| At Present，Digital Elevation Models(DEMs), especially the GRID DEMs, is the maindata sources for the research of soil erosion and terrain analysis. Numerous studies show thatthe grid size of DEMs greatly influences the results of terrain analysis. However, up to now, itis not clear and definite how large the grid size of the DEMs is required to demonstrate fullyand correctly the terrain information. This question has not answered clearly in the previouslystudies. In another word, the relationship between the grid size of DEMs and the ability todescribe the terrain information of DEMs is still not clear. This problem to some extent leadsto the blindness in the practical application of DEMs in the analysis of soil erosion and terrain.Based on the DEM generated by the full digital photogrammetry and field measurements inYaojiawangou watershed, Suide, Shaanxi Province, and taking the gullies of loess plateau asthe studying objects, this paper uses the Fourier Analysis to solve the problem mentionedabove. Firstly, this paper discusses the relationship between the elevation error of DEMs andgrid size. According to this result, it analyzes the influence of grid size on the extraction oferosion gullies network from DEM. Secondly, the paper analyzes the spatial frequencycharacters of different grade gullies and summaries the spatial frequency range of each gradegully with the analysis of spectrum on one dimension of24profiles lying on the gulliesnetwork. At last, the paper extends the results of spectrum analysis of one dimension profilesto two-dimensional spectral analysis, and then designs the two-dimensional frequencylow-pass filter to filter the information of each grade gully. According to the comparisonbetween the filtered DEMs and the original DEMs with different grid size, the study matchesspatial scale of erosion gullies with the grid size of DEMs. The conclusion of this paper solvesthe corresponding relationship between the expression ability of the terrain information for DEMs and the grid size of DEMs.The main conclusions of this paper are as follows:1. The relationship between the elevation error of DEMs and the grid sizeThe influence of grid size on the elevation error of DEMs is shown as follows: theelevation on a grid is overestimated in down-slope direction, while underestimated inup-slope direction. As a result, the value of elevation error on a grid is decided by the slopegradient, while the complication of distribution of elevation error is decided by the size ofgrid. The analysis of elevation error calculated from the DEMs series generated by samplingdirectly shows that The RMSE and the maximum error of elevation DEMs increases with thegrid size in the way that is quadratic function which is very similar with a linear relationship.The maximum error on a grid far exceeds the2times of RMSE.2. The relationship between the characters of gullies network extracted from DEMs andthe grid sizeBy means of analyzing the characters of gullies network extracted from DEMs serieswhich have different grid sizes, the main influence of the grid size on the extraction of gulliesnetwork is reflected in two aspects---the flow direction and the threshold of flowaccumulation. The change of grid size causes the flow direction’s turning dramatically in thecomplicated topography area. The relationship between the grid size and the threshold of flowaccumulation shows that the reasonable threshold decreases while the grid size increases bythe way of negative second order power function. Generally, the change of grid size doesn’tinfluence the structure of the gullies network while the reasonable flow accumulationthreshold is determined. However, the position of gullies will move from the original positionand the shape of gullies will be changed. The larger the grid size is, the simpler the shape ofgullies.3. One-dimensional spectrum of gullies based on profile data1）The comparison between the spatial characters of profiles which are perpendicularwith the direction of the gullies and its One-dimensional spectrum shows that: the gully whichis in higher level, in general, has the greater depth and the wider interval, meanwhile, thecorresponding spatial frequency is lower, the period is longer and the amplitude is larger. Onthe contrary, the lower the level of gully is, the smaller the fluctuation, the narrower theinterval, the higher the frequency, the shorter the period, the smaller the amplitude. The spectrum could reflect the spatial frequency with varying amplitude clearly, and couldcorrespond to the spatial characters of fluctuation of gullies.2）According to the result of comparison between the profiles reconstructed by thevarying spatial frequency and the original profiles, the main spatial frequency range oferosion gullies is concentrated in the low frequency part. The gullies with different gradescorrespond to the different spatial frequency: The minor fluctuation including rills on theslope has the frequency range higher than0.1cycle per meter; the frequency range of shallowfurrow is from0.03to0.1cycle per meter; the gully has the frequency range from0.015to0.085cycle per meter, while the gullies which are in higher grade correspond to the frequencyrange lower than0.015cycle per meter.3）In terms of the spectrum of profiles extracted from the DEMs data series which havedifferent grid size, the analysis of profile characters using Fourier transformation requires thatthe DEMs should have smaller grid size, and that profile line should be as longer as possible.4. Two-dimensional spectrum Analysis and the relationship between the expressionability of the terrain information for DEMs and the grid size1）Based on the analysis of two-dimensional spectrum of DEMs of the studied area, thetwo-dimensional spectrum could reflect the scale of the relief. However, it is difficult toobtain the corresponding relationship between the two-dimensional spectrum and spatialcharacters. Therefore, according to the statistic of directions of gullies, the result of analysisof one-dimensional spectrum is decomposed to the horizontal and vertical direction to achievethe two-dimensional frequency range of gullies with different grades. This spatial range is thebasic parameter to design the two-dimensional frequency low-pass filter.2） Using the two-dimensional frequency low-pass filters to remove the gulliesinformation step by step, three DEMs which do not contain the information of the rills,shallow furrows, gullies basically could be obtained respectively. The Comparison betweenthese three DEMs and the DEMs with varying grid sizes indicates the relationship betweenthe expression ability of the terrain information for DEMs and the grid size: the fluctuationincluding rills nearly could not be described on the DEMs whose grid size is larger than about2meters. When the grid size of DEMs is larger than about5meters, the shallow furrowscould be represented clearly. If the grid size of DEMs is larger than about10meters, thegullies information will nearly disappear. |
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