# Laws Governing Nitrogen Loss and Its Numerical Simulation in the Sloping Farmland of the Miyun Reservoir

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

^{2}) of the effective mixing depth model in the numerical simulation of TN loss through SF in the sloping farmland in the Miyun Reservoir were 0.74 and 0.831, respectively, whereas those of the convection-dispersion equation for SSF were 0.81 and 0.811, respectively, thus indicating good simulation results. Therefore, this paper provides a reference for studying the mechanism of N migration and loss in sloping farmland in the Miyun Reservoir.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Test Soil

#### 2.2. Test Devices and Materials

#### 2.3. Experimental Design

#### 2.4. Data Acquisition and Analysis

^{2}), S is the area of loss (m

^{2}), C

_{i}is the TN loss concentration at the ith sampling (mg/L), q

_{vi}is the flow at the ith sampling (mL/s), and t

_{i}is the time interval between two samplings (s).

#### 2.5. Numerical Simulation

#### 2.5.1. Theoretical Model

#### Model of Simulating N Loss through SF

_{m}stands for the effective mixing depth (cm), C is the lost solute concentration (mg/L), C

_{0}is the solute concentration initially migrating to SF (mg/L), θ

_{S}is the saturated water content (cm

^{3}/cm

^{3}), ρ

_{s}is the soil bulk density (g/cm

^{3}), K is the soil adsorption coefficient (cm

^{3}/g), R is the rainfall intensity (cm/min), T is the rainfall time (min), and T

_{p}is the runoff generation time on land surface (min).

^{32}P and bromides taken as test materials. Herein, the continuous raindrops hitting the soil surface gradually increased the mixing depth, until a sealed water layer was formed on the soil surface after rainfall had formed stable runoff on it. This prevented the mixing depth from increasing, thereby reducing the increase rate. Therefore, the effective mixing depth was improved in this study, thereby allowing the establishment of an effective mixing depth model that is consistent with the changes previously proposed by Ahuja [30].

_{0}is the initial mixing depth (cm), and h

_{n}is the basic mixing parameter (cm). By substituting Equation (3) in Equation (2), a revised concentration model of the solutes migrated and lost with SF was obtained.

#### Model of Simulating N Loss through SSF

^{3}/cm

^{3}), t denotes the rainfall time (min), D

_{ij}denotes the dispersion coefficient (cm

^{2}/min), C denotes the soil TN mass concentration (mg/cm

^{3}), Q

_{i}denotes the water flux (cm/min), and R

_{i}denotes the spatial coordinate (i = 1, 2, r

_{1}= x, r

_{2}= z, D

_{11}= D

_{xx}, D

_{12}= D

_{xz}).

^{3}). θ

_{s}and θ

_{r}were given initial values by the Rosetta model according to the measured soil particle distribution, followed by adjustment and correction of the simulation process. k was determined by applying the linear isothermal adsorption method. DL and DW indicate the longitudinal dispersion of TN and the diffusion coefficient in free water, respectively, which were determined through backward deduction based on the simulation results.

#### 2.5.2. Verification and Evaluation of the Model

_{i}refers to the simulated value, Q

_{i}stands for the measured value, and Q is the mean value of the measured value. Among them, the optimal MAE and RMSE values are 0, while the optimal value of NSE is 1.

## 3. Results

#### 3.1. Characteristics of TN Loss through SF

#### 3.2. Characteristics of TN Loss through SSF

#### 3.3. Comparison of TN Loss between SF and SSF

#### 3.4. TN Loss Loading of SF and SSF

#### 3.5. Numerical Simulation of SF and SSF

^{2}) reaching 0.9539, 0.9015, and 0.9480, respectively. The Nash–Suttcliffe efficient NSEs were 0.73, 0.75, and 0.95, respectively, at the slope gradients of 5°, 10°, and 15°, with a rainfall intensity of 30 mm/h (Table 3), thereby indicating that not only were the simulation results good, but also the MAE and RMSE values were within a reasonable range. However, the precision of the simulation results decreased with the increasing rainfall intensity, which was mainly because the measured initial loss concentration under great rainfall intensities was small and the TN concentration rapidly stabilized, thus causing an insignificant concentration increase in the actual measurement. Therefore, there was a large error between the exponential decline trend simulated by the model and changes in the measured values. A negative NSE value denoted a poor simulation effect. Nevertheless, NSE was only a part of the evaluation of the simulation results and the MAE and RMSE values and R

^{2}should be considered. At the rainfall intensities of 30 and 40 mm/h, the MAE and RMSE values were close to the optimal value of 0, while R

^{2}reached 0.8 and 0.5, respectively, which indicated that the simulation results were acceptable. The simulated and measured values of the surface loss concentration are shown in a scatterplot (Figure 5a). The linear fitting relationship line between the two was y = 1.0656x + 0.2871 and R

^{2}was 0.83 after linear regression, which was very close to the 1:1 line. Additionally, MAE, RMSE, and NSE were 0.95 mg/L, 1.54 mg/L, and 0.74, respectively. In general, the revised effective mixing depth model presented good simulation results when simulating N migration and loss with SF in the sloping farmland in the Miyun Reservoir.

^{2}value fluctuated greatly (minimum of 0.21 and a maximum of 0.76), which was related to the large error between the measured values and simulated values. The NSE values shown in Table 3 also demonstrated fluctuations between positive and negative values under various rainfall intensities and slope gradients, thereby suggesting that the simulation results of TN concentration carried by SSF were as complex and uncertain as the actual loss process. According to the linear regression of the scatter plot of the simulated and measured values of TN concentration carried by SSF shown in Figure 5b, y = 0.8257x + 10.766 was obtained and R

^{2}was 0.81, which was also very close to the 1:1 line, with MAE, RMSE, and NSE being 24.99 mg/L, 39.25 mg/L, and 0.81, respectively, thus indicating a good fitting result. Although the MAE and RMSE values of the underground loss simulation results were >25 times those of the surface loss, the error values under each treatment (Table 3) were considered to be within the permissible range, as the TN concentration of groundwater loss was 14–78 times higher than that of surface loss. By comparing the simulation results of TN loss through SF and SSF under various rainfall intensities and slope gradients, the simulation precision on the surface was found to decrease with the increasing rainfall intensity, while the precision underground fluctuated and was uncertain. In conclusion, the simulation precision was satisfactory.

## 4. Discussion

^{2}= 0.8308).

## 5. Conclusions

^{2}of the effective mixing depth model in the numerical simulation of TN loss through SF from the sloping farmland in the Miyun Reservoir were 0.95 mg/L, 1.54 mg/L, 0.74, and 0.831, respectively. The same values of the convection-dispersion equation in simulating the change in TN concentration carried by the SSF were 24.99 mg/L, 39.25 mg/L, 0.81, and 0.811, respectively, which overall indicated good simulation results.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Borrelli, P.; Robinson, D.A.; Fleischer, L.R.; Lugato, E.; Ballabio, C.; Alewell, C.; Meusburger, K.; Modugno, S.; Schütt, B.; Ferro, V. An assessment of the global impact of 21st century land use change on soil erosion. Nat. Commun.
**2017**, 8, 2013. [Google Scholar] [CrossRef] [PubMed] - Pimentel, D.; Burgess, M. Soil Erosion Threatens Food Production. Agriculture
**2013**, 3, 443–463. [Google Scholar] [CrossRef] - Clark, E.H. Soil Erosion: Offsite Environmental Effects. In Soil Loss: Processes, Policies, and Prospects; Harlin, J.M., Bernardi, G.M., Eds.; Westview: New York, NY, USA, 1987; pp. 59–89. [Google Scholar]
- Doetterl, S.; Berhe, A.A.; Nadeu, E.; Wang, Z.; Sommer, M.; Fiener, P. Erosion, deposition and soil carbon: A review of process-level controls, experimental tools and models to address C cycling in dynamic landscapes. Earth-Sci. Rev.
**2016**, 154, 102–122. [Google Scholar] [CrossRef] - Chen, L.; Liu, D.; Song, L.; Cui, Y.; Xiao, S.; Fan, D. Characteristics of soil nitrogen loss under artificial rainfall in slope farmland of Xiangxi River basin J. J. Ecol. Rural. Environ.
**2012**, 6, 616–621. [Google Scholar] [CrossRef] - Qiu, L.; Zhu, H.; Liu, J.; Yao, Y.; Wang, X.; Rong, G.; Zhao, X.; Shao, M.; Wei, X. Soil erosion significantly reduces organic carbon and nitrogen mineralization in a simulated experiment. Agric. Ecosyst. Environ.
**2021**, 307, 107232. [Google Scholar] [CrossRef] - Wu, X.; Wei, Y.; Wang, J.; Xia, J.; Cai, C.; Wei, Z. Effects of soil type and rainfall intensity on sheet erosion processes and sediment characteristics along the climatic gradient in central-south china. Sci. Total Environ.
**2018**, 621, 54. [Google Scholar] [CrossRef] - Yao, Y.; Liu, J.; Wang, Z.; Wei, X.; Shao, M. Responses of soil aggregate stability, erodibility and nutrient enrichment to simulated extreme heavy rainfall. Sci. Total Environ.
**2019**, 709, 136150. [Google Scholar] [CrossRef] - Wu, L.; Peng, M.; Qiao, S.; Ma, X.Y. Effects of rainfall intensity and slope gradient on runoff and sediment yield characteristics of bare loess soil. Environ. Sci. Pollut. Res.
**2018**, 25, 3480–3487. [Google Scholar] [CrossRef] - Shen, H.; Zheng, F.; Wen, L.; Han, Y.; Hu, W. Impacts of rainfall intensity and slope gradient on rill erosion processes at loessial hillslope. Soil Tillage Res.
**2016**, 155, 429–436. [Google Scholar] [CrossRef] - Peng, X.; Dai, Q.; Li, C.; Yuan, Y.; Zhao, L. Simulate the impact of rainfall intensity and underground fissures on nutrient loss of slope farmland in karst areas. J. Agric. Eng.
**2017**, 2, 131–140. [Google Scholar] - Wang, L.; Wang, L.; Wang, Q. The process of soil nitrogen and phosphorus loss and migration in slope farmland with different slopes. J. Soil Water Conserv.
**2015**, 2, 69–75. [Google Scholar] [CrossRef] - Zhou, J.; Fu, B.; Gao, G. Effects of precipitation and restoration vegetation on soil erosion in a semi-arid environment in the Loess Plateau, China. Catena
**2016**, 137, 1–11. [Google Scholar] [CrossRef] - Zhou, L.; Hao, L.; Sun, Z. Characteristics of nitrogen and phosphorus loss from surface runoff and soil flow of different land types in Hunhe River Basin, Liaoning Province. J. Ecol. Environ.
**2011**, 20, 737–742. [Google Scholar] - Wang, G.; Li, Z.; Tian, Y.; Qu, J.; Xu, J.; Liu, Z. Effects of rainfall intensity and land use on nitrogen and phosphorus loss in mountainous areas of southwest Henan. People’s Yangtze River
**2016**, 47, 5. [Google Scholar] [CrossRef] - Lv, T.; Liao, M.; Ye, Z. Study on characteristics of runoff nitrogen loss under different land use patterns in Hexi Reservoir catchment area of Changxing County. J. Agric. Environ. Sci.
**2017**, 36, 9. [Google Scholar] [CrossRef] - Wang, L.; Wu, J.; Xie, J.; Wei, D.; Li, Y.; Wang, J.; Xu, T.; Yang, Z.; Jin, L. Effects of Different Hedgerow Patterns on the SoilPhysicochemical Properties, Erodibility, and Fractal Characteristics of Slope Farmland in the Miyun Reservoir Area. Plants
**2022**, 11, 2537. [Google Scholar] [CrossRef] - Wang, Q.; Zhao, G.; Liu, Y.; Zhang, P.; Chai, J. Effects of vegetation types on runoff, sediment and nitrogen and phosphorus loss on loess slope. J. Agric. Eng.
**2016**, 32, 195–201. [Google Scholar] [CrossRef] - Choi, K.-S.; Lee, S.G.; Jang, R.-J. Vegetative filter strip (Vfs) applications for runoff and pollution management in the saemangeum area of Korea. Irrig. Drain.
**2016**, 65, 168–174. [Google Scholar] [CrossRef] - Chen, X.; Cao, Z.; Yu, R.; Zhang, L.; Chen, H.; Cai, Y.; Feng, Y. Comparison of sediment concentration measurement methods in collecting bucket of slope runoff plot. J. Agric. Eng.
**2020**, 21, 130–136. [Google Scholar] [CrossRef] - Li, K.; Cheng, J.; Qi, S. Characteristics of slope erosion and non-point source pollution in different ecological revetment forms in Yongding River basin (Beijing section). Sci. Soil Water Conserv. China
**2022**, 1, 74–83. [Google Scholar] [CrossRef] - Wang, L.; Suo, L.; Wei, D.; Ding, J.; Zheng, Y.; Su, L.; An, Z. Ecological resistance and control characteristics of non-point source pollution of slope farmland under different plant allocation modes. Water Soil Conserv. Res.
**2021**, 28, 29–34. [Google Scholar] [CrossRef] - Feng, X.; Zheng, Z.; Li, T. Characteristics of surface runoff and nitrogen loss in maize season of slope farmland in purple soil area. J. Soil Water Conserv.
**2017**, 1, 43–48+54. [Google Scholar] [CrossRef] - Wang, L.; Li, Y.; Wu, J.; An, Z.; Suo, L.; Ding, J.; Li, S.; Wei, D.; Jin, L. Effects of the Rainfall Intensity andSlope Gradient on Soil Erosion andNitrogen Loss on the Sloping Fields of Miyun Reservoir. Plants
**2023**, 12, 423. [Google Scholar] [CrossRef] [PubMed] - Zhou, B.; Vogt, R.D.; Lu, X.; Yang, X.; Lü, C.; Mohr, C.W.; Zhu, L. Land use as an explanatory factor for potential phosphorus loss risk, assessed by P indices and their governing parameters. Environ. Sci. Process. Impacts
**2015**, 17, 1443–1454. [Google Scholar] [CrossRef] - Panagos, P.; Ballabio, C.; Borrelli, P.; Meusburger, K.; Klik, A.; Rousseva, S.; Alewell, C. Rainfall erosivity in Europe. Sci. Total Environ.
**2015**, 511, 801–814. [Google Scholar] [CrossRef] - Fiener, P.; Auerswald, K.; Van Oost, K. Spatio-temporal patterns in land use and management affecting surface runoff response of agricultural catchments—A review. Earth-Sci. Rev.
**2011**, 106, 92–104. [Google Scholar] [CrossRef] - Auerswald, K.; Fiener, P.; Martin, W.; Elhaus, D. Use and misuse of the K factor equation in soil erosion modeling: An alternative equation for determining USLE nomograph soil erodibility values. Catena
**2014**, 118, 220–225. [Google Scholar] [CrossRef] - Nekhay, O.; Arriaza, M.; Boerboom, L. Evaluation of soil erosion risk using Analytic Network Process and GIS: A case study from Spanish mountain olive plantations. J. Environ. Manag.
**2009**, 90, 3091–3104. [Google Scholar] [CrossRef] - Ahuja, L.R. Release of a soluble chemical from soil to runof. J. Trans. ASAE
**1982**, 25, 948–953. [Google Scholar] [CrossRef] - Wang, Q.; Wang, H. Analysis on the feature of effective mixing depth model for soil solute transporting with surface runoff on loess slope. J. Shuili Xuebao
**2010**, 41, 671–676. [Google Scholar] - Tonitto, C.; Li, C.; Seidel, R.; Drinkwater, L. Application of the DNDC model to the Rodale Institute Farming Systems Trial: Challenges for the validation of drainage and nitrate leaching in agroecosystem models. Nutr. Cycl. Agroecosyst.
**2010**, 87, 483–494. [Google Scholar] [CrossRef] - Ahuja, L.R. Characterization and Modeling of Chemical Transfer to Runoff; Springer: New York, NY, USA, 1986. [Google Scholar]
- Mohammed, D.; Kohl, R.A. Infiltration response to kinetic energy. Trans. ASAE
**1987**, 30, 108–111. [Google Scholar] [CrossRef] - Yang, T.; Wang, Q.; Wu, L.; Zhao, G.; Liu, Y.; Zhang, P. A mathematical model for soil solute transfer into surface runoff as influenced by rainfall detachment. Sci. Total Environ.
**2016**, 557, 590–600. [Google Scholar] [CrossRef] - Yang, T.; Wang, Q.; Liu, Y.; Zhang, P.; Wu, L. A comparison of mathematical models for chemical transfer from soil to surface runoff with the impact of rain. Catena
**2016**, 137, 191–202. [Google Scholar] [CrossRef] - Fu, B.; Wang, Y.K.; Zhu, B.; Wang, D.J.; Wang, X.T.; Wang, Y.Q.; Ren, Y. Experimental study on rainfall infiltration in sloping farmland of purple soil. Trans. CSAE
**2008**, 24, 39–43. [Google Scholar] - Pei, X.; Yu, K.W.; Bin, F. Interflow occurrence characters and their analysis on slope cropland with purple soil. Bull. Soil Water Conserv.
**2006**, 26, 14–18. [Google Scholar] - Peterson, E.W.; Davis, R.K.; Brahana, J.V.; Orndorff, H.A. Movement of nitrate through regolith covered karst terrane, northwest Arkansas. J. Hydrol.
**2002**, 256, 35–47. [Google Scholar] [CrossRef] - Zakari, S.; Liu, H.; Li, Y.X.; He, X.; Tong, L. Transport and sorption behavior of individual phthalate esters in sandy aquifer: Column experiments. Environ. Sci. Pollut. Res.
**2016**, 23, 15749–15756. [Google Scholar] [CrossRef] - Yu, G.J.; Huang, J.S.; Gao, Z.Y. Study on water and salt transportation of different irrigation modes by the simulation of HYDRUS model. J. Hydraul. Eng.
**2013**, 44, 826–834. [Google Scholar] - Huo, H.; Wang, T.; Wei, S. Characteristics of nitrogen loss from hillslope croplands of purple soil in the Three Gorges Reservoir Area and impacts of slope gradients. J. Southwest Univ. Nat. Sci. Ed.
**2013**, 35, 112–117. [Google Scholar] [CrossRef] - Veizaga, E.A.; Rodríguez, L.; Ocampo, C.J. Water and chloride transport in a fine-textured soil in a feedlot pen. J. Contam. Hydrol.
**2015**, 182, 91–103. [Google Scholar] [CrossRef] [PubMed] - Jia, H.; Lei, A.; Lei, J.; Ye, M.; Zhao, J. Effects of hydrological processes on nitrogen loss in purple soil. Agric. Water Manag.
**2007**, 89, 89–97. [Google Scholar] [CrossRef] - Xie, M.; Zhang, Z.; Zhang, P.; Xu, J.; Lin, Q. Migration and loss of nitrate nitrogen in purple soil slope farmland and its numerical simulation. J. Agric. Eng.
**2018**, 19, 147–154. [Google Scholar] [CrossRef]

**Figure 1.**Schematic diagram of experimental structure. Note: R is rainfall intensity, mm/h; CSF is concentration of solute in surface flow, mg/L; CSSF is concentration of solute in subsurface flow, mg/L; hm is effective mixing depth, cm; JU and JD are upward and downward solute flux from soil layer, respectively, mg/cm·min; α is depth gradient, (°).

**Figure 2.**Comparison of measured and simulated concentrations of TN loss through surface flow. The error bars refer to the standard deviation.

**Figure 3.**Comparison of measured and simulated concentration of TN loss through subsurface flow. The error bars refer to the standard deviation.

**Figure 5.**Scatter diagram of simulated and measured TN loss concentrations. (

**a**). TN loss via surface flow (

**b**). TN loss via subsurface flow.

Parameters | ρs/ (g·cm ^{−3}) | $\mathit{\theta}$s/ (cm ^{3}·cm^{−3}) | k/ (cm ^{3}·g^{−1}) | D_{L}/ cm | Dw/ (cm ^{2}·min^{−1}) | $\mathit{\theta}$r/ (cm ^{3}·cm^{−3}) |
---|---|---|---|---|---|---|

Surface | 1.16 | 0.424 | 0.77 | - | - | - |

Subsurface | 1.16 | 0.424 | 0.77 | 1.19 | 0.03 | 0.0348 |

_{L}is longitudinal dispersity of TN, D

_{W}is molecular diffusion coefficient in free water of TN.

Rainfall Intensity/(mm·h^{−1}) | Slope Gradient/(°) | Mean Concentration ± Standard Deviation/(mg·L^{−1}) | Mean Load ± Standard Deviation (kg/ha) | ||
---|---|---|---|---|---|

Surface Flow | Subsurface Flow | Surface Flow | Subsurface Flow | ||

30 | 5 | 0.195 ± 0.350b | 21.483 ± 1.100a | 0.016 ± 0.002b | 0.098 ± 0.002a |

10 | 0.159 ± 0.255b | 27.898 ± 3.055a | 0.014 ± 0.004b | 0.247 ± 0.011a | |

15 | 0.089 ± 0.200b | 56.868 ± 5.282a | 0.011 ± 0.005b | 0.359 ± 0.017a | |

40 | 5 | 0.454 ± 0.436b | 56.421 ± 4.478a | 0.041 ± 0.006b | 0.405 ± 0.077a |

10 | 0.255 ± 0.267b | 87.932 ± 1.586a | 0.025 ± 0.005b | 0.857 ± 0.004a | |

15 | 0.189 ± 0.157b | 137.715 ± 9.576a | 0.053 ± 0.071b | 1.452 ± 0.122a | |

50 | 5 | 1.221 ± 0.961b | 180.013 ± 14.808a | 0.067 ± 0.013b | 3.586 ± 0.093a |

10 | 2.487 ± 1.132b | 108.718 ± 4.322a | 0.083 ± 0.008b | 1.648 ± 0.022a | |

15 | 4.277 ± 1.442b | 124.464 ± 1.938a | 0.151 ± 0.013b | 1.950 ± 0.074a | |

60 | 5 | 1.738 ± 1.108b | 122.612 ± 2.594a | 0.092 ± 0.015b | 0.395 ± 0.040a |

10 | 2.394 ± 0.614b | 47.245 ± 3.381a | 0.101 ± 0.021b | 0.528 ± 0.035a | |

15 | 4.705 ± 1.520b | 48.417 ± 1.994a | 0.141 ± 0.018b | 0.667 ± 0.023a | |

70 | 5 | 4.236 ± 1.983b | 107.244 ± 4.978a | 0.356 ± 0.014b | 1.017 ± 0.012a |

10 | 5.536 ± 2.145b | 79.586 ± 1.619a | 0.459 ± 0.032b | 0.884 ± 0.030a | |

15 | 9.395 ± 2.884b | 63.044 ± 2.207a | 0.455 ± 0.027b | 0.739 ± 0.059a | |

80 | 5 | 3.134 ± 0.926b | 110.316 ± 2.946a | 0.263 ± 0.044b | 1.163 ± 0.138a |

10 | 4.817 ± 1.742b | 55.251 ± 3.036a | 0.327 ± 0.022b | 0.586 ± 0.002a | |

15 | 7.894 ± 1.910b | 65.977 ± 2.847a | 0.458 ± 0.044b | 1.118 ± 0.057a |

Rainfall Intensity /(mm·h ^{−1}) | Slope Gradient /(°) | Surface | Subsurface | ||||
---|---|---|---|---|---|---|---|

MAE | RMSE | NSE | MAE | RMSE | NSE | ||

30 | 5 | 0.07 | 0.18 | 0.73 | 24.84 | 34.08 | −0.13 |

10 | 0.06 | 0.12 | 0.75 | 16.33 | 30.84 | 0.57 | |

15 | 0.02 | 0.05 | 0.95 | 23.90 | 31.26 | 0.68 | |

40 | 5 | 0.18 | 0.31 | 0.45 | 31.35 | 45.98 | 0.32 |

10 | 0.11 | 0.17 | 0.57 | 36.63 | 57.50 | 0.55 | |

15 | 0.17 | 0.24 | −1.52 | 65.44 | 95.01 | 0.36 | |

50 | 5 | 0.71 | 0.96 | 0.24 | 110.15 | 136.61 | 0.45 |

10 | 0.70 | 0.80 | 0.45 | 32.14 | 40.39 | 0.79 | |

15 | 1.00 | 1.16 | 0.29 | 52.30 | 78.53 | 0.16 | |

60 | 5 | 0.01 | 0.78 | 0.46 | 57.27 | 74.11 | 0.40 |

10 | 0.92 | 1.08 | −1.34 | 61.27 | 72.38 | −1.20 | |

15 | 0.80 | 0.96 | 0.56 | 42.38 | 57.38 | −0.67 | |

70 | 5 | 1.06 | 1.24 | 0.57 | 65.97 | 81.48 | 0.27 |

10 | 1.14 | 1.48 | 0.48 | 44.55 | 51.98 | 0.30 | |

15 | 1.74 | 2.17 | −0.31 | 42.76 | 50.05 | −0.52 | |

80 | 5 | 2.06 | 2.73 | −0.68 | 26.93 | 36.89 | 0.72 |

10 | 2.10 | 2.43 | −1.12 | 23.99 | 32.74 | 0.17 | |

15 | 1.42 | 1.57 | 0.27 | 28.88 | 41.33 | −0.28 | |

All treatments | 0.95 | 1.54 | 0.74 | 24.99 | 39.25 | 0.81 |

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**MDPI and ACS Style**

Li, Y.; Jin, L.; Wu, J.; Shi, C.; Li, S.; Xie, J.; An, Z.; Suo, L.; Ding, J.; Wei, D.;
et al. Laws Governing Nitrogen Loss and Its Numerical Simulation in the Sloping Farmland of the Miyun Reservoir. *Plants* **2023**, *12*, 2042.
https://doi.org/10.3390/plants12102042

**AMA Style**

Li Y, Jin L, Wu J, Shi C, Li S, Xie J, An Z, Suo L, Ding J, Wei D,
et al. Laws Governing Nitrogen Loss and Its Numerical Simulation in the Sloping Farmland of the Miyun Reservoir. *Plants*. 2023; 12(10):2042.
https://doi.org/10.3390/plants12102042

**Chicago/Turabian Style**

Li, Yan, Liang Jin, Jiajun Wu, Chuanqi Shi, Shuo Li, Jianzhi Xie, Zhizhuang An, Linna Suo, Jianli Ding, Dan Wei,
and et al. 2023. "Laws Governing Nitrogen Loss and Its Numerical Simulation in the Sloping Farmland of the Miyun Reservoir" *Plants* 12, no. 10: 2042.
https://doi.org/10.3390/plants12102042