Variational Data Assimilation for a Lorenz Model Usinga Non-Standard Genetic Algorithm

Summary  Data assimilation in meteorology and oceanography for strongly nonlinear dynamical systems is challenging. The dynamical system studied here is the classical three-variable Lorenz model. In this context data assimilation with weak-constraint variational methods performs better than other methods like strong-constraint variational methods or Kalman filters. The difficulty in tracking the chaotic Lorenz orbit by assimilation of noisy observations results from the inherent instability in the system. In variational methods a cost function has to be minimized. It is known, that in the Lorenz case the structure of the cost function becomes more and more complex with increasing length of the assimilation time interval and with reduction of the observational data quality. This paper proposes a non-standard implementation of a genetic algorithm for searching the global minimum in case of a weak-constraint formulation. The good performance of this non-local search is shown, but the algorithm is computationally demanding due to a very large number of control parameters within the weak-constraint formulation and, thus, the algorithm is applicable for simple systems only. Received December 12, 1998 Revised May 11, 1999