A POD reduced - order 4 D - Var adaptive mesh ocean modelling approach 3

A novel proper orthogonal decomposition (POD) inverse model, developed for an adaptive mesh ocean model (the Imperial College Ocean Model, ICOM), is presented here. The new POD model is validated 11 using the Munk gyre flow test case, where it inverts for initial conditions. The optimized velocity fields exhibit overall good agreement with those generated by the full model. The correlation between the 13 inverted and the true velocity is 80–98% over the majority of the domain. Error estimation was used to judge the quality of reduced-order adaptive mesh models. The cost function is reduced by 20% of its 15 original value, and further by 70% after the POD bases are updated. In this study, the reduced adjoint model is derived directly from the discretized reduced forward model. 17 The whole optimization procedure is undertaken completely in reduced space. The computational cost for the four-dimensional variational (4D-Var) data assimilation is significantly reduced (here a decrease 19 of 70% in the test case) by decreasing the dimensional size of the control space, in both the forward and adjoint models. Computational efficiency is further enhanced since both the reduced forward and adjoint 21 models are constructed by a series of time-independent sub-matrices. The reduced forward and adjoint models can be run repeatedly with negligible computational costs. 23 An adaptive POD 4D-Var is employed to update the POD bases as minimization advances and loses control, thus adaptive updating of the POD bases is necessary. Previously developed numerical approaches 25 Fang et al. (Int. J. Numer. Methods Fluids 2008) are employed to accurately represent the geostrophic balance and improve the efficiency of the POD simulation. Copyright q 2008 John Wiley & Sons, Ltd. 27