Bayesian Inference for Climate prediction

Bayesian Inference in the geosciences is called data assimilation. It studies how to best combine information from complex numerical models with information from observations of the system at hand, given limited computational resources. This requires knowledge of the physics, numerical modeling including computer architecture, quantification of deficiencies in the numerical models, characteristics of observation errors, and Bayesian inference for very high dimensional highly nonlinear systems.
An important characteristic of the climate system is that the different Earth system components (e.g. atmosphere, ocean ,land surface and icecaps) have vastly different internal time scales. The main work horse for weather prediction, a (variational) smoother in which observations over a time window of 6-12 hours are used to find the best starting point for predictions, is problematic because the optimal time window length is substantially different for the different components. Even after 20 years of intensive research no satisfying smoother solution has been found.
This suggests to use a filter solution without an assimilation window, but the main workhorse there, the Ensemble Kalman Filter, suffers from too small ensemble sizes to accommodate the large number of observations (even when so-called localization is applied).
Another issue is that with its many feedbacks the climate system is highly nonlinear, while the standard methods for weather predictions are only optimal for linear, and perhaps weakly nonlinear systems. Furthermore, system updates are typically too abrupt and need to be added incrementally during the prediction.
We will discuss potential solutions based on existing techniques, and alternative ideas based on so-called particle flows.The latter are fully nonlinear while combining the strong points of smoothers and filters mentioned above, and have the potential to make substantial strides forwards towards better climate prediction.