Recipes for adjoint code construction

Adjoint models are increasingly being developed for use in meteorology and oceanography. Typical applications are data assimilation, model tuning, sen sitivity analysis, and determination of singular vectors. The adjoint model computes the gradient of a cost function with respect to control variables . Generation of adjoint code may be seen as the special case of differentia tion of algorithms in reverse mode, where the dependent function is a scala r. The described method for adjoint code generation is based on a few basic principles, which permits the establishment of simple construction rules f or adjoint statements and complete adjoint subprograms. These rules are pre sented and illustrated with some examples. Conflicts that occur due to loop s and redefinition of variables are also discussed. Direct coding of the ad joint of a more sophisticated model is extremely time consuming and subject to errors. Hence, automatic generation of adjoint code represents a distin ct advantage. An implementation of the method, described in this article, i s the tangent linear and adjoint model compiler (TAMC).