Abstract
Initial errors in weather prediction grow in time. As errors become larger, their growth slows down and then stops at an asymptotic value.
Time of reaching this value represents the limit of predictability. Other time limits that measure the error growth are doubling time τd, and times when the forecast error reaches 95%, 71%, 50%, and 25% of the limit of predictability.
This paper studies asymptotic value and time limits in a low-dimensional atmospheric model for five initial errors, using ensemble prediction method as well as error approximation by quadratic and logarithmic hypothesis. We show that quadratic hypothesis approximates the model data better for almost all initial errors and time lengths.
We also demonstrate that both hypotheses can be further improved to achieve even better match of the asymptotic value and time limits with the model.