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Model Classes

In order to engage the largest segment of the ice sheet modeling community as possible, we will define the following four classes of ice sheet models.

Large scale is defined as models capable of simulating the entire Antarctic or Greenland ice sheets at 10 km or less resolution on presently available computer hardware.

  1. Thermomechanically coupled models with a shallow ice approximation (SIA) for the momentum balance.
  2. Thermomechanically coupled models with a higher order stress balance. Presently, models in involved have vertically integrated Stokes's flow hybridized with SIA, or a so called first order model, similar to either Blatter 95 or Pattyn 03.

Regional models.

  1. Ice stream/ice shelf models.
  2. Ice-Shelf/Ocean

Each of the four classes will be assigned specific aspects of the simulations. The third and fourth classes are regional models and interact with the whole ice sheet models as outlined below. Each class is described in more detail below, along with the experiments intended for each.

Model Verification

Testing models against analytic metrics and model intercomparisons are valuable means of model verification. Test results that that should be considered for participating models are

  3. Buler's exact solutions for isothermal and thermomechanically coupled shallow ice flow.
  4. Ross Ice shelf intercomparison.

Set-Up and Initialization

Surface and bed geometries, ice thickness and precipitation are available for both Greenland and Antarctica through the Community Ice Sheet Model (CISM) project (see Table 2). Most of the whole ice sheet models can use a similar grid size, so spatial interpolations of these data sets should create only small variations between the geometric initializations of different models. Geothermal heat flux is included for Antarctica in Table 2, but a similar field for Greenland is missing and must be produced. Could possibly do this based on the results of lithospheric thickness map from Braun et al., 2007 (EPSL, v.262, 138-158).Kees has something from CReSIS that I need to follow up on.

Initial temperature fields are missing and are frequently generated through the procedure of “spin-up”. Table 2 includes fields of past temperature and sea level to guide the spinning up of a model. Often spin-up spans many glacial-interglacial cycles in order to diminish numerical artifacts from initialization. Spin up is a very computationally demanding process, and it is unlikely that models other than the whole ice sheet models with a shallow ice balance of stresses can complete the process. Recognizing this, data sets based on a long (150,000 year) spin up process will be provided as a reference by CISM efforts. These reference spin ups can then be used as an initial condition for models that must utilize some other spin up procedure due to differences in stress balance or other model features. Additionally, in regions where interferometrically derived velocity data is not available, such as the upper reaches of the drainage basins investigated by regional models, output from reference spin ups can be used for kinematic boundary conditions.

One requirement for this effort is for the model to be devoid of non-physical transients in the future behavior of the ice sheet at T0, i.e. the present day, so that control and future climate experiment runs can be made without needing to consider these non-physical transients. It is also important to keep in mind that the primary time horizon of interest in this effort is 100 years, with secondary interest extending out to as long as 500 years.

The second requirement for spin up of models is that data provided by CISM efforts are used for whatever spin up process is utilized. This consists of modern day fields for surface, mean annual accumulation, InSAR surface velocity, and temperature. If lapse rates, sea level records, or ice core data are used as part of a spin up process, values consistent with those in references provided in Table 2 should be used.

Similarly, basal conditions, subglacial hydrology and other internal or boundary fields may have to be generated by individual models, unless models are so similar in their parameterization that it makes sense to specify these for all models. Again, there are reference spin up results from SIA models to initialize the process.

A vexing problem to decide will be the prescribed state of balance at T0. One target could be equilibrium, but this is known to be incorrect. It might be appropriate to specify a spatial field of the rate of elevation change at T0. This is becoming well determined from satellite altimetry for most of the ice sheets, although it is changing rapidly in some areas. There are published fields that could be applied appropriate for specific time periods approaching T0. It’s unclear to me how one is supposed to tune a model to match an observed field of dH/dt. Is there a suggested procedure for how to do this? Is that what is being suggested here? It’s an interesting idea that I’ve heard before, but seems to be really unconstrained. Too many parameters could contribute to a dH/dt value in a non-linear way.

Again, what is most important is that each model has a minimal amount of non-physical transients at T0 and that it be a close approximation of the current geometric and dynamic state of either ice sheet. The degree to which it deviates from any other model is of lesser concern than the fact that its own deviations of future climate experiments from its own control run accurately capture predictions of physical changes in ice sheet mass.

Control Run

The control run of each model is the reference against which all climate change experiments will be compared. A reasonable choice for this control run is a continuation of the present climate run for 500 years into the future. All forcing fields such as temperature, precipitation and basal conditions (if these are prescribed) can be held fixed to their T0 values. In cases where the T0 state is not equilibrium state, the control run will contain a prediction of ice mass changes. These will be subtracted from ice mass changes resulting from changed-climate experiments to obtain the full sea level contribution.

Future Climate Experiments

The experiments described below are intended to give an initial quantitative assessment of how large the ice sheet contribution to sea level could be. The experiments are discussed separately for Greenland and Antarctica.

There are two important ways climate can quickly alter ice sheet dynamics. In terms of how the ice sheet model is formulated these amount to

  • perturbations that are imposed at the ice sheet margin, or
  • perturbations that are imposed at the base of the ice sheet.

There is also significant coupling between the two types of perturbations. For example, the rate at which a marginal perturbation propagates to the interior of the ice sheet will depend strongly on the nature of the bed.

Basal Perturbations

Significantly different outcomes can result from the model for bed strength that is used. The two most commonly used models are for plastic and power law materials. Plastic bed models are believed to be appropriate for ice that rests on marine sediments, whereas a power law relation for bed strength might be more appropriate for ice resting on a layer of exposed bedrock.

Hard Bed

A model for basal traction in cases where the bed consists of exposed bedrock is formulated as a power law material.

\tau_{bx} = \beta^2 u^{\left(\frac{1}{m} - 1\right)} |\mathbf{v}|

\tau_{by} = \beta^2 v^{\left(\frac{1}{m} - 1\right)} |\mathbf{v}|

Soft Bed

The formulation for basal traction due to plastic bed is

\tau_{bx} = \tau_0 \frac{u}{ |\mathbf{v}|}

\tau_{by} = \tau_0 \frac{v}{|\mathbf{v}|}.

Where |\mathbf{v}| = (u^2 + v^2)^{\frac{1}{2}}

Penetration of Surface Melt to the Bed

It has often been speculated that surface melt that reaches the bed can provide lubrication, and result in enhanced basal sliding. There is some empirical evidence of this; Shepard et. al. 2008 provides an estimate of 35% increase in velocity for each positive degree day. This is quite easy to parameterize, and is a good base line for a set of experiments. It also has the advantage of being an experiment that all models (SIA and HO) could participate in.

Basal Hydrology

Even in cases where there is no penetration of surface melt, changes in bed strength may be occurring as a result of internal changes in the distribution of basal melt water. Modeling of this behavior is still quite speculative, as there are few direct measurements for comparison with modeling results. One approach is to assume that the basal traction, which can be computed from an inversion of the surface velocity data, is coupled to the distribution of basal water. This amounts to a fitting exercise, correlating bed strength with modeled basal water distribution. The strength of this approach is that it is constrained by data, and would allow for the dynamical evolution of the bed strength. A method of strengthening the correlation between water distribution and bed strength is to introduce a generalized linear model with inputs of both basal water distribution and bed curvature. This would isolate the roles of basal water from that of bed protrusions. Finally, basal water distribution could interact with surface melt that reaches the bed. Again, it might be possible to isolate the role of each component of the system (basal water, surface melt, geometric features of the bed) in basal traction with generalized linear models.

Marginal Perturbations

Many deep outlet glaciers at Greenland’s perimeter are experiencing dramatic acceleration, increasing the present rate of ice loss. These changes appear to resemble drastic retreat of tidewater glaciers, a phenomenon known to lead to sustained and rapid retreat of calving glacier termini, and both flow acceleration and ice thinning, each propagating upstream. Increasingly, modeling results demonstrate that application of perturbations at the terminus of glaciers result in larger dynamical responses than application of perturbations within the ice, in the form of altered basal sliding. This result is concerning due to data on warming oceans.

There are three methods for introducing a perturbation at or near the grounding line.

1. Altering the Force Balance at the Margin

There are two entry points for this perturbation.

  1. The basal traction is lowered.
  2. The longitudinal stress balance (dynamic boundary condition at the margin) is altered.

1. is used in Joughin et. al. (in Press) and 2. is used by Nick et. al. (2008). Both have significant impacts on the interior of the glacier on short time scales. Both are justified by ice in contact with a warming ocean. Neither is possible for SIA type models, but both can be used with the vertically integrated and first order models of Stokes flow.

2. Thinning an Ice Shelf

This can be done by simply increasing the melt rate on the ice shelf. Rignot reports that there is good empirical evidence of a cubic (?) relation between the melt rate and the ocean temperature.

3. Removal of an Ice Shelf

The most dramatic perturbation too the terminus of an ice sheet would be complete removal of an ice shelf. These experiments must be done with some care, as there is a real danger of introducing numerical artifacts with the abrupt removal of an ice shelf. Diagnostic solutions for velocities fields with and with out an ice shelves present are a possibility for ice sheet models capable of resolving the ice shelf ice stream system. The greater concern would be the prognostic solutions for the ice streams over the coming 100 year. As this is an exercise in finding upper bounds it would probably be appropriate to just take the ice flux after removal and maintain it for the next 100 years.

Climate Forcing

For the next 100 years, climate forcing data sets will be prepared based on AR4 forecasts. Because upper bounds on sea level rise are being sought, the most extreme scenarios (A1F1) will be used. The data will consist of daily surface temperature and total precipitation fields, from a weighted average of AR4 climate models. Because the more customary forcing fields for ice sheet models are mean annual surface temperature and accumulation, CISM group participants will apply positive degree day schemes to the data and provide reduced data sets as well. Additional assumptions about lapse rates will have to be made in order to downscale the GCM data (~140 km grid) to ice sheet model grids (2-10 km). This will also be done by the CISM group.


Scenarios that will be tested in Antarctica include:

  • Removal of ice shelves, both likely cases, as well as dramatic cases.
  • Grounding line perturbations in the ASE by altering dynamic boundary condition.
  • Investigation of surface melting if AR4 climate forcing does this.
  • Investigation of plastic vs. power law beds.


Modeling scenarios to be investigated here will include:

  • The marginal perturbations applied to major outlet glaciers. Changing the dynamic boundary condition at the terminus is best. Altering the basal traction should be done too.
  • The parameterization of surface melt and basal sliding should be explored in depth.

The danger with these experiments is that with out carefully controlled ones, the signals arising from each forcing will be difficult to isolate.