| Slope gradient and slope length are two of the most important terrain indexes whichinfluence soil erosion. These two indexes are normally extracted from DEMs with lowerresolution in the research of regional soil erosion. However, slope gradient tends to decreaseand slope length tends to increase as resolution becomes coarser. These make the calculatedslope gradient and slope length not accurate enough to describe the real relief of terrain. Thusthe accuracy of hydrology and soil erosion model is declined. With the comprehensiveapplication of wavelet analysis theory, digital image analysis and digital terrain analysis, thispaper firstly realizes the multi-scale representation of DEM by using the multi-resolutionanalysis method of wavelet. By systematically analyzing the relationship between the soilerosion terrain factor and resolution, it then deeply reveals that slope gradient decreases andthe slope length increases as the resolution of DEMs becomes coarser. Thirdly, the paperestablishes the slope gradient and slope length re-scaling mathematical model by using themethod of histogram matching. Next, taking Shannxi province as research area, we transformthe slope gradient and slope length extracted from the low-resolution DEMs. We also useChinese Soil Loess Equation （CSLE） to calculate the soil erosion volume, and validate thesuitability of the slope gradient and slope length re-scaling model in assessment of regionalsoil erosion. The main conclusions are as follows.1. Based on the multi-resolution analysis of wavelet, the multi-scale representation ofsoil erosion terrain is realized.A database of DEM is established, which has a gradually-changing resolution and aunified position control base, and effective ability in representing the overall topographiccharacteristics and landform macro structure. The database is generated by using the multi-resolution analysis method of wavelet, and the biorthogonal wavelet function Bior4.4was selected as the wavelet basis function. The Radical Law Selection Principles, traditionallyused in cartographic generalization, was used to set different scale parameters during thethreshold processing on the wavelet high frequency coefficients. Meanwhile, the research areais a typical small-scale watershed, i.e., XianNanGou mountains and gully district, and theoriginal DEM data is the hydrological correct DEMs （hc-DEMs） of high resolution （2.5m）.2. This paper deeply reveals that slope gradient decreases and the slope length increasesas the resolution of DEMs becomes coarser.（1） Taking the Hc-DEM data with the resolution of10m,25m and50m in XianNanGouwatershed as reference data, the paper evaluates the quality of the generated DEMs, whichhave different scalar parameters and obtained by using wavelet transform method. Then, therelationship between the scale parameter and resolution of DEMs is established. Hence, thegeneration of DEMs with arbitrary coarser resolutions is realized.（2） Based on the multi-resolution database obtained by using wavelet transform, thevariation pattern of terrain along with the changing of resolution is analyzed. With thereduction of DEM resolution, the gully elevation is rising, while the Liang and Mao topelevation is decreasing, and the small-scale gully, Liang and Mao top are graduallydisappeared. Average slope shows a linearly decreasing trend with the reduction of DEMresolution, and slope frequency and cumulative frequency curves are moving towards gentleslope. In general, the overall slope gradient is declined, and the declining mainly happens insteep slope and with a changing order from main channel to small gully. Average slope lengthhas a linearly increasing trend with the reduction of DEM resolution, and slope lengthcumulative frequency curve is moving towards larger value. In general, the overall slopelength is enlarged, and the enlarging mainly happens in the middle and bottom of slopes.3. This work establishes slope gradient and slope length re-scaling transformationmodels based on histogram matching principle.（1） After scale transformation, in the area of complex topography, the value of slopegradient and slope length are more close to those derived from high-resolution DEMs: theslope become steeper and the slope length becomes shorter. Compared to the area of complextopography, the effects of slope scale transformation is not crucial at the flat topography.Therefore, it was not necessary to do the slope scale transformation in the regions with flat topography. In addition, after scale transformation, the spatial distribution of outlines ofmountains and channels is corrected and the spatial pattern is kept without distortion. Scaletransformation can improve terrain interpretation ability.（2） In drawing the maps of slope gradient and slope length with small-scale scalar, toomuch detail is kept and little overall characteristics is obviously shown when50m resolutionis chosen. This case gives a poor mapping quality. While, our experimental results show theresolution of250m can provide better representation of terrain macro-structure. However, itsreduction of slope gradient and the expansion of slope length seriously impacted theapplication in soil erosion assessment. So it was necessary to do scale transformation ofterrain indexes. The slope gradient and slope length after transform generally meet thereference standard. That is, the scale transformation results not only satisfy the requirement ofsmall-scale terrain indexes mapping but also improve calculated accuracy of soil erosionassessment.4. The effectiveness of the slope gradient and slope length scale transformation model isassessed taking the application in Shaanxi province as an example.Using CSLE in soil erosion intensities assessment, the soil erosion intensity without andwith the scale transformation are calculated and compared. The result showed that, in the flatarea, the soil erosion intensity is declined and the force of slope length enlarging is more thanthat of slope gradient. In the steep area of the north part of the loess gully of Northern Shaanxiprovince, the erosion intensity has a little increase, and the forces of slope length and gradientis equal. In the steep area of the QinBa mountain area, the erosion intensity module decreasesfrom4544.92t×km-2×a-1to3796.48×km-2×a-1, and the forces of slope length enlarging is morethan that of the slope gradient declining. In the steep area of the south part of the loess gullyof Northern Shaanxi province, the erosion intensity module decreases from5118.15t×km-2×a-1to6590.29t×km-2×a-1, and the forces of slope length enlarging is less than that of the slopegradient declining. These means the main impacts of scale transform depend on the mainforce type （the force of slope length enlarging or that of slope gradient declining）. Therefore,it is crucial to do the slope gradient and slope length scale transformation in the assessment ofregional soil erosion in future. |
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