Dynamics of information and uncertainty

The question of what information might be inferred from a set of data is posed in terms of the uncertainties of model variables determined by a least-squares fit. When a dynamical model is fitted to asynoptic data, the uncertainty can be characterized by a region in the model’s phase space surrounding the point associated with the best fit. Changes in the shape and orientation of this region as it evolves indicate how information is redistributed dynamically among the model variables, much as kinetic and potential energy might be redistributed. These ideas are illustrated within the context of single and double oscillator systems. Information about the state of a shallow-water model is shown to depend sensitively on the sampling interval of fictitious altimetric data.