Role of the metric in forecast error growth: how chaotic is the weather?

The atmosphere is often cited as an archetypal example of a chaotic system, where prediction is limited by the model's sensitivity to initial conditions. Experiments have indeed shown that forecast errors, as measured in 500 hPa heights, can double in 1.5 d or less. Recent work, however, has shown that, when errors are measured in total energy, model error is the primary contributor to forecast inaccuracy. In this paper we attempt to reconcile these apparently conflicting sets of results by examining the role of the chosen metric. Using a simple medium-dimensional model for illustration, it is found that the metric has a strong effect, not just on apparent error growth, but on the perceived causes of error. If an insufficiently global metric is used, then it may appear that error is due to sensitivity to initial condition, when in fact it is caused by sensitivity to error in the other variables. If the goal is to diagnose the causes of error, a sufficiently global metric must be used. The simple model is used to predict the internal rate of growth of the ECMWF operational model, and preliminary results compared. It is found that both 500 hPa and total energy results are consistent with high model error and a relatively low internal rate of growth. Experiments are suggested to further verify the results for weather models.