Two Kinds of Predictability in the Lorenz System

The Lorenz system is used to discuss two kinds of predictability: the model sensitivity to inaccurate initial conditions (first kind) and to inaccurate boundary conditions (second kind). The first kind of predictability has been investigated for a long time, but not the second kind. It was found that the Lorenz system has a capability to detect both kinds of predictability since the boundary condition is represented by a model parameter, r. Two sensitivity runs are designed by perturbing the initial condition and the model parameter r by the same small relative error (1024), which is equivalent to 10% of the instrumentational accuracy for surface temperature measurement. Comparison of model output between the control run and the sensitivity runs shows that the model error growth and the growing period are comparable between the two kinds of predictability. This indicates the importance of preparing accurate boundary conditions in numerical prediction.