# SKM 2023 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 37: Data Analytics of Complex Dynamical Systems (joint session DY/SOE)

### DY 37.6: Hauptvortrag

### Donnerstag, 30. März 2023, 11:00–11:30, MOL 213

**Power law error growth rates -- a dynamical mechanism for a strictly finite prediction horizon in weather forecasts** — Hynek Bednar^{1,2}, Jonathan Brisch^{1}, Burak Budanur^{1}, and •Holger Kantz^{1} — ^{1}Max Planck Insstiute for the Physics of Complex Systems, Dresden, Germany — ^{2}Dept. of Atmospheric Physics, Charles University, Prague, Czech Republic

While conventional chaotic systems have a finite positive Lyapunov exponent, physical arguments and observations suggest that the maximal Lyapunov exponent of the model equations of the atmosphere is the larger the smaller are the resolved spatial scales. Specifically, a power law divergence of the scale dependent error growth rate would translate into a strictly finite prediction horizon, since due to the divergence, additional accuracy of initial conditions is not translated into longer prediction times. We present conceptual toy models with such behavior, we show its presence in a more realistic spatially extended system with advective transport, and we present numerical results from turbulence simulations where the largest Lyapunov exponent scales as an inverse power of spatial resolution. The idea of a power law scale dependence of error growth rates and of a finite prediction horizon is also supported by re-analysis of numerical error growth experiments performed with an operational weather model. Altogether, this suggests that the prediction horizon of numerical weather prediction is strictly finite.