . The modules on the right-hand side integrate the slow response processes, and are used to compute the set of daily values for unit worth of photosynthate. This part need only be run once at the start of the crop season if the prices are well established, but it can be run again whenever the user makes a revision to the estimates of future prices. The current day’s value of photosynthate worth is used by the modules on the left-hand side. These modules cover the faster processes and are for use in real time control. For simplicity, the derivation will assume that CO2 is available from some fixed price source such as liquid CO2.

2.1 . Canopy photosynthesis The major effect of CO2 levels is on photosynthesis in the leaves. A number of relations for predicting the CO2-dependent rate of photosynthesis have been published. At one extreme, there is a mechanistic model based on the temperature-dependent biochemical relations12,13 which may be coupled with routines for energy balance of foliage, stomatal responses and flux interactions. On a more empirical basis are those of Acock14 and Thornley et al.15 A module for leaf photosynthesis must be combined with one for light interception within a row crop to obtain a model for canopy photosynthesis. The predictions from models of canopy photosynthesis are generally close to each other16,17 and the choice of an appropriate suite of modules for a canopy photosynthesis is left to the user. Although the light interception module would be based, theoretically, on the crop Leaf Area Index (LAI), direct measurement of this is destructive. Measurements of canopy transmission and row geometry would provide a nondestructive basis for deducing the relevant information. As indicated in Fig. 1 the computer system must have real-time access to the environmental variables required by the canopy photosynthesis routine, e.g. the incident flux of photosynthetically active radiation (PAR), and, if the routine includes a dependence on leaf temperature, air temperature and humidity.

173

OPTIMIZING CARBON DIOXIDE ENRICHMENT

Real time

Background information

[CO2] Vent apertures

Wind speed

Temp (ext)

Temp (int)

Glasshouse air exchange model

Solar radiation

Canopy photosynthesis model

Air exchange rate m3/ m2s

CO2 cost £/m2s

Predicted return £/m2s

Glasshouse climate model

Model for market prices

Canopy growth model

Thermal time

Date

CO2 price £/kg

–

Fruit growth model

Delay distribution of photosynthate

Anticipated worth for assimilate in fruit

Revised worth for assimilate £/kg

+ Predicted profit £/m2s

Fig. 1. A flow diagram of the relations between the modules of a procedure to optimize the concentration of CO2 for a glasshouse tomato crop. Using a predicted worth per unit mass of assimilated CO2 , the concentration that maximizes the predicted profit will be the required set-point

2.2. Partitioning of photosynthate and respiration The photosynthate supports maintenance-related respiration and, with allowance for some loss for transport and chemical conversions, growth of fruit and vegetative mass. In tomato, a total of 40% of a day’s assimilate, as measured by steady state labelling of leaf photosynthate with 14CO2, may be lost by respiration over 24 h from sinks and overnight from the source leaf.18 Over the longer term, daily respiration losses would be of the order of 1% per day. The biochemical efficiency of conversion of glucose to average plant biomass may be estimated at 76%, assuming that the nitrogen is derived from ammonia, or 68%, if the nitrogen is derived from nitrate.19 For this application, a growth conversion efficiency of 72% will be assumed. These losses, however, would contribute to the daily respiration. A maintenance respiration of 0?3% of the amount remaining per day, over a mean residence time of 60 d, would give an accumulated respirational loss of approximately 17%. Over a year, the net production of dry matter in the UK glasshouse tomato crop amounts to about 2?8 kg m22 in the fruit, 1?3 kg m22 in the vegetative parts of the shoot and 0?2 kg m22 in the root.20 Similar

results are obtained in the Netherlands: 2?96 kg m22 in the fruit and 1?19 kg m22 in the shoot.21 Hence the harvest index will be about 67%. A dry matter content of 6% is typical in fruits. Thus 1 mol of carbon assimilated as CO2 would give about 1 3 0?72 3 0?83 3 0?67 < 0?4 mol harvested in carbohydrate, 12 g harvested biomass or 200 g harvested fresh mass. 2.3. Kinetics of the crop response to photosynthetic treatments In experiments with shading by 6?4% and by 23%, on a crop planted out in December, there were yield losses of 7?5% and 20% respectively.22 In related investigations in which shading was removed from different plots in January, February and March, the shading resulted in a reduction in yields that persisted for some time after shade removal (Cockshull, personal communication): the differences from an unshaded control reduced to zero after delays of some 5 to 8 weeks although some initial change was apparent some 3 weeks earlier. The relative magnitudes of the initial yield losses were somewhat greater than with the long term experiment. There was also a lag, of some 7 weeks, before the

174

D. P. AIKMAN

effect of a CO2 depletion treatment was seen in the tomato yields.23

2.4. Fruit growth kinetics Ho et al.24 measured the dry matter gain of tomato fruit. The accumulation of dry matter was followed for 55 d, was maximal around 23 d after pollination but persisted through to the end of the period. A Gompertz function gives a good fit to the data as shown in Fig. 2 . Using a loge transformation, the mean square deviation was 0?014, implying deviations of about 12% between observed and fitted masses. The equation for the relation between time, t , and mass, m , is a m 5 m 0 exp (1) (1 2 e 2bt) b

H

J

where m0 is the initial mass. The meaning of the parameters is best illustrated by differentiating Eqn (1) and obtaining the specific growth rate which falls with time: dm (2) 5 am exp (2bt ) dt

2.5. Temperature dependence of fruit maturation A useful relation for temperature dependence of the duration of some biological processes, based on a linear approximation, is that of thermal time in degree-days (deg d), an integral of temperature above some base reference temperature T0 QT 5

0·5

8

0·4

100

6

0·3

80

4

0·2

2

0·1

0·0 0

10

20

30

40

Days from flowering

Fig. 2. A Gompertz function , m 5 m0 exp

50

Fruit volume (ml)

10

0

E (T 2 T ) dt

(3)

0

T0 is the intercept on the T -axis at which an extrapolated rate would be zero. Verkerk26 found 90 d at an average temperature of

Growth rate (g / d)

Fruit dry mass (g per fruit)

The initial growth approximates to an exponential with a being the initial specific growth rate. However the specific growth reduces with time, b giving the rate

of its reduction from its initial value. The absolute growth rate increases initially and then decreases as the mass tends to an asymptotic value m` 5 m 0 e a/b. The absolute growth rate, as predicted by the Gompertz function, is also shown in Fig. 2 . A good fit from the Gompertz model is also obtained to the increase in tomato fruit volume as recorded by Monselise et al.25 as shown in Fig. 3 . Some extended runs of deviations are apparent. However, volume measurement is not as direct an assay of the partitioning from photosynthesis since fruit volume includes a variable fraction of gas space and the percentage dry matter may be higher in the young fruit than in the more mature fruit. Nevertheless, there was a similar timescale, with a maximum rate of increase of fruit volume about 25 d after anthesis.

60

40

20

60

Hba (1 2 e )J, for 2bt

the growth of tomato fruit, ——; fitted to data for the increase in dry weight of tomato, d (Ho et al.24); using m0 5 0?00017 g, a 5 1?34 d21 and b 5 0?106 d21, and the corresponding rate of growth, - - -

0 0

10

20 30 40 Days from flowering

50

60

Fig. 3. A Gompertz function , - - -; fitted to data for the increase in y olume of tomato (Obsery ed y alues taken from Monselise et al.25) ——

OPTIMIZING CARBON DIOXIDE ENRICHMENT

138C for the maturation of tomato fruit from anthesis to picking, 53 d at 198C and 40 d at 24?678C. An empirical approximation to these data is that there is a requirement for an integral of temperature of 840 deg d above a base of 3?58C for fruit maturation from anthesis to picking. Hurd and Graves27 suggested that the effect of temperature on the rate of maturation of tomato fruit (73 d at an air average temperature of about 16?78C and 65 d at 18?28C) can be summarized by a Q10 of 2, (i.e. an extrapolated temperature increase of 10 K would double the maturation rate). Their data would give an integral of 890 deg d over a base of 4?58C. Combining the two sets, and refitting suggests a requirement of 806 deg d above a base temperature of 4?758C. Hurd and Graves27 noted that later trusses tend to mature earlier than a Q10 of 2 would predict, perhaps because insolation elevates the fruit temperatures. The faster crop response later in the season noted above is consistent with this suggestion. In experiments with variations in temperature, de Koning28 found that the time to ripening in tomato varied with temperature, and was particularly sensitive during the earliest and final periods of growth. Fruit growth in tomato would also be influenced by competiton between fruit within a truss.29

2.6. Delay time distribution of the appearance of photosynthate in hary ested fruit To predict the distribution over time for the appearance of photosynthate, it may be assumed that photosynthate is partitioned between fruits of different ages according to sink demands which are proportional to their potential growth rates.30,31 For CO2 optimization, it will be assumed that, after first anthesis, there is an increasing span of fruit ages with associated fruit masses, whose sink demands will be predicted by Eqn (2). Each day, a fixed proportion of the daily photosynthate production will be distributed over the fruits in proportion to their demands, the fruits are incremented in thermal age and a new cohort will be started. After they have totalled up a sufficient thermal integral, each cohort will be picked in turn. For simplicity, a uniform distribution of numbers from youngest to oldest will be assumed. A small correction would be made if one were to allow for a variation in the numbers set. This can arise from a feedback with the supply of photosynthate being pre-empted by existing sink demand, or from explicit management of fruit numbers. Either way there can be an increasing number of fruits to match demand

175

with supply from the seasonal increase in light levels from winter to spring and summer, and then a reducing number into autumn. similarly, for the purpose of CO2 control, variation in temperature sensitivity with age will be ignored, and it will be assumed that fruit growth and fruit maturation share a common dependence on temperature. Thus photosynthate, produced in any particular day, will appear in a subsequent series of harvests: soonest from the photosynthate going to the oldest fruits, and latest from that to the youngest. The distribution of photosynthate over subsequent harvests will be determined by a thermal timescale and by the relative growth rates for the fruits. Assuming comparable temperatures and a uniform fruit load, the function shown in Fig. 2 gives a growth rate at age 54 d of 0?034 g d21 out of a total of 8?5 g. Hence, of the photosynthate produced in any day, 0?4% would be assimilated by fruit of age 54 d and would appear in the earliest harvest. The proportion in daily harvests would then rise progressively for a period, and 4% would have been assimilated by fruit with the fastest growth rate at age 23 d, 0?34 g d21, and thus be harvested after a further 31 d. After that, the expected proportion harvested per day would fall. With a seasonal trend in temperature, it is more appropriate to use a thermal time scale, in deg d, rather than calendar time when following fruit development. A prediction for the thermal climate for fruit can be based on the glasshouse air temperature regime, i.e. its heating and venting set-points, and on the external climate, i.e. the external air temperature and the solar radiation, to the extent that this may raise the internal temperature above the heating control temperature. Allowance can also be made for some additional solar gain by the fruit. A predicted thermal scale for fruit growth may be linked to the calendar time scale, and hence the distribution of harvesting of the photosynthate over subsequent thermal time mapped onto the calendar, stretched over longer times in periods of lower expected temperatures, and shorter times at higher temperatures. Thus, the models for the glasshouse climate and for the temperature-dependent fruit growth can be used to generate prediction for the delay distribution for photosynthate as indicated on the right-hand side of Fig. 1 .

2.7 . Tomato price The financial return from photosynthesis comes from the subsequent sale of the harvested fruit. For predicting the economically optimal CO2 set-point, it

D. P. AIKMAN

is necessary to make an estimate of the market prices that will be obtained for the fruits that contain the photosynthate and which will be picked subsequently. Fenlon (personal communication) performed a statistical analysis of the market prices of UK Class 1 tomatoes over the years 1983 – 1989. The prices show variations between years although they have certainly not increased fully in line with increases in the Retail Price Index. There was a general trend with higher prices in the earlier part of the year that fall to a minimum in the late summer, perhaps with a slight recovery in the autumn. Although there are differences between the years and fluctuations within years, an approximation was obtained from a quadratic function y 5 215 2 8?2n w 1 0?1n 2w (4) where y is the market price, in pence kg21, for week number nw after the start of a year, over the period of the marketing of UK tomatoes, weeks 9 to 45. To allow for proportional costs that change with yield, such as those for harvesting, transport and marketing, and for a reduction in worth for some downgrading of fruit, a sum, e.g. 20 pence kg21, could be deducted. The UK prices from 1990 to 1994 were of a similar trend but lower in magnitude, influenced by some macro-economic changes. The actual market prices earlier in a year would appear to offer a practical predictor by scaling the price prediction for use later in the same year, with a likely need for revision at intervals. The function should be replaced by a set of defined contract prices if the grower will be selling the produce under such an agreement.

2.8. Estimate of fruit photosynthate worth The market price of fruit can be expressed as a worth per mol of carbon in the fruit if one allows for the water content, ,94%, and for the ratio of carbon to dry matter, ,30%: 1 kg of fruit contains about 60 g carbohydrate; i.e. 1?5 mol C. An estimate of an anticipated worth factor, in cash units per mole of carbon dioxide assimilated, can be made for any day by generating a weighted average from the predicted market price for fruit: multiply the function for predicted fruit price over the relevant future time by the function for the distribution for the delays to picking and selling. To link the fruit market worth back to the assimilated CO2, one must allow, of course, for the fraction that is partitioned to vegetative structure and for the loss by respiration. Allowance is also made for the proportional costs involved, e.g. nutrient uptake, labour and marketing, etc. The

procedure also makes allowance for the cost of the CO2 as though all were derived from the enrichment supply. This is, of course, valid when the internal set-point is greater than or equal to the external concentration. The rationale for doing so when the internal concentration is below the external will be discussed in the next section. This estimate of anticipated worth is analogous to the intensity of cultivation as proposed by Seginer.32 For a crop of tomato plants, which is planted out at the start of week 24, i.e. 4 weeks before 1 January, which flowers from week 23 to week 37 and which is removed at week 43, Fig. 4 shows the trends, as functions of date, for estimates of worth per mole of assimilated CO2. Firstly, curve (a) shows the estimate formed directly from the market prices for tomatoes, expressed relative to net CO2 assimilated. Allowance has been made for the water content, for the fraction partitioning to other sinks, for respiration losses and for the proportional costs. It also allows for the cost of the CO2 supplied. This estimate commences from the date of the first harvest in week 5, i.e. 8 weeks after first anthesis. Also shown in Fig. 4 , curve (b) is the estimate of worth anticipated from CO2 assimilated on that date, partitioned over the range of ages of fruits on the plant and so appearing in harvested fruit with a 35 30 Estimated worth (pence / mol CO2)

176

25 20 15 10 5 0 0

50

100

150

200

250

300

350

Time from planting (d)

Fig. 4. Estimates of the financial worth of CO2 assimilate in tomato oy er the season , (a) from market prices of fruit , —— from the start of hary esting; (b) as an anticipated worth from the distribution in fruits maturing oy er a period and then being marketed , —– ? ? , starting from first anthesis; and (c) as the rey ised anticipated worth from fruit incorporating an allowance for a return from an iny estment in early y egetatiy e growth but a reduced fraction in the initial partitioning to fruit , ? ? ? ? , starting from planting out

OPTIMIZING CARBON DIOXIDE ENRICHMENT

distribution of delays of up to 8 weeks. The estimates were calculated using the Gompertz parameters of Fig. 2 . Since the modal delay is about 5 weeks from maximal sink demand till harvest, the estimate generally approximates to the value for fruit that will be expected 5 weeks later. However the delays are longer initially, e.g. up to 8 weeks at the time of first anthesis, but reducing as the first fruit increase in age to maturity. In the final weeks of the crop, after the shoot is stopped, the delay progressively reduces as the remaining fruit on the plant mature and are picked. This prediction of worth commences at date of first anthesis. The third curve (c) will be explained later.

2.9. Cost of CO2 enrichment Let us assume that there is a fixed price for CO2 in cash units per kg of carbon dioxide, as from a tank of pure liquid CO2 for example. Let us also assume that there is a model to predict the rate for gas exchange based on a leakage rate, including door openings, and a ventilation rate. While the former should be based on experimental measurements for the particular glasshouse, using the kinetics of a chemical tracer, possibly CO2 before the crop planting,33 the latter might be estimated from vent apertures and wind-speed as suggested in Fig. 1 . Alternatively, since the object of ventilation control is to limit the glasshouse temperature rise, one could estimate ventilation exchange from a model with a leakage term plus an energy balance using temperatures, radiation and humidities. The two methods of estimation agree well at higher ventilation rates.34 The total cost of the CO2 supply to the glasshouse is that of the assimilated CO2 plus, if the internal concentration is above the external ambient concentration, that of the net ventilation efflux. Allowance for the cost of the CO2 assimilated has already been made in the estimate of the worth of the photosynthate (Section 2.8). Multiplication of the air exchange rate by the difference between a potential CO2 set-point and the external concentration, gives the net efflux which, multiplied by the price of the CO2, gives the cost of the ventilation loss. Potentially the optimal set-point could be below the external ambient concentration, if some, even all, of the assimilation rate is met by a net influx of atmospheric CO2. The negative flux now gives a negative cost for the ventilation flux which will offset part of the allowance for cost of CO2 made in the assimilate. The procedure adopted is still valid. While there are alternative procedures that will give the same end

177

result, the one described here has the advantage of preserving the linearity of the cost function. Note, however, that the set-point should not fall below that sufficient to supply all the assimilation for free: no extra influx of CO2 can be used to generate additional income as the system cannot extract the gas to replenish the supply tank.

2.10. First estimate of optimal CO2 concentration A module for canopy photosynthesis will give a function with diminishing marginal returns for increasing [CO2]. That for air exchange will be linearly dependent on [CO2]. These may be converted to cash equivalents by the estimate of photosynthate worth, and the cost per unit of CO2 supply respectively. Note that the estimate of the photosynthate worth at this stage is that associated with the fraction partitioned to fruit and which is sold later. The maximum profit rate would be given by the concentration at which these two marginal rates are equal in cash terms. The value of the worth factor will be modified as a result of the concept introduced in the next section, but the revised factor will be used in a similar fashion. 2.11 . Vegetatiy e growth Vegetative growth is required by the plants for light interception to drive fruit growth. The canopy photosynthesis module demands an estimate of the interception to predict photosynthesis and its response to [CO2]. The proportion of the incident light that is intercepted can be supplied as a predetermined function of time. However the application software should allow this to be amended on the basis of the environment experienced by the crop or by using measured values of LAI. The vegetative mass of a tomato plant may be viewed as having some capital worth. Seginer et al.35 describe the optimization of CO2 for the growth of tomato seedlings to a mass of 0?8 kg m21. A grower buys young plants and grows them on, maintaining photosynthesis before first anthesis. It is essential to allocate a worth to photosynthate being produced before first anthesis: if not, then the instantaneous optimization would attempt to maximize net profit by ceasing any steps to assist growth if they incurred costs. On the contrary a 50% supplementation of illumination, given during the last 5 weeks of the propagation phase, gave a 70% increase in the first 3 or 4 weeks’ pick (Cockshull, personal communication). Tomato seedlings propagated with CO2 enrichment

178

D. P. AIKMAN

went on to give greater yields than control seedlings.36 The effects of CO2 enrichment and light increase are comparable in young plants, except that the latter had the greater effect on a shortening of the internode length.37 Increases in initial yields will be the result, in part at least, of an earlier date of first anthesis but may also be due to a boost to vegetative plant structure and reserves. Low irradiances, and therefore low rates of photosynthesis can delay floral initiation,38,39 and can result in reduced setting and complete abortion.40 An estimate for the marginal worth of initial vegetative mass gain in a young tomato plant may be based on the deferred benefit: in young plants, an increase in photosynthesis can increase leaf area, e.g. with elevated [CO2] in cucumber,41 and hence a marginal increase to the radiation intercepted in future. Therefore the directly anticipated photosynthate worth should be amended to include the effect, if any, on subsequent responses. Potentially, the marginal change in leaf area could persist for a period comparable with the growth period of a fruit since the leaves, associated with a fruit truss, are pruned off the stem as the truss nears harvesting. Thus, part of the effect of current photosynthesis on total financial benefit will arise from an expected improvement to subsequent photosynthesis, in addition to the more direct return expected from current photosynthate going to fruit growth. Indeed, before first anthesis, no direct benefit from fruit growth will exist: the delayed benefit would provide the only basis for assessing an optimal [CO2]. Once leaf growth ceases, shortly after removal of the shoot apices towards the end of the season, there will be no delayed benefit, only that from photosynthate going to fruit. Similarly, if additional photosynthate does not increase LAI, then no additional benefit will arise. In the mid-season tomato crop, additional photosynthesis can result in thicker and shorter leaves.42,43 A hypothesis is that these responses occur when the sinks demands are not able to match the potential production of carbohydrate. Such an effect will reduce or negate the addition of a delayed worth from additional photosynthate. 2.12. Rey ised estimate of photosynthate worth After first anthesis, the estimate of the anticipated worth of photosynthate going to fruit provides a fast means of making a first estimate of an instantaneous set-point for CO2. If the canopy photosynthesis rate and the CO2 flux are predicted as functions of [CO2], given the other current relevant variables, then the

cash conversion factor allows us to find the set-point: it is the [CO2] at which the derivative of the estimated net profit is zero. The procedure will result in a partitioning of photosynthate between fruits and vegetative sinks, in proportion to the sink strengths. A higher value of [CO2] might be advantageous, particularly early in growth, as it would lead to a larger LAI which then, in turn, would have a greater rate of canopy photosynthesis and a greater subsequent profit potential. The direct worth conversion factor allows for the derivative with respect to the current [CO2] of the cash worth associated with current photosynthate goint to fruit. The additional worth under consideration here is also associated with the derivative with respect to current [CO2], of a deferred potential gain. So the procedure should be based on an estimate of the total gain from photosynthesis that may be split into medium term, direct to fruit, and longer term, a deferred benefit arising from investment in structure improvement. After first anthesis, sink strengths will result in the partitioning of photosynthate to developing leaves and to developing fruits. It is necessary to check whether this would provide sufficient resources for structure development or, after leaf removal has started, for replacement. If extra net benefit would result from an increased CO2 level, then the CO2 set-point should be increased by using an increased value for the photosynthate worth conversion factor. The extra credit should be scaled down or eliminated when the predicted benefit or increment in LAI is less than proportional or zero. For example, if the predicted supply – demand balance is such that additional photosynthate merely increases leaf thickness as may occur in mid or late season, then no additional photosynthate would be desired and no increase should be given to the photosynthate worth factor. Given the observations on tomato crop described earlier, it was decided to phase out the delayed benefit, and a linearly decreasing fraction will be applied over a period of 56 d from first authesis. Photosynthesis before first anthesis should, however, be given full credit for the delayed benefit from the structure it creates. An algorithm for determining an increase in the conversion factor, before and for a period after first anthesis, is given in the Appendix. In Fig. 4 , curve (c) shows the revised estimate that includes the extra allowance for the delayed benefit from vegetative growth, before first anthesis and, decreasingly, for the following 8 weeks. This ensures an estimate of worth from the time of planting out of the crop and for the benefit in early vegetative growth. To avoid an unrealistically abrupt change in the estimate of worth at first anthesis, a sinusoidal relation

OPTIMIZING CARBON DIOXIDE ENRICHMENT

is used to increase the proportion of photosynthate partitioning to fruit smoothly from a minimum of zero, at first anthesis, to the steady rate of 67%, 4 weeks later. For application, a set of values, similar to those in curve (c), are generated by a computer program. It allows for the expected temperature climate for a glasshouse, given the external climate and a crop regime, and hence for the variation in the temperature-dependent rate of fruit growth and maturation. This results in longer delays in colder periods, e.g. with lower heating set-points and / or low solar gain, early in the crop growth, and shorter ones during warmer periods.

2.13. Summary of the procedure for CO2 optimization in the glasshouse tomato The procedure has two parts, as indicated in Figure 1. 2.13.1. Off-line , before the start of the season Simulate the glasshouse internal climate, hence predict values for tomato fruit temperatures Predict a time course for the crop LAI and height Thus for each day of crop from the day of first anthesis, D1A, onwards: (1) use the fruit growth model to predict the proportions of the day’s photosynthate that will appear over a sequence of subsequent days’ harvests; (2) combine with the predicted values of those days’ prices to predict the anticipated worth from partitioning to fruit for that day; (3) convert from a basis of fruit fresh weight to that of moles of net photosynthetic assimilate and allow for the cost of CO2 assimilated.* For the first 56 days after first anthesis: additionally and progressively allow for a proportion of delayed worth from vegetative partitioning, starting from D1A 1 56 working back to D1A, phasing the direct estimate out progressively from D1A 1 28 back to D1A. For any days prior to first anthesis: allow for the delayed worth from vegetative partitioning, starting from D1A and working back to the day of planting out, and thus obtain the set of values for the revised anticipated worth for assimilated CO2. * One may assume, for computation, that all the CO2 assimilated is supplied at full cost and that the ventilation flux of CO2 is also at full cost, a negative cost in the case of net influx supplying all or part of the net assimilation with a set-point below the external ambient concentration

179

2.13 .2 . On -line , during the day at 10 min intery als Read I , T and [CO2], estimate ventilation rate and note canopy radiation levels. Search on potential CO2 levels: (1) total the net photosynthetic rate over the canopy; (2) multiply by the day’s factor to predict the rate of gain of anticipated worth; (3) calculate the cost of CO2 ventilation loss (or gain*); (4) find the economic optimal CO2 level, i.e. the CO2 level at which the gradient of the non-linear canopy photosynthesis worth curve matches that of the ventilation cost linear relation. Send CO2 set-point. 2.13 .3. At the end of the day Update crop status, LAI and height by values, estimated by computation or recorded from the crop. If necessary, update future market price estimates and recalculate the remaining anticipated values.

3. Illustrative example The photosynthate worth factor is the key for separating the procedure into the two parts shown in Fig. 1, allowing the modules of a simulation model to be configured for use in an on-line control system. To illustrate the system, suppose that the cost of CO2 is £100 per tonne, or 0?48 pence per mol CO2, and the system estimates that there is currently an air exchange rate of five changes per hour. If the glasshouse has a mean height of 3 m, then the ventilation rate would be 4?2 3 1023 m3 m22 s21. A concentration of 1 p.p.m. in a gas at 228C corresponds to 4?1 3 1025 mol m23. And hence the cost, per p.p.m. of concentration enrichment, of the loss of CO2 would be 8?3 3 1028 pence m22 s21 (p.p.m.)21, giving a ventilation cost, linear with respect to [CO2], as shown by the broken line in Fig. 5 . For this illustration, let us assume that it is day 67 and hence, according to Fig. 4 , curve (c), the worth of photosynthate is 25 pence per mol CO2 assimilated. This is the average of the future market worth of assimilated photosynthate based on its partitioning over the full range of ages of fruits on the plants according to their potential growth rates, and on the associated delays before it appears in harvested fruits as they mature successively over the following 8 weeks. No allowance is made for any increase in vegetative value since, by this time, the crop is in full canopy expansion and any additional photosynthetic rate does not increase the LAI. The procedure does not specify the photosynthesis model: the user may select that considered the most

Benefit and cost (10–3 pence m–2 s–1)

180

D. P. AIKMAN

0·25

4. Discussion

0·20

4.1 . General discussion

0·15

A range of experimental information has been reviewed to derive a procedure for estimating the worth of per unit of CO2 assimilated by a tomato crop from (a) its distribution over fruits of differing ages and hence delays before sale, and (b) the benefit of early vegetative growth in increasing subsequent photosynthesis and fruit yields. This factor allows a direct comparison between the financial benefit from CO2 enrichment and its cost, and allows the identification of the optimal set-point well within the timescale of the CO2 kinetics of a glasshouse. By inference, data sets with a similar relevant information content would be required to train a neural network. A caution is that, although the modules of the procedure are based on theory and, individually, agree with the corresponding experimental observations cited, it will be important that they are tested, assembled in a simulation model, against data from a crop experiment with a range of CO2 regimes. In particular, the responses to CO2 during early growth, before and shortly after first anthesis, should be checked. A further test could be to run the procedure in a glasshouse to control the CO2 regime and compare the net profit against those from other regimes, although the precision of such an experiment might be limited. The CO2 level cannot respond instantaneously to a change in set-point. If the procedure is being incorporated into an environmental control computer, it may, perhaps, not be necessary to iterate to identify and implement an optimal CO2 set-point. It may be sufficient to check whether an increase in predicted profit is obtained by increasing the CO2 level from the current value: if so then the supply valve should be open, if not, it should be closed. The response to light levels that fluctuate more rapidly than the CO2 concentration will implicitly give an averaging of the non-linear dependence. This modification would give a procedure that would run even faster. For simplicity, the control of CO2 in this procedure is not linked to the control of temperature although there may be additional benefit from doing so.44,45

0·10

0·05

0·00 0

200

400

600

800

1000

1200

CO2 concentration (p.p.m.)

Fig. 5. Illustration of a CO2 set-point ey aluation . An estimated worth of photosynthate for the day has been used to scale a canopy photosynthesis rate for the current light ley el as a function of the potential CO2 concentrations , —— . The predicted benefit rates can be compared with the corresponding costs of CO2 loss from the y entilation air exchange , — ? — ? ; and the concentration that maximizes the marginal profit rate obtained , m. Below 320 ppm , the CO2 influx would exceed the assimilation rate

appropriate. For this illustration, however, a rectangular hyperbola is taken for the response to [CO2] as in the modified Acock model described by Nederhoff and Vegter.17 The parameters of the curve would depend, amongst other factors, on the crop canopy LAI and on the current radiation level. Fig. 5 arbitrarily assumes a canopy photoassimilation rate up to 8 3 1026 mol m22 s21, at 1200 p.p.m. [CO2], which converts to a potential return of up to 2 3 1024 pence m22 s21. As it is in the same units, it can be directly compared with the ventilation cost. The optimal set-point, that which would give the maximal rate of net cash return, is where the slopes are parallel and would be at a [CO2] of 717 p.p.m. in this example. The feasible region is from 320 p.p.m. upwards for these conditions: below that concentration, the influx rate would exceed the assimilation rate and thus a set-point below 320 p.p.m. could not be effected. The curve for the estimated benefit would move upwards if light level were higher. However, the ventilation rate and its cost would also tend to increase to prevent a temperature rise. If the rate of increase of benefit with respect to [CO2] never exceeds that of the supply cost, then the net benefit is maximal at zero CO2 supply with all of the net assimilation being derived from ventilation influx.

4.2 . Resery ations about the procedure The procedure is designed only for the control of CO2 and does not include temperature control. As

OPTIMIZING CARBON DIOXIDE ENRICHMENT

described, it does not adjust the CO2 set-point to allow for the average daily trends in light, rising earlier in the day and falling later, nor for any prediction of the radiation variations over the period in which an input of CO2 is reflected in the glasshouse concentration. No allowance is made for boosting photosynthate storage during days when ventilation losses are low for improved availability of reserved during days of higher ventilation. The procedure does not include a linked control of intermittent CO2 supply and ventilation.44,45 It does not allow for any linkage between current weather and future market price, although, of course, a grower may elect to modify the prediction for market prices personally. There are limitations to the accuracy of prediction of market prices over the period of up to 7 weeks which has the greatest influence on the anticipated return. Although a contract price would give a stable factor, amendment is required if a grower anticipates selling an excess yield at market prices during some periods. The algorithm would require some modification for use with CO2 generated in association with heat production and storage. 4.3. Ady antages Many of the reservations discussed above would apply to most CO2 control procedures. The advantages are more specific. The procedure here is mechanistically related. It makes use of relatively simple descriptions of the most relevant modules of a simulation model. It covers the vegetative and fruiting stages. The structure associated with the proposed procedure means that it can easily use any particular choice of modules e.g. for canopy photosynthesis, or some future improvement to the modelling of ventilation. The implications of any alterations are clear. The relevant details could be modified, e.g. if a change in the management of the numbers of shoots, fruits or leaves, resulted in changes in the supply and demand for photosynthate. A change in future contract or market prices or in CO2 price will be reflected in the computed set-point. The configuration produces a procedure that is sufficiently fast to use for real-time control since it has reduced the complexity of the processes that are required for running on-line. It makes use of our understanding of the crop and glasshouse, developed from a wide range of existing data. It has not demanded the performance of a large and costly series of specifically designed replicated experiments to produce multiple sets of time-series data. Individual

181

parameters, e.g. dates of planting and first anthesis, dates of shoot stopping and crop clearance, temperature regime, glasshouse leakage, crop height and LAI, etc., can be readily be supplied by the grower for use by the procedure in any particular implementation. The procedure may not be perfect, but it is practical. It should, however, allow the user to obtain a high proportion of the benefit theoretically available from a full optimization, if such existed and could be implemented. Indeed, if the same modules were used in a simulation program and then used in an optimization search, there would be little, if any, difference.

5. Conclusions

The glasshouse crop system discussed is complex. A wide range of relevant experimental information has been used in developing the approach to CO2 optimization. Modules, that could have been used for the longer timescale processes of a simulation model for the responses to CO2 concentration, have been used in a different configuration to give a conversion factor for the worth of photosynthate that varies appropriately over the season. The factor reflects the changes in future market price and the variation in time delays from photosynthesis to harvesting. The factor is amended, for early growth, to allow for the indirect worth of an increase in foliage increasing future photosynthesis and yields. The factor can be used with the modules that predict canopy photosynthesis as a function of [CO2] to give a real time estimate of the potential cash benefit for any concentration. This can directly be compared with a function of [CO2] that gives an estimate of the ventilation cost. This configuration of the modules provides a practical procedure for quickly obtaining an optimal set-point. The modules should be tested, assembled in a simulation model, against data from crop experiments with a range of different CO2 regimes to provide additional validation for the procedure developed here.

Acknowledgements

The work has been financially supported by MAFF. I wish to thank Lim Ho for supplying the original values used in plotting Fig. 2 , and Ken Cockshull, John Fenlon, Zaid Chalabi, Bernard Bailey and others for valuable discussions.

182

D. P. AIKMAN

References 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

Hand D W CO2 enrichment, the benefits and problems. Scientia Horticulturae 1982, 33: 14 – 43 Challa H; Schapendonk A H M C Dynamic optimisation of CO2 concentration in relation to climate control in greenhouses. In Carbon dioxide enrichment of greenhouse crops, Enoch H. Z., Kimball B. A. (eds), Boca Raton: CRC Press, 1986, 147 – 160 Ehler N; Karlsen F OPTICO—a model based real-time expert system for dynamic optimisation of CO2 enrichment of greenhouse vegetable crops. Journal of Horticultural Science 1993, 68: 485 – 494 Nederhoff E M; de Koning A N M; Rijsdijk A A Dynamic optimisation of the CO2 concentration in greenhouses: an experiment with cucumber (Cucumis satiy us , L.). Acta Horticulturae 1988, 229: 341 – 348 Challa H Prediction of production: requisite of an integrated approach. Acta Horticulturae 1988, 229: 133 – 141 Chalabi Z; Fernandez J E Spatiotemporal responses of a glasshouse to gaseous enrichment. Journal of Agricultural Engineering Research 1992, 51: 139 – 151 Hand D W Crop responses to winter and summer CO2 enrichment. Acta Horticulturae 1984, 162: 45 – 60 Challa H Crop growth models for greenhouse climate control. In Theoretical Production Ecology: reflections and prospects, Rabbinge R., Goudriaan J., van Keulen H., Penninig de Vries F. W. T., van Laar H. H. (eds), Simulation Monographs 34, Wageningen, The Netherlands, PUDOC, 1990, 125 – 145 Dayan E; Keulen H van; Jones J W; Zipori I; Shmuel D; Challa H Development, calibration and validation of a greenhouse tomato growth model: I. Description of the model. Agricultural Systems 1993, 43: 145 – 163 Nederhoff E M; Gijzen H; Vegter J G; Rijsdijk A A T I Dynamic model for greenhouse crop photosynthesis: validation by measurements and application for CO2 optimization. Acta Horticulturae 1989, 260: 137 – 147 Seginer I; Boulard T; Bailey B Neural network models of the greenhouse climate. Journal of Agricultural Engineering Research 1995, 55: 139 – 151 Farquhar G D; von Caemerer S; Berry J A A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 1980, 149: 78 – 90 Farquhar G D; von Caemerer S Modelling of photosynthetic response to environmental conditions. In Physiological Plant Ecology II 12 B, Lange, O. L., Nobel, P. S.; Osmond, C. B.; Zeigler, H. (eds), Basel, Springer, 1982, 549 – 587 Acock B Modeling canopy photosynthetic response to carbon dioxide, light interception, temperature and leaf traits. In Modeling crop photosynthesis from biochemistry to canopy, CSSA 19, Boote, K. J.; Loomis, R. S. (eds). Madison, Crop Science Society of America, 1991, 41 – 55 Thornley J H M; Hand D W; Warren-Wilson J Modelling light absorption and canopy net photosynthesis of glasshouse row crops and application to cucumber. Journal of Experimental Botany 1992, 43: 383 – 391 Chalabi Z S; Fernandez J E Estimation of net photosynthesis of a greenhouse canopy using a mass balance method and mechanistic models. Agricultural and Forest Meteorology 1994, 71: 165 – 182 Nederhoff E M; Vegter J G Canopy photosynthesis of

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

tomato, cucumber and sweet pepper in greenhouses: measurements compared to models. Annals of Botany 1994, 73: 421 – 427 Shishido Y; Seyama N; Imada S; Hori Y Carbon budget in tomato plants as affected by night temperature evaluated by steady state feeding with 14CO2. Annals of Botany 1989, 63: 357 – 367 Thornley J H M; Johnson I R Plant and Crop Modelling. Oxford, Oxford University Press, 1990 Aikman D P Potential increase in photosynthetic efficiency from the redistribution of solar radiation in a crop. Journal of Experimental Botany 1989, 40: 855 – 864 de Koning A M N Growth of a tomato crop: measurements for model validation. Acta Horticulturae 1993, 328: 141 – 146 Cockshull K; Graves C J; Cave C R J The influence of shading on yield of glasshouse tomatoes. Journal of Horticultural Science 1992, 67: 11 – 24 Drakes G D Summer CO2 for tomatoes. Reviews of Stockbridge House Experimental Horticultural Station for 1984: 15 – 21 Ho L C; Sjut V; Hoad G V The effect of assimilate supply in fruit growth and hormone level in tomato plants. Plant Growth Regulation 1983, 1: 155 – 171 Monselise S P; Varga A; Bruinsma J Growth analysis of the tomato fruit, Lycopersicon esculentum Mill. Annals of Botany 1978, 42: 1245 – 1247 Verkerk K Temperature, light and the tomato. Mededelingen Landbouwhogeschool, Wageningen 1955, 55: 175 – 224 Hurd, R G; Graves C J Influence of different temperature patterns having the same integral on the earliness and yield of tomatoes. Acta Horticulturae 1983, 148: 547 – 554 de Koning A M N Effect of temperature on development rate and length increase of tomato cucumber and sweet pepper. Acta Horticulturae 1992, 305: 51 – 55 Bangerth F; Ho L C Fruit position and fruit set sequence in a truss as factors determining final size of tomato fruits. Annals of Botany 1984, 53: 315 – 319 Evans L T Assimilation, allocation, explanation, extrapolation In Theoretical production ecology: reflections and prospects. Rabbinge, R.; Goudriaan, J.; Van Keulen, H.; Penning De Vries, F. W. T., Van Laar, H. H. (eds), PUDOC, Wageningen, The Netherlands 1990, 77 – 87 Marcelis, L F M Fruit growth and dry matter allocation to the fruits in cucumber. 1. Effect of fruit load and temperature. Scientia Horticulturae 1993, 54: 107 – 121 Seginer I Optimal greenhouse production under economic constraints. Agricultural Systems 1989, 29(1): 67 – 80 Nederhoff E M; Vooren J van de; Udink ten Cate A J A practical tracer gas method to determine ventilation in greenhouses. Journal of Agricultural Engineering Research. 1985, 31: 309 – 319 Fernandez J E; Bailey B J; Measurement and prediction of greenhouse ventilation rates. Agricultural and Forest Meteorology 1992, 58: 229 – 245 Seginer I; Angel A; Gal S; Kantz D Optimal CO2 enrichment strategy: a simulation study. Journal of Agricultural Engineering Research 1986, 34: 285 – 304 Anon A comparison of container sizes in growing rooms

183

OPTIMIZING CARBON DIOXIDE ENRICHMENT

37

38

39

40

41

42

43

44

45

and the effect of CO2 with lighted bench propagation. Review of Fairfield Experimental Horticultural Station for 1971, 33 – 37 Hurd R G Effects of CO2-enrichment on the growth of young tomato plants in low light. Journal of Experimental Botany 1968, 32: 531 – 542 Calvert A Effect of the early environment on development of flowering in tomato. II. Light and temperature interactions. Journal of Horticultural Science 1959, 34: 154 – 162 Wittwer S H Photoperiod and flowering in the tomato. Proceedings of the American Society of Horticultural Science 1963, 83: 688 – 694 Kinet J M Effects of light conditions on the development of the inflorescence in tomato. Scientia Horticulturae 1977, 6: 27 – 35 Aoki M; Yabuki K Studied on the carbon dioxide enrichment for plant growth, VII. changes in dry matter production and photosynthetic rate of cucumber during carbon dioxide enrichment. Agricultural Meteorology 1977, 18: 475 – 485 Velden P van Zomerklimaat vleestomaat: planten met goede conditie leveren topprestaties. Tuinderij 1990, 70(13): 14 – 17 Nederhoff E M; de Koning A N M; Rijsdijk A A Leaf deformation and fruit production of glasshouse grown tomato (Lycopersicon esculentum L.) as affected by CO2, plant density and pruning. Journal of Horticultural Science 1992, 67: 411 – 420 Enoch H Z Carbon dioxide uptake efficiency in relation to crop intercepted radiation. Acta Horticulturae 1984, 162: 137 – 147 Zipori I; Dayan E; Enoch H Z A comparison of two techniques for CO2 enrichment in greenhouses in regions with high levels of solar radiation. Biotronics 1986 15: 9 – 14

Appendix Estimation of a deferred worth arising from an iny estment of additional photosynthate in y egetatiy e growth If additional photosynthate would give a deferred benefit from an increase to the LAI, then the following gives a mathematical basis for estimating the

magnitude. With an LAI L and an extinction coefficient k , then the fraction of incident light intercepted by a canopy would be approximated by 1 2 exp (2kL)

(A1)

Assuming proportionality, an incremental relative ind Pi crease in the photosynthesis on day i , , will Pi increase the LAI produced on that day by the same ratio. If the duration of leaf life is τ 1 days, then the relative increment to the total plant LAI due to an increment in one day’s photosynthesis is

d L d Pi 1 < L Pi τ 1

(A2)

The resultant relative increment in light absorbed during the remaining period of the leaf’s action, t1 (equal to τ 1 except after stopping the crop) will be given by

dL d(1 2 exp (2kL)) dL 1 2 exp (2kL) <

k exp (2kL) d Pi L 1 2 exp (2kL) Pi τ 1

(A3)

Thus, for any day j within the next t1 days after day i , allowance should be made for the net profit arising kLj exp (2kLj ) 1 from an additional proportion of 1 2 exp (2kLj ) τ 1 the predicted photosynthate on day j where Lj is the anticipated crop LAI on day j. Thus, if Ii and Ij are the expected radiation values for days i and j , and if photosynthesis is roughly proportional to radiation kLj exp (2kLj ) 1 Ij intercepted, then fractions of the 1 2 exp (2kLj ) τ 1 Ii anticipated worth for every day j within the subsequent period t1 should be added to that for day i. The extra credit reduces as the anticipated LAI increases.