d

method to obtain gradients in numerical discretization. Using the ISP sensitivity analysis method the adjoint code becomes simple to deriveevenwith complexgoverningequations, discretizationmeth-ods and non-linear parameterizations. Importantly, this greatly re-duces the effort required to implement the tangent linear model (differentiation of the discrete forward model) and its adjoint, and code continues to ations. velop variational/ ased on F cient sen ete linear non-linear systems, possibly with bifurcations, critical poin global optimisation. Shortly thereafter, this method was generalised using Gateaux differential operators [9] for a non-lin-ear operator of the system response along an arbitrary direction. Adjoint sensitivity analysis methods are widely applied to chemi-cal kinetics [2], optimisation [3,8,15], ocean and atmospheric sci-ences [4–7,31,44–48] and nuclear science [10]. Furthermore, Bischof et al. developed the pseudo-adjoint method for efficient computation of Jacobian matrices using colouring approaches [26,29]