Study On Frequency Of Erosion Landform Based On Fourier Transform

The expression of the erosion topography is great significant to the study of soil erosionand erosion landform. Nowadays the quantitative research of erosion topography of the LoessPlateau mostly focused on the area of geomorphology and erosion development, channelmapping of the erosion ditch network, general and classification statistical characteristicsanalysis of the extraction of erosion ditch based on DEM. However, there is lack of effectivemethods in quantitatively studying the spatial pattern and the combination characteristics ofthe erosion topography. The paper used the terrain elevation profile always adopted in thetopography study to achieve the quantitative analysis of erosion topography in the gully areaof the Loess Plateau. After extracting some one-dimensional terrain profiles by differentresolution DEM, one can take into account the Fast Fourier transformed when analyzing theseone-dimensional spatial signals. The paper researched the characteristics and the scope of theerosion terrain frequency of the terrain profile by using Fast Fourier transform and spectrumanalysis. The main research results are as follow:1. Discussing and constructing the methods of the terrain profile layout based on DEM.With the principles of the basin erosion geomorphology and the soil erosion, the paper drewthe terrain profiles along the contour and edge-line, and located the places where erosionterrain developed by using different resolution Hc-DEM. The fixed location and direction ofthe terrain profile established a good foundation for terrain profile analysis. Meanwhile, ourwork located the profile along the contour derived by the low-resolution data. The resultsshowed that the range of terrain frequency is wide, and can comprehensively reflect theerosion topography of the study area.2. Initiatively realizing the mathematical expression of the terrain profile. The amplitudespectrogram and phase spectrogram of the terrain profile were obtained by using Fast Fouriertransforms with MATLAB software. By spectrum analysis, the frequency value, the amplitudevalues and phase values of the terrain in the profile were obtained, as well as the mathematicalfunction of the terrain profile composed of the Fourier series.3. Determining the thresholds to divide the frequency band of the erosion terrain. It wasobserved that the2.5m resolution DEM contains low frequency, intermediate frequency andhigh frequency erosion terrain, the25m resolution DEM contains low frequency and intermediate frequency erosion terrain, and the150m resolution DEM only has low frequencyerosion terrain. Extracting the terrain profile by these DEM and analyzing frequency spectrumof the terrain, the frequencies of2.25and62.5(Hz) were showed as two thresholds to dividethe low frequency, intermediate frequency and high frequency terrain information, with initialsuccess achieved in quantitative division of the band of terrain information.4. Realizing the separation of the three kinds of terrain frequency: the low, intermediateand high terrain frequency. The low frequency, intermediate and high terrain frequencyinformation were separated by the two thresholds. Through comparative analysis, it can befound that, low frequency terrain is bigger ditch which mostly affects the overall trend oftopographic relief and the relative elevation, and high frequency terrain is smaller ditch whichmainly affect the roughness of the terrain profile.