xarray select 具有多維坐標的最近緯度/經度

Question

我有一個帶有不規則間隔緯度和經度坐標的 xarray 數據集。 我的目標是在最接近某個緯度/經度的點處找到變量的值。

由於x和y維度不是 lat/lon 值，因此在這種情況下似乎不能單獨使用ds.sel()方法。 是否有以 xarray 為中心的方法通過參考多維緯度/經度維度來定位最接近所需緯度/經度的點？ 例如，我想提取最接近lat=21.2和lon=-122.68的 SPEED 值。

下面是一個示例數據集...

lats = np.array([[21.138  , 21.14499, 21.15197, 21.15894, 21.16591],
                 [21.16287, 21.16986, 21.17684, 21.18382, 21.19079],
                 [21.18775, 21.19474, 21.20172, 21.2087 , 21.21568],
                 [21.21262, 21.21962, 21.22661, 21.23359, 21.24056],
                 [21.2375 , 21.2445 , 21.25149, 21.25848, 21.26545]])  

lons = np.array([[-122.72   , -122.69333, -122.66666, -122.63999, -122.61331],
                 [-122.7275 , -122.70082, -122.67415, -122.64746, -122.62078],
                 [-122.735  , -122.70832, -122.68163, -122.65494, -122.62825],
                 [-122.7425 , -122.71582, -122.68912, -122.66243, -122.63573],
                 [-122.75001, -122.72332, -122.69662, -122.66992, -122.64321]])

speed = np.array([[10.934007, 10.941321, 10.991583, 11.063932, 11.159435],
                  [10.98778 , 10.975482, 10.990983, 11.042522, 11.131154],
                  [11.013505, 11.001573, 10.997754, 11.03566 , 11.123781],
                  [11.011163, 11.000227, 11.010223, 11.049   , 11.1449  ],
                  [11.015698, 11.026604, 11.030653, 11.076904, 11.201464]])

ds = xarray.Dataset({'SPEED':(('x', 'y'),speed)},
                    coords = {'latitude': (('x', 'y'), lats),
                              'longitude': (('x', 'y'), lons)},
                    attrs={'variable':'Wind Speed'})

ds的值：

<xarray.Dataset>
Dimensions:    (x: 5, y: 5)
Coordinates:
    latitude   (x, y) float64 21.14 21.14 21.15 21.16 ... 21.25 21.26 21.27
    longitude  (x, y) float64 -122.7 -122.7 -122.7 ... -122.7 -122.7 -122.6
Dimensions without coordinates: x, y
Data variables:
SPEED      (x, y) float64 10.93 10.94 10.99 11.06 ... 11.03 11.03 11.08 11.2
Attributes:
    variable:  Wind Speed

同樣， ds.sel(latitude=21.2, longitude=-122.68)不起作用，因為緯度和經度不是數據集維度。

Answer 1

在這里聚會有點晚了，但我已經多次回到這個問題。 如果您的 x 和 y 坐標位於地理空間坐標系中，則可以使用 cartopy 將 lat/lon 點轉換為該坐標系。 如果您查看 netcdf 中的元數據，構建 cartopy 投影通常很簡單。

import cartopy.crs as ccrs

# Example - your x and y coordinates are in a Lambert Conformal projection
data_crs = ccrs.LambertConformal(central_longitude=-100)

# Transform the point - src_crs is always Plate Carree for lat/lon grid
x, y = data_crs.transform_point(-122.68, 21.2, src_crs=ccrs.PlateCarree())

# Now you can select data
ds.sel(x=x, y=y)

Answer 2

我想出了一個不純粹使用 xarray 的方法。 我首先手動找到最近鄰居的索引，然后使用該索引訪問 xarray 維度。

# A 2D plot of the SPEED variable, assigning the coordinate values,
# and plot the verticies of each point
ds.SPEED.plot(x='longitude', y='latitude')
plt.scatter(ds.longitude, ds.latitude)

# I want to find the speed at a certain lat/lon point.
lat = 21.22
lon = -122.68

# First, find the index of the grid point nearest a specific lat/lon.   
abslat = np.abs(ds.latitude-lat)
abslon = np.abs(ds.longitude-lon)
c = np.maximum(abslon, abslat)

([xloc], [yloc]) = np.where(c == np.min(c))

# Now I can use that index location to get the values at the x/y diminsion
point_ds = ds.sel(x=xloc, y=yloc)

# Plot requested lat/lon point blue
plt.scatter(lon, lat, color='b')
plt.text(lon, lat, 'requested')

# Plot nearest point in the array red
plt.scatter(point_ds.longitude, point_ds.latitude, color='r')
plt.text(point_ds.longitude, point_ds.latitude, 'nearest')

plt.title('speed at nearest point: %s' % point_ds.SPEED.data)

---

另一個潛在的解決方案（同樣，不是 xarray）是使用 scipy 的 KDTree，或者更好的是 scikit-learn 的 BallTree（ https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.BallTree.ZFC35FDC70D5FC69D269883A822CA ） https://github.com/xarray-contrib/xoak 。

Answer 3

我認為您需要以不同的方式創建數據集，以確保latitude和longitude具有可解釋的維度（請參閱xarray 的基本數據結構一文）。

例如：

import numpy as np
import pandas as pd
import xarray
import matplotlib.pyplot as plt
from scipy.interpolate import griddata

lats = np.array([21.138, 21.14499, 21.15197, 21.15894, 21.16591,
                 21.16287, 21.16986, 21.17684, 21.18382, 21.19079,
                 21.18775, 21.19474, 21.20172, 21.2087, 21.21568,
                 21.21262, 21.21962, 21.22661, 21.23359, 21.24056,
                 21.2375, 21.2445, 21.25149, 21.25848, 21.26545])

lons = np.array([-122.72, -122.69333, -122.66666, -122.63999, -122.61331,
                 -122.7275, -122.70082, -122.67415, -122.64746, -122.62078,
                 -122.735, -122.70832, -122.68163, -122.65494, -122.62825,
                 -122.7425, -122.71582, -122.68912, -122.66243, -122.63573,
                 -122.75001, -122.72332, -122.69662, -122.66992, -122.64321])

speed = np.array([10.934007, 10.941321, 10.991583, 11.063932, 11.159435,
                  10.98778, 10.975482, 10.990983, 11.042522, 11.131154,
                  11.013505, 11.001573, 10.997754, 11.03566, 11.123781,
                  11.011163, 11.000227, 11.010223, 11.049, 11.1449,
                  11.015698, 11.026604, 11.030653, 11.076904, 11.201464])

fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(12, 5))

idx = pd.MultiIndex.from_arrays(arrays=[lons, lats], names=["lon", "lat"])
s = pd.Series(data=speed, index=idx)
da = xarray.DataArray.from_series(s)
print(da)
da.plot(ax=ax1)

print('-'*80)
print(da.sel(lat=21.2, lon=-122.68, method='nearest'))

# define grid.
num_points = 100
lats_i = np.linspace(np.min(lats), np.max(lats), num_points)
lons_i = np.linspace(np.min(lons), np.max(lons), num_points)

# grid the data.
speed_i = griddata((lats, lons), speed,
                   (lats_i[None, :], lons_i[:, None]), method='cubic')

# contour the gridded data
ax2.contour(lats_i, lons_i, speed_i, 15, linewidths=0.5, colors='k')
contour = ax2.contourf(lats_i, lons_i, speed_i, 15, cmap=plt.cm.jet)
plt.colorbar(contour, ax=ax2)

# plot data points.
for i, (lat, lon) in enumerate(zip(lats, lons)):
    label = f'{speed[i]:0.2f}'
    ax2.annotate(label, (lat, lon))

ax2.scatter(lats, lons, marker='o', c='b', s=5)

ax2.set_title(f'griddata test {num_points} points')

plt.subplots_adjust(wspace=0.2)
plt.show()

結果

<xarray.DataArray (lat: 25, lon: 25)>
array([[      nan,       nan,       nan,       nan,       nan, 10.934007,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan, 10.941321,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan, 10.991583,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan, 11.063932,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan, 10.98778 ,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
        11.159435],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan, 10.975482,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan, 10.990983,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
        11.042522,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan, 11.013505,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan, 11.131154,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan, 11.001573,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
        10.997754,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan, 11.03566 ,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan, 11.011163,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan, 11.123781,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
        11.000227,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan, 11.010223,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan, 11.049   ,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [11.015698,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan, 11.1449  ,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan, 11.026604,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan, 11.030653,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan, 11.076904,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan, 11.201464,       nan,       nan,       nan,       nan,
              nan]])
Coordinates:
  * lat      (lat) float64 21.14 21.14 21.15 21.16 ... 21.24 21.25 21.26 21.27
  * lon      (lon) float64 -122.8 -122.7 -122.7 -122.7 ... -122.6 -122.6 -122.6
--------------------------------------------------------------------------------
<xarray.DataArray ()>
array(10.997754)
Coordinates:
    lat      float64 21.2
    lon      float64 -122.7

和一個 plot 包括網格只是為了它的樂趣

Answer 4

我喜歡@blaylockbk 給出的答案，但我無法理解計算到數據點的最短距離的方式。 下面我提供了一個替代方案，它只是利用畢達哥拉斯加上一種網格數據集ds的方法。 為了不將數據集中的 (x, y) 與 x, y 大地坐標混淆，我將它們重命名為 (i, j)。

import numpy as np
import xarray
import matplotlib.pyplot as plt
from scipy.interpolate import griddata

lats = np.array([[21.138, 21.14499, 21.15197, 21.15894, 21.16591],
                 [21.16287, 21.16986, 21.17684, 21.18382, 21.19079],
                 [21.18775, 21.19474, 21.20172, 21.2087, 21.21568],
                 [21.21262, 21.21962, 21.22661, 21.23359, 21.24056],
                 [21.2375, 21.2445, 21.25149, 21.25848, 21.26545]])

lons = np.array([[-122.72, -122.69333, -122.66666, -122.63999, -122.61331],
                 [-122.7275, -122.70082, -122.67415, -122.64746, -122.62078],
                 [-122.735, -122.70832, -122.68163, -122.65494, -122.62825],
                 [-122.7425, -122.71582, -122.68912, -122.66243, -122.63573],
                 [-122.75001, -122.72332, -122.69662, -122.66992, -122.64321]])

speed = np.array([[10.934007, 10.941321, 10.991583, 11.063932, 11.159435],
                  [10.98778, 10.975482, 10.990983, 11.042522, 11.131154],
                  [11.013505, 11.001573, 10.997754, 11.03566, 11.123781],
                  [11.011163, 11.000227, 11.010223, 11.049, 11.1449],
                  [11.015698, 11.026604, 11.030653, 11.076904, 11.201464]])

ds = xarray.Dataset({'SPEED': (('i', 'j'), speed)},
                    coords={'latitude': (('i', 'j'), lats),
                            'longitude': (('i', 'j'), lons)},
                    attrs={'variable': 'Wind Speed'})

lat_min = float(np.min(ds.latitude))
lat_max = float(np.max(ds.latitude))
lon_min = float(np.min(ds.longitude))
lon_max = float(np.max(ds.longitude))
margin = 0.02

fig, ((ax1, ax2)) = plt.subplots(nrows=1, ncols=2, figsize=(12, 5))

ax1.set_xlim(lat_min - margin, lat_max + margin)
ax1.set_ylim(lon_min - margin, lon_max + margin)
ax1.axis('equal')
ds.SPEED.plot(ax=ax1, x='latitude', y='longitude', cmap=plt.cm.jet)
ax1.scatter(ds.latitude, ds.longitude, color='black')

# find nearest_point for a requested lat/ lon
lat_requested = 21.22
lon_requested = -122.68

d_lat = ds.latitude - lat_requested
d_lon = ds.longitude - lon_requested
r2_requested = d_lat**2 + d_lon**2
i_j_loc = np.where(r2_requested == np.min(r2_requested))

nearest_point = ds.sel(i=i_j_loc[0], j=i_j_loc[1])

# Plot nearest point in the array red# Plot nearest point in the array red
ax1.scatter(lat_requested, lon_requested, color='green')
ax1.text(lat_requested, lon_requested, 'requested')
ax1.scatter(nearest_point.latitude, nearest_point.longitude, color='red')
ax1.text(nearest_point.latitude, nearest_point.longitude, 'nearest')
ax1.set_title(f'speed at nearest point: {float(nearest_point.SPEED.data):.2f}')

# define grid from the dataset
num_points = 100
lats_i = np.linspace(lat_min, lat_max, num_points)
lons_i = np.linspace(lon_min, lon_max, num_points)

# grid and contour the data.
speed_i = griddata((ds.latitude.values.flatten(), ds.longitude.values.flatten()),
                   ds.SPEED.values.flatten(),
                   (lats_i[None, :], lons_i[:, None]), method='cubic')

ax2.set_xlim(lat_min - margin, lat_max + margin)
ax2.set_ylim(lon_min - margin, lon_max + margin)
ax2.axis('equal')
ax2.set_title(f'griddata test {num_points} points')

ax2.contour(lats_i, lons_i, speed_i, 15, linewidths=0.5, colors='k')
contour = ax2.contourf(lats_i, lons_i, speed_i, 15, cmap=plt.cm.jet)
plt.colorbar(contour, ax=ax2)

# plot data points and labels
ax2.scatter(ds.latitude, ds.longitude, marker='o', c='b', s=5)

for i, (lat, lon) in enumerate(zip(ds.latitude.values.flatten(),
                                   ds.longitude.values.flatten())):
    text_label = f'{ds.SPEED.values.flatten()[i]:0.2f}'
    ax2.text(lat, lon, text_label)

# Plot nearest point in the array red
ax2.scatter(lat_requested, lon_requested, color='green')
ax2.text(lat_requested, lon_requested, 'requested')
ax2.scatter(nearest_point.latitude, nearest_point.longitude, color='red')

plt.subplots_adjust(wspace=0.2)
plt.show()

結果：

Answer 5

如另一個答案中所述，要基於此數據格式的投影進行查找，不幸的是，您必須將投影信息添加回數據中。

import cartopy.crs as ccrs

# Projection may vary
projection = ccrs.LambertConformal(central_longitude=-97.5,
                             central_latitude=38.5,
                             standard_parallels=[38.5])
transform = np.vectorize(lambda x, y: projection.transform_point(x, y, ccrs.PlateCarree()))

# The grid should be aligned such that the projection x and y are the same
# at every y and x index respectively
grid_y = ds.isel(x=0)
grid_x = ds.isel(y=0)

_, proj_y = transform(grid_y.longitude, grid_y.latitude)
proj_x, _ = transform(grid_x.longitude, grid_x.latitude)

# ds.sel only works on the dimensions, so we can't just add
# proj_x and proj_y as additional coordinate variables
ds["x"] = proj_x
ds["y"] = proj_y

desired_x, desired_y = transform(-122.68, 21.2)
nearest_point = ds.sel(x=desired_x, y=desired_y, method="nearest")

print(nearest_point.SPEED)

Output：

<xarray.DataArray 'SPEED' ()>
array(10.934007)
Coordinates:
    latitude   float64 21.14
    longitude  float64 -122.7
    x          float64 -2.701e+06
    y          float64 -1.581e+06

Answer 6

只是一個評論和一些運行時：
對於 5000 × 5000 個數據點，每個查詢占用的時間和空間與 2500 萬個成正比。 以下，我認為相當於你的代碼，在我的舊 2.7 GHz iMac 上每次查詢大約需要 1 秒：

import sys
import numpy as np
from scipy.spatial.distance import cdist

n = 5000
nask = 1
dim = 2
# to change these params, run this.py  a=1  b=None  'c = expr' ... in sh or ipython --
for arg in sys.argv[1:]:
    exec( arg )
rng = np.random.default_rng( seed=0 )

X = rng.uniform( -100, 100, size=(n*n, dim) )  # data, n^2 × 2
ask = rng.uniform( -100, 100, size=(nask, dim) )  # query points

dist = cdist( X, ask, "chebyshev" )  # -> n^2 × nask

    # 1d index -> 2d index, e.g. 60003 -> row 12, col 3
jminflat = dist[:,0].argmin()
jmin = np.unravel_index( jminflat, (n,n) )
print( "cdist  N %g  dim %d  ask %s: dist %.2g to X[%s] = %s " % (
        n*n, dim, ask[0], dist[jminflat], jmin, X[jminflat] ))
# cdist  N 25000000  dim 2  ask [-4.6 94]: dist 0.0079 to X[(4070, 2530)] = [-4.6 94]

作為比較， scipy KDTree需要約 30 秒來為 25M 2d 點構建樹，然后每個查詢需要毫秒。 優點：輸入點可以任意散布，找到 5 或 10 個最近鄰進行插值不會比 1 長多少。

另見： scipy cdist
gis.stack 上的重新項目匹配和 interp 之間的差異
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