Inaccordancewithanewcompensationprincipleofdiscretecomputations,thetraditionalmeteo-rologicalglobal(pseudo-)spectralschemesofbarotropicprimitiveequation(s)aretransformedintoperfectenergyconservativefidelityschemes,thusresolvingtheproblemsofbothnonlinearcomputa-tionalinstabilityandincompleteenergyconservation,andraisingthecomputationalefficiencyofthetraditionalschemes.Asthenumericaltestsofthenewschemesdemonstrate,insolvingtheproblemofenergyconser-vationinoperationalcomputations,thenewschemescaneliminatethe(nonlinear)computationalin-stabilityand,tosomeextenteventhe(nonlinear)computationalpergingasfoundinthetraditionalschemes,Furthercontrastsbetweennewandtraditionalschemesalsoindicatethat,indiscreteopera-tionalcomputations,thenewschemeinthecaseofnonpergenceiscapableofprolongingthevalidin-tegraltimeofthecorrespondingtraditionalscheme,andeliminatingcertainkindofsystematicalcom-putational“climatedrift”,meanwhileincreasingitscomputationalaccuracyandreducingitsamountofcomputation.Theworkingprincipleofthispaperisalsoapplicabletotheproblemconcerningbaroclin-icprimitiveequations.
