使用 python 将高程 (XYZ) 数据映射到 slope/gradient 地图
Elevation (XYZ) data to slope/gradient map using python
我有一个包含东距 (x)、北距 (y) 和高程数据 (z) 的文本文件，如下所示：
x y z
241736.69 3841916.11 132.05
241736.69 3841877.89 138.76
241736.69 3841839.67 142.89
241736.69 3841801.45 148.24
241736.69 3841763.23 157.92
241736.69 3841725.02 165.01
241736.69 3841686.80 171.86
241736.69 3841648.58 178.80
241736.69 3841610.36 185.26
241736.69 3841572.14 189.06
241736.69 3841533.92 191.28
241736.69 3841495.71 193.27
241736.69 3841457.49 193.15
241736.69 3841419.27 194.85
241736.69 3841381.05 192.31
241736.69 3841342.83 188.73
241736.69 3841304.61 183.68
241736.69 3841266.39 176.97
241736.69 3841228.18 160.83
241736.69 3841189.96 145.69
241736.69 3841151.74 129.09
241736.69 3841113.52 120.03
241736.69 3841075.30 111.84
241736.69 3841037.08 104.82
241736.69 3840998.86 101.63
241736.69 3840960.65 97.66
241736.69 3840922.43 93.38
241736.69 3840884.21 88.84
...
我可以使用 plt.contour 和 plt.contourf 从上述数据中轻松获得海拔图，如下所示：
但是，我正在尝试获取我拥有的数据的坡度图，如下所示：
我尝试做的是使用 GDAL 将我的 XYZ 数据转换为 DEM，如 here, and loading the DEM with richdem, as explained here 所述，但我得到了错误的斜率值。
转换为 .tif 得到的结果：
这是我用 richdem:
试过的代码
import richdem as rd
dem_path = 'convertedXYZ.tif'
dem = rd.LoadGDAL(dem_path, no_data=-9999)
slope = rd.TerrainAttribute(dem, attrib='slope_riserun')
rd.rdShow(slope, axes=True, cmap='gist_yarg', figsize=(16, 9))
我得到的情节：
颜色条上的值太高而不正确，必须反转绘图才能与上面的绘图匹配（现在不是我的主要问题）。
我不是将 python 用于 GIS 目的的专家（我主要使用 python 进行数据分析），我希望这没有我想象的那么复杂。
假设您的数据位于 n x 3 Numpy 数组中，首先将海拔列重新解释为矩阵（表示均匀网格）：
m=data[:,2].reshape(ny,nx)
然后执行几个切片和减法以获得单元中心的导数：
dx=m[:,1:]-m[:,:-1]
dy=m[1:,:]-m[:-1,:]
mag=numpy.hypot(dx[1:,:]+dx[:-1,:],
dy[:,1:]+dy[:,:-1])
mag*=abs(data[1][1]-data[1][0])/2
系数校正单位（否则应为每 单元格 米，而不是每米）并将总和转换为平均值。 （如果每个维度中的间距不同，您可以将参数分别缩放为 hypot。）请注意，结果数组在每个维度中都比输入小一个；如果大小需要相同，则可以使用其他更复杂的差分方案。 numpy.gradient 实现了其中的一些，允许一个简单的
mag=numpy.hypot(*numpy.gradient(m,abs(data[1][1]-data[1][0])))
e我能够编写一个正确完成工作的函数，但首先我需要感谢这个 为我编写自己的移动 windows 函数节省了一些时间（完美运行!):
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from tqdm import trange
def window3x3(arr, shape=(3, 3)):
r_win = np.floor(shape[0] / 2).astype(int)
c_win = np.floor(shape[1] / 2).astype(int)
x, y = arr.shape
for i in range(x):
xmin = max(0, i - r_win)
xmax = min(x, i + r_win + 1)
for j in range(y):
ymin = max(0, j - c_win)
ymax = min(y, j + c_win + 1)
yield arr[xmin:xmax, ymin:ymax]
def gradient(XYZ_file, min=0, max=15, figsize=(15, 10), **kwargs):
"""
:param XYZ_file: XYZ file in the following format: x,y,z (inlcuding headers)
:param min: color bar minimum range.
:param max: color bar maximum range.
:param figsize: figure size.
:param kwargs:
plot: to plot a gradient map. Default is True.
:return: returns an array with the shape of the grid with the computed slopes
The algorithm calculates the gradient using a first-order forward or backward difference on the corner points, first
order central differences at the boarder points, and a 3x3 moving window for every cell with 8 surrounding cells (in
the middle of the grid) using a third-order finite difference weighted by reciprocal of squared distance
Assumed 3x3 window:
-------------------------
| a | b | c |
-------------------------
| d | e | f |
-------------------------
| g | h | i |
-------------------------
"""
kwargs.setdefault('plot', True)
grid = XYZ_file.to_numpy()
nx = XYZ_file['x'].unique().size
ny = XYZ_file['y'].unique().size
xs = grid[:, 0].reshape(ny, nx, order='F')
ys = grid[:, 1].reshape(ny, nx, order='F')
zs = grid[:, 2].reshape(ny, nx, order='F')
dx = abs((xs[:, 1:] - xs[:, :-1]).mean())
dy = abs((ys[1:, :] - ys[:-1, :]).mean())
gen = window3x3(zs)
windows_3x3 = np.asarray(list(gen))
windows_3x3 = windows_3x3.reshape(ny, nx)
dzdx = np.empty((ny, nx))
dzdy = np.empty((ny, nx))
loc_string = np.empty((ny, nx), dtype="S25")
for ax_y in trange(ny):
for ax_x in range(nx):
# corner points
if ax_x == 0 and ax_y == 0: # top left corner
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][0][1] - windows_3x3[ax_y, ax_x][0][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][0] - windows_3x3[ax_y, ax_x][0][0]) / dy
loc_string[ax_y, ax_x] = 'top left corner'
elif ax_x == nx - 1 and ax_y == 0: # top right corner
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][0][1] - windows_3x3[ax_y, ax_x][0][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][0][1]) / dy
loc_string[ax_y, ax_x] = 'top right corner'
elif ax_x == 0 and ax_y == ny - 1: # bottom left corner
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][1][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][0] - windows_3x3[ax_y, ax_x][0][0]) / dy
loc_string[ax_y, ax_x] = 'bottom left corner'
elif ax_x == nx - 1 and ax_y == ny - 1: # bottom right corner
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][1][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][0][1]) / dy
loc_string[ax_y, ax_x] = 'bottom right corner'
# top boarder
elif (ax_y == 0) and (ax_x != 0 and ax_x != nx - 1):
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][0][-1] - windows_3x3[ax_y, ax_x][0][0]) / (2 * dx)
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][0][1]) / dy
loc_string[ax_y, ax_x] = 'top boarder'
# bottom boarder
elif ax_y == ny - 1 and (ax_x != 0 and ax_x != nx - 1):
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][-1] - windows_3x3[ax_y, ax_x][1][0]) / (2 * dx)
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][0][1]) / dy
loc_string[ax_y, ax_x] = 'bottom boarder'
# left boarder
elif ax_x == 0 and (ax_y != 0 and ax_y != ny - 1):
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][1][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][-1][0] - windows_3x3[ax_y, ax_x][0][0]) / (2 * dy)
loc_string[ax_y, ax_x] = 'left boarder'
# right boarder
elif ax_x == nx - 1 and (ax_y != 0 and ax_y != ny - 1):
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][1][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][-1][-1] - windows_3x3[ax_y, ax_x][0][-1]) / (2 * dy)
loc_string[ax_y, ax_x] = 'right boarder'
# middle grid
else:
a = windows_3x3[ax_y, ax_x][0][0]
b = windows_3x3[ax_y, ax_x][0][1]
c = windows_3x3[ax_y, ax_x][0][-1]
d = windows_3x3[ax_y, ax_x][1][0]
f = windows_3x3[ax_y, ax_x][1][-1]
g = windows_3x3[ax_y, ax_x][-1][0]
h = windows_3x3[ax_y, ax_x][-1][1]
i = windows_3x3[ax_y, ax_x][-1][-1]
dzdx[ax_y, ax_x] = ((c + 2 * f + i) - (a + 2 * d + g)) / (8 * dx)
dzdy[ax_y, ax_x] = ((g + 2 * h + i) - (a + 2 * b + c)) / (8 * dy)
loc_string[ax_y, ax_x] = 'middle grid'
hpot = np.hypot(abs(dzdy), abs(dzdx))
slopes_angle = np.degrees(np.arctan(hpot))
if kwargs['plot']:
slopes_angle[(slopes_angle < min) | (slopes_angle > max)]
plt.figure(figsize=figsize)
plt.pcolormesh(xs, ys, slopes_angle, cmap=plt.cm.gist_yarg, vmax=max, vmin=min)
plt.colorbar()
plt.tight_layout()
plt.show()
return slopes_angle
if __name__ == '__main__':
XYZ = pd.read_csv('xyz_file')
slopes = gradient(XYZ)
最后的情节：
我有一个包含东距 (x)、北距 (y) 和高程数据 (z) 的文本文件，如下所示：
x y z
241736.69 3841916.11 132.05
241736.69 3841877.89 138.76
241736.69 3841839.67 142.89
241736.69 3841801.45 148.24
241736.69 3841763.23 157.92
241736.69 3841725.02 165.01
241736.69 3841686.80 171.86
241736.69 3841648.58 178.80
241736.69 3841610.36 185.26
241736.69 3841572.14 189.06
241736.69 3841533.92 191.28
241736.69 3841495.71 193.27
241736.69 3841457.49 193.15
241736.69 3841419.27 194.85
241736.69 3841381.05 192.31
241736.69 3841342.83 188.73
241736.69 3841304.61 183.68
241736.69 3841266.39 176.97
241736.69 3841228.18 160.83
241736.69 3841189.96 145.69
241736.69 3841151.74 129.09
241736.69 3841113.52 120.03
241736.69 3841075.30 111.84
241736.69 3841037.08 104.82
241736.69 3840998.86 101.63
241736.69 3840960.65 97.66
241736.69 3840922.43 93.38
241736.69 3840884.21 88.84
...
我可以使用 plt.contour 和 plt.contourf 从上述数据中轻松获得海拔图，如下所示：
但是，我正在尝试获取我拥有的数据的坡度图，如下所示：
我尝试做的是使用 GDAL 将我的 XYZ 数据转换为 DEM，如 here, and loading the DEM with richdem, as explained here 所述，但我得到了错误的斜率值。
转换为 .tif 得到的结果：
这是我用 richdem:
import richdem as rd
dem_path = 'convertedXYZ.tif'
dem = rd.LoadGDAL(dem_path, no_data=-9999)
slope = rd.TerrainAttribute(dem, attrib='slope_riserun')
rd.rdShow(slope, axes=True, cmap='gist_yarg', figsize=(16, 9))
我得到的情节：
颜色条上的值太高而不正确，必须反转绘图才能与上面的绘图匹配（现在不是我的主要问题）。
我不是将 python 用于 GIS 目的的专家（我主要使用 python 进行数据分析），我希望这没有我想象的那么复杂。
假设您的数据位于 n x 3 Numpy 数组中，首先将海拔列重新解释为矩阵（表示均匀网格）：
m=data[:,2].reshape(ny,nx)
然后执行几个切片和减法以获得单元中心的导数：
dx=m[:,1:]-m[:,:-1]
dy=m[1:,:]-m[:-1,:]
mag=numpy.hypot(dx[1:,:]+dx[:-1,:],
dy[:,1:]+dy[:,:-1])
mag*=abs(data[1][1]-data[1][0])/2
系数校正单位（否则应为每 单元格 米，而不是每米）并将总和转换为平均值。 （如果每个维度中的间距不同，您可以将参数分别缩放为 hypot。）请注意，结果数组在每个维度中都比输入小一个；如果大小需要相同，则可以使用其他更复杂的差分方案。 numpy.gradient 实现了其中的一些，允许一个简单的
mag=numpy.hypot(*numpy.gradient(m,abs(data[1][1]-data[1][0])))
e我能够编写一个正确完成工作的函数，但首先我需要感谢这个
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from tqdm import trange
def window3x3(arr, shape=(3, 3)):
r_win = np.floor(shape[0] / 2).astype(int)
c_win = np.floor(shape[1] / 2).astype(int)
x, y = arr.shape
for i in range(x):
xmin = max(0, i - r_win)
xmax = min(x, i + r_win + 1)
for j in range(y):
ymin = max(0, j - c_win)
ymax = min(y, j + c_win + 1)
yield arr[xmin:xmax, ymin:ymax]
def gradient(XYZ_file, min=0, max=15, figsize=(15, 10), **kwargs):
"""
:param XYZ_file: XYZ file in the following format: x,y,z (inlcuding headers)
:param min: color bar minimum range.
:param max: color bar maximum range.
:param figsize: figure size.
:param kwargs:
plot: to plot a gradient map. Default is True.
:return: returns an array with the shape of the grid with the computed slopes
The algorithm calculates the gradient using a first-order forward or backward difference on the corner points, first
order central differences at the boarder points, and a 3x3 moving window for every cell with 8 surrounding cells (in
the middle of the grid) using a third-order finite difference weighted by reciprocal of squared distance
Assumed 3x3 window:
-------------------------
| a | b | c |
-------------------------
| d | e | f |
-------------------------
| g | h | i |
-------------------------
"""
kwargs.setdefault('plot', True)
grid = XYZ_file.to_numpy()
nx = XYZ_file['x'].unique().size
ny = XYZ_file['y'].unique().size
xs = grid[:, 0].reshape(ny, nx, order='F')
ys = grid[:, 1].reshape(ny, nx, order='F')
zs = grid[:, 2].reshape(ny, nx, order='F')
dx = abs((xs[:, 1:] - xs[:, :-1]).mean())
dy = abs((ys[1:, :] - ys[:-1, :]).mean())
gen = window3x3(zs)
windows_3x3 = np.asarray(list(gen))
windows_3x3 = windows_3x3.reshape(ny, nx)
dzdx = np.empty((ny, nx))
dzdy = np.empty((ny, nx))
loc_string = np.empty((ny, nx), dtype="S25")
for ax_y in trange(ny):
for ax_x in range(nx):
# corner points
if ax_x == 0 and ax_y == 0: # top left corner
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][0][1] - windows_3x3[ax_y, ax_x][0][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][0] - windows_3x3[ax_y, ax_x][0][0]) / dy
loc_string[ax_y, ax_x] = 'top left corner'
elif ax_x == nx - 1 and ax_y == 0: # top right corner
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][0][1] - windows_3x3[ax_y, ax_x][0][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][0][1]) / dy
loc_string[ax_y, ax_x] = 'top right corner'
elif ax_x == 0 and ax_y == ny - 1: # bottom left corner
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][1][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][0] - windows_3x3[ax_y, ax_x][0][0]) / dy
loc_string[ax_y, ax_x] = 'bottom left corner'
elif ax_x == nx - 1 and ax_y == ny - 1: # bottom right corner
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][1][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][0][1]) / dy
loc_string[ax_y, ax_x] = 'bottom right corner'
# top boarder
elif (ax_y == 0) and (ax_x != 0 and ax_x != nx - 1):
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][0][-1] - windows_3x3[ax_y, ax_x][0][0]) / (2 * dx)
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][0][1]) / dy
loc_string[ax_y, ax_x] = 'top boarder'
# bottom boarder
elif ax_y == ny - 1 and (ax_x != 0 and ax_x != nx - 1):
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][-1] - windows_3x3[ax_y, ax_x][1][0]) / (2 * dx)
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][0][1]) / dy
loc_string[ax_y, ax_x] = 'bottom boarder'
# left boarder
elif ax_x == 0 and (ax_y != 0 and ax_y != ny - 1):
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][1][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][-1][0] - windows_3x3[ax_y, ax_x][0][0]) / (2 * dy)
loc_string[ax_y, ax_x] = 'left boarder'
# right boarder
elif ax_x == nx - 1 and (ax_y != 0 and ax_y != ny - 1):
dzdx[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][1][1] - windows_3x3[ax_y, ax_x][1][0]) / dx
dzdy[ax_y, ax_x] = (windows_3x3[ax_y, ax_x][-1][-1] - windows_3x3[ax_y, ax_x][0][-1]) / (2 * dy)
loc_string[ax_y, ax_x] = 'right boarder'
# middle grid
else:
a = windows_3x3[ax_y, ax_x][0][0]
b = windows_3x3[ax_y, ax_x][0][1]
c = windows_3x3[ax_y, ax_x][0][-1]
d = windows_3x3[ax_y, ax_x][1][0]
f = windows_3x3[ax_y, ax_x][1][-1]
g = windows_3x3[ax_y, ax_x][-1][0]
h = windows_3x3[ax_y, ax_x][-1][1]
i = windows_3x3[ax_y, ax_x][-1][-1]
dzdx[ax_y, ax_x] = ((c + 2 * f + i) - (a + 2 * d + g)) / (8 * dx)
dzdy[ax_y, ax_x] = ((g + 2 * h + i) - (a + 2 * b + c)) / (8 * dy)
loc_string[ax_y, ax_x] = 'middle grid'
hpot = np.hypot(abs(dzdy), abs(dzdx))
slopes_angle = np.degrees(np.arctan(hpot))
if kwargs['plot']:
slopes_angle[(slopes_angle < min) | (slopes_angle > max)]
plt.figure(figsize=figsize)
plt.pcolormesh(xs, ys, slopes_angle, cmap=plt.cm.gist_yarg, vmax=max, vmin=min)
plt.colorbar()
plt.tight_layout()
plt.show()
return slopes_angle
if __name__ == '__main__':
XYZ = pd.read_csv('xyz_file')
slopes = gradient(XYZ)
最后的情节：