# Nonlinear Water Quality Response to Numerical Simulation of In Situ Phosphorus Control Approaches

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## Abstract

**:**

## 1. Introduction

^{2}, according to the manufacturer’s website (www.phoslock.com.au, accessed on 16 February 2021). The application scheme for Phoslock is determined by pilot testing and experience [27,28], including position, frequency, and dose for spraying. It might be a reasonable approach for small-scale application, as the diffusion process often takes place relatively fast. However, each individual lake is an open complex system, and there are intricate nonlinear relationships between subsystems or various factors that make the response of nutrient concentration to treatment show nonlinearity and spatiotemporal heterogeneity [29,30]. For a large water body, like a lake with a surface area of several tens or even hundreds of square kilometers, empirical-based methods have difficulty dealing with such a complicated nonlinear system, and small-scale testing is not helpful. Therefore, a Phoslock application scheme determined by experience cannot achieve the expected effect for a large lake, and may result in huge waste. Apparently, from the perspective of cost-effectiveness, more precise and defensible methods are needed to guide the application of Phoslock for large projects.

## 2. Materials and Methods

#### 2.1. Materials

_{4}·nH

_{2}O), which is highly insoluble and stable across a wide range of pH and redox conditions [24], such as those found in lake water and sediment. This property makes it ideal as a phosphorus binding agent, which can be put to use in lake restoration.

#### 2.2. Methodology

#### 2.2.1. Description of OOID

- Compute the water quality response when applied to one single treating facility, expressed as the following equation.$$F\left(i\right)={f}_{i}\left(X{1}_{i},X{2}_{i},X{3}_{i}\cdots ,X{n}_{i}\right)$$
- Compute the water quality response when applied to multiple facilities, expressed as the following equation:$$G\left(i\right)={g}_{i}\left[{m}_{i},{f}_{i}\left(X{1}_{i},X{2}_{i},X{3}_{i}\cdots ,X{n}_{i}\right)\right]$$
- Compute the water quality response when applied to multiple treatment technologies, expressed as the following equation:$$G\left(i\right)={\displaystyle \int}{g}_{i}\left[{m}_{i},{f}_{i}\left(X{1}_{i},X{2}_{i},X{3}_{i}\cdots ,X{n}_{i}\right)\right].$$
- Compute the object-oriented intelligent design.$$\left[{m}_{i},X{1}_{i},X{2}_{i},X{3}_{i}\cdots ,X{n}_{i}\right]=\mathrm{lnv}G()$$

#### 2.2.2. Technical Framework of OOID-Phoslock

#### 2.3. Case Study

#### 2.3.1. Study Area

^{2}, and the lake surface area is 34.7 km

^{2}with a volume of 1.84 × 10

^{8}m

^{3}[42,43]. It is hydrologically recharged by precipitation and seasonal inflows from more than 12 small, intermittent rivers. The mean annual water inflow is about 6.2 × 10

^{7}m

^{3}[44].

#### 2.3.2. Scenario Generation

#### 2.3.3. Modeling Process

^{2}. The smallest grid is about 0.016 km

^{2}and the largest is about 0.23 km

^{2}. The average depth is about 6.8 m, the minimum depth is 2.7 m, and the maximum depth is 9.79 m. In addition, the water surface elevation is 1722.5 m. In order to accurately represent the effects of light and nutrients on phytoplankton dynamics, it was necessary to characterize the vertical variation of light and nutrient utilization in three-dimensional spatial resolution. Therefore, in this model, the horizontal grid was further divided into four layers, and a total of 1448 computational grids were generated from top to bottom to represent the entire lake.

^{2}), and root-mean-squared error (RMSE) between simulated and measured water levels were 0.81, 0.90, and 0.13 m, respectively. The RMSE between simulated and measured TP concentration was 0.10, 0.11, and 0.12 mg/L, respectively. Figure 6 plots the model simulated data against the observed data.

## 3. Results

#### 3.1. Temporal Variability of the Response

#### 3.2. Spatial Variability of the Response

- Including more internal sites tends to get a better result. A0 and A3 have five internal sites. A4 and A1 have four internal sites. A6 has three internal sites. A5 and A7 have two internal sites, and A2 has no internal sites. Although not strictly, that sequence is basically the decreasing order in Figure 12, which, more or less, verifies the same finding discussed in Section 3.2.
- The differences in the water quality response between scenarios are not significant with a low dose, but become more clear with increased doses. The improvement of A0, A4, and A3 is not far from A2 when the dose is 10 t/d, but is more than twice as much as A2 when it is over 40 t/d.
- The TP improvement rises with the dosage for all scenarios, but the trend rate is different. For positions of A2, if the improvement of TP concentration needs to be increased from 0.01 to 0.02 mg/L, the dose has to be increased from 40 to 300 t/d (seven times). For positions of A4, it has to be increased from 20 to 40 t/d (two times).
- A4 is better than A3 when the dose does not exceed 180 t/d, but the situation is reversed when the dose is 300 t/d, and similarly for A3 and A0. Therefore, there is no unique “best scenario” here, and the best set of positions could not be determined. In practical circumstances, it still makes sense to find the best positions under more constraints, even if it may not remain the best when conditions change.

#### 3.3. Dose-Response Relationship

- How does the TP concentration improvement with Phoslock per weight vary with design parameters?
- What is the potential range of TP concentration improvement for each dose level?
- What is the probability of improving TP concentration by using a certain dose to get within the potential range?

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Hayes, N.M.; Vanni, M.J. Microcystin concentrations can be predicted with phytoplankton biomass and watershed morphology. Inland Waters
**2018**, 8, 273–283. [Google Scholar] [CrossRef] - Jing’an, M.; Hongqing, L. On eutrophication of rivers, lakes and reservoirs at home and abroad. Resour. Environ. Yangtze River Basin
**2002**, 11, 575–578. (In Chinese) [Google Scholar] - Ministry of Ecology and Environment of the People’s Republic of China [EB/OL]. Available online: http://www.mee.gov.cn/hjzl/sthjzk/zghjzkgb/ (accessed on 2 June 2020). (In Chinese)
- Beusen, A.H.W.; Bouwman, A.F.; Van Beek, L.P.H.; Mogollón, J.M.; Middelbur, J.J. Global riverine N and P transport to ocean increased during the 20th century despite increased retention along the aquatic continuum. Biogeosciences
**2016**, 13, 2441–2451. [Google Scholar] [CrossRef][Green Version] - Huang, J.; Xu, C.; Ridoutt, B.G.; Wang, X.; Ren, P. Nitrogen and phosphorus losses and eutrophication potential associated with fertilizer application to cropland in China. J. Clean. Prod.
**2017**, 159, 171–179. [Google Scholar] [CrossRef] - Li, X.Y.; Li, H.P.; Jiang, S.Y.; Ma, P.; Lai, X.; Deng, J.C.; Chen, D.Q.; Geng, J.W. Temporal-spatial variations in nutrient loads in river-lake system of Changdang Lake catchment during 2016–2017. Environ. Sci.
**2020**, 41, 4042–4052. (In Chinese) [Google Scholar] - Daneshgar, S.; Callegari, A.; Capodaglio, A.G.; Vaccari, D. The Potential Phosphorus Crisis: Resource Conservation and Possible Escape Technologies: A Review. Resour. Basel
**2018**, 7, 37. [Google Scholar] [CrossRef][Green Version] - Zhang, H.; Shang, Y.; Lyu, T.; Chen, J.; Pan, G. Switching Harmful Algal Blooms to Submerged Macrophytes in Shallow Waters Using Geo-engineering Methods: Evidence from a N-15 Tracing Study. Environ. Sci. Technol.
**2018**, 52, 11778–11785. [Google Scholar] [CrossRef][Green Version] - Pan, G.; Miao, X.; Bi, L.; Zhang, H.; Wang, L.; Wang, L.; Wang, Z.; Chen, J.; Ali, J.; Pan, M.; et al. Modified Local Soil (MLS) Technology for Harmful Algal Bloom Control, Sediment Remediation, and Ecological Restoration. Water
**2019**, 11, 16. [Google Scholar] [CrossRef][Green Version] - Zhang, H.; Lyu, T.; Bi, L.; Tempero, G.; Hamilton, D.P.; Pan, G. Combating hypoxia/anoxia at sediment-water interfaces: A preliminary study of oxygen nanobubble modified clay materials. Sci. Total Environ.
**2018**, 637–638, 550–560. [Google Scholar] [CrossRef][Green Version] - Oglesby, R.T.; Edmondson, W.T. Control of eutrophication. J. Water Pollut. Control. Fed.
**1966**, 38, 1452. [Google Scholar] - Welch, E.B. The dilution-flushing technique in lake restoration. Water Resour. Bull.
**1981**, 17, 558–564. [Google Scholar] [CrossRef] - Jeppesen, E.; Søndergaard, M.; Meerhoff, M.; Lauridsen, T.L.; Jensen, J.P. Shallow lake restoration by nutrient loading reduction—Some recent findings and challenges ahead. Hydrobiologia
**2007**, 584, 239–252. [Google Scholar] [CrossRef] - Hu, L.; Hu, W.; Zhai, S.; Wu, H. Effects on water quality following water transfer in Lake Taihu, China. Ecol. Eng.
**2010**, 36, 471–481. [Google Scholar] [CrossRef] - Liu, Y.; Wang, Y.; Sheng, H.; Dong, F.; Zou, R.; Zhao, L.; Guo, H.; Zhu, X.; He, B. Quantitative evaluation of lake eutrophication responses under alternative water diversion scenarios: A water quality modeling based statistical analysis approach. Sci. Total Environ.
**2014**, 468–469, 219–227. [Google Scholar] [CrossRef] - Camacho, R.A.; Zhang, Z.; Chao, X. Receiving Water Quality Models for TMDL Development and Implementation. J. Hydrol. Eng.
**2019**, 24, 04018063. [Google Scholar] [CrossRef] - Mohamoud, Y.; Zhang, H. Applications of Linked and Nonlinked Complex Models for TMDL Development: Approaches and Challenges. J. Hydrol. Eng.
**2019**, 24, 11. [Google Scholar] [CrossRef] - You, X.-Y.; Zhang, C.-X. On improvement of water quality of a reservoir by optimizing water exchange. Environ. Prog. Sustain. Energy
**2018**, 37, 399–409. [Google Scholar] [CrossRef] - Capodaglio, A.G.; Boguniewicz, J.; Llorens, E.; Salerno, F.; Copetti, D.; Legnani, E.; Buraschi, E.; Tartari, G. Integrated lake/catchment approach as a basis for the implementation of the WFD in the Lake Pusiano watershed. In Proceedings of the River Basin Management—Progress Towards Implementation of the European Water Framework Directive, Budapest, Hungary, 19–20 May 2005. [Google Scholar]
- Zhang, F.; Zhang, M.; Gao, L.; Li, K. Pilot-scale test of treating eutrophication water in Chaohu lake using biological pond. Environ. Eng.
**2009**, 27, 9–11. (In Chinese) [Google Scholar] - Wang, W.-H.; Wang, Y.; Sun, L.-Q.; Zheng, Y.-C.; Zhao, J.-C. Research and application status of ecological floating bed in eutrophic landscape water restoration. Sci. Total Environ.
**2020**, 704, 135434. [Google Scholar] [CrossRef] - Chen, X.; Chen, X.; Zhao, Y.; Zhou, H.; Xiong, X.; Wu, C. Effects of microplastic biofilms on nutrient cycling in simulated freshwater systems. Sci. Total Environ.
**2020**, 719, 137276. [Google Scholar] [CrossRef] [PubMed] - Liu, H.; Cao, L.; Xu, G.J.; Wang, T.J. Study on the remediation of eutrophic water by enhanced biomanipulation of Daphnia magna. Environ. Sci. Technol.
**2020**, 43, 156–161. (In Chinese) [Google Scholar] - Li, X.; Zhang, Z.; Xie, Q.; Yang, R.; Guan, T.; Wu, D. Immobilization and Release Behavior of Phosphorus on Phoslock-Inactivated Sediment under Conditions Simulating the Photic Zone in Eutrophic Shallow Lakes. Environ. Sci. Technol.
**2019**, 53, 12449–12457. [Google Scholar] [CrossRef] [PubMed] - Yang, Y.Q.; Chen, J.A.; Wang, J.F.; Yan, Z. Research progress of sediments phosphorus in-situ inactivation. Adv. Earth Sci.
**2013**, 28, 674–683. (In Chinese) [Google Scholar] - Copetti, D.; Finsterle, K.; Marziali, L.; Fabrizio, S.; Gianni, T.; Grant, D.; Kasper, R.; Bryan, S.; Spearse, M.; Ian, J.; et al. Eutrophication management in surface waters using lanthanum modified bentonite: A review. Water Res.
**2016**, 97, 162–174. [Google Scholar] [CrossRef] [PubMed][Green Version] - Liu, Y.G.; Tian, K.; Winks, A. Phoslock, a Soluble Phosphorus Binding Technology, Application in Lake Dianchi Eutrophic Water Purification. In Proceedings of the 2009 International Conference on Environmental Science and Information Application Technology, Wuhan, China, 4–5 July 2009. [Google Scholar]
- Pan, M.; Lyu, T.; Zhang, M.; Zhang, H.; Bi, L.; Wang, L.; Chen, J.; Yao, C.; Ali, J.; Best, S.; et al. Synergistic Recapturing of External and Internal Phosphorus for In Situ Eutrophication Mitigation. Water
**2019**, 12, 2. [Google Scholar] [CrossRef][Green Version] - Wei, H.; Chai, L. Non-linear dynamic characteristics of phosphorus cycle and eutrophication. Hupo Kexue
**2006**, 18, 557–564. (In Chinese) [Google Scholar] - Liu, Y.; Wang, Y.L.; Sheng, H.; Dong, F.F.; Zou, R.; Zhao, L.; Guo, H.C.; Zhu, X.; He, B. Lake eutrophication responses modeling and watershed management optimization algorithm: A review. Hupo Kexue
**2021**, 33, 49–63. (In Chinese) [Google Scholar] - Zou, R.; Zhou, J.; Liu, Y.; Zhu, X.; Zhao, L.; Yang, P.-J.; Guo, H.-C. An object-oriented intelligent engineering design approach for lake pollution control. Huan Jing Ke Xue= Huanjing Kexue
**2013**, 34, 892–899. [Google Scholar] [PubMed] - Li, Z.-F.; Liu, H.-Y.; Li, Y. Review on HSPF model for simulation of hydrology and water quality processes. Huanjing Kexue
**2012**, 33, 2217–2223. (In Chinese) [Google Scholar] [PubMed] - Arnold, J.G.; Moriasi, D.N.; Gassman, P.W.; Abbaspour, K.C.; White, M.J.; Srinivasan, R.; Santhi, C.; Harmel, R.D.; Van Griensven, A.; Van Liew, M.W.; et al. SWAT: Model Use, Calibration, and Validation. Trans. ASABE
**2012**, 55, 1491–1508. [Google Scholar] [CrossRef] - Yuan, L.; Sinshaw, T.; Forshay, A.K.J. Review of Watershed-Scale Water Quality and Nonpoint Source Pollution Models. Geosciences
**2020**, 10, 25. [Google Scholar] [CrossRef] [PubMed][Green Version] - DHI. Mike she volume 1: User guide. The experts in water environments. DHI Softw. Licence Agreem.
**2017**, 27, 91–95. [Google Scholar] - DHI. MIKE 21 & MIKE 3 Hydrodynamic and Transport Scientific Documentation. Danish Hydraulic Institute. 2017. Available online: https://manuals.mikepoweredbydhi.help/2020/Coast_and_Sea/MIKE_FM_ELOS_2D.pdf (accessed on 20 February 2021).
- Hamrick, J.M. A Three-Dimensional Environmental Fluid Dynamics Computer Code: Theoretical and Computational Aspects; Special paper 317; The College of William and Mary, Virginia Institute of Marine Science: Williamsburg, NY, USA, 1992. [Google Scholar]
- Delft3D-FLOW User Manual, 710. Available online: https://usermanual.wiki/Pdf/Delft3DFLOWUserManual.885467064/help (accessed on 20 February 2021).
- D-Water Quality User Manual, 414. Available online: https://content.oss.deltares.nl/delft3d/manuals/D-Water_Quality_User_Manual.pdf (accessed on 20 February 2021).
- DHI. MIKE 3 Flow Model User Guide and Scientific Documentation. Danish Hydraulic Institute. 2017. Available online: https://manuals.mikepoweredbydhi.help/2017/Coast_and_Sea/MIKE_321_FM_Scientific_Doc.pdf (accessed on 20 February 2021).
- Gao, C.; Yu, J.; Min, X.; Cheng, A.; Hong, R.; Zhang, L. Heavy metal concentrations in sediments from Xingyun lake, southwestern China: Implications for environmental changes and human activities. Environ. Earth Sci.
**2018**, 77, 1–13. [Google Scholar] [CrossRef] - Wang, S.; Dou, H. Chinese Lakes; Science Press: Beijing, China, 1998; p. 580. (In Chinese) [Google Scholar]
- Liu, Y.; Chen, G.; Hu, K.; Shi, H.; Huang, L.; Chen, X.; Lu, H.; Zhao, S.; Chen, L. Biological responses to recent eutrophication and hydrologic changes in Xingyun Lake, southwest China. J. Paleolimnol.
**2017**, 57, 343–360. [Google Scholar] [CrossRef] - Zheng, T.; Zu, Z.; Xiao, Z.; Ze, G.; Jun, P.; Feifeiet, L. Water quality change and humanities driving force in Lake Xingyun, Yunnan Province. Hupo Kexue
**2018**, 30, 79–90. (In Chinese) [Google Scholar] - Zhong, J.; Wen, S.; Zhang, L.; Wang, J.; Liu, C.; Yu, J.; Zhang, L.; Fan, C. Nitrogen budget at sediment–water interface altered by sediment dredging and settling particles: Benefits and drawbacks in managing eutrophication. J. Hazard. Mater.
**2021**, 406, 124691. [Google Scholar] [CrossRef]

**Figure 6.**Model validation: simulated water level and water quality vs. observed data at the gauging station and monitoring stations: (

**a**) water level validation. (

**b**–

**d**) Total phosphorus (TP) concentration validation.

**Figure 7.**Time series graph of total phosphorus (TP) concentration for a typical scenario of Phoslock application (base0, T2, A0, 300 t/d).

**Figure 9.**Spatial distribution of TP concentration at different moments during the Phoslock release cycle (base0-T1-A0-300t): (

**a**) 1st day, (

**b**) 5th day, (

**c**) 15th day, and (

**d**) 30th day.

**Figure 10.**Time series graph of TP concentration for different sets of release positions (base1, T2, and 300 t/d).

**Figure 12.**Relationship between the release position and response (average for the simulation period, T1–T4, and base0–base2).

**Figure 13.**Response produced by Phoslock per weight for scenarios (average for simulation period, T1–T4, and base–base2).

**Figure 14.**Response and effective boundary for 1944 scenarios (average for simulation period and seasons).

Domain | Description | Output | Software Available |
---|---|---|---|

Basin | Distributed or semi-distributed hydrological model | Flow time series | HSPF, SWAT, LSPC, MIKE SHE+MIKE ECO-Lab, etc. |

Watershed-scale water quality and nonpoint source (NPS) pollution model | Pollutant flux time series | ||

Lake | Hydrodynamic simulation | Water level and flow direction time series | EFDC, Delft 3D, MIKE3+MIKE ECO-Lab, etc. |

Heat exchange simulation | Water temperature time series | ||

Nutrient transport and transformation simulation | Water quality time series | ||

Endogenous dynamic simulation | |||

Simulate dissolution, binding (with phosphate), precipitation process of Phoslock in the lake | _ |

Season | Sets of Positions | Number of Dose Ranks | Uncertainty Classification | Count |
---|---|---|---|---|

First (T1) | 8 (artificial) | 9 (10–300 t/d) | 3 (base 0~base 2) | 216 |

10 (random) | 9 (10–300 t/d) | 3 (base 0~base 2) | 270 | |

Second (T2) | 8 (artificial) | 9 (10–300 t/d) | 3 (base 0~base 2) | 216 |

10 (random) | 9 (10–300 t/d) | 3 (base 0~base 2) | 270 | |

Third (T3) | 8 (artificial) | 9 (10–300 t/d) | 3 (base 0~base 2) | 216 |

10 (random) | 9 (10–300 t/d) | 3 (base 0~base 2) | 270 | |

Fourth (T4) | 8 (artificial) | 9 (10–300 t/d) | 3 (base 0~base 2) | 216 |

10 (random) | 9 (10–300 t/d) | 3 (base 0~base 2) | 270 |

Code Name | Position Numbers |
---|---|

A0 | 1, 2, 3, 4, 5 |

A1 | 1, 2, 3, 4, 13 |

A2 | 10, 11, 12, 14, 15 |

A3 | 1, 2, 5, 6, 7 |

A4 | 2, 3, 4, 5, 13 |

A5 | 1, 2, 10, 14, 15 |

A6 | 3, 4, 5, 11, 12 |

A7 | 1, 2, 10, 13, 15 |

Dose | Lowest TP Conc Improvement | Worst Scenario | Highest TP Conc Improvement | Cost-Effective Scenario |
---|---|---|---|---|

10 t/d | 0.003955 mg/L | base1-A2 | 0.006676 mg/L | base0-A4 |

20 t/d | 0.006356 mg/L | base1-A2 | 0.013003 mg/L | base0-A4 |

30 t/d | 0.007541 mg/L | base1-A2 | 0.018867 mg/L | base0-A4 |

40 t/d | 0.008267 mg/L | base1-A2 | 0.023763 mg/L | base0-A4 |

60 t/d | 0.009361 mg/L | base1-A2 | 0.030537 mg/L | base0-A4 |

90 t/d | 0.010631 mg/L | base1-A2 | 0.036812 mg/L | base0-A4 |

120 t/d | 0.011614 mg/L | base1-A2 | 0.041296 mg/L | base0-A4 |

180 t/d | 0.013029 mg/L | base1-A2 | 0.048266 mg/L | base0-A4 |

300 t/d | 0.014773 mg/L | base1-A2 | 0.057726 mg/L | base0-A3 |

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**MDPI and ACS Style**

Zhang, B.; Lin, N.; Chen, X.; Fan, Q.; Chen, X.; Ren, T.; Zou, R.; Guo, H.
Nonlinear Water Quality Response to Numerical Simulation of In Situ Phosphorus Control Approaches. *Water* **2021**, *13*, 725.
https://doi.org/10.3390/w13050725

**AMA Style**

Zhang B, Lin N, Chen X, Fan Q, Chen X, Ren T, Zou R, Guo H.
Nonlinear Water Quality Response to Numerical Simulation of In Situ Phosphorus Control Approaches. *Water*. 2021; 13(5):725.
https://doi.org/10.3390/w13050725

**Chicago/Turabian Style**

Zhang, Baichuan, Ningya Lin, Xi Chen, Qiaoming Fan, Xing Chen, Tingyu Ren, Rui Zou, and Huaicheng Guo.
2021. "Nonlinear Water Quality Response to Numerical Simulation of In Situ Phosphorus Control Approaches" *Water* 13, no. 5: 725.
https://doi.org/10.3390/w13050725