The local ensemble transform Kalman filter and the running-in-place algorithm applied to a global ocean general circulation model

Abstract. The most widely used methods of data assimilation in large-scale oceanography, such as the Simple Ocean Data Assimilation (SODA) algorithm, specify the background error covariances and thus are unable to refine the weights in the assimilation as the circulation changes. In contrast, the more computationally expensive Ensemble Kalman Filters (EnKF) such as the Local Ensemble Transform Kalman Filter (LETKF) use an ensemble of model forecasts to predict changes in the background error covariances and thus should produce more accurate analyses. The EnKFs are based on the approximation that ensemble members reflect a Gaussian probability distribution that is transformed linearly during the forecast and analysis cycle. In the presence of nonlinearity, EnKFs can gain from replacing each analysis increment by a sequence of smaller increments obtained by recursively applying the forecast model and data assimilation procedure over a single analysis cycle. This has led to the development of the "running in place" (RIP) algorithm by Kalnay and Yang (2010) and Yang et al. (2012a,b) in which the weights computed at the end of each analysis cycle are used recursively to refine the ensemble at the beginning of the analysis cycle. To date, no studies have been carried out with RIP in a global domain with real observations.

This paper provides a comparison of the aforementioned assimilation methods in a set of experiments spanning seven years (1997–2003) using identical forecast models, initial conditions, and observation data. While the emphasis is on understanding the similarities and differences between the assimilation methods, comparisons are also made to independent ocean station temperature, salinity, and velocity time series, as well as ocean transports, providing information about the absolute error of each. Comparisons to independent observations are similar for the assimilation methods but the observation-minus-background temperature differences are distinctly lower for LETKF and RIP. The results support the potential for LETKF to improve the quality of ocean analyses on the space and timescales of interest for seasonal prediction and for RIP to accelerate the spin up of the system.