A Weak Constraint 4D-Var Assimilation System for the Navy Coastal Ocean Model Using the Representer Method - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 377

The second experiment used the observations collected during AOSN II. Starting
from a free run solution that completely misrepresented both the data and the
dynamics of the region during the selected time period, the assimilation was able
to accurately fit the assimilated data. Also, contrary to the free run and the first
guess, the upwelling and relaxation events that dominate the dynamics of the regions
were accurately described by the analysis which benefited from a good observation
coverage of the domain and a robust assimilation system.
To avoid redundancy, some glider profiles were withheld from the assimilation
and used for evaluation. The analysis fitted the withheld observations with the same
accuracy as the assimilated observations. This was due in part to the proximity of
the withheld observations with those that were assimilated.
The assimilated solution with MODAS data fits 80 % and 90 % of the
observations to within one and two standard deviations respectively, while the
corresponding numbers for the first guess are 60 % and 75 %, and 45 % and 63 % for
the free running model. Some posterior misfits, although only a small percentage,
are larger than 7 observations standard deviations, which obviously violate the
Gaussian assumption on the errors in general. Similarly, for the AOSN II data, the
assimilated solution fits 86 % and 95 % of the observations to within one and two
standard deviations respectively, while the corresponding numbers for the first guess
are 68 % and 80 %, and 64 % and 76 % for the free running model.
The largest discrepancies between the first guess and the observations were
mostly confined to the upper ocean. After the first 5-day assimilation the first guess
discrepancies grew quickly from their small initial values, confirming that the model
is being forced by surface fluxes that are not compatible with the observations.
This was purposefully set up in order to test the assimilation's ability to efficiently
reduce these discrepancies while estimating what appears to be magnitude-wise a
reasonable correction to the surface fluxes.

Acknowledgements This work was sponsored by the office of Naval Research program element
number 0601153N as part of the projects “Exploring Covariances for Ocean Variational Data
Assimilation” and “Variational Data Assimilation for Ocean Predicition.” This paper is the Naval
Research Laboratory paper contribution number JA/7320-11-646. The authors are thankful to
the anonymous reviewers for their constructive remarks that helped improve the quality of this
manuscript.

Appendix

The discretization of NCOM uses second-order interpolation and differentiation as
defined with the notations:

D 0:5 x C x=2 C x x=2 ;

x

ˇ ˇ ˇ ˇ x

x C x=2 x x=2 ;

@
@x

1
x ı x D

1
x

D