利用GEE计算遥感生态指数(RSEI)

// 第一步:定义研究区，自行更换自己的研究区
var roi = 
    /* color: #98ff00 */
    /* displayProperties: [
      {
        "type": "rectangle"
      }
    ] */
    ee.Geometry.Polygon(
        [[[120.1210075098537, 35.975189051414006],
          [120.1210075098537, 35.886229778229115],
          [120.25764996590839, 35.886229778229115],
          [120.25764996590839, 35.975189051414006]]], null, false);
          
Map.centerObject(roi);
 
// 第二步：加载数据集,定义去云函数
function removeCloud(image){
  var qa = image.select('BQA')
  var cloudMask = qa.bitwiseAnd(1 << 4).eq(0)
  var cloudShadowMask = qa.bitwiseAnd(1 << 8).eq(0)
  var valid = cloudMask.and(cloudShadowMask)
  return image.updateMask(valid)
}

// 数据集去云处理
var L8 = ee.ImageCollection('LANDSAT/LC08/C01/T1_TOA')
           .filterBounds(roi)
           .filterDate('2018-01-01', '2019-12-31')
           .filterMetadata('CLOUD_COVER', 'less_than',50)
           .map(function(image){
                    return image.set('year', ee.Image(image).date().get('year'))                           
                  })
           .map(removeCloud)
 

// 影像合成
var L8imgList = ee.List([])
for(var a = 2018; a < 2020; a++){
   var img = L8.filterMetadata('year', 'equals', a).median().clip(roi)
   var L8img = img.set('year', a)
   L8imgList = L8imgList.add(L8img)
 }

// 第三步：主函数,计算生态指标
var L8imgCol = ee.ImageCollection(L8imgList)
                 .map(function(img){
                      return img.clip(roi)
                   })
                 
L8imgCol = L8imgCol.map(function(img){
  
  // 湿度函数:Wet
  var Wet = img.expression('B*(0.1509) + G*(0.1973) + R*(0.3279) + NIR*(0.3406) + SWIR1*(-0.7112) + SWIR2*(-0.4572)',{
       'B': img.select(['B2']),
       'G': img.select(['B3']),
       'R': img.select(['B4']),
       'NIR': img.select(['B5']),
       'SWIR1': img.select(['B6']),
       'SWIR2': img.select(['B7'])
     })   
  img = img.addBands(Wet.rename('WET'))
  
  
  // 绿度函数:NDVI
  var ndvi = img.normalizedDifference(['B5', 'B4']);
  img = img.addBands(ndvi.rename('NDVI'))
  
  
  // 热度函数:lst 直接采用MODIS产品
  var lst = ee.ImageCollection('MODIS/006/MOD11A1').map(function(img){
                return img.clip(roi)
           })
           .filterDate('2014-01-01', '2019-12-31')
  
  var year = img.get('year')
  lst=lst.filterDate(ee.String(year).cat('-01-01'),ee.String(year).cat('-12-31')).select(['LST_Day_1km', 'LST_Night_1km']);
      
  // reproject主要是为了确保分辨率为1000
  var img_mean=lst.mean().reproject('EPSG:4326',null,1000);
  //print(img_mean.projection().nominalScale())
  
  img_mean = img_mean.expression('((Day + Night) / 2)',{
      'Day': img_mean.select(['LST_Day_1km']),
      'Night': img_mean.select(['LST_Night_1km']),
       })
  img = img.addBands(img_mean.rename('LST'))
  
  
  // 干度函数:ndbsi = ( ibi + si ) / 2
  var ibi = img.expression('(2 * SWIR1 / (SWIR1 + NIR) - (NIR / (NIR + RED) + GREEN / (GREEN + SWIR1))) / (2 * SWIR1 / (SWIR1 + NIR) + (NIR / (NIR + RED) + GREEN / (GREEN + SWIR1)))', {
      'SWIR1': img.select('B6'),
      'NIR': img.select('B5'),
      'RED': img.select('B4'),
      'GREEN': img.select('B3')
    })
  var si = img.expression('((SWIR1 + RED) - (NIR + BLUE)) / ((SWIR1 + RED) + (NIR + BLUE))', {
      'SWIR1': img.select('B6'),
      'NIR': img.select('B5'),
      'RED': img.select('B4'),
      'BLUE': img.select('B2')
    }) 
  var ndbsi = (ibi.add(si)).divide(2)
  return img.addBands(ndbsi.rename('NDBSI'))
})
 
 
var bandNames = ['NDVI', "NDBSI", "WET", "LST"]
L8imgCol = L8imgCol.select(bandNames)
 
//定义归一化函数:归一化
var img_normalize = function(img){
      var minMax = img.reduceRegion({
            reducer:ee.Reducer.minMax(),
            geometry: roi,
            scale: 1000,
            maxPixels: 10e13,
        })
      var year = img.get('year')
      var normalize  = ee.ImageCollection.fromImages(
            img.bandNames().map(function(name){
                  name = ee.String(name);
                  var band = img.select(name);
                  return band.unitScale(ee.Number(minMax.get(name.cat('_min'))), ee.Number(minMax.get(name.cat('_max'))));
                    
              })
        ).toBands().rename(img.bandNames()).set('year', year);
        return normalize;
}
var imgNorcol  = L8imgCol.map(img_normalize);
 
 
// 第四步:PCA融合，提取第一主成分
var pca = function(img){
      
      var bandNames = img.bandNames();
      var region = roi;
      var year = img.get('year')
      // Mean center the data to enable a faster covariance reducer
      // and an SD stretch of the principal components.
      var meanDict = img.reduceRegion({
            reducer:  ee.Reducer.mean(),
            geometry: region,
            scale: 1000,
            maxPixels: 10e13
        });
      var means = ee.Image.constant(meanDict.values(bandNames));
      var centered = img.subtract(means).set('year', year);
      
      
      // This helper function returns a list of new band names.
      var getNewBandNames = function(prefix, bandNames){
            var seq = ee.List.sequence(1, 4);
            //var seq = ee.List.sequence(1, bandNames.length());
            return seq.map(function(n){
                  return ee.String(prefix).cat(ee.Number(n).int());
              });      
        };
      
      // This function accepts mean centered imagery, a scale and
      // a region in which to perform the analysis.  It returns the
      // Principal Components (PC) in the region as a new image.
      var getPrincipalComponents = function(centered, scale, region){
            var year = centered.get('year')
            var arrays = centered.toArray();
        
            // Compute the covariance of the bands within the region.
            var covar = arrays.reduceRegion({
                  reducer: ee.Reducer.centeredCovariance(),
                  geometry: region,
                  scale: scale,
                  bestEffort:true,
                  maxPixels: 10e13
              });
            
            // Get the 'array' covariance result and cast to an array.
            // This represents the band-to-band covariance within the region.
            var covarArray = ee.Array(covar.get('array'));
            
            // Perform an eigen analysis and slice apart the values and vectors.
            var eigens = covarArray.eigen();
        
            // This is a P-length vector of Eigenvalues.
            var eigenValues = eigens.slice(1, 0, 1);
            // This is a PxP matrix with eigenvectors in rows.
            var eigenVectors = eigens.slice(1, 1);
        
            // Convert the array image to 2D arrays for matrix computations.
            var arrayImage = arrays.toArray(1)
            // Left multiply the image array by the matrix of eigenvectors.
            var principalComponents = ee.Image(eigenVectors).matrixMultiply(arrayImage);
        
            // Turn the square roots of the Eigenvalues into a P-band image.
            var sdImage = ee.Image(eigenValues.sqrt())
            .arrayProject([0]).arrayFlatten([getNewBandNames('SD',bandNames)]);
        
            // Turn the PCs into a P-band image, normalized by SD.
            return principalComponents
            // Throw out an an unneeded dimension, [[]] -> [].
            .arrayProject([0])
            // Make the one band array image a multi-band image, [] -> image.
            .arrayFlatten([getNewBandNames('PC', bandNames)])
            // Normalize the PCs by their SDs.
            .divide(sdImage)
            .set('year', year);
        }
        
        // Get the PCs at the specified scale and in the specified region
        img = getPrincipalComponents(centered, 1000, region);
        return img;
  };
  
var PCA_imgcol = imgNorcol.map(pca)
 
Map.addLayer(PCA_imgcol.first(), {"bands":["PC1"]}, 'pc1')
 
// 第五步：利用PC1，计算RSEI，并归一化
var RSEI_imgcol = PCA_imgcol.map(function(img){
        img = img.addBands(ee.Image(1).rename('constant'))
        var rsei = img.expression('constant - pc1' , {
             constant: img.select('constant'),
             pc1: img.select('PC1')
         })
        rsei = img_normalize(rsei)
        return img.addBands(rsei.rename('rsei'))
    })
print(RSEI_imgcol)
 
var visParam = {
    palette: '040274, 040281, 0502a3, 0502b8, 0502ce, 0502e6, 0602ff, 235cb1, 307ef3, 269db1, 30c8e2, 32d3ef, 3be285, 3ff38f, 86e26f, 3ae237, b5e22e, d6e21f, fff705, ffd611, ffb613, ff8b13, ff6e08, ff500d, ff0000, de0101, c21301, a71001, 911003'
 };
 
Map.addLayer(RSEI_imgcol.first().select('rsei'), visParam, 'rsei')