Category 1: Whole Ice Sheet

SeaRISE began with commitments from leaders of six whole ice sheet models. A number of models have been added strengthening the multi-model ensemble approach. The original models (along with the lead institutions or modeler) were: 3D
• CCSM (Community Climate System Model; Los Alamos)
• PISM (Parallel Ice Sheet Model; University of Alaska)
• UMISM (University of Maine Ice Sheet Model; University of Maine)
• PSU (Penn State University; Penn State University)
• GLAM (GLimmer with Advanced Mechanics; Los Alamos and University of Bristol)
• SICOPOLIS (SImulation COde for POLythermal Ice Sheets; Hokkaido University)

2D
• Parizek Flowline (Penn State University)
• GLAM (Los Alamos and University of Bristol)

Table 1 presents some specific characteristics for each of these models for comparisons.

Models (and modelers) added and not yet with their characteristics included in Table 1 are:

• ELMER (Hakime Seddik)
• Goddard (Weili Wang)
• GRISLI (Catherine Ritz)
• PISM+ (Maria Martin)

Contents

Model Tests

Testing models against analytic solutions is a valuable means of model verification. For the research effort described in this document, such verification will be bypassed because the results sought from the individual models are the deviations in ice sheet volume over the next 100-200 years from a control run of the same model. It is less essential to have agreement of absolute behaviors among models. Even so, many of the above models have already been verified through model intercomparison studies such as EISMINT (I and II), MISMIP and ISMIP-HOM. Such heritage adds credibility to the results of the experiment set.

A principal advantage sought by using multiple models is the power of ensemble studies and is a well-accepted method of detecting less reliable results. Many of the above models derive from GLIMMER and share some common numerical components, so model-to-model independence is not as large as the sheer number of models might suggest. Nevertheless, there are enough differences between even similarly constructed models to make the ensemble methodology worthwhile as an evaluation criterion. Large excursions of one model’s results from the ensemble mean will help identify model components that must be examined carefully and will figure into the derivation of confidence in the associated ice-sheet response.

Set-Up and Initialization

Surface and bed geometries, ice thickness, precipitation and near-surface air temperature, along with other datasets, are available for both Greenland and Antarctica through the Community Ice Sheet Model (CISM) project. Most of the whole ice sheet models use a similar grid size, so spatial interpolations of these data sets should create only small variations between the geometric initializations of different models.

Initial internal ice temperature fields are missing and are frequently generated through the procedure of “spin-up”. To guide the spinning up of a model, past near-surface air temperature and sea level are available in the Model Initialization section. Often spin-up spans many glacial-interglacial cycles in order to diminish numerical artifacts from initialization and to “set” its internal temperatures in accord with a long history of variable external temperature conditions (i.e., temperature diffusion within the ice column is very slow, and current ice temperatures reflect past climates). Alternatively, assimilation procedures can be used to force the model to match currently observed fields (e.g., velocity, bed and surface topography).

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-approximation (SIA) balance of stresses will chose to 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 100-200 years, with secondary interest extending out to as long as 500 years.

A second requirement for model spin-up 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 the Data and Model Initialization sections should be used. Measurements of velocity over large parts of both ice sheets are available and balance velocities can be used, in some cases, to fill gaps.

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.

Our initial target for the prescribed state of balance at t0 is equilibrium, i.e., no net or local rate of volume change, even though this is known to be incorrect. It is a vexing modeling problem to initialize to a spatial field of non-zero elevation changes at t0, even though these changes are becoming well determined from satellite altimetry for most of the ice sheets. Many parameters could contribute to elevation change, some in a non-linear way, creating a highly unconstrained situation. This initial equilibrium condition might be relaxed in specific areas known to be changing rapidly to prevent a blatantly incorrect initial state.

The primary goal in set-up, spin-up and initialization 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.

Initialization data sets were frozen in October 2009 for the purposes of producing control runs. However, further discussion among SeaRISE participants have made it apparent that there is value in allowing parallel "developmental" data sets that either incorporate new observations and/or that improve model simulations. Developmental data sets may replace some of the original data sets and modelers are free to replace previous control and experiment runs with improved runs.

Control Run

The control run of each model is the reference against which all climate change experiments with that model will be compared. A reasonable choice for a control run is a continuation of the present climate run for 200 to 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 an equilibrium state, the control run will contain a prediction of additional ice mass changes. A “control-run” ice mass changes will be subtracted from ice mass changes resulting from changed-climate experiments to isolate the change that comes from experiment forcing.

Two control runs have been agreed upon:

• "Constant Climate Control (CC)” is, as it sounds, a run beginning at present and running for 200 (or 500) years holding the climate constant to the present climate.
• “4th Assessment Climate Control Run (AR4)” starts with the same present day condition, but the climate is modified according to anomalies from the present climate based on anomalies of the 4th Assessment model from a constant (t0) climate, up to year 2100. Beyond 2100, the year 2100 climate will persist to the end of the run (200 or 500 years).

For guidelines on how to submit your control run, see the Output Format section.

Experiments

Useful and feasible experiments are currently being fleshed out by the SeaRISE group. Agreed upon experiments are described below in sufficient detail for modelers to run the experiments and supply results to Sophie. (Please follow the submission requirements described in the Output Format section.)

The wiki format allows discussion of the experiments if they are either insufficiently clear or not feasible. Feedback is welcomed.

Greenland

Initial Experiment - E1 - Increased Basal Lubrication

The purpose of the initial Greenland experiment is to get a feel for the results of increased flux across the grounding line. Because most of Greenland's outlet glaciers lack an ice shelf large enough to be resolved in whole ice sheet models, the experiment forces an increase in modeled outlet glacier speed by doubling sliding speed everywhere. This condition has subtleties (next) but there are enough "adjustable knobs" on the basal relations in ice sheet models so as to make a version of this condition implementable.

Models vary in how sliding speed is calculated, and it is left up to the modeler to determine how to impose the doubling of sliding speed condition. The sliding speed and the basal shear stress are, generally, model results, not model inputs. Thus the implementation of this sliding speed doubling will likely involve adjustment of a lubrication or friction factor. An example mechanism is to halve the friction coefficient $C$ if sliding follows a linear relation: $\tau_b = C u$.

This is straightforward to understand and implement if the sliding velocity is a pointwise (local) function of basal shear stress, and vice-versa, and the basal shear stress is determined directly by the geometry (e.g. is the basal value of the driving stress). Such is true in the SIA. In the SIA case, therefore, a halving of $C$ for some patch of the ice base becomes a doubling of sliding speed in the same region directly. Dynamically, this doubling is sustained until the geometry (thus driving stress) undergoes significant change.

In models with longitudinal (membrane) stresses, however, sliding speed is not such a local function of ice sheet geometry. In most models we can still make an approximately-local assumption about the nature of sliding, and still replace a doubling of sliding speed condition by a halving of coefficient condition. With such a coefficient change there must be the understanding that the sliding speed will only actually double in the interior of large-ish patches where the basal shear stress was already fairly high. (At the extreme case we could replace $\tau_b = C u$ by $\tau_b = 0$, which multiplies $C$ by zero instead of 1/2, giving no basal resistance as in an ice shelf. But we would not expect the sliding velocity to be infinite because, as in ice shelves, membrane stresses connect to distant ice with high basal resistance.) If $C$ goes down by half in small patches, or even to zero, the velocity might not increase much at all because the ice flow is held steady by higher-basal-resistance neighboring columns.

A further condition is to require the basal ice to be at the pressure-melting point. This is likely already a condition for a non-zero sliding speed in most (all?) models. Thermodynamic feedbacks (i.e. not just geometry changes) may lead to the sliding speed initially doubling in response to a sliding coefficient change and then dropping again as basal strength increases; witness the century-scale response of Kamb Ice Stream (Kamb = C). It is preferred (by Bindschadler) that this doubling of sliding speed condition be dynamic, possibly spreading to formerly bed-frozen areas as the ice sheet evolves. Not all models may be able to respond so dynamically.

Antarctica

Initial Experiment - E1 - Increased Ice Shelf Melting

The initial experiment in Antarctica deals with increasing flux across the grounding line by manipulating the ice shelves. In experiments E1a, E1b, and E1c, a uniform sub-ice-shelf melting rate of 2, 20 and 200 meters per year (of ice equivalent) is applied, respectively. Ice shelves are treated differently in different models. If a whole ice sheet model lacks ice shelves, stopping at the grounding line, the above melt rates can be imposed at the grounding line. It is not certain that this prescription works for all models.

Discussion of Future Climate Experiments

The experiments described below are NOTIONAL ONLY and are ONLY FOR DISCUSSION . They are intended to give examples of how initial quantitative assessments of how large the ice sheet contribution to sea level could be generated. The experiments are discussed separately for Greenland and Antarctica.

Greenland

These experiments are of two types: those that addresses the role of surface meltwater on subglacial lubrication, and those that addresses the role of imposed changes at the margins of major outlet glaciers.

When the future climate experiment requires the forcings resulting from an IPCC scenario, these fields will be produced from the ensemble (ideally weighted in some manner) of results from all the GCMs used in the IPCC-Fourth Assessment Report.

Surface Melting

The correlation of surface meltwater production and ice flow has led to inferences that this meltwater penetrates to the bed and lubricates the ice-bed interface, reducing resistive stresses and/or decreasing bed normal stresses, much like mountain glaciers. The quantitative impact on overall ice dynamics is an active area of research, so the possible contribution of this effect on ice sheet mass loss in warmer future climates deserves careful examination. Three experiments are suggested aimed at examining this sensitivity. Details of their implementation have yet to be agreed upon.

No lubricative effect of meltwater: The most extreme IPCC climate scenario (A1F1: temperature rise of 4.0 °C with a likely range of 2.4 to 6.4 °C) could be used to force the ice sheets for 100 years into the future. Beyond 100 years, the final climate state wouldbe sustained by repeating the final year. The surface meltwater that is produced is deemed to have no impact on ice flow and is deposited directly into the ocean. Dynamic changes in ice flow will result primarily from changes in ice-sheet geometry driven by surface mass balance changes. Models that have actively evolving margins, especially at calving ice fronts will be encouraged to run this experiment both with the active evolution components “on” and, separately, with them “off”.

Meltwater penetrates vertically and lubricates bed: This experiment would impose the same forcing as above, but now the surface water is prescribed to reach the bed causing subglacial lubrication. The water is assumed to penetrate vertically, accessing the bed immediately below the production area. This water then leaves the ice sheet without further influence on ice flow. Previously frozen bed areas that become wetted could support basal sliding, creating changes in the ice flow and causing changes in ice-sheet geometry.

Horizontal propagation of subglacial water: This experiment also has the same climatic forcing as above, but horizontal water transport is included. For those models that include a subglacial water balance component, the water can move within the ice-bed interface, pool in lakes, influence effective pressure and basal lubrication, and move to other areas where it extends its influence on ice flow before exiting the subglacial system. Treatment of the water’s effect on lubrication will depend on the model. Here the challenge is a hydrological model that relates to surface meltwater input to basal sliding and seasonal acceleration.

Marginal Changes

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.

How to impose these margin-focused changes on whole ice sheet models is problematic. Grid resolution is often inadequate to capture the spatial details of narrow outlet glaciers, calving relationships and flow transitions at the grounding line are often ad hoc. Specifying discharge flux could be considered a possible approach, but so doing predetermines the sea level contribution, the primary predictive objective of this model exercise. The approach described below avoids this unwanted interdependency while making a simple prescription of marginal changes.

Single retreating glacier: The first case could be to force a retreat of the Jakobshavns Isbrae in western Greenland. This glacier has accelerated and retreated markedly in the past decade. It is wide enough that the main outlet can be resolved in most whole ice sheet models. The retreat will be prescribed by a time series of positions of the terminus (or grounding line) over the next 100 years. The retreat rate will continue the 10 km retreat in 5 years observed in the early 21st century. As the retreat proceeds beyond the present single ice-filled fjord, a more complex set of terminus positions will need to be specified. A modified experiment would be to half the retreat rate.

Due to grid size limitations, only the largest outlet glaciers can be resolved in whole ice sheet models. This is an example of where the regional models, with their higher spatial resolution and more complete physics, can provide a more realistic spatial and temporal prescription of margin changes. This is discussed more completely later. Half-dozen retreating glaciers Six deep outlet glaciers around Greenland will be selected and a Jakobshavns-level retreat imposed for each, also by a prescribed time series of terminus (or grounding-line) positions. A sub-case of halving the retreat rate could be an auxiliary experiment.

All tidewater glaciers: The most extreme case would be the imposing of drastic retreat on all the major tidewater glaciers around Greenland. Again, the half-speed retreat is a viable sub-case.

Calving Flux: Another method to force retreat and one that might be more amenable to the parameterizations of many models, would be to specify a calving flux in a variety of ways. A simple approach is to make the calving flux some fraction of the discharge flux. A fraction greater than unity will force retreat. The fraction could be prescribed as a time series to force accelerating retreat. Alternatively, the fraction could be tied to a physical parameter, such as water depth or height of ice thickness above flotation; and approach that expresses properties of earlier calving laws. Another alternative is to follow a recent paper on calving rate parameterization and make it dependent on the longitudinal stretching rate near the terminus.

Antarctica

Near-term climate change is impacting Antarctica within the Antarctic Peninsula and at the floating ice shelves through which most ice exits the ice sheet. The rugged topography and the glaciological complexity of the Antarctic Peninsula are beyond the abilities of most whole ice sheets to simulate. Based on the dramatic response of the feeding glaciers to the sudden removal (disintegration) of fringing ice shelves, a limiting scenario for the Peninsula is that all of its grounded ice will be removed this century through the eventual disintegration of its ice shelves. This will contribute a maximum of 34 cm to global sea level. The temporal schedule of this addition is beyond the capability of models to determine, at present.

Surface melting

Although there has not being strong evidence of the surface melting in Antarctica, except within the Antarctic Peninsula, there is no reason to assume that it would not play a role in a warming climate. These experiments would be similar to the surface melting experiments described for Greenland. If the initial surface melting experiment produced negligible surface water, the remaining surface melting experiments, where meltwater water lubricates the bed, might be abandoned.

The observations of grounded ice response to rapid ice shelf removal confirm that the ice shelf provides a significant longitudinal resistance to ice discharging across the grounding line. This interaction offers a convenient method to simulate the impact of ice shelf removal on Antarctic ice mass loss.

Marginal Changes

Remove all ice shelves currently thinning rapidly: The Pine Island Glacier ice shelf in West Antarctica and the Cook Ice Shelf in East Antarctica are observed to be thinning rapidly. This experiment would remove these ice shelves suddenly (either instantaneously or very rapidly) resulting in the hydrostatic equilibrium boundary condition being applied at the grounding line. Depending on the rate and spatial pattern of removal, there would be dramatic changes in the stress state at the margin that will result in large and rapid changes in ice flow and shape. Again, regional models could assist in providing more realism in the temporal pattern of change.

Remove all major Antarctic ice shelves: There are approximately 25 major outlet glaciers and ice streams in Antarctica that discharge more than half of the ice sheet’s annual flux to the ocean. Sudden removal, again guided by regional models, would explore a more radical scenario driven by the loss of multiple buttressing ice shelves.

Other

Jed Brown pointed the following out at the Summer 2009 CCSM/seaRISE meeting and it seemed too sensible an idea to leave off the wiki. At some level, all models solve the continuity equation

$\frac{\partial H}{\partial t} = -\nabla \cdot \left(\mathbf{u} H\right) + a$

to determine the thickness evolution. The details of how this equation is solved vary, but it is a starting point for reasoning about a class of experiments that appear to be straight forward to implement.

In SeaRISE experiments, arbitrarily increasing the flux at the grounding line is not useful because a primary goal of SeaRISE is to quantify the ice mass loss (i.e., the increase in grounding line flux) in a deterministic way using a dynamic ice sheet model forced by a specified environmental forcing condition. In SIA models, it is likely that the mass loss is attributed to either increased flow rates caused by a decrease in basal, lateral or longitudinal stresses) or increased melt. In SSA/SIA hybrid models, the additional flux of ice onto the shelf may be more problematic. Dave Pollard pointed out that it is probably better to impose the change by increasing the basal melt rate.

The difficulty arises in reconciling the various participating models. SIA models provide SeaRISE with a baseline, and are an important part of the exercise. However, prescription of experiments that are comparable across participating models can be very challenging.