# Analyzing Evapotranspiration in Greenhouses: A Lysimeter-Based Calculation and Evaluation Approach

^{1}

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## Abstract

**:**

_{C}) was compared with lysimeter-measured crop evapotranspiration (ET

_{C}) in the National Precision Agriculture Demonstration Station in Beijing, China. The results showed that the actual ET

_{C}over the entire experimental period was 176.67 mm. The ET

_{C}calculated with the PM, HS, PAN, and ANN model were 146.07 mm, 189.45 mm, 197.03 mm, and 174.7 mm, respectively, which were different from the actual value by −17.32%, 7.23%, 11.52%, and −1.12%, respectively. The order of the calculation accuracy for the four models is as follows: ANN model > PAN model > PM model > HS model. By comprehensively evaluating the statistical indicators of each model, the ANN model was found to have a significantly higher calculation accuracy compared to the other three models. Therefore, the ANN model is recommended for estimating ET

_{C}under greenhouse conditions. The PM and PAN models can also be used after improvement.

## 1. Introduction

_{C}) [4,5,6].

_{O}in plastic greenhouses in Mediterranean climatic conditions, as, in the conditions of Mediterranean plastic greenhouses, the original Penman–Monteith equation clearly underestimated measured ET

_{O}[3].

_{C}calculation models, four models were selected in this article to calculate ET

_{C}in a greenhouse, and these were then compared with actual ET

_{C}values. A detailed description of the methods used in this study is provided in Section 2 of this paper. Firstly, a small-scale lysimeter was installed in the greenhouse for data collection and obtaining ET

_{C}. Additionally, a small meteorological station and an evaporimeter were installed in the experimental area to gather meteorological and water evaporation data within the experimental range. The Penman–Monteith, Hargreaves–Samani, Pan Evaporation, and Artificial Neural Network models were employed in this study to calculate the ET

_{O}. The crop coefficient was determined using empirical coefficients, which were then used to calculate daily crop evapotranspiration. As described in Section 3 and Section 4, the measured data obtained from the field measurement method were compared with the calculated data from the meteorological models, evaporimeter method, and AI model. This comparison allowed for the analysis of the advantages and disadvantages of each calculation method for determining ET

_{C}in a greenhouse. Finally, based on the advantages and disadvantages of each model and the actual equipment conditions of the users, this paper provides recommendations for selecting models when measuring ET

_{C}in a greenhouse.

## 2. Materials and Methods

#### 2.1. Test Overview

#### 2.2. Measurement Items

#### 2.2.1. Crop Evapotranspiration Measurement

#### 2.2.2. Meteorological Environment Measurement

#### 2.3. Model and Evaluation Indicators

#### 2.3.1. Penman–Monteith Model

_{O}calculation model proposed in Technical Report No. 56 by the Food and Agriculture Organization of the United Nations [21]. The PM model takes multiple meteorological factors into account, such as air temperature, humidity, wind speed, and net radiation to estimate ET

_{O}. Compared to the simplified models, the PM model is more accurate in calculating ET

_{O}and is suitable for a wider range of climate conditions and regions [22]. When calculating ET

_{O}, the PM model requires a large amount of meteorological data, including net radiation, soil heat flux, daily average temperature, wind speed, saturated water vapor pressure, and actual water vapor pressure. These data can be obtained through meteorological observation stations or other meteorological data. The calculation formula of the PM model is as follows:

_{O}is reference crop evapotranspiration (mm/d), R

_{n}is net radiation (MJ/m

^{2}/d), G is soil heat flux (MJ/m

^{2}/d), T is air temperature (°C), U is wind speed (m/s), e

_{s}is saturation vapor pressure (kPa), e

_{a}is actual vapor pressure (kPa), Δ is slope of the saturation vapor pressure–temperature relationship (kPa/°C), and γ is psychometric constant (kPa/°C).

#### 2.3.2. Hargreaves–Samani Model

_{O}, and it collects the lowest, highest, and average temperature data of the day; calculates the local net radiation through longitude and latitude; and then estimates the ET

_{O}of the day [23,24]. The HS model assumes a linear relationship between ET

_{O}and surface temperature, and it estimates ET

_{O}based on the daily average temperature. The calculation formula is as follows:

_{O}is reference crop evapotranspiration (mm/d), R

_{a}is daily radiation, T is daily average air temperature (°C), T

_{max}is daily maximum air temperature (°C), and T

_{min}is daily minimum air temperature (°C).

#### 2.3.3. Pan Evaporation Model

_{O}, suitable for use in areas lacking meteorological observation data. When using the Pan Evaporation method, it is important to first select a suitable evaporation pan, typically a shallow flat-bottomed container, and ensure that it can hold an adequate amount of water. The evaporation pan should be placed in the vicinity of the vegetation in the experimental area, such as next to a lawn, soil, or potted plants. Obstruction and interference must be avoided so that the pan evaporation can remain consistently exposed to the natural environment. At the same time, water level reduction in the evaporation pan must be observed daily at regular intervals and the measurement data obtained should be recorded. The formula for calculating ET

_{O}using the Pan Evaporation method is as follows:

_{O}represents reference crop evapotranspiration (mm/d); k

_{p}represents the pan coefficient, with k

_{p}at 0.85 [21]. E represents the amount of water surface reduction in the evaporation pan (mm).

#### 2.3.4. Neural Network Model

_{O}as output data. In the case of using a lysimeter to obtain crop evapotranspiration data, 80% of the data was used for training the model, while the remaining 20% was used for model validation.

#### 2.3.5. ET_{C} Calculation Model

_{C}represents the current crop water requirement; K

_{C}is the crop coefficient, which reflects the ratio of the crop’s water requirement to the reference crop’s water requirement based on standard evapotranspiration (ET

_{O}); and ET

_{O}represents the reference evapotranspiration (mm/d).

_{C}) for different growth stages of tomatoes by the Food and Agriculture Organization (FAO) are as follows: seedling stage K

_{C}was 0.6; anthesis stage K

_{C}was 1.15; mature stage K

_{C}was 0.8.

_{O}). By multiplying these crop coefficients with region-specific reference evapotranspiration data (ET

_{O}), the current crop water requirement (ET

_{C}) for tomatoes can be calculated at each growth stage.

#### 2.3.6. Evaluation Indicators

_{C}sample data obtained using the PM, HS, PAN, and ANN models. This analysis can utilize statistical indicators such as Mean Absolute Error (MAE), Mean Bias Error (MBE), Root Mean Square Error (RMSE), and Index of Agreement (d). By calculating these statistical indicators, we can assess the differences and consistency between the ET

_{C}sample data obtained from different models. These statistical indicators provide an evaluation of model performance and accuracy, helping to optimize and improve the predictive capabilities of the models. The formula for calculating the sample statistical indicators is as follows:

_{i}and Q

_{i}represent the simulated values (mm/day) and measured values (mm/day) of each model method, respectively; O represents the average of the measured values (mm/day); n represents the number of samples.

## 3. Results

#### 3.1. Analysis of the Test Environment

^{2}/d and 9.16 MJ/m

^{2}/d, respectively. During the mature stage, the daily average net radiation was 10.04 MJ/m

^{2}/d. Due to the fact that this experiment was conducted in a solar greenhouse, indoor wind speed can be ignored.

#### 3.2. Analysis of Evapotranspiration Variation

_{C}values obtained through actual measurements using the lysimeter, as well as those predicted by the PM model, HS model, PAN model, and ANN model, with the field data. The cumulative ET

_{C}values of the tomatoes measured using the lysimeter system was 17.84 mm during the seedling stage, 73.74 mm during the anthesis stage, and 85.09 mm during the mature stage. The total ET

_{C}value of tomatoes measured using the lysimeter system was 176.67 mm. The total ET

_{C}value of tomatoes calculated using the PM model was 13.33 mm during the seedling stage, 60.2 mm during the anthesis stage, and 72.54 mm during the mature stage. The total ET

_{C}of tomatoes measured using the PM model was 146.07 mm, and the difference between the total ET

_{C}calculated and the measured value using the lysimeter system was about −17.32%. The cumulative ET

_{C}values of the tomatoes calculated using the HS model were 16.73 mm during the seedling stage, 73.24 mm during the anthesis stage, and 99.48 mm during the mature stage. The total ET

_{C}value of the tomatoes calculated using the HS model was 189.45 mm, with a difference of approximately 7.23% between the total ET

_{C}calculated and the measured value using the lysimeter system. The cumulative ET

_{C}values of the tomatoes calculated using the PAN model were 21.61 mm during the seedling stage, 76.91 mm during the anthesis stage, and 98.51 mm during the mature stage. The total ET

_{C}value of the tomatoes calculated using the PAN model was 197.03 mm, and the difference between the total ET

_{C}calculated and the measured value using the lysimeter system was about 11.52%. The cumulative ET

_{C}values of the tomatoes calculated using the ANN model were 17.72 mm during the seedling stage, 72.93 mm during the anthesis stage, and 84.05 mm during the mature stage. The total ET

_{C}value of the tomatoes calculated using the ANN model was 174.7 mm, and the difference between the total ET

_{C}calculated and the measured value using the lysimeter system was about −1.12%. The cumulative ET

_{C}value of outdoor fields during the seedling stage was 19.87 mm; during the anthesis stage, it was 104.51 mm; during the mature stage, it was 117.42 mm; and the total ET

_{C}value of the tomatoes in open fields was 241.8 mm. The difference between the total ET

_{C}calculated value and the measured value using the lysimeter system was about 36.87%.

_{C}gradually increased from 0.32 to 0.49, with an average K

_{C}of 0.43. During the anthesis stage, the Kc increased from 0.49 to 0.87, with an average K

_{C}of 0.77. During the mature stage, the K

_{C}gradually stabilized, increasing from 0.87 to 1.05, with an average K

_{C}of 1.05. Throughout the entire experimental period, the K

_{C}gradually increased during the seedling and anthesis stages; when the tomatoes reached maturity, it tended to stabilize.

_{C}values in the greenhouse and outside the greenhouse are not significantly different. From the anthesis stages to the mature stage, the ET

_{C}values in the open field gradually surpassed those in the greenhouse. The maximum difference between the total ET

_{C}calculated using the PM model in the greenhouse and the values calculated using the lysimeter system was −30.6 mm, with an error of −17.32% of the total amount. The difference between the total ET

_{C}calculated using the ANN model and the values calculated using the lysimeter system was the smallest, with a difference of −1.97 mm and an error of −1.12% of the total. The difference between the calculated values of the HS model and PAN model and the calculated values of the lysimeter system was relatively small—12.78 mm and 20.36 mm, respectively—with errors reaching 7.23% and 11.52% of the total amount.

#### 3.3. Irrigation Effect Analysis

_{C}calculated using four models—namely, the PM model, HS model, PAN model, and ANN model—using a lysimeter system. Based on preliminary findings, it was noted that the ANN model had the smallest error in calculating the ET

_{C}, while the PM model had the highest error in calculating the ET

_{C}. In Figure 6, a scatter plot was created by using actual ET

_{C}data as the x-axis and the ET

_{C}values calculated using the PM model, HS model, PAN model, and ANN model as the y-axis. Regression analysis was then conducted to analyze the relationship between the model-calculated values and the actual ET

_{C}values.

_{C}values calculated using the PM model were lower than the actual cumulative ET

_{C}values, this deviation could be calibrated using coefficients based on the data model, which provided better simulation results.

_{C}data using the HS model exhibited significant fluctuations compared to the actual cumulative ET

_{C}values. Although the cumulative ET

_{C}values calculated using the HS model were slightly close to the actual values, correlation analysis indicated that the HS model had high variability and relatively low accuracy when used in greenhouse environments. In summary, the HS model showed a relatively low correlation with the actual values, and the calculated cumulative ET

_{C}values exhibited significant fluctuations compared to the real values in greenhouse settings. Although the HS model provided relatively small differences from the actual cumulative ET

_{C}values, its relatively low precision was not suitable for practical usage.

_{C}data calculated using the PAN model tended to be slightly higher than the actual cumulative ET

_{C}values. Overall, the data consistency between the PAN model and the actual values was relatively good, with only small differences in the total cumulative ET

_{C}values. In summary, the PAN model exhibited a high correlation with the actual values, and the calculated cumulative ET

_{C}values were generally consistent with the real values in greenhouse environments. Therefore, the PAN model can be considered as having good accuracy and reliability in predicting evapotranspiration in greenhouse settings.

_{C}values calculated using the PM model, HS model, PAN model, ANN model, and the ET

_{C}values measured using several statistical indicators. These indicators include the coefficient of determination (R

^{2}), mean absolute error (MAE), mean bias error (MBE), root mean square error (RMSE), and index of agreement (d). The statistical results are shown in Table 1 below.

^{2}), the obtained R

^{2}for the HS model was 0.58, while the R

^{2}values calculated for the PM, PAN, and ANN models were 0.91, 0.88, and 0.94, respectively. It is possible to observe that the ET

_{C}data obtained from the HS model calculation were more scattered, indicating the lower reliability of its regression model. From the MAE analysis, it is possible to see that the ANN model obtained the highest accuracy for ET

_{C}, with an MAE of 0.3 mm/d. The PM and PAN models had slightly lower accuracy for ET

_{C}, with MAE values of 0.6 mm/d and 0.54 mm/d, respectively. The HS model had the lowest accuracy for ET

_{C}, with an MAE value of 0.88 mm/d. As for the MBE, it is possible to observe the fact that the ANN model had the highest accuracy for ET

_{C}, with a computed MBE of −0.15 mm/d. The HS model had a uniform distribution around the 1:1 line, resulting in an MBE of 0.19 mm/d. The PAN model had a better MBE than the PM model, with values of 0.3 mm/d and −0.57 mm/d, respectively. From the perspective of RMSE, the ANN model had the smallest calculated RMSE value for ET

_{C}, which was 0.42 mm/d. The HS model, with a uniform distribution around the 1:1 line, had an RMSE of 1.19 mm/d. The PAN model had a better RMSE than the PM model, with values of 0.7 mm/d and 0.8 mm/d, respectively.

_{C}values and the measured ET

_{C}values, with a consistency index (d) of 0.95. The HS model had the lowest consistency between the calculated ET

_{C}values and the measured ET

_{C}values, with a consistency index (d) of 0.73. The PAN model had better consistency than the PM model, with consistency index (d) values of 0.9 and 0.81, respectively, for the two models.

^{2}) and the consistency index (d), the higher the correlation between the model’s calculated values and the actual values. On the other hand, the smaller the values of the mean absolute error (MAE), mean bias error (MBE), and root mean square error (RMSE), the smaller the difference between the model’s calculated values and the actual values. The accuracy of calculating ET

_{C}is as follows: ANN model > PAN model > PM model > HS model (Figure 7).

_{C}calculated with the corresponding model. The daily irrigation volume of each group during the experiment is shown in Figure 8. During the experiment, the PM model, HS model, PAN model, and ANN model were used to irrigate 7.01 m

^{3}, 9.09 m

^{3}, 9.46 m

^{3}, and 8.39 m

^{3}, respectively. At the same time, 258.62 kg, 298.62 kg, 331.68 kg, and 339.38 kg of tomatoes were produced in each experimental area. The water use efficiency of the PM model, HS model, PAN model, and ANN model during the experiment was 36.89 kg/m

^{3}, 32.85 kg/m

^{3}, 35.06 kg/m

^{3}, and 40.45 kg/m

^{3}, respectively. The statistical results of the experiment are shown in Table 2.

^{3}, which was less than the water required for the crops. The yield was only 258.62 kg. The use of the HS model resulted in significant fluctuations in daily irrigation volume due to its low accuracy in calculating ET

_{C}, resulting in the lowest water use efficiency of 32.85 kg/m

^{3}among the experimental groups. The maximum irrigation amount using the PAN model in each experimental group was 9.46 m

^{3}, which was 12.75% higher than the ANN model. However, the crop yield and water use efficiency were lower than the ANN model. By using the ANN model, the irrigation amount was closest to the actual water demand of the crops, and its yield and water use efficiency were the highest among the various experimental groups. In summary, the irrigation experiment results of each model are as follows: ANN model > PAN model > PM model > HS model.

## 4. Discussion

_{C}was calculated assuming no wind speed because this experiment was carried out in a greenhouse, only using temperature, humidity, and net radiation in a comprehensive manner, resulting in a significant difference between the calculated ET

_{C}and the measured values. By conducting statistical analysis on the sample data of the PM model, the MAE and MBE were 0.6 mm/d and −0.57 mm/d, respectively. The RMSE of 0.8 mm/d indicates a significant fluctuation in the data. The d value of 0.81 suggests poor consistency with the measured ET

_{C}values. This indicates that the ET

_{C}values calculated using the PM model are underestimated in comparison to the actual values.

_{C}values and only requires temperature values. Previous research has shown that it performs well in calculating ET

_{C}values in arid and semi-arid regions [23]. This paper applied the HS model to calculate ET

_{C}in a greenhouse. In our experiment, the statistical results showed that the data had a relatively scattered distribution, and the reliability of the regression model was low (R

^{2}= 0.58). The MAE was 0.88 mm/d, and the MBE was 0.19 mm/d, suggesting that the HS model overestimated the ET

_{C}values compared to the actual measurements. It had the highest RMSE value among the four calculation models used, indicating a large dispersion in the HS model’s results and poor predictive correlation overall. The consistency index (d) was 0.73, indicating poor consistency with the actual measured ET

_{C}values. The HS model is better applied in arid areas based on temperature and empirical coefficients, and the ET

_{C}calculated using the HS Method are higher in humid environments such as greenhouses.

_{C}values based on the water evaporation recorded. In theory, the larger the size of the evaporation pan, the more accurate the calculated values are. In reality, the limited size of the evaporation pan definitely results in an overestimation of ET

_{C}. Although the cumulative ET

_{C}values calculated were higher than the actual measurements and the RMSE was 0.7 mm/d, indicating some level of data fluctuation, the statistical analysis of the sample data demonstrated good consistency in the sample data (Table 1). The PAN model demonstrated high data consistency in terms of data correlation, which could improve the accuracy of ET

_{C}estimation. The RMSE was 0.7 mm/d, indicating some level of data fluctuation. The d value of 0.9 implies high consistency with the actual measured ET

_{C}values.

_{C}data as training data for the model. By inputting environmental variables like temperature, humidity, and net radiation from different locations within the greenhouse into the ANN model, ET

_{C}values can be directly calculated. The results also indicated that the R

^{2}value was 0.92, demonstrating a high level of consistency in the regression of the calculated results. Also, the calculated data were more accurate compared to other models, with small data fluctuation. The d value of 0.95 indicates the highest level of consistency with the actual measured values.

## 5. Conclusions

_{C}of greenhouse crops was measured using lysimeter as a reference. Then, based on greenhouse meteorological conditions, four models (the PM model, HS model, PAN model, and ANN model) were used to calculate the ET

_{C}. Finally, by comprehensively evaluating statistical indicators such as R

^{2}, MAE, MBE, RMSE, and d, the accuracy of the ET

_{C}models for greenhouse crop calculations was discovered to be as follows: ANN model > PAN model > PM model > HS model. Although the HS model outperformed the PM model in terms of calculating the ET

_{C}, it had significantly lower accuracy in calculating daily ET

_{C}. Therefore, from a production standpoint, the HS model is not suitable for effectively guiding greenhouse irrigation practices. Additionally, based on statistical data from the PM and PAN models, it is possible to observe that, when applying these models directly to different locations, it is necessary to calibrate the coefficients of the PM and PAN models using standard data. This calibration process can further enhance the accuracy of the model calculations and predictions.

_{C}in a greenhouse. If the user is in a remote rural area with a low automation level in greenhouse production equipment, this article recommends using the PAN model to calculate ET

_{C}. The main advantage of using the PAN model for measurement is that it requires fewer instruments and is relatively convenient to install and maintain compared to other measurement methods.

_{C}is beneficial for maintaining crop growth while effectively avoiding environmental pollution caused by excessive water and fertilizer usage. This current study only compares the differences in ET

_{C}calculation among four models in a greenhouse. In the future, we will further investigate the impact of different irrigation models on crop quality and yield in greenhouses, in order to provide more effective irrigation management advice to users.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Meteorological stations inside the greenhouse and meteorological stations outside the greenhouse, as well as the evaporation pan.

**Figure 4.**The daily variation chart of the greenhouse climate in the experimental area: (

**A**) describes the temperature change curve inside the greenhouse during the experiment; (

**B**) describes the humidity change curve inside the greenhouse during the experiment; (

**C**) describes the change curve of net radiation inside the greenhouse during the experiment.

**Figure 5.**Comparison of ET

_{C}calculated with different models in the greenhouse and in the fields, with measured values. (

**A**) Describes the comparison of daily ET

_{C}calculated using different models. (

**B**) Describes the comparison of cumulative ET

_{C}calculated using different models. (

**C**) Describes changes in K

_{C}during the experiment.

**Figure 6.**Comparison chart of the correlation between four ET

_{C}calculation models and measured values. (

**A**) Describes the comparison between the calculated values obtained using the PM model and the actual values; (

**B**) describes the comparison between the calculated values obtained using the HS model and the actual values; (

**C**) describes the comparison between the calculated values obtained using the PAN model and the actual values; (

**D**) describes the comparison between the calculated values obtained using the ANN model and the actual values.

**Figure 7.**Distribution of statistical indicators for ET

_{C}calculations and data measured using different models.

**Figure 8.**Daily irrigation volume of ET

_{C}calculated based on different models. (

**A**) Describes the daily irrigation amount based on the PM model; (

**B**) Describes the daily irrigation amount based on the HS model; (

**C**) Describes the daily irrigation amount based on the PAN model; (

**D**) Describes the daily irrigation amount based on the ANN model.

Method | R^{2} | MAE mm/d | MBE mm/d | RMSE mm/d | d |
---|---|---|---|---|---|

PM model | 0.91 | 0.6 | −0.57 | 0.8 | 0.81 |

HS model | 0.58 | 0.88 | 0.19 | 1.19 | 0.73 |

PAN model | 0.88 | 0.54 | 0.3 | 0.7 | 0.9 |

ANN model | 0.94 | 0.3 | −0.15 | 0.42 | 0.95 |

Method | Output kg | Total Water Consumption m ^{3} | Water Use Efficiency kg/m ^{3} |
---|---|---|---|

PM model | 258.62 | 7.01 | 36.89 |

HS model | 298.62 | 9.09 | 32.85 |

PAN model | 331.68 | 9.46 | 35.06 |

ANN model | 339.38 | 8.39 | 40.45 |

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**MDPI and ACS Style**

Shi, W.; Zhang, X.; Xue, X.; Feng, F.; Zheng, W.; Chen, L.
Analyzing Evapotranspiration in Greenhouses: A Lysimeter-Based Calculation and Evaluation Approach. *Agronomy* **2023**, *13*, 3059.
https://doi.org/10.3390/agronomy13123059

**AMA Style**

Shi W, Zhang X, Xue X, Feng F, Zheng W, Chen L.
Analyzing Evapotranspiration in Greenhouses: A Lysimeter-Based Calculation and Evaluation Approach. *Agronomy*. 2023; 13(12):3059.
https://doi.org/10.3390/agronomy13123059

**Chicago/Turabian Style**

Shi, Wei, Xin Zhang, Xuzhang Xue, Feng Feng, Wengang Zheng, and Liping Chen.
2023. "Analyzing Evapotranspiration in Greenhouses: A Lysimeter-Based Calculation and Evaluation Approach" *Agronomy* 13, no. 12: 3059.
https://doi.org/10.3390/agronomy13123059