Weak constraint R4D-Var or 4D-PSAS: Systematic Model Errors?

[lmp4]

I am seeking to eventually apply weak constraint R4D-Var or 4D-PSAS to my model and am wondering about the type of model error that can be incorporated.

Currently my model has a significant systematic error in temperature at a specific location in the domain (around +5K) for most months throughout the year.

Jan/Aug/Sept Average Temp: Model, Obs, Difference

Model_JAS_Error.png (32.14 KiB) Viewed 2968 times

Even through reading 'The Regional Ocean Modeling System (ROMS) 4-dimensional variational data
assimilation systems
Part I, II & II' (Moore et al, 2011), I still can't grasp what error the prior model error covariance Q includes with the ROMS formulation of R4D-Var or 4D-PSAS.

Yannick Tremolet (2006) seems to suggest that there would be different formulation of weak constraint 4D-Var for including either the random or systematic error.

To my understanding from the ROMS 4DVAR tutorials, the ROMS weak constraint formulation has model-error forcing η as the control variable (thus random error)?
So is this formulation 'implicitly attributing the model error entirely to a stochastic (Gaussian) noise' (Ning, et al 2014)? And if so will my inclusion of model basis performed in a similar way to the tutorials i.e 'as a first attempt, a prior model error covariance
Q = Kb W Σ C W(T) Σ (T) Kb(T) is assumed' be acceptable practice?

Does the weak constraint R4D-Var or 4D-PSAS have a way of accounting for both random model error and model bias?

Sorry for all the questions, this has been puzzling me quite a bit. Any thoughts on this would be greatly welcomed!

References

1. Moore, A. M., H. G. Arango, G. Broquet, B. S. Powell, A. T. Weaver, and J. Zavala-Garay, 2011: The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems. Prog. Oceanogr., 91, 34–49, doi:10.1016/j.pocean.2011.05.004. http://www.sciencedirect.com/science/ar ... 1111000516 (Accessed October 9, 2014).

• Tr’emolet, Y., 2006: Accounting for an imperfect model in 4D-Var. Q. J. R. Meteorol. Soc., 132, 2483–2504, doi:10.1256/qj.05.224. http://doi.wiley.com/10.1256/qj.05.224 (Accessed October 14, 2014).

• Ning, L., F. P. Carli, A. M. Ebtehaj, E. Foufoula-Georgiou, and T. T. Georgiou, 2014: Coping with model error in variational data assimilation using optimal mass transport. Water Resour. Res., 50, 5817–5830, doi:10.1002/2013WR014966. http://doi.wiley.com/10.1002/2013WR014966 (Accessed October 14, 2014).