Finite mixtures of normal distributions in the study of the error in altimetry

José Rodríguez-Avi,Francisco Javier Ariza-López

doi:10.5194/ica-adv-3-13-2021

José Rodríguez-Avi, Francisco Javier Ariza-López

Open Access

https://doi.org/10.5194/ica-adv-3-13-2021

Copy DOI

Abstract

Abstract. The modelling of the altimetric error is proposed by means of the mixture of normal distributions. This alternative allows to avoid the problems of lack of normality of the altimetric error and that have been indicated numerous times. The conceptual bases of the mixture of distributions are presented and its application is demonstrated with an applied example. In the example, the altimetric errors existing between a DEM with 5 × 5 m resolution and another DEM with 2 × 2 m resolution are modelled, which is considered as a reference. The application demonstrates the feasibility and power of analysis of the proposal made.

Highlights

Digital Elevation Models (DEM) are topographic data that following a model digitally represent the elevations of the bare terrain
The quality of DEMs is usually understood as the altimetric positional accuracy of point data
The best way to evaluate or control positional accuracy is by applying standardized methods, for example the new ASPRS standard (ASPRS, 2015), but there are many others

Summary

Introduction

Digital Elevation Models (DEM) are topographic data that following a model (e.g., contour lines, point clouds, meshes, triangle networks, etc.) digitally represent the elevations (elevations or altimetry) of the bare terrain. The best way to evaluate or control positional accuracy is by applying standardized methods, for example the new ASPRS standard (ASPRS, 2015), but there are many others (see a current guide of the most outstanding in Ariza-López et al, 2019). Until now, these standards are based on the assumption of the normality of errors (e.g., ASCE 1983, FGDC 1998, ASPRS 2015) which allows to the application of a parametric model: the normal distribution where the mean (μ) and the standard distribution (σ) are the position and scale parameters of the distribution. Non-normality violates a basic assumption of the method, and this violation is important from a strict perspective

Objectives

Results

Discussion

Conclusion