Localization　is　critical　to　the　effective　use　of　an　(iterative)　ensemble　Kalman　filter　or　ensemble　smoother　to　estimate　uncertain　quantities　of　interest.　Here,　we　propose　a　novel,　fully　adaptive,　correlation-based　localization　method　(termed　FBadap).　We　embed　our　FBadap　approach　within　an　iterative　ensemble　smoother　to　estimate　three-dimensional　spatially　heterogeneous　log-conductivity　(Y)　fields.　The　latter　are　characterized　through　a　Generalized　sub-Gaussian　model,　which　includes　the　Gaussian　distribution　as　a　particular　case.　They　constitute　random　fields　within　which　head　and　concentration　observations　are　collected　at　monitoring　wells　screened　at　multiple　depths.　To　ensure　transparent　comparisons,　we　study　and　analyze　the　performance　of　our　approach　through　a　wide　range　of　synthetic　test　cases.　These　comprise　diverse　configurations,　including　(a)　various　ensemble　sizes,　(b)　various　degrees　of　departure　of　the　description　of　the　spatial　heterogeneity　from　a　Gaussian　model,　as　well　as　(c)　different　values　of　the　mean　and　variance　of　the　initial　ensemble　of　Y.　Our　results　show　that　(i)　FBadap　is　robust　adaptive　approach　enabling　one　to　tackle　a　variety　of　settings;　(ii)　FBadap　exhibits　stronger　adaptivity　to　cope　with　diverse　ensemble　sizes　than　FBconst,　and　can　provide　improved　accuracy　of　conductivity　estimates　in　comparison　with　traditional　methods;　and　(iii)　the　quality　of　conductivity　estimates　is　jointly　impacted　by　the　degree　of　departures　of　the　reference　Y　field　and　of　the　initial　ensemble　of　Y　from　a　description　based　on　a　Gaussian　model.