Hybrid data assimilation techniques using the adjoint method in a coupled Lorenz system

A hybrid 4D-variational data assimilation method for numerical climate models is introduced using the Lorenz '63 model. This new approach has the potential to optimise a high complexity Earth system model (ESM) by utilising the adjoint equations of an intermediate complexity ESM. The method is conceptually demonstrated by consecutively synchronising two Lorenz '63 systems to observations before optimisation. The first represents a 'high complexity' model and the second an 'intermediate complexity' model which has adjoint equations. This method will save computational power for a full ESM and has negligible error and uncertainty change compared to the optimisation of a single model with adjoint equations. A similar setup can be applied to sparse observations. An alternative assimilation setup, with two identical models, is used to filter noisy data. This reduces optimised parametric model uncertainty by approximately one third. Such a precision gain could prove valuable for seasonal, annual, and decadal predictions.