Comparison of the Influences of Initial Errors and Model Parameter Errors on Predictability of Numerical Forecast

AbstractBased on the nonlinear local Lyapunov exponent (NLLE) approach introduced by the authors recently, the influences of initial errors and parameter errors on the predictability of the Lorenz system are studied. The major results are summarized as follows: (i) When only initial errors or only parameter errors exist in the Lorenz system, the error growth and predictability limit are comparable between two kinds of predictability problems. This result holds basically for the wide range of parameter space of the Lorenz system. (ii) When initial errors and parameter errors exist together in the Lorenz system, their effects on the predictability of the Lorenz system mainly depend on their relative magnitudes. When the magnitude of initial errors is much greater than that of parameter errors, the predictability limit of the Lorenz system is mainly determined by initial errors. On the contrary, when the magnitude of parameter errors is much greater than that of initial errors, the predictability limit is mainly determined by parameter errors. When the magnitude of initial errors is close to that of parameter errors, initial errors and parameter errors contribute together to the predictability limit of the Lorenz system. These results indicate that when numerical weather forecast is made, we should pay great attention to the determination of model parameters, as well as to the determination of initial conditions.