# Treating the Hooking Effect in Satellite Altimetry Data: A Case Study along the Mekong River and Its Tributaries

^{*}

## Abstract

**:**

## 1. Introduction

**Figure 1.**Off-nadir measurement of the slant distance to the water body (${\rho}_{i}$) generates a parabolic profile of the heights above the geoid. The vertex of this parabola is the height ${H}_{0}$ at the nadir position. On the right side the situation of non-perpendicular intersection is shown.

## 2. Study Area

## 3. Data

#### 3.1. Altimetry Data

Correction | Model/Source | Reference |
---|---|---|

ionosphere | NOAA Ionosphere Climatology 2009 (NIC09) | Scharroo and Smith [30] |

dry troposphere | ECMWF (2.5°× 2.0°) for Vienna Mapping Functions 1 | Boehm et al. [31] |

wet troposphere | ECMWF (2.5°× 2.0°) for Vienna Mapping Functions 1 | Boehm et al. [31] |

polar tides | IERS Conventions 2003 | McCarthy and Petit [32] |

earth tides | IERS Conventions 2003 | McCarthy and Petit [32] |

geoid | EIGEN-6C3stat | Förste et al. [33] |

oerr | MMXO14 | Bosch et al. [34] |

#### 3.2. In-Situ Gauging Data

**Figure 2.**Study area of the lower Mekong River, indicating the gauging stations used in the validation (name of the nearest settlement and ID issued by the Mekong River Commission), the virtual stations, and the Envisat altimetry tracks.

## 4. Hooking Effect

**Figure 3.**Profile of measured Envisat data over the Mekong River near Luang Prabang (see Figure 2). The figure shows all available passes at this location. The data were retracked beforehand using the Multi-Subwaveform Retracker (MSR) (see Section 5.1). The blue region indicates the actual location of the river.

## 5. Method

#### 5.1. Multi-Subwaveform Retracker MSR

**Figure 4.**Typical waveform near the water-land transition. The identified sub-waveforms are marked with different colors. The most intense sub-waveform (red stars) is assumed to come from the water surface. The vertical lines indicate the leading edge of each sub-waveform.

**Figure 5.**Altimeter profiles obtained by two retrackers during one pass over the Mekong River. The heights obtained from all subwaveforms of the MSR are marked in black dots, the heights of the best waveforms in the MSR and Improved Threshold Retracker (ITR) data are marked as red stars and green squares, respectively.

#### 5.2. RANSAC Algorithm for Hooking Effect Estimation

- Select the initial values: A sufficient number of points to unambiguously define the model are randomly picked from all data points (e.g., 3 for a parabola and 2 for a line; see Figure 6a).
- Calculate the a-priori model: This step uses the randomly chosen points from step 1 (See Figure 6b).
- Find the consensus set:
- (a)
- The consensus set contains all data points that fit the model within a specified limit, which is determined by the accuracy of the points. Given the uncertainty in the data, if many data points fit the model the randomly picked starting points have probably homed-in on the correct model (See Figure 6c).
- (b)
- Recalculate the model using all points in the consensus set, and determine and save the new consensus set.

#### 5.3. Final Parameter Estimation

#### 5.4. Post-Processing of the Time Series

#### 5.4.1. Slope Correction

#### 5.4.2. Outlier Detection

## 6. Results, Validation and Discussion

#### 6.1. Results and Validation of the Water-Level Time Series Derived by the Hooking Approach

^{2}), and the number of points in the time series and all available Envisat cycles. For both the RMS and R

^{2}coefficient we remove the long term mean from both the altimetry and gauge time series as the gauge data is not height referenced. The long term mean is only calculated with time points which are in both time series. An interpolation is not needed because of the daily resolution of the gauge data. The hooking approach outputs two values: the first from the time series without outlier detection and the second with outlier detection (see Section 5.4.2).

^{2}lies between 0.55 and 0.97 with a mean of 0.83 (improving to 0.91 for the main river only). The RMS exceeds 2 m in only one time series (Luang Prabang 1), where the river topography is especially prone to seasonal effects (see Section 6.2). Excluding outliers (at the expense of reducing the number of data points) improves the derived time series in 8 out of 14 cases. In three cases, outlier detection does not change the results; in two cases, it slightly deteriorates the results; and in one case, the RMS decreases but also the correlation.

^{2}) of the gauging-station data is generally poorer along the tributaries of the Mekong River than along the main river. At only one station (Voeun Sai 1), R

^{2}exceeds 0.8 and the RMS is very low (0.34 m). However, the low R

^{2}at other stations does not necessarily imply defects in the hooking approach; rather, it depends largely on the quality of the gauging data. Despite our choice of gauging data (see Section 3.2), both the quality and length of the in situ data are inferior. As the time series shortens, the determination of R

^{2}becomes more unstable and more strongly influenced by single outliers. In addition, the amplitudes of the annual variations are smaller along the tributaries (6–11 m) than along the main river (10–18 m). Assuming the same uncertainty in all water levels, smaller signal amplitudes will yield smaller R

^{2}, although the magnitude of the absolute RMS difference is independent of amplitude. Along the tributaries, where the RMS is less sensitive to the signal amplitude, the RMS values are comparable (within the same order of magnitude) to those of the main river.

**Table 2.**Comparison of results obtained by the hooking approach and the median approach. The MCR code is the code of the gauging station assigned by the Mekong River Commission and the station name is the nearest settlement. The stations above the double lines reside along the main Mekong River; those below the double lines reside along the tributaries. Listed are the pass numbers of the intersecting Envisat track, the location of the intersection, the distance between the gauge and the intersection in kilometer, the intersection length of the water body measured by the altimeter in meter, and the approximate amplitude measured at the gauge in meters. The quality of the results is indicated by three measures: the root mean square error (RMS) in meter between the altimetry time series and the gauging data, the squared correlation coefficient (R

^{2}), and the number of epochs in the time series (compared to the number of all available altimeter epochs).

Hooking Approach | Median Approach | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

without Outlier Detetction | with Outlier Detetction | |||||||||||||||||

MCR Code | Station Name | Dist. | River Name | Pass | Lon | Lat | Intersect. Length | max. Amplitude | RMS | R^{2} | # Epochs | RMS | R^{2} | # Epochs | RMS | R^{2} | # Epochs | # Avail. Epochs |

010501 | Chiang Saen | 30 | Mekong River | 294 | 100.339 | 20.390 | 350 | 10 | 2.25 | 0.61 | 59 | 1.83 | 0.84 | 55 | 6.04 | 0.29 | 50 | 80 |

011201 | Luang Prabang 1 | 24 | Mekong River | 651 | 101.949 | 20.027 | 250 | 15 | 2.51 | 0.94 | 81 | 2.26 | 0.97 | 77 | 3.64 | 0.71 | 77 | 81 |

Luang Prabang 2 | 16 | Mekong River | 651 | 102.000 | 19.814 | 500 | 15 | 1.23 | 0.88 | 76 | 1.20 | 0.91 | 73 | 6.96 | 0.26 | 76 | 79 | |

011903 | Chiang Khan 1 | 60 | Mekong River | 193 | 101.612 | 18.424 | 240 | 13 | 0.87 | 0.94 | 72 | 0.86 | 0.94 | 72 | 3.58 | 0.48 | 71 | 80 |

Chiang Khan 2 | 5 | Mekong River | 193 | 101.730 | 17.919 | 2860 | 13 | 1.28 | 0.86 | 65 | 1.08 | 0.89 | 62 | 10.23 | 0.00 | 52 | 80 | |

Chiang Khan 3 | 35 | Mekong River | 666 | 101.943 | 18.084 | 340 | 13 | 1.46 | 0.91 | 70 | 1.48 | 0.90 | 67 | 1.96 | 0.75 | 73 | 80 | |

011901 | Vientiane | 19 | Mekong River | 651 | 102.436 | 17.980 | 1800 | 11 | 1.63 | 0.76 | 71 | 1.22 | 0.86 | 69 | 6.30 | 0.03 | 82 | 82 |

013402 | Mukdahan 1 | 39 | Mekong River | 21 | 104.984 | 16.283 | 3220 | 12 | 1.35 | 0.78 | 71 | 0.97 | 0.89 | 67 | 4.61 | 0.25 | 79 | 83 |

Mukdahan 2 | 60 | Mekong River | 952 | 105.068 | 16.109 | 1000 | 12 | 0.51 | 0.97 | 79 | 0.50 | 0.97 | 77 | 5.47 | 0.16 | 84 | 86 | |

120101 | Ban Mixai | 18 | Nam Khan | 666 | 102.3240 | 19.6856 | 90 | 4.50 | 1.79 | 0.58 | 46 | 1.68 | 0.70 | 43 | 3.90 | 0.32 | 67 | 81 |

350101 | Ban Keng Done | 42 | Xe Bangfai River | 479 | 105.6986 | 16.3180 | 180 | 14 | 1.44 | 0.78 | 74 | 1.40 | 0.55 | 68 | 6.32 | 0.25 | 80 | 85 |

440102 | Voeun Sai 1 | 18 | Tonle San River | 322 | 106.7130 | 13.8421 | 460 | 7 | 0.97 | 0.79 | 73 | 0.34 | 0.88 | 69 | 3.44 | 0.39 | 82 | 84 |

Voeun Sai 2 | 16 | Tonle San River | 937 | 106.9437 | 14.0426 | 320 | 7 | 0.98 | 0.61 | 63 | 0.89 | 0.59 | 61 | 3.11 | 0.30 | 81 | 85 | |

430102 | Siempang | 31 | Tonle Kong River | 479 | 106.2653 | 13.8467 | 430 | 10 | 1.49 | 0.72 | 69 | 1.49 | 0.72 | 69 | 2.29 | 0.44 | 84 | 85 |

#### 6.2. Effects Influencing the Accuracy of the Water-Level Time Series

^{2}). This effect becomes obvious at the virtual stations of Chiang Saen and Luang Prabang 1.

^{2}; for Luang Prabang 2 we find a height difference of 5 m, and area change of 2300 m

^{2}; and for the gauge the height difference is 7 m which leads to an area change of 2450 m

^{2}. Considering the assumption of the simplified river shape and the accuracy of width measurement which of least one pixel on each side of the river and a pixel size of 15 m, no significant difference can be determined.

**Figure 8.**Landsat 7 images at the Luang Prabang sites during the dry season (

**top**) and the wet season (

**bottom**).

**Figure 10.**Along-track heights at Ban Mixai, Envisat cycle 16, retracked with MSR, showing all heights of all sub-waveforms in black and the best one in red.

#### 6.3. Comparison with Other Altimetry Products

^{2}values reduce with increasing intersection length, whereas the results of the hooking approach are independent of intersection length. The median approach yields a meaningful time series only at the Chiang Khan 3 station. At all other stations, the resulting time series are of insufficient quality for further analysis.

^{2}of 0.76 compared to 0.97 m and 0.89 in our results; the Mukdahan 2 ESA time series has an RMS value of 0.43 m and R

^{2}of 0.99 compared to 0.50 m and 0.97 in our results.

#### 6.4. Application of the Hooking Approach to Other Missions

^{2}of 1.33 m and 0.85, respectively. Given the aforementioned limitations, the quality of these results is comparable to that of the Envisat analysis.

^{2}= 0.93 versus the gauging station data). The SARAL/AltiKa measurements should yield better results than Envisat, especially over smaller inland waters, because of the higher repetion rate (40 MHz) and smaller footprint. In fact, the time series derived from SARAL/AltiKa and Envisat were comparable in quality because the SARAL/AltiKa data are degraded by atmospheric water content.

## 7. Conclusions

^{2}value ranged between 0.97 and 0.55, with a mean of 0.83 (improving to 0.91 when the tributaries were excluded).

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Boergens, E.; Dettmering, D.; Schwatke, C.; Seitz, F. Treating the Hooking Effect in Satellite Altimetry Data: A Case Study along the Mekong River and Its Tributaries. *Remote Sens.* **2016**, *8*, 91.
https://doi.org/10.3390/rs8020091

**AMA Style**

Boergens E, Dettmering D, Schwatke C, Seitz F. Treating the Hooking Effect in Satellite Altimetry Data: A Case Study along the Mekong River and Its Tributaries. *Remote Sensing*. 2016; 8(2):91.
https://doi.org/10.3390/rs8020091

**Chicago/Turabian Style**

Boergens, Eva, Denise Dettmering, Christian Schwatke, and Florian Seitz. 2016. "Treating the Hooking Effect in Satellite Altimetry Data: A Case Study along the Mekong River and Its Tributaries" *Remote Sensing* 8, no. 2: 91.
https://doi.org/10.3390/rs8020091