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, pattern formation and emergence, (random and non-autonomous ) dynamical systems, large deviation theory, response theory, tipping points, 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.

Several subsystems of the Earth system have been suggested to react abruptly at critical levels of anthropogenic forcing. Well-known examples of such Tipping Elements include the Atlantic Meridional Overturning Circulation, the polar ice sheets and sea ice, tropical and boreal forests, as well as the Asian monsoon systems. Interactions between the different Tipping Elements may either have stabilizing or destabilizing effects on the other subsystems, potentially leading to cascades of abrupt transitions. The critical forcing levels at which abrupt transitions occur have recently been associated with Tipping Points.

It is paramount to determine the critical forcing levels (and the associated uncertainties) beyond which the systems in question will abruptly change their state, with potentially devastating climatic, ecological, and societal impacts. For this purpose, we need to substantially enhance our understanding of the dynamics of the Tipping Elements and their interactions, on the basis of paleoclimatic evidence, present-day observations, and models spanning the entire hierarchy of complexity. Moreover, to be able to mitigate - or prepare for - potential future transitions, early warning signals have to be identified and monitored in both observations and models.

This interdisciplinary session invites contributions that address Tipping Points in the Earth system from the different perspectives of all relevant disciplines, including

- the mathematical theory of abrupt transitions in (random) dynamical systems,
- paleoclimatic studies of past abrupt transitions,
- data-driven and process-based modelling of past and future transitions,
- early-warning signals
- the implications of abrupt transitions for Climate sensitivity and response,
- ecological and societal impacts, as well as
- decision theory in the presence of uncertain Tipping Point estimates

Confirmed invited speaker: Michael Ghil

Hydroinformatics has emerged over the last decades to become a recognised and established field of independent research within the hydrological sciences. Hydroinformatics is concerned with the development and hydrological application of mathematical modelling, information technology, systems science and computational intelligence tools. We also have to face the challenges of Big Data: large data sets, both in size and complexity. Methods and technologies for data handling, visualization and knowledge acquisition are more and more often referred to as Data Science.

The aim of this session is to provide an active forum in which to demonstrate and discuss the integration and appropriate application of emergent computational technologies in a hydrological modelling context. Topics of interest are expected to cover a broad spectrum of theoretical and practical activities that would be of interest to hydro-scientists and water-engineers. The main topics will address the following classes of methods and technologies:

* Predictive and analytical models based on the methods of statistics, computational intelligence, machine learning and data science: neural networks, fuzzy systems, genetic programming, cellular automata, chaos theory, etc.
* Methods for the analysis of complex data sets, including remote sensing data: principal and independent component analysis, time series analysis, information theory, etc.
* Specific concepts and methods of Big Data and Data Science
* Optimisation methods associated with heuristic search procedures: various types of genetic and evolutionary algorithms, randomised and adaptive search, etc.
* Applications of systems analysis and optimisation in water resources
* Hybrid modelling involving different types of models both process-based and data-driven, combination of models (multi-models), etc.
* Data assimilation and model reduction in integrated modelling
* Novel methods of analysing model uncertainty and sensitivity
* Software architectures for linking different types of models and data sources

Applications could belong to any area of hydrology or water resources: rainfall-runoff modelling, flow forecasting, sedimentation modelling, analysis of meteorological and hydrologic data sets, linkages between numerical weather prediction and hydrologic models, model calibration, model uncertainty, optimisation of water resources, etc.

Hydrology is a rich multidisciplinary field encompassing a complex process network involving interactions of diverse nature and scales. Still, it abides to core dynamical principles regulating individual and cooperative processes and interactions, ultimately relating to the overall Earth System dynamics. This session focuses on advances in theoretical and applied studies in hydrologic dynamics, regimes, transitions and extremes along with their physical understanding, predictability and uncertainty. Moreover, it welcomes research on dynamical co-evolution, feedbacks and synergies among hydrologic and other earth system processes at multiple spatiotemporal scales. The session further encourages discussion on physical and analytical approaches to hydrologic dynamics ranging from stochastic, computational and system dynamic analysis, to more general frameworks addressing non-ergodic and thermodynamically unstable processes and interactions.
Contributions are welcome from a diverse community in hydrology and the broader physical geosciences, working with diverse approaches ranging from dynamical modelling to data mining, machine learning and analysis with physical understanding in mind.