Are the observation error covariances in wc13 actually instrument errors?

[stef]

I was wondering if the observation error covariances in the tutorial represent instrument errors or the actual spread of the data around a valid model. In the tutorial excerise 1, WC13 is described as:

While 30 km resolution is inadequate for capturing much of the energetic meso-scale circulation associated with the CCS, WC13 captures the broad scale features of the circulation quite well...

If I understand the foundations [1] correctly (which I may not as I'm just starting), the observation error covariances should describe the spread around the "true" circulation, and "true" in this context does not mean the observed instantaneous state, but the time-averaged state as potentially computable from a model of 30km resolution (or not?).

The observation error covariances in wc13_obs.nc for SSH are 0.004 m^2, which corresponds to 2cm error as assumed in d_ssh_obs.m. Aren't these instrument errors? In the for Sea Level TAC DUACS Products [2] it says

Sea level Errors for mesoscales vary between 1 cm^2 in low variability areas to more than ~18 cm^2 in high variability areas. This estimation is based on a 4-satellite constellation in DT conditions.

Aren't these altimetry products designed to capture higher detail than what could be resolved by a 30km model, i.e. the "energetic meso-scale circulation" that is not resolved by WC13? If so, shouldn't the observation error covariances higher to reflect this?

[1] Wikle, C.K. and L.M. Berliner, 2007: A Bayesian tutorial for data
assimilation. Physica D, 230, 1-16.

[2] http://marine.copernicus.eu/documents/Q ... 32-068.pdf

[arango]

The observation error covariance, R, is assumed to be a diagonal matrix for simplicity. The whole R cannot be computed directly but is modeled. The cross-correlations are ignored. Basically, R has two terms: error of measurement (usually small) plus error of representation (tricky). This error of representation is much larger and more cunning to determine. It depends on application grid resolution, data processing (binning, averaging, filtering, etc.), dynamical scales, and super-obs generation. It is a challenging subject in data assimilation, and there is extensive literature for both atmosphere and ocean applications. ROMS 4D-Var includes the Desroziers et al. (2005) statistics essential to examine the error hypothesis assumed in 4D-Var.

Desroziers, G., Berre, L., Chapnik, B., Poli, P. (2005) Diagnosis of observation, background and analysis error statistics in observation space QJRMS, 131:3385–3396.

[stef]

Thanks for the information! Searching for references to Desroziers et al., I found Fig. 12a) of [1] where I think the 2 cm error for the 30km experiment are justified.

[1] The Regional Ocean Modeling System (ROMS) 4-dimensional variational data
assimilation systems. Part II – Performance and application to the California Current System