# Impact of Altimeter Data Processing on Sea Level Studies

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study area and data used

## 3. Data Processing

#### 3.1. Computation of along-track sea level anomalies

- DataSet1 - all corrections according to Table 1.
- DataSet3 - all corrections according to Table 1, except for the wet tropospheric correction where a slightly modified version of the Ruf model [35] for modelling the TMR drift has been used instead. The modification consisted in the extension of a constant drift rate until cycle 241, followed by a constant drift correction after cycle 241, according to [28]. The parameter ΔL defined in [35] has been replaced by$$\{\begin{array}{ll}\mathrm{\Delta}\text{L}=0.0186722*\text{cycle}\_\text{number dB}/\text{cycle}\hfill & \text{if cycle}\_\text{number}<241\hfill \\ \mathrm{\Delta}\text{L}=4.5\phantom{\rule{0.2em}{0ex}}\text{dB}/\text{cycle}\hfill & \text{if cycle}\_\text{number}\ge 241\hfill \end{array}$$
- DataSet4 - all corrections according to Table 1, except for the inverse barometer which has been applied by adopting a model which makes use of a constant reference atmospheric pressure (CRP) of 1013.3 mbar, [24], according to (3).$$IB=-9.948*\mathit{(}{P}_{\mathit{\text{atm}}}-1013.3\mathit{)}$$
_{atm}is the surface atmospheric pressure in mbar, computed from the dry tropospheric correction (dry_corr) field provided in the GDR-Ms, using Equation (4), where φ is the geodetic latitude.$${P}_{\mathit{\text{atm}}}=\frac{\mathit{\text{dry}}\_\mathit{\text{corr}}}{-2.277\phantom{\rule{0.2em}{0ex}}(1+0.0026cos\left(2\mathrm{\phi}\right))}$$ - DataSet5 - all corrections according to Table 1, except for the inverse barometer which has been applied by adopting a model which makes use of a variable reference surface atmospheric pressure (VRP) interpolated from global average values obtained from the Centre National d'Études Spatiales (CNES/CLS), [36], according to equation (5).$$IB=-9.948*({\text{P}}_{\mathit{\text{atm}}}-\overline{P})$$
_{atm}is the surface atmospheric pressure in mbar, computed according to (4) and P̅ is the global average pressure interpolated to the time of the measurement from values determined at 6 hour intervals from CNES. According to [36], the values of P̅ have been smoothed using a (2-day)^{-1}cut-off frequency. - DataSet6 - all corrections according to Table 1, except for the inverse barometer which has been applied by adopting a combined model where the low frequencies are taken from the inverse barometer correction according to (5) and the high frequency effects are given by the MOG2D barotropic model [37]. This combined correction has been interpolated from global grids (0.25° × 0.25°) at 6 hour intervals provided by AVISO and it will be referred as “combined-MOG2D IB model”.

#### 3.2. Determination of interannual variation and sea level trend

## 4. Results and Discussion

#### 4.1. Sea state bias

#### 4.2. Radiometer wet tropospheric correction

#### 4.3 Inverse barometer correction

^{-1}cut-off frequency. However it was found that the smoothing does not affect the mean sea level determination since the maximum difference in the values of P̅ is 0.7 mbar, which causes a maximum SLA change of 7 mm.

#### 4.4 Satellite orbit field

^{2}relative to the NASA orbit [25], with a degradation of the CNES orbit particularly high from cycle 100 to cycle 246.

## 5. Conclusions

## Acknowledgments

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**Figure 3.**

**a**Various curves for DataSet1 in the Tropical region. : SLA; : interannual variations; : linear trend.

**b**Various curves for DataSet1 in the Sub-Tropical region. : SLA; : interannual variations; : linear trend.

**c**Various curves for DataSet1 in the Sub-Arctic region. : SLA; : interannual variations; : linear trend.

**Figure 4.**SLA differences for the Tropical region. - DataSet1- DataSet2; - DataSet1- DataSet3; - DataSet1- DataSet5; - DataSet1- DataSet7; –DataSet5- DataSet4.

**Figure 5.**SLA differences DataSet1-DataSet2 (different SSB models: Chambers – Labroue). - Tropical; : Sub-Tropical; Sub-Arctic.

**Figure 6.**SLA differences DataSet1-DataSet3 (different wet_cor models: Scharroo - Ruf). - Tropical; : Sub-Tropical; Sub-Arctic.

**Figure 7.**

**a**SLA differences DataSet1-DataSet4 (non-IB-corrected versus IB Constant Reference Pressure) - Tropical; : Sub-Tropical; Sub-Arctic.

**b**SLA differences DataSet1-DataSet5 (non-IB-corrected versus IB Variable Reference Pressure). - Tropical; : Sub-Tropical; Sub-Arctic.

**Figure 8.**

**a**SLA differences DataSet5-DataSet4 (different IB models: Variable Reference Pressure - Constant Reference Pressure) - Tropical; : Sub-Tropical; Sub-Arctic.

**b**SLA differences DataSet5-DataSet6 (different IB models: Variable Reference Pressure - combined_MOG2D) - Tropical; : Sub-Tropical; Sub-Arctic.

**Figure 9.**SLA differences DataSet1-DataSet7 (different orbits) - Tropical; : Sub-Tropical; Sub-Arctic.

**Figure 10.**

**a**Interannual variation of sea level for the tropical region. – DataSet1; – DataSet2 (Labroue SSB); – DataSet3 (Ruf wet_cor); –DataSet4 (IB-CRP); – DataSet5 (IB-VRP);

**dashed black**– DataSet6 (IB-MOG2D); – DataSet7 (CNES orbit).

**b**Interannual variation of sea level for the Sub-Tropical region. – DataSet1; – DataSet2 (Labroue SSB); – DataSet3 (Ruf wet_cor); –DataSet4 (IB-CRP); – DataSet5 (IB-VRP);

**dashed black**– DataSet6 (IB-MOG2D); – DataSet7 (CNES orbit).

**c**Interannual variation of sea level for the Sub-Arctic region. – DataSet1; – DataSet2 (Labroue SSB); – DataSet3 (Ruf wet_cor); –DataSet4 (IB-CRP); – DataSet5 (IB-VRP);

**dashed black**– DataSet6 (IB-MOG2D); – DataSet7 (CNES orbit).

**Figure 11.**

**a –**Chambers SSB model for TOPEX A (metres).

**b –**Labroue SSB model for TOPEX A (metres).

**c –**Difference between Labroue and Chambers SSB models for TOPEX A (metres).

**Figure 12.**

**a –**Chambers SSB model for TOPEX B (metres).

**a –**Labroue SSB model for TOPEX B (metres).

**c –**Difference between Labroue and Chambers SSB models for TOPEX B (metres).

**Figure 13.**

**a –**Average SWH. - Tropical; : Sub-Tropical; Sub-Arctic.

**b –**SWH standard deviation (σ). - Tropical; : Sub-Tropical; Sub-Arctic.

**Figure 14.**

**a –**Average WS. - Tropical; : Sub-Tropical; Sub-Arctic.

**b –**WS standard deviation (σ). - Tropical; : Sub-Tropical; Sub-Arctic.

**Figure 15.**

**a**Significant wave height for cycle 273 (February 2000).

**b**Wind speed for cycle 273 (February 2000).

**Figure 16.**

**a**Significant wave height for cycle 364 (August 2002).

**b**Wind speed for cycle 364 (August 2002).

**Table 1.**Geophysical corrections and models used in the processing of TOPEX altimeter data (DataSet1).

Corrections/models | T/P |
---|---|

Mean Sea Surface | GSFC00.1, [33] |

Orbit | NASA JGM3, [24] |

Dry troposphere | ECMWF, [24] |

Wet troposphere | Scharroo TMR model (yaw state and drift effect on TMR TBs applied, [26]) |

Ionosphere | TOPEX: dual-frequency (filtered, [32]) |

Sea state bias | Chambers model, [27]; additional +2 mm for TOPEX B |

Earth tide | Applied, [24] |

Ocean tide | NAO99, [31] |

Pole tide | Applied, [24] |

Inverse barometer | Not Applied |

**Table 2.**Geophysical corrections and models used in the processing of the various TOPEX altimeter data sets. The box corresponding to the correction that has been changed with respect to DataSet1 is shaded.

Data Sets/Corrections | Radiometer Wet troposphere (wet_cor) | Sea state bias (SSB) | Inverse barometer (IB) | Orbit |
---|---|---|---|---|

DataSet1 | Scharroo TMR model, [26] | Chambers model, [27] | Not Applied | NASA |

DataSet2 | Scharroo TMR model, [26] | Labroue model, [34] | Not Applied | NASA |

DataSet3 | Ruf TMR model,[35] | Chambers model, [27] | Not Applied | NASA |

DataSet4 | Scharroo TMR model, [26] | Chambers model, [27] | Constant reference atmospheric pressure of 1013.3, [24] | NASA |

DataSet5 | Scharroo TMR model, [25 | Chambers model, [27] | Non-constant reference surface atmospheric pressure. [36] | NASA |

DataSet6 | Scharroo TMR model, [26] | Chambers model, [27] | Combined-MOG2D model [37] | NASA |

DataSet7 | Scharroo TMR model, [26] | Chambers model, [27] | Not Applied | CNES |

**Table 3.**Linear trends (mm/yr) and corresponding standard errors (mm/yr) obtained by OLS fit to the time series of the interannual SLA signal.

Tropical | Sub-Tropical | Sub-Arctic | ||||
---|---|---|---|---|---|---|

trend | s. e. | trend | s. e. | trend | s. e. | |

DataSet1 | 3.24 | 0.08 | 1.97 | 0.11 | 3.26 | 0.18 |

DataSet2 | 3.07 | 0.08 | 1.86 | 0.11 | 3.22 | 0.18 |

DataSet3 | 3.35 | 0.08 | 2.10 | 0.11 | 3.38 | 0.18 |

DataSet4 | 3.14 | 0.08 | 1.82 | 0.09 | 4.14 | 0.13 |

DataSet5 | 2.99 | 0.08 | 1.68 | 0.08 | 3.99 | 0.12 |

DataSet6 | 3.00 | 0.08 | 1.69 | 0.08 | 4.01 | 0.13 |

DataSet7 | 3.25 | 0.09 | 1.99 | 0.09 | 3.19 | 0.17 |

**Table 4.**Linear trends (mm/yr) and corresponding standard errors (mm/yr) obtained by OLS fit to the original SLA time series (after removing the seasonal signal).

Tropical | Sub-Tropical | Sub-Arctic | ||||
---|---|---|---|---|---|---|

trend | s. e. | trend | s. e. | trend | s. e. | |

DataSet1 | 3.22 | 0.20 | 2.04 | 0.40 | 3.40 | 0.74 |

DataSet2 | 3.05 | 0.20 | 1.93 | 0.40 | 3.37 | 0.72 |

DataSet3 | 3.33 | 0.21 | 2.16 | 0.41 | 3.52 | 0.73 |

DataSet4 | 3.14 | 0.17 | 1.83 | 0.18 | 4.14 | 0.23 |

DataSet5 | 3.00 | 0.16 | 1.68 | 0.17 | 4.00 | 0.23 |

DataSet6 | 3.00 | 0.16 | 1.69 | 0.17 | 4.02 | 0.22 |

DataSet7 | 3.23 | 0.20 | 2.05 | 0.40 | 3.33 | 0.74 |

**Table 5.**Linear trends differences (mm/yr) between various datasets (obtained by OLS fit to the time series of the interannual SLA signal).

Tropical | Sub-Tropical | Sub-Arctic | |
---|---|---|---|

DataSet1 - DataSet2 | 0.17 | 0.11 | 0.04 |

DataSet1 - DataSet3 | -0.11 | -0.13 | -0.12 |

DataSet1 - DataSet4 | 0.10 | 0.15 | -0.88 |

DataSet1 - DataSet5 | 0.25 | 0.29 | -0.73 |

DataSet1 - DataSet6 | 0.24 | 0.28 | -0.75 |

DataSet1 - DataSet7 | -0.01 | -0.02 | 0.07 |

DataSet5 - DataSet4 | -0.15 | -0.14 | -0.15 |

DataSet5 - DataSet6 | -0.01 | -0.01 | -0.02 |

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Fernandes, M.J.; Barbosa, S.; Lázaro, C. Impact of Altimeter Data Processing on Sea Level Studies. *Sensors* **2006**, *6*, 131-163.
https://doi.org/10.3390/s6030131

**AMA Style**

Fernandes MJ, Barbosa S, Lázaro C. Impact of Altimeter Data Processing on Sea Level Studies. *Sensors*. 2006; 6(3):131-163.
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**Chicago/Turabian Style**

Fernandes, M. Joana, Susana Barbosa, and Clara Lázaro. 2006. "Impact of Altimeter Data Processing on Sea Level Studies" *Sensors* 6, no. 3: 131-163.
https://doi.org/10.3390/s6030131