# Validation of an Empirical Subwaveform Retracking Strategy for SAR Altimetry

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

#### 2.1. Data

#### 2.2. Methods: Retracking

#### 2.2.1. Functional Form

#### 2.2.2. Leading Edge Detection

#### 2.2.3. Choice of Trailing Edge Slope

#### 2.2.4. Subwaveform Retracking

#### 2.3. Methods: Sea State Bias

#### 2.4. Methods: Comparison with Tide Gauges

#### 2.5. Methods: Crossover Analysis

#### 2.6. Methods: Gridded Sea-Level Variance Analysis

#### 2.7. Methods: Spectral Analysis

## 3. Results

#### 3.1. Sea State Bias

#### 3.2. Comparison with Tide Gauges

#### 3.3. Crossover Analysis

#### 3.4. Gridded Sea Level Variance

#### 3.5. Spectral Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Three examples of ALES + SAR fitting applied to a SAR altimetry waveform from (

**a**) typical open ocean conditions, (

**b**) coastal-like interference along the trailing edge and (

**c**) lead-like peaky leading edge.

**Figure 2.**Map of root mean squared error (RMSE) and correlation (r) computed against the TGs for ALES + SAR, SAMOSA2 and SAMOSA+ (considering altimetry points from 0 to 3 km from the coast). The results are displayed for ALES + SAR (left panel) and then for SAMOSA2 and SAMOSA+ as the difference from the ALES + SAR results (middle and right panels respectively). The number of pairs denotes the amount of comparable altimeter and TG sea level measurements and is reported for SAMOSA2 and SAMOSA+ as a difference from ALES + SAR results in the left panel. Grey dots denote not enough good data to form time series or statistically insignificant correlation (p-value > 0.05).

**Figure 3.**Zoom of Figure 2 in the Danish Straits.

**Figure 4.**Map of root mean squared error (RMSE) and correlation (r) computed against the TGs for ALES + SAR, SAMOSA2 and SAMOSA+ (considering altimetry points from 3 to 10 km from the coast). The results are displayed for ALES + SAR (left panel) and then for SAMOSA2 and SAMOSA+ as the difference from the ALES + SAR results (middle and right panels respectively). The number of pairs denotes the amount of comparable altimeter and TG sea level measurements and is reported for SAMOSA2 and SAMOSA+ as a difference from ALES + SAR results in the left panel. Grey dots denote not enough good data to form time series or statistically insignificant correlation (p-value > 0.05).

**Figure 5.**Zoom of Figure 4 in the Danish Straits.

**Figure 6.**Range bias of Sentinel-3A (ALES+SAR retracker) with respect to Jason-3 (per 10-day Jason-3 cycle) as estimated by a multi-mission crossover analysis.

**Figure 7.**The gridded SLAVA from the (

**a**) SAMOSA2 and (

**b**) ALES+SAR retrackers respectively as well as (

**c**) the scaled differences between the respective variances. The coastal grid cells, i.e., grid cells within two degrees of the coast, have been removed due to the two-degree grid size not giving an accurate representation of the coastal variances.

**Figure 8.**The 3-km gridded standard deviation of sea level observations obtained using the SAMOSA2 and the ALES+SAR retrackers. The greyed out area is designated to show the first 10 km of the comparison.

**Figure 9.**PSD spectrum of sea surface heights computed using ALES + SAR and SAMOSA2. The spectrum is based on 8 full cycles (cycles 30 to 37) over the global ocean. To avoid outliers, points located closer than 20 km to the coast and sea level anomalies exceeding 2 m in absolute value are excluded.

**Table 1.**Variance at crossover locations (XO var) before and after the application of the SSB. The first row provides the corresponding numbers reported in [27] for a global solution using 1 Hz data.

Dataset | XO var before SSB [cm^{2}] | XO var after SSB [cm^{2}] | Variance Explained |
---|---|---|---|

Gaspar et al. (1994) [27] | 127.7 | 120.4 | 6% |

SGDR Jason-1 Mediterranean Sea | 135.6 | 108.4 | 20% |

ALES + SAR Sentinel-3A | 106.0 | 84.9 | 20% |

**Table 2.**Statistics of the validation of ALES + SAR, SAMOSA+ and SAMOSA2 sea level retrievals against tide gauge data: correlation, root mean square error and number of paired altimetry and tide gauge measurements. Altimetry data are grouped according to their distance to the coast (0–3 km and 3–10 km). Valid ALES + SAR retrievals are selected using a quality flag based on classification, applied to distinguish returns from leads among sea ice, and fitting error. The same statistics derived using SAMOSA2 sea level retrievals on the same points are shown for comparison. SAMOSA+ retrievals are filtered using the same quality flag based on classification and their own misfit quality flag.

Dataset | Correlation [r] | RMSE [m] | Number of Points |
---|---|---|---|

ALES + SAR (0–3 km) | 0.50 | 0.35 | 4826 |

SAMOSA+ (0–3 km) | 0.59 | 0.27 | 2177 |

SAMOSA2 (0–3 km) | 0.44 | 0.43 | 4735 |

ALES + SAR (3–10 km) | 0.70 | 0.22 | 4502 |

SAMOSA+ (3–10 km) | 0.58 | 0.26 | 3978 |

SAMOSA2 (3–10 km) | 0.38 | 0.49 | 4415 |

**Table 3.**Results of SXO analysis: mean of crossover differences (mxo), mean of absolute crossover differences (maxo), standard deviation of crossover differences (stdxo), averages standard deviation of crossovers (msxo) [all in cm], as well as number of SXO points. Statistics are given for all crossovers (first two rows) as well as for coastal points only (closer than 10 km from the coast).

Dataset | mxo | maxo | stdxo | msxo | Number of SXO |
---|---|---|---|---|---|

ALES + SAR (all) | −0.18 | 5.27 | 7.77 | 1.55 | 657,731 |

SAMOSA2 (all) | −0.08 | 5.07 | 7.58 | 1.66 | 663,743 |

ALES + SAR (<10 km) | −1.62 | 9.60 | 16.79 | 1.30 | 432 |

SAMOSA2 (<10 km) | −1.51 | 9.65 | 16.87 | 1.47 | 429 |

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**MDPI and ACS Style**

Passaro, M.; Rautiainen, L.; Dettmering, D.; Restano, M.; Hart-Davis, M.G.; Schlembach, F.; Särkkä, J.; Müller, F.L.; Schwatke, C.; Benveniste, J.
Validation of an Empirical Subwaveform Retracking Strategy for SAR Altimetry. *Remote Sens.* **2022**, *14*, 4122.
https://doi.org/10.3390/rs14164122

**AMA Style**

Passaro M, Rautiainen L, Dettmering D, Restano M, Hart-Davis MG, Schlembach F, Särkkä J, Müller FL, Schwatke C, Benveniste J.
Validation of an Empirical Subwaveform Retracking Strategy for SAR Altimetry. *Remote Sensing*. 2022; 14(16):4122.
https://doi.org/10.3390/rs14164122

**Chicago/Turabian Style**

Passaro, Marcello, Laura Rautiainen, Denise Dettmering, Marco Restano, Michael G. Hart-Davis, Florian Schlembach, Jani Särkkä, Felix L. Müller, Christian Schwatke, and Jérôme Benveniste.
2022. "Validation of an Empirical Subwaveform Retracking Strategy for SAR Altimetry" *Remote Sensing* 14, no. 16: 4122.
https://doi.org/10.3390/rs14164122