On mass conservation in high-order high-resolution rigorous remapping schemes on the sphere

For applications on the sphere these integral constraints may be violated primarily as a result of inexact or ill-conditioned integration and the authors propose a generic, local, and multitracer efficient method that guarantees that the integral constraints are satisfied in discrete space irrespective of the accuracy of the numerical integration method and slight inaccuracies in the computation of overlap areas.

The authors refer to this method as enforcement of consistency as it is based on integral constraints valid in continuous space. The consistency enforcement method is illustrated in idealized transport tests with the Conservative Semi-Lagrangian Multitracer scheme (CSLAM) in the High Order