# Time Evolution of Initial Errors in Lorenz's 05 Chaotic Model

## TL;DR

This paper studies how initial errors in a chaotic weather model grow over time and how different hypotheses can approximate their behavior.

## Contribution

The paper introduces modified hypotheses that better approximate time limits of error growth in a chaotic model.

## Key findings

- Modified hypotheses approximate the model's time limits better than original ones.
- Quadratic hypothesis best approximates the model's asymptotic error values.
- Improvements to hypotheses enhance their match with the model's time limits for most errors.

## Abstract

Initial errors in weather prediction grow in time and, as they become larger, their growth slows down and then stops at an asymptotic value. Time of reaching this saturation point represents the limit of predictability. This paper studies the asymptotic values and time limits in a chaotic atmospheric model for five initial errors, using ensemble prediction method (model's data) as well as error approximation by quadratic and logarithmic hypothesis and their modifications. We show that modified hypotheses approximate the model's time limits better, but not without serious disadvantages. We demonstrate how hypotheses can be further improved to achieve better match of time limits with the model. We also show that quadratic hypothesis approximates the model's asymptotic value best and that, after improvement, it also approximates the model's time limits better for almost all initial errors and time lengths.