Modelling the Climate and Weather of a 2D LagrangianAveraged EulerBoussinesq Equation with Transport Noise
Abstract
The prediction of climate change and its impact on extreme weather events is one of the great societal and intellectual challenges of our time. The first part of the problem is to make the distinction between weather and climate. The second part is to understand the dynamics of the fluctuations of the physical variables. The third part is to predict how the variances of the fluctuations are affected by statistical correlations in their fluctuating dynamics. This paper investigates a framework called LA SALT which can meet all three parts of the challenge for the problem of climate change. As a tractable example of this framework, we consider the EulerBoussinesq (EB) equations for an incompressible stratified fluid flowing under gravity in a vertical plane with no other external forcing. All three parts of the problem are solved for this case. In fact, for this problem, the framework also delivers global wellposedness of the dynamics of the physical variables and closed dynamical equations for the moments of their fluctuations. Thus, in a wellposed mathematical setting, the framework developed in this paper shows that the mean field dynamics combines with an intricate array of correlations in the fluctuation dynamics to drive the evolution of the mean statistics. The results of the framework for 2D EB model analysis define its climate, as well as climate change, weather dynamics, and change of weather statistics, all in the context of a model system of SPDEs with unique global strong solutions.
 Publication:

Journal of Statistical Physics
 Pub Date:
 January 2020
 DOI:
 10.1007/s10955019024439
 arXiv:
 arXiv:1909.00388
 Bibcode:
 2020JSP...179.1267A
 Keywords:

 Mean field;
 Fluctuations;
 Lagrangian averaging;
 Stochastic transport noise;
 EulerBoussinesq fluid equations;
 Mathematical Physics
 EPrint:
 doi:10.1007/s10955019024439