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Remote Sensing IV: Measuring ice elevation

Karen Alley

International Summer School in

Glaciology, 2024

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-Ed Bueler, 2024

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Thwaites Eastern Ice Shelf (TEIS)

  • Thwaites Glacier drains much of West Antarctica
    • Changing rapidly, large potential for instability and future sea-level rise
  • TEIS = Thwaites Eastern Ice Shelf; TWIT = Thwaites Western Ice Tongue

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REMA Mosaic (Howat et al. 2019) with Rignot et al. (2016) grounding line

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TEIS change

  • Visible changes in surface features
  • Big changes in velocity (recent acceleration)
  • How is its thickness changing over time?

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Landsat 7 and 8 time series

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Project: Thwaites Eastern Ice Shelf thinning

  • Establish coordinate system
  • Product options:
    • Stereo-derived digital elevation models
    • Altimetry
  • Change detection
    • DEM differencing
    • Crossovers
    • Lagrangian vs. Eulerian reference frames
  • Floating ice challenges

​

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Project: Thwaites Eastern Ice Shelf thinning

  • Establish coordinate system
  • Product options:
    • Stereo-derived digital elevation models
    • Altimetry
  • Change detection
    • DEM differencing
    • Crossovers
    • Lagrangian vs. Eulerian reference frames
  • Floating ice challenges

​

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Coordinate systems

  • When we measure locations on the Earth’s surface, we can use latitude and longitude
    • Latitude is measured from the equator, which is located based on the Earth’s rotation
    • Longitude is measured from the Prime Meridian, which is an arbitrary line from a set of lines that run through both poles
  • What do we measure elevation from?

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By Unknown author - Vector version of public domain image https://web.archive.org/web/20140813074310/http://www.fedstats.gov/kids/mapstats/concepts_latlg.html, Public Domain, https://commons.wikimedia.org/w/index.php?curid=92353626

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Measuring elevations

  • Options:
    • Above mean sea level
    • Above ground level
    • Distance from the center of the Earth
    • Above an ellipsoid
    • Above a geoid
  • Every one of these options is a “vertical datum”

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Height AGL

Height ASL

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Ellipsoids and geoids

  • Most people think of mean sea level when they think of a vertical datum, but this is difficult to approximate
  • A first attempt is the ellipsoid: a regular shape that approximates the shape of the Earth
    • Easy to calculate with a single equation
  • A more accurate attempt is a geoid, which takes into account gravitational differences
    • Not a straightforward calculation
    • Many published geoids, including World Geodetic System 84 (WGS84)
    • Still not quite the same as sea level

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Ellipsoid

Geoid

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Ellipsoids and geoids

  • Most GPS, altimetry data, and DEMs will have elevations as ellipsoid heights
  • Anything that depends on gravity, such as how things float in the ocean, will need to be converted to orthometric height
  • Many programs that can handle spatial data can provide geoid heights at any lat/lon, making it possible to convert
  • Make sure you know what system you’re using and be consistent!

Ground surface

Ellipsoid

Geoid

Orthometric

height

Ellipsoid

height

Geoid height or undulation height

Orthometric height = ellipsoid height – geoid height

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Project: Thwaites Eastern Ice Shelf thinning

  • Establish coordinate system
  • Product options:
    • Stereo-derived digital elevation models
    • Altimetry
  • Change detection
    • DEM differencing
    • Crossovers
    • Lagrangian vs. Eulerian reference frames
  • Floating ice challenges

​

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Stereo imagery

  • When you look at an area from multiple viewpoints, objects appear to shift relative to each other
  • This apparent shift occurs in mathematically predictable ways
  • By taking images of the same area from multiple angles, correlating features, and calculating positional changes, you can derive a digital elevation model (DEM)

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Wang et al. 2019, Geomorphology

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DEM generation from stereo satellite imagery

  • Some satellites, e.g. Worldview, take an image of an area, travel along their path for a short time, then flip the camera backwards and take another image of the same area
  • Worldview very precisely knows where it is relative to an ellipsoid
  • After correlating all overlapping pixels, the apparent shift and the position of the satellite can be used to solve for the ground surface height at each location
    • But there’s a good bit of vertical error in this – you really need ground control points for vertical accuracy

Source: Maxar, via Polar Geospatial Center (https://www.pgc.umn.edu/guides/stereo-derived-elevation-models/introduction-to-stereoscopic-imagery/)

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DEM Generation from historical air photos

  • Similar procedures can be used to generate DEMs from historical imagery
  • Many flights from the 1940s-1960s with continuous vertical and oblique images
  • Stereo calculations still apply, but in this case we don’t know the exact position of the sensor – need to reference generated DEMs using ground control points
    • Ground control must be from elevations that haven’t changed
    • Really hard with ice! Need exposed bedrock nearby

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1966 USGS TMA Air Photos, video courtesy of Sarah Child

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DEMs from interferometry

  • Viewing the same point from two locations creates parallax effects, similar to optical imagery
  • In this case, parallax is measured by phase differences, rather than distance on the photo
  • Creates very accurate relative elevations, but will need some sort of ground reference elevation for absolute elevations

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DEMs from interferometry

  • Viewing the same point from two locations creates parallax effects, similar to optical imagery
  • In this case, parallax is measured by phase differences, rather than distance on the photo
  • Creates very accurate relative elevations, but will need some sort of ground reference elevation for absolute elevations

Keydel 2007, Polarimetry and Interferometry Applications

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DEMs available for TEIS

  • Reference Elevation Model of Antarctica (REMA)
  • Other stereo satellites (eg. ASTER)
  • Historical air photos
  • TanDEM-X and other InSAR-derived DEMs

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DEMs available for TEIS

  • Reference Elevation Model of Antarctica (REMA)
  • Other stereo satellites (eg. ASTER)
  • Historical air photos
  • TanDEM-X and other InSAR-derived DEMs

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Reference Elevation Model of Antarctica (REMA)

  • Derived from DigitalGlobe optical stereopairs, mostly from 2015 and 2016
  • Antarctic mosaic available at 8 m resolution
  • Individual strips available at 2 m resolution
  • DEMs vertically referenced using altimetry data (more on that in a minute)
  • Very similar product available for the entire Arctic (ArcticDEM)

Howat et al. (2019)

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Reference Elevation Model of Antarctica (REMA)

  • Derived from DigitalGlobe optical stereopairs, mostly from 2015 and 2016
  • Antarctic mosaic available at 8 m resolution
  • Individual strips available at 2 m resolution
  • DEMs vertically referenced using altimetry data (more on that in a minute)
  • Very similar product available for the entire Arctic (ArcticDEM)

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Reference Elevation Model of Antarctica (REMA)

  • Derived from DigitalGlobe optical stereopairs, mostly from 2015 and 2016
  • Antarctic mosaic available at 8 m resolution
  • Individual strips available at 2 m resolution
  • DEMs vertically referenced using altimetry data (more on that in a minute)
  • Very similar product available for the entire Arctic (ArcticDEM)

REMA Strip Index

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Reference Elevation Model of Antarctica (REMA)

  • Derived from DigitalGlobe optical stereopairs, mostly from 2015 and 2016
  • Antarctic mosaic available at 8 m resolution
  • Individual strips available at 2 m resolution
  • DEMs vertically referenced using altimetry data (more on that in a minute)
  • Very similar product available for the entire Arctic (ArcticDEM)

Example REMA strip

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Reference Elevation Model of Antarctica (REMA)

  • Derived from DigitalGlobe optical stereopairs, mostly from 2015 and 2016
  • Antarctic mosaic available at 8 m resolution
  • Individual strips available at 2 m resolution
  • DEMs vertically referenced using altimetry data (more on that in a minute)
  • Very similar product available for the entire Arctic (ArcticDEM)

REMA Mosaic

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Project: Thwaites Eastern Ice Shelf thinning

  • Establish coordinate system
  • Product options:
    • Stereo-derived digital elevation models
    • Altimetry
  • Change detection
    • DEM differencing
    • Crossovers
    • Lagrangian vs. Eulerian reference frames
  • Floating ice challenges

​

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Altimetry

  •  

https://icesat-2.gsfc.nasa.gov

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Radar altimeters

  • Relatively large footprint
    • e.g. Cryosat-2 has a 1.67 km footprint across-track
  • Will penetrate some distance into the snow surface

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Topex/Poseidon data:

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Laser altimeters

  • Operate in optical (or near optical) wavelengths
  • Much smaller footprint size (e.g. ICESat-2 is ~15 m)
  • Does not penetrate the snow surface
  • Extremely accurate – on the order of centimeters
  • Disadvantages?

https://icesat-2.gsfc.nasa.gov

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Referencing DEMs

  • Altimeters have a limited footprint
    • Don’t completely cover the Earth, need to be interpolated for continuous grids
  • DEMs need ground control to be accurate
  • Can use altimetry from the same time period as a DEM to provide ground control for the DEM
    • (Assume horizontal positioning is correct)

Example REMA strip with ICESat-2 data

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Altimetry for TEIS

  • Cryosat
  • ICESat and ICESat-2
  • IceBridge ATM

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Altimetry for TEIS

  • Cryosat
  • ICESat and ICESat-2
  • IceBridge ATM

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ICESat and ICESat-2

  • Ice, Cloud, and land Elevation Satellites
  • ICESat: 2003-2009
  • ICESat-2: 2018-present
    • 90-day repeats

Smith et al. 2020

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ICESat-2 at TEIS

  • All available tracks

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ICESat-2 at TEIS

  • Tracks with good quality in the 2023-2024 summer season

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ICESat-2 at TEIS

  • And, as mentioned previously, can use ICESat-2 to reference DEMs

Example REMA strip with ICESat-2 data

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Project: Thwaites Eastern Ice Shelf thinning

  • Establish coordinate system
  • Product options:
    • Stereo-derived digital elevation models
    • Altimetry
  • Change detection
    • DEM differencing
    • Crossovers
    • Lagrangian vs. Eulerian reference frames
  • Floating ice challenges

​

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DEM differencing

  • Once you have a set of correctly referenced DEMs, height change estimates are straightforward
  • Easy to see spatial variations at relatively high resolution

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TanDEM-x DEM differencing at the grounding line of Thwaites, Bevan et al. (2021)

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Crossover analysis

  • Altimetry paths cross at oblique angles, allowing for direct differencing of values at those points
  • Coarse resolution; lots of data can’t be used
    • Can be gridded at coarse resolution, good for large-area changes

Smith et al. (2020)

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Crossover analysis

  • Altimetry paths cross at oblique angles, allowing for direct differencing of values at those points
  • Coarse resolution; lots of data can’t be used
    • Can be gridded at coarse resolution, good for large-area changes

​

Smith et al. (2020)

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Careful with slopes

  • ICESat-2 has multiple beams
  • Tracks don’t always exactly align
    • E.g. May solar storm knocked ICESat-2 slightly out of its intended orbit; have to make orbital corrections to return to intended ground tracks
  • If working in an area with high slopes, small errors in ground tracks lead to big errors in change estimates

Smith et al. (2020)

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Careful with slopes

  • ICESat-2 has multiple beams
  • Tracks don’t always exactly align
    • E.g. May solar storm knocked ICESat-2 slightly out of its intended orbit; have to make orbital corrections to return to intended ground tracks
  • If working in an area with high slopes, small errors in ground tracks lead to big errors in change estimates

Smith et al. (2020)

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Solution: Difference altimetry with DEMs

  • Can use all available tracks that overlap with the DEM
  • Slopes are accounted for in the DEM

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Lagrangian and Eulerian reference frames

t1

Ice flow direction

  • Eulerian reference frame: measures change at a fixed point in space
  • Lagrangian reference frame: measures change following the flow of ice parcels

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Lagrangian and Eulerian reference frames

t1

Ice flow direction

t2

  • Eulerian reference frame: measures change at a fixed point in space
  • Lagrangian reference frame: measures change following the flow of ice parcels

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Lagrangian and Eulerian reference frames

  • Eulerian reference frame: measures change at a fixed point in space
  • Lagrangian reference frame: measures change following the flow of ice parcels

t1

Ice flow direction

t2

Average surface decreased

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Lagrangian and Eulerian reference frames

  • Eulerian reference frame: measures change at a fixed point in space
  • Lagrangian reference frame: measures change following the flow of ice parcels

t1

Ice flow direction

t2

Average surface decreased

Surface height here increased

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Lagrangian and Eulerian reference frames

  • Eulerian reference frame: measures change at a fixed point in space
  • Lagrangian reference frame: measures change following the flow of ice parcels

t1

Ice flow direction

t2

Average surface decreased

Surface height here increased

Alternative: use ice flow observations to re-align parcels

Eulerian

t1

t2

Lagrangian

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Lagrangian and Eulerian reference frames

  • Thought question:
    • True or false: On a steady-state, unconfined ice shelf, Lagrangian measurements of change should always show thinning

​

t1

Ice flow direction

t2

Average surface decreased

Surface height here increased

Alternative: use ice flow observations to re-align parcels

Eulerian

t1

t2

Lagrangian

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Thinning on Thwaites Eastern Ice Shelf

  • Differenced ICESat-2 (2018-2020) to REMA (~2016)

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Eulerian elevation change

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Lagrangian elevation change

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Project: Thwaites Eastern Ice Shelf thinning

  • Establish coordinate system
  • Product options:
    • Stereo-derived digital elevation models
    • Altimetry
  • Change detection
    • Crossovers
    • DEM differencing
    • Lagrangian vs. Eulerian reference frames
  • Floating ice challenges

​

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Note on altimetry corrections

  • Raw data often requires correction to be accurate
    • E.g. ICESat developed a laser bias over time
  • Data also come with quality flags that can be used to filter bad measurements
  • Derived products might have some errors already corrected

https://icesat-2.gsfc.nasa.gov

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Additional corrections for floating ice

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Additional corrections for floating ice

Ocean tides

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Additional corrections for floating ice

Ocean tides

Load tides

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Additional corrections for floating ice

Ocean tides

Load tides

Inverse barometric effect