A new high precision data assimilation method for the barotropic primitive equation

To overcome a lot of shortcomings of gradient computations in the variational data assimilation by the adjoint method, such as low accuracy, difficult implementation and great complexity et al. a new data assimilation method based on dual-number theory is proposed. The new data assimilation method can avoid the complicated reverse integration of the tangent-linear/adjoint model. It only need a forward integration in dual-number space to obtain the cost function and the corresponding gradient vector. The numerical experiment is implemented for the barotropic primitive equation. The results show that the new method can reconstruct the initial conditions of the baroscopic primitive equation conveniently and accurately and has a strong anti-noise characteristic.