坡度算法比.doc

主要坡度计算模型
坡度计算模型： ，式中 、 分别表示x，y方向的偏导数，P为坡度。
图2-38
图2-38中g表示格网分辨率。Zi（i=1，2，…，9）分别表示中心点5 周围格网点的高程。 、 均是对中心点5而言。坡度的计算一般使用3*3窗口，主要的坡度计算模型见表2.8。
表2.8  坡度计算模型
算法

二阶差分
（z8 - z2)/（2 g）
（z6 - z4）/（2 g）
三阶不带权差分（Sharpnack 算法）
（z7 - z1 + z8 - z2 + z9 - z3）/（6 g）
（z3 - z1 + z6 - z4 + z9 - z7）/（6 g）
三阶反距离平方权差分(Horn 算法)
（z7 - z1 + 2 （z8 - z2） + z9 - z3）/（8 g）
（z3 - z1 + 2（z6 - z4） + z9 - z7）/（8 g）
三阶反距离权差分
（ z7 - z1 + 2（z8 - z2） + z9 - z3）/（（4 + 2√2）g）
(z3 - z1 + 2 (z6 - z4) + z9 - z7)/（（4 + 2√2）g）
Frame 差分
（z7 - z1 + z9 - z3）/（4 g）
（z3 - z1 + z9 - z7）/（4 g）
简单差分
（z5 - z2）/g
（z5 - z4）/g

②不同地形地貌坡度计算模型选择
采用简单差分算法和三阶反距离权差分计算坡度时，≤2°和>25°坡度面积相对其他算法偏高或偏低；采用Frame 差分、简单差分算法计算坡度时，2°～6°坡度面积较其他算法小；二阶差分、三阶反距离平方权差分、三阶不带权差分算法计算各耕地坡度分级面积比较接近。

在ArcGIS中，采用的是三阶反距离平方权差分算法(Horn 算法)
The rate of change (delta) of the surface in the horizontal (dz/dx) and vertical (dz/dy) directions from the center cell determines the slope. The basic algorithm used to calculate the slope is:
slope_radians = ATAN ( √ ( [dz/dx]2 + [dz/dy]2 ) )

Slope is commonly measured in degrees, which uses the algorithm:
slope_degrees = ATAN ( √ ( [dz/dx]2 + [dz/dy]2 ) ) * 57.29578

The slope algorithm can also be interpreted as:
slope_degrees = ATAN (rise_run) * 57.29578
where:
rise_run = √ ( [dz/dx]2 + [dz/dy]2 ]

The values of the center cell and its eight neighbors determine the horizontal and vertical deltas. The neighbors are identified as letters from 'a' to 'i', with 'e' representing the cell for which the aspect is being calculated.

The rate of change in the x direction for cell 'e' is calculated with the algorithm:
[dz/dx] = ((c + 2f + i) - (a + 2d + g) / (8 * x_cell_size)

The rate of change in the y direction for cell 'e' is calculated with the following algorithm:
[dz/dy] = ((g + 2h + i) - (a + 2b + c)) / (8 * y_cell_size)
References
Burrough, P. A. and McDonell, R.A., 1998. Principles of Geographical Information Systems (Oxford University Press, New York), p. 190.
A Slope calculation example
As an example, the slope value of the center cell of the moving window will be calculated.

The cell size is 5 units. The default slope measure of degrees will be used.

The rate of change in the x direction for the center cell 'e' is:
[dz/dx] = ((c + 2f + i) - (a + 2d + g)) / (8 * x_cell_size)
= ((50 + 60 + 10) - (50 + 60 + 8)) / (8 * 5)
= (120 - 118) / 40
= 0.05

The rate of change in the y direction for cell 'e' is:
[dz/dy] = ((g + 2h + i) - (a + 2b + c)) / (8 * y_cell_size)
= ((8 + 20 + 10) - (50 + 90 + 50)) / (8 * 5)
= (38 - 190 ) / 40
= -3.8

Taking the rate of change in the x and y direction, the slope for the center cell 'e' is calculated using:
rise_run = √ ( [dz/dx]2 + [dz/dy]2 )
= √ ( (0.05)2 + (-3.8)2 ]
= √ [ 0.0025 + 14.44 ]
= 3.80032
slope_degrees = ATAN (rise_run) * 57.29578
= ATAN (3.80032) * 57.29578
= 1.31349 * 57.29578
= 75.25762

The integer slope value for cell 'e' is 75 degrees.

Grid 重采样：Resample
Alters the proportions of a raster dataset by changing the cell size. The cell size will be changed, but the extent of the raster dataset will remain the same.

Illustration

地理运算方法的选取：
Specifies the resampling algorithm to be used when resampling the raster.
NEAREST—Nearest neighbor assignment. This is the default.
BILINEAR—Bilinear interpolation.
CUBIC—Cubic convolution.
MAJORITY—Majority resampling.
如果Grid数据不是连续性变化的，最好不要应用BILINEAR和CUBIC,它们主要用于连续性变化的数据，运用它们可以使数据变化更加平滑。如土地利用分级，或地形表示就不要运用它们进行重采样。