Statistical field estimation for complex coastal regions and archipelagos

► Derived schemes for mapping ocean fields in complex multiply-connected domains and studied computational properties. ► The new OA schemes estimate the length of shortest sea paths using the Level Set Method and Fast Marching Method (FMM). ► An FMM-based methodology for estimating total velocity under geostrophic balance in complex domains is developed. ► Using idealized and realistic ocean cases, we find that the FMM-based OA scheme is the most efficient and accurate. ► Mathematical and computational properties are studied in detail, using fundamental theorems and illustrations.