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Introduction to CESM [Reprint]

 
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This article comes from : http://websrv.cs.umt.edu/isis/index.php/Introduction_to_CESM

 

Introduction to CESM

From Interactive System for Ice sheet Simulation

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Contents

  • 1 Back to Thursday, March 24th
  • 2 Land Ice in the Community Earth System Model
    • 2.1 A brief introduction to CESM
    • 2.2 Land-ice models and sea-level rise
    • 2.3 Ice sheets in CESM
    • 2.4 Simulating the surface mass balance of ice sheets
      • 2.4.1 Motivation for a surface mass balance scheme in CLM
      • 2.4.2 Details of the new SMB scheme
    • 2.5 References

 

Land Ice in the Community Earth System Model

William Lipscomb, Los Alamos National Laboratory

A brief introduction to CESM

The Community Earth System Model (CESM; http://www.cesm.ucar.edu/ ) is a global, fully-coupled climate model that provides state-of-the-art computer simulations of the Earth's past, present, and future climate. It is one of three U.S. global climate models featured prominently in the assessment reports of the Intergovernmental Panel on Climate Change (IPCC). (The others are the NASA GISS model and the NOAA GFDL model.) As the name suggests, CESM is a broad community effort. Although model development is centered at the National Center for Atmospheric Research (NCAR) in Boulder, Colorado, there have been substantial contributions from scientists at several national laboratories and many universities, with support from the U.S. Department of Energy (DOE) and the National Science Foundation (NSF).

CESM is the successor to the Community Climate System Model (CCSM). The initial version of CESM was released in June 2010. Model development is carried out by twelve working groups that focus on different aspects of model development and application, overseen by a Scientific Steering Committee. The CESM community meets once a year, usually in June in Breckenridge, Colorado. In addition, each working group holds a winter meeting, usually in Boulder.

The newest CESM working group is the Land Ice Working Group (LIWG), whose main missions are to develop and apply a dynamic ice sheet model in CESM and to predict the contribution of land ice to sea-level rise. The LIWG is co-chaired by Jesse Johnson and William Lipscomb, and Stephen Price is the scientific liaison. See here for details: http://www.cesm.ucar.edu/working_groups/Land+Ice/

CESM consists of five physical models: atmosphere (atm), ocean (ocn), land (lnd), sea ice (ice), and land ice (glc). The land ice component is new to CESM; it was not included in CCSM. A central coupler coordinates the models and passes information between them. Each model can have active, data, dead, and stub components. An active component is a prognostic physical model. Data components provide scientifically valid input data for cases where an active model is not needed, whereas dead components generate invalid data that is used only for system testing. Stub components are present only to meet interface requirements when a component is not needed.

The active components of CESM are CAM (the Community Atmosphere Model), POP (the Parallel Ocean Program), CLM (the Community Land Model), CICE (the Community Ice Code), and CISM (the Community Ice Sheet Model). The current version on CISM is also known as Glimmer-CISM, since it is based on the Glimmer ice sheet model developed by Tony Payne and colleagues at the University of Bristol.

These components can be run in many different configurations. A particular mix of components is called a component set, or “compset”. Among the common compsets are B (fully coupled, with all active components), F (active CAM, CLM, and CICE, with a data ocean), and I (active CLM, data atmosphere, and stub sea ice and ocean). These configurations all use a stub land-ice component. The corresponding configurations with an active land-ice component are called BG, FG, and IG, respectively.

The CESM components can be run on a variety of grids. Often, one global grid is used for the atmosphere and land, and a second global grid is used for the ocean and sea ice. The ice-sheet component has a regional grid for each active ice sheet. Currently, CESM allows simulations only for the Greenland ice sheet; Antarctic simulations will be supported later. Three Greenland grids are supported, with resolutions of 5, 10 and 20 km. Each of these grid is a polar stereographic projections with rectangular grid cells.

CESM is always run in parallel, on anywhere from ~10 to ~10,000 processors. The components can be run either concurrently (all at the same time, but on different sets of processors) or sequentially (one after the other, with each component using all the available processors).

CESM code is publicly available through a Subversion repository. The code can be checked out using Subversion client software, such as the command tool svn, or viewed with a web browser. To access the repository, you can register here:

http://www.cesm.ucar.edu/models/cesm1.0/register/register_cesm1.0.cgi

After registering, you will receive an email containing a user name and password that is required for access to the repository.

For a detailed description of CESM, see the CESM1.0 User's Guide: http://www.cesm.ucar.edu/models/cesm1.0/cesm/

Land-ice models and sea-level rise

Historically, ice sheet models were not included in global climate models (GCMs), because ice sheets were thought to be too sluggish to respond to climate change on decade-to-century time scales. In CCSM, as in many other global climate models, the extent and elevation of the Greenland and Antarctic ice sheets were fixed in time. Interactions between ice sheets and other parts of the climate system were largely ignored.

Recent observations, however, have shown that the Greenland and Antarctic ice sheets can respond to atmospheric and ocean warming on time scales of a decade or less. Satellite gravity measurements indicate that both ice sheets are losing mass at a rate of more than 200 Gt/yr, roughly double the values from earlier this decade (Velicogna 2009). (A mass loss of 360 Gt corresponds to global sea-level rise of 1 mm.) Greenland mass loss is caused by increased surface melting and the acceleration of large outlet glaciers (van den Broeke et al. 2009). In Antarctica, mass is being lost primarily because of the acceleration of outlet glaciers, especially in the Amundsen Sea Embayment of West Antarctica (Rignot et al. 2008).

Small glaciers and ice caps (GIC) also have retreated in recent years. Although the total volume of GIC (~0.6 m sea-level equivalent; Radić and Hock 2010) is much less than that of the Greenland ice sheet (~7 m) and the Antarctic ice sheet (~60 m), glaciers and ice caps can respond quickly to climate change. Mass loss from GIC has grown during the past decade and is now about 400 Gt/yr (Meier et al. 2007). Climate models generally assume that the mass of glaciers and ice caps, like that of ice sheets, is fixed.

During the past two decades, global sea level has been rising by about 3 mm/yr (i.e., 30 cm/century), with primary contributions from land-ice retreat and ocean thermal expansion. A recent study (Cazenave et al. 2008) suggests that land ice has accounted for up to 80% of recent sea-level rise. Estimates of 21st century ice-sheet mass loss and sea-level rise are highly uncertain. The IPCC Fourth Assessment Report (Meehl et al. 2007) projected 18 to 59 cm of sea-level rise by 2100 but specifically excluded ice-sheet dynamical feedbacks, in part because existing ice sheet models were deemed inadequate. A widely cited semi-empirical study (Rahmstorf 2007) estimated 40 to 150 cm of 21st century sea-level rise, based on the assumption that the rate of rise is linearly proportional to the increase in global mean temperatures from preindustrial values. This assumption may not be valid as additional land-ice processes come into play.

Modeling of land ice has therefore taken on increased urgency. Many recent workshops (e.g., Little et al. 2007; Lipscomb et al. 2009) have called for developing improved ice sheet models. There is general agreement on the need for (1) “higher-order” flow models with a unified treatment of vertical shear stresses and horizontal-plane stresses, (2) finer grid resolution (~5 km or less) for ice streams, outlet glaciers, and other regions where the flow varies rapidly on small scales, and (3) improved treatments of important physical processes such as basal sliding, sub-glacial water transport, iceberg calving, and grounding-line migration. These improvements are beginning to be incorporated in numerical ice sheet models. One such model is the Glimmer Community Ice Sheet Model (Glimmer-CISM), which was recently coupled to CESM.

Although much can be learned from ice sheet models in standalone mode, coupled models are required to capture important feedbacks. For example, surface ablation may be underestimated if the ice sheet model is not allowed to interact with an atmospheric model (Pritchard et al. 2008). At ice sheet margins, floating ice shelves are closely coupled to the ocean in ways that are just beginning to be understood and modeled. Also, changes in ice sheet elevation and surface runoff could have significant effects on the regional and global circulation of the atmosphere and ocean.

Two major community efforts are under way to assess the future ice-sheet contribution to sea-level rise and try to narrow the range of uncertainty. The European Union is supporting a large multinational effort called Ice2sea (http://www.ice2sea.eu/ ). Bob Bindschadler of NASA is leading a broad but less formal effort called SeaRISE (Sea-level Response to Ice Sheet Evolution; http://websrv.cs.umt.edu/isis/index.php/SeaRISE_Assessment .) Both Ice2sea and SeaRISE will provide input for the IPCC's Fifth Assessment Report, AR5, which is scheduled for release in 2013.

Ice sheets in CESM

Since 2006, researchers in the Climate, Ocean and Sea Ice Modeling (COSIM) group at Los Alamos National Laboratory (LANL) have worked with scientists at the National Center for Atmospheric Research (NCAR) to incorporate an ice sheet model in the CCSM/CESM framework. The Glimmer ice sheet model (Rutt et al. 2009 was chosen for coupling. Although Glimmer’s dynamical core was relatively basic, a higher-order dynamics scheme was under development. In addition, the model was well structured and well documented, with an interface (Glint) to enable coupling to climate models.

In 2009, the U.K. researchers who designed Glimmer joined efforts with U.S. scientists who were developing a Community Ice Sheet Model (CISM), and the model was renamed Glimmer-CISM. Model development is overseen by a six-member steering committee including Magnus Hagdorn (U. Edinburgh), Jesse Johnson (U. Montana), William Lipscomb (LANL), Tony Payne (U. Bristol), Stephen Price (LANL), and Ian Rutt (U. Swansea). The model resides on the BerliOS repository (http://glimmer-cism.berlios.de/ ). It is an open-source code and is freely available to all. The version included in the initial CESM release is a close approximation of Glimmer-CISM version 1.6.

Glimmer-CISM (or CISM for short) has been coupled to CESM version 1.0. The surface mass balance (SMB; the difference between annual accumulation and ablation) is not computed within CISM, but is passed to CISM via the coupler from the Community Land Model (CLM). This scheme computes the SMB in each of ~10 elevation classes per grid cell in glaciated regions. The SMB is passed via the coupler to the ice sheet component, where it is averaged, downscaled, and used to force the dynamic ice sheet model at the upper surface.

The ice sheet model in the initial CESM release has several significant limitations:

  • The model is technically supported but is still undergoing scientific testing. Default values of model parameters may not give an optimal simulation. Scientific validation is under way, and optimized configuration files will be included in future releases.
  • Glimmer-CISM has been coupled to CLM, but the current coupling is one-way. That is, the surface mass balance computed by CLM is passed to Glimmer-CISM and used to drive ice sheet evolution, but the resulting ice sheet topography is not used to update the surface elevation or landunit types in CLM. Two-way coupling is under development.
  • The dynamical core is similar to that in the original Glimmer code and is based on the shallow-ice approximation (SIA). The SIA is valid in the interior of ice sheets, but not in fast-flowing regions such as ice shelves, ice streams, and outlet glaciers. A higher-order scheme that is valid in all parts of the ice sheet is being tested and will become part of CESM in 2011 with the release of Glimmer-CISM version 2.0.
  • The current Glimmer-CISM code is serial. This is not a limitation for the SIA model, which is computationally fast, but will be an issue for the higher-order model. Glimmer-CISM 2.0 will support parallel simulations.
  • The ice sheet model has not been coupled to the ocean model; this coupling is still under development. Since ice-ocean coupling is critical for the dynamics of the Antarctic ice sheet, the initial ice-sheet implementation in CESM is for Greenland only.

Ongoing work will result in an improved ice sheet model in CESM. Here are a few of the projects under way:

  • In 2009 the U.S. DOE began the three-year Ice Sheet Initiative for Climate Extremes (ISICLES; http://www.csm.ornl.gov/ISICLES/ ), with the goal of developing advanced ice sheet models. Several groups have been funded to develop efficient, scalable solvers for higher-order approximations as well as the full-Stokes equations on unstructured and/or adaptive grids. As this work matures, new ice-sheet dynamical cores (“dycores”) will be added to Glimmer-CISM and to CESM.
  • Under the DOE IMPACTS project (http://esd.lbl.gov/research/projects/abrupt_climate_change/impacts/ ), scientists at LANL and elsewhere are developing methods for coupling ice sheet models to ocean circulation models. The major challenges include (1) modifying the ocean upper boundary condition so that water can circulate beneath ice shelves, (2) changing the ocean topography as ice shelves advance and retreat, and (3) simulating realistic migration of the grounding line, which will require very fine grid resolution and/or improved numerical methods.
  • A suite of climate change experiments using CESM with dynamic ice sheets will be run during the next year in preparation for IPCC AR5. We are currently using the shallow-ice version of Glimmer-CISM, but we will transition to a parallel, higher-order code when it is available.

Glimmer-CISM has already been described in detail by Steve Price. The rest of this document focuses on the surface-mass-balance scheme for ice sheets in CESM.

Simulating the surface mass balance of ice sheets

We can think of an ice sheet model as having two distinct physical components:

  • a surface mass balance (SMB) scheme, which computes accumulation and ablation at the upper ice/snow surface. Ablation is defined as the amount of water that runs off to the ocean. Not all the surface meltwater runs off; some of the melt percolates into the snow and refreezes.
  • a dynamic component, which computes ice velocities and the resulting evolution of the ice-sheet geometry and temperature fields.

The dynamic component of Glimmer-CISM is called Glide. The surface mass balance calculations are part of Glint, the Glimmer interface. Glint receives the required fields from a climate model or meteorological data set, accumulates and averages the data over a specified time period, and downscales the data to the finer ice-sheet grid. (In climate models, the land and atmosphere components are typically run at a grid resolution of ~100 km, whereas ice sheet models require a grid resolution of ~1--10 km.) The downscaled data is used to compute the surface mass balance, which is passed to Glide.

There are two broad classes of surface mass balance schemes:

  • positive-degree-day (PDD) schemes, in which the melting is parameterized as a function of the number of degree-days above the freezing temperature. The proportionality factor is empirical and may vary in time and space. This factor is larger for bare ice than for snow, since ice has a lower albedo.
  • surface energy-balance (SEB) schemes, in which the melting depends on the sum of the radiative, turbulent, and conductive fluxes reaching the surface. SEB schemes are more physically realistic than PDD schemes, but also are more expensive and complex.

Glimmer-CISM has a PDD scheme based on that of Huybrechts et al. (1991) and others. (See the Glimmer documentation for details.) However, PDD schemes are not ideal for climate change studies, because empirical degree-day factors could change in a warming climate. Comparisons of PDD and energy-balance schemes (e.g., van de Wal 1996; Bougamont et al. 2007) suggest that PDD schemes may be overly sensitive to warming temperatures. For example, Bougamont et al. found that a PDD scheme generates runoff rates nearly twice as large as those computed by an SEB scheme.

Glimmer-CISM does not currently have an SEB scheme, but might include one in the future. If such a scheme were available, one approach to computing surface melting would be as follows: The incoming shortwave and longwave fluxes, temperature, and humidity would be passed from the CESM atmosphere to Glint via the coupler. These fields would be downscaled to the ice sheet grid, using an assumed lapse rate to interpolate temperatures to the appropriate elevations on the ice sheet grid. The surface mass balance would then be computed from the downscaled atmosphere fields combined with a detailed snow model.

This approach would be sensible for working with meteorological data, e.g. from atmospheric reanalyses. In CESM, however, the preferred approach is to compute the surface mass balance for ice sheets in CLM, the land component, on the coarse-resolution land grid. To improve accuracy on the coarse grid, the mass balance is computed for ~10 elevation classes in each gridcell. The mass balance for each elevation class is accumulated and averaged over a coupling interval (typically ~1 day), then passed to Glint via the coupler. Glint accumulates and averages the mass balance over a longer interval (typically 1 year) and downscales it to the ice sheet grid. The ice sheet evolves dynamically, then returns the new ice geometry to CLM via the coupler.

Motivation for a surface mass balance scheme in CLM

There are several advantages to computing the surface mass balance in CLM as opposed to Glimmer:

  • It is much less computationally expensive to compute the SMB on the coarse land grid for ~10 elevation classes per grid cell than on the finer ice sheet grid. For example, suppose we are running CLM at a resolution of ~50 km and Glimmer at ~5 km. Greenland has dimensions of about 1000 x 2000 km. For CLM we would have 20 x 40 x 10 = 8,000 columns, whereas for Glimmer we would have 200 x 400 = 80,000 columns.
  • We take advantage of the fairly sophisticated snow physics parameterization already in CLM instead of implementing a separate scheme for Glimmer. When the CLM scheme is improved, the improvements are applied to ice sheets automatically.
  • The atmosphere model can respond during runtime to ice-sheet surface changes. As shown by Pritchard et al. (2008), runtime albedo feedback from the ice sheet is critical for simulating ice-sheet retreat on paleoclimate time scales. Without this feedback, the atmosphere warms much less, and the retreat is delayed.
  • It is easier to conserve mass, in the sense that the rate of surface ice growth or melting computed in CLM is equal to the rate seen by the dynamic ice sheet model.
  • The improved surface mass balance is available in CLM for all glaciated grid cells (e.g., in the Alps, Rockies, Andes, and Himalayas), not just grid cells that are part of ice sheets.

Details of the new SMB scheme

CLM has a hierarchical data structure that makes it relatively straightforward to model glaciated regions with multiple elevation classes. In the standard version of CLM, each grid cell is partitioned into one or more of five landunit types: vegetated, lake, wetland, urban, and glacier. Each landunit consists of a user-defined number of columns, and each column has its own vertical profile of temperature and water content.

When CLM is configured for ice sheets, there is a sixth landunit called glacier_mec, where “mec” stands for “multiple elevation classes.” Glacier_mec landunits are similar to glacier landunits, except that each elevation class is represented by a separate column. By default there are 10 elevation classes in each glaciated gridcell. The upper elevation bounds (in meters) of these classes are 200, 400, 700, 1000, 1300, 1600, 2000, 2500, 3000, and 10000.

The atmospheric surface temperature and specific humidity are downscaled from the mean gridcell elevation to the column elevation using a specified lapse rate (typically 6 deg/km). At a given time, the lower-elevation columns can undergo surface melting while columns at higher elevations remain frozen. This results in a more accurate simulation of summer melting, which is a nonlinear function of air temperature. The precipitation rate and radiative fluxes are not currently downscaled, but they could be, if care were taken to preserve the cell-integrated values. At some point we would like to use a more sophisticated orographic downscaling scheme, but this will require significant recoding.

When run without glacier_mec landunits, CLM has a fairly crude treatment of accumulation and melting on ice sheets. The snow depth is limited to a prescribed depth of 1 m liquid water equivalent, with any additional snow assumed to run off instantaneously to the ocean. Snow melting is treated more realistically, with meltwater percolating downward through snow layers as long as the snow is unsaturated. Once the underlying snow is saturated, any additional meltwater runs off. When glacier ice melts, however, the meltwater is assumed to remain in place until it refreezes. In warm parts of the ice sheet, the meltwater does not refreeze, but stays in place indefinitely.

In the modified CLM with glacier_mec landunits, snow in excess of the prescribed maximum depth is converted to ice, contributing a positive SMB to the ice sheet model. When ice melts, the meltwater is assumed to run off to the ocean, contributing a negative surface mass balance. The net SMB associated with ice formation (by conversion from snow) and melting/runoff is computed for each column, averaged over the coupling interval, and sent to the coupler. This quantity, denoted qice , is then passed to Glint, along with the surface elevation topo in each column. Glint downscales qice to the ice sheet grid, interpolating the values in adjacent elevation classes. The units of qice are mm/s, or equivalently km/m2 /s.

Note that the surface mass balance typically is defined as the total accumulation of ice and snow, minus the total ablation. The qice flux passed to Glint is the mass balance for ice alone, not snow. We can think of CLM as owning the snow, whereas CISM owns the underlying ice. The snow depth can fluctuate between 0 and 1 m LWE without this information being passed to CISM.

In addition to qice and topo , the ground surface temperature tsfc is passed from CLM to Glint via the coupler. This temperature serves as the upper boundary condition for the CISM temperature calculation.

Given the SMB from the land model, CISM executes one or more dynamic time steps and returns the new ice sheet geometry to CLM via the coupler. The fields passed to the coupler are the ice sheet fractional area and surface elevation, along with the conductive heat flux at the top surface and the freshwater fluxes from basal melting and iceberg calving. Glint upscales these fields from the ice sheet grid to the coarser land grid and bins them into elevation classes before sending them to the coupler.

The current coupling is one-way only. That is, CLM sends the SMB and surface temperature to Glint but does not do anything with the fields that are returned. This is permissible for century-scale runs in which the geometry changes are modest. In order to do longer runs with large geometry changes, we need to enable two-way coupling. That work is in progress.

The purpose of the surface mass balance scheme is to provide CISM with a realistic upper surface boundary condition in past, present, and future climates. To the extent that the present-day SMB is inaccurate (because of atmospheric biases, incomplete land model physics, or downscaling errors), the present-day ice sheet will have the wrong geometry, even if the ice sheet model is perfect. The greater the inaccuracy, the less confidence we will have in future projections.

So what is the quality of the results from the SMB scheme? We will explore that question in the lab exercise.

 

References

  • Bougamont, M., J.L. Bamber, J.K. Ridley, R.M. Gladstone, W. Greuell, E. Hanna, A.J. Payne, and I. Rutt, 2007: Impact of model physics on estimating the surface mass balance of the Greenland ice sheet, Geophysical Research Letters, 34, 10.1029/2007GL030700.
  • Cazenave, A., K. Dominh, S. Guinehut, E. Berthier, W. Llovel, G. Ramilien, M. Ablain, and G. Larnicol, 2008: Sea level budget over 2003-2008: A reevaluation from GRACE space gravimetry, satellite altimetry, and Argo, Global Planet. Change, doi:10.1016/j.gloplacha.2008.10.004.
  • Huybrechts, P., A. Letreguilly, and N. Reeh, 1990: The Greenland ice sheet and greenhouse warming, Palaeogeogr., Palaeoclimatol., Palaeoecol., (Global Planet. Change Sect.) 89, 399-412.
  • Lipscomb, W., R. Bindschadler, E. Bueler, D. Holland, J. Johnson, and S. Price, 2009: A community ice sheet model for sea level prediction, Eos Trans. AGU, 90, 23.
  • Little, C.M., M. Oppenheimer, R.B. Alley, V. Balaji, G.K.C. Clarke, T.L. Delworth, R. Hallberg, D.M. Holland, C.L. Hulbe, S. Jacobs, J.V. Johnson, H. Levy, W.H. Lipscomb, S.J. Marshall, B.R. Parizek, A.J. Payne, G.A. Schmidt, R.J. Stouffer, D.G. Vaughan, and M. Winton, 2007: Toward a new generation of ice sheet models, Eos Trans. AGU, 88, 578-579, doi:10.1029/2007EO520002.
  • Meehl, G.A., et al., 2007: Global climate projections, in Climate Change 2007: Contribution of Working Group I to the Fourth Assessment Report of the IPCC, edited by S. Solomon et al., pp. 747–846, Cambridge Univ. Press, New York.
  • Meier, M.F., M.B. Dyurgerov, U.K. Rick, S. O’Neel, W.T. Pfeffer, R.S. Anderson, S.P. Anderson, and A.F. Glazovsky, 2007: Glaciers dominate eustatic sea-level rise in the 21st century, Science, 317, 1064-1067.
  • Oppenheimer, M., B.C. O'Neill, M. Webster, and S. Agrawala, 2007: Climate change: The limits of consensus, Science 317 (5844), 1505.
  • Pritchard, M. S., A. B. G. Bush, and S. J. Marshall, 2008: Neglecting ice-atmosphere interactions underestimates ice sheet melt in millennial-scale deglaciation simulations, Geophys. Res. Lett. 35, L01503, doi:10.1029/2007GL031738.
  • Radić, V., and R. Hock, 2010: Regional and global volumes of glaciers derived from statistical upscaling of glacier inventory data, J. Geophys. Res., 2215, F01010.
  • Rahmstorf, S., 2007: A semi-empirical approach to projecting future sea-level rise, Science, 315, 368-370.
  • Rignot, E., J.L. Bamber, M.R. van den Broeke, C. Davis, Y. Li, W.J. van de Berg, and E. van Meijgaard, 2008: Recent Antarctic ice mass loss from radar interferometry and regional climate modeling, Nature Geo., 1, 106-110.
  • Rutt, I., M. Hagdorn, N.J.R. Hulton, and A.J. Payne, 2009: The Glimmer community ice sheet model, J. Geophys. Res., 114, F02004.
  • van de Wal, R.S.W. 1996: Mass-balance modeling of the Greenland ice sheet: A comparison of an energy-balance and a degree-day model, Annals of Glaciology 23: 36-45.
  • van den Broeke, M., J. Bamber, J. Ettema, E. Rignot, E. Schrama, W.J. van der Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, 2009: Partitioning recent Greenland mass loss, Science, 326, 984-986.
  • Velicogna, I., 2009: Increasing rates of ice mass loss from the Greenland and Antarctic ice sheets revealed by GRACE, Geophys. Res. Lett., 36, L19503.
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