Application of seeding and automatic differentiation in a large scale ocean circulation model

Computation of the Jacobian in a 3-dimensional general ocean circulation model is considered in this paper. The Jacobian matrix considered in this paper is square, large and sparse. When a large and sparse Jacobian is being computed, proper seeding is essential to reduce computational times. This paper presents a manually designed seeding motivated by the Arakawa-C staggered grid, and gives results for the manually designed seeding as compated to identity seeding and optimal seeding. Finite differences are computed for reference.