Impacts of model design on the chaotic properties of the logistic map

What is it about?

This study uses a simple chaotic system (the logistic map) to show that both model error and initial condition errors have profound impacts on predictability. These findings may have very important ramifications for how to design computer forecast models (and models in other fields where computer simulations are used) to improve their predictability. It is also shown for the first time that small changes to the equations have a similar impact on the predictability limit as changes to the initial conditions, which can influence how sets of computer forecast models (i.e., ensembles) are designed and run.

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Photo by Brian McGowan on Unsplash

Photo by Brian McGowan on Unsplash

Why is it important?

Limited predictability is an important characteristic of chaotic systems. Regardless of how well a model is designed, if its underlying predictability is limited, one can only use it for prediction for a limited length of period. Think of weather prediction: We know that the atmosphere is a chaotic system with limited predictability. So even if we design a really good computer model to predict it, we know that our forecasts can be accurate only within a certain time window dictated by this predictability limit. In this study, it is shown that even chaotic systems that don't typically exhibit such limited predictability change this behavior if, in addition to errors at the initial time, there are also errors in the model design itself. This becomes especially critical if ensembles are used in the prediction. In modern-day computer prediction applications, ensembles have become common place to predict not just one possible future of an event but the range of possibilities if conditions at the initial time are slightly different. It is shown here that in such ensemble applications, the specific design of an ensemble itself may have profound impacts on the predictability of the modeled phenomenon.