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Explorer of the Seas

Introduction

Institutions

Data

Observations

About the Model

Data Assimilation

Assimilation Products

Assimilation Impact

Ensemble Archives

References

Acknowledgements

Explorer of the Seas

Introduction

Institutions

Data

Observations

About the Model

Data Assimilation

Assimilation Products

Assimilation Impact

Ensemble Archives

References

Acknowledgements

## Data Assimilation

The data assimilaton approach used is a incremental 4-Dimensional Variational (IS4DVAR) method. IS4DVAR seeks to minimize the cost function J given by:

where x denotes the ROMS state-vector (T, S, u, v, ζ), and δx denotes increments about a background or first-guess solution denoted x

_{b}; d

_{i}= y

_{i}- Hx

_{i}is the observation increment at time

*i*, where y

_{i}are the observed values of x

_{i}and H (the observation operator) maps x

_{i}to the observation points; and B and O are the background and observations error covariance matrices respectively.

The gradient ∂J/∂x(0) with respect to variations in the model initial conditions can be computed by running the adjoint of ROMS forced by the innovations O

^{-1}(δx

_{i}- d

_{i}). A preconditioned conjugate gradient method uses the gradient information to adjust x(0) so that J decreases during the next integration of ROMS. An iterative algorithm is used to minimize J and utilizes ROMS, the tangent linear version of ROMS, and the adjoint of ROMS. The background error covariance matrix B is modeled as a diffusion operator, and the conjugate gradient algorithm is preconditioned by B

^{1/2}following Weaver and Courtier (2001). The ROMS IS4DVAR system follows closely similar approaches described by Weaver et al (2003) and Vialard et al (2003).