Dual number-based variational data assimilation: Constructing exact tangent linear and adjoint code from nonlinear model evaluations

Abstract

Dual numbers allow for automatic, exact evaluation of the numerical derivative of highdimensional functions at an arbitrary point with minimal coding effort. We use dual numbers to construct tangent linear and adjoint model code for a biogeochemical ocean model and apply it to a variational (4D-Var) data assimilation system when coupled to a realistic physical ocean circulation model with existing data assimilation capabilities. The resulting data assimilation system takes modestly longer to run than its hand-coded equivalent but is considerably easier to implement and updates automatically when modifications are made to the biogeochemical model, thus making its maintenance with code changes trivial.