Advanced data assimilation methods become extremely complicated and challenging when used with strongly nonlinear models. Several previous works have reported various problems when applying existing popular data assimilation techniques with strongly nonlinear dynamics. Common for these techniques is that they can all be considered as extensions to methods that have proved to work well with linear dynamics.
This paper examines the properties of three advanced data assimilation methods when used with the highly nonlinear Lorenz equations. The ensemble Kalman filter is used for sequential data assimilation and the recently proposed ensemble smoother method and a gradient descent method are used to minimize two different weak constraint formulations.
The problems associated with the use of an approximate tangent linear model when solving the Euler–Lagrange equations, or when the extended Kalman filter is used, are eliminated when using these methods. All three methods give reasonable consistent results with the data coverage and quality of measurements that are used here and overcome the traditional problems reported in many of the previous papers involving data assimilation with highly nonlinear dynamics.