The critical threshold for the ice sheet is reached overshooting
The Lingle-Clark model for the Earth’s atmosphere. I. The MARv3.12 regional climate model and the temperature and precipitation rates
The model Yelmo26 resolves ice dynamics using the higher-order DIVA solver62. The dynamics can be linked to the effective viscosity through the Glen’s flow law formula and the enhancement factors in the shearing, streaming and floating regimes. The basal friction is determined with a regularized Coulomb law63 of the form
with the basal shear stress τb, basal sliding velocity u, yield stress τc and a threshold velocity u0. q and a threshold velocity of 100 m year1 was chosen for our simulations.
The effective pressure Ntill, the material property field and the till cohesion are connected by that. The till friction angle is a piecewise linear function of bed elevation56 and is determined by the effective pressure Ntill. The till is set to 0.
The Lingle– Clark model helps us to understand how the Earth is changed by the ice load. 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.
We use a recently developed formula to calculate the surface mass balance. The coefficients c1 and c2 are used to calibrate the energy balance in the melt equation. The MARv3.12 regional climate model’s surface mass balance is fixed at 25 W m2 K and c2 at 50 W m2. We keep the orbital parameters fixed to the present-day values25. The transmissivity of the atmosphere is given by a linear function and assumed not to change in future climate. For an extensive description of the dEBM and the implementation in PISM, see refs. 25,37,39
The model MARv3.12 gives the temperature and precipitation rates of the present day. The lapse rate is 6 K km1 if we apply the elevation-dependent correction of precipitation and temperature. The change in precipitation is proportional to the temperature change. A linear fit of annual precipitation against the surface air temperature is used to derive the change of precipitation with increasing temperature. The default ocean boundary conditions are constant sub-shelf melt rates of 0.05 m annually.
The simulations are made using a reference equilibrium state of the Gr IS that is very similar to the current configuration. The ice- surface elevation and ice surface velocity deviation are shown in extended data. The ice-sheet model was taken from BedMachine v5 and includes ice thickness and bedrock elevation. We run the model until an equilibrium state is reached, but for at least 50,000 years. The simulations were done on a grid with a horizontal resolution of 20 km and a vertical resolution of 40 m.
Source: Overshooting the critical threshold for the Greenland ice sheet
Greenland and the effect of climate change on the global ice sheet from 2023 to 2023: a conceptual study and an accounting for structural uncertainties
$${{\boldsymbol{\tau }}}{{\rm{b}}}=-{c}{{\rm{b}}}{\left(\frac{\left|{{\bf{u}}}{{\rm{b}}}\right|}{\left|{{\bf{u}}}{{\rm{b}}}\right|+{u}{0}}\right)}^{q}\frac{{{\bf{u}}}{{\rm{b}}}}{\left|{{\bf{u}}}_{{\rm{b}}}\right|},$$
There are many caveats. The work does not incorporate a host of shorter-term planetary changes, such as shifts in ocean currents, that could affect Greenland’s ice. The authors look at the effect of average global temperature increases over the course of a year, while examining the effect of temperature increases in the Arctic which are three times faster than other parts of the planet. The study assumes that carbon-capture technology will be the way to slash greenhouse-gas emissions in the future. This is a conceptual experiment and we have to keep that in mind.
We address both possible structural and parametric uncertainties of 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.
We account for structural uncertainties by carrying out our experiments with two independent ice-sheet models, PISM-dEBM and Yelmo-REMBO. The results obtained with both models side by side are robust and unlikely to be affected by structural uncertainties, which is one of the reasons we show them side by side in the figures.
The scientists who wrote the study say that it doesn’t mean that the ice sheet is tip over just because they crossed thresholds.
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. “It’s a bet against time if we don’t do anything now,” Bochow says. The longer we wait, the harder it gets.
June, July, August and September 2023 all saw record high global temperatures, and 2023 is likely to be the hottest year for which data exist. 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’s a worthwhile tool to explore because what we are doing so far, policy wise, is not enough to be within the limits,” says Michele Petrini, an Earth-system scientist at the NORCE Norwegian Research Centre and Bjerknes Centre for Climate Research in Bergen.
