Efficient estimation of time-mean states of ocean models using 4D-Var and implicit time-stepping

• Published in: Nonlinear processes in geophysics Vol. 14; no. 6; pp. 777 - 788
• Main Authors: Terwisscha van Scheltinga, A. D., Dijkstra, H. A.
• Format: Journal Article
• Language: English
• Published: Gottingen Copernicus GmbH 01.01.2007; European Geosciences Union (EGU); Copernicus Publications
• Subjects: Astrophysics; Cosmology and Extra-Galactic Astrophysics; Earth Sciences; Estimating techniques; Oceanography; Physics; Sciences of the Universe; Signal to noise ratio; Spectrum analysis
• ISSN: 1607-7946; 1023-5809; 1607-7946
• DOI: 10.5194/npg-14-777-2007

We propose an efficient method for estimating a time-mean state of an ocean model subject to given observations using implicit time-stepping. The new method uses (i) an implicit implementation of the 4D-Var method to fit the model trajectory to the observations, and (ii) a pre-processor which applies a multi-channel singular spectrum analysis to enhance the signal-to-noise ratio of the observational data and to filter out the high frequency variability. This approach enables one to estimate the time-mean model state using larger time-steps than is possible with an explicit model. The performance of the method is presented for two test cases within a barotropic quasi-geostrophic nonlinear model of the wind-driven double-gyre ocean circulation. The method turns out to be accurate and, in comparison with the time-mean state computed with an explicit version of the model, relatively cheap in computational cost.