Thermomechanically Coupled Hybrid Ice-Sheet/Ice-Shelf Model: Application to the Lingle-Clark Model 57,58
We use a PISM version that is open-sourced, state-of-the-art, and has the dEBM surface mass balance module. PISM is a three-dimensional, thermomechanically coupled ice-sheet/ice-shelf model that combines the shallow-ice approximation (SIA) and shallow-shelf approximation (SSA) of the non-Newtonian Stokes model. The entire domain from ice-sheet flow zone with grounded ice to the ice-shelf flow zones can be modeled using this hybrid SSA + SIA approach. The ice rheology is based on the Glen–Paterson– Budd–Lliboutory–Duval flow law with an enhancement factor of 1 and 3, respectively, for SSA and SIA.
The shear stress b, sliding rate, yield stress c and threshold velocity is included with the equation. We chose q = 0.5 and a threshold velocity of u0 = 100 m year−1 for our simulations.
That connects the pressure Ntill and the material property field. The till angle is a linear function of bed elevation56 and is determined by the effective pressure Ntill. The till cohesion c0 is set to 0.
We model the deformation of the Earth owing to the changes in the ice load using the Lingle–Clark model57,58. The model is described by a purely elastic lithosphere with a flexural rigidity of 5 × 1024 N m−1 and the upper mantle is represented as a three-dimensional viscous half-space with a viscosity of 1021 Pa s−1. The model uses a time-dependent partial differential equation that generalizes and improves on the standard elastic plate lithosphere model (ELRA)58.
The dEBM25,38,39 is a recently developed surface mass balance calculator. In order to calibrate the energy balance of the snow, we use the coefficients c1 and c2, which are the standard parameters used in the equation. We set the final values for c1 and c2 to be 20 W m2 K and 50 W m2, respectively, based on an optimal product of the temporal and spatial root-mean-square error of the surface mass balance. The values are fixed to the present-day values. The transmissivity of the atmosphere is given by a linear function and assumed not to change in future climate. See the refs for an extensive description of the implementation in PISM. 25,37,39.
The present-day near-surface temperature and precipitation rates are given by climatological means (monthly 1980–2000) from the regional climate model MARv3.12 (ref. 59). We apply an elevation dependent correction of the precipitation and temperature and impose a lapse rate of 6 K km. The precipitation P changes 3.6% per degree of temperature change. The change of precipitation with increased temperature is a result of a linear fit of the mean annual precipitation against surface air temperature from 37 CMIP6 SSP585 runs. We use the default spatiotemporal constant ocean boundary conditions with a constant sub-shelf melt rate of 0.05 m year−1.
Our simulations are initialized from a reference equilibrium state of the GrIS that resembles the present-day configuration. We show the ice-surface elevation and ice-surfacevelocity deviation from observational data. In order to get our reference state, we bootstrap the model from the present-day conditions, including ice thickness and bedrock elevation. For 50,000 years, the model is run until equilibrium is reached. The simulations were performed on a regular rectangular grid with a horizontal resolution of 20 km and a parallel grid in the vertical direction with a resolution of 40 m.
_rmb is a symbol for left and right.
Climate Change and the Ice Sheet: A Comparison of Structural Uncertainties and a Possible Action Plan for the Next Generation of Greenland Climate Models
There are many caveats. The work doesn’t incorporate any of the shorter-term planetary changes that could affect Greenland’s ice. The authors examine the effect of average global temperature increases rather than temperature increases in the Arctic, which are happening at least three times faster than those in the rest of the planet. And the study assumes that society will somehow work out a way to slash greenhouse-gas emissions drastically in the future, perhaps through carbon-capture technology. “We must keep in mind that this is just a conceptual experiment,” says Petrini.
We address the uncertainties that come with our results. Here structural uncertainties are those associated with the model mechanisms and the structure of the model, whereas parametric uncertainties refer to those that are because of incomplete knowledge of the optimal values for the parameters of a given model.
Two ice-sheet models were used to carry out our experiments. We show all our results obtained with both models side by side in the figures and conclude that our results are remarkably robust for both models; they are thus unlikely to be affected by structural uncertainties in general, although important differences do arise in the details.
The models were used by researchers to see how the ice sheet would respond to different scenarios. If warming is kept below 2.5 C, the worst impacts of warming could be avoided.
Still, he and others are quick to note that taking action against climate change now will be cheaper and easier than trying to claw back global temperatures later. Bochow says, it is a bet against time if we don’t do anything now. It gets harder the longer we wait.
The summer months of June, July, August and September saw record high temperatures and it’s likely that the year will be the hottest on record. Against this backdrop, Bochow and his colleagues wanted to look at what would happen if humanity overshot the 1.5 °C temperature target, even by a lot, and then managed to cool things down again.
It is a worthwhile tool to look at what we are doing so far, policy wise, and not enough to be within the limits.