Then we can combine AD and numerical solvers like is found in modern weather and climate models. I don't quite understand but it has something to do with sensitivity analysis and improving data assimilation. (Google "4dvar ecmwf" for more details... eg: https://www2.atmos.umd.edu/~dkleist/docs/da/ECMWF_DA_TUTORIA...)

I think the idea is to use the "tangent linear model" to decide how much importance to give to a particular observation of the initial state.