Manylow-ordermodelingstudiesindicatethattheremaybemultipleequilibriaintheatmosphereinducedbythermalandtopographicforcings.However,mostworkusesuncoupledatmosphericmodelandjustfocusesonthemultipleequilibriawithdistinctwaveamplitude,i.e.,thehigh-andlow-indexequilibria.Here,alow-ordercoupledland-atmospheremodelisusedtostudythemultipleequilibriawithbothdistinctwavephaseandwaveamplitude.Themodelcombinesatwo-layerquasi-geostrophicchannelmodelandanenergybalancemodel.Highlytruncatedspectralexpansionsareusedandtheresultsshowthattheremaybetwostableequilibriawithdistinctwavephaserelativetothetopography:one(theother)hasalowerlayerstreamfunctionthatisnearlyin(outof)phasewiththetopography,i.e.,thelowerlayerridges(troughs)areoverthemountains,calledridge-type(trough-type)equilibria.Thewavephaseofequilibriumstatedependsonthedirectionoflowerlayerzonalwindandhorizontalscaleofthetopography.Themultiplewavephaseequilibriaassociatedwithridge-andtrough-typesoriginatefromtheorographicinstabilityoftheHadleycirculation,whichisapitch-forkbifurcation.Comparedwiththeuncoupledmodel,theland-atmospherecoupledsystemproducesmorestableatmosphericflowandmoreridge-typeequilibriumstates,particularly,theseeffectsareprimarilyattributedtothelongwaveradiationfluxes.Theupperlayerstreamfunctionsofbothridge-andtrough-typeequilibriaarealsocharacterizedbyeitherahigh-orlow-indexflowpattern.However,themultiplewavephaseequilibriaassociatedwithridge-andtrough-typesaremoreprominentthanmultiplewaveamplitudeequilibriaassociatedwithhigh-andlow-indextypesinthisstudy.
