The Bayliss-lsaacson Algorithm and the Constraint Restoration Method are Equivalent

Bayliss and Isaacson (1975) method of modifying any given difference scheme so as to ensure total conservation of the appropriate physical invariants is shown to be equivalent to the constraint restoration method of Miele et al. (1968, 1969) subject to the requirement of least-square change of the statevector coordinates. Both methods are applied to enforce conservation of total energy and potential enstrophy in global shallow-water equations models. Some algorithmic differences between the methods are discussed as well as some implications of a posteriori enforcement of conservation of integral invariants on the performance of meteorological numerical weather prediction (NWP) models and the internal energy distribution.