Slope gradient and slope length are two of the most important terrain indexes which
influence soil erosion. These two indexes are normally extracted from DEMs with lower
resolution in the research of regional soil erosion. However, slope gradient tends to decrease
and slope length tends to increase as resolution becomes coarser. These make the calculated
slope gradient and slope length not accurate enough to describe the real relief of terrain. Thus
the accuracy of hydrology and soil erosion model is declined. With the comprehensive
application of wavelet analysis theory, digital image analysis and digital terrain analysis, this
paper firstly realizes the multi-scale representation of DEM by using the multi-resolution
analysis method of wavelet. By systematically analyzing the relationship between the soil
erosion terrain factor and resolution, it then deeply reveals that slope gradient decreases and
the slope length increases as the resolution of DEMs becomes coarser. Thirdly, the paper
establishes the slope gradient and slope length re-scaling mathematical model by using the
method of histogram matching. Next, taking Shannxi province as research area, we transform
the slope gradient and slope length extracted from the low-resolution DEMs. We also use
Chinese Soil Loess Equation (CSLE) to calculate the soil erosion volume, and validate the
suitability of the slope gradient and slope length re-scaling model in assessment of regional
soil erosion. The main conclusions are as follows.
1. Based on the multi-resolution analysis of wavelet, the multi-scale representation of
soil erosion terrain is realized.
A database of DEM is established, which has a gradually-changing resolution and a
unified position control base, and effective ability in representing the overall topographic
characteristics and landform macro structure. The database is generated by using the multi-resolution analysis method of wavelet, and the biorthogonal wavelet function Bior4.4
was selected as the wavelet basis function. The Radical Law Selection Principles, traditionally
used in cartographic generalization, was used to set different scale parameters during the
threshold processing on the wavelet high frequency coefficients. Meanwhile, the research area
is a typical small-scale watershed, i.e., XianNanGou mountains and gully district, and the
original 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 increases
as the resolution of DEMs becomes coarser.
(1) Taking the Hc-DEM data with the resolution of 10m, 25m and 50m in XianNanGou
watershed as reference data, the paper evaluates the quality of the generated DEMs, which
have different scalar parameters and obtained by using wavelet transform method. Then, the
relationship between the scale parameter and resolution of DEMs is established. Hence, the
generation of DEMs with arbitrary coarser resolutions is realized.
(2) Based on the multi-resolution database obtained by using wavelet transform, the
variation pattern of terrain along with the changing of resolution is analyzed. With the
reduction of DEM resolution, the gully elevation is rising, while the Liang and Mao top
elevation is decreasing, and the small-scale gully, Liang and Mao top are gradually
disappeared. Average slope shows a linearly decreasing trend with the reduction of DEM
resolution, and slope frequency and cumulative frequency curves are moving towards gentle
slope. In general, the overall slope gradient is declined, and the declining mainly happens in
steep slope and with a changing order from main channel to small gully. Average slope length
has a linearly increasing trend with the reduction of DEM resolution, and slope length
cumulative frequency curve is moving towards larger value. In general, the overall slope
length 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 transformation
models based on histogram matching principle.
(1) After scale transformation, in the area of complex topography, the value of slope
gradient and slope length are more close to those derived from high-resolution DEMs: the
slope become steeper and the slope length becomes shorter. Compared to the area of complex
topography, 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 of
mountains and channels is corrected and the spatial pattern is kept without distortion. Scale
transformation can improve terrain interpretation ability.
(2) In drawing the maps of slope gradient and slope length with small-scale scalar, too
much detail is kept and little overall characteristics is obviously shown when 50m resolution
is chosen. This case gives a poor mapping quality. While, our experimental results show the
resolution of 250m can provide better representation of terrain macro-structure. However, its
reduction of slope gradient and the expansion of slope length seriously impacted the
application in soil erosion assessment. So it was necessary to do scale transformation of
terrain indexes. The slope gradient and slope length after transform generally meet the
reference standard. That is, the scale transformation results not only satisfy the requirement of
small-scale terrain indexes mapping but also improve calculated accuracy of soil erosion
4. The effectiveness of the slope gradient and slope length scale transformation model is
assessed taking the application in Shaanxi province as an example.
Using CSLE in soil erosion intensities assessment, the soil erosion intensity without and
with the scale transformation are calculated and compared. The result showed that, in the flat
area, the soil erosion intensity is declined and the force of slope length enlarging is more than
that of slope gradient. In the steep area of the north part of the loess gully of Northern Shaanxi
province, the erosion intensity has a little increase, and the forces of slope length and gradient
is equal. In the steep area of the QinBa mountain area, the erosion intensity module decreases
from 4544.92 t×km -2
-1 to 3796.48×km -2
-1 , and the forces of slope length enlarging is more
than that of the slope gradient declining. In the steep area of the south part of the loess gully
of Northern Shaanxi province, the erosion intensity module decreases from 5118.15 t×km -2
to 6590.29 t×km -2
-1 , and the forces of slope length enlarging is less than that of the slope
gradient declining. These means the main impacts of scale transform depend on the main
force 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 of
regional soil erosion in future.
Keywords: DEM multi-scale representation, scale effect of slope gradient and slope length,
scale transformation of slope gradient and slope length, soil erosion