- Stochastic vs. deterministic descriptions? Is climate intrinsically random, or are we just using probabilistic concepts? Is the uncertainty stochastic, or is it something else?
- How can stochastic methods best be used to help bridge the enormous range of spatial and temporal scales in the atmosphere, oceans, and other geophysical processes? What if there is no clear separation of scales?
- How does gridscale noise get transferred upscale to affect the global-scale flow (and the climate)?
- What are all the different possible sources of stochasticity, and should they all be approached and treated in the same way?
- Consider a complex climate model or any comprehensive model for physical or geophysical flows that is based on known deterministic equations of motion. Is it possible to derive master equations, for instance in form of Fokker-Planck equations, that describe the PDFs (or statistics) of relevant variables of the model, both in equilibrium and non-equilibrium states? Are there special conditions to be satisfied in order for such master equations to emerge? What is the connection between the deterministic equations of motion and the master equations?
- Suppose that the system of our interests (climate, or physical flows) cooperates with an external forcing and that we have successfully derived the master equation for a relevant variable of our system. Whether and to what extent can we use the master equation to describe the changes in statistics of the variable in response to changes in the external forcing? In other words and in the context of climate change sciences, can we use master equations to predict climate changes in response to increasing GHG concentration and how do these equations look like? Note that when following the conventional wisdom that climate is statistics of weather, we need a master equation for predicting climate changes.
- How does stochasticity manifest itself in disk-integrated observations of exoplanets and brown dwarfs? What do we learn if we observe or don't observe variability?
- Are stochastic descriptions of transitions between different phases useful?
- Chaos vs. persistent structures. Small-scale forcing can create large-scale structures.
- Can a cookbook or flow-chart be created for introducing stochastic ideas into models?
- How to think about external forcing that is stochastic?
- When is equilibrium (or near equilibrium) statistical mechanics useful?
- The concept of quasi-equilibrium (a possible misnomer!) was developed in turbulence, when there is a conserved flux (specifically a flux of energy) instead of a constant energy. It is therefore relevant to dissipative systems and enabled to develop non-equilibrium statistical physics, underpinning e.g. canonical vs. micro-canonical cascades, fractal and multifractal intermittency vs. homogeneous turbulence, etc.
- Absence of clear separation of scales put in disarray classical approaches based on its existence. It is therefore often seen as a problem. On the contrary, it is in general related to the presence of scale symmetry or invariance. It is therefore no longer a problem, but a hint to simplify the system by taking into account this symmetry!