Taking inspiration from the Mathematics of Planet Earth 2013 initiative, this session aims at bringing together contributions from the growing interface between the geophysical, the mathematical, and the theoretical physical communities. Specific topics include: PDEs, numerical methods, extreme events, statistical mechanics, large deviation theory, response theory, model reduction techniques, coarse graining, stochastic processes, parametrizations, data assimilation, and thermodynamics. We invite talks and poster both related to specific applications as well as more speculative and theoretical investigations. We particularly encourage early career researchers to present their interdisciplinary work in this session.

The Earth system, consisting many interacting (sub)components, has strong internal variability on many time scales, is subject to a non-stationary forcing and mostly out of equilibrium with the changes in the radiative forcing. Large-scale transitions occur, for example due to the existence of tipping points in components of the climate system, and these in many cases depend on the complex interaction between different sub-systems. Moreover, the role of small-scale processes (in many models represented as noise) to induce these transitions is not well known for many important tipping elements.

In climate science, the concept of equilibrium and transient climate sensitivity is widely used for understanding how the climate changes in response to natural and anthropogenic radiative forcing. Over the last decade considerable progress has been made in understanding and defining climate sensitivity. Nevertheless, the uncertainty in climate sensitivity remains high. Moreover, its scope is quite limited, because it deals only with long term changes of the globally averaged surface temperature and is unable to account for the existence of tipping elements and large scale transitions.

The session aims at addressing the problem of connecting fluctuations and response for the climate system, including issues like climate sensitivity, climate variability, extreme events and tipping points. In particular, general approaches and novel measures to quantify the climate response to non-stationary forcing in the climate system are encouraged.
We also aim at studying the complex interactions between the different components and subcomponents of Earth system in order to understand how these interactions influence on system/subsystems (potentially tipping) behavior. External forcing may also impact the nature of interaction between connected subsystems. The submissions which are focused on the study of reasons and mechanisms of the emergent behavior are especially welcome. Such behavior may be inferred from time-dependent connectivity in data, first principle and data-driven modelling.

We welcome contributions that investigate specific feedbacks and their impact on climate sensitivity in all components of the climate system; processes on intermediate to long time scales that are generally difficult quantify such as ocean heat uptake are particularly encouraged. In addition, we welcome contributions studying the state dependence of climate sensitivity, including those focusing on the potential proximity of tipping points.

This is a merged session of 'Climate Sensitivity, Climate Response, and Tipping Points' and 'Networked connections in geosystems: revealing, studying of mechanisms, evolution in time, influence on emergent behavior'.

In both climate modelling and numerical weather prediction, numerical models of the Earth System are used extensively. For the both the atmosphere and ocean such models consist of a fluid dynamics solver (dynamical core) coupled to physics parameterizations to represent processes that occur below the grid scale (physics). Over time these models have become capable of sophisticated simulations, incorporating such features as multi-scale prediction, structure-preserving discretization and a detailed treatment of physics. New work is constantly being undertaken to improve the accuracy and efficiency of these models, both the dynamical core and the physics.

This session encompasses the development, testing and application of novel numerical techniques for Earth system models, including new discretizations, test cases, advection schemes, vertical discretizations, adaptive multi-scale models, physics-dynamics coupling, global and regional climate and NWP models, structure-preserving discretizations and parameterizations (that are not covered in other sessions).

The quality of predictions of weather and climate depends on both resolution and complexity of the models that are used. However, resolution and complexity are limited by the computational performance that is available on today's supercomputers. While weather and climate models run on some of the fastest supercomputers of the world, models typically fail to run close to peak performance such that there is still room for a significant speed-up if efficiency is improved. The increase in parallelisation in high performance computing and the availability of various computing platforms is imposing significant challenges for the community to find the optimal hardware/model configuration and to achieve the best performance. On the other hand, the evaluation of high resolution simulations is often tedious due to large data volumes, limited statistic that is affordable and changed model behaviour that needs to be studied (e.g. if convection or eddies are resolved explicitly or if non-hydrostatic equations need to be used).
These challenges can only be addressed appropriately in a close collaboration between Computing and Earth System Scientists. This session aims to bring together scientists who run and evaluate atmosphere and ocean models with high resolution and complexity as well as scientists who enable these models to run as efficiently as possible on existing and future high performance computing architectures (regarding both model development and model optimisation). The session will also be an opportunity for scientists from the EU projects PRIMAVERA, ESCAPE and ESiWACE as well as HighResMIP from CMIP6 to meet and interact.

V. Balaji from Princeton University will be our keynote speaker invited by the ESiWACE EU Horizon2020 COE (grant number 675191).

Prediction of the areas threatened by landslides and gravity-driven mass flows are a key part of hazard assessment in mountainous regions. Whatever the material transported (debris, snow, etc.), the granular flow process involves determining the initiation mechanisms, initial volume, physical transport, entrainment processes as well as deposition and phase-separation mechanisms. Because of the number of scientific disciplines needed to solve it, there is a substantial benefit from interdisciplinary research. Furthermore, the definition of a unified rheology that accounts for the different regimes characterizing granular-fluid mixture flows is still lacking. The co-existence of the
collisional regime and the dense regime that have a very different behavior, makes the definition of a proper rheology quite challenging. So is the transition from dilute to dense regimes in granular-fluid
mixture flows.

This session aims to bring together new research results from a variety of different approaches to understanding these kinds of processes. In particular, we encourage presentations on physical modelling, innovative laboratory research, theoretical studies on the physics of multiphase and multiscale phenomena and detailed field observations, which yield insight into the triggering mechanisms, the mass movement or mass flow process. Another important aspect, still unclear, that will be addressed in the session, is the mechanism and consequence of grain sorting and particle-fluid separation, entrainment and deposition in debris and hyperconcentrated flows. A proper description of the granular-fluid mixture flow phenomena is fundamental in order to properly define the design criteria of the protection structures and to have reliable risk maps. So, contributions related to the numerical modelling of landslides and granular geophysical flows, including torrential sediment transport, debris flows, rock and snow avalanches, and similar flows are expected.

Selected contributions will be considered for a special issue of a relevant international journal.

Tipping elements in the Earth's climate system are continental-scale subsystems that are characterized by a threshold behavior. It has been suggested that these include biosphere components (e.g. the Amazon rainforest and coral reefs), cryosphere components (e.g. the Greenland and Antarctic ice sheets) and large-scale atmospheric and oceanic circulations (e.g. the thermohaline circulation, ENSO and Indian summer monsoon). Once operating near a threshold or tipping point, these components can transgress into a qualitatively different state by small external perturbations. The large-scale environmental consequences could impact the livelihoods of millions of people.

In this session, we aim to bring together experts presenting and discussing the state-of-the-art research on tipping elements in the Earth's climate system, both in empirical data and numerical modelling of past, present and future climate. Among other topics, issues to be addressed in this session include critical thresholds for specific tipping elements, typical time scales of tipping, interactions and feedbacks between tipping elements, the potential for tipping cascades as well as environmental and socio-economic impacts of tipping.