The　recently　emerged　compressive　sensing　(CS)　theory　provides　a　whole　new　avenue　for　data　gathering　in　wireless　sensor　networks　with　benefits　of　universal　sampling　and　decentralized　encoding.　However,　existing　compressive　sensing　based　data　gathering　approaches　assume　the　sensed　data　has　a　known　constant　sparsity,　ignoring　that　the　sparsity　of　natural　signals　vary　in　temporal　and　spatial　domain.　In　this　paper,　we　present　an　adaptive　data　gathering　scheme　by　compressive　sensing　for　wireless　sensor　networks.　By　introducing　autoregressive　(AR)　model　into　the　reconstruction　of　the　sensed　data,　the　local　correlation　in　sensed　data　is　exploited　and　thus　local　adaptive　sparsity　is　achieved.　The　recovered　data　at　the　sink　is　evaluated　by　utilizing　successive　reconstructions,　the　relation　between　error　and　measurements.　Then　the　number　of　measurements　is　adjusted　according　to　the　variation　of　the　sensed　data.　Furthermore,　a　novel　abnormal　readings　detection　and　identification　mechanism　based　on　combinational　sparsity　reconstruction　is　proposed.　Internal　error　and　external　event　are　distinguished　by　their　specific　features.　We　perform　extensive　testing　of　our　scheme　on　the　real　data　sets　and　experimental　results　validate　the　efficiency　and　efficacy　of　the　proposed　scheme.　Up　to　about　8dB　SNR　gain　can　be　achieved　over　conventional　CS　based　method　with　moderate　increase　of　complexity.　©　2012　IEEE.