矢量到光栅插值

在 Earth Engine 中,从矢量到光栅的插值会根据 FeatureCollection 创建 Image。具体而言,Earth Engine 会使用存储在地图项属性中的数值数据,对地图项之外的新位置插值值。插值会产生连续的 Image,其中包含指定距离范围内的内插值。

反距离加权插值

Earth Engine 中的反距离权重 (IDW) 函数基于 Basso 等人 (1999) 所述的方法。在反距离上添加了额外的控制参数,形式为衰减系数 (gamma)。其他参数包括要插值的属性的平均值和标准差,以及插值的最大范围距离。以下示例创建了 一氧化碳浓度的插值表面,以填补原始栅格数据集中的空间空白。FeatureCollection 是通过对两周的甲烷复合物进行采样生成的。

// Import two weeks of S5P methane and composite by mean.
var ch4 = ee.ImageCollection('COPERNICUS/S5P/OFFL/L3_CH4')
  .select('CH4_column_volume_mixing_ratio_dry_air')
  .filterDate('2019-08-01', '2019-08-15')
  .mean()
  .rename('ch4');

// Define an area to perform interpolation over.
var aoi =
  ee.Geometry.Polygon(
    [[[-95.68487605978851, 43.09844605027055],
       [-95.68487605978851, 37.39358590079781],
       [-87.96148738791351, 37.39358590079781],
       [-87.96148738791351, 43.09844605027055]]], null, false);

// Sample the methane composite to generate a FeatureCollection.
var samples = ch4.addBands(ee.Image.pixelLonLat())
  .sample({region: aoi, numPixels: 1500,
    scale:1000, projection: 'EPSG:4326'})
  .map(function(sample) {
    var lat = sample.get('latitude');
    var lon = sample.get('longitude');
    var ch4 = sample.get('ch4');
    return ee.Feature(ee.Geometry.Point([lon, lat]), {ch4: ch4});
  });

// Combine mean and standard deviation reducers for efficiency.
var combinedReducer = ee.Reducer.mean().combine({
  reducer2: ee.Reducer.stdDev(),
  sharedInputs: true});

// Estimate global mean and standard deviation from the points.
var stats = samples.reduceColumns({
  reducer: combinedReducer,
  selectors: ['ch4']});

// Do the interpolation, valid to 70 kilometers.
var interpolated = samples.inverseDistance({
  range: 7e4,
  propertyName: 'ch4',
  mean: stats.get('mean'),
  stdDev: stats.get('stdDev'),
  gamma: 0.3});

// Define visualization arguments.
var band_viz = {
  min: 1800,
  max: 1900,
  palette: ['0D0887', '5B02A3', '9A179B', 'CB4678',
            'EB7852', 'FBB32F', 'F0F921']};

// Display to map.
Map.centerObject(aoi, 7);
Map.addLayer(ch4, band_viz, 'CH4');
Map.addLayer(interpolated, band_viz, 'CH4 Interpolated');

请注意,如 range 参数所指定,插值仅在距离最近测量站不超过 70 公里的范围内有效。

Kriging

Kriging 是一种插值方法,它使用半变异的模型估计值来创建插值值的图像,该图像是已知位置值的最佳组合。 Kriging 估算器需要参数来描述拟合到已知数据点的半变异函数的形状。这些参数如图 1 所示。

方差图
图 1. 理想化变异函数上显示的 nuggetsillrange 参数。

以下示例在随机位置对海表温度 (SST) 图像进行采样,然后使用克里格插值法从样本中插值 SST:

// Load an image of sea surface temperature (SST).
var sst = ee.Image('NOAA/AVHRR_Pathfinder_V52_L3/20120802025048')
  .select('sea_surface_temperature')
  .rename('sst')
  .divide(100);

// Define a geometry in which to sample points
var geometry = ee.Geometry.Rectangle([-65.60, 31.75, -52.18, 43.12]);

// Sample the SST image at 1000 random locations.
var samples = sst.addBands(ee.Image.pixelLonLat())
  .sample({region: geometry, numPixels: 1000})
  .map(function(sample) {
    var lat = sample.get('latitude');
    var lon = sample.get('longitude');
    var sst = sample.get('sst');
    return ee.Feature(ee.Geometry.Point([lon, lat]), {sst: sst});
  });

// Interpolate SST from the sampled points.
var interpolated = samples.kriging({
  propertyName: 'sst',
  shape: 'exponential',
  range: 100 * 1000,
  sill: 1.0,
  nugget: 0.1,
  maxDistance: 100 * 1000,
  reducer: 'mean',
});

var colors = ['00007F', '0000FF', '0074FF',
              '0DFFEA', '8CFF41', 'FFDD00',
              'FF3700', 'C30000', '790000'];
var vis = {min:-3, max:40, palette: colors};

Map.setCenter(-60.029, 36.457, 5);
Map.addLayer(interpolated, vis, 'Interpolated');
Map.addLayer(sst, vis, 'Raw SST');
Map.addLayer(samples, {}, 'Samples', false);

执行插值的邻域的大小由 maxDistance 参数指定。大小越大,输出越流畅,但计算速度越慢。