# Mapping of Ice Motion in Antarctica Using Synthetic-Aperture Radar Data

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## Abstract

**:**

## 1. Introduction

## 2. Data

## 3. Methods

#### 3.1. Speckle Tracking

_{rg}and δ

_{az}, respectively) with a sub-pixel quantization noise of 1/128 th of a pixel; in practice, we achieve a noise level of 1/100 th of a pixel (Figure 2(a)). The cross-correlation program is a modified version of

`ampcor`from the JPL/Caltech repeat orbit interferometry package (

`ROI_PAC`) [8]. Speckle tracking is performed on sub-images 600 m (range) × 1,000 m (azimuth) in size, on a regular grid with a grid spacing of 150 m × 300 m, and a search domain, which is size dependent on flow speed, i.e., a larger search window is used for larger offsets. The offsets are median filtered to remove poor matches. To do so, we eliminate pixels for which the pixel offsets deviate more than 3 units from offsets filtered by a 9 pixel × 9 pixel median filter (see Figure 2(a,b)).

#### 3.2. Calibration

_{x}, δ

_{y}, δ

_{z}) in a local Cartesian coordinate system are estimated from the slant range and azimuth displacements, δ

_{rg}and δ

_{az}respectively, as:

_{irg}and σ

_{iaz}are the ionospheric noise contributions; σ

_{Brg}and σ

_{Baz}are the residual errors in interferometric baseline in range and azimuth; θ is the incidence angle with respect to the local vertical direction; and ∊

_{rg}and ∊

_{az}are residual noise contributions in range and azimuth.

_{z}is related to the horizontal displacements by:

_{az}and α

_{rg}are the surface slopes in the azimuth and range directions, respectively.

_{Brg}, σ

_{Baz}) are modeled as two-dimensioned quadratic polynomial functions as:

_{rgi,j}and k

_{azi,j}are the polynomial coefficients, rg and az are respectively the slant range and azimuth position in the offset map, and i and j are the polynomial exponents for slant range and azimuth, respectively.

_{x}, δ

_{y}and δ

_{z}). This process employs a digital elevation model of Antarctica, here from [9]. Geocoded tracks are assembled in a reference mosaic at 300 m spacing in Polar Stereographic projection with true scale at 71°S and a central meridian at zero degree longitude. Assuming a constant displacement between acquisitions, the ice velocity v in meters per year is calculated as v

_{x,y,z}= 365.25 δ

_{x,y,z}/T, where T is the time interval in days between image acquisitions.

#### 3.3. Combining Speckle Tracking and Interferometric Phase

_{rg}with the interferometric phase to improve the quality of the results. From the phase and the azimuth offset, the 3-D ice velocity v

_{x,y,z}is then computed as described previously.

#### 3.4. Gap Filling with Historic Data

## 4. Results

#### 4.1. Error Analysis

_{i}as defined:

_{x}, v

_{y}) is the mean velocity (each component is calculated separately), v

_{i}and w

_{i}are respectively the velocity and weight of each individual track, σ

_{v}is the error associated with v, and σ

_{i}is the error attributed to each track as discussed above.

_{v}converges to zero, which is unrealistic and underestimates the actual error. For instance, the standard deviation of the ice speed measured in a sector of zero motion and large number (>20) of stacked tracks is 0.989 m/yr. We therefore force the error σ

_{v}to always exceed 1 m/y. The error mosaic map is displayed in Figure 3(f). The largest errors are found along the coast of East Antarctica, which is only covered with PALSAR and where ionospheric noise is high. The lowest errors are found in the interior of East Antarctica (up to 79°S) where ASAR tracks overlap up to 36 times.

_{x},v

_{y},v

_{z}) in Antarctica assembled from multiple satellite interferometric synthetic-aperture radar (Figure 3(e)). The map reveals widespread, enhanced flow with tributary ice streams reaching hundreds to thousands of kilometers inland [13].

_{θ}(Figure 3(c)) as:

_{x}and v

_{y}are, respectively, the velocity magnitude along x and y axis in a local Cartesian system, and σ

_{θ}(in radians), σ

_{vx}and σ

_{vy}are the errors associated with θ, v

_{x}and v

_{y}, respectively. If we define the velocity magnitude v as ${v}^{2}={v}_{x}^{2}{v}_{y}^{2}$ and, if we assume that the associated error σ

_{v}is approximated by ${\sigma}_{{v}_{x}}\hspace{0.17em}~\hspace{0.17em}{\sigma}_{{v}_{y}}~\hspace{0.17em}{\sigma}_{v}\hspace{0.17em}/\hspace{0.17em}\sqrt{2}$, the previous equation is rewritten as:

#### 4.2. Validation

## 5. Discussion

## 6. Conclusions

## Acknowledgments

## References

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**Figure 1.**Maps of Antarctica with the footprint of processed tracks for each year employed in this study. More tracks are available, especially for RADARSAT-1, ERS-1/-2 and ALOS PALSAR. Maps are displayed in south polar stereographic projection.

**Figure 2.**From top to bottom, (

**a**) azimuth initial offsets (δ

_{az}); (

**b**) offsets after median filtering; (

**c**) offsets after calibration; (

**d**) initial (black line) and calibrated (red line) azimuth offsets versus azimuth; triangles denote zero-motion control points; diamonds indicate where balance velocity (blue line) is used as a reference; 1 azimuth pixel = 4.0 m; (

**e**) Map of Antarctic balance velocity for speed < 10 m/yr [9] with topographic divides (red lines for slope < 0.1°, blue otherwise). The footprint of track A-B is in blue.

**Figure 3.**(

**a**) Flow direction for the IPY map, black lines represent major topographic divides; (

**b**) Antarctic ice speed; (

**c**) error in flow direction; (

**d**) error in velocity magnitude or speed; (e) set of ENVISAT reference tracks used for calibration, track outlines also shown in (b). Color coding in (b) and (c) is on a logarithmic scale. Maps (a–c) are overlaid on a MODIS mosaic of Antarctica (MOA) [14]. Maps are displayed in south polar stereographic projection.

**Figure 4.**Ice velocity of the Wilkes Land sector using polar stereographic projection and overlaid on MOA, from (

**a**) RAMP in year 2000 [6]; (

**b**) IPY [13]; (

**c**) difference between RAMP and IPY. Control points of zero motion are in dashed yellow. Topographic divides are in blue and red as described in Figure 2. The solid black line in (a–c) is the InSAR grounding line [20]. The dashed black line in (b) indicates the position of the velocity line used in Table 2; white markers correspond to control point locations (Table 2).

**Table 1.**Characteristics of the SAR instruments used in this study. Left-looking capability provides the opportunity to cover areas south of 80°S. Details about the acquisition modes can be found on the agency websites. Repeat Cycle corresponds to the period between two consecutive acquisitions. The incidence angle is the angle defined by the incident radar beam and the vertical (normal) to the intercepting surface. Spacing are given for single look complex images.

Platform | Look Dir. | Mode | Repeat Cycle [day] | Incidence Angle [degree] | Spacing Rg×Az [m] | Swath [km] | Frequency [GHz] | # of tracks | Raw data volume [Tbyte] | Season Year |
---|---|---|---|---|---|---|---|---|---|---|

ERS-1 & -2 | Right | IS2 | 1 | 23 | 13×4 | 100 | 5.3 | 60 | 0.5 | Spring 1996 |

RADARSAT-1 | Left | S2–S7 | 24 | 28–47 1 | 12×5–17×6 ^{1} | 100 | 5.3 | 72 | 0.5 | Fall 1997 |

Right | various | 24 | 18–38 1 | 7×5–12×5 ^{1} | 50–100 ^{1} | 5.3 | 84 | 0.5 | Fall 2000 | |

ENVISAT | Right | IS2 | 35 | 23 | 13×5 | 100 | 5.331 | 115/130/210 ^{2} | 1/1/2 ^{2} | Summer 2007/2008/2009 |

RADARSAT-2 | Left | S5-EH4 | 24 | 41–57 ^{1} | 12×5–12×5 ^{1} | 100 | 5.405 | 135/14 ^{2} | 4/1 ^{2} | Spring 2009/2011 |

ALOS/PALSAR | Right | FBS | 46 | 39 | 7×4 | 70 | 1.27 | 64/204/296 ^{2} | 2/6/9 ^{2} | Fall 2006/2007/2008 |

^{1}Multiple values correspond to different acquisition modes. See the column “Mode”;

^{2}Multiple values correspond to different years. See the column “Season/Year”.

**Table 2.**Influence of the track length on the velocity calibration for Totten Glacier. The second column indicates the reference velocity at the end of the track (the white markers in Figure 4(b)). Totten flux taken as 73.6 Gt from [1].

Track Length [km] | Velocity [m/yr] | Speed Error Flux at the GL [%] | Error [Gt/yr] |
---|---|---|---|

1,000 | 1.8 | >0.1 | >0.1 |

900 | 6.4 | 0.3 | 0.2 |

800 | 4.3 | 0.2 | 0.2 |

700 | 4.3 | 0.3 | 0.2 |

600 | 7.1 | 0.5 | 0.4 |

500 | 22.4 | 1.8 | 1.4 |

400 | 43.9 | 4.5 | 3.3 |

300 | 65.8 | 9.0 | 6.7 |

## Share and Cite

**MDPI and ACS Style**

Mouginot, J.; Scheuchl, B.; Rignot, E.
Mapping of Ice Motion in Antarctica Using Synthetic-Aperture Radar Data. *Remote Sens.* **2012**, *4*, 2753-2767.
https://doi.org/10.3390/rs4092753

**AMA Style**

Mouginot J, Scheuchl B, Rignot E.
Mapping of Ice Motion in Antarctica Using Synthetic-Aperture Radar Data. *Remote Sensing*. 2012; 4(9):2753-2767.
https://doi.org/10.3390/rs4092753

**Chicago/Turabian Style**

Mouginot, Jeremie, Bernd Scheuchl, and Eric Rignot.
2012. "Mapping of Ice Motion in Antarctica Using Synthetic-Aperture Radar Data" *Remote Sensing* 4, no. 9: 2753-2767.
https://doi.org/10.3390/rs4092753