Modelling the uncertainty of slope estimation from a LIDAR-derived DEM: a case study from a large-scale area in the Czech republic

Abstract

This paper summarizes the methods and results of error modelling and propagation analyses in the Olše and Stonávka confluence area. In terrain analyses, the outputs of the aforementioned analysis are always a function of input. Two approaches according to the input data were used to generate field elevation errors which subsequently entered the error propagation analysis. The main goal solved in this research was to show the importance of input data in slope estimation and to estimate the elevation error propagation as well as to identify DEM errors and their consequences. Dependencies were investigated as well to achieve a better prediction of slope errors. Four different digital elevation model (DEM) resolutions (0.5, 1, 5 and 10 meters) were examined with the Root Mean Square Error (RMSE) rating up to 0.317 meters (10 m DEM). They all originated from a LIDAR survey. In the analyses, a stochastic Monte Carlo simulation was performed with 250 iterations. The article focuses on the error propagation in a large-scale area using high quality input DEM and Monte Carlo methods. The DEM uncertainty (RMSE) was obtained by sampling and ground research (RTK GPS) and from subtraction of two DEMs. According to empirical error distribution a semivariogram was used to model spatially autocorrelated uncertainty in elevation. The second procedure modelled the uncertainty without autocorrelation using a random N(0,RMSE) error generator. Statistical summaries were drawn to investigate the expected hypothesis. As expected, the error in slopes increases with the increasing vertical error in the input DEM. According to similar studies the use of different DEM input data, high quality LIDAR input data decreases the output uncertainty. Errors modelled without spatial autocorrelation do not result in a greater variance in the resulting slope error. In this case, although the slope error results (comparing random uncorrelated and empirical autocorrelated error fields) did not show any statistical significant difference, the input elevation error pattern was not normally distributed and therefore the random error generator realization is not a suitable interpretation of the true state of elevation errors. The normal distribution was rejected because of the high kurtosis and extreme values (outliners). On the other hand, it can show an important insight into the expected elevation and slope errors. Geology does not influence the slope error in the study area.