Brief description
The climate is a multiphase system featuring variability over many temporal and spatial scales. Its evolution can be written in terms of extremely complicated conservation laws for energy, momentum, and chemical species for three-dimensional fields. Given such a level of complexity, it is far from trivial to relate data, theories, and numerical models. So, the investigation of the climate system relies on the use of models that wildly differ in terms of scope, details, and overall complexity, ranging from extremely low dimensional models to Earth system models, which are some of the heaviest users of computing facilities.
This project will focus on theoretical advancements in the study of some models that describe climate variability on medium and long time-scales. Our program is to analyse, first, actions that may affect climate change and their consequences on the environment, and then to detect possible policies towards a climate-neutral society.
This project will develop and analyse two main related lines of research.
- Models to address climate change
- Deterministic energy balance models (EBMs): we propose to improve the analysis of the climate system derived from standard EBMs by increasing the vertical resolution in order to represent, at least approximately, the very important vertical exchanges processes occurring between surface and the atmosphere.
- Stochastic models: we propose to investigate the issue of Tipping Points using mathematical techniques from the theory of Stochastic Partial Differential Equations. Our aim is understanding how the fluctuations change when we are in the proximity of a tipping point.
- Fluid dynamical models: for the deterministic TROPICAL CLIMATE MODEL we will provide a rigorous qualitative and quantitative mathematical study on the solutions. Concerning the stochastic model we consider an extension of the 2Layer QG incorporating also thermal interactions between the layers.
- Models to describe the impacts of climate change on the environment and, in particular,
- Mean Field Games: we intend to address, both from a theoretical and a computational point of view, two problems related to the control of atmospheric pollution. The first problem concerns the study of the economic mechanism of carbon allowance price formation. The second problem concerns an MFG approach to model climate change negotiations among countries interacting through a CO2 emission permit market.
- Multi-agent models: a first structural problem that we intend to study concerns the impact of the nature of the agent on the mathematical model. A second problem that we plan to study concerns the development of mathematical models specific to irrational agents.
Our approach will not only produce theoretical results but provide numerical simulations as well. Moreover, all the units will contribute to the research of both lines (1) and (2) above.
The climate is a multiphase system featuring variability over many temporal and spatial scales. Its evolution can be written in terms of extremely complicated conservation laws for energy, momentum, and chemical species for three-dimensional fields. Given such a level of complexity, it is far from trivial to relate data, theories, and numerical models. So, the investigation of the climate system relies on the use of models that wildly differ in terms of scope, details, and overall complexity, ranging from extremely low dimensional models to Earth system models, which are some of the heaviest users of computing facilities. This project will focus on theoretical advancements in the study of some models that describe climate variability on medium and long time-scales. Our program is to analyse, first, actions that may affect climate change and their consequences on the environment, and then to detect possible policies towards a climate-neutral society. This project will develop and analyse two main related lines of research.
- Models to address climate change
- Deterministic energy balance models (EBMs): we propose to improve the analysis of the climate system derived from standard EBMs by increasing the vertical resolution in order to represent, at least approximately, the very important vertical exchanges processes occurring between surface and the atmosphere.
- Stochastic models: we propose to investigate the issue of Tipping Points using mathematical techniques from the theory of Stochastic Partial Differential Equations. Our aim is understanding how the fluctuations change when we are in the proximity of a tipping point.
- Fluid dynamical models: for the deterministic TROPICAL CLIMATE MODEL we will provide a rigorous qualitative and quantitative mathematical study on the solutions. Concerning the stochastic model we consider an extension of the 2Layer QG incorporating also thermal interactions between the layers.
- Models to describe the impacts of climate change on the environment and, in particular,
- Mean Field Games: we intend to address, both from a theoretical and a computational point of view, two problems related to the control of atmospheric pollution. The first problem concerns the study of the economic mechanism of carbon allowance price formation. The second problem concerns an MFG approach to model climate change negotiations among countries interacting through a CO2 emission permit market.
- Multi-agent models: a first structural problem that we intend to study concerns the impact of the nature of the agent on the mathematical model. A second problem that we plan to study concerns the development of mathematical models specific to irrational agents.