There are two different approaches on how to formulate adjoint numerical model (ANM). Aiming at the disputes arising from the construction methods of ANM, the differences between nonlinear shallow water equation and its adjoint equation are analyzed; the hyperbolicity and homogeneity of the adjoint equation are discussed. Then, based on unstructured meshes and finite volume method, a new adjoint model was advanced by getting numerical model of the adjoint equations directly. Using a gradient check, the correctness of the adjoint model was verified. The results of twin experiments to invert the bottom friction coefficient (Manning’s roughness coefficient) indicate that the adjoint model can extract the observation information and produce good quality inversion. The reason of disputes about construction methods of ANM is also discussed in the paper.
"Analysis of the Properties of Adjoint Equations and Accuracy Verification of Adjoint Model Based on FVM." Abstr. Appl. Anal. 2014 (SI31) 1 - 7, 2014. https://doi.org/10.1155/2014/407468