A Comparison of Two Nonlinear Data Assimilation Methods

Abstract. Advanced numerical data assimilation (DA) methods, such as the four-dimensional variational (4DVAR) method, are elaborate and computationally expensive. Simpler methods exist that take time-variability into account, providing the potential of accurate results with a reduced computational cost. Recently, two of these DA methods were proposed for a nonlinear ocean model. The first method is Diffusive Back and Forth Nudging (D-BFN) which has previously been implemented in several complex models, most specifically, an ocean model. The second is the Concave-Convex Nonlinearity (CCN) method provided by Larios and Pei that has a straightforward implementation and promising results. D-BFN is less costly than a traditional variational DA system but it requires integrating the model forward and backward in time over a number of iterations, whereas CCN only requires integration of the forward model once. This paper will investigate if Larios and Pei's CCN algorithm can provide competitive results with the already tested D-BFN within simple chaotic models. Results show that observation density and/or frequency, as well as the length of the assimilation window, significantly impact the results for CCN, whereas D-BFN is fairly adaptive to sparser observations, predominately in time.