# Seasonal Variation of GPS-Derived the Principal Ocean Tidal Constituents’ Loading Displacement Parameters Based on Moving Harmonic Analysis in Hong Kong

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Region

#### 2.2. GPS Data

#### 2.3. Tide Gauge Data

#### 2.4. Mass Loading Data

#### 2.5. Moving Harmonic Analysis Method

#### 2.6. Enhanced Harmonic Analysis

## 3. Results

#### 3.1. Analysis of Time-Varying Characteristics of Amplitude

#### 3.2. Analysis of Time-Varying Characteristics of Phase

#### 3.3. Accuracy Verification of Moving Harmonic Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geographical distribution of Global Navigation Satellite System (GNSS) station (Black spot) and tide gauge station (Black pentagram).

**Figure 2.**Seasonal variation of the amplitude parameter of K1 ocean tide loading displacement (OTLD).

**Figure 9.**Seasonal variations of amplitude parameters of 6 principal tidal constituents at Quarry Bay.

Site | Index | M2 | S2 | N2 | K1 | O1 | Q1 |
---|---|---|---|---|---|---|---|

HKKT | Range | 9.7 | 9.3 | 15.2 | 13.8 | 20.2 | 20.4 |

Cycle | 1,1/2,1/3,1/4 | 1,1/2,1/3 | 1,1/2 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | |

HKMW | Range | 9.4 | 9.6 | 15.3 | 12.5 | 19.3 | 21.5 |

Cycle | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | |

HKNP | Range | 9.6 | 9.4 | 16.9 | 12.8 | 19.9 | 18.6 |

Cycle | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | |

HKOH | Range | 8.9 | 9.5 | 14.2 | 12.3 | 18.6 | 15.7 |

Cycle | 1,1/2,1/3 | 1,1/2,1/3,1/4 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2 | |

HKSC | Range | 9.2 | 8.8 | 16.7 | 13.6 | 20.1 | 17.5 |

Cycle | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | |

HKST | Range | 9.0 | 9.3 | 17.1 | 14.1 | 19.5 | 18.9 |

Cycle | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 | 1,1/2,1/3 |

**Table 2.**Root mean squared error (RMSE) statistics of moving harmonic analysis (MHA)-derived OTLD parameters.

Ocean Tidal Constituents | O1 | K1 | Q1 | M2 | S2 | N2 | |
---|---|---|---|---|---|---|---|

Amplitude (mm) | MAX | 0.81 | 0.79 | 0.56 | 0.80 | 0.68 | 0.48 |

MIN | 0.05 | 0.07 | 0.02 | 0.09 | 0.07 | 0.03 | |

MEAN | 0.49 | 0.54 | 0.25 | 0.31 | 0.44 | 0.22 | |

STD | 0.12 | 0.15 | 0.09 | 0.10 | 0.10 | 0.09 | |

Phase (°) | MAX | 5.21 | 10.25 | 11..2 | 7.24 | 6.25 | 10.24 |

MIN | 0.75 | 2.01 | 3.61 | 1.01 | 1.32 | 2.68 | |

MEAN | 2.33 | 7.15 | 7.14 | 3.49 | 4.41 | 3.21 | |

STD | 1.15 | 1.51 | 1.44 | 1.31 | 1.03 | 1.21 |

Tidal Constituents | Variation of the OTLD’s Amplitude by GNSS | Variation of the Ocean Tide’s Amplitude by Tide Gauge |
---|---|---|

K1 | About 8.3–11.2% | About 26.0% |

O1 | About 4–6.3% | About 6.3% |

Q1 | About 17.6–25.1% | About 26.3% |

M2 | About 4–8.2% | About 4.8–5.1% |

N2 | About 13.8–21.2% | About 22.2% |

S2 | About 14.7–22.2% | About 20.8% |

**Table 4.**Difference of seasonal variation sequence of amplitude parameter with/without hydrological loading (HYDL) correction (mm).

Ocean Tidal Constituents | M2 | S2 | N2 | K1 | O1 | Q1 | |
---|---|---|---|---|---|---|---|

HKKT | MAX | 0.4 | 0.3 | 0.3 | 0.1 | 0.5 | 0.4 |

MIN | −1.2 | −3.8 | −2.4 | −1.6 | −0.8 | −1.8 | |

MEAN | −0.1 | −0.4 | −0.5 | −0.3 | −0.1 | −0.3 | |

STD | 0.3 | 0.2 | 0.2 | 0.3 | 0.1 | 0.2 | |

HKMW | MAX | 1.0 | 5.0 | 2.2 | 1.3 | 0.8 | 0.7 |

MIN | −1.6 | −1.5 | −0.9 | −1.4 | −0.9 | −1.0 | |

MEAN | −0.2 | 0.1 | 0.2 | −0.2 | −0.1 | −0.1 | |

STD | 0.4 | 0.3 | 0.4 | 0.3 | 0.1 | 0.3 | |

HKNP | MAX | 5.2 | 7.2 | 2.6 | 4.7 | 3.4 | 1.5 |

MIN | −1.1 | −1.7 | −1.1 | −1.1 | −0.3 | −1.1 | |

MEAN | 0.2 | 0.4 | 0.4 | 0.1 | 0.6 | 0.4 | |

STD | 0.3 | 0.5 | 0.4 | 0.7 | 1.01 | 0.5 | |

HKOH | MAX | 0.7 | 0.2 | 0.6 | 0.5 | 0.4 | 0.3 |

MIN | −1.6 | −2.0 | −1.2 | −0.7 | −0.9 | −0.7 | |

MEAN | −0.3 | −0.5 | −0.4 | −0.1 | −0.2 | −0.2 | |

STD | 0.3 | 0.3 | 0.2 | 0.3 | 0.1 | 0.2 | |

HKSC | MAX | 6.2 | 8.1 | 2.5 | 5.2 | 3.3 | 1.7 |

MIN | −1.3 | −2.5 | −1.8 | −1.6 | −1.3 | −1.0 | |

MEAN | 1.1 | 1.3 | 0.6 | 1.2 | 0.4 | 0.4 | |

STD | 2.0 | 2.4 | 0.9 | 2.2 | 1.0 | 0.6 | |

HKST | MAX | 0.8 | 2.7 | 0.7 | 0.4 | 1.4 | 0.8 |

MIN | −1.5 | −2.3 | −0.9 | −1.3 | −1.1 | −1.2 | |

MEAN | −0.3 | −0.3 | 0.2 | −0.2 | 0.1 | −0.3 | |

STD | 0.2 | 0.6 | 0.1 | 0.2 | 0.3 | 0.2 |

**Table 5.**Difference of seasonal change sequence of amplitude parameter with/without atmospheric loading (ATL) correction (mm).

Ocean Tidal Constituents | M2 | S2 | N2 | K1 | O1 | Q1 | |
---|---|---|---|---|---|---|---|

HKKT | MAX | 0.6 | 0.2 | 0.4 | 0.1 | 1.1 | 0.6 |

MIN | −2.4 | −3.2 | −2.8 | −2.4 | −0.9 | −1.5 | |

MEAN | −1.1 | −1.4 | −1.5 | −1.2 | 0.7 | −0.8 | |

STD | 1.1 | 1.2 | 1.2 | 1.2 | 0.6 | 0.9 | |

HKMW | MAX | 1.3 | 5.4 | 2.6 | 1.5 | 0.6 | 1.2 |

MIN | −2.2 | −2.3 | −2.5 | −1.5 | −1.3 | −1.6 | |

MEAN | −1.1 | −1.2 | −0.8 | −0.9 | −0.7 | −1.1 | |

STD | 1.0 | 1.3 | 1.4 | 1.2 | 0.6 | 1.1 | |

HKNP | MAX | 5.5 | 7.4 | 5.6 | 4.5 | 3.5 | 3.4 |

MIN | −2.3 | −2.2 | −1.8 | −2.4 | −0.8 | −1.5 | |

MEAN | 1.2 | 1.3 | 1.2 | 1.3 | 0.6 | 1.7 | |

STD | 2.3 | 2.2 | 1.9 | 1.6 | 1.2 | 1.1 | |

HKOH | MAX | 0.6 | 0.4 | 1.0 | 0.5 | 0.7 | 1.2 |

MIN | −1.8 | −2.4 | −2.5 | −1.7 | −0.9 | −1.1 | |

MEAN | −1.1 | −1.3 | −1.4 | −1.1 | 0.1 | 0.6 | |

STD | 1.0 | 1.1 | 1.3 | 0.8 | 0.4 | 0.9 | |

HKSC | MAX | 6.7 | 8.4 | 7.5 | 5.7 | 3.0 | 4.8 |

MIN | −1.4 | −2.7 | −3.2 | −1.3 | −1.1 | −0.9 | |

MEAN | 1.3 | 1.6 | 2.4 | 1.1 | 0.5 | 2.0 | |

STD | 2.2 | 2.8 | 2.3 | 2.0 | 1.1 | 1.3 | |

HKST | MAX | 0.7 | 2.9 | 1.9 | 0.3 | 1.4 | 2.0 |

MIN | −2.1 | −2.5 | −2.6 | −2.0 | −1.2 | −1.6 | |

MEAN | −1.4 | −1.4 | −1.3 | −1.1 | 0.8 | 0.8 | |

STD | 1.2 | 1.1 | 1.3 | 1.0 | 0.9 | 0.7 |

**Table 6.**Difference of seasonal change sequence of amplitude parameter with/without non-tidal ocean loading (NTOL) correction (mm).

Ocean Tidal Constituents | M2 | S2 | N2 | K1 | O1 | Q1 | |
---|---|---|---|---|---|---|---|

HKKT | MAX | 1.5 | 2.5 | 1.6 | 1.5 | 3.5 | 2.8 |

MIN | −1.7 | −3.2 | −1.7 | −1.4 | −2.2 | −2.5 | |

MEAN | −0.2 | −0.4 | −0.3 | −0.2 | −0.1 | 0.2 | |

STD | 0.5 | 0.2 | 0.3 | 0.4 | 0.7 | 0.5 | |

HKMW | MAX | 1.6 | 6.1 | 0.9 | 1.1 | 3.0 | 3.4 |

MIN | −2.7 | −4.1 | −1.6 | −3.2 | −2.4 | −2.5 | |

MEAN | −0.2 | 0.1 | −0.5 | −0.2 | −0.2 | 0.4 | |

STD | 0.5 | 0.6 | 0.6 | 0.6 | 0.7 | 0.8 | |

HKNP | MAX | 5.2 | 7.5 | 4.2 | 4.6 | 3.9 | 3.8 |

MIN | −1.4 | −2.1 | −2.1 | −1.5 | −1.6 | −1.5 | |

MEAN | 0.2 | 0.8 | 0.9 | 0.3 | 0.6 | 0.9 | |

STD | 0.2 | 0.7 | 0.8 | 0.9 | 0.3 | 0.6 | |

HKOH | MAX | 2.5 | 3.5 | 1.9 | 1.3 | 2.4 | 2.7 |

MIN | −2.1 | −3.7 | −2.1 | −1.1 | −2.5 | −2.6 | |

MEAN | −0.2 | −0.5 | −0.3 | −0.3 | 0.1 | 0.3 | |

STD | 0.6 | 0.1 | 0.5 | 0.5 | 0.7 | 0.6 | |

HKSC | MAX | 6.6 | 8.3 | 4.2 | 5.5 | 4.2 | 3.9 |

MIN | −1.7 | −2.7 | −3.8 | −1.6 | −2.5 | −2.6 | |

MEAN | 1.6 | 0.5 | 0.3 | 0.3 | 0.6 | 0.4 | |

STD | 0.3 | 0.1 | 0.3 | 0.1 | 0.2 | 0.5 | |

HKST | MAX | 1.6 | 3.7 | 2.2 | 1.7 | 2.6 | 2.1 |

MIN | −2.4 | −3.5 | −3.2 | −1.4 | −2.5 | −2.6 | |

MEAN | −0.1 | −0.3 | −0.5 | 0 | 0 | −0.1 | |

STD | 0.5 | 1.1 | 0.7 | 0.5 | 0.5 | 0.6 |

**Table 7.**Contribution rate of the mass loading at each station to the seasonal variation of OTLD parameter.

Correction | Site | M2 | S2 | N2 | K1 | O1 | Q1 |
---|---|---|---|---|---|---|---|

ATL | HKKT | 9.17% | 12.74% | 5.21% | 7.54% | 4.04% | 4.31% |

HKMW | 11.05% | 4.79% | 4.24% | 5.54% | 5.62% | 3.24% | |

HKNP | 10.11% | 5.13% | 6.16% | 10..17% | 9.14% | 3.99% | |

HKOH | 9.40% | 10..01% | 5.67% | 5.01% | 2.96% | 2.10% | |

HKSC | 7.46% | 3.95% | 4.09% | 6.72% | 4.68% | 2.07% | |

HKST | 6.87% | 7.26% | 5.81% | 6.18% | 6.85% | 3.61% | |

HYDL | HKKT | 0.43% | 0.16% | 0.09% | 0.57% | 0.84% | 0.12% |

HKMW | 0.06% | 0.21% | 0.11% | 0.61% | 0.75% | 0.09% | |

HKNP | 0.29% | 0.69% | 0.41% | 0.34% | 0.23% | 0.47% | |

HKOH | 0.58% | 0.03% | 0.08% | 0.18% | 0.40% | 0.29% | |

HKSC | 0.29% | 0.64% | 0.54% | 0.21% | 0.26% | 0.34% | |

HKST | 0.34% | 0.37% | 0.24% | 1.69% | 0.11% | 0.18% | |

NTOL | HKKT | 0.96% | 0.35% | 0.34% | 1.01% | 0.67% | 0.38% |

HKMW | 0.27% | 1.01% | 0.71% | 0.64% | 0.61% | 0.51% | |

HKNP | 1.30% | 0.62% | 0.59% | 0.94% | 0.54% | 0.49% | |

HKOH | 1.04% | 0.85% | 0.61% | 0.54% | 0.41% | 0.24% | |

HKSC | 0.78% | 0.71% | 0.54% | 0.69% | 1.14% | 0.62% | |

HKST | 0.89% | 0.69% | 0.83% | 0.51% | 0.87% | 0.58% |

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**MDPI and ACS Style**

Zhou, M.; Liu, X.; Yuan, J.; Jin, X.; Niu, Y.; Guo, J.; Gao, H.
Seasonal Variation of GPS-Derived the Principal Ocean Tidal Constituents’ Loading Displacement Parameters Based on Moving Harmonic Analysis in Hong Kong. *Remote Sens.* **2021**, *13*, 279.
https://doi.org/10.3390/rs13020279

**AMA Style**

Zhou M, Liu X, Yuan J, Jin X, Niu Y, Guo J, Gao H.
Seasonal Variation of GPS-Derived the Principal Ocean Tidal Constituents’ Loading Displacement Parameters Based on Moving Harmonic Analysis in Hong Kong. *Remote Sensing*. 2021; 13(2):279.
https://doi.org/10.3390/rs13020279

**Chicago/Turabian Style**

Zhou, Maosheng, Xin Liu, Jiajia Yuan, Xin Jin, Yupeng Niu, Jinyun Guo, and Hao Gao.
2021. "Seasonal Variation of GPS-Derived the Principal Ocean Tidal Constituents’ Loading Displacement Parameters Based on Moving Harmonic Analysis in Hong Kong" *Remote Sensing* 13, no. 2: 279.
https://doi.org/10.3390/rs13020279