Sea Level Rise

Hybrid Gravimetry and Altimetry Mass Balance

Posted by William Colgan on July 07, 2015
Communicating Science, New Research, Sea Level Rise / No Comments

We have a new study in this month’s Remote Sensing of Environment, which examines satellite-derived glacier mass balance in Greenland and the Canadian Arctic1. Satellites are generally used to assess glacier mass balance through changes in volume (via satellite altimetry) or changes in mass (via satellite gravimetry). While satellite altimetry observes volume changes at relatively high spatial resolution, it necessitates the forward modeling of firn processes to convert volume changes into mass changes. Conversely, the cryosphere-attributed mass changes observed by satellite gravimetry, while very accurate in absolute terms, have relatively low spatial resolution. In this study, we sought to combine the complementary strengths of both approaches. Using an iterative inversion process that was essentially sequential guess-and-check with a supercomputer, we refined gravimetry-derived observations of cryosphere-attributed mass changes to the relatively high spatial resolution of altimetry-derived volume changes. This gave us a 26 km spatial resolution mass balance field across Greenland and the Canadian Arctic that was simultaneously consistent with: (1) glacier and ice-sheet extent derived from optical imagery, (2) cryospheric-attributed mass trends derived from gravimetry, and (3) ice surface elevation changes derived from altimetry. We have made digital versions of this product available in the supplementary material associated with the publication.


Figure 1 – Observational data inputs to our inversion algorithm. A: Cryosphere-attributed mass changes observed by gravimetry. B: Land ice extent observed by optical imagery. C: Ice surface elevation changes observed by altimetry.

To make sure our inferred mass balance field was reasonable, we evaluated it against all in situ point mass balance observations we could find. Statistically, the validation was great, yielding an RMSE of 15 cm/a between the inversion product and in situ measurements. Practically, however, this apparent agreement largely stems from the fact that we could only find forty in situ point mass balance observations against which to compare. Evaluating our area-aggregated sector-scale mass balance estimates against all previously published sector-scale estimates provides a more meaningful validation. This suggests the magnitude and spatial distribution of inferred mass balance is reasonable, but highlights that the community needs more in situ point observations of mass balance, especially from peripheral glaciers and regions of high dynamic drawdown in Greenland. (For the glaciology hardcores I will note that “mass balance” is distinct from “surface mass balance”, in that the former measurement also includes the ice dynamic portion of mass change.)


Figure 2 – A comparison of similar sector scale mass balance estimates and associated uncertainties across Greenland and the Canadian Arctic. Dashed lines denote estimates that pertain to the Greenland ice sheet proper (i.e. exclusive of peripheral glaciers). Jacob et al. (2012) estimates pertain to Canada, while Sasgen et al. (2012) estimates pertain to Greenland.

This new inversion mass balance product, which we are calling “HIGA” (Hybrid glacier Inventory, Gravimetry and Altimetry), suggests that between 2003 to 2009 Greenland lost 292 ± 78 Gt/yr of ice and the Canadian Arctic lost  42 ± 11 Gt/yr of ice. While the majority of Greenland’s ice loss was associated with the ice sheet proper (212 ± 67 Gt/yr), peripheral glaciers and ice caps, which comprise < 5 % of Greenland’s ice-covered area, produced ~ 15 % of Greenland mass loss (38 ± 11 Gt/yr). A good reminder that ice loss from “Greenland” is not synonymous with ice loss from the “Greenland ice sheet”. Differencing our tri-constrained mass balance product from a simulated surface mass balance field allowed us to assess the ice dynamic component of mass balance (technically termed the “horizontal divergence of ice flux”). This residual ice dynamic field infers flux divergence (or submergent ice flow) in the ice sheet accumulation area and at tidewater margins, and flux convergence (or emergent ice flow) in land-terminating ablation areas. This is consistent with continuum mechanics theory, and really highlights the difference in ice dynamics between the ice sheet’s east and west margins.


Figure 3 – Spatially partitioning the glacier continuity equation in surface and ice dynamic components. A: Transient glacier and ice sheet mass balance. B: Simulated surface mass balance. C: Residual ice dynamic (or horizontal divergence of ice flux) term. The ∇Q color scale is reversed to maintain blue shading for mass gain and red shading for mass loss in all subplots. Color scales saturate at minimum and maximum values. Black contours denote zero.

As with some scientific publications, this one has a bit of a backstory. In this case, we submitted a preliminary version of the study to The Cryosphere in December 2013. After undergoing three rounds of review at The Cryosphere, the first one of which is archived in perpetuity here, it was rejected, primarily for insufficient treatment of the uncertainty associated with firn compaction. Coincidentally, on the same day I received The Cryosphere rejection letter, I received a letter from the European Space Agency (ESA) granting funding for a follow-up study. A mixed day on email indeed! After substantial retooling, including a discussion section dedicated to firn compaction and the most conservative error bounds conceivable, we were happy to see this GRACE-ICESat study funded by NASA and the Danish Council for Independent Research appear in Remote Sensing of Environment. The editors at both journals, however, were very helpful in moving us forward. Our ESA-funded GRACE-CryoSat product development is now ongoing, but a sneak peek is below.


Figure 4 – Same as Figure 3, except using a 5 km resolution GRACE-CryoSat inversion product instead of a 26 km resolution GRACE-ICESat inversion product. Colorbars are different in shading, but identical in magnitude.


1W. Colgan, W. Abdalati, M. Citterio, B. Csatho, X. Fettweis, S. Luthcke, G. Moholdt, S. Simonsen, M. Stober. 2015. Hybrid glacier Inventory, Gravimetry and Altimetry (HIGA) mass balance product for Greenland and the Canadian Arctic. Remote Sensing of Environment. 168: 24-39.

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Greenland ice loss: 8300 tonnes per second

Posted by William Colgan on November 19, 2014
Communicating Science, New Research, Sea Level Rise / No Comments

We have a new study coming out in Earth and Planetary Science Letters that looks into the mass loss of the Greenland ice sheet (Andersen et al., 2015). We used the “input-output” approach, whereby an estimated iceberg production rate is differenced from an estimated snow accumulation rate. The input-output approach we used was slightly different from previous studies (such as Rignot et al., 2008 or Enderlin et al., 2014) because the ice sheet perimeter across which we observed ice flow (or the “flux gate”) was relatively far inland. That meant we had to make a different assumption about the vertical velocity profile at the flux gate, as well as account for changes in ice volume between the flux gate and the tidewater glacier grounding lines. We also used a new combination of satellite-derived ice surface velocity product, airborne radar-derived ice thickness observations, and surface mass balance simulations. Despite all this, our mass loss estimate agrees pretty well with previous studies!

The numbers are pretty striking: We estimate that between 2007 and 2011 the Greenland ice sheet alone, not counting all the peripheral glaciers in Greenland, lost 262 Gt of ice per year. That works out to about 8300 tonnes per second! That means the Greenland ice sheet probably weighs 250,000 tonnes less than when you started reading this blog post. No wonder we can measure its mass loss by gravitational anomalies! The ice sheet is currently losing mass via both surface runoff (the difference between accumulation and melt) and ice dynamics (the production of icebergs). We estimate that runoff comprised about 61 % of the ice sheet’s mass loss, or about 5000 tonnes per second, with iceberg production comprising the remaining 3300 tonnes per second of mass loss. Some big numbers that confirm the Greenland ice sheet is presently raising global mean sea level by about 0.73 mm per year.

Enderlin, E., I. Howat, S. Jeong, M. Noh, J. van Angelen & M. van den Broeke. 2014. An improved mass budget for the Greenland ice sheet. Geophysical Research Letters. 41: doi:10.1002/2013GL059010.

Rignot, E., J. Box, E. Burgess & E. Hanna. 2008. Mass balance of the Greenland ice sheet from 1958 to 2007. Geophysical Research Letters. 35: doi:10.1029/2008GL035417.

Andersen, M., L. Stenseng, H. Skourup, W. Colgan, S. Khan, S. Kristensen, S. Andersen, J. Box, A. Ahlstrøm, X. Fettweis & R. Forsberg. 2015. Basin-scale partitioning of Greenland ice sheet mass balance components (2007–2011). Earth and Planetary Science Letters. 409: 89–95. doi:10.1016/j.epsl.2014.10.015.


Diagram showing differences in methodology between our study (TOP) and previous studies (BOTTOM) in converted estimated ice flux (F) into estimated iceberg production (D). We adopt a higher elevation “flux gate”, which necessitates accounting for downstream changes in ice volume (∆S), as well as making a different assumption about the vertical velocity profile at the flux gate. We also use different velocity and ice thickness observations, and a different surface mass balance (SMB) model (from Andersen et al., 2015).

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