# A Novel Multi-Candidate Multi-Correlation Coefficient Algorithm for GOCI-Derived Sea-Surface Current Vector with OSU Tidal Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data Set

#### 2.1. In-Situ Data

^{2}, and the area of the buoy under the sea surface is (0.031 + 0.7) m

^{2}. The ratio of the upper and lower areas was as low as 0.04. The center point of the sail below the sea surface was 3 m underwater. The structure of the drifting buoy shows that the movements of the drifting buoy are mainly controlled by SSC.

#### 2.2. GOCI Data

#### 2.3. OSU Tidal Current Model Data

## 3. Methodology

#### 3.1. GOCI Data Processing

#### 3.2. Drifting Buoy Data Processing

#### 3.3. Multi-Candidate Multi-Correlation Coefficient Optimization Algorithm

#### 3.4. Evaluation Method

## 4. Results

#### 4.1. Vector Processing Results Based on the Multi-Correlation Coefficient Algorithm

#### 4.2. Average Magnitude and Angular Error

#### 4.3. OSU Tidal Model Data Evaluation

#### 4.4. SSC Mapping from GOCI and OSU

## 5. Discussion

#### 5.1. The Proportion of Accurate Vectors

#### 5.2. Window Size Selection

#### 5.3. Condition Analysis of Current Detection

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The study area and its bathymetry. From light blue to dark blue, the water depth ranges from 10 to 200 m. The color lines show the tracks of three drifting buoys. Red dots represent the buoy locations of selected cases, which are distributed in the northern Yellow Sea, southern Yellow Sea, and East China Sea from north to south.

**Figure 3.**A schematic diagram of the MCC algorithm for estimating SSC field. Taking the first invertible current field as an example, the images on the left and right represent satellite remote sensing images observed in the same sea area and on the same day at 8:30 and 9:30, respectively. The solid box in the left panel is the template window, the solid box in the right panel is the matching window, and the dashed box is the same template window as that in the left panel.

**Figure 4.**(

**a**) A vector diagram formed by calculating the buoy points (A, B, and C represent the three points on the projection surface of the sphere, and the angle of the “arc” on the sphere at that point, respectively; a, b, and c represent the arc of the ABC three-point pair, O is the center of the sphere). (

**b**) A right triangle composed of three points A, B, and C and the coordinates of each point.

**Figure 5.**Workflow of the OSU-based multi-correlation coefficient algorithm to identify and substitute spurious vectors. MCC: Maximum cross-coefficient.

**Figure 6.**(

**a**) An illustration of SSC vector estimation by multi-correlation coefficient inversion algorithm. $T$ is the matching template, ${T}^{\prime}$ is the mapping of the matching template at the same position in the search area, ${I}_{1}$, ${I}_{2}$ and ${I}_{3}$ are the regions searched by the matching template, and ${a}_{1}$, ${a}_{2}$ and ${a}_{3}$ are the current field vectors under the corresponding correlation coefficients; (

**b**) an illustration of vector direction judgment. (

**c**) An illustration of spurious vector judgment.

**Figure 7.**A group of daily surface vectors obtained by the multi-correlation coefficient algorithm with TSM as the background on 13 August 2013. The three colored vector arrows and boxes in (

**a**–

**g**) correspond to the SSC vectors and matching windows obtained under the first three correlation coefficients, respectively. The red box in (

**h**) is where subplots (

**a**–

**g**) are located.

**Figure 8.**(

**a**) Distribution of measured data and case data, where the red dots are the selected measured data points, the red crosses are the selected data case points, and the blue crosses are the remaining case points. (

**b**) Comparison results of GOCI vectors under different correlation coefficients. Black represents the first vector, blue represents the second vector, red represents the third vector, and the dotted arrow represents the spurious vector.

**Figure 9.**(

**a**)-Ⅰ showing the observed SSC vectors from the drifting buoy (BUOY; black arrows) and estimated from the satellite (GOCI; blue arrows) in the East China Sea. The blue dashed arrows represent the spurious vectors, and the red dashed arrows represent the substitution vectors. (

**a**)-Ⅱ showing the corresponding OSU tidal current vectors. The rotation direction can be determined. (

**b**) Observed SSC vectors from drifting buoy and estimated from GOCI in the southern Yellow Sea. (

**c**) Observed SSC vectors from drifting buoy and estimated from GOCI in the northern Yellow Sea.

**Figure 10.**(

**a**) Comparison results of partial continuous measured data and OSU model data in this study. (

**b**) Comparison of buoy vectors and OSU vectors for some case data during the GOCI active period, which is 8:30–15:30 local time.

**Figure 13.**(

**a**) The vector proportion obtained under each correlation coefficient after algorithm processing. MCC 1st, MCC 2cd, and MCC 3rd represent the vectors obtained under the first, second and third correlation coefficients, respectively. (

**b**) The proportion of replacement vectors in each period after multi-correlation coefficient algorithm processing.

**Figure 14.**(

**a**–

**g**): SSC vectors obtained under each window size parameter. Red dots in (

**h**) are the position of the target vectors selected.

Area | Time | Original Data | Angular Limitation Filter | Multi-Correlation Coefficient Optimization | |||
---|---|---|---|---|---|---|---|

AME | AAE (°) | AME | AAE (°) | AME | AAE (°) | ||

ECS | 10 August | 0.27 | 18.83 | 0.26 | 13.35 | 0.23 | 13.43 |

11 August | 0.34 | 55.01 | 0.25 | 49.42 | 0.26 | 49.84 | |

13 August | 0.78 | 33.16 | 0.86 | 19.42 | 0.75 | 18.92 | |

SYS | 27 June | 0.34 | 40.46 | 0.37 | 40.08 | 0.33 | 38.14 |

11 July | 0.61 | 34.89 | 0.62 | 26.93 | 0.61 | 25.84 | |

16 July | 1.61 | 42.87 | 1.50 | 46.99 | 1.45 | 30.39 | |

NYS | 5 August | 0.40 | 16.66 | 0.40 | 11.26 | 0.41 | 14.08 |

6 August | 0.47 | 66.88 | 0.47 | 72.31 | 0.52 | 54.83 | |

7 August | 0.35 | 31.59 | 0.40 | 31.25 | 0.38 | 27.06 | |

Average | 0.57 | 37.82 | 0.57 | 34.56 | 0.55 | 30.28 |

Buoy Number | Number of Sites | BUOY-ACS (m/s) | OSU-ACS (m/s) | AAE (°) |
---|---|---|---|---|

1132711 | 1759 | 0.43 | 0.41 | 44.16 |

1131901 | 1787 | 0.28 | 0.34 | 49.90 |

1227890 | 320 | 0.45 | 0.38 | 37.82 |

Average | 1289 | 0.39 | 0.38 | 43.96 |

MCC | W (=H) | W1 | W2 | W3 | W4 | W5 | W6 | W7 |
---|---|---|---|---|---|---|---|---|

T_{sub} | pixels | 10 | 10 | 20 | 20 | 28 | 20 | 28 |

S_{sub} | pixels | 24 | 36 | 24 | 36 | 36 | 48 | 48 |

_{sub}: template window; S

_{sub}: search window.

W1 | W2 | W3 | W4 | W5 | W6 | W7 | |
---|---|---|---|---|---|---|---|

Max-speed (m/s) | 1.11 | 2.95 | 1.57 | 1.39 | 1.18 | 2.95 | 1.46 |

Min-speed (m/s) | 0.23 | 0.36 | 0.79 | 0.22 | 0.01 | 0.15 | 0.05 |

Ave-speed (m/s) | 0.60 | 1.09 | 1.00 | 0.68 | 0.28 | 0.74 | 0.51 |

PCV (%) | 86.54 | 97.65 | 56.20 | 96.58 | 70.09 | 87.61 | 77.56 |

**Table 5.**AME and AAE values of the three target vectors and their adjacent vectors under each window size.

Target Vector | W1 | W2 | W3 | W4 | ||||
---|---|---|---|---|---|---|---|---|

AME | AAE(°) | AME | AAE(°) | AME | AAE(°) | AME | AAE(°) | |

Ⅰ | 0.07 | 10.43 | 0.10 | 9.70 | 0.09 | 2.08 | 0.09 | 13.63 |

Ⅱ | 0.24 | 54.72 | 0.36 | 42.48 | —— | —— | 0.76 | 39.24 |

Ⅲ | 0.07 | 16.70 | 0.26 | 29.73 | —— | —— | 0.45 | 29.94 |

Average | 0.13 | 27.28 | 0.24 | 27.31 | —— | —— | 0.43 | 27.60 |

Target Vector | W5 | W6 | W7 | |||||

AME | AAE(°) | AME | AAE(°) | AME | AAE(°) | |||

Ⅰ | 0.20 | 5.21 | 0.10 | 13.18 | 0.13 | 11.76 | ||

Ⅱ | 6.61 | 59.76 | 0.69 | 56.20 | 0.38 | 20.41 | ||

Ⅲ | 0.46 | 23.16 | 0.49 | 32.10 | —— | —— | ||

Average | 2.42 | 29.37 | 0.43 | 33.83 | —— | —— |

Date | Time | Chl-a | Rrs | TSM | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Number of Vectors | AME | AAE (°) | Number of Vectors | AME | AAE (°) | Number of Vectors | AME | AAE (°) | ||

27 June | 11:30–12:30 | 1010 | 1.13 | 21.83 | 955 | 1.22 | 27.04 | 1005 | 0.67 | 13.62 |

12:30–13:30 | 976 | 1.90 | 27.15 | 952 | 0.54 | 16.17 | 981 | 1.59 | 18.31 | |

11 July | 11:30–12:30 | 472 | 0.30 | 13.99 | 448 | 0.62 | 13.51 | 476 | 0.53 | 15.34 |

12:30–13:30 | 580 | 0.25 | 6.44 | 487 | 0.50 | 16.10 | 553 | 0.52 | 12.54 | |

16 July | 11:30–12:30 | 467 | 0.32 | 24.74 | 464 | 0.76 | 39.16 | 484 | 0.32 | 29.59 |

12:30–13:30 | 534 | 0.73 | 15.95 | 503 | 1.42 | 24.14 | 541 | 0.99 | 12.34 | |

Average | 673 | 0.77 | 18.35 | 634 | 0.84 | 22.69 | 673 | 0.77 | 16.96 |

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**MDPI and ACS Style**

Cui, H.; Chen, J.; Cao, Z.; Huang, H.; Gong, F.
A Novel Multi-Candidate Multi-Correlation Coefficient Algorithm for GOCI-Derived Sea-Surface Current Vector with OSU Tidal Model. *Remote Sens.* **2022**, *14*, 4625.
https://doi.org/10.3390/rs14184625

**AMA Style**

Cui H, Chen J, Cao Z, Huang H, Gong F.
A Novel Multi-Candidate Multi-Correlation Coefficient Algorithm for GOCI-Derived Sea-Surface Current Vector with OSU Tidal Model. *Remote Sensing*. 2022; 14(18):4625.
https://doi.org/10.3390/rs14184625

**Chicago/Turabian Style**

Cui, He, Jianyu Chen, Zhenyi Cao, Haiqing Huang, and Fang Gong.
2022. "A Novel Multi-Candidate Multi-Correlation Coefficient Algorithm for GOCI-Derived Sea-Surface Current Vector with OSU Tidal Model" *Remote Sensing* 14, no. 18: 4625.
https://doi.org/10.3390/rs14184625