# A Greedy Algorithm for Optimal Sensor Placement to Estimate Salinity in Polder Networks

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Case Study Area and Salinization Problem

#### 2.2. Modeling Spatial and Temporal Salinity Distributions

#### 2.3. Principal Component Analysis for Estimating Salinity

#### 2.4. Sensor Placement Using a Greedy Algorithm

Algorithm 1: Pseudo code of sensor placement. |

## 3. Results and Discussions

#### 3.1. Reference Scenario

#### 3.2. Principal Component Analysis

#### 3.3. Optimum Sensor Placement Based on the Low-Order PCA Model

#### 3.4. Optimality of Placements Using Greedy Algorithm

#### 3.5. A Posteriori Assessment of Robustness of Sensor Placement to Measurement and Modeling Errors

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Delsman, J.R.; Waterloo, M.J.; Groen, M.M.; Groen, J.; Stuyfzand, P.J. Investigating summer flow paths in a Dutch agricultural field using high frequency direct measurements. J. Hydrol.
**2014**, 519, 3069–3085. [Google Scholar] [CrossRef] - Delsman, J.R.; Oude Essink, G.H.P.; Beven, K.J.; Stuyfzand, P.J. Uncertainty estimation of end-member mixing using generalized likelihood uncertainty estimation (GLUE), applied in a lowland catchment. Water Resour. Res.
**2013**, 49, 4792–4806. [Google Scholar] [CrossRef] [Green Version] - De Louw, P.; Oude Essink, G.; Stuyfzand, P.; van der Zee, S. Upward groundwater flow in boils as the dominant mechanism of salinization in deep polders, The Netherlands. J. Hydrol.
**2010**, 394, 494–506. [Google Scholar] [CrossRef] - Oude Essink, G.H.P.; Van Baaren, E.S.; De Louw, P.G.B. Effects of climate change on coastal groundwater systems: A modeling study in the Netherlands. Water Resour. Res.
**2010**, 46, W00F04. [Google Scholar] [CrossRef] - Delsman, J.R. Saline Groundwater-Surface Water Interaction in Coastal Lowlands; IOS Press, Inc.: Amsterdam, The Netherlands, 2015; pp. 1–188. [Google Scholar]
- Aydin, B.E.; Tian, X.; Delsman, J.; Oude Essink, G.H.; Rutten, M.; Abraham, E. Optimal salinity and water level control of water courses using Model Predictive Control. Environ. Model. Softw.
**2019**, 112, 36–45. [Google Scholar] [CrossRef] - Mahjouri, N.; Kerachian, R. Revising river water quality monitoring networks using discrete entropy theory: The Jajrood River experience. Environ. Monit. Assess.
**2011**, 175, 291–302. [Google Scholar] [CrossRef] - Noori, R.; Sabahi, M.S.; Karbassi, A.R.; Baghvand, A.; Zadeh, H.T. Multivariate statistical analysis of surface water quality based on correlations and variations in the data set. Desalination
**2010**, 260, 129–136. [Google Scholar] [CrossRef] - Ouyang, Y. Evaluation of river water quality monitoring stations by principal component analysis. Water Res.
**2005**, 39, 2621–2635. [Google Scholar] [CrossRef] - Alfonso, L.; Lobbrecht, A.; Price, R. Optimization of water level monitoring network in polder systems using information theory. Water Resour. Res.
**2010**, 46, 595–612. [Google Scholar] [CrossRef] - Alfonso, L.; He, L.; Lobbrecht, A.; Price, R. Information theory applied to evaluate the discharge monitoring network of the Magdalena River. J. Hydroinform.
**2013**, 15, 211. [Google Scholar] [CrossRef] - Raso, L.; Weijs, S.V.; Werner, M. Balancing Costs and Benefits in Selecting New Information: Efficient Monitoring Using Deterministic Hydro-economic Models. Water Resour. Manag.
**2018**, 32, 339–357. [Google Scholar] [CrossRef] - Cohen, K.; Siegel, S.; McLaughlin, T. A heuristic approach to effective sensor placement for modeling of a cylinder wake. Comput. Fluids
**2006**, 35, 103–120. [Google Scholar] [CrossRef] - Yildirim, B.; Chryssostomidis, C.; Karniadakis, G.E. Efficient sensor placement for ocean measurements using low-dimensional concepts. Ocean Model.
**2009**, 27, 160–173. [Google Scholar] [CrossRef] [Green Version] - Gangopadhyay, S.; Das Gupta, A.; Nachabe, M. Evaluation of Ground Water Monitoring Network by Principal Component Analysis. Ground Water
**2001**, 39, 181–191. [Google Scholar] [CrossRef] [PubMed] - Mishra, A.K.; Coulibaly, P. Developments in hydrometric network design: A review. Rev. Geophys.
**2009**, 47, RG2001. [Google Scholar] [CrossRef] - Keum, J.; Kornelsen, K.C.; Leach, J.M.; Coulibaly, P. Entropy applications to water monitoring network design: A review. Entropy
**2017**, 19, 613. [Google Scholar] [CrossRef] - Hart, W.E.; Murray, R. Review of Sensor Placement Strategies for Contamination Warning Systems in Drinking Water Distribution Systems. J. Water Resour. Plan. Manag.
**2010**, 136, 611–619. [Google Scholar] [CrossRef] - Shannon, C.E. A Mathematical Theory of Communication. Bell Syst. Tech. J.
**1948**, 27, 379–423. [Google Scholar] [CrossRef] [Green Version] - Lee, C.; Paik, K.; Yoo, D.G.; Kim, J.H. Efficient method for optimal placing of water quality monitoring stations for an ungauged basin. J. Environ. Manag.
**2014**, 132, 24–31. [Google Scholar] [CrossRef] - Memarzadeh, M.; Mahjouri, N.; Kerachian, R. Evaluating sampling locations in river water quality monitoring networks: Application of dynamic factor analysis and discrete entropy theory. Environ. Earth Sci.
**2013**, 70, 2577–2585. [Google Scholar] [CrossRef] - Boroumand, A.; Rajaee, T. Discrete entropy theory for optimal redesigning of salinity monitoring network in San Francisco bay. Water Sci. Technol. Water Supply
**2017**, 17, 606–612. [Google Scholar] [CrossRef] - Banik, B.K.; Alfonso, L.; Torres, A.S.; Mynett, A.; Di Cristo, C.; Leopardi, A. Optimal placement of water quality monitoring stations in sewer systems: An information theory approach. Procedia Eng.
**2015**, 119, 1308–1317. [Google Scholar] [CrossRef] - Lee, J.H. Determination of optimal water quality monitoring points in sewer systems using entropy theory. Entropy
**2013**, 15, 3419–3434. [Google Scholar] [CrossRef] - Masoumi, F.; Kerachian, R. Assessment of the groundwater salinity monitoring network of the Tehran region: Application of the discrete entropy theory. Water Sci. Technol.
**2008**, 58, 765–771. [Google Scholar] [CrossRef] - Mogheir, Y.; Singh, V.P. Application of information theory to groundwater quality monitoring networks. Water Resour. Manag.
**2002**, 16, 37–49. [Google Scholar] [CrossRef] - Owlia, R.R.; Abrishamchi, A.; Tajrishy, M. Spatial-temporal assessment and redesign of groundwater quality monitoring network: A case study. Environ. Monit. Assess.
**2011**, 172, 263–273. [Google Scholar] [CrossRef] [PubMed] - Banik, B.K.; Alfonso, L.; Di Cristo, C.; Leopardi, A. Greedy algorithms for sensor location in sewer systems. Water
**2017**, 9, 856. [Google Scholar] [CrossRef] - Banik, B.K.; Alfonso, L.; Di Cristo, C.; Leopardi, A.; Mynett, A. Evaluation of Different Formulations to Optimally Locate Sensors in Sewer Systems. J. Water Resour. Plan. Manag.
**2017**, 143, 04017026. [Google Scholar] [CrossRef] - Uber, J.; Janke, R.; Murray, R.; Meyer, P. Greedy Heuristic Methods for Locating Water Quality Sensors in Distribution Systems. In Critical Transitions in Water and Environmental Resources Management; American Society of Civil Engineers: Reston, VA, USA, 2004; Volume 40737, pp. 1–9. [Google Scholar]
- Krause, P.; Boyle, D.; Bäse, F. Comparison of different efficiency criteria for hydrological model assessment. Adv. Geosci.
**2005**, 5, 89–97. [Google Scholar] [CrossRef] [Green Version] - Hoes, O.; Luxemburg, W.; Westhof, M.C.; van de Giesen, N.; Selker, J. Identifying seepage in ditches and canals in polders in The Netherlands by Distributed Temperature Sensing. Lowl. Technol. Int.
**2009**, 11, 21–26. [Google Scholar] - Delsman, J.R.; de Louw, P.G.; de Lange, W.J.; Oude Essink, G.H. Fast calculation of groundwater exfiltration salinity in a lowland catchment using a lumped celerity/velocity approach. Environ. Model. Softw.
**2017**, 96, 323–334. [Google Scholar] [CrossRef] - Kelderman, I. Slimmer Inlaten in de Haarlemmermeerpolder. Technical Report, Deltares. 2015. Available online: https://publicwiki.deltares.nl/display/ZOETZOUT/Slimmer+doorspoelen (accessed on 24 March 2019).
- Hof, A.; Schuurmans, W. Water quality control in open channels. Water Sci. Technol.
**2000**, 42, 153–159. [Google Scholar] [CrossRef] - Udell, M.; Horn, C.; Zadeh, R.; Boyd, S. Generalized low rank models. Found. Trends
^{®}Mach. Learn.**2016**, 9, 1–118. [Google Scholar] [CrossRef]

**Figure 1.**Location of the case study area (Lissertocht catchment) shown in Netherlands (adopted from [5]).

**Figure 2.**The layout of the Lissertocht catchment showing the structures, main channels and boil locations.

**Figure 3.**The spatial variation of salinity in the Lissertocht catchment for a snapshot (daily average of 15 July 2012) taken from the reference scenario; modeled with the SOBEK model.

**Figure 4.**Variance explained by the first five principal components (PCs). The solid line represents the total variance explained.

**Figure 5.**Comparison of the reconstructed salinity using three PCs and the simulated salinity at node 172.

**Figure 7.**Principal component values, ${\underline{\theta}}_{j}$, corresponding to each location for (

**a**) first (

**b**) second principal components. The boil locations are also shown with red dots in the ditches.

**Figure 8.**Optimum sensor locations obtained by minimization of root mean square error (RMSE) (indicated by red circles) and three test locations (blue squares) for showing the performance of the placement.

Node Number(s) | RMSE (mg/L) |
---|---|

543 | 140.02 |

543, 131 | 84.31 |

543, 131, 731 | 82.18 |

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## Share and Cite

**MDPI and ACS Style**

Aydin, B.E.; Hagedooren, H.; Rutten, M.M.; Delsman, J.; Oude Essink, G.H.P.; van de Giesen, N.; Abraham, E.
A Greedy Algorithm for Optimal Sensor Placement to Estimate Salinity in Polder Networks. *Water* **2019**, *11*, 1101.
https://doi.org/10.3390/w11051101

**AMA Style**

Aydin BE, Hagedooren H, Rutten MM, Delsman J, Oude Essink GHP, van de Giesen N, Abraham E.
A Greedy Algorithm for Optimal Sensor Placement to Estimate Salinity in Polder Networks. *Water*. 2019; 11(5):1101.
https://doi.org/10.3390/w11051101

**Chicago/Turabian Style**

Aydin, Boran Ekin, Hugo Hagedooren, Martine M. Rutten, Joost Delsman, Gualbert H. P. Oude Essink, Nick van de Giesen, and Edo Abraham.
2019. "A Greedy Algorithm for Optimal Sensor Placement to Estimate Salinity in Polder Networks" *Water* 11, no. 5: 1101.
https://doi.org/10.3390/w11051101