The Study On The Validity Of The Tangent Linear Model Of The Lorenz Model

In this study, the validity of tangent linear model(TLM) is investigated using the Lorenz model, and some numerical examples are presented to check the theoretical analysis. Firstly, the optimal perturbation of the largest difference between TLM and nonlinear model has been development, by the implicit filtering derivative-free op-timization algorithm. Secondly, we get the relationship between several parameters and the validity of TLM, such as the initial perturbation, the time prediction, the time step, the Rayleigh number and so on, by the method of mathematical statistics. When the initial states are different, the relationship between the parameters and the valid-ity of TLM is the same. Besides, relationship between the limit of validity time of TLM and initial perturbation in Lorenz model is studied using Monte Carlo sampling method. Our result shows that the logarithmic function performs well in describing the relationship between the limit of validity time of TLM and the initial perturbation.