We will develop mathematical formalism for estimating fluctuations in parameters in stochastic parametrizations due to changes in the large-scale forcing (forcing applied to the large-scale structures). The forcing will be chosen to mimic the global warming scenario. Therefore, the proposed research will elucidate the validity of stochastic parametrizations estimated from the present-day climate for other climatological conditions. We propose a novel technique for estimating parameters in stochastic parametrizations of small-scale processes from the data of the large (resolved) scales alone. In the course of the proposed research we will develop rigorous mathematical foundation for accurate estimation of parameters from the time-series of large scale.
Stochastic models (also known as stochastic parametrizations) play an important role in Global Circulation Models of the atmosphere and ocean. In particular, stochastic models represent small-scale physical processes which cannot be sufficiently accurately resolved by modern numerical methods. Typically, parameters in these stochastic models are estimated from the present-day climate. The key question is how stochastic parametrizations will change in response to global climate change. In particular, estimation of stochastic models from time-series of large-scale structures can fail if the time-step of observation is too small. This is due to the fundamental differences between the trajectories of stochastic models and observed data. We will develop mathematical techniques to overcome this problem.