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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.