Nonlinear Optimization Method To Sensitivity Analysis Of The Numerical Model

The accuracy of numerical weather (climate) prediction is decreasing along with prediction time because initial field and numerical model have errors. To reduce these two kinds of error, Meteorologists have done a lot of work by making sensitivity analysis of numerical model.Presently there are three methods to make sensitivity analysis: numerical simulation, adjoint and linear singular vectors (LSVS). Numerical simulation method has many advantages. For example, it can avoid finding an analytic solution and reflect the physical factors that affect prediction results and how the atmosphere develops. However, this method can not give all possible significative combinations of physical processes and parameters (initial fields) when making sensitivity analysis to model (initial) errors. Moreover, the initial and model errors may be large when the numerical simulation is good. Adjoint method provides an efficient tool to calculate the gradient vector of the cost function to the initial field. The gradient vector can be used to construct the initial errors. An important application of linear singular vectors is to make sensitivity study of the numerical model. Linear singular vector represents the direction that initial errors increase fastest during the validity period of TLM. LSVS can be used to construct initial errors in an ensemble prediction system. But adjoint method and LSV method are based on linear theory and can only describe the development of small perturbations during the validity period of tangent linear model.It is firstly suggested by Mu Mu that nonlinear optimization method can be used to make sensitivity analysis of numerical model. But as one of nonlinear optimization problems in atmosphere and ocean science, it was very simply described in Mu Mu's paper and not verified by numerical experiment results.Based on Mu Mu's research, nonlinear optimization method to make sensitivity analysis of numerical model is particularly explored in the thesis. It is also extended on how to estimate model errors when numerical model can simulate observational data at time T well. With two-dimensional quasi-geostrophic motion, a series ofnumerical experiments are made to prove the theoretical results. The main conclusions are as follows:(1) This new method can give a quantitative standard to estimate whether this numerical model is able to simulate the observational data at time T. Moreover, it can directly find the initial field to simulate optimally the observational data at time T, namely, the optimal initial field. This is the main difference between nonlinear optimization method and other methods.(2) Given a numerical model and a kind of observational data, it is difficult for traditional methods to separate model errors and initial errors. But nonlinear optimization method can do it by comparing the observational accuracy with the difference between the optimal initial field and initial observational data, even if when simulation results are good.