Numerical Validations of the Tangent Linear Model for the Lorenz Equations

The validity of the tangent linear model(TLM)is studied numerically using the example of the Lorenz equations in this paper.The relationship between the limit of the validity time of the TLM and initial perturbations for the Lorenz equations is investigated using the Monte Carlo sampling method.A new error function between the nonlinear and the linear evolution of the perturbations is proposed.Furthermore,numerical sensitivity analysis is carried to establish the relationship between parameters and the validity of the TLM,such as the initial perturbation,the prediction time,the time step size and so on,by the method of mathematical statistics.