# Retrieval of the Absorption Coefficient of L-Band Radiation in Antarctica From SMOS Observations

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## Abstract

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## 1. Introduction

- The Tiuri model is correct, implying that Mätzler absorption is too low. In this case, bias is small and emissivity is very close to 1, which would correspond to negligible scattering effects. The warm bias computed with the Mätzler model is basically due to the overestimation of the deep layers’ contribution to the brightness-temperature signal. However, the Tiuri absorption is too strong to account for apparent spatial variations of the brightness temperature with the ice thickness.
- The Mätzler model is correct, implying that Tiuri absorption is too high. In this case, a mechanism that reduces ice emissivity to explain the warm bias is missing. Surface- and internal-layer roughnesses [39], or snow and firn heterogeneities, are potential sources of reflectivity and scattering that are able to lower emissivity, but they have to be quantified.
- None of the Mätzler and Tiuri models is appropriate, and an intermediate formulation is needed, possibly featuring a different dependence on temperature. Scattering processes should be considered in this case, as in the case of the second hypothesis.

## 2. Materials and Methods

#### 2.1. SMOS Brightness Temperature

#### 2.2. Temperature Field from the GRISLI Ice-Sheet Model

#### 2.3. Borehole Temperature Profiles

#### 2.4. Absorption and Emissivity Retrieval

#### 2.4.1. Forward Model

#### 2.4.2. Retrieval Algorithm

## 3. Results

#### 3.1. Preliminary Comparison With Borehole Measurements

#### 3.2. Lagrangian Function Optimization

#### 3.3. Absorption Coefficients and Permittivity

#### 3.4. Effective Temperature and Emissivity

#### 3.5. Relationship between Emissivity, Wind, and Accumulation Fields

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Correction of the Temperature Profiles on Ice Thickness

## Appendix B. Minimization of the Lagrangian Function

## References

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**Figure 1.**(

**a**) Brightness temperature ${T}_{B}$ measured by the Soil Moisture and Ocean Salinity (SMOS) satellite sensor at the L-band and vertical polarisation, averaged over two years (2013–2014). Black contours are 5 K apart. (

**b**) Surface temperature ${T}_{s}$ (K) from the Crocus snowpack model. Contour lines are 5 ${}^{\xb0}$C apart and delineate the thermally homogeneous areas used in the retrieval algorithm. Areas undergoing more than five days of melt over the 1979–2007 period are masked in grey and are not accounted for in the study.

**Figure 3.**Borehole temperature profiles at several drilling sites in Antarctica from in situ measurements (solid line) and GRISLI (dashed line). The circles drawn at the surface indicate the value of the SMOS ${T}_{B}$ for each site (the red point is partly hidden by the blue and green ones.)

**Figure 4.**Evolution of: (

**a**) the square root of cost function $\sqrt{\mathcal{J}}$ (K), (

**b**) correlation function $\sqrt{\mathcal{R}}$, (

**c**) mean emissivity $\overline{\eta}$, and (

**d**) e-folding depth $1/{\kappa}_{a}$ (m) along the iteration steps of the retrieval process. Temperature slice: between $-45$ and $-40{\phantom{\rule{0.166667em}{0ex}}}^{\xb0}$C in East Antarctica.

**Figure 5.**Imaginary part of ice permittivity computed from the Tiuri (orange) and Mätzler (blue) models, depending on ice temperature. The dashed line shows the initial guess of the retrieval process. The result of the retrieval is shown with red (East Antarctica) and green (West Antarctica) diamond markers.

**Figure 6.**Areas undergoing more than five days of melt over the 1979–2007 time period are masked in grey and were not taken into account in the study. (

**a**) Difference between ${T}_{E}$ and ${T}_{s}$ (K). Contour lines are 1 K apart. (

**b**) Emissivity spatial variations as computed from the Mätzler model. DML: Dronning Maud Land, MRL: MacRobertson Land, VL: Victoria Land, GVL: George V Land, PEL: Princess Elizabeth Land, QML: Queen Mary Land, WL: Wilkes Land. Contour lines are 1% apart. (

**c**) Ice thickness (m) from Bedmap 2 [55]. Emissivity contour lines are superimposed.

**Figure 8.**Scatter plot of emissivity vs. accumulation rate. The color scale correspond to the wind speed of ERA Interim at 10 m.

**Table 1.**Square root of components $\mathcal{J}$ and $\mathcal{R}$ of the Lagrangian function, and corresponding best-fit values of $1/{\kappa}_{a}$ and $\overline{\eta}$, for each temperature slice (${}^{\xb0}$C), designed by its mean. For the sake of clarity, results are shown for e-folding depth $1/{\kappa}_{a}$, expressed in meters.

East Ant. | −57.5 ${}^{\xb0}$C | −52.5 ${}^{\xb0}$C | −47.5 ${}^{\xb0}$C | −42.5 ${}^{\xb0}$C | −37.5 ${}^{\xb0}$C | −32.5 ${}^{\xb0}$C | −27.5 ${}^{\xb0}$C |

$\sqrt{\mathcal{J}}$ (K) | 1.47 | 1.41 | 0.80 | 0.28 | 0.35 | 0.66 | 1.1 |

$\sqrt{\mathcal{R}}$ | 0.17 | 0.22 | 0.17 | 0.10 | 0.03 | 0.02 | 0.09 |

$1/{\kappa}_{a}$ (m) | 466 | 560 | 460 | 365 | 297 | 288 | 216 |

$\overline{\eta}$ | 0.989 | 0.976 | 0.972 | 0.972 | 0.972 | 0.973 | 0.978 |

West Ant. | −42.5 ${}^{\xb0}$C | −37.5 ${}^{\xb0}$C | −32.5 ${}^{\xb0}$C | −27.5 ${}^{\xb0}$C | |||

$\sqrt{\mathcal{J}}$ (K) | 1.56 | 0.96 | 0.67 | 0.84 | |||

$\sqrt{\mathcal{R}}$ | 0.09 | 0.03 | 0.18 | 0.15 | |||

$1/{\kappa}_{a}$ (m) | 275 | 319 | 299 | 216 | |||

$\overline{\eta}$ | 0.979 | 0.987 | 0.986 | 0.976 |

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## Share and Cite

**MDPI and ACS Style**

Passalacqua, O.; Picard, G.; Ritz, C.; Leduc-Leballeur, M.; Quiquet, A.; Larue, F.; Macelloni, G.
Retrieval of the Absorption Coefficient of L-Band Radiation in Antarctica From SMOS Observations. *Remote Sens.* **2018**, *10*, 1954.
https://doi.org/10.3390/rs10121954

**AMA Style**

Passalacqua O, Picard G, Ritz C, Leduc-Leballeur M, Quiquet A, Larue F, Macelloni G.
Retrieval of the Absorption Coefficient of L-Band Radiation in Antarctica From SMOS Observations. *Remote Sensing*. 2018; 10(12):1954.
https://doi.org/10.3390/rs10121954

**Chicago/Turabian Style**

Passalacqua, Olivier, Ghislain Picard, Catherine Ritz, Marion Leduc-Leballeur, Aurélien Quiquet, Fanny Larue, and Giovanni Macelloni.
2018. "Retrieval of the Absorption Coefficient of L-Band Radiation in Antarctica From SMOS Observations" *Remote Sensing* 10, no. 12: 1954.
https://doi.org/10.3390/rs10121954