Contributors: Jan Wuite, Thomas Nagler (ENVEO IT GmbH)

Issued by: ENVEO / Jan Wuite

Date: 08/02/2024

Ref: C3S2_312a_Lot4.WP2-FDDP-IS-v2_202312_IV_ATBD-v5_i1.1

Official reference number service contract: 2021/C3S2_312a_Lot4_EODC/SC1

Table of Contents

History of modifications

Version

Date

Description of modification

Chapters / Sections

i0.1

20/12/2023

Update from v5 dATBD (compared to v4: Antarctic Ice Sheet IV product was included)

All

i1.0

10/01/2024

Internal review and document finalization

All

i1.1

08/02/2024

Document finalization after external review

All

List of datasets covered by this document

Deliverable ID

Product title

Product type (CDR, ICDR)

C3S version number

Public version number

Delivery date

WP2-FDDP-IV-CDR-v5

Ice velocity

CDR

5.0

1.5

31/12/2023

Related documents 

Reference ID

Document

RD.1

Wuite, J. et al. (2024) C3S Ice Velocity version 1.5: Product Quality Assessment Report. Document ref. C3S2_312a_Lot4.WP2-FDDP-IS-v2_202312_IV_PQAR-v5_i1.0

RD.2

Wuite, J. et al. (2024) C3S Ice Velocity version 1.5: Product User Guide and Specification. Document ref. C3S2_312a_Lot4.WP2-FDDP-IS-v2_202312_IV_PUGS-v5_i1.1

RD.3

Wuite, J. et al. (2024) C3S Ice Velocity version 1.5: System Quality Assurance Document. Document ref. C3S2_312a_Lot4.WP3-SQAD-IS-v2_202401_IV_SQAD-v5_i1.1

RD.4

Wuite, J. et al. (2023) C3S Ice Velocity version 1.5: Product Quality Assurance Document. Document ref. C3S2_312a_Lot4.WP1-PDDP-IS-v2_202306_IV_PQAD-v5_i1.1

Acronyms 

Acronym

Definition

AIS

Antarctic Ice Sheet

ALOS

Advanced Land Observing Satellite

ASAP

Austrian Space Applications Programmes

ASAR

Advanced SAR

ATBD

Algorithm Theoretical Basis Document

AWS

Automatic Weather Stations

CATS2008

Circum-Antarctic Tidal Simulation version 2008

CCI

Climate Change Initiative

CDR

Climate Data Record

CFL

Calving Front Location

CPOD

Copernicus Precise Orbit Determination

CSA

Canadian Space Agency

DEM

Digital Elevation Model

DInSAR

Differential SAR Interferometry

DLR

Deutsches Zentrum für Luft- und Raumfahrt e.V.

DTU

Technical University of Denmark

ECMWF

European Centre for Medium-Range Weather Forecasts

ECV

Essential Climate Variable

ENVISAT

Environmental Satellite

ERA5

fifth generation ECMWF atmospheric reanalysis

ESA

European Space Agency

ESRI

Environmental Systems Research Institute

GEUS

Geological Survey of Denmark and Greenland

GIS

Geographic Information System

GrIS

Greenland Ice Sheet

GPS

Global Positioning System

ICDR

Interim Climate Data Record

ICESat

Ice, Cloud and Elevation Satellite

InSAR

Interferometric SAR

IV

Ice Velocity

IW

Interferometric Wide-swath mode

JAXA

Japanese Space Agency

LOS

Line of Sight

MEaSUREs

Making Earth System Data Records for Use in Research Environments

NASA

The National Aeronautics and Space Administration

NDSI

Normalized Difference Snow Index

NIR

Near Infrared

NSIDC

National Snow and Ice Data Center

OT

Offset Tracking

OLI

Operational Land Imager

PALSAR

Phased Array L-band SAR

PGC

Polar Geospatial Center

POE

Precise Orbit Ephemerides

PROMICE

Programme for monitoring of the Greenland ice sheet

QA

Quality Assurance

REMA

Reference Elevation Model of Antarctica

RGI

Randolph Glacier Inventory

S1

Sentinel-1

SAR

Synthetic Aperture Radar

SLC

Single Look Complex

TCM

Tidal Correction Module

TOPS

Terrain Observation by Progressive Scans

TSX

TerraSAR-X

TDX

TanDEM-X

USGS

United States Geological Survey

General definitions 

Single Look Complex (SLC): Level-1 Single Look Complex (SLC) products are Synthetic Aperture Radar (SAR) images in the slant range by azimuth imaging plane, in the image plane of satellite data acquisition. Each image pixel is represented by a complex magnitude value and therefore contains both amplitude and phase information. The imagery is geo-referenced using orbit and attitude data from the satellite. SLC images are produced in a zero Doppler geometry. (Adapted from: https://sentinels.copernicus.eu/)

Interferometric Wide (IW): The Interferometric Wide (IW) swath mode is the main acquisition mode of Sentinel-1 over land, including ice sheets. It acquires data with a 250 km swath at 5 m by 20 m spatial resolution. IW mode captures three sub-swaths using Terrain Observation with Progressive Scans SAR (TOPS). (Adapted from: https://sentinels.copernicus.eu/)

Terrain Observation with Progressive Scans (TOPS): With the TOPS(AR) technique, in addition to steering the radar beam in range, the beam is also electronically steered from backward to forward in the azimuth direction for each burst, avoiding scalloping and resulting in homogeneous image quality throughout the swath (De Zan and Guarnieri, 2006)

Offset Tracking (OT): OT refers to several related methods that include speckle tracking, coherence tracking and amplitude tracking or feature tracking. Feature tracking uses cross-correlation of image patches to find the displacement of surface features such as crevasses or rifts and edges, that move with the same speed as the ice and are identifiable on two co-registered amplitude images, to derive ice flow velocity. In coherence tracking, the offset which maximises the interferometric coherence within a certain window size is determined and used to derive the ice velocity. Speckle tracking uses the cross-correlation function of radar speckle patterns, rather than visible features, to derive ice flow velocity.

Scope of the document

 This document is the Algorithm Theoretical Basis Document (ATBD) for the Ice Velocity (IV) product, v1.5 produced as part of the Copernicus Ice Sheets and Ice Shelves service. It describes the satellite-mounted instruments, auxiliary datasets, auxiliary models and basic algorithms used to create the data products.

Executive summary

The v1.5 Ice Velocity product consists of two gridded products representing the mean annual ice surface velocity (IV) of the Greenland and Antarctic Ice Sheet. The Antarctic Ice Sheet Velocity is provided as a new product within the service from v1.5 onwards. The Climate Data Record (CDR) closely follows the Greenland IV product as the retrieval algorithm is largely identical. The main input data for IV consist of Sentinel-1A and Sentinel-1B synthetic aperture radar (SAR) data.

In Chapter 1 we introduce the satellite source for IV retrieval (Sentinel-1) including the mission's acquisition strategy, technical details of the SAR sensor and characteristics of the Interferometric Wide (IW) swath mode. Chapter 0 describes the input and auxiliary data needed for the IV retrieval algorithm and quality assessment. The primary input data are Level-1 Single Look Complex (SLC) images acquired in IW swath mode. Auxiliary data, used in the processing chain for IV production and quality assessment, include precise orbit files, a digital elevation model (DEM), ocean/ice land masks and validation data. The retrieval algorithm and processing line for IV and the uncertainty characterization is specified and explained in Chapter 3. The algorithm is based on offset tracking (OT), utilizing long stripes of Sentinel-1 data. Offset tracking refers to several related methods that include amplitude tracking or feature tracking, coherence tracking and speckle tracking. OT requires less operator interaction than interferometric techniques (InSAR) and can be more easily and reliably automated. Another advantage of the OT technique over InSAR is the provision of two components of the velocity vector (along track and line-of-sight, LOS) from data of a single track. The generation of a regional ice velocity map requires the combination of OT results, from several tracks, each providing slant range and azimuth displacements at local incidence and heading angle. For various reasons the algorithm sometimes fails to find matching features or erroneous matches are returned leading to gaps and/or errors in the velocity fields. These are to some extent dealt with using a filtering and gap filling approach. Ice velocity retrieval over ice shelves and floating extensions of outlet glaciers is strongly affected by vertical motion induced by ocean tides and atmospheric pressure changes. This is of particular relevance for Antarctica, as most of the Antarctic coastline is fringed by ice shelves and floating ice tongues. The robustness of IV retrieval in these regions is improved by implementing a tidal correction module (TCM). As the calving front location (CFL) is a highly dynamical environment, dynamic ice/ocean masking for outlet glaciers based on annually/periodically updated CFL's is added as a technical enhancement for future CDRs. Details and examples of the output IV products are provided in Chapter 4.

1. Instruments

The primary satellite sources for generation of the ice velocity (IV) fields are Copernicus Sentinel-1A and Sentinel-1B. The Sentinel-1 (S1) satellites carry a C-band synthetic aperture radar (SAR) instrument providing high resolution SAR images in different acquisition modes. The Interferometric Wide-Swath mode (IW) is the main acquisition mode over land areas, including Greenland. The IW mode combines a large swath width (250 km) with a moderate ground resolution (5 m x 20 m in range and azimuth, respectively).  

Sentinel-1A provides continuous coverage for the entire Greenland Ice Sheet margin and large parts of the Antarctic Ice Sheet margin since October 2014 with a 12-day repeat pass period. Sentinel-1B was launched in April 2016 and, in combination with Sentinel-1A, reduced the repeat pass period from 12 to 6 days. Besides the continuous coverage of the margin, the Greenland Ice Sheet is covered completely during dedicated annual (winter) campaigns, with 4 to 6 repeat observations per track. In 2019, further expansion of the continuous coverage in Greenland commenced including also the interior ice sheet. This provides an opportunity to produce Greenland wide velocity maps at sub-annual, and even monthly, intervals. In Antarctica, the extent of the ice velocity map is limited to the ice sheet margin, where repeat pass observations of Sentinel-1 are available, and excludes the polar gap which extends from the South Pole up to a latitude of ~78.5°S. The S1 dedicated acquisition plan for polar regions makes the constellation the primary source for monitoring of IV, providing year-round, day/night, all-weather observing capability. The main instrument parameters and IW mode are described in Table 1 and Table 2.

Since 23rd December 2021, there has been a technical problem with Sentinel-1B related to the power supply of the SAR system and no data has been acquired since. Recovery attempts have been unsuccessful, and the European Space Agency (ESA) has ended the S1B mission, while Sentinel-1A remains fully operational. The launch of Sentinel-1C, which will replace Sentinel-1B, is pending.

Table 1: Sentinel-1 sensor specifications 

Property

Value

Sensor

C-SAR (C-band Synthetic Aperture Radar)

Emitted frequency

5.4 GHz

Pulse repetition frequency

1 000 - 3 000 Hz

Pulse duration

5-100 μs

Bandwidth

0-100 MHz

Antenna length

12.3 m

Antenna beamwidth

0.23°

Slant range resolution

5 m

Azimuth resolution

20 m


Table 2: Characteristics of Sentinel-1 IW mode 

Parameter

Value

Swath width (ground range)

250 km

Nom. L1b product length

50 km

Full performance incidence angle range

20° - 46°

Data access incidence angle range

30° - 42°

Azimuth resolution

20 m

Ground range resolution

5 m

Polarizations

HH+HV, VV+VH, VV, HH

2. Input and auxiliary data

2.1. SAR data

Primary input data for IV retrieval are repeat pass Sentinel-1A and Sentinel-1B Level-1 Single Look Complex (SLC) images acquired in the Interferometric Wide (IW) swath mode. These products consist of focused SAR data geo-referenced using orbit and altitude data from the satellite and provided in zero-Doppler slant-range geometry. IW implements the Terrain Observation by Progressive Scans (TOPS) mode, consisting of 3 or 5 sub-swaths, each consisting of a series of bursts. Each burst has been processed as a separate SLC image. Sentinel-1 data is provided free of charge through the Copernicus Data Space Ecosystem1.

1 https://dataspace.copernicus.eu/  [Last accessed 20th Dec 2023]

2.2. Auxiliary data

Auxiliary data, used in the processing chain for IV production and quality assessment, include precise orbit files, a digital elevation model, ocean/ice land masks and validation data. Details are provided in the following:

2.2.1. Orbits


Orbit files (Precise Orbit Ephemerides, POE) are required for IV processing to enable accurate co-registration. Precise orbit files for Sentinel-1 are provided in ASCII XML format by the Copernicus Precise Orbit Determination (CPOD) service available from the Copernicus Data Space Ecosystem. approximately 3 weeks after acquisition. POE files cover periods of approximately 26 hours (one complete day in Global Positioning System (GPS) time, plus overlap of two hours between consecutive files) and contain orbit state vectors at 10-second intervals.

2.2.2. DEM

A contemporary high-resolution digital elevation model (DEM) is required in the processing chain for co-registration, calculation of the vertical component of velocity (vz) and final geocoding of the product. The DEM used for the annual Greenland Ice Sheet velocity map is compiled from TanDEM-X 90m DEM tiles provided by the German Aerospace Center DLR2. This is a product variant of the original 12m (0.4 arcsec) DEM product with reduced pixel spacing (Wessel et al., 2018a). The extent and grid spacing of the DEM is equal to the IV product. Further information can be found in the TanDEM-X Ground Segment DEM Products Specification Document (Wessel, 2018b).

For Antarctica the 200m void-filled version of the Reference Elevation Model of Antarctica (REMA) DEM is used. The REMA DEM is a high-resolution elevation model covering the entire continent provided by the Polar Geospatial Center (PGC) at the University of Minnesota (Howat et al., 2019)3. The DEM is based on stereoscopic image pairs from WorldView-1, -2, -3 and GeoEye-1 satellites acquired between 2009 and 2017, with most data from 2015-2016. Data are available both as individual strip files, with spatial resolution of 2 to 8 m, as well as mosaics covering the whole continent with a reduced resolution. The DEMs are vertically registered to satellite altimetry measurements from Cryosat-2 and Ice, Cloud and Elevation Satellite (ICESat), resulting in reported absolute uncertainties of less than 1 m over most of the ice sheet area, and relative uncertainties in the order of decimetres. The extent and grid spacing of the 200 m void-filled version of the REMA DEM is equal to the IV product. A 25x25 median filter was used to smooth the DEM in order to avoid the impact of large rifts, undulations and crevasses on (fast moving) outlet glaciers and ice shelves on the velocity maps. The DEM (referenced to the WGS84 ellipsoid) is referenced to sea level using the using the GOCO05s geoid (Mayer-Gürr, et al. 2015).

2 https://geoservice.dlr.de/web/dataguide/tdm90/ [Last accessed 20th December 2023]

3 https://www.pgc.umn.edu/data/rema/ [Last accessed 20th December 2023]

2.2.3. Land/Ice/Ocean Mask

Because the ice extent is continuously changing as the ice advances or icebergs break off, the ice sheet boundaries are based on a regularly updated ice-ocean masks. These are shapefiles of the ocean, land and ice boundaries, based on recent optical or SAR imagery and used for masking the retrievals in the ocean (usually coming from tracked sea ice). For Greenland the ice sheet and glacier boundaries are based on the Randolph Glacier Inventory (RGI 6.0, RGI Consortium, 2017) with updated glacier fronts. The inventory has been compiled from more than 70 Landsat scenes (mostly acquired between 1999 and 2002) using semi-automated glacier mapping techniques (Rastner et al., 2012). For C3S2 dynamic ice/ocean masking for outlet glaciers based on annually updated calving front locations (CFLs) was added as technical development (See Chapter 3.5). For delineating the Antarctic coastal margin, a 200 m geocoded Sentinel-1 amplitude mosaic covering the ice sheet margin in April 2022 was generated. Gaps in the S1 coverage were filled with cloud free Sentinel-2 images from the same time period. Based on the mosaic, the delineation of the calving front was performed semi-automatically, using an edge detection technique, and manually checked and - when needed - corrected. 

2.2.4. Tide model and atmospheric pressure reanalysis 

Ice velocity retrieval over ice shelves and floating extensions of outlet glaciers is strongly affected by vertical motion induced by ocean tides and, to a lesser degree, by atmospheric pressure changes. For this, a correction is applied (See Chapter 3.4) using a regional ocean tide model (CATS2008) and atmospheric pressure data (ERA5). CATS2008 (Circum-Antarctic Tidal Simulation version 2008; Erofeeva et al., 2019) is a regional ocean tide model provided at 4 km resolution. ERA5 is the fifth generation European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis of the global climate and provides hourly estimates of variables on pressure levels on a global grid with a spatial resolution of 0.25° × 0.25° 4

4 ERA5 data can be found on CDS: https://cds.climate.copernicus.eu/ Last accessed 10th January 2024].

2.2.5. Validation data

The quality assessment for ice velocity includes detailed validation with contemporaneous in-situ GPS data at various sites across the Greenland Ice Sheet (see: RD.1 and RD.4). The GPS instruments are attached to Automatic Weather Stations (AWS) operated by the Geological Survey of Denmark and Greenland (GEUS) in collaboration with the National Space Institute at the Technical University of Denmark (DTU Space) and ASIAQ Greenland Survey as part of the Danish Programme for Monitoring of the Greenland Ice Sheet (PROMICE; Fausto and Van As, 2019). The product is also evaluated against publicly available ice velocity products covering the same area and time span. These IV maps were produced as part of the NASA 'Making Earth System Data Records for Use in Research Environments' (MEaSUREs) program (Joughin et al., 2021; Joughin, 2021).

Due to sparsity of in-situ GPS data acquired in Antarctica the validation and Quality Assurance (QA) activities are restricted to intercomparisons with existing ice velocity maps for close or overlapping periods and the stable terrain test (assessment of ice velocity in stable terrain with no velocity) based on a published map of rock outcrops in Antarctica. The external IV maps are provided as part of the National Aeronautics and Space Administration (NASA) MEaSUREs Program. The annual Antarctic IV maps were derived from multi-sensor SAR data and optical imagery acquired between 2005 and 2020 (Mouginot et al., 2017). The maps combine data derived from the Japanese Space Agency's (JAXA) Advanced Land Observing Satellite (ALOS) Phased Array L-band SAR (PALSAR), the European Space Agency's (ESA) Environmental Satellite (ENVISAT) Advanced SAR (ASAR) and Copernicus Sentinel-1, the Canadian Space Agency's (CSA) RADARSAT-1, RADARSAT-2 and the German Aerospace Agency's (DLR) TerraSAR-X (TSX) and TanDEM-X (TDX), and are integrated with optical imagery from the U.S. Geological Survey's (USGS) Landsat-8. Data are available in NetCDF format through NSIDC at 1 km spatial resolution (Data Set ID: NSIDC-0720; Mouginot et al., 2017)5.

For the stable terrain test we use a rock outline shapefile derived from Landsat-8 Operational Land Imager (OLI) images. The dataset is generated using a new and automated methodology for snow and rock differentiation that excludes areas of snow (both illuminated and shaded), clouds and liquid water whilst identifying both sunlit and shaded rock. The method achieves higher and more consistent accuracies than alternative data and methods such as the normalized difference snow index (NDSI). The images were acquired in austral summers between October 2013 and March 2015. The dataset is provided as a supplement with the paper (Burton-Johnson et al., 2016)6

5 Dataset available at https://doi.org/10.5067/9T4EPQXTJYW9 Last accessed 10th January 2024].

6 Dataset available at https://tc.copernicus.org/articles/10/1665/2016/tc-10-1665-2016-supplement.zip Last accessed 10th January 2024].

3.  Algorithms

3.1. Coherent and Incoherent Offset Tracking using Sentinel-1

Offset tracking (OT) is the principal method for generating velocity fields on glacier surfaces from Sentinel-1 operationally. OT refers to several related methods that include amplitude tracking or feature tracking, coherence tracking and speckle tracking. Feature tracking uses cross-correlation of image patches to find the displacement of surface features such as crevasses or rifts and edges, that move with the same speed as the ice and are identifiable on two co-registered amplitude images, and subsequently ice flow velocity (Figure 3.1). In coherence tracking, the offset which maximises the interferometric coherence within a certain window size is determined and used to derive the ice velocity. Speckle tracking uses the cross-correlation function of radar speckle patterns, rather than visible features, to derive ice flow velocity. 


Figure 3.1: Concept of Feature tracking. Two correlation plots derived from comparing a reference image template with a larger search window extracted from two different SAR scenes. The peak of the surface corresponds to the reported match. The shape of the correlation function is an important indicator of the measurement accuracy. Sharp pronounced peaks (a) have a higher accuracy then broader peaks (b). (Figure adapted from Wuite, 2006)

OT requires less operator interaction than interferometric techniques (such as Interferometric SAR (InSAR)) and can be more easily and reliably automated. Another advantage of the OT technique over InSAR is the provision of two components of the velocity vector (along track and line-of-sight, LOS) from data of a single track. Also, the Greenland and Antarctic Ice Sheet are subject to highly variable meteorological conditions, resulting in rapid temporal decorrelation of the radar signal phase impairing the comprehensive application of InSAR. OT is less sensitive or insensitive to temporal decorrelation of the radar phase signal, albeit at a lower accuracy of velocity. In areas with distinct and stable surface features, as common on mountain glaciers and outlet glaciers of ice sheets, coherence of the repeat-pass SAR data is not required because the cross-correlation of image-templates is based on the amplitude signal. In the level interior sections of ice sheets, without distinct amplitude features, temporal stability of the target phase (coherence) is required for speckle tracking. Loss of stability of the target phase (temporal decorrelation) is less critical than for the InSAR method because a continuous path is not required for deriving velocities of an isolated patch in an image, as is the case with InSAR.  

The ice velocity algorithm is developed as part of the ESA Climate Change Initiative (CCI) and Austrian Space Applications (ASAP) Programmes. The IV system's core module performs coherent and incoherent OT, utilizing long stripes of Sentinel-1 data acquired in interferometric wide swath (IW) mode. For Sentinel-1 Terrain Observation by Progressive Scans (TOPS) mode acquisitions, OT algorithms need to support burst handling and stitching. Also, the azimuth-varying phase introduced by the TOPS beam steering must be accounted for, both for complex offset tracking and for incoherent offset-tracking, where a factor of two oversampling of the SLCs is required prior to detection. 

OT accuracies depend on various factors, including on the level of coherence, on the correlation window size (Bamler and Eineder, 2005) as well as on the type of features that are being tracked. In addition, ionospheric scintillations can have a large impact on offset tracking by causing azimuth shifts that are introduced by the fluctuating electron density along the sensor path. Misregistration is not a problem, but the large azimuth shifts are interpreted as ice motion and observed offsets can exceed the azimuth pixel size. DEM errors have less impact on the algorithm performance compared to InSAR, since there is no phase unwrapping. However, since offset-tracking can be applied with longer temporal baselines, and even though larger spatial baselines can be used for offset-tracking, in the typical scenario the sensitivity to DEM errors is much smaller. 

For further details the reader is referred to the Algorithm Theoretical Basis Documents of the Greenland and Antarctic Ice Sheet CCI projects (Wuite et al. 2021, Wuite et al. 2020) and Nagler et al. (2015). 

3.2. Generation of Regional Ice Velocity Maps from Multiple Tracks using OT

The generation of a regional ice velocity map requires the combination of offset tracking results, from several tracks, each providing slant range and azimuth displacements at local incidence and heading angle. Figure 3.2 illustrates the high-level processing line for IV production. The system includes 3 main modules: 1) the IV Module; 2) the Merge Module; and 3) the Validation Module. These modules are detailed in the System Quality Assurance Document, but briefly explained here. 

Figure 3.2: High-level flow chart of the IV processing system. Green – input data, Blue – processing modules, Red - product and intermediate products, Yellow – product data base.

3.2.1. IV Module

Within the IV module SAR data and orbit data are imported into the system and velocity maps are generated for pairs of repeat pass data of the same track. The long tracks are geocoded into the common map projection of the output grid, providing observations of slant range displacement and azimuth for each track separately. The local incidence and heading angle are calculated using the annotated image and orbit parameters and a DEM as input. The IV Module includes an outlier removal/filter and gap filling interpolation scheme (See Chapter 3.3) and, specifically for Antarctica, a Tidal Correction Module (TCM) to correct the ice velocity retrieval on floating ice shelves and glacier tongues for the influence of vertical motion induced by ocean tides and atmospheric pressure changes (See Chapter 3.4).

3.2.2. Merge Module

The Merge module combines all IV products from all tracks and image pairs over a specified time span (i.e. 1 year), applying a weighted average approach. The combination of displacement observations of multiple tracks applies a weighted least squares model to fit the multiple observed displacements according to:

$$y=Ax + \epsilon \quad (eq. 1)$$

where x is the horizontal velocity vector (in local Easting/Northing coordinates), y is a vector with the observed velocities (in slant range/azimuth), A is the matrix projecting the horizontal velocity to slant range/azimuth geometry, and ε is a noise vector. The matrices are defined as:

$$(eq. 2)$$
This equation is solved for each output pixel separately: n is the number of pairs with a valid slant range and azimuth displacement estimate at the current output pixel position, $(\Delta sr_n, \Delta a z_n)$ is the measured slant range/azimuth velocity from pair number $n$, $(\theta_n, \phi_n)$ is the elevation and azimuth angle (the latter measured counter-clockwise from East) of the look vector from the pixel to the sensor for pair $n$, $(\frac{\partial z}{\partial x}, \frac{\partial z}{\partial y})$ is the local height gradient at the pixel (from the DEM), and $(\nu_E, \nu_N)$ is the horizontal ice velocity to be calculated. The noise vector,$\epsilon$, is assumed normal distributed with zero mean and diagonal covariance matrix $\Sigma$:

$$(eq. 3)$$
where $(\sigma_{sr_i}, \sigma_{az_i})$ corresponds to the weighted pixel spacing in slant range and azimuth direction and is calculated according to: $$\sigma^2_{sr} = NCC \cos(\theta)/p_{sz} \quad (eq. 4)$$ $$\sigma^2_{sr} = NCC /p_{az} \quad (eq. 5)$$ Where $p_{sz}$ and $p_{az}$ correspond to the slant range and azimuth pixel spacing and $NCC$ is the Normalised Cross-Correlation Coefficient: $$NCC(u,v)=\frac{\sum \left[f(x,y)-\overline{f}_{u,v} \right] [t(x-u,y-v)-\overline{t}]}{\sqrt{\sum \left[ f(x,y) - \overline{f}_{u,v} \right]^2 \sum [t(x-u,y-v)- \overline{t}]^2}} \quad (eq. 6)$$

where f() is the master, t() is the template image (sub-image you are searching for in matrix form) at the pixel position (u,v). The peak in the correlation matrix corresponds to the best matching shift of the slave window with respect to the master window.
The weighted least squares estimate of the horizontal velocity vector is then:

$$\hat{x} = (A^T \Sigma^{-1}A)A^T \Sigma^{-1} y \quad (eq. 7)$$

An advantage of the approach above is that if crossing tracks (ascending/descending) are used, the displacement measurement in the direction with higher resolution dominates in the velocity retrieval.

3.2.3. Validation Module

Lastly, the Validation Module facilitates quality assessment of the IV products, by automating standard validation tests, consisting of internal consistency checks and intercomparisons with independent data sets (e.g. in-situ, GPS, or other published velocity maps). The output is statistical information (e.g. scatter plots, bias, root-mean-square error) on the intercomparisons compiled in the Product Quality and Assessment Report (PQAR, RD.1).

3.3. Filtering and interpolation

For various reasons the OT algorithm sometimes fails to find matching features or erroneous matches are returned leading to gaps and/or errors in the velocity fields. Most frequently this is caused by a lack of traceable surface features or low coherence between image pairs due to for example summer surface melt. In order to smooth and remove outliers a 3x3 simple median filter is applied, after which a 9x9 first order plane fit filter is applied to fill small data gaps. Further filtering/gap filling is left to the user if required. 

3.4. Tidal Correction Module

Ice velocity retrieval over ice shelves and floating extensions of outlet glaciers is strongly affected by vertical motion induced by ocean tides and, to a lesser degree, by atmospheric pressure changes. The vertical displacement between repeat acquisitions introduces an error in the reported horizontal velocity magnitude that hampers the identification of dynamical signals due to, for example, ungrounding through basal melt and/or iceberg calving. This issue is of particular relevance for Antarctica, as most of the Antarctic coastline is fringed by ice shelves and floating ice tongues, many of which underwent large changes in recent decades. The robustness of IV retrieval in these regions is improved by implementing a tidal correction module (TCM), which compensates for the vertical motion caused by tides and atmospheric pressure changes. Figure 3.3 shows the high-level processing chain of the TCM, further details are provided in the ATBD of the Antarctic Ice Sheet CCI+ project (Wuite et al., 2020)7.

Figure 3.3: High level processing chain for compensating ice velocity variations induced by tides and inverse barometric effect (adapted from ESA CCI+ ATBD: Wuite. et al., 2020).

3.5. Dynamic ice/ocean masking

Since the calving front location (CFL) is a highly dynamic environment, dynamic ice/ocean masking for outlet glaciers based on annually/periodically updated CFL's is added as a technical enhancement for future CDR's. For CDR v5.0 we use updated ice/ocean masks that are applied to all layers in the velocity product in a final step. For Greenland we generated a 10 m geocoded and cloudless Copernicus Sentinel-2 mosaic (band 8 Near Infrared (NIR)) covering the ice sheet margin. All Sentinel-2 images were acquired in the period August-September 2022. This is at the end of the summer when most of the fjords8 are ice free and hence ice fronts are easily distinguishable from open water. The main focus was on updating the calving fronts for 28 large glaciers. These glaciers have been identified in the ESA Greenland Ice Sheet CCI project as key outlet glaciers and are all major active glacier systems or ice streams (Figure 3.4). The delineation of the calving front is performed manually in QGIS (open-source GIS; Geographic Information System; software) by an experienced operator. Figure 3.5 shows an example of the updated ice mask in the vicinity of Steenstrup Gletsjer (NW-Greenland). 

For delineating the Antarctic coastal margin, a 200 m geocoded Sentinel-1 amplitude mosaic covering the ice sheet margin in April 2022 was generated (Figure 3.6). Gaps in the S1 coverage were filled with cloud free Sentinel-2 images from the same time period. Based on the mosaic, the delineation of the calving front was performed semi-automatically, using an edge detection technique, and manually checked and - when needed - corrected. 

8 A fjord is a long, narrow, deep inlet of the sea formed by glacial erosion. Fjords are characterized by steep cliffs on either side, and are often found in regions where mountains or glaciers meet the ocean.

Figure 3.4: Cloudless 10 m Copernicus Sentinel-2 mosaic of the Greenland Ice Sheet margin. The images are acquired in the period August-September 2022. Shown are the selection of glaciers for updating the calving front/ice edge. All of these glaciers are marine terminating, except Isunnguata Sermia.

Figure 3.5: Left: Ice velocity map with old land/ice/ocean mask in the vicinity of Steenstrup Gletsjer. Right: same with updated masking. Inset: location in Greenland. Background: Sentinel-2 image mosaic from August-Sept 2022.

Figure 3.6: Sentinel-1 Mosaic covering the Antarctic margin. The black line indicates the ice sheet extent/coastline in April 2022.

3.6. Uncertainty characterisation 

For incoherent offset tracking (the general case), the uncertainty is characterised for each pixel by calculating a local offset-map standard deviation in a 5x5 neighbourhood. A plane fit to the offset map in the 5x5 neighbourhood is subtracted prior to calculating the standard deviation, so that an actual velocity gradient is not interpreted as a noise signal. The standard deviation estimate is corrected for any averaging carried out, as well as correlation between neighbouring samples (i.e. if the radar data are oversampled). The ice velocity maps are accompanied by their associated error standard deviation. The latter is also a map, in the same geometry as the associated measurement, providing a measure of uncertainty on a per-pixel basis.  

4. Output data

The ice velocity products cover the Greenland and Antarctic Ice Sheet and are provided as a NetCDF files with 7 separate layers/maps representing different variables: the 3 velocity components: vx, vy, vz as well as vv (the magnitude of the horizontal components), and gridded maps showing the valid pixel count and the uncertainty/standard deviation (easting & northing) (Table 3, Figure 4.1). The ice velocity map is annually averaged. For Greenland, they are provided at 250m grid spacing in North Polar Stereographic projection (EPSG: 3413) and for Antarctica at 200m grid spacing in Antarctic Polar Stereographic projection (EPSG: 3031). A new NetCDF file of annually averaged IV is produced each year. The horizontal velocity is provided in true meters per day, towards easting (vx) and northing (vy) direction of the grid, and the vertical displacement (vz), is derived from a digital elevation model. More details are given in the C3S Product User Guide and Specification document for Ice Velocity [RD.2].

Table 3: The variables provided in the IV output product for the Greenland Ice Sheet. 

Variable name

Variable description

land_ice_surface_easting_velocity (vx)

Ice velocity East component [m/day]

land_ice_surface_northing_velocity (vy)

Ice velocity North component [m/day]

land_ice_surface_vertical_velocity (vz)

Ice velocity Vertical component [m/day]

land_ice_surface_velocity_magnitude (vv)

Ice velocity magnitude [m/day]

land_ice_surface_measurement_count

Valid pixel count [#]

land_ice_surface_easting_stddev

Standard deviation easting [m/day]

land_ice_surface_northing_stddev

Standard deviation northing [m/day]


 
Figure 4.1: Example IV product covering the Greenland Ice Sheet (2020-2021), depicted are the easting component (vx), the northing component (vy), the magnitude of velocity (vv), the standard deviation of the easting velocity component (vx STD) and the valid measurement count (Count).

Figure 4.2: Example IV product covering the Antarctic Ice Sheet (2020-2021), depicted are from left to right the easting component, the northing component and the magnitude of velocity.

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This document has been produced in the context of the Copernicus Climate Change Service (C3S).

The activities leading to these results have been contracted by the European Centre for Medium-Range Weather Forecasts, operator of C3S on behalf of the European Union (Contribution agreement signed on 22/07/2021). All information in this document is provided "as is" and no guarantee or warranty is given that the information is fit for any particular purpose.

The users thereof use the information at their sole risk and liability. For the avoidance of all doubt , the European Commission and the European Centre for Medium - Range Weather Forecasts have no liability in respect of this document, which is merely representing the author's view.

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