In many applications of 3DVAR, the balance constraints can be considered via two main approaches: weak constraint method which adds penalty terms to the cost function; and proper defi- nition of the background error c...In many applications of 3DVAR, the balance constraints can be considered via two main approaches: weak constraint method which adds penalty terms to the cost function; and proper defi- nition of the background error covariance matrix with non-zero cross-correlation sub-matrices. The weak constraint approach requires determining the weighting matrices of the penalty terms. The background error covariance approach does not require determining those additional weighting ma- trices. However, it is only applicable to those linear or linearized balance constraints. A novel ap- proach is proposed based on the background error covariance approach by generalizing the so-called Derber-Bouttier formulation. An assimilation experiment of estimating temperature and salinity from the sea surface dynamic height observation is given to illustrate the proposed treatments of nonlinear balance constraints.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.40225015 and 40221503).
文摘In many applications of 3DVAR, the balance constraints can be considered via two main approaches: weak constraint method which adds penalty terms to the cost function; and proper defi- nition of the background error covariance matrix with non-zero cross-correlation sub-matrices. The weak constraint approach requires determining the weighting matrices of the penalty terms. The background error covariance approach does not require determining those additional weighting ma- trices. However, it is only applicable to those linear or linearized balance constraints. A novel ap- proach is proposed based on the background error covariance approach by generalizing the so-called Derber-Bouttier formulation. An assimilation experiment of estimating temperature and salinity from the sea surface dynamic height observation is given to illustrate the proposed treatments of nonlinear balance constraints.
