# GNSS-Based Dam Monitoring: The Application of a Statistical Approach for Time Series Analysis to a Case Study

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. GNSS Equipment, Installation and Raw Data Processing

#### 2.2. Displacement Time Series Analysis

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Presidency of the Council of Ministers, Civil Protection Department. Seismic Classification. Available online: https://rischi.protezionecivile.it/it/sismico/attivita/classificazione-sismica (accessed on 7 September 2022).
- Institute for Environmental Protection and Research. Landslides and Floods in Italy: Hazard and Risk Indicators—2021 Edition. Available online: https://www.isprambiente.gov.it/it/pubblicazioni/rapporti/dissesto-idrogeologico-in-italia-pericolosita-e-indicatori-di-rischio-edizione-2021 (accessed on 7 September 2022).
- Presidency of the Council of Ministers, Casa Italia Department. Rapporto sulla Promozione della Sicurezza dai Rischi Naturali del Patrimonio Abitativo. Available online: https://www.casaitalia.governo.it/media/1317/casa-italia_rapporto-online.pdf (accessed on 7 September 2022).
- Alonso, E.E.; Pinyol, N.M. Criteria for rapid sliding I. A review of Vaiont case. Eng. Geol.
**2010**, 114, 198–210. [Google Scholar] [CrossRef][Green Version] - Xu, Y.; Zhang, L.; Jia, J. Lessons from catastrophic dam failures in August 1975 in Zhumadian, China. In Geocongress 2008: Geosustainability and Geohazard Mitigation; Reddy, K.R., Khire, M.V., Alshawabkeh, A.N., Eds.; ASCE: Reston, VA, USA, 2008; pp. 162–169. [Google Scholar]
- CIGB ICOLD. Dam Surveillance Guide—Bulletin 158, 1st ed.; Routledge: Milton Park, UK, 2018. [Google Scholar]
- Mills, J.; Barber, D. Geomatics Techniques for Structural Surveying. J. Surv. Eng.
**2004**, 130, 56–64. [Google Scholar] [CrossRef] - De Lacy, M.C.; Ramos, M.I.; Gil, A.J.; Franco, Ó.D.; Herrera, A.M.; Avilés, M.; Domínguez, A.; Chica, J.C. Monitoring of vertical deformations by means high-precision geodetic levelling. Test case: The Arenoso dam (South of Spain). J. Appl. Geod.
**2017**, 11, 31–41. [Google Scholar] [CrossRef] - Kronenberg, P.; Casanova, N.; Inaudi, D.; Vurpillot, S. Dam monitoring with fiber optics deformation sensors. In Smart Structures and Materials 1997: Smart Systems for Bridges, Structures, and Highways; Stubbs, N., Ed.; SPIE: Bellingham, WA, USA, 1997; Volume 3043, pp. 2–11. [Google Scholar]
- Bonelli, S.; Tourment, R.; Felix, H. Analysis of earth dam monitoring data. In Selected Problems of Water Engineering, Politechnika Krakowsha Cemagref: Results of Cooperation; Nachlik, E., Witkowska, H., Szczesny, J., Ratomski, J., Givone, P., Paquier, A., Royet, P., Eds.; CEMAGREF: Antony, France, 2004; pp. 133–150. [Google Scholar]
- Alcay, S.; Yigit, C.O.; Inal, C.; Ceylan, A. Analysis of Displacement Response of the Ermenek Dam Monitored by an Integrated Geodetic and Pendulum System. Int. J. Civ. Eng.
**2017**, 16, 1279–1291. [Google Scholar] [CrossRef] - Casaca, J.; Henriques, M.J. The geodetic surveying methods in the monitoring of large dams in Portugal. In Proceedings of the XXII International Federation of Surveyors International Congress, Washington, DC, USA, 19–26 April 2002. [Google Scholar]
- Zhou, J.; Shi, B.; Liu, G.; Ju, S. Accuracy analysis of dam deformation monitoring and correction of refraction with robotic total station. PLoS ONE
**2021**, 16, e0251281. [Google Scholar] [CrossRef] [PubMed] - Casaca, J.; Braz, N.; Conde, V. Combined adjustment of angle and distance measurements in a dam monitoring network. Surv. Rev.
**2015**, 47, 181–184. [Google Scholar] [CrossRef] - Scaioni, M.; Marsella, M.; Crosetto, M.; Tornatore, V.; Wang, J. Geodetic and Remote-Sensing Sensors for Dam Deformation Monitoring. Sensors
**2018**, 18, 3682. [Google Scholar] [CrossRef][Green Version] - Wang, G.; Li, P.; Li, Z.; Ding, D.; Qiao, L.; Xu, J.; Li, G.; Wang, H. Coastal Dam Inundation Assessment for the Yellow River Delta: Measurements, Analysis and Scenario. Remote Sens.
**2020**, 12, 3658. [Google Scholar] [CrossRef] - Maltese, A.; Pipitone, C.; Dardanelli, G.; Capodici, F.; Muller, J.-P. Toward a Comprehensive Dam Monitoring: On-Site and Remote-Retrieved Forcing Factors and Resulting Displacements (GNSS and PS–InSAR). Remote Sens.
**2021**, 13, 1543. [Google Scholar] [CrossRef] - Jänichen, J.; Schmullius, C.; Baade, J.; Last, K.; Bettzieche, V.; Dubois, C. Monitoring of Radial Deformations of a Gravity Dam Using Sentinel-1 Persistent Scatterer Interferometry. Remote Sens.
**2022**, 14, 1112. [Google Scholar] [CrossRef] - Montillet, J.-P.; Szeliga, W.M.; Melbourne, T.I.; Flake, R.M.; Schrock, G. Critical Infrastructure Monitoring with Global Navigation Satellite Systems. J. Surv. Eng.
**2016**, 142, 4016014. [Google Scholar] [CrossRef][Green Version] - Barzaghi, R.; Cazzaniga, N.E.; De Gaetani, C.I.; Pinto, L.; Tornatore, V. Estimating and Comparing Dam Deformation Using Classical and GNSS Techniques. Sensors
**2018**, 18, 756. [Google Scholar] [CrossRef][Green Version] - Sanjaya, M.D.A.; Sunantyo, T.A.; Widjajanti, N. Geometric Aspects Evaluation of GNSS Control Network for Deformation Monitoring in the Jatigede Dam Region. Int. J. Remote Sens. Earth Sci.
**2019**, 15, 167–176. [Google Scholar] [CrossRef][Green Version] - Cinque, D.; Saccone, M.; Capua, R.; Spina, D.; Falcolini, C.; Gabriele, S. Experimental Validation of a High Precision GNSS System for Monitoring of Civil Infrastructures. Sustainability
**2022**, 14, 10984. [Google Scholar] [CrossRef] - Wang, Y.; Shen, D.; Chen, J.; Pei, L.; Li, Y.; Lu, X.; Zhang, L. Research and Application of a Smart Monitoring System to Monitor the Deformation of a Dam and a Slope. Adv. Civ. Eng.
**2020**, 2020, 9709417. [Google Scholar] [CrossRef] - Yeon, S.; Yeon, C. Smart Construction Monitoring for Disaster Prevention Based on Spatial Information and GNSS/USN/IoT. In Proceedings of the International Symposium on Automation and Robotics in Construction, Banff, CA, USA, 21–24 May 2019. [Google Scholar]
- Caldera, S.; Realini, E.; Barzaghi, R.; Reguzzoni, M.; Sansò, F. Experimental study on low-cost satellite-based geodetic monitoring over short baselines. J. Surv. Eng.
**2016**, 142, 4015016. [Google Scholar] [CrossRef] - Sampietro, D.; Caldera, S.; Capponi, M.; Realini, E. Geoguard—An innovative technology based on low-cost GNSS receivers to monitor surface deformations. In Proceedings of the First EAGE Workshop on Practical Reservoir Monitoring, Amsterdam, The Netherlands, 6–9 March 2017. [Google Scholar]
- Barzaghi, R.; Reguzzoni, M.; De Gaetani, C.I.; Caldera, S.; Rossi, L. Cultural heritage monitoring by low-cost GNSS receivers: A feasibility study for San Gaudenzio’s cupola, Novara. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.—ISPRS Arch.
**2019**, XLII-2/W11, 209–216. [Google Scholar] [CrossRef][Green Version] - Poluzzi, L.; Tavasci, L.; Corsini, F.; Barbarella, M.; Gandolfi, S. Low-cost GNSS sensors for monitoring applications. Appl. Geomat.
**2020**, 12, 35–44. [Google Scholar] [CrossRef] - Barzaghi, R.; Cazzaniga, N.E.; Pinto, L.; Tornatore, V. GNSS methods in dam monitoring: Case studies and future perspectives. In Proceedings of the 3rd Joint International Symposium on Deformation Monitoring (JISDM), Vienna, Austria, 30 March–1 April 2016. [Google Scholar]
- Xiao, R.; Shi, H.; He, X.; Li, Z.; Jia, D.; Yang, Z. Deformation Monitoring of Reservoir Dams Using GNSS: An Application to South-to-North Water Diversion Project, China. IEEE Access
**2019**, 7, 54981–54992. [Google Scholar] [CrossRef] - Pipitone, C.; Maltese, A.; Dardanelli, G.; Brutto, M.L.; La Loggia, G. Monitoring Water Surface and Level of a Reservoir Using Different Remote Sensing Approaches and Comparison with Dam Displacements Evaluated via GNSS. Remote Sens.
**2018**, 10, 71. [Google Scholar] [CrossRef] - Li, B.; Yang, J.; Hu, D. Dam monitoring data analysis methods: A literature review. Struct. Control Health Monit.
**2020**, 27, e2501. [Google Scholar] [CrossRef] - Jin-Ping, H.; Yu-Qun, S. Study on TMTD Statistical Model of Arch Dam Deformation Monitoring. Procedia Eng.
**2011**, 15, 2139–2144. [Google Scholar] [CrossRef][Green Version] - Tatin, M.; Briffaut, M.; Dufour, F.; Simon, A.; Fabre, J.P. Thermal displacements of concrete dams: Accounting for water temperature in statistical models. Eng. Struct.
**2015**, 91, 26–39. [Google Scholar] [CrossRef] - Mata, J.; Tavares de Castro, A.; Sá da Costa, J. Constructing statistical models for arch dam deformation. Struct. Health Monit.
**2014**, 21, 423–437. [Google Scholar] [CrossRef][Green Version] - Yigit, C.O.; Alcay, S.; Ceylan, A. Displacement response of a concrete arch dam to seasonal temperature fluctuations and reservoir level rise during the first filling period: Evidence from geodetic data. Geomatics Nat. Hazards Risk
**2007**, 7, 1489–1505. [Google Scholar] [CrossRef][Green Version] - U-blox. Product Specification. Available online: https://www.u-blox.com/en/product/neolea-m8t-series (accessed on 19 September 2022).
- Dach, R.; Hugentobler, U.; Fridez, P.; Meindl, M. Bernese GPS Software, Version 5.0; Astronomical Institute, University Bern: Bern, Switzerland, 2007. [Google Scholar]
- Baroni, L.; Cauli, F.; Farolfi, G.; Maseroli, R. Final results of the Italian “Rete Dinamica Nazionale” (RDN). In Proceedings of the EUREF Symposium, Florence, Italy, 27–29 May 2009. [Google Scholar]
- He, X.; Yu, K.; Montillet, J.-P.; Xiong, C.; Lu, T.; Zhou, S.; Ma, X.; Cui, H.; Ming, F. GNSS-TS-NRS: An Open-Source MATLAB-Based GNSS Time Series Noise Reduction Software. Remote Sens.
**2020**, 12, 3532. [Google Scholar] [CrossRef] - He, X.; Bos, M.S.; Montillet, J.P.; Fernandes, R.M.S. Investigation of the noise properties at low frequencies in long GNSS time series. J. Geod.
**2019**, 93, 1271–1282. [Google Scholar] [CrossRef] - Wackernagel, H. Multivariate Geostatistics: An Introduction with Applications, 3rd ed.; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2003. [Google Scholar]
- Barzaghi, R.; Borghi, A. Theory of second order stationary random processes applied to GPS coordinate time-series. GPS Solut.
**2018**, 22, 86. [Google Scholar] [CrossRef] - Koch, K.R. Parameter Estimation and Hypothesis Testing in Linear Models; Springer Science & Business Media: Berlin/Heidelberg, Germany, 1999. [Google Scholar]

**Figure 1.**Map of the monitored points on the dam, showing the orientation of the axes of the local reference system.

**Figure 2.**Steel pillars supporting the antennas for points PT3 (

**left**) and PT4 (

**right**). The other points are materialized with the same kinds of structures.

**Figure 3.**Fourier analysis on the x, y, z components of the point PT1. Dashed blue line is the empirical ASD, red solid line is the model ASD computed by the median filter, and yellow and green stars are the identified periodical components in the low and high-frequency ranges, respectively.

**Figure 4.**Estimated displacements for all the points. Solid lines represent the estimated displacements, including both the deterministic and stochastic components, while black dots joined by dashed lines represent the GNSS observations. The colors refer to the analyzed coordinate.

**Figure 5.**Time series of the reservoir water level (on the

**left**) and time series of air and water temperatures (on the

**right**).

**Figure 6.**Time series of filtered GNSS displacement (solid line) versus the estimated autoregressive model (dashed lines) for each point and coordinate.

**Figure 7.**Sketch of the evolution in time of the relative alignment between the four monitored points in the XY plane. Dam orthophoto as background.

Coordinate | PT1 | PT2 | PT3 | PT4 |
---|---|---|---|---|

x | cubic | cubic | cubic | cubic |

y | cubic | cubic | cubic | quadratic |

z | cubic | cubic | cubic | cubic |

**Table 2.**Estimated covariance models for all the components at all the points. Red lines represent the estimated models, while blue dots the empirical covariance functions. Units are days for the $\tau $ axis (abscissa) and ${\mathrm{mm}}^{2}$ for the covariance axis (ordinate). The ${\sigma}_{\eta}^{2}$ is the difference between the red curve and the blue dot at the origin ($\tau =0$).

PT1 | PT2 | PT3 | PT4 | |
---|---|---|---|---|

x | ||||

y | ||||

z |

**Table 3.**RMS of the differences between the estimated displacements and corresponding raw GNSS observations. Units are mm.

Coordinate | PT1 | PT2 | PT3 | PT4 |
---|---|---|---|---|

x | 0.51 | 0.50 | 0.51 | 0.53 |

y | 0.34 | 0.32 | 0.34 | 0.36 |

z | 0.93 | 0.88 | 0.88 | 0.79 |

**Table 4.**Linear correlation index computed between the filtered GNSS displacement time series and the reservoir water level.

Coordinate | PT1 | PT2 | PT3 | PT4 |
---|---|---|---|---|

x | −0.13 | −0.21 | −0.49 | −0.16 |

y | 0.68 | 0.76 | 0.63 | 0.06 |

z | 0.04 | 0.05 | −0.07 | −0.46 |

**Table 5.**Linear correlation index computed between the filtered GNSS displacement time series and the air temperature.

Coordinate | PT1 | PT2 | PT3 | PT4 |
---|---|---|---|---|

x | 0.83 | 0.78 | 0.52 | 0.82 |

y | −0.16 | −0.22 | −0.04 | −0.48 |

z | −0.66 | −0.59 | −0.66 | −0.74 |

**Table 6.**Linear correlation index computed between the filtered GNSS displacement time series and the autoregressive model of the displacement based on air temperature and water level.

Coordinate | PT1 | PT2 | PT3 | PT4 |
---|---|---|---|---|

x | 0.95 | 0.93 | 0.88 | 0.95 |

y | 0.79 | 0.90 | 0.67 | 0.53 |

z | 0.71 | 0.64 | 0.68 | 0.79 |

**Table 7.**Correlation of the displacement along the crest direction (X-axis) of all the possible couples of points.

PT Station | 2 | 3 | 4 |
---|---|---|---|

1 | 0.99 | 0.87 | 0.97 |

2 | 0.92 | 0.96 | |

3 | 0.85 |

**Table 8.**Correlation of the displacement along the stream direction (Y-axis) of all the possible couples of points.

PT Station | 2 | 3 | 4 |
---|---|---|---|

1 | 0.92 | 0.75 | 0.49 |

2 | 0.86 | 0.58 | |

3 | 0.70 |

**Table 9.**Correlation of the displacement along the vertical direction (Z-axis) of all the possible couple of points.

PT Station | 2 | 3 | 4 |
---|---|---|---|

1 | 0.96 | 0.97 | 0.69 |

2 | 0.97 | 0.70 | |

3 | 0.75 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Reguzzoni, M.; Rossi, L.; De Gaetani, C.I.; Caldera, S.; Barzaghi, R.
GNSS-Based Dam Monitoring: The Application of a Statistical Approach for Time Series Analysis to a Case Study. *Appl. Sci.* **2022**, *12*, 9981.
https://doi.org/10.3390/app12199981

**AMA Style**

Reguzzoni M, Rossi L, De Gaetani CI, Caldera S, Barzaghi R.
GNSS-Based Dam Monitoring: The Application of a Statistical Approach for Time Series Analysis to a Case Study. *Applied Sciences*. 2022; 12(19):9981.
https://doi.org/10.3390/app12199981

**Chicago/Turabian Style**

Reguzzoni, Mirko, Lorenzo Rossi, Carlo Iapige De Gaetani, Stefano Caldera, and Riccardo Barzaghi.
2022. "GNSS-Based Dam Monitoring: The Application of a Statistical Approach for Time Series Analysis to a Case Study" *Applied Sciences* 12, no. 19: 9981.
https://doi.org/10.3390/app12199981