Effects of using a posteriori methods for the conservation of integral invariants. [for weather forecasting]

Abstract An examination is made on the nature and effect of using a posteriors adjustments on nonconservative finite-difference schemes to enforce integral invariants of the corresponding analytic system. Using the one-dimensional linear advection equation and the first-order forward in time and upstream in space scheme, it is shown that using an a posteriors constraint restoration technique conserves the globally integrated mass and energy of the system by falsely generating energy in scales which survive the numerical integration. Next, the restoration technique is applied to the nonlinear shallow water system on a sphere using a fourth-order accurate model on a nonstaggered A-grid, which analytically conserves mass, total energy, and momentum but needs periodic global filtering to control nonlinear instability due to aliasing. Using a modification of the a posteriors constraint restoration technique to ensure global conservation of mass, energy and potential enstrophy, nearly perfect conservation is ob...