Determination of Open Boundary Conditions with an Optimization Method

Peter C. Chu Department of Oceanography, Naval Postgraduate School, Monterey, California

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Chenwu Fan Department of Oceanography, Naval Postgraduate School, Monterey, California

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Laura L. Ehret Department of Oceanography, Naval Postgraduate School, Monterey, California

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Abstract

The optimization method proposed in this paper is for determining open boundary conditions from interior observations. Unknown open boundary conditions are represented by an open boundary parameter vector (B), while known interior observational values are used to form an observation vector (O). For a hypothetical B* (generally taken as the zero vector for the first time step and as the optimally determined B at the previous time step afterward), the numerical ocean model is integrated to obtain solutions (S*) at interior observation points. The root-mean-square difference between S* and O might not be minimal. The authors change B* with different increments δB. Optimization is used to get the best B by minimizing the error between O and S.

The proposed optimization method can be easily incorporated into any ocean models, whether linear or nonlinear, reversible or irreversible, etc. Applying this method to a primitive equation model with turbulent mixing processes such as the Princeton Ocean Model (POM), an important procedure is to smooth the open boundary parameter vector. If smoothing is not used, POM can only be integrated within a finite period (45 days in this case). If smoothing is used, the model is computationally stable. Furthermore, this optimization method performed well when random noise was added to the “observational” points. This indicates that real-time data can be used to inverse the unknown open boundary values.

Corresponding author address: Dr. Peter C. Chu, Naval Postgraduate School, Department of Oceanography, Code OC/CU, Monterey, CA 93943-5000.

Email: chu@nps.navy.mil

Abstract

The optimization method proposed in this paper is for determining open boundary conditions from interior observations. Unknown open boundary conditions are represented by an open boundary parameter vector (B), while known interior observational values are used to form an observation vector (O). For a hypothetical B* (generally taken as the zero vector for the first time step and as the optimally determined B at the previous time step afterward), the numerical ocean model is integrated to obtain solutions (S*) at interior observation points. The root-mean-square difference between S* and O might not be minimal. The authors change B* with different increments δB. Optimization is used to get the best B by minimizing the error between O and S.

The proposed optimization method can be easily incorporated into any ocean models, whether linear or nonlinear, reversible or irreversible, etc. Applying this method to a primitive equation model with turbulent mixing processes such as the Princeton Ocean Model (POM), an important procedure is to smooth the open boundary parameter vector. If smoothing is not used, POM can only be integrated within a finite period (45 days in this case). If smoothing is used, the model is computationally stable. Furthermore, this optimization method performed well when random noise was added to the “observational” points. This indicates that real-time data can be used to inverse the unknown open boundary values.

Corresponding author address: Dr. Peter C. Chu, Naval Postgraduate School, Department of Oceanography, Code OC/CU, Monterey, CA 93943-5000.

Email: chu@nps.navy.mil

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