Uncertainties and errors in algorithms for elevation gradients

ABSTRACT

Elevation gradients are primary components of slope and aspect. Significant concerns remain when computing gradients if noise (perturbing non-DEM data) is present. There is still a need to find ways to balance accuracy of the gradient and stability to noise for specific types of DEM. In this study, six algorithms are compared using four DEMs and analyzed for stability to base level DEM noise and added random noise. Theoretical stability and accuracy of the formulae are analyzed using harmonic (frequency or spatial scale) response. The results provide a basis to determine the most appropriate algorithm for different situations. They show that: (1) the set (Evans-Young (EY), Sharpnack (Sp), Sobel (Sb)) has a better stability to noise ratio than the set (Zevenbergen (Z), Florinsky (F), Horn (H)). EY has the smoothest surface and the highest stability to noise ratio. If stability is the primary measure in mid-frequencies, EY is a good choice. (2) Sb is good because of its accuracy in mid to high frequencies. Out to the highest frequencies, Sb is the best. (3) F has potential but should not be used with very high-frequency noise. (4) H and Z should not be used when there is substantial noise.

KEYWORDS:

• Elevation gradient
• optimal algorithm
• harmonic response
• stability
• accuracy

Acknowledgments

Special thanks to Chunmei Wang and Guowei Pang of Northwest University in China for reading the paper and providing suggestions. The authors appreciate anonymous reviewers whose comments significantly improved the paper and the Editor and publications section of IJGIS for their help.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data and code availability statement

The data and codes that support the findings of this study are available on Figshare at https://doi.org/10.6084/m9.figshare.12228656.v2.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grant number 41371274] and [41601290]

Notes on contributors

Dong Shi

Dong Shi is a Ph.D. candidate in Northwest University, China. She majors in terrain factor analysis and geographic information system.

Qinke Yang

Qinke Yang is a Professor in Northwest University, China. His field is digital terrain analysis, especially slope research.

Qifeng Zhu

Qifeng Zhu received a master’s degree in Northwest University, China. He works in Shaanxi Institute of Zoology, China. He majors in algorithm comparison.

David L. B. Jupp

David L. B. Jupp is a Senior Principal Research Scientist in Land&Water, CSIRO, Australia. His field is remote sensing and digital image processing.

Yongqing Long

Yongqing Long is a Lecturer in Northwest University, China. He majors in accuracy evaluation and noise measurement.