Despite significant progress in modelling Quaternary climate dynamics, a comprehensive theory of glacial cycles is still lacking. Here, using the results of model simulations and data analysis, I present a framework of the generalized Milankovitch theory (GMT), which further advances the concept proposed by Milutin Milankovitch over a century ago. The theory explains a number of facts which were not known during Milankovitch time's, such as the 100 kyr periodicity of the late Quaternary.

To quantify the sensitivity of the earth system to orbital-scale forcings, we conducted an unprecedented quasi-continuous coupled general climate model simulation with the Community Earth System Model, which covers the climatic history of the past 3 million years. This study could stimulate future transient paleo-climate model simulations and perspectives to further highlight and document the effect of anthropogenic CO₂ emissions in the broader paleo-climatic context.

In this paper we present the carbon cycle component of the newly developed fast Earth system model CLIMBER-X. The model can be run with interactive atmospheric CO₂ to investigate the feedbacks between climate and the carbon cycle on temporal scales ranging from decades to > 100 000 years. CLIMBER-X is expected to be a useful tool for studying past climate–carbon cycle changes and for the investigation of the long-term future evolution of the Earth system.

In this paper we present the climate component of the newly developed fast Earth system model CLIMBER-X. It has a horizontal resolution of 5°x5° and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to >100 000 years. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.

We propose a model for glacial cycles and produce an assessment of possible trajectories for the next 1 million years. Under natural conditions, the next glacial inception would most likely occur ∼50 kyr after present. We show that fossil-fuel CO₂ releases can have an extremely long-term effect. Potentially achievable CO₂ anthropogenic emissions during the next centuries will most likely provoke ice-free conditions in the Northern Hemisphere landmasses throughout the next half a million years.

Submarine melting (SM) has been discussed as potentially triggering the recently observed retreat at outlet glaciers in Greenland. How much it may contribute in terms of future sea level rise (SLR) has not been quantified yet. When accounting for SM in our experiments, SLR contribution of 12 outlet glaciers increases by over 3-fold until the year 2100 under RCP8.5. Scaling up from 12 to all of Greenland's outlet glaciers increases future SLR contribution of Greenland by 50 %.

We present RCP 4.5 and 8.5 projections for the Greenland glacial system with the new glacial system model IGLOO 1.0, which incorporates the ice sheet model SICOPOLIS 3.3, a model of basal hydrology and a parameterization of submarine melt of outlet glaciers. Surface temperature and mass balance anomalies from the MAR climate model serve as forcing delivering projections for the contribution of the Greenland ice sheet to sea level rise and submarine melt of Helheim and Store outlet glaciers.

The surface energy and mass balance of ice sheets strongly depends on surface albedo. Here, using an Earth system model of intermediate complexity, we explore the role played by surface albedo for the simulation of glacial cycles. We show that the evolution of the Northern Hemisphere ice sheets over the last glacial cycle is very sensitive to the parameterization of snow grain size and the effect of dust deposition on snow albedo.

Greenland's glaciers that are in contact with the ocean undergo a special ice–ocean melting. To project numerically Greenland's centennial contribution to sea level rise, it is crucial to incorporate this special melting. We demonstrate that a numerically cheap model shows the qualitative same behavior as numerical expensive 2–3-dimensional models and calculates the same melting as empirical data show. Our analytical solution gives some insight in the yet poorly understood melting behavior.

Ice cores reveal that atmospheric CO₂ concentration varied synchronously with the global ice volume. Explaining the mechanism of glacial–interglacial variations of atmospheric CO₂ concentrations and the link between CO₂ and ice sheets evolution still remains a challenge. Here using the Earth system model of intermediate complexity we performed for the first time simulations of co-evolution of climate, ice sheets and carbon cycle using the astronomical forcing as the only external forcing.

Transient glacial cycle simulations with an EMIC and the PDD method require smaller melt factors for inception than for termination and larger factors for American than European ice sheets. The PDD online method with standard values simulates a sea level drop of 250 m at the LGM. The PDD online run reproducing the LGM ice volume has deficient ablation for reversing from glacial to interglacial climate, so termination is delayed. The SEB method with dust impact on snow albedo is seen as superior.

We present the snowpack model SEMIC. It calculates snow height, surface temperature, surface albedo, and the surface mass balance of snow- and ice-covered surfaces while using meteorological data as input. In this paper we describe how SEMIC works and how well it compares with snowpack data of a more sophisticated regional climate model applied to the Greenland ice sheet. Because of its simplicity and efficiency, SEMIC can be used as a coupling interface between atmospheric and ice sheet models.

PALADYN is presented; it is a new comprehensive and computationally efficient land surface–vegetation–carbon cycle model designed to be used in Earth system models of intermediate complexity for long-term simulations and paleoclimate studies.

In this paper we explore the permafrost–ice-sheet interaction using the fully coupled climate–ice-sheet model CLIMBER-2 with the addition of a newly developed permafrost module. We find that permafrost has a moderate but significant effect on ice sheet dynamics during the last glacial cycle. In particular at the Last Glacial Maximum the inclusion of permafrost leads to a 15m sea level equivalent increase in Northern Hemisphere ice volume when permafrost is included.

Ice discharge into the ocean from outlet glaciers is an important component of mass loss of the Greenland ice sheet. Here, we present a simple parameterization of ice discharge for coarse resolution ice sheet models, suitable for large ensembles or long-term palaeo simulations. This parameterization reproduces in a good approximation the present-day ice discharge compared with estimates, and the simulation of the present-day ice sheet elevation is considerably improved.