Employment of Continuous Slope Cumulative Frequency Spectrum in geomorphology quantitative analysis – a case study on Loess Plateau

Slope spectrum is an effective methodology of digital terrain analysis in geomorphology. However, some limitations are still encountered in the construction of the slope spectrum. E.g., the uncertainties caused by slope classification and resolution of digital elevation model (DEM) may restrict the development of slope spectrum and cause a certain spatial information loss. In this paper, a new spectrum method, defined as continuous slope cumulative frequency (CSCF) spectrum, is proposed. Compared with the slope spectrum, the CSCF spectrum does not require slope classification and combines the spatial information of all grids. Hence, it possesses richer terrain feature information and minimal spatial information loss. Meanwhile, it is more convenient to be used in different study areas without requiring heavy work of slope spectrum in determining the suitable slope classification. We also found that the CSCF spectrum can be generally extracted from DEM with different resolutions, whereas the slope spectrum cannot. Experiment results show that the CSCF spectrum is an efficient geomorphology quantitative analysis method that can quantitatively depict the spatial distribution and evolution process of the typical loess landforms from different angles. Besides, the CSCF spectrum can accurately deduce the stable slope spectrum, whereas the slope spectrum cannot deduce the CSCF spectrum, which further suggests that the previous studies in slope spectrum can be conducted on the basis of the CSCF spectrum. Furthermore, the CSCF spectrum shows well application potentials in landform classification with comparative performance to previous methods. Overall, the CSCF spectrum is an effective method in geomorphology quantitative analysis. Considering that the CSCF spectrum solves two key deficiencies in the present model of slope spectrum (slope classification and DEM resolution) and extends the application scope and concept of spectrum method, it is promising to be the research paradigm of the spectrum method in digital terrain analysis.