We　propose　a　fundamental　theorem　for　eco-environmental　surface　modelling　(FTEEM)　in　order　to　apply　it　into　the　fields　of　ecology　and　environmental　science　more　easily　after　the　fundamental　theorem　for　Earth’s　surface　system　modeling　(FTESM).　The　Beijing-Tianjin-Hebei　(BTH)　region　is　taken　as　a　case　area　to　conduct　empirical　studies　of　algorithms　for　spatial　upscaling,　spatial　downscaling,　spatial　interpolation,　data　fusion　and　model-data　assimilation,　which　are　based　on　high　accuracy　surface　modelling　(HASM),　corresponding　with　corollaries　of　FTEEM.　The　case　studies　demonstrate　how　eco-environmental　surface　modelling　is　substantially　improved　when　both　extrinsic　and　intrinsic　information　are　used　along　with　an　appropriate　method　of　HASM.　Compared　with　classic　algorithms,　the　HASM-based　algorithm　for　spatial　upscaling　reduced　the　root-mean-square　error　of　the　BTH　elevation　surface　by　9　m.　The　HASM-based　algorithm　for　spatial　downscaling　reduced　the　relative　error　of　future　scenarios　of　annual　mean　temperature　by　16%.　The　HASM-based　algorithm　for　spatial　interpolation　reduced　the　relative　error　of　change　trend　of　annual　mean　precipitation　by　0.2%.　The　HASM-based　algorithm　for　data　fusion　reduced　the　relative　error　of　change　trend　of　annual　mean　temperature　by　70%.　The　HASM-based　algorithm　for　model-data　assimilation　reduced　the　relative　error　of　carbon　stocks　by　40%.　We　propose　five　theoretical　challenges　and　three　application　problems　of　HASM　that　need　to　be　addressed　to　improve　FTEEM.　©　2020,　Science　China　Press　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.