A comparison of two nonlinear data assimilation methods

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, an implementation which is costly in time and expertise, developing the need to first evaluate a simpler comparison between these two nonlinear methods. 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 that has a straightforward implementation and promising results with a toy model. D-BFN is less costly than a traditional variational DA system but requires an iterative implementation of equations that integrate the nonlinear model forward and backward in time, whereas CCN only requires integration of the nonlinear model forward in time. This paper investigates if the 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 experiment window, significantly impacts the results for CCN, whereas D-BFN is fairly robust to sparser observations, predominately in time.