【GEE】基于PCA的LANDSAT 8计算遥感生态指数（RSEI）

var table = ee.FeatureCollection("projects/ee-1261423515/assets/aibihu");
Map.centerObject(table, 8);
function maskL8sr(image) {
  // Bit 0 - Fill
  // Bit 1 - Dilated Cloud
  // Bit 2 - Cirrus
  // Bit 3 - Cloud
  // Bit 4 - Cloud Shadow
  var qaMask = image.select('QA_PIXEL').bitwiseAnd(parseInt('11111', 2)).eq(0);
  var saturationMask = image.select('QA_RADSAT').eq(0);

  // Apply the scaling factors to the appropriate bands.
  var opticalBands = image.select('SR_B.').multiply(0.0000275).add(-0.2);
  var thermalBands = image.select('ST_B.*').multiply(0.00341802).add(149.0);

  // Replace the original bands with the scaled ones and apply the masks.
  return image.addBands(opticalBands, null, true)
      .addBands(thermalBands, null, true)
      .updateMask(qaMask)
      .updateMask(saturationMask);
} 
function SI_cal(img) {
 var blue = img.select("SR_B2");
 var red = img.select("SR_B4");
 var nir = img.select("SR_B5");
 var swir1 = img.select("SR_B6");
 var swir2 = img.select("SR_B7");
 var SI_temp =((swir1.add(red)).subtract(blue.add(nir)))
              .divide((swir1.add(red)).add(blue.add(nir)))
 //print(SI_temp);
 return SI_temp;
}
function IBI_cal(img) {
 var green = img.select("SR_B3");
 var red = img.select("SR_B4");
 var nir = img.select("SR_B5");
 var swir1 = img.select("SR_B6");
 var IBI_temp =(((swir1.multiply(2.0)).divide(swir1.add(nir)))
               .subtract((nir.divide(nir.add(red))).add(green.divide(green.add(swir1)))))
               .divide((((swir1.multiply(2.0)).divide(swir1.add(nir)))
               .add((nir.divide(nir.add(red))).add(green.divide(green.add(swir1))))))
 //print(IBI_temp);
 return IBI_temp;
}
function NDVI_cal(img) {
 var ndvi_temp = img.normalizedDifference(["SR_B5","SR_B4"]);
 //print(ndvi_temp);
 return ndvi_temp;
}
function Wet_cal(img) {
 var blue = img.select("SR_B2");
 var green = img.select("SR_B3");
 var red = img.select("SR_B4");
 var nir = img.select("SR_B5");
 var swir1 = img.select("SR_B6");
 var swir2 = img.select("SR_B7");
 var wet_temp =blue.multiply(0.1511)
              .add(green.multiply(0.1973))
              .add(red.multiply(0.3283))
              .add(nir.multiply(0.3407))
              .add(swir1.multiply(-0.7117))
              .add(swir2.multiply(-0.4559))
 //print(wet_temp);
 return wet_temp;
}
function NDWI_cal(img) {
 var nir = img.select("SR_B5");
 var green = img.select("SR_B3");
 var ndwi_temp = green.subtract(nir).divide(green.add(nir));
 return ndwi_temp;
}
function img_normalize(img){
      var minMax = img.reduceRegion({
            reducer:ee.Reducer.minMax(),
            geometry: table,
            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());
        return normalize;
} ;
// Map the function over one year of data.
var dataset = ee.ImageCollection("LANDSAT/LC08/C02/T1_L2")
    .filterDate('2020-06-01', '2020-10-31')
    .map(maskL8sr)
    .mean()
var dataset1 = ee.ImageCollection("MODIS/006/MOD11A2")
    .filterDate('2020-06-01', '2020-10-31')
    .mean()
var ndwi=NDWI_cal(dataset);
var NDWI_mask = ndwi.lt(0.1);
var dataset_no_water = dataset.updateMask(NDWI_mask).clip(table);
var dataset1_no_water = dataset1.updateMask(NDWI_mask).clip(table);

var lst = dataset1_no_water.expression(
    'a*0.02-273.15',
    {
        a:dataset1_no_water.select('LST_Day_1km'), 
    });
var SI = SI_cal(dataset_no_water);
var IBI = IBI_cal(dataset_no_water);
var NDBSI =(SI.add(IBI)).divide(2.0);
var ndvi = NDVI_cal(dataset_no_water);
var wet = Wet_cal(dataset_no_water);
var visParams1 = {
 palette: '313695,4575b4,74add1,abd9e9,e0f3f8,ffffbf,fee090,fdae61,f46d43,d73027,a50026'
};
var visParams = {
 min: -1,
 max: 1,
 palette: ['0000FF','ff0000','00ff00']
};
var visParams2 = {
 palette: 'a50026,d73027,f46d43,fdae61,fee090,ffffbf,e0f3f8,abd9e9,74add1,4575b4,313695'
};
var unit_ndvi = img_normalize(ndvi);
dataset_no_water=dataset_no_water.addBands(unit_ndvi.rename('NDVI').toFloat())
var unit_NDBSI = img_normalize(NDBSI);
dataset_no_water=dataset_no_water.addBands(unit_NDBSI.rename('NDBSI').toFloat())
var unit_Wet = img_normalize(wet);
dataset_no_water=dataset_no_water.addBands(unit_Wet.rename('Wet').toFloat())
var unit_lst = img_normalize(lst);
dataset_no_water=dataset_no_water.addBands(unit_lst.rename('LST').toFloat())
//print(dataset_no_water);
var bands = ["Wet","NDVI","NDBSI","LST"]
var sentImage =dataset_no_water.select(bands)

var region = table;
var image =  sentImage.select(bands);
var scale = 1000;
var bandNames = image.bandNames();
// 图像波段重命名函数
var getNewBandNames = function(prefix) {
    var seq = ee.List.sequence(1, bandNames.length());
    return seq.map(function(b) {
      return ee.String(prefix).cat(ee.Number(b).int());
    });
  };
//数据平均

var meanDict = image.reduceRegion({
    reducer: ee.Reducer.mean(),
    geometry: region,
    scale: scale,
    maxPixels: 1e9
});
var means = ee.Image.constant(meanDict.values(bandNames));
var centered = image.subtract(means);


//主成分分析函数
var getPrincipalComponents = function(centered, scale, region) {
    // 图像转为一维数组
    var arrays = centered.toArray();

    // 计算协方差矩阵
    var covar = arrays.reduceRegion({
      reducer: ee.Reducer.centeredCovariance(),
      geometry: region,
      scale: scale,
      maxPixels: 1e9
    });
    // 获取“数组”协方差结果并转换为数组。
    // 波段与波段之间的协方差
    var covarArray = ee.Array(covar.get('array'));

    // 执行特征分析，并分割值和向量。
    var eigens = covarArray.eigen();

    // 特征值的P向量长度
    var eigenValues = eigens.slice(1, 0, 1);
   

    //计算主成分载荷
    var eigenValuesList = eigenValues.toList().flatten()
    var total = eigenValuesList.reduce(ee.Reducer.sum())
    var percentageVariance = eigenValuesList.map(function(item) {
      return (ee.Number(item).divide(total)).multiply(100).format('%.2f')
    })
    print('特征值',eigenValues )
    print("贡献率", percentageVariance)  

    // PxP矩阵，其特征向量为行。
    var eigenVectors = eigens.slice(1, 1);
    // 将图像转换为二维阵列
    var arrayImage = arrays.toArray(1);

    //使用特征向量矩阵左乘图像阵列
    var principalComponents = ee.Image(eigenVectors).matrixMultiply(arrayImage);

    // 将特征值的平方根转换为P波段图像。
    var sdImage = ee.Image(eigenValues.sqrt())
      .arrayProject([0]).arrayFlatten([getNewBandNames('sd')]);

    //将PC转换为P波段图像，通过SD标准化。
    principalComponents=principalComponents
      // 抛出一个不需要的维度，[[]]->[]。
      .arrayProject([0])
      // 使单波段阵列映像成为多波段映像，[]->image。
      .arrayFlatten([getNewBandNames('pc')])
      // 通过SDs使PC正常化。
      .divide(sdImage);
    return principalComponents
  };
//进行主成分分析，获得分析结果
var pcImage = getPrincipalComponents(centered, scale, region);

var rsei_un_unit = pcImage.expression(
  'constant - pc1' , 
  {
             constant: 1,
             pc1: pcImage.select('pc1')
         });
var rsei = img_normalize(rsei_un_unit);


//Map.addLayer(table,{color:'FFFF00'});
Map.addLayer(rsei, {}, 'PCA');
//Map.addLayer(dataset_no_water, {bands: ['SR_B4', 'SR_B3', 'SR_B2'], min: 0, max: 0.3});
//Map.addLayer(lst, visParams1, "LST");
//Map.addLayer(NDBSI, {}, "NDBSI");
//Map.addLayer(ndvi, visParams, "NDVI");
//Map.addLayer(wet, visParams2, "Wet");