Dual number-based variational data assimilation: Constructing exact tangent linear and adjoint code from nonlinear...

Area of Science:

• Oceanography
• Computational Science
• Biogeochemistry

Background:

• Complex biogeochemical ocean models require accurate derivatives for data assimilation.
• Manual coding of tangent linear and adjoint models is labor-intensive and error-prone.

Purpose of the Study:

• To leverage dual numbers for automatic derivative calculation in ocean models.
• To implement a variational data assimilation system using dual number-generated code.
• To assess the efficiency and ease of implementation compared to traditional methods.

Main Methods:

• Utilized dual numbers to automatically generate tangent linear and adjoint model code.
• Integrated the dual number-based code into a variational (4D-Var) data assimilation system.
• Coupled the system with a realistic physical ocean circulation model.

Main Results:

• Successfully constructed and applied dual number-based code for a biogeochemical ocean model.
• The resulting data assimilation system showed comparable performance to hand-coded equivalents.
• Implementation was significantly easier, and maintenance became trivial with automatic updates.

Conclusions:

• Dual numbers offer an efficient and accessible approach for developing derivative-based computational tools.
• This method simplifies the implementation and maintenance of complex data assimilation systems in oceanography.
• Automatic differentiation using dual numbers is a valuable technique for scientific modeling.