A theoretical approach to modeling the accuracy assessment of digital elevation models

In this paper, a theoretical analysis is presented of the degree of correctness to which the accuracy figures of a grid Digital Elevation Model (DEM) have been estimated, measured as Root Mean Square Error (RMSE) depending on the number of checkpoints used in the accuracy assessment process. The latter concept is sometimes referred to as the Reliability of the DEM accuracy tests. Two theoretical models have been developed for estimating the reliability of the DEM accuracy figures using the number of checkpoints and parameters related to the statistical distribution of residuals (mean, variance, skewness, and standardized kurtosis). A general case was considered in which residuals might be weakly correlated (local spatial autocorrelation) with non-zero mean and non-normal distribution. Thus, we avoided the "strong assumption" of distribution normality accepted in some of the previous works and in the majority of the current standards of positional accuracy control methods. Sampled data were collected using digital photogrommetric methods applied to large scale stereo imagery (1:5 000). In this way, seven morphologies were sampled with a 2 in by 2 m sampling interval, ranging from flat (3 percent average slope) to the highly rugged terrain of marble quarries (82 percent average slope). Two local schemes of interpolation have been employed, using Multiquadric Radial Basis Functions (MRBF) and Inverse Distance Weighted (IDW) interpolators, to generate interpolated surfaces from high-resolution grid DEMs. The theoretical results obtained were experimentally validated using the Monte Carlo simulation method. The proposed models provided a good fit for the raw simulated data for the seven morphologies and the two schemes of interpolation tested (r(2) > 0.96 as mean value). The proposed theoretical models performed very well for modeling the non-gaussian distribution of the errors at the checkpoints, a property which is very common in geographically distributed data.