3. Microclimate evaluation with manipulated set points

#### 3.1. Optimality degrees of microclimate

esculentum); however, with slight modification, the framework can be reprogrammed to work with other greenhouse crops provided that their yield prediction and growth response models are available. Results of microclimate evaluation and set-point manipulation discussed in Sections 3 and 4 can contribute to dynamic greenhouse climate control strategies [18] such as the one in Ref. [19]. An example is provided by comparing a model reference-adaptive greenhouse microclimate controller with conventional closed-loop feedback shown in Figure 4. In this scheme, the control law is adapted with the new greenhouse states based on the optimized set points as shown in the diagram of Figure 5 [19] for a specific microclimate

172 Plant Engineering

Figure 5. Adaptive control of greenhouse air temperature based on manipulated set point as discussed in Ref. [19].

Figure 4. Demonstration of conventional greenhouse controller (left) versus model reference adaptive controller (right).

Optimality degree of a microclimate parameter denoted by Optð Þ¼ M α is a quantitative value between 0 and 1 that represents how close a microclimate measurement (T, RH, or VPD) is to its ideal value as required by the greenhouse crop at specific growth stage and climate condition. This value can be computed from experimental models that correlate different levels of microclimate parameters with yield and quality of the greenhouse crop. An example of such models is the one developed for air temperature and relative humidity by the Ohio Agricultural Research and Development Center [20, 21]. These models define optimality degrees of T, RH for greenhouse cultivation of tomato with independent trapezoid membership-function growth response plots that are specific for different growth stages and three light conditions (night, sun, and cloud). These plots were originated using utility theory with the goal of simultaneously achieving high-yield and high-quality fruit. The knowledge behind these plots was condensed from extensive scientific literature and peer-reviewed published research on greenhouse tomato production and physiology. Mathematical expressions and plots of membership functions for defining optimality degrees of T and RH are available in Ref. [22]. The sets of membership functions for defining optimality degrees of VPD are presented in the work of Ref. [23]. According to this model, a membership function for specific growth stage and light condition on the universe of discourse is defined as Optð Þ <sup>M</sup> GS, ð Þ Light : <sup>M</sup> ! ½ � <sup>0</sup>, <sup>1</sup> , where M : T, RH, and VPD is the universe of discourse (input). In other words, each M reading in the greenhouse at time tm,n, is mapped to a value between 0 and 1 that quantifies its optimality for tomato production. The two indexes m and n refer to specific minute and date of a measurement. In this model, an optimality degree equal to 1 refers to a potential yield with marketable value high-quality fruit. For example, Opt Tð Þ¼ 1 is associated with T ∈ ½ � 24, 27 � C at the vegetative to mature fruiting growth stage during sun hours. For the same growth stage and light condition, a wider reference border, that is, T ∈½ � 18:4, 32:2 � C, is associated with a lower range of optimality degrees, Opt Tð Þ ∈½ � 0:6, 1 . In other words, a greenhouse air temperature equal to 32:2� C during sun hours is 60% optimal for tomato production in the vegetative to mature fruiting growth stage. The reference values corresponding to the optimal, marginal, and failure T and RH are summarized in Table 1. These values for VPD depend on the range of T and RH and are discussed in Ref. [23]. The optimality-degree model was implemented in the framework as a toolbox and was successfully used in evaluating microclimate parameters. Results of an actual case study on a net-screen-covered greenhouse in tropical lowlands of Malaysia are provided in Figures 6 and 7 [22].

#### 3.2. Comfort ratio of microclimate

Comfort ratio of a microclimate parameter, denoted by Cf tð Þ M,t,α<sup>s</sup> GS ¼ β, is defined as the percentage of M data collected during time frame t that falls inside reference borders of M


Indices are: L: lower border, H: higher border, N: night, C: cloud, S: sun, α0: index of failure, α<sup>0</sup>:5: index of Opt¼0.5, α1: index of Opt¼1.

Table 1. Reference values of optimal and failure T and RH at different growth stages and light conditions.

Figure 6. Plots of daily averaged air temperature, RH, and associated optimality degrees from a tropical greenhouse experiment (Source: [22]).

Adaptive Management Framework for Evaluating and Adjusting Microclimate Parameters in Tropical Greenhouse… http://dx.doi.org/10.5772/intechopen.69972 175

Temperature Relative humidity

T1<sup>α</sup>1<sup>H</sup> 26.1

Early growth (GS1) T1<sup>α</sup>0<sup>L</sup> 9 Early growth (GS1) RH1<sup>α</sup>0<sup>L</sup> 60

T2<sup>α</sup>1H,N 20 Flowering to termination

Indices are: L: lower border, H: higher border, N: night, C: cloud, S: sun, α0: index of failure, α<sup>0</sup>:5: index of Opt¼0.5, α1:

Figure 6. Plots of daily averaged air temperature, RH, and associated optimality degrees from a tropical greenhouse

Table 1. Reference values of optimal and failure T and RH at different growth stages and light conditions.

Value (�C) Growth stage Reference

T1<sup>α</sup>0<sup>H</sup> 35 RH1<sup>α</sup>1<sup>L</sup> 75 T1<sup>α</sup>1<sup>L</sup> 24 RH1<sup>α</sup>1<sup>H</sup> 99

T2<sup>α</sup>0<sup>L</sup> 10 Vegetative (GS2) RH2<sup>α</sup>0<sup>L</sup> 40 T2<sup>α</sup>0<sup>H</sup> 40 RH2<sup>α</sup>0<sup>H</sup> 99 T2<sup>α</sup>0:5N 17 RH2<sup>α</sup>1<sup>L</sup> 70 T2α1L,<sup>N</sup> 18 RH2<sup>α</sup>1<sup>H</sup> 80

(GS3-5) <sup>T</sup>2α1L,<sup>S</sup> <sup>24</sup> RH3<sup>α</sup>0<sup>L</sup> <sup>30</sup> T2<sup>α</sup>1H,S 27 RH3<sup>α</sup>0<sup>H</sup> 99 T2<sup>α</sup>1L,C 22 RH3<sup>α</sup>1<sup>L</sup> 60 T2<sup>α</sup>1H,C 24 RH3<sup>α</sup>1<sup>H</sup> 80

border

Value (%)

border

Growth stage Reference

Vegetative to termination

(GS2-5)

174 Plant Engineering

index of Opt¼1.

experiment (Source: [22]).

Figure 7. Demonstration of real-time measured air temperature and RH (left) and corresponding optimality degrees (right) for a random cultivation day at the flowering to mature fruiting growth stage (date: March 11, 2015) in a tropical greenhouse. Each color represents a light condition, back: night, red: sun, blue: cloud (Source: [22]).

associated with α<sup>s</sup> at a specific growth stage. A 100% ideal microclimate growth condition is therefore defined as Cf tð Þ¼ M, t, 1 1. The notation α<sup>s</sup> refers to user-preferred optimality degree for adjusting the reference borders that is desired for microclimate evaluation or control. The reference borders for a given α<sup>s</sup> are calculated from available simulation models (i.e., from the membership function growth response models of [21, 23]). For the purpose of this chapter, mathematical descriptions of Ref. [21] model for defining reference borders of air temperature and relative humidity are adapted and provided in Table 2. An example is demonstrated in Figure 8 for constructing reference borders of air temperature associated with α<sup>s</sup> ¼ 0:8 at the vegetative to mature fruiting growth stage. The procedure is similar for other microclimate parameters (RH and VPD) at other growth stages and for any selection of 0 ≤ α<sup>s</sup> ≤ 1. The framework algorithm automatically selects proper membership functions from database according to the light condition and growth stage and computes the reference borders for the given αs. The light condition in this demonstration belongs to a random day, date: December 15, 2013. The reference borders corresponding to α<sup>s</sup> ¼ 0, α<sup>s</sup> ¼ 0:8 and α<sup>s</sup> ¼ 1 are shown in red, blue, and green colors, respectively. The framework plots data inside each reference border in different colors (black for α<sup>s</sup> ¼ 0, blue for a preferred αs, and green for α<sup>s</sup> ¼ 1). If a measurement lies outside marginal reference borders (α<sup>s</sup> ¼ 0), it will be plotted in red.

The main purpose of introducing comfort ratio and corresponding graphical demonstration is to address deviation of microclimate responses with respect to different reference borders and to compare it for different cultivation days or greenhouse designs. A practical example is provided in Figure 9 for air temperature collected from a naturally ventilated greenhouse in two random days, one at the early growth and the other at the mature fruiting stage. The reference borders associated with a preferred optimality degree (i.e., α<sup>s</sup> ¼ 0:7) are shown in blue color-dashed lines. Moreover, the reference borders corresponding to failure air


Table 2. Membership function model for adjusting reference borders of air temperature and RH.

temperature (α<sup>s</sup> ¼ 0) and optimum air temperature (α<sup>s</sup> ¼ 1) are, respectively, shown in redand green-dashed lines. In this example, the percentage of data that falls inside these three reference borders (α<sup>s</sup> ¼ 0, 0.7 and 1) are 100, 92 and 41% for the early growth stage, and 100, 73, and 3% for the mature fruiting stage. These values are expressed on the plots of Figure 9 as Cf t Tð Þ , 24,0 GS<sup>1</sup> ¼ 1, Cf t Tð Þ , 24,0:7 GS<sup>1</sup> ¼ 0:92, Cf t Tð Þ ,24,1 GS<sup>1</sup> ¼ 0:41, Cf t Tð Þ ,24, 0 GS<sup>5</sup> ¼ 1, Cf t Tð Þ ,24, 0:7 GS<sup>5</sup> ¼ 0:73, and Cf t Tð Þ ,24,1 GS<sup>5</sup> ¼ 0:03. In other words, Cf t Tð Þ , 24,0:7 GS<sup>1</sup> ¼ 0:92 and Cf t Tð Þ , 24,0:7 GS<sup>5</sup> ¼ 0:73 imply that for nearly 22 h (92% of the entire 24 h) of the random day at the early growth, and for 17.5 h (73% of the entire 24 h) of the random day at the mature fruiting stage, the climate controller (for this example, natural ventilation) provided the greenhouse with air temperature that was at least 70% optimal for tomato cultivation. Moreover, Cf t Tð Þ ,24, 1 GS<sup>1</sup> ¼ 0:41 implies that at the early growth stage, the greenhouse was controlled

Adaptive Management Framework for Evaluating and Adjusting Microclimate Parameters in Tropical Greenhouse… http://dx.doi.org/10.5772/intechopen.69972 177

Figure 8. Demonstration of adjusting reference borders with light condition and a preferred optimality degree of α ¼ 0:8 for air temperature control and evaluation in a random day at the flowering to mature fruiting growth stage.

with 100% optimal air temperature for a total of 9.6 h (41% of the total 24 h, shown by green color between hours of 00:00–11:00 on the left plot of Figure 9). For the random day at the mature fruiting stage, it can be seen that only 3% of the air temperature response is inside α<sup>s</sup> ¼ 1 reference borders (around hour 8:00 to 8:30 am).

temperature (α<sup>s</sup> ¼ 0) and optimum air temperature (α<sup>s</sup> ¼ 1) are, respectively, shown in redand green-dashed lines. In this example, the percentage of data that falls inside these three reference borders (α<sup>s</sup> ¼ 0, 0.7 and 1) are 100, 92 and 41% for the early growth stage, and 100, 73, and 3% for the mature fruiting stage. These values are expressed on the plots of Figure 9 as Cf t Tð Þ , 24,0 GS<sup>1</sup> ¼ 1, Cf t Tð Þ , 24,0:7 GS<sup>1</sup> ¼ 0:92, Cf t Tð Þ ,24,1 GS<sup>1</sup> ¼ 0:41, Cf t Tð Þ ,24, 0 GS<sup>5</sup> ¼ 1, Cf t Tð Þ ,24, 0:7 GS<sup>5</sup> ¼ 0:73, and Cf t Tð Þ ,24,1 GS<sup>5</sup> ¼ 0:03. In other words, Cf t Tð Þ , 24,0:7 GS<sup>1</sup> ¼ 0:92 and Cf t Tð Þ , 24,0:7 GS<sup>5</sup> ¼ 0:73 imply that for nearly 22 h (92% of the entire 24 h) of the random day at the early growth, and for 17.5 h (73% of the entire 24 h) of the random day at the mature fruiting stage, the climate controller (for this example, natural ventilation) provided the greenhouse with air temperature that was at least 70% optimal for tomato cultivation. Moreover, Cf t Tð Þ ,24, 1 GS<sup>1</sup> ¼ 0:41 implies that at the early growth stage, the greenhouse was controlled

Reference function Preferred optimality

½T1<sup>α</sup>1L, T1<sup>α</sup>1<sup>H</sup>� α ¼ 1

½T2α1L,S, T2α1H,S� α ¼ 1

½T2<sup>α</sup>1L,C, T2<sup>α</sup>1H,C� α ¼ 1

RH1<sup>α</sup>0<sup>L</sup> α ¼ 0 αðRH1<sup>α</sup>1<sup>L</sup> � RH1<sup>α</sup>0<sup>L</sup>Þ þ RH1<sup>α</sup>0<sup>L</sup> 0 < α < 1 RH1<sup>α</sup>1<sup>H</sup> α ¼ 1

½RH2<sup>α</sup>1L, RH2<sup>α</sup>1<sup>H</sup>� α ¼ 1

½RH3<sup>α</sup>1L, RH3<sup>α</sup>1<sup>H</sup>� α ¼ 1

Table 2. Membership function model for adjusting reference borders of air temperature and RH.

<sup>V</sup> RH2<sup>α</sup>0<sup>H</sup> <sup>α</sup> <sup>¼</sup> <sup>0</sup>

<sup>V</sup> RH3<sup>α</sup>0<sup>H</sup> <sup>α</sup> <sup>¼</sup> <sup>0</sup>

<sup>V</sup> <sup>T</sup>1<sup>α</sup>0<sup>H</sup> <sup>α</sup> <sup>¼</sup> <sup>0</sup>

<sup>V</sup> <sup>T</sup>2<sup>α</sup>0<sup>H</sup> <sup>α</sup> <sup>¼</sup> <sup>0</sup>

<sup>V</sup> <sup>T</sup>2<sup>α</sup>0<sup>H</sup> <sup>α</sup> <sup>¼</sup> <sup>0</sup>

<sup>V</sup> <sup>T</sup>2<sup>α</sup>0<sup>H</sup> <sup>α</sup> <sup>¼</sup> <sup>0</sup> 2αðT2<sup>α</sup>0:5N � T2<sup>α</sup>0<sup>L</sup>Þ þ T2<sup>α</sup>0<sup>L</sup> 0 < α < 0:5 T2<sup>α</sup>0:5N α ¼ 0:5 2αðT2α1L,<sup>N</sup> � T2<sup>α</sup>0:5NÞ þ T2<sup>α</sup>0:5N � ðT2α1L,<sup>N</sup> � T2<sup>α</sup>0:5NÞ 0:5 < α < 1 ½T2α1L,N, T2<sup>α</sup>1H,N� α ¼ 1 αðT2<sup>α</sup>1H,N � T2<sup>α</sup>0<sup>H</sup>Þ þ T2<sup>α</sup>0<sup>H</sup> 0 < α < 1

<sup>V</sup> <sup>α</sup>ðT1<sup>α</sup>1<sup>H</sup> � <sup>T</sup>1<sup>α</sup>0<sup>H</sup>Þ þ <sup>T</sup>1<sup>α</sup>0<sup>H</sup> <sup>0</sup> <sup>&</sup>lt; <sup>α</sup> <sup>&</sup>lt; <sup>1</sup>

<sup>V</sup> <sup>α</sup>ðT2α1H,<sup>S</sup> � <sup>T</sup>2<sup>α</sup>0<sup>H</sup>Þ þ <sup>T</sup>2<sup>α</sup>0<sup>H</sup> <sup>0</sup> <sup>&</sup>lt; <sup>α</sup> <sup>&</sup>lt; <sup>1</sup>

<sup>V</sup> <sup>α</sup>ðT2<sup>α</sup>1H,C � <sup>T</sup>2<sup>α</sup>0<sup>H</sup>Þ þ <sup>T</sup>2<sup>α</sup>0<sup>H</sup> <sup>0</sup> <sup>&</sup>lt; <sup>α</sup> <sup>&</sup>lt; <sup>1</sup>

<sup>V</sup> <sup>α</sup>ðRH2<sup>α</sup>1<sup>H</sup> � RH2<sup>α</sup>0<sup>H</sup>Þ þ RH2<sup>α</sup>0<sup>H</sup> <sup>0</sup> <sup>&</sup>lt; <sup>α</sup> <sup>&</sup>lt; <sup>1</sup>

<sup>V</sup> <sup>α</sup>ðRH3<sup>α</sup>1<sup>H</sup> � RH3G0,maxÞ þ RH3<sup>α</sup>0<sup>H</sup> <sup>0</sup> <sup>&</sup>lt; <sup>α</sup> <sup>&</sup>lt; <sup>1</sup>

TðαÞG1<sup>A</sup> ¼

176 Plant Engineering

TðαÞG2<sup>S</sup> ¼

TðαÞG2<sup>C</sup> ¼

TðαÞG2<sup>N</sup> ¼

RHðαÞG1<sup>A</sup> ¼

RHðαÞG2<sup>A</sup> ¼

RHðαÞG3<sup>A</sup> ¼

8 >>< >>:

8 >>< >>:

8 >>< >>:

> 8 >>>>>>>>>><

> >>>>>>>>>>:

8 >>< >>:

8 >>< >>:

8 >>< >>:

RH2<sup>α</sup>0<sup>L</sup>

RH3<sup>α</sup>0<sup>L</sup>

αðRH2<sup>α</sup>1<sup>L</sup> � RH2<sup>α</sup>0<sup>L</sup>Þ þ RH2<sup>α</sup>0<sup>L</sup>

αðRH3<sup>α</sup>1<sup>L</sup> � RH3<sup>α</sup>0<sup>L</sup>Þ þ RH3<sup>α</sup>0<sup>L</sup>

T1<sup>α</sup>0<sup>L</sup>

T2<sup>α</sup>0<sup>L</sup>

T2<sup>α</sup>0<sup>L</sup>

T2<sup>α</sup>0<sup>L</sup>

αðT1<sup>α</sup>1<sup>L</sup> � T1<sup>α</sup>0<sup>L</sup>Þ þ T1<sup>α</sup>0<sup>L</sup>

αðT2α1L,<sup>S</sup> � T2<sup>α</sup>0<sup>L</sup>Þ þ T2<sup>α</sup>0<sup>L</sup>

αðT2<sup>α</sup>1L,C � T2<sup>α</sup>0<sup>L</sup>Þ þ T2<sup>α</sup>0<sup>L</sup>

The discussion for comfort ratio is extended to compare VPD response in three different greenhouses for a random data collection day during the flowering growth stage (GS3). The greenhouses had different covering materials and climate control system (labeled by A, B, and C in Figure 10, respectively, covered with net-screen mesh, polyethylene film, and polycarbonate panels). The preferred reference border for this evaluation is α<sup>s</sup> ¼ 0:6 (blue-color borders). It can be observed that VPD response never crossed α ¼ 0 or the failure reference borders in greenhouses A and C. This can be expressed by saying that Cf t VPD ð Þ , 24,0 GS<sup>3</sup> was never less

Figure 9. Demonstration of air temperature response and corresponding comfort ratios for two random days of experiment at the early growth (left) and mature fruiting stage (right) in a tropical greenhouse.

Figure 10. A comparison between comfort ratio of VPD at reference borders of α ¼ 0, α ¼ 0:6, and α ¼ 1 in three different greenhouses. Date of data collection March 18, 2013.

than 1 in greenhouses A and C. It should be mentioned that these two greenhouses were, respectively, operating on natural ventilation and evaporative cooling system during the experiment. According to the plots of the three greenhouses in Figure 10, no significant difference can be observed in their VPD responses between 0.1 and 1.2 kPa (corresponding to air temperature between 20 and 30�C, and RH between 80 and 100%); however, as air temperature starts rising above 30�C, differences in the environments start growing nonlinearly. The hourly averaged values of microclimate parameters for this experiment reveal that the major differences between these greenhouses occur between hours of 11:30 am to 4:00 pm. The mean VPD value for greenhouses B and C was equal to 2.9 and 1.19 kPa, respectively, which are less desirable for plant growth compared with the 0.97-kPa value observed from greenhouse A. This observation indicates that as long as the outside temperature is less than 30�C, no major differences between the three greenhouses resulted. This example indicates that for this particular day of experiment, the net-screen-covered greenhouse operating on natural ventilation had a comfort ratio equal to 1 at α<sup>s</sup> ¼ 0:6, which is slightly higher than Cf t Tð Þ , 24,0:6 GS<sup>5</sup> ¼ 0:95 of the polycarbonate panel greenhouse with evaporative cooling system. It should be noted that greenhouse C was constructed with more expensive materials, including polycarbonate panels to reduce direct sun radiation, and was operating on evaporative cooling system with large fans that consume substantial amount of electricity. This example clearly shows the potential of natural ventilation in providing more desirable response for tomato cultivation under tropical climate conditions.

#### 3.3. Simulation of expected yield

than 1 in greenhouses A and C. It should be mentioned that these two greenhouses were, respectively, operating on natural ventilation and evaporative cooling system during the experiment. According to the plots of the three greenhouses in Figure 10, no significant difference can be observed in their VPD responses between 0.1 and 1.2 kPa (corresponding to air temperature between 20 and 30�C, and RH between 80 and 100%); however, as air temperature starts rising above 30�C, differences in the environments start growing nonlinearly. The hourly averaged values of microclimate parameters for this experiment reveal that the major differences between these greenhouses occur between hours of 11:30 am to 4:00 pm. The mean VPD value for greenhouses B and C was equal to 2.9 and 1.19 kPa, respectively, which are less desirable for plant growth compared with the 0.97-kPa value observed from greenhouse A.

Figure 10. A comparison between comfort ratio of VPD at reference borders of α ¼ 0, α ¼ 0:6, and α ¼ 1 in three

Figure 9. Demonstration of air temperature response and corresponding comfort ratios for two random days of experi-

ment at the early growth (left) and mature fruiting stage (right) in a tropical greenhouse.

different greenhouses. Date of data collection March 18, 2013.

178 Plant Engineering

A peer-reviewed published state-variable tomato growth model, developed by Ref. [24] in Microsoft Excel spreadsheets, was studied and implemented in MATLAB Simulink (shown by Simulink blocks in Figures 11–13). The objective was to provide a standalone application in a way that end users unfamiliar with programming languages and/or crop modeling would have an easier access to yield prediction in different greenhouse environments. Data from spreadsheet version of the model were used for testing the Simulink blocks and validation of the results [25]. The five state variables included in the tomato growth model of Ref. [24] were node number (N), leaf area index (LAI), total plant weight (W) or biomass, total fruit weight (WF), and mature fruit weight (WM). Vegetative node development is calculated on an hourly time step using greenhouse temperature (T). The state-variable equation for the rate of node development (dN=dt) is expressed by dN=dt ¼ Nm:f <sup>N</sup>ð Þ T , where Nm is the maximum rate of node appearance per day and f <sup>N</sup>ð Þ T , is a function to reduce node development under nonoptimal temperatures on an hourly basis. Based on studies of tomato phenology, Nm was established to be 0.02083 nodes:d�<sup>1</sup> in the model, and the function, f <sup>N</sup>ð Þ T , is f <sup>N</sup>ð Þ¼ T min 1ð Þ , min 0ð Þ :25 þ 0:025T, 2:5 � 0:05T , where T is the hourly greenhouse temperature in �C. Gross hourly photosynthesis (Ph) was calculated as a function of hourly temperature, incoming solar radiation, and LAI using Eq. (1) developed by Ref. [26]. The Simulink blocks for hourly node development and hourly photosynthesis are shown in Figure 11. Here, D is a coefficient to convert Ph from <sup>μ</sup>mol CO ð Þ<sup>2</sup> <sup>m</sup>�<sup>2</sup>: <sup>s</sup>�<sup>1</sup> to g CH ð Þ <sup>2</sup><sup>O</sup> <sup>m</sup>�<sup>2</sup>: <sup>d</sup>�<sup>1</sup> , K is the light extinction coefficient, m is the leaf light transmission coefficient, LFmax is the maximum leaf photosynthetic rate, Qeð Þ T is the leaf quantum efficiency and a function of temperature, PPFD is the photosynthetic photon flux density or the level of incoming solar radiation, and PGRED Tð Þ is a function to modify Ph under suboptimal temperatures. Based on previous work with tomato growth models [24], D, K, m, and LFmax were set to 0.108, 0.58, 0.1, and 26, respectively. The function for Qeð Þ T can be expressed by Qeð Þ¼ <sup>T</sup> <sup>0</sup>:<sup>084</sup> : <sup>1</sup> � <sup>0</sup>:143 exp 0ð Þ :0295:ð Þ <sup>T</sup> � <sup>23</sup> .

The function for PGRED Tð Þ was disregarded for this model because environmental conditions inside a greenhouse will not fluctuate significantly enough such that this function would have an effect on tomato growth simulations. Temperature and incoming solar radiation information necessary for computation of Ph were obtained from hourly measured data in

Figure 11. Simulink blocks for hourly node development and hourly photosynthesis.

the greenhouses under study, and LAI was obtained using a feedback loop in the model. Gross daily photosynthesis (Pg) was found by integrating over the 24-hourly photosynthesis calculations during each day. Hourly maintenance respiration (Rh) was computed as Rh <sup>¼</sup> rm:Qð Þ <sup>T</sup>�<sup>20</sup> <sup>=</sup><sup>10</sup> <sup>10</sup> , where rm and Q<sup>10</sup> are maintenance respiration coefficients for tomato with values of 0.019 and 1.4, respectively. Daily maintenance respiration (Rm) was computed by integrating over the 24-hourly respiration calculations during the day. Vegetative node development was the only state variable computed on an hourly time step. The remaining state variables were calculated on a daily time step. The state-variable equation for computing LAI was derived from the work of [27, 28]. This state-variable equation is expressed by Eq. (2), where ρ is the plant density, λð Þ Td is a function to reduce the rate of leaf area expansion for nonoptimal temperatures, and δ, β, and Nb are coefficients in the expolinear growth equation developed by Ref. [27]. For this work, the values for ρ, δ, β, and Nb were 3.12 plants m�2, 0.038 m�<sup>2</sup> node�1, 0.169 node�1, and

Adaptive Management Framework for Evaluating and Adjusting Microclimate Parameters in Tropical Greenhouse… http://dx.doi.org/10.5772/intechopen.69972 181

Figure 12. Simulink blocks for daily biomass accumulation and senescence.

the greenhouses under study, and LAI was obtained using a feedback loop in the model. Gross daily photosynthesis (Pg) was found by integrating over the 24-hourly photosynthesis calculations during each day. Hourly maintenance respiration (Rh) was computed as

Figure 11. Simulink blocks for hourly node development and hourly photosynthesis.

values of 0.019 and 1.4, respectively. Daily maintenance respiration (Rm) was computed by integrating over the 24-hourly respiration calculations during the day. Vegetative node development was the only state variable computed on an hourly time step. The remaining state variables were calculated on a daily time step. The state-variable equation for computing LAI was derived from the work of [27, 28]. This state-variable equation is expressed by Eq. (2), where ρ is the plant density, λð Þ Td is a function to reduce the rate of leaf area expansion for nonoptimal temperatures, and δ, β, and Nb are coefficients in the expolinear growth equation developed by Ref. [27]. For this work, the values for ρ, δ, β, and Nb were 3.12 plants m�2, 0.038 m�<sup>2</sup> node�1, 0.169 node�1, and

<sup>10</sup> , where rm and Q<sup>10</sup> are maintenance respiration coefficients for tomato with

Rh <sup>¼</sup> rm:Qð Þ <sup>T</sup>�<sup>20</sup> <sup>=</sup><sup>10</sup>

180 Plant Engineering

16 nodes, respectively. The function, λð Þ Td , was not necessary for this model because temperatures within a greenhouse will not fluctuate enough for this function to significantly affect leaf area expansion simulations. The value for N is the node count at the end of the previous day, and dN=dt is the change in node count during the current day. The model assumes that when LAI reaches LAImax, any additional leaf growth will be either pruned or senesced to maintain LAI at a constant value for the remainder of the growing period. For this work, the value of LAImax was set to 4 as recommended by Ref. [24]. The state-variable equation for computing the accumulation of aboveground biomass (W) is based on the equation for daily plant growth (GRnet), that is, GRnet ¼ E: Pg � Rmð Þ W � WM : <sup>1</sup> � <sup>f</sup> <sup>R</sup>ð Þ <sup>N</sup> . Here, (<sup>W</sup> � WM) is the difference between the total aboveground biomass and the total mature fruit, and this difference represents the growing and respiring plant mass. This difference is multiplied by the daily respiration rate (Rm) to get the amount of carbon necessary for plant maintenance. Subtracting this value from the total carbon assimilated during the day (Pg) gives the total carbon available for plant growth. The coefficient, E, represents the efficiency at converting photosynthate to crop biomass, and this value was set to 0.75 in this work. The function, f <sup>R</sup>ð Þ N , determines the proportion of carbon that is partitioned to roots as a function of the number of nodes, and it can be expressed as f <sup>R</sup>ð Þ¼ N max 0ð Þ :02, 0:18 � 0:0032:N . The function allows a relatively large portion of carbon to

Figure 13. Simulink blocks for daily mature fruit weight and daily fruit growth.

be allocated to roots when the plant is young, and this portion tapers off to 0.02 as the plant matures. The state-variable equation for computing the accumulation of aboveground biomass (W) is dW=dt ¼ GRnet � p1:ρ:dN=dt, where p<sup>1</sup> is the dry matter weight of leaves removed per day due either to senescence or to pruning after LAImax is achieved. For this work, the value of p<sup>1</sup> was 0 g:node�<sup>1</sup> before LAImax was reached and 2 g:node�<sup>1</sup> after LAImax was reached. The state-variable equation to calculate the total fruit weight (WF) is expressed by Eq. (3). Simulink blocks for daily biomass accumulation and senescence are shown in Figure 12.

Here, α<sup>F</sup> is the maximum partitioning of new growth to fruit, f <sup>F</sup>ð Þ Td is a function to modify partitioning to fruit according to the average daily temperature (Td), ϑ is the transition coefficient between vegetative and full fruit growth, NFF is the nodes per plant when the first fruit appears, and g Tdaytime is a function to reduce fruit growth due to high daytime temperature. For this work, αF, ϑ, and NFF were 0.95 d�<sup>1</sup> , 0.2 node�1, and 10 nodes, respectively. The function f <sup>F</sup>ð Þ Td is expressed as f <sup>F</sup>ð Þ¼ Td max 0ð Þ , min 1ð Þ , 0:0625:ð Þ Td � Tmin , where Tmin is the minimum temperature below which no fruit growth occurs. The function g Tdaytime is expressed by Eq. (4) where Tdaytime is the average temperature during daylight hours and Tcrit is the temperature above which fruit abortion begins. For tomato, Tmin and Tcrit are 8.5 and 24.4�C, respectively. The state-variable equation to calculate the total weight of mature fruit or the total tomato yield is expressed by Eq. (5) where DFð Þ Td is a function for the rate of fruit development according to the average daily temperature, and κ<sup>F</sup> is the development time from first fruit to first ripe fruit. For this work, κ<sup>F</sup> was five nodes, and the function, DFð Þ Td , is expressed as DFð Þ¼ Td 0:04 :max 0ð Þ , min 1ð Þ , 0:0714:ð Þ Td � 9 . Mature fruit is assumed to be harvested from the plants immediately upon ripening, as shown by the subtraction of WM during each time step from net crop growth explained by GRnet equation. Simulink blocks for daily mature fruit weight and daily fruit growth are shown in Figure 13. This description completely explicates the reduced state-variable tomato model implemented in Simulink for this project, and the state-variable equations for LAI, total biomass accumulation (dW=dt), total fruit weight (dWF=dt), and mature fruit weight ((dWM=dt)) are highlighted. The implemented model was validated [25] using the Lake City experiment datasets of Ref. [24] to show that the Simulink version of the model is an exact replication of the original spreadsheet version. It was then used in yield prediction from the three greenhouses shown in Figure 10. Results of the prediction are summarized in Figure 14, showing that the net-screen greenhouse operating on natural ventilation (greenhouse labeled A) had the highest yield compared with the polycarbonate panel and polyethylene film greenhouses. This result is completely consistent with results of the optimality degrees and comfort ratios obtained in the previous sections.

Figure 14. Simulated results with TOMGRO model for three experimental greenhouses.

be allocated to roots when the plant is young, and this portion tapers off to 0.02 as the plant matures. The state-variable equation for computing the accumulation of aboveground biomass (W) is dW=dt ¼ GRnet � p1:ρ:dN=dt, where p<sup>1</sup> is the dry matter weight of leaves removed per day due either to senescence or to pruning after LAImax is achieved. For this work, the value of p<sup>1</sup> was 0 g:node�<sup>1</sup> before LAImax was reached and 2 g:node�<sup>1</sup> after LAImax was reached. The state-variable equation to calculate the total fruit weight (WF) is expressed by Eq. (3). Simulink

Here, α<sup>F</sup> is the maximum partitioning of new growth to fruit, f <sup>F</sup>ð Þ Td is a function to modify partitioning to fruit according to the average daily temperature (Td), ϑ is the transition coefficient between vegetative and full fruit growth, NFF is the nodes per plant when the first fruit

f <sup>F</sup>ð Þ Td is expressed as f <sup>F</sup>ð Þ¼ Td max 0ð Þ , min 1ð Þ , 0:0625:ð Þ Td � Tmin , where Tmin is the minimum

is a function to reduce fruit growth due to high daytime temperature.

, 0.2 node�1, and 10 nodes, respectively. The function

blocks for daily biomass accumulation and senescence are shown in Figure 12.

Figure 13. Simulink blocks for daily mature fruit weight and daily fruit growth.

appears, and g Tdaytime

182 Plant Engineering

For this work, αF, ϑ, and NFF were 0.95 d�<sup>1</sup>
