How can complex models be efficiently analyzed for sensitivity and optimization? This research introduces a method for constructing adjoint models, which are increasingly used in meteorology and oceanography for data assimilation, model tuning, and sensitivity analysis. The study focuses on reverse mode differentiation of algorithms, specifically for scalar-dependent functions. The described approach establishes simple construction rules for adjoint statements and subprograms, addressing conflicts arising from loops and variable redefinition. The method's implementation, known as the Tangent Linear and Adjoint Model Compiler (TAMC), offers a distinct advantage over direct coding, which is time-consuming and prone to errors. This paper presents a practical solution for automatic generation of adjoint code, enhancing the efficiency and accuracy of complex model analysis in various scientific fields. By providing clear guidelines and a working implementation, this research contributes to advancing computational techniques in mathematical software.
Published in ACM Transactions on Mathematical Software, this paper is relevant to the journal's focus on algorithms, mathematical software, and related tools. The article addresses the computational challenges in constructing adjoint models, providing a practical methodology and software implementation that align with the journal's emphasis on innovative and efficient software solutions.