Google Earth Engine笔记-计算时间序列hurst指数

3 计算时间序列hurst指数

• 理论介绍

这篇http://club.excelhome.net/thread-1414154-1-1.html文章对hurst计算介绍非常详细，讲得非常详细。

hurst指数的意义

• 数据准备

var wuhan = ee.FeatureCollection("users/yp7454982/wuhan");
Map.centerObject(wuhan,8);
var startDate=ee.Date('2000-01-01');
var endDate=ee.Date('2020-01-01');
var dataset=ee.ImageCollection("MODIS/006/MOD13Q1")
              .filterDate(startDate,endDate)
              .filterBounds(wuhan)
              .select("EVI")
              .map(function (image){return image.clip(wuhan).divide(10000).toFloat()})
print(dataset)

选择武汉市2000年到2020年的MODIS的MOD13Q1的16天时间序列产品，选择其中的EVI波段，并乘上scale因子，转换为浮点类型，进行裁剪。最终形成了457张时间序列影像

• 定义子序列长度列表$r_1,r_2,...,r_m$

var sub_list_dist=4;
var sub_list_len=ee.List.sequence(2,dataset.size().divide(2).int(),sub_list_dist);

为计算方便，定义子序列长度间隔为4,由于$r_m$要等于$n/2$的整数部分，因此有如上定义子序列长度列表

• hurst指数$R/S$计算函数

function hurst(time_series,sub_len){
    var RS_list=sub_len.map(function (dist){
    var index_seq=ee.List.sequence(0,time_series.size(),dist)
    var sub_R_S=ee.List.sequence(0,index_seq.size().subtract(2),1).map(function (i){
      var sub_series=ee.ImageCollection(time_series.toList(time_series.size())
                        .slice(index_seq.get(ee.Number(i)),index_seq.get(ee.Number(i).add(1))))
      var sub_series_mean=sub_series.mean()
    var sub_x_subtract_mean=sub_series.map(function (image){return image.subtract(sub_series_mean)})
    //Calculate the deviation
    var first = ee.List([
    // Rename the first image
    ee.Image(0)]);
// This is a function to pass to Iterate().
// As anomaly images are computed, add them to the list.
  var accumulate = function(image,list) {
  // Get the latest cumulative anomaly image from the end of the list with
  // get(-1).  Since the type of the list argument to the function is unknown,
  // it needs to be cast to a List.  Since the return type of get() is unknown,
  // cast it to Image.
  var previous = ee.Image(ee.List(list).get(-1));
  // Add the current anomaly to make a new cumulative anomaly image.
  var added = image.add(previous);
  // Return the list with the cumulative anomaly inserted.
    return ee.List(list).add(added);
    };
    // Create an ImageCollection of cumulative anomaly images by iterating.
    // Since the return type of iterate is unknown, it needs to be cast to a List.
    var cum_deviation = ee.ImageCollection(ee.List(sub_x_subtract_mean.iterate(accumulate, first)).removeAll(first));
    var range=cum_deviation.max().subtract(cum_deviation.min())
    var standard_dev=sub_x_subtract_mean.map(function (image){return image.pow(ee.Image(2))})
                                        .sum().divide(sub_x_subtract_mean.size().subtract(1)).sqrt()
    var R_S= range.divide(standard_dev).rename('RS').toFloat();
    return R_S
    })
    var R_S_mean=ee.ImageCollection(sub_R_S).mean().set('dist',dist);
    return R_S_mean
  })
  var R_Smean_series=ee.ImageCollection(RS_list)
  return R_Smean_series;
}

算法核心思想：代码的所有实现均根据计算hurst指数理论分部往下写，其中要注意的是利用了两个map循环，其中第一个对dist进行map循环是对其中子序列长度进行遍历，每进行一次遍历，需要对原始时间序列进行划分为若干组，然后再对每个组的时间序列进行整合成新的ImageCollection，这里必须要将其转为list来进行slice选择，再进行类型转换，对每一个组内计算离差，累计离差，累计离差这里要用到iterate的迭代的思想，求其累加的和，然后求极差，最终求得每组的$R/S$然后再对所有组形成的$R/S$形成的ImageCollection求mean,返回当前dist下的$R/S$最终返回了一个再每个子序列长度不同下，计算的$R/S$

• hurst指数计算——最小二乘拟合

var RS=hurst(dataset,sub_list_len)
print(RS)
var RS_list=RS.toList(RS.size()); //transfrom List we can loop in i in[1,RS.size()]
var lnRS_ln_i=ee.ImageCollection(ee.List.sequence(0,RS.size().subtract(1),1).map(function (i){
  var lnRS_i=ee.Image(RS_list.get(i)).log().rename('ln_RS');
  var ln_i=ee.Image(ee.Number(sub_list_len.get(i)).log()).rename('ln_r_i').toFloat();
  return lnRS_i.addBands(ln_i)
}));
print(lnRS_ln_i);
var hurst=lnRS_ln_i.select(['ln_r_i','ln_RS']).reduce(ee.Reducer.linearFit()).select('scale');
print(hurst)

• 异常值检查与数据可视化与导出

var viz={
  min:0,
  max:1,
  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(hurst,viz,'hurst')
var chart=ui.Chart.image.histogram(hurst, wuhan, 250)
print(chart)
Export.image.toDrive({
  image: hurst.clip(wuhan),
  description: "hurst_wuhan",
  scale: 250,
  region: wuhan.geometry(),
  maxPixels: 1e13
});


var legend = ui.Panel({
style: {
position: 'bottom-left',
padding: '8px 15px'
}
});
 
// Create legend title
var legendTitle = ui.Label({
value: 'scale',
style: {
fontWeight: 'bold',
fontSize: '18px',
margin: '0 0 4px 0',
padding: '0'
}
});
 
// Add the title to the panel
legend.add(legendTitle);
 
// create the legend image
var lon = ee.Image.pixelLonLat().select('latitude');
var gradient = lon.multiply((viz.max-viz.min)/100.0).add(viz.min);
var legendImage = gradient.visualize(viz);
 
// create text on top of legend
var panel = ui.Panel({
widgets: [
ui.Label(viz['max'])
],
});
 
legend.add(panel);
 
// create thumbnail from the image
var thumbnail = ui.Thumbnail({
image: legendImage,
params: {bbox:'0,0,10,100', dimensions:'10x200'},
style: {padding: '1px', position: 'bottom-center'}
});
 
// add the thumbnail to the legend
legend.add(thumbnail);
 
// create text on top of legend
var panel = ui.Panel({
widgets: [
ui.Label(viz['min'])
],
});
legend.add(panel);
Map.add(legend);

从数据直方图来看，有少量的栅格hurst指数小于0，属于异常值现象，大部分都在0.4-0.8左右，趋于正常，数据可视化范围显示如下图所示