Cycling the Representer Method for 4D-variational data assimilation with the Navy Coastal Ocean Model

The Cycling Representer Method, which is a technique for solving 4D-variational data assimilation problems, has been demonstrated to improve the assimilation accuracy with simpler nonlinear models. In this paper, the Cycling Representer Method will be used to assimilate an array of ADCP velocity observations with the Navy Coastal Ocean Model (NCOM). Experiments are performed in a high-resolution Mississippi Bight domain for the entire month of June, 2004 and demonstrate the usefulness of this assimilation technique in a realistic application.The Representer Method is solved by minimizing a cost function containing the weighted squared errors of velocity measurements, initial conditions, boundary conditions, and model dynamics. NCOM, however, is a highly nonlinear model and in order to converge towards the global minimum of this cost function, NCOM is linearized about a background state using tangent linearization. The stability of this tangent linearized model (TLM) is a very sensitive function of the background state, the level of nonlinearity of the model, open boundary conditions, and the complexity of the bathymetry and flow field. For the Mississippi Bight domain, the TLM is stable for only about a day. Due to this short TLM stability time period, the Representer Method is cycled by splitting the time period of the assimilation problem into short intervals. The interval time period needs to be such that it is short enough for the TLM to be stable, but long enough to minimize the loss of information due to reducing the temporal correlation of the dynamics and data. For each new cycle, a background is created as a nonlinear forecast from the previous cycle’s assimilated solution. This background, along with the data that falls within this new cycle, is then used to calculate a new assimilated solution. The experiments presented in this paper demonstrate the improvement of the assimilated solution as the time window of the cycles is reduced to 1 day. The 1-day cycling, however, was only optimal for the first half of the experiment. This is because there was a strong wind event near the middle of June that significantly reduced the stability of the 1-day cycling and caused substantial errors in the assimilation. Therefore, the 12-h cycling worked best for the second half of the experiment. This paper also demonstrates that the forecast skill is improved as the assimilation system progresses through the cycles.