# Precision Nitrogen Fertilizer and Irrigation Management for Apple Cultivation Based on a Multilevel Comprehensive Evaluation Method of Yield, Quality, and Profit Indices

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{−2}and 38.4–42.7 mm, respectively. We recommend using this irrigation and fertilizer management scheme for apple orchards in China’s Loess Plateau.

## 1. Introduction

## 2. Materials and Method

#### 2.1. Experimental Site and Planting Details

#### 2.2. Experimental Design

_{2}O

_{5}, 240 kg·hm

^{−1}) and K fertilizer (K

_{2}O, 180 kg·hm

^{−1}), was initially applied to the roots of the apple trees in each experimental plot before the apple trees broke dormancy. All experimental plots were then irrigated to field capacity. After the apple trees were past the sprouting stage, all irrigation and nitrogen application treatments were initiated. For different irrigation treatments, we used a soil moisture conductivity sensor to obtain the moisture content of the soil to ensure that the soil moisture content was 50%, 70%, and 90% of the field capacity. The actual irrigation period was every 3–6 days for 2021, and on rainy days, no irrigation was applied. Fertilizers were applied using high-frequency drip fertigation. That is, we placed N fertilizer (three-quarters of total nitrogen) and water at the roots of the apple trees through drip irrigation tapes at the beginning of each phenological period (7 April 2021, 7 May 2021, 9 June 2021, 24 August 2021) of the apples.

#### 2.3. Data Measurement

#### 2.3.1. Yield Data

#### 2.3.2. Fruit Shape and Quality Data

^{−1}NaOH were used to measure the organic acids (OA); and total soluble solids (TSS) and sugar-acid ratio (SAR) was measured by a digital PAL-Easy ACID3 tonic system (ATAGO, Tokyo, Japan).

#### 2.3.3. Profit Index Data

^{−1}); Y is the apple fruit yield (kg∙hm

^{−2}), and I is the drip irrigation water applied (mm∙hm

^{−2}).

_{N}) was calculated as follows:

_{N}is the partial factor productivity of applied N (kg∙kg

^{−1}), Y is the apple fruit yield (kg∙hm

^{−2}), and F

_{N}is the amount of nitrogen application (kg∙hm

^{−2}).

#### 2.4. Multilevel Fuzzy Comprehensive Evaluation Method

_{11}is the single fruit weight (SFW), a

_{12}is the fruit number per plant (FNP), a

_{13}is the apple yield (Y), a

_{21}is the fruit shape index (FSI), a

_{22}is the fruit firmness (FF), a

_{31}is the total soluble solids (TSS), a

_{32}is the organic acids (OA), a

_{33}is the soluble sugar content (SSC), a

_{34}is the sugar-acid ratio (SAR), a

_{41}is the irrigation water use efficiency (IWUE), and a

_{42}is the partial factor productivity of applied N (PFP

_{N}).

_{i}) and sub-indicators (v

_{i}) for the nine treatments.

_{ij}) as follows:

_{i}) and obtained the dataset of these weights (l). The consistency ratio (CR) test indicated that the weight of the factors conformed to the subjective judgment of human thinking. When CR < 0.1, the consistency ratio test is rational, so the weight of the factor is effective. First, we calculated the maximum characteristic root (λ

_{max}) and consistency index (I

_{C}) and then used I

_{C}and average random consistency index (IR) to calculate CR. The calculation process for all parameters is as follows:

_{jz}is the actual measured data.

_{ij}is the information entropy of the j-th subfactor of the i-th factor.

_{ij}) of the j-th subfactor is measured as

_{iz}is the fuzzy evaluation index of the i-th indicator set.

## 3. Results

#### 3.1. Effects of Nitrogen and Irrigation on Yield Indicators of Apple

#### 3.2. Effects of Nitrogen and Irrigation on Shape and Quality of Apple Fruit Indicators

#### 3.3. Effects of Nitrogen and Irrigation on the Apple Profit Index

_{N}was not significantly affected by irrigation and nitrogen but was affected by their interactions. A negative feedback effect existed between nitrogen application and PFP

_{N}; that is, PFP

_{N}first increased and then decreased with increasing nitrogen application. However, PFP

_{N}showed an upwards trend with increasing irrigation amount, indicating that irrigation had a positive feedback effect on PFP

_{N}(Table 3). T5 (N2W2) achieved the highest PFP

_{N}among all the treatments. Notably, the PFP

_{N}values of T1, T4, and T7 were nearly indistinguishable due to the low irrigation amount (Figure 6).

#### 3.4. Comprehensive Evaluation of Apple Indicators Based on Multilevel Fuzzy Comprehensive Evaluation

_{N}> IWUE (Table 4). Therefore, apple yield, SAR, PFP

_{N,}and FF mainly affected the comprehensive growth of apples among all sub-indicators (Table 4). The MFCE method can yield a comprehensive evaluation value for all treatments based on the AHP and entropy method (Figure 7). In other words, the amount of nitrogen and irrigation applied in treatment was most favorable for the comprehensive growth of apples when the MFCE value was the highest. Therefore, the amount of nitrogen and irrigation in T5 (N2 W2) were most favorable for the comprehensive growth of apples because this treatment had the highest MFCE value. T1 (N1W1) was most unfavorable for the comprehensive growth of apples. Similarly, excessive amounts of nitrogen and irrigation were not conducive to the comprehensive growth of apples.

#### 3.5. Responses in the Comprehensive Growth of Apples to the Coupling of Nitrogen and Water Based on Multilevel Fuzzy Comprehensive Evaluation

_{1}+ 0.1813x

_{2}− 0.0007x

_{1}

^{2}− 0.0004x

_{2}

^{2}− 0.0001x

_{1}x

_{2}

_{1}is the amount of nitrogen, and x

_{2}is the amount of irrigation. In this model, the coefficient of determination (R

^{2}) of y was calculated as 0.801, and the regression was significant at the 0.01 level (p-value = 0.002).

^{−2}and 38.4–42.7 mm, respectively.

## 4. Discussion

_{N}were clearly and significantly affected by irrigation and nitrogen application, respectively (Table 3). The IWUE of T7 was the highest of all the treatments, but the difference between T5 and T7 was minimal. The PFP

_{N}of T5 also had optimal values. Therefore, nitrogen and irrigation levels that are very high or very low may have adverse effects on the profit index [44,45]. In fact, the quality of apple fruits was affected not only by irrigation and nitrogen but also by the duration of open-air storage after harvest. In addition, the concentration of CO

_{2}in the environment can also significantly affect the quality of apple fruits [46,47].

_{N}had greater impacts on the comprehensive growth of apples. The final results also indicated that the largest MFCE value occurred in T5, which ranked in the top three for yield and quality indicators among all treatments (Figure 7). Subsequently, we evaluated the effect of irrigation and fertilizer coupling on the comprehensive growth of apples. We found that the coupling effect of nitrogen and irrigation significantly promoted the comprehensive growth of apples when irrigation was below a medium level. However, the MFCE value of apples showed a downward trend when irrigation was above a medium level, and the nitrogen application was at a high level (Figure 8). In fact, other studies have shown that excessive amounts of nitrogen application and irrigation can reduce apple yield and quality, respectively [52,53,54]. Therefore, we obtained the optimal amount of nitrogen application and irrigation for apples in the Loess Plateau, and these were obtained based on the comprehensive evaluation of apples. The results of this study may differ from those of others, possibly due to the age and variety of the apple trees or their geographical location. However, the MFCE method systematically and scientifically considers different indicators related to various aspects of apples; thus, the final result is credible.

## 5. Conclusions

^{−2}and 38.4–42.7 mm, respectively.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Meteorological information from the experimental site in Baishui, Shaanxi Province, China. Radiation (grey line), rain (blue line), maximum temperature (red line), and minimum temperature (green line) were recorded daily in 2021.

**Figure 2.**The comprehensive hierarchical evaluation system for apples in Baishui, Shaanxi Province, China. The a1–a4 is yield, the shape of the fruit, the fruit quality indicators, and the profit index, respectively. The a11 is the single fruit weight (SFW), a12 is fruit number per plant (FNP), a13 is the apple yield (Y); a21 is the fruit shape index (FSI), a22 is the fruit firmness (FF); a31 is the total soluble solids (TSS), a32 is the organic acids (OA), a33 is the soluble sugar content (SSC), a34 is the sugar-acid ratio (SAR); a41 is the irrigation water use efficiency (IWUE), and a42 is the partial factor productivity of applied N (PFP

_{N}).

**Figure 3.**Single fruit weight (SFW), fruit number per plant (FNP), and yield (Y) are influenced by irrigation (W1, W2, and W3) and nitrogen (N1, N2, and N3). Error bars indicate the standard error of the mean values (n = 3). The different letters for each data point represent the differences between the treatments based on Duncan’s analysis at p < 0.05. The statistical comparisons between different factors are listed in Table 3.

**Figure 4.**Fruit shape index (FSI) and fruit firmness (FF) as influenced by irrigation (W1, W2, and W3) and nitrogen (N1, N2, and N3). The error bars indicate the standard error of the mean values (n = 3). The different letters for each data point represent the differences between the treatments based on Duncan’s analysis at p < 0.05. The statistical comparisons between different factors are listed in Table 3.

**Figure 5.**Total soluble solids (TSS), organic acids (OA), soluble sugar content (SSC), and sugar-acid ratio (SAR) as influenced by irrigation (W1, W2, and W3) and nitrogen (N1, N2, and N3). The error bars indicate the standard error of the mean values (n = 3). The different letters for each data point represent the differences between the treatments based on Duncan’s analysis at p < 0.05. The statistical comparisons between different factors are listed in Table 3.

**Figure 6.**Irrigation water use efficiency (IWUE) and partial factor productivity of applied N (PFP

_{N}) as influenced by irrigation (W1, W2, and W3) and nitrogen (N1, N2, and N3). The error bars indicate the standard error of the mean values (n = 3). The different letters for each data point represent the differences between the treatments based on Duncan’s analysis at p < 0.05. The statistical comparisons between different factors are listed in Table 3.

**Figure 7.**Multilevel comprehensive fuzzy evaluation value of all treatments of apple in Baishui, Shaanxi province, China.

**Figure 8.**Interactive effects of irrigation and N fertilizer application on the comprehensive growth of apples in Baishui, Shaanxi Province, China. The x, y, and z axes represent the values for irrigation, N fertilization, and standardized comprehensive evaluation based on the multilevel fuzzy comprehensive evaluation method. The depth of the color bar denotes the size of the standardized comprehensive evaluation value.

**Table 1.**Soil nutrient concentrations in the initial soil profile (0–100 cm soil layer at the experimental site at Baishui, Shaanxi province, China).

Layer | pH | SOM | Nitrate−N | Ammonia−N | P_{a} | K_{a} | SBD | PWP | FC |
---|---|---|---|---|---|---|---|---|---|

0−20 cm | 8.22 | 14.40 | 41.74 | 1.59 | 12.00 | 410.68 | 1.44 | 10.4 | 22.39 |

20−40 cm | 8.29 | 11.95 | 27.46 | 1.28 | 4.66 | 502.03 | 1.55 | 10.4 | 24.76 |

40−60 cm | 8.03 | 11.3 | 25.24 | 0.91 | 4.10 | 480.20 | 1.34 | 11.5 | 25.24 |

60−80 cm | 8.14 | 12.1 | 20.4 | 0.86 | 3.85 | 402.35 | 1.50 | 12.8 | 26.30 |

80−100 cm | 8.28 | 11.8 | 18.2 | 0.85 | 3.24 | 380.21 | 1.56 | 14.3 | 26.10 |

^{−1}); nitrate-N is the nitrate nitrogen content of the soil (mg∙kg

^{−1}); ammonia-N is ammonia nitrogen content of the soil (mg∙kg

^{−1}); P

_{a}is available phosphorus content of the soil (mg∙kg

^{−1}); K

_{a}is available potassium content of the soil (mg∙kg

^{−1}); SBD is soil bulk density (g∙cm

^{−3}); PWP is the permanent wilting point (%); FC is the field capacity (%).

**Table 2.**Amounts of irrigation and N fertilizer at the experimental site in Baishui, Shaanxi Province, China.

Treatment | Nitrogen Level | Amount of Nitrogen/kg·hm ^{−2} | Irrigation Level | Amount of Irrigation/mm |
---|---|---|---|---|

T1 | N1 | 160 | W1 (50% Δf) | 18.4 |

T2 | N2 | 180 | 18.4 | |

T3 | N3 | 200 | 18.4 | |

T4 | N1 | 160 | W2(70% Δf) | 36.8 |

T5 | N2 | 180 | 36.8 | |

T6 | N3 | 200 | 36.8 | |

T7 | N1 | 160 | W3(90% Δf) | 64.8 |

T8 | N2 | 180 | 64.8 | |

T9 | N3 | 200 | 64.8 |

**Table 3.**Effect of different levels of nitrogen application (N) and irrigation (W) and their interaction effects (N × W) on different apple indicators in Baishui, Shaanxi Province, China.

Factors | SFW | FNP | Y | FSI | FF | TSS | OA | SSC | SAR | IWUE | PFP_{N} |
---|---|---|---|---|---|---|---|---|---|---|---|

N1 | 145.73 b | 45.00 c | 11,004.57 c | 0.87 | 10.86 a | 13.82 b | 0.41 a | 11.21 b | 28.87 b | 307.54 b | 68.78 c |

N2 | 162.24 a | 54.44 ab | 14,964.26 ab | 0.86 | 10.36 a | 14.26 a | 0.32 b | 12.83 a | 45.82 a | 409.43 ab | 83.13 a |

N3 | 162.60 a | 56.00 a | 15,202.94 a | 0.88 | 9.87 b | 14.57 a | 0.29 c | 12.30 a | 47.21 a | 438.80 a | 76.01 b |

W1 | 135.81 b | 37.67 b | 8488.28 b | 0.87 | 10.68 | 14.79 a | 0.32 b | 12.59 a | 42.02 b | 461.32 a | 46.86 b |

W2 | 166.59 a | 58.44 a | 16,188.54 a | 0.88 | 10.32 | 14.12 b | 0.24 c | 12.38 a | 54.81 a | 439.91 ab | 89.40 a |

W3 | 168.19 a | 59.33 a | 16,494.95 a | 0.86 | 10.09 | 13.73 b | 0.46 a | 11.38 b | 25.09 c | 254.55 c | 91.66 a |

N | * | * | * | ns | * | * | *** | ** | ** | * | *** |

W | * | * | * | ns | ns | * | *** | ** | *** | *** | * |

N × W | * | ns | * | ns | ns | * | *** | *** | ** | * | * |

^{−2}); FSI is the fruit shape index, FF is the fruit firmness (kg∙cm

^{−2}); TSS is the total soluble solids (%), OA is the organic acids (%), SSC is the soluble sugar content (%), SAR is the sugar-acid ratio; IWUE is the irrigation water use efficiency (kg∙mm

^{−1}), PFP

_{N}is the partial factor productivity of applied N (kg∙kg

^{−1}). The letters after values indicate significant differences after ANOVA based on Duncan’s analysis. In addition, * = p < 0.05, ** = p < 0.01, *** = p < 0.001, ns = no significance.

**Table 4.**Subjective weights of factors and objective weights of subfactors based on AHP and entropy method.

Treatment | a1 | a2 | a3 | a4 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

a11 | a12 | a13 | a21 | a22 | a31 | a32 | a33 | a34 | a41 | a42 | |

N1W1 | 0.090 | 0.072 | 0.057 | 0.112 | 0.125 | 0.111 | 0.128 | 0.106 | 0.081 | 0.111 | 0.065 |

N2W1 | 0.098 | 0.074 | 0.064 | 0.110 | 0.114 | 0.111 | 0.107 | 0.111 | 0.102 | 0.125 | 0.065 |

N3W1 | 0.100 | 0.096 | 0.085 | 0.110 | 0.104 | 0.125 | 0.078 | 0.129 | 0.161 | 0.164 | 0.076 |

N1W2 | 0.110 | 0.098 | 0.095 | 0.110 | 0.112 | 0.105 | 0.103 | 0.109 | 0.103 | 0.092 | 0.107 |

N2W2 | 0.127 | 0.140 | 0.156 | 0.112 | 0.110 | 0.120 | 0.064 | 0.129 | 0.199 | 0.151 | 0.156 |

N3W2 | 0.117 | 0.138 | 0.142 | 0.115 | 0.110 | 0.106 | 0.067 | 0.102 | 0.148 | 0.138 | 0.128 |

N1W3 | 0.109 | 0.119 | 0.115 | 0.112 | 0.113 | 0.108 | 0.173 | 0.093 | 0.052 | 0.063 | 0.130 |

N2W3 | 0.120 | 0.136 | 0.143 | 0.107 | 0.109 | 0.103 | 0.145 | 0.112 | 0.075 | 0.079 | 0.144 |

N3W3 | 0.128 | 0.127 | 0.143 | 0.111 | 0.103 | 0.112 | 0.134 | 0.108 | 0.078 | 0.078 | 0.129 |

AHP | 0.324 | 0.125 | 0.304 | 0.247 | |||||||

Entropy | 0.073 | 0.315 | 0.613 | 0.112 | 0.888 | 0.013 | 0.036 | 0.369 | 0.582 | 0.499 | 0.501 |

_{N}). Regarding the AHP method, the consistency ratio index (CR) is 0.027 < 0.1, so subjective weights are reasonable.

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## Share and Cite

**MDPI and ACS Style**

Cai, S.; Zheng, B.; Zhao, Z.; Zheng, Z.; Yang, N.; Zhai, B. Precision Nitrogen Fertilizer and Irrigation Management for Apple Cultivation Based on a Multilevel Comprehensive Evaluation Method of Yield, Quality, and Profit Indices. *Water* **2023**, *15*, 468.
https://doi.org/10.3390/w15030468

**AMA Style**

Cai S, Zheng B, Zhao Z, Zheng Z, Yang N, Zhai B. Precision Nitrogen Fertilizer and Irrigation Management for Apple Cultivation Based on a Multilevel Comprehensive Evaluation Method of Yield, Quality, and Profit Indices. *Water*. 2023; 15(3):468.
https://doi.org/10.3390/w15030468

**Chicago/Turabian Style**

Cai, Shibiao, Bangyu Zheng, Zhiyuan Zhao, Zhaoxia Zheng, Na Yang, and Bingnian Zhai. 2023. "Precision Nitrogen Fertilizer and Irrigation Management for Apple Cultivation Based on a Multilevel Comprehensive Evaluation Method of Yield, Quality, and Profit Indices" *Water* 15, no. 3: 468.
https://doi.org/10.3390/w15030468