m = transmission coefficient of leaves (0.15). K = canopy extinction .... house is only valid as an average value over long time-spans. In the present model, the ...
Scientia Horticulturae, 23 (1984) 2 1 7 - - 2 2 9
217
Elsevier Science Publishers B.V., A m s t e r d a m - - Printed in The Netherlands
A SIMULATION STUDY ON CO: C O N C E N T R A T I O N IN PROTECTED CULTIVATION
A.H.C.M. S C H A P E N D O N K and P. G A A S T R A
Centre for Agrobiological Research, P.O. Box 14, 6700 AA Wageningen (The Netherlands) (Accepted for publication 27 January 1984)
ABSTRACT S c h a p e n d o n k , A.H.C.M. and Gaastra, P., 1984. A simulation study on CO 2 c o n c e n t r a t i o n in p r o t e c t e d cultivation. Scientia Hortic., 23: 217--229. In p r o t e c t e d cultivation in The Netherlands, it is c o m m o n practice that CO 2 enrichm e n t is supplied by the heating system. The i m p r o v e m e n t s in glasshouse insulation achieved during the last decade decreased b o t h the air exchange of the glasshouse and the heat deraand. During periods o f low heat d e m a n d and high irradiance~ the cumulative effect is a decrease of the CO~ c o n c e n t r a t i o n considerably below ambient. Moreover, even with open ventilators, certain climatological conditions m a y cause a marked decrease of the CO 2 level in the glasshouse. This paper presents some physiological aspects of the problem. With emphasis on the CO 2-concentration level, estimates of the p r o d u c t i o n of a typical glasshouse crop were made, as related to climate control in early spring. E c o n o m i c aspects of additional CO 2 supply (independent of the heat demand) are presented. Keywords: CO 2 depletion; glasshouse; photosynthesis; simulation model.
INTRODUCTION
Optimization of glasshouse climate-control requires an economical evaluation of different control algorithms. Fluctuations in the magnitude of various environmental factors require an adaptable method of control, b u t the effect of instantaneous control action can only be estimated at the time of harvest. In recent optimization studies (Challa and van de Vooren, 1980, Seginer, 1980)~ it has been shown that glasshouse temperature-control can be achieved b y continuously maximizing the difference between the rate of expect~.~d production and the rate of fuel consumption~ both expressed on a financial basis. However, any interaction between factors that determine the climate in the glasshouse will increase the complexity of the climate control. Therefore, it is important to have the possibility of controlling climatic factors (temperature, humidity, CO2, etc.) independently of one another. In The Netherlands, CO2 in glasshouses is usually produced b y the com-
0304-4238/84/$03.00
© 1984 Elsevier Science Publishers B.V.
218 bustion of natural gas in the heating system, and so the heating demands of the glasshouse and the CO2 concentration are linked. There is an inverse relationship between these factors, because at high irradiance the heating load is low and the CO2 demand is high, while in winter conditions, there will be an excess of CO2. In early spring, high irradiance may give rise to CO2 concentrations that are well below the ambient concentration of about 340 pl 1-1 (340 v.p.m.). A decrease of the heating-load coefficient b y insulation of the glasshouse will extend the period that heating during the day is unnecessary. This, in turn, may lead to a further depletion of CO2 during days with a relatively high irradiance, when crop photosynthesis is very much dependent on the CO2 concentration. This study presents a simulation of CO2 levels in a glasshouse as a function o f crop photosynthesis, heating load and ventilation. The consequences for crop production, based on short-term measurements of photosynthesis, are given for a period from 10 March to 7 April 1982. Data on outside and inside irradiance, outside and Inside temperature and windspeed were recorded every minute with a computerized data acquisition system. Simulation runs were made for a minimum temperature set-point of 18°C and a ventilation set-point of 28°C. MATHEMATICAL ANALYSES The CO2 concentration in a glasshouse is the composite result of 3 processes: CO2 supply from the heating system, canopy photosynthesis and ventilation through the glasshouse cover and ventilators. These fluxes of CO2, never leading to a steady-state condition, can be simulated dynamically. In the present model, an integrating step of 10 min was used. This may lead to a small deviation from the actual dynamic properties of the system. However, the responsiveness of the glasshouse including the canopy is rather slow. This justifies the use of rather large time-steps. Canopy photosynthesis. -- Light response curves for canopy gross-photosynthesis were obtained from the equations presented by Acock et al. (1978). rC ~ l K I o + ( 1 - m) rC Pc = In K a l K I o e x p ( - K L ) + (1 - m) rC
ax Pc r I0 m K C L
= = = = = = = =
leaf light-use efficiency gross photosynthesis leaf conductance to CO2 transfer light intensity at t o p of the canopy transmission coefficient of leaves canopy extinction coefficient CO2 concentration (external) leaf area index
(1) (mg CO2 j - l ) (mg CO2 m-2s -1) (m s -1) (W m -2 (PAR)) (0.15) (0.52) (mg m -3) (L -- 3 in the present study)
219
The quantum efficiency of carboxylation is dependent on the CO2 concentration that competes with oxygen for binding on the ribulose biphosphate--carboxylase--oxygenase enzyme. The leaf light-use efficiency (~,) should be a function of internal CO2 concentration, because the quantum efficiency is dependent on the concentration at the carboxylation site. Because photosynthesis, quantum efficiency and internal CO2 concentration are implicit functions, the problem cannot be solved analytically. As a simplification, it may be argued that the light-use efficiency is defined as the initial slope of the relationship between net photosynthesis and irradiance. At very low irradiance, the difference between intercellular and external CO2 will be negligible. By approximation, the relationship for internal CO2 concentration and quantum efficiency (Peisker and Apel, 1981) will be valid for external CO2. a,
C/1.8=
7
a
C/1.8 + '~67
(2)
= maximum quantum yield at zero 02 concentration or at high CO2 concentration. A value of 0.014 mg CO2 J-' for the empirical lightuse efficiency has commonly been found for most C3 and C4 plants (Goudriaan, 1982). 1~6 = ratio of the amount of NADPH delivered by photorespiration and consumed by CO2 fixation, 6 = 4 in the present study (Peisker and Apel, 1981). 7 = CO2 compensation point in the absence of dark respiration at normal partial pressure of 02 (210 m bar.). In the present study 7 = 44 v.p.m. ~i = the actual light-use efficiency (mg CO2 J-'). From eqn. (2), it can be calculated that a, is 0.0097 at a CO: concentration of 340 v.p.m., which is in accordance with experimental results of Acock et al., (1978) for a tomato crop. One of the shortcomings of eqn. (1) is the apparent unlimited increase of the maximum rate of carboxylation (rC) with increasing carbon concentration. For the present purpose, however, this is of minor importance, because the CO:. concentration range studied lies between 80 and 1000 v.p.m. Variations in r have been suggested to be proportional to the averaged light flux density (S) at the leaf surface during a certain period in the past. The relationship proposed by Acock et al. (1978) gives aS r =
(I + bS)
(3)
a = 8.5.10 -s m3 j-1 b = 2.1.10 -2 j-1 m2s Over that total leaf area, S (and concurrently r) will decrease with depth in the canopy because the light flux density incident on the leaf in the canopy is approximated by the relationship proposed by Saeki (1960).
220 SoK
S - - - exp(-gL) ( 1 - m) So
(4)
= averaged light flux density (W m -2) incident at the top of the canopy during one week prior to the day of measurement.
Substituting eqns. (2), (3) and (4) into eqn. (1) and integrating over the entire leaf area of the canopy, according to Acock et al. (1978), results in Pc =
aC bK
In
b(~l loSo K + (1 - m) (cLl Io + aSoC } bo~lIoSoK e x p ( - K L ) + (1 - m) (cLiIo + a S o C }
(5)
Pc = gross photosynthesis (mg CO2 s-l). Dark respiration, a process coupled with oxidative phosphorylation and actually occurring both in the dark and the light, can be subdivided into growth respiration and oxidative processes that are not related to growth; maintenance respiration and idle respiration. Growth respiration is tightly coupled with the absolute assimilation rate. The assimilated sugar is converted into structural dry weight. The a m o u n t of energy needed for conversion processes can be derived from the chemical composition of the dry weight accretion, according to Penning de Vries (1975). In our case, calculations for cucumber plants and fruits revealed that 0.247 g CO2 is formed due to sugar combustion for the formation of 1 g structural dry weight. The chemical composition of the dry weight accretion of various organs was derived from Challa (1976). The carbon content of the structural dry weight is about 0.354 g g-l, which is equivalent to the uptake of 1.298 g CO2. The efficiency is therefore 1.298 1.298 + 0.247
= 0.84
In the light period, the short-term efficiency will be higher because some of the assimilates are converted into structural dry weight during the dark period. According to respiration measurements on cucumber fruits, growth activity is equally distributed over light and dark period (Schapendonk and Challa, 1980). This would mean that the efficiency for a 12-h light period would be 0.92. However, as pointed out by Ho and Thornley (1978), the efficiency o f sucrose transport from the source leaf to the sink is approximately 0.82. In analogy with earlier reasoning for the distribution of growth over the light and dark periods (12 h/12 h), transport efficiency during the light period will be 0.91. The total efficiency for structural dry matter formation in a 12-h light period is therefore about 0.84. Maintenance respiration was estimated from experiments on dark-grown cucumber fruits. Growth was inhibited because import of assimilates was blocked (Schapendonk and Challa, 1980). Maintenance respiration per g dry weight was converted to maintenance respiration per unit protein. The protein content of various plant organs was known, and hence the maintenance respiration coefficient was calculated.
221
B = 2.08 • 10 -7 s -1 CO: The net photosynthesis rate can n o w be presented as Ps
=
W PN
0.84 ( P c - B W)
(6)
= dry weight of the crop (280 g m -2 in the present study), = net photosynthesis (mg COs s -1 m-2).
Figure 1 shows the light-response curves of the net photosynthesis rate of a canopy with a leaf area index of 3 for different CO2 concentrations. g m'2hour q CO 2 4.7 F
ppm
42 3.7
:550
3.2
/
2.7!-
/
2.2p
/
/
/[C02J
/
~....-.--[C 0.,]: 250
:350
1.7
Ico2H5o
1.2 0.7 0.2 ~ ~ . _ - - - - - - - - - _ _ . 1 _ _ _ 1 .20-----40 -0.3
80
100
120
140
[C02]:50
160 180 200 W m -2 PAR
-0.8~
Fig. 1. N e t p h o t o s y n t h e s i s
r a t e o f a t o m a t o c r o p w i t h a l e a f a r e a r a t i o o f 3. S i m u l a t i o n runs weze made for different CO 2 concentrations.
C 0 2 s u p p l y . - - Representing the heating demand per unit of floor area as a function of the temperature difference between indoors and outdoors will give a straight line with a slope that depends on windspeed only (Bot, 1981). Q" = A K ( T i - T o ) - - c R s
(7)
Ti and To are inside and outside temperatures (°C). The minimum temperature setpoint in this case study was 18°C. Rs = solar irradiance (W m-2). Q"
= :heat demand per unit floor area (W m-S),
K A
= :heating load coefficient (W m -2 K-l), = the normalised area of outside cover (= 1.2 for a Venlo-type green:house),
222 c Rs
= a constant representing the additional heat gained as a result of itradiance (= 0.33 for Dutch weather conditions), = global radiation measured outside (W m-2).
According to estimates of Schockert and von Zabeltitz (1980), K can be written as K = (6.1 + 0.25 u) u = windspeed (m s-'). The assumption that 1/3 of the incoming radiation is heating the glasshouse is only valid as an average value over long time-spans. In the present model, the incoming radiation is filtered to account for the slow responsiveness of the glasshouse. The digital smoothing filtering assumes a reaction constant of 0.5 h which may, although n o t fully, justify the assumption made. The heat demand can be converted to the a m o u n t of natural gas that has to be burned by Q" G a = Q" 3.89 • 10 -~ rn 3 m -2 s -1 (8) 35.7 • 106 E where G a = gas consumption, E = a boiler efficiency of about 0.72, and 35.7 • 106 represents the combustion value of one normal m 3 of natural gas. Ventilation. - - Extensive studies of ventilation rates as a function of percentage ventilator opening and windspeed revealed the following relationship for a normal Venlo-type glasshouse (Bot, 1983):
Ve
= 5 . 6 8 " 10 - s ( R + l )
e x p ( - 8 . 4 2 " 10 - 3 ( R + I ) ) u
R Ve u
= % ventilator opening, = ventilation = windspeed
(m 3m -2s-I),
(9)
(m3m-2s-1), (m s-l).
In the present study, ventilation was controlled so that a setpoint temperature of 28°C was not exceeded. This was achieved by calculating the inside temperature based on the heat capacity of the glasshouse air, the components of the building and the incoming radiation. If the ventilator setpoint was reached, an amount of air was ventilated (Vt) sufficient to maintain the ventilation setpoint temperature. Ve in eqn. (9) was only used to calculate the ventilation with closed ventilators, i.e. R = 0.
__QP? Vt = Vt Cp t
( T i - T0) Cpt
(10)
= extra ventilation (m 3 m -2 s-') = heat capacity of air and :greenhouse components {2580 J m -3 K - ' )
223 RESULTS AND DISCUSSION
All results presented in this section are obtained from a case study with a minimum temperature of 18°C and a ventilation temperature of 28°C. Analysis of a particular day (Fig. 2b, c) shows that the CO2 concentration drops below 330 v.p.m, soon after the heating system is turned off. The CO2 concentration remains low during a significant part of the day until the evening, when the heating is switched on. At high irradiance (Fig. 3), the CO2 concentration decreases rapidly at sunset and remains below the ambient concentration even though, at mid-day, the open ventilators cause an air exchange of 48 m 3 per unit of ground surface (Fig. 3d). Over the total period :investigated, CO2 depletion, averaged over 29 days, could be seen during 52% of the total light-period. This was confirmed experimentally by measurements in glasshouses (Hey and Schapendonk, 1983). Therefore, it is to be expected that in normal practice, CO2 depletion may result in considerable losses of production. This is illustrated by Figs. 2a and 3a for a dull
1000 Ico2] pp~
°/o Ps/Pr
120 100
- - - - ~ ~ /
80
800
C[
600
60 4O0
40
2OO
20 O.
,
[
9
,
,
11
,
,
13
,
15
,
,
17 gas
PAR W m -2 300
,
~
1 h
m 3 h a ' l h "1
250 200
'~
100
vent rate 50
,
11
,
,
13
,
,
15
,
,
,
17
5
~
:
'~'
9
4
30:, • ~2°]40~° I d /'
.
80
60 20
20
13
15
17
0
100" ,
19 h
7
3
",
-.:,.
:
11
,
19 h
windsp ms "1 6
m3m'2h -I
r~
,f 7
,
,:'-~ loo
", 150
0
,
9
40 C
50
% ,
11
13
2
i', ,,", .
/'"'""[,"'"~'%^J , I "+,V'-. 9
"
15
~'I'J I0 17
19 h
Fig. 2. (a) R a t i o o f the p h o t o s y n t h e t i c rates at s i m u l a t e d CO 2 c o n c e n t r a t i o n s . Ps is calculated for the s i t u a t i o n that CO 2 is o n l y supplied by the heating s y s t e m or b y ventilation, but no a d d i t i o n a l CO 2 is supplied t o prevent o c c a s i o n a l depletion. Pr is calculated for the s i t u a t i o n that additional CO 2 is supplied to reach a m i n i m u m CO 2 c o n c e n t r a t i o n o f 340 v.p.m. (b) S i m u l a t e d CO 2 c o n c e n t r a t i o n in the g r e e n h o u s e w h e n CO 2 is o n l y supplied from the heating system. (c) T i m e - c o u r s e o f P A R during daylight (solid line), and heat d e m a n d ( b r o k e n line). (d) Windspeed.
224
and bright day, respectively. A comparison is made between the net photosynthesis rates for two conditions: (1) CO2 is only supplied when the heating system is working or, in case of CO2 depletion, by normal air exchange (Ps); (2) additional CO2 is supplied when the CO2 concentration drops below 340 v.p.m. (Pr). The ratio Ps/Pr, plotted as a percentage, shows the calculated losses due to a decrease of CO2 below 340 v.p.m.
8oo
°/o Ps/er 120
[C02] ppm 1000
100 80
--
600 6O 400 4O 200
2o 0
,
i 9
I
11
i
13
I 15
I 17
,
I 19 h
gas rn3ha'lh 4 140
PAR W rn "2 300 250
~
I
9
I
11
i
I
13
J
I
I
15
17
v e n t . r a t e m3m'2h 4 50
120
C
I
40
/
19 h
windsp rns
-1
6
d
',
5
IO0 200 80
30
60
20
'
150 100
2
4O
50 0
,",. 3
2O i
9
11
13
15
17
190 h
10
O7
' :'/i%
11
13
15
17
)h
Fig. 3. (a) Ratio of the p h o t o s y n t h e t i c rates at simulated CO 2 concentrations. Ps is calculated for the situation that CO 2 is o n l y supplied by the heating system or by ventilation, but no additional CO 2 is supplied to prevent occasional depletion. Pr is calculated for the situation that additional CO 2 is supplied to reach a m i n i m u m CO 2 concentration of 3 4 0 v.p.m. ( b ) Simulated CO s concentration in the glasshouse w h e n CO s is only supplied from the heating system. (c) Time-course of P A R during daylight (solid line), and heat d e m a n d (broken line). (d) Windspeed (broken line), and ventilation rate (solid line).
As a consequence of the linkage between heating and CO2 availability high CO2 concentrations coincide with low light conditions (< 130 J cm -2 day -1) because in that case, the outside temperature will generally be low and the greenhouse air is not heated by irradiance. In fact, this occurred for 5 days when the heating system supplied an excess of CO2. In that case, the CO~ concentration will not fall below 340 v.p.m, and Ps and Pr are equal (Fig. 4). However, the Ps/Pr ratio, integrated over the total period of 29 days, showed a relative loss of 15% in CO2 assimilation when no additional CO2 was dosed.
225 The Ps/Pr ratio only considers short-term effects of COs and light intensit y on n e t photosynthesis. It should be emphasized t h a t plant responses to CO2-concentration with respect to p r o d u c t i o n of harvestable material result from reactions with different time-constants, integrated over longer timeperiods. This may lead to less p r o n o u n c e d effects than those predicted by short-term shifts in net photosynthesis. F o r the m o m e n t , this consideration c an n o t be validated quantitatively. Therefore, the net photosynthesis m ay only be taken as a rough estimation of expectations for economic profit. g m - 2 d a y -1 C O 2 20
xx x
0
0o 0
0 0
15 XX X X 0
x
x
0
X XX xOx
x
0
0
000
0
lO
o
0 o
0 OK
O
O
