Models for stochastic climate prediction

There has been a recent burst of activity in the atmosphere/ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degree of freedom in stochastic climate prediction. Here several idealized models for stochastic climate modeling are introduced and analyzed through unambiguous mathematical theory. This analysis demonstrates the potential need for more sophisticated models beyond stable linear Langevin equations. The new phenomena include the emergence of both unstable linear Langevin stochastic models for the climate mean and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances. The strategy for stochastic climate modeling that emerges from this analysis is illustrated on an idealized example involving truncated barotropic flow on a beta-plane with topography and a mean flow. In this example, the effect of the original 57 degrees of freedom is well represented by a theoretically predicted stochastic model with only 3 degrees of freedom.

Perceptual learning reflects external noise filtering and internal noise reduction through channel reweighting

To investigate the nature of plasticity in the adult visual system, perceptual learning was measured in a peripheral orientation discrimination task with systematically varying amounts of external (environmental) noise. The signal contrasts required to achieve threshold were reduced by a factor or two or more after training at all levels of external noise. The strong quantitative regularities revealed by this novel paradigm ruled out changes in multiplicative internal noise, changes in transducer nonlinearites, and simple attentional tradeoffs. Instead, the regularities specify the mechanisms of perceptual learning at the behavioral level as a combination of external noise exclusion and stimulus enhancement via additive internal noise reduction. The findings also constrain the neural architecture of perceptual learning. Plasticity in the weights between basic visual channels and decision is sufficient to account for perceptual learning without requiring the retuning of visual mechanisms.