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

Abstract

The atmosphere is often cited as an archetypal example of a chaotic system, where predictionis limited by the model’s sensitivity to initial conditions. Experiments have indeed shown thatforecast 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 primarycontributor to forecast inaccuracy. In this paper we attempt to reconcile these apparentlyconflicting sets of results by examining the role of the chosen metric. Using a simple mediumdimensionalmodel for illustration, it is found that the metric has a strong effect, not just onapparent error growth, but on the perceived causes of error. If an insufficiently global metricis used, then it may appear that error is due to sensitivity to initial condition, when in fact itis caused by sensitivity to error in the other variables. If the goal is to diagnose the causes oferror, a sufficiently global metric must be used. The simple model is used to predict the internalrate of growth of the ECMWF operational model, and preliminary results compared. It is foundthat both 500 hPa and total energy results are consistent with high model error and a relativelylow internal rate of growth. Experiments are suggested to further verify the results forweather models.