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An intuitively necessary requirement of models used to provide forecasts of asystem's future is the existence of shadowing trajectories that are consistentwith past observations of the system: given a system-model pair, do modeltrajectories exist that stay reasonably close to a sequence of observations ofthe system? Techniques for finding such trajectories are well-understood inlow-dimensional systems, but there is significant interest in their applicationto high-dimensional weather and climate models. We build on work by Smith etal. [2010, Phys. Lett. A, 374, 2618-2623] and develop a method for measuringthe time that individual "candidate" trajectories of high-dimensional modelsshadow observations, using a model of the thermally-driven rotating annulus inthe perfect model scenario. Models of the annulus are intermediate incomplexity between low-dimensional systems and global atmospheric models. Wedemonstrate our method by measuring shadowing times againstartificially-generated observations for candidate trajectories beginning afixed distance from truth in one of the annulus' chaotic flow regimes. Thedistribution of candidate shadowing times we calculated using our methodcorresponds closely to (1) the range of times over which the trajectoriesvisually diverge from the observations and (2) the divergence time using asimple metric based on the distance between model trajectory and observations.An empirical relationship between the expected candidate shadowing times andthe initial distance from truth confirms that the method behaves reasonably asparameters are varied.

Shadowing the rotating annulus. Part I: Measuring candidate trajectory shadowing times