Qualitative and quantitative comparative analysis of the relationship between sampling density and DEM error by bilinear and bicubic interpolation methods

The accuracy of a digital elevation model (DEM) is at stake, critically affecting the success of DEM applications. One important issue of DEM research concerns those factors that touch the generated DEM accuracy. The relationship between DEM error and the sampling density is still a worthy question, especially for nonlinear interpolations. This research comparatively analyzes the qualitative and quantitative relationship between the sampling density and DEM error by both bilinear and bicubic interpolation methods. First, the qualitative relationships between the DEM error and the sampling density for both bilinear interpolation and bicubic interpolation models are investigated based on convergence analysis. Second, the quantitative relationships between the DEM error and the sampling density are further derived by means of the numerical approaches. Here the model error is specified by its right upper bound of the truncated error function, with the sampling density as its variable. Third, experimental studies, involving both mathematical and real DEM surfaces, are conducted to verify the foregoing theoretical findings. The theoretical derivations and experimental studies both demonstrate that the DEM quality by a bicubic interpolation method, in terms of model error, is superior to the counterpart generated by a bilinear interpolation method under the assumption of the original sample data being error-free. The new findings about the model errors for bicubic interpolated DEM, together with the previous work on bilinear interpolated DEM drawn from an earlier study, form a full picture depicting the model errors of an interpolated DEM surface. These results can serve as a guideline for interpolation model selection regarding the practical DEM production.