Adjoint models are used in meteorology and oceanography for data assimilation, model tuning, sensitivity analysis, and singular vector determination. They compute gradients of cost functions with respect to control variables. Generating adjoint code is a special case of reverse-mode differentiation. The method for adjoint code generation is based on simple rules that allow the construction of adjoint statements and subprograms. Conflicts due to loops and variable redefinition are discussed. Automatic generation of adjoint code is more efficient than manual coding. The tangent linear and adjoint model compiler (TAMC) is an implementation of this method. Adjoint models are used for inverse modeling, where a physical system is modeled as a mapping from control variables to predictions. The tangent linear model maps variations of control variables to variations in predictions, while the adjoint model maps variations in predictions back to control variables. Sensitivity analysis and singular vector determination are applications of adjoint models. Adjoint models are more efficient than finite differences for optimization, especially for large-scale problems. The article discusses the differentiation of algorithms using reverse mode. It explains how to differentiate a function defined by a numerical algorithm using the chain rule. The adjoint model is used to compute gradients for optimization. The article presents rules for constructing adjoint statements and subprograms, including handling of active and passive variables, locality, modularity, and readability. It also discusses conflicts that arise due to variable redefinition and provides solutions. The adjoint code is constructed by reversing the order of statements in the original code. The article provides examples of adjoint statements for assignments, conditional statements, loops, and procedure calls. It also discusses the use of auxiliary variables and the importance of modularity in adjoint code generation. The adjoint model is a powerful tool for optimization and data assimilation in meteorology and oceanography.Adjoint models are used in meteorology and oceanography for data assimilation, model tuning, sensitivity analysis, and singular vector determination. They compute gradients of cost functions with respect to control variables. Generating adjoint code is a special case of reverse-mode differentiation. The method for adjoint code generation is based on simple rules that allow the construction of adjoint statements and subprograms. Conflicts due to loops and variable redefinition are discussed. Automatic generation of adjoint code is more efficient than manual coding. The tangent linear and adjoint model compiler (TAMC) is an implementation of this method. Adjoint models are used for inverse modeling, where a physical system is modeled as a mapping from control variables to predictions. The tangent linear model maps variations of control variables to variations in predictions, while the adjoint model maps variations in predictions back to control variables. Sensitivity analysis and singular vector determination are applications of adjoint models. Adjoint models are more efficient than finite differences for optimization, especially for large-scale problems. The article discusses the differentiation of algorithms using reverse mode. It explains how to differentiate a function defined by a numerical algorithm using the chain rule. The adjoint model is used to compute gradients for optimization. The article presents rules for constructing adjoint statements and subprograms, including handling of active and passive variables, locality, modularity, and readability. It also discusses conflicts that arise due to variable redefinition and provides solutions. The adjoint code is constructed by reversing the order of statements in the original code. The article provides examples of adjoint statements for assignments, conditional statements, loops, and procedure calls. It also discusses the use of auxiliary variables and the importance of modularity in adjoint code generation. The adjoint model is a powerful tool for optimization and data assimilation in meteorology and oceanography.