Water Demand Pattern and Irrigation Decision-Making Support Model for Drip-Irrigated Tomato Crop in a Solar Greenhouse

Abstract

The knowledge of crop water requirements is critical for agricultural water conservation, especially for accurate irrigation decision making in the greenhouse. Investigating the water demand pattern of the tomato in the solar greenhouse environment and constructing an appropriate irrigation decision-making model are urgently needed to improve irrigation water use efficiency. We designed four irrigation-level treatments: 100% ET₀ (T1), 85% ET₀ (T2), 70% ET₀ (T3), and 55% ET₀ (T4), and conducted a two-vegetation-season tomato planting trial under drip irrigation conditions in a solar greenhouse. The Pearson’s correlation coefficient method analyzed the intrinsic linkage and influence between soil–crop–environment and tomatoes’ water demand patterns. Indicators suitable for irrigation decision making in greenhouse tomatoes were selected, and regression functions were constructed for environmental and crop physiological parameters by combining path analysis and multiple regression methods. Finally, a fusion irrigation decision-making model was constructed by introducing a distance function in the Dempster–Shafer (D–S) theory primary probability assignment (BPA) synthesis algorithm and combining it with a triangular affiliation function. The results showed that: (1) the soil coefficient of variation was shallow > middle > deep, and tomatoes absorbed water mainly in the 0–60 cm soil layer; (2) the crop stem flow rate, net photosynthetic rate, and transpiration rate were positively correlated with irrigation water and had the highest correlation with net radiation, relative humidity, and relative humidity, with correlation coefficients of 0.9441, 0.9441, and 0.7679, respectively; (3) the constructed decision model had a significantly lower value of uncertainty than other methods, while the highest decision value could reach over 0.99, which achieved the best decision accuracy compared to other algorithms.

1. Introduction

The tomato is one of the most popular and appreciated horticultural fruits and has a significant economic value [1]. Consumers accept it well due to its multiple gourmet uses and its richness in bioactive compounds [2]. Therefore, research-oriented, intensive tomato cultivation technology is of great importance. Cultivating the solar greenhouse tomato still uses manual empirical judgments of soil moisture for crude irrigation decisions in many areas [3]. Agricultural information processing is urgently needed to implement precise irrigation to improve water efficiency. Traditional irrigation decision-making methods include crop evapotranspiration-based [4], tensiometer-based [5], and event-based [6] simulated irrigation control. Based on the Soil–Plant–Atmosphere–Continuum (SPAC) theory [7,8], irrigation decision-making indicators could be divided into three categories: soil, crop physiological, and meteorological factors [9,10]. Meteorological and soil moisture parameters could be collected through well-established on-farm weather monitoring stations [11]. Understanding crop water demand patterns and the relationship between crop photosynthetic and meteorological factors is critical. Comparing crop physiological and ecological indicators requires more complex professional instruments [12]. Thus, analyzing crop water requirements and building functional relationships between photosynthetic and meteorological parameters is imperative.

The fuzzy algorithm is a decision-making support algorithm proposed by Professor Zadeh, an American expert in automatic control theory, in 1965. After years of theoretical development, several submodules were established, such as fuzzy-integrated decision making, fuzzy cluster analysis, fuzzy pattern recognition, and fuzzy control [13]. Fuzzy integrated judging is a fuzzy integrated decision-making method, a comprehensive and practical evaluation and determination of a given objective influenced by multiple factors [14,15]. The applications of fuzzy algorithms in the field of agricultural water resources were mainly focused on the design of water-saving irrigation systems [16,17,18], water pollution evaluation [19,20], agricultural land resource evaluation [21,22], and greenhouse environmental control [23,24]. The authors in [15] evaluated the water consumption characteristics and yield of summer maize in different furrow irrigation methods utilizing the fuzzy integrated judgment method, resulting in decent agreement with the results of the field trials. The authors of [25] combined fuzzy control and loss regulation theory to design an intelligent irrigation strategy for cold rice, improving the water use efficiency by 20.5%. Fuzzy algorithms can not only be used to evaluate greenhouse irrigation systems, but can also be combined with greenhouse irrigation theory to develop rational irrigation strategies. It can help build a reasonable irrigation strategy, which has more potential for development in applying agricultural production practices.

In multifactor irrigation decision making, the fuzzy decision algorithm can obtain the degree of support of each decision factor for the irrigation decision, i.e., the basic probability assignment (BPA) matrix [26]. However, the degree of support for irrigation decision making varies among the factors. Sometimes, conflicting or even contradictory decision probabilities can occur. Dempster–Shafer’s (D–S) evidence theory is usually used to synthesize BPA at the decision level to eliminate possible redundancy and contradiction between information. However, D–S evidence theory algorithms often produce conclusions contrary to human intuition in highly conflicting situations [27]. Some studies have measured the similarity between evidence by introducing an inter-evidence distance function to address this problem. Conflict coefficients were used to measure the degree of conflict between evidence, improving decision accuracy by updating the highly conflicting terms in the BPA matrix.

The main objectives were: (1) to investigate the water demand pattern of tomatoes under drip irrigation conditions in a solar greenhouse and clarify the key influencing factors of crop water regulation; (2) to analyze the relationship between environmental meteorology, crop physiological, and ecological indicators, construct a multiple regression function model, and realize the simulation of crop physiological indicators using easily accessible meteorological data; and (3) to propose an improved D–S synthesis BPA algorithm and verify its improvement of the accuracy of multifactor fuzzy decision BPA synthesis.

2. Materials and Methods

2.1. Overview of the Experimental Site

The experiment was carried out in the greenhouse of the National Agricultural Information Technology Research Center’s precision agriculture demonstration base, which is located in Xiaotangshan Town, Changping District, Beijing, China, with longitude 116°34′–117°00′ E, latitude 40°00′–40°21′ N, altitude 36 m. The average annual outdoor temperature is 10–13 °C. The average daily sunshine hours range from 6.5 to 8.5 h. The annual radiation dose is 5413 MJ/m². The multi-year sunshine hours are 2700.3 h. The frost-free period lasts approximately 186–200 days. The annual rainfall average is 602.2 mm. The rainfall from June to August accounts for about 80% of the year. The ground-water depth is 10 m. The experimental area is flat, and the fertility is medium to high, typical in the North China Plain. The greenhouse has a small weather station recording meteorological parameters such as air temperature, air humidity, light, and effective radiation. The length of the experimental solar greenhouse was 30 m, the span was 6.5 m, and the maximum height was 3 m. The basic physicochemical properties of the soil in the greenhouse are shown in

Table 1. Basic physical properties of soil in the greenhouse.

Depth cm	Soil Type	Soil Particle Size Distribution			Volume Weight g/cm3	Field Capacity cm3/cm3	Saturated Water Content cm3/cm3
		Viscous %	Powder %	Sand %
0–20	clay	33.88	30.00	36.12	0.95	0.28	0.56
20–40	clay	45.88	40.00	14.12	1.33	0.27	0.47
40–60	clay	35.88	28.00	36.12	1.36	0.24	0.34
60–80	clay	35.88	52.00	12.12	1.55	0.22	0.20

.

2.2. Experimental Materials

The experimental tomato variety was Cassina. The crop was grown in plastic seedling trays and planted in the corresponding experimental plots in the greenhouse. The seedlings were planted in greenhouse trial plots with 5 to 6 leaves. The main fertilizers were urea and ammonium dihydrogen phosphate. The drip irrigation pipe was an inlaid sheet-type with an inner diameter of 16 mm, a drip head flow rate of 0.95 L/h, a drip head spacing of 30 cm, and a standard water pressure of 0.1 MPa for drip irrigation work.

2.3. Experimental Design

The experiment was conducted at four irrigation levels: T1: 100% ET₀; T2: 85% ET₀; T3: 70% ET₀; and T4: 55% ET₀. The irrigation implementation process was shown in Figure 1, with four replications for each treatment and 16 plots, each plot being a square field of 6 m in length and width and 36 m² in area. The tomatoes were planted in two rows in one tube with a spacing of 40 cm between rows and 40 cm between plants.

The tomatoes were planted in two crops in spring and autumn, from planting on 20 March 2018 to harvesting on 2 July 2018, and planting on 24 August 2018 to harvesting on 3 January 2019. For the excellent growth of seedlings, 50 mm of water was irrigated after planting. The treatments were irrigated at a gradient in the flowering stage with a frequency of 7 d. The cumulative irrigation volumes for the four treatments of T1–T4 in spring crop (from 20 March 2018 to 2 July 2018) were 347.6 mm, 299.8 mm, 245.5 mm, and 227.3 mm, respectively. In the fall crop (from 24 August 2018 to 3 January 2019), the cumulative irrigation amounts for the four treatments T1–T4 were 338.7 mm, 282.4 mm, 241.6 mm, and 226.8 mm, respectively. The total evapotranspiration for seven days was collected from the micro weather monitoring station in the greenhouse, and ET₀ was calculated using the modified Penman–Monteith equation (see Appendix A) for the solar greenhouse in a greenhouse environment [28].

2.4. Main Measurement Items

• Soil water monitoring

One soil water content sensor (WITU-GeoScan) was installed in each treatment and buried in the middle part of the tomato plants in the same monopoly of each treatment. The sensor is characterized by its ability to accurately obtain the average soil moisture content of a nearby 10 cm radius cylinder with an error of less than 1%. Each sensor monitored soil water content at four depths, 0–20 cm, 20–40 cm, 40–60 cm, and 60–80 cm, with a data collection frequency of 1 h.

2.

Chlorophyll index (SPAD) assessment

The values of leaves were measured using a SPAD analysis analyzer (SPAD-502Plus. Konica Minolta Optics Inc. Tokyo, Japan) [29]. During the day, measurements were performed at ten o’clock in the morning. For each treatment, three tomato plants were fixedly selected. Six points were measured for each leaf (avoiding leaf veins), and the average value was taken as the final result.

3.

Measurement of photosynthetic parameters

Photosynthetic parameters were measured using a photosynthesis meter (CIRAS-3). The main parameters were: net photosynthetic rate (NPR), transpiration rate (TR), and intercellular CO₂ concentration of tomato leaves under daylight, and NPR, TR, and intercellular CO₂ concentration of tomato leaves under artificially applied light sources of different light intensities. Each fertility stage was monitored two to three times, according to the fertility stage. The monitoring was carried out in clear weather, from 8:00 a.m. to 6:00 p.m., once every 2 h.

4.

Stem flow rate (SFR)

A stem flow measurement system (Dynamax SGEX with CR1000 data logger) was used to collect data. The collars work according to the heat balance method [30] and are indexed to the stem diameter [31] to determine sap flow. A heating strip (source of the heat pulse) was located between two thermocouples; the temperature difference between the thermocouples could be used to calculate Tc. The stem diameter was approximately 9.5 mm. The sensors were installed at 5 cm from the ground for each plant. Three plants per irrigation gradient treatment were selected for measurement. Equipment recorded data at 15-min intervals from 2 June 2018 to 5 June 2018, and 19 October 2018 to 22 October 2018. The hourly stem flow rate (g/h) was converted by averaging.

5.

Meteorology

Data were collected using a micro weather monitoring station (WSWW) in the middle of the greenhouse, 2 m from the ground. Air temperature (Temp, °C), relative humidity (RH, %), and net radiation (Rs, MJ/(m²/d)) were among the variables that could be measured.

2.5. Irrigation Decision-Making Model Construction

Figure 1 shows the technical route of decision model construction. Based on the soil moisture, crop physiological, and meteorological data collected during two vegetation seasons of tomato cultivation under different moisture gradients, we identified the key factors affecting crop water use using the through-path analysis method. We constructed a proper function with difficult-to-acquire parameters using multiple regression methods. Then, we improved the performance of the fuzzy decision model by introducing the inter-evidence distance function in the D–S evidence theory BPA synthesis method to achieve accurate irrigation decision making.

2.5.1. Fuzzy Decision Theory

Fuzzy set theory is a representation that converts a binary relationship into continuous uncertainty and evaluates it with an affiliation function. The sets in classical theory were well-defined boundaries with only two states, 0 or 1. However, since irrigation decisions were affected by multiple environmental factors and were uncertain in crop irrigation applications, fuzzy sets need to be used for description.

There were many methods to determine the affiliation function [25]. The one-dimensional affiliation functions were triangular, trapezoidal, Gaussian, and bell-type affiliation functions [32]. The fuzzy theoreticals rubricated for crop irrigation contain two states, irrigated and non-irrigated. The triangular affiliation function determined each irrigation decision indicator [18,28]. The triangular affiliation function was of the following form.

$${\mu }_1=\left\{\begin{array}{cc}1,& x\le d_1\\ {\left(\frac{d_2-x}{d_2-d_1}\right)}^2,& d_1<x<d_2\\ 0,& x\ge d_2\end{array}\right.$$

(1)

$${\mu }_2=\left\{\begin{array}{cc}1,& x\le d_1\\ {\left(\frac{x-d_1}{d_2-d_1}\right)}^2,& d_1<x<d_2\\ 0,& x\ge d_2\end{array}\right.$$

(2)

where ${\mu }_1$ denoted the affiliation function under irrigation and ${\mu }_2$ denoted the affiliation function under no-irrigation, $x$ denoted the parameter involved in the decision, and $d_1$ and $d_2$ denoted the lower and upper bounds of the parameter, respectively.

The basic probability distribution function equation was determined using fuzzy theory:

$$\left\{\begin{array}{c}m\left(A_1\right)={\mu }_1\\ m\left(A_2\right)={\mu }_2\\ m\left(\Theta \right)=1-m\left(A_1\right)-m\left(A_2\right)\end{array}\right.$$

(3)

where $m\left(A_1\right)$ denoted the state under irrigation water, $m\left(A_2\right)$ denoted the state under suitable moisture, $\Theta$ denoted the identification frame $\Theta =\left\{\left.A_1, A_2\right\}\right.$, and $m\left(\Theta \right)$ denoted the established identification frame.

2.5.2. Improved D–S Evidence Theory BPA Synthesis Method

In the classical D–S theory of evidence, Dempster’s law of synthesis could be expressed as:

$$\mathrm{m}=\left\{\left[\left(m_1\oplus m_2\right)\oplus m_3\right]\oplus \dots \right\}\oplus m_n$$

(4)

where $m_1,m_2,\dots ,m_n$ were the values of the confidence function on the unified identification framework.

To improve the reliability of the fusion results, we improved the BPA synthesis method of D–S evidence theory by introducing the concept of distance to calculate the weights of each decision factor and realizing the optimization of the synthesis method by updating the factors with high conflict coefficients. The specific synthesis rules were as follows.

Calculate the mean value of the j-th irrigation decision by fusing irrigation factor information ${\overline{m}}_j$:

$${\overline{m}}_j={\displaystyle \sum }_{i=1}^n{m}_{ij}/n$$

(5)

where n was the number of irrigation decision factors.

The method for calculating the average worthwhile distance from each piece of fused irrigation factor information to said irrigation decision was:

$$d_i=e^{-\left|m_{i1}-{\overline{m}}_1\right|}+e^{-\left|m_{i2}-{\overline{m}}_2\right|}+\cdots +e^{-\left|m_{ij}-{\overline{m}}_j\right|},i=1,2,\dots ,n$$

(6)

where $m_{ij}$ denoted the degree of support of the i-th irrigation decision factor for the j-th irrigation decision.

The weight coefficient, ${\omega }_i$, and the average evidence, $\overline{m^{\prime }}$, for each decision factor were calculated as:

$${\omega }_i=\frac{d_i}{{{\displaystyle \sum }}_{i=1}^n{d}_i}$$

(7)

$$\overline{m^{\prime }}={\omega }_i{m}_i$$

(8)

The conflict coefficient, K, was calculated as:

$$K=1-{\displaystyle \sum }_{A_1,A_2,\cdots ,A_n\subset \Theta }{m}_1\left(A_1\right)m_2\left(A_2\right)\cdots m_n\left(A_n\right)$$

(9)

If the conflict coefficient K exceeded the preset value, the conflicting indicators in the identification framework were replaced with $\overline{m^{\prime }}$ to form the improved BPA matrix.

The fusion decision value of the improved BPA matrix was calculated using Dempster’s synthesis rule.

2.6. Data Analysis

Table 2. Statistics of soil moisture, and meteorological and crop physiological parameters for spring and autumn crops.

		Spring Crop					Autumn Crop
Indicator	Unit	Mean	Standard Deviation	Min	Median	Max	Mean	Standard Deviation	Min	Median	Max
Soil moisture (0–20 cm)	%	12.24	4.47	7.30	10.54	23.83	12.66	6.72	7.22	9.27	27.77
Soil moisture (20–40 cm)	%	21.71	3.88	16.40	22.57	31.52	22.08	4.78	15.82	21.42	32.73
Soil moisture (40–60 cm)	%	23.75	4.23	14.11	24.49	32.57	22.29	4.49	16.64	23.02	32.96
Soil moisture (60–80 cm)	%	28.56	1.69	24.68	28.30	32.28	24.51	4.15	17.91	24.18	31.86
Net radiation (Rs)	W/m2	94.57	53.49	9.91	91.07	188.33	59.44	29.87	0.73	52.20	179.83
Air temperature (Temp)	°C	25.22	2.75	17.80	25.79	31.4	17.88	3.74	10.41	17.45	26.18
Vapor pressure deficit (VPD)	KPa	0.91	0.41	0.12	0.91	2.09	0.47	0.31	0.09	0.36	1.46
Relative humidity (RH)	%	72.09	11.71	48.4	72.07	95.70	79.05	9.26	50.79	81.61	94.75
ET0	mm	3.29	1.59	0.46	3.12	6.09	1.90	1.04	0.37	1.55	5.54
Net photosynthetic rate (NPR)	μmol/(m2·s)	12.29	7.86	−2.81	13.12	30.62	11.95	5.48	−2.10	12.35	20.82
Transpiration rate (TR)	mmol/(m2·s)	6.27	1.64	3.50	6.32	10.35	5.62	1.77	3.10	5.42	9.91
Stem flow rate (SFR)	g/h	24.79	39.63	0	0	186.05	18.18	29.56	0	0	134.03

shows the statistical results for the name, units, mean, standard deviation, minimum, median, and maximum values of all the data collected in this study. Overall, the data for all indicators are relatively similar between the spring and autumn cropping seasons for tomatoes. The mean soil moisture content gradually increases with increasing soil depth. Compared to the autumn crop, the mean Rs, Temp, VPD, and ET₀ are higher by 35.13 W/m², 7.34 °C, 0.44 KPa, and 1.39 mm, respectively, for the spring crop. The spring crop has higher mean values for the three indicators NPR, TR, and SFR, with increases of 0.34 μmol/(m²·s), 0.65 mmol/(m²·s), and 6.61 g/h, respectively, compared to the autumn crop.

3. Results and Analysis

3.1. Analysis of Soil Water Content Indicators

Figure 2 and Figure 3 show the average soil moisture content trends at a 0–80 cm depth for different periods of the two crops, respectively. For each treatment, the average soil moisture content in the 0–20 cm layer was 9.03%, 11.72%, 10.23%, and 9.01%; in the 20–40 cm layer, it was 24.32%, 19.89%, 17.43%, and 16.85%; in the 40–60 cm layer, it was 27.49%, 23.23%, 21.35%, and 16.22%; and in the 60–80 cm layer, it was 30.93%, 27.46%, 28.85%, and 28.27%, respectively. The soil water content of each treatment is consistent with irrigation water. The water content variation in the 60–80 cm layer is slight because of the deeper depth. Most can demonstrate that the amount of irrigation in the soil layer of 0–20 cm, 20–40 cm, 40–60 cm, and 60–80 cm between treatments is small and consistent at around 29%. The soil water content of the autumn crop varied in the same way as the spring crop. The yield of the spring crop was 5.42 t/hm², 4.91 t/hm², 4.52 t/hm², and 4.38 t/hm², respectively, and the autumn crop was 2.97 t/hm², 2.78 t/hm², 2.68 t/hm², and 2.44 t/hm², respectively, corresponding to irrigation gradients T1–T4. The yield of the spring crop was overall higher than that of the autumn crop, and the yield decreased with the decrease in total irrigation water.

Table 3. Comparison of variation coefficient of soil moisture content under different treatments.

Crop	Moisture Gradient	Soil Depth				Mean
		0–20 cm	20–40 cm	40–60 cm	60–80 cm
Spring	T1	0.14	0.07	0.09	0.02	0.08
	T2	0.10	0.07	0.06	0.02	0.06
	T3	0.12	0.11	0.10	0.02	0.09
	T4	0.13	0.09	0.08	0.01	0.08
Autumn	T1	0.33	0.12	0.11	0.15	0.18
	T2	0.47	0.17	0.18	0.14	0.24
	T3	0.47	0.19	0.16	0.16	0.25
	T4	0.33	0.19	0.16	0.16	0.21

shows the variation coefficients of the soil water content at different soil depths, with an overall trend of decreasing coefficients of variation as depth increases. A shallow soil water content at the 0–20 cm depth is more influenced by external factors such as temperature, weather, and light. The coefficients of the variation of different treatments are higher than those at other depths. The T4 treatment has the least amount of irrigation and the smallest coefficient of variation of 0.01 at a 60–80 cm depth. In addition, the coefficient of variation of the spring crop treatments T1–T4 was between [0.06, 0.14] at a 0–60 cm depth, which was much higher than the maximum coefficient of variation of 0.02 at a 60–80 cm depth.

3.2. Analysis of Crop Physiological and Ecological Indicators

3.2.1. Effect of Different Irrigation Rates on Tomato Stem Flow Rate

Figure 4 illustrates the changes in the SFR of tomatoes under different moisture treatments in the spring crop. During the growth of tomatoes, the SFR was the maximum at noon and almost zero at night, and the peak SFR differed among the different moisture treatments. The peak SFR was larger and unimodal during sunny days of the spring crop (4 June and 5 June), and the SFR started to appear around 7:00 a.m. The increase in solar radiation intensity and Temp peaked at 179.6 g/h and 186.05 g/h at around 11:00–12:00 a.m. and in the afternoon. As the solar radiation decreased and the temperature in the greenhouse decreased, the SFR gradually decreased and tended to zero around 17:00. On cloudy days (2 June), the SFR of tomato plants followed approximately the same pattern as on sunny days, with lower peaks than on sunny days. It was found that the pattern of SFR changes in the fall crop (Figure 5) was generally consistent with that of the spring crop. The peak size was ranked as T1 > T2 > T3 > T4, indicating a positive correlation between TR and the soil water content status of tomatoes.

3.2.2. Effect of Different Irrigation Water Treatments on Net Photosynthetic and Transpiration Rate of Tomato

The formation of plant yields and fertility are both based on photosynthesis. The measurement of plant photosynthesis is the NPR. The daily variation of photosynthesis in greenhouse tomatoes during the flowering, fruiting, and ripening stages is depicted in Figure 6 at various irrigation levels. The daily interpretation of the NPR for each fertility stage of each treatment was a “single-peaked” curve, and the NPR at the fruiting stage was significantly higher than the other two fertility stages. From 8:00 to 10:00, the NPR of the tomato plants was low. As the sun rose, the intensity of light radiation gradually became more substantial, and the temperature steadily increased. The NPR gradually increased and reached a peak at around noon. At the flowering stage, the maximum difference occurred at noon. The NPR of 100% ET₀ in the T1 treatment with sufficient irrigation reached 17.5 μmol/(m²·s), higher than 55% ET₀ in the T4 treatment by 29.6%. The NPR between treatments was T1 > T2 > T3 > T4 within a single day; the difference between treatments became larger after entering the fruit set stage, and the NPR of the T1 treatment reached 31 μmol/(m²·s) at noon, which was 13.1%, 26.9%, and 36.9% higher than that of T2, T3, and T4 treatments, respectively. Throughout the tomatoes’ reproduction, the pattern of the NPR of plants was fruiting > flowering > ripening, and it decreased with the decrease of the soil water content at both the flowering and fruiting stages.

Figure 7 shows the daily variation of the TR of tomatoes under different irrigation levels. The trends of TR and NPR for tomatoes were consistent. The TR in T1 was higher than in the other three treatments during all-day hours because of the adequate irrigation. At 9:00, the TR of the plants was slow due to the low temperature and high humidity among the treatments. With the increase in temperature and light intensity, the TR accelerated sharply. At about 11:00, it was highest in the T1 treatment, reaching 10.4 mmol/(m²·s). The other three treatments were much more different, with T2, T3, and T4 being 24.0%, 28.5%, and 30.5% higher, respectively. The differences between T2, T3, and T4 were minor between 9:00 and 13:00. After 11:00, the TR of the plants gradually decreased until it reached the lowest at 17:00. The variation characteristics of the transpiration rate during the fruit set period under different moisture treatments were similar to those of the flowering period. The trend of TR showed a “single-peak” curve with a peak at 11:00 a.m. and a gradual decrease after that.

3.3. Analysis of Greenhouse Environmental Indicators

3.3.1. Microclimate Changes in the Solarium during the Tomatoes’ Reproductive Period

Microclimatic conditions in the solar greenhouse are among the most important factors affecting the tomato plants’ growth, development, and water consumption.

Table 4. For each reproductive stage, net radiation, air temperature, vapor pressure deficit, relative humidity, and ET₀.

Crop Seasons	Stage	Data	Net Radiation (Rs, W/m2)	Air Temperature (Temp, °C)	Vapor Pressure Deficit (VPD, KPa)	Relative Humidity (RH, %)	ET0 (mm)
Spring	Flowering period	19 April 2018	101.35	23.2	0.86	68.65	3.44
	Fruiting period	17 May 2018	127.13	24.9	1.22	66.93	4.22
	Ripening period	5 June 2018	68.17	26.7	0.94	77.83	2.55
	Full fertility period	-	94.57	25.2	0.98	72.33	3.29
Autumn	Flowering period	15 September 2018	94.69	22.0	0.88	67.47	3.24
	Fruiting period	11 October 2018	58.53	19.58	0.48	79.41	1.92
	Ripening period	9 November 2018	43.49	15.12	0.28	84.26	1.27
	Full fertility period	-	59.44	17.89	0.47	79.05	1.90

shows the Rs, ET₀, Temp, VPD, and RH in the solar greenhouse during the spring and fall tomato crops. From the whole fertility period, Rs was within [68.17 W/m², 127.13 W/m²] and [43.49 W/m², 94.69 W/m²] for both crops, ET₀ was within [2.55 mm, 4.22 mm] and [1.27 mm, 3.24 mm], respectively, Temp was within [23.2 °C, 26.7 °C] and [15.12 °C, 22.0 °C], VPD within [0.86 KPa, 1.22 KPa] and [0.28 KPa, 0.88 KPa], RH within [66.93%, 77.83%] and [67.47%, 84.26%], respectively, and there was no obvious trend pattern for each index within the same crop. When comparing the two crops, all indicators were significantly higher in spring than autumn, except RH. The spring crop’s RS, Temp, VPD, and ET0 were 59%, 41%, 108%, and 73% higher than the autumn crop.

Figure 8 shows the daily variation of each meteorological indicator during the two crop seasons. From the whole reproductive period, the daily meteorological indicators varied drastically, with Rs within [9.91 W/m², 188.33 W/m²] and [0.73 W/m², 179.83 W/m²], ET₀ within [0.45 mm, 6.08 mm] and [0.36 mm, 5.54 mm], Temp within [17.8 °C, 31.4 °C] and [10.4 °C, 26.2 °C], VPD within [0.20 KPa, 2.09 KPa] and [0.10 KPa, 1.41 KPa], RH within [48.4%, 95.7%] and [50.79%, 94.75%], respectively, and no obvious trend pattern for each index within the same crop.

3.3.2. Relationship between SFR, NPR, TR, and Meteorological Factors

Table 5. Coefficient correlation between stem flow rate, net photosynthetic rate, transpiration rate, and meteorological factors (all correlation results passed a two-tailed significance test at 0.05).

Indicator	Stem Flow Rate (SFR)	Net Photosynthetic Rate (NPR)	Transpiration Rate (TR)
Temp (X1)	0.3399	0.3083	0.3294
VPD (X2)	0.4772	0.3474	0.2173
RH (X3)	−0.4549	0.9140	0.7679
Rs (X4)	0.9441	−0.1516	−0.1024

shows the results of the correlation coefficients between SFR, NPR, TR, and meteorological factors calculated using Pearson’s correlation coefficient method. Temp and VPD positively correlated with all three rates, with correlation coefficients between [0.3083, 0.3399] and [0.2173, 0.4772], respectively. RH showed a negative correlation with SFR, and Rs negatively correlated with NPR and TR. Among all the results, Rs and RH are associated with SFR, NPR, and TR, with correlation coefficients of 0.9441, 0.9441, and 0.7679, respectively.

Table 6. Path analysis between stem flow rate and meteorological factors (net radiation, air temperature, vapor pressure deficit, and relative humidity).

Indicator	Simple Correlation Coefficient with Stem Flow Rate	Direct Path Coefficient	Indirect Path Coefficient			Decision Coefficient
			X2 (Vapor Pressure Deficit)	X3 (Relative Humidity)	X4 (Net Radiation)
X2 (vapor pressure deficit)	0.4772	0.799	-	−0.646	0.324	0.1242
X3 (relative humidity)	−0.4549	0.666	−0.422	-	−0.346	−1.0495
X4 (net radiation)	0.9441	0.913	0.283	−0.253	-	0.8904

,

Table 7. Path analysis between net photosynthetic rate and meteorological factors (net radiation, air temperature, vapor pressure deficit, and relative humidity).

Indicator	Simple Correlation Coefficient with Net Photosynthetic Rate	Direct Path Coefficient	Indirect Path Coefficient		Decision Coefficient
			X2 (Vapor Pressure Deficit)	X3 (Relative Humidity)
X2 (vapor pressure deficit)	0.3474	−0.0531	-	0.4004	−0.0397
X3 (relative humidity)	0.9140	0.9367	−0.0227	-	0.8349

and

Table 8. Path analysis between transpiration rate and meteorological factors (net radiation, air temperature, vapor pressure deficit, and relative humidity).

Indicator	Simple Correlation Coefficient with Transpiration Rate	Direct Path Coefficient	Indirect Path Coefficient		Decision Coefficient
			X2 (Vapor Pressure Deficit)	X3 (Relative Humidity)
X2 (vapor pressure deficit)	0.2173	−0.1311	-	0.3485	−0.0742
X3 (relative humidity)	0.7679	0.8234	−0.0555	-	0.5866

show the results of the path analysis between SFR, NPR, TR, and meteorological factors, respectively, and the unrelated factors were excluded in the stepwise regression process. RH had the most substantial decision power on plant SFR, with a decision coefficient of 0.8904; Rs had the most vital decision power on NPR and TR with decision coefficients of 0.8349 and 0.5866, respectively.

Based on the relationship between SFR, NPR, TR, and the four meteorological factors, the fitted regression equations were as:

$$Y_{SFR}=-115.1+31.128X_2+120.443X_3+0.253X_4$$

(10)

$$Y_{NPR}=1.702-2.321X_2+0.036X_3$$

(11)

$$Y_{TR}=3.325-1.013X_2+0.005X_3$$

(12)

3.4. Construction and Validation of Fuzzy Decision Irrigation Model

Using data on 14 May 2018 and 24 May 2018, model function thresholds were developed using the tomato irrigation indicators’ measured soil water content and SFR, NPR, and TR derived from meteorological data. The affiliation function of each irrigation indicator was determined based on the thresholds. Thus, the probability distribution function was calculated (

Table 9. Membership function values of four irrigation indexes of tomato.

Indicator	Lower Bound (d1)	Upper Bound (d2)	Interval (d2–d1)
Soil water content	16.4163	17.8201	1.4039
Stem flow rate (SFR)	12.7908	48.7600	35.9692
Transpiration rate (TR)	4.4191	6.1302	1.7111
Net photosynthetic rate (NPR)	13.1747	23.5600	10.3853

).

Table 10. Basic probability distribution (BPA) function of each irrigation index of tomato.

Date	Indicator	Needs Irrigation	No Irrigation	Uncertain	Conflict Coefficient (K)
14 May	Soil Moisture	0.8361	0.0073	0.1566	0.7501
	SFR	0.6271	0.0325	0.3404
	TR	0.6328	0.0418	0.3254
	NPR	0.7407	0.0194	0.2399
24 May	Soil Moisture	0.0061	0.8503	0.1436	0.7302
	SFR	0.0423	0.6277	0.3292
	TR	0.0267	0.6997	0.2735
	NPR	0.0241	0.7135	0.2623

shows the BPA of the four irrigation factors calculated from the above-established affiliation functions of the four indicators. The probability distribution functions were used to indicate the degree of support of each irrigation indicator for irrigation decisions and the conflict coefficients of each group of decision indicators, K. The decision trends of each indicator for the three irrigation states were approximately the same. However, the conflict coefficients of both groups of BPA exceeded 0.7, showing a high decision conflict state. The SFR indicator on 14 May and the SFR indicator on 24 May had apparent conflicts with other indicators on the uncertainty decision term.

Table 11. The result of data fusion of basic probability distribution (BPA) in the decision layer.

Date	Algorithm	Need Irrigation	No Irrigation	Uncertain
14 May	Averaging algorithm	0.7092	0.0119	0.2656
	D–S theory of evidence	0.9833	0.0001	0.0166
	Improved D–S algorithm	0.9885	0	0.0115
24 May	Averaging algorithm	0.0248	0.7228	0.25215
	D–S theory of evidence	0.0001	0.9874	0.0125
	Improved D–S algorithm	0	0.9916	0.0084

shows the conflict coefficients of the fuzzy decision BPA for the two experimental days and the fusion decision results obtained using the averaging method, D–S evidence theory, and the improved D–S algorithm. The values of uncertain decision terms of the enhanced D–S algorithm were significantly lower than those of other methods. In contrast, the highest decision value of the improved D–S algorithm could reach more than 0.99, which had higher decision accuracy than different algorithms, and the results of each decision phase were integrated. The decision ability of the three methods was ranked as the improved D–S algorithm > D–S evidence theory > average. In addition, the results of the improved D–S algorithm could clearly show that May 14 was an irrigation day and May 24 was a non-irrigation day, which was consistent with the actual irrigation plan.

4. Discussion and Conclusions

4.1. Discussion

Tomatoes were grown in a solar greenhouse. Data were collected at different irrigation deficit levels. By combining correlation analysis, the long time-series data from the multi-stubbles experiments were used to clarify the influence of the soil–crop–environment on crop water regulation and identify the key influencing factors. The authors of [33] also mentioned that crop SFR, NPR, and TR were vital parameters for crop water uptake. We used a multiple regression method to construct a functional relationship between the environment and the crop to calculate the complex physiological parameters using easily accessible environmental parameters. The irrigation decision method based on soil water content and crop physiological parameters could consider the actual water requirement of the crop, which was consistent with the findings of [27], compared with the irrigation decision method based on ET₀ and water balance [34,35].

The water consumption patterns of crops were related to complex multidimensional conditions, such as variety, environment, and soil, which required fuzzy decision-making methods. The decision model utilized the fuzzy set theory, with the affiliation function instead of the fundamental probability distribution function. Therefore, the selection of the appropriate affiliation function was vital. Fewer limit cases characterize the experimental index under the collection. The trapezoidal and bell-shaped affiliation functions have more interval distributions in the case of $\mu =1$. At the same time, the primary distribution affiliation function calculation is too complicated, both of which are unsuitable for irrigation decision making.

In contrast, the decision state in tomato irrigation was only two states, need irrigation and no irrigation. Therefore, the triangular affiliation function was suitable for irrigation decisions [13]. It had a reference value for irrigation decisions of actual solar greenhouse tomato planting. The improved D–S algorithm presented a better decision-making ability. It may be since the improved BPA matrix obtained by combining the distance function to calculate the weights of each decision factor could reduce the conflict within the matrix, thus solving the problem of the representation and synthesis of uncertain information. In Ref. [27], by combining the fuzzy rough set and D–S theory with the distance function method to calculate the factor weights, better decision accuracy was obtained, which was consistent with the findings of this study.

To better reflect the universal crop water demand law, it is necessary to consider further the potential and direct effects of different greenhouse scales, crop varieties, and planting methods in future research. In addition, with the continuous development of sensor technology, it is possible to continue the investigation into the physiological indicators of the crops themselves, such as the drought resistance genes associated with plants and the sound signals emitted by plants when water stress occurs. With the increasing maturity of artificial intelligence theory, using artificial intelligence models to build intelligent irrigation decision models also has a good prospect for scientific research and application.

4.2. Conclusions

We analyzed the effects of the soil water content on SFR, NPR, and TR under different irrigation level treatments using data from IoT sensing devices and data analysis techniques by irrigating tomatoes under drip irrigation in a solar greenhouse with varying irrigation levels. The intrinsic link between the soil–crop–environment and tomato water demand patterns was explored to form an irrigation decision-making support model integrating greenhouse meteorological information. The following conclusions were obtained.

• The variation of soil water content under different degrees of deficit irrigation and water content in soil layers below 20 cm was proportional to the irrigation water. The soil variation coefficient was shallow > middle > deep, and the tomato absorbed water mainly from 0 to 60 cm in the soil layers. The indicators related to the water deficit in tomatoes included SFR, NPR, and TR. SFR, NPR, and TR were positively correlated with irrigation water under different degrees of water deficit irrigation.
• Pearson’s correlation coefficient method calculated the correlation coefficients between the four meteorological data and SFR, NPR, and TR. The key indicators of irrigation decisions suitable for greenhouse tomatoes were selected.
• We created a multi-data fusion irrigation decision model using fuzzy set theory for soil water content, SFR, NPR, and TR. We then validated the viability of the model for four irrigation decision indicators. Finally, we improved the D–S algorithm to get the best decision accuracy for synthesizing the BPA matrix for fuzzy decisions.