Getting local incidence angle from Sentinel-1 GRD image collection in Google Earth Engine

Question

I am using python API in google earth engine (colab) to retrieve local incidence angle from sentinel-1 GRD data. However, the .select ('') function only allows the VV, VH, HH, HV, and 'angle' band selection. The angle band is viewing angle of the sensor, and I need a local incidence angle (retrieved as a by-product of the terrain correction step). Does anyone have the answer? Thanks

Answer 1

The terrain correction implemented by Andreas Vollrath calculates the local incidence angle. You can modify the implementation to return that angle.

// Implementation by Andreas Vollrath (ESA), inspired by Johannes Reiche (Wageningen)
function terrainCorrection(image) {
  var imgGeom = image.geometry()
  var srtm = ee.Image('USGS/SRTMGL1_003').clip(imgGeom) // 30m srtm 
  var sigma0Pow = ee.Image.constant(10).pow(image.divide(10.0))

  // Article ( numbers relate to chapters)
  // 2.1.1 Radar geometry 
  var theta_i = image.select('angle')
  var phi_i = ee.Terrain.aspect(theta_i)
    .reduceRegion(ee.Reducer.mean(), theta_i.get('system:footprint'), 1000)
    .get('aspect')

  // 2.1.2 Terrain geometry
  var alpha_s = ee.Terrain.slope(srtm).select('slope')
  var phi_s = ee.Terrain.aspect(srtm).select('aspect')

  // 2.1.3 Model geometry
  // reduce to 3 angle
  var phi_r = ee.Image.constant(phi_i).subtract(phi_s)

  // convert all to radians
  var phi_rRad = phi_r.multiply(Math.PI / 180)
  var alpha_sRad = alpha_s.multiply(Math.PI / 180)
  var theta_iRad = theta_i.multiply(Math.PI / 180)
  var ninetyRad = ee.Image.constant(90).multiply(Math.PI / 180)

  // slope steepness in range (eq. 2)
  var alpha_r = (alpha_sRad.tan().multiply(phi_rRad.cos())).atan()

  // slope steepness in azimuth (eq 3)
  var alpha_az = (alpha_sRad.tan().multiply(phi_rRad.sin())).atan()

  // local incidence angle (eq. 4)
  var theta_lia = (alpha_az.cos().multiply((theta_iRad.subtract(alpha_r)).cos())).acos()
  var theta_liaDeg = theta_lia.multiply(180 / Math.PI)
  // 2.2 
  // Gamma_nought_flat
  var gamma0 = sigma0Pow.divide(theta_iRad.cos())
  var gamma0dB = ee.Image.constant(10).multiply(gamma0.log10())
  var ratio_1 = gamma0dB.select('VV').subtract(gamma0dB.select('VH'))

  // Volumetric Model
  var nominator = (ninetyRad.subtract(theta_iRad).add(alpha_r)).tan()
  var denominator = (ninetyRad.subtract(theta_iRad)).tan()
  var volModel = (nominator.divide(denominator)).abs()

  // apply model
  var gamma0_Volume = gamma0.divide(volModel)
  var gamma0_VolumeDB = ee.Image.constant(10).multiply(gamma0_Volume.log10())

  // we add a layover/shadow maskto the original implmentation
  // layover, where slope > radar viewing angle 
  var alpha_rDeg = alpha_r.multiply(180 / Math.PI)
  var layover = alpha_rDeg.lt(theta_i);

  // shadow where LIA > 90
  var shadow = theta_liaDeg.lt(85)

  // calculate the ratio for RGB vis
  var ratio = gamma0_VolumeDB.select('VV').subtract(gamma0_VolumeDB.select('VH'))

  var output = gamma0_VolumeDB.addBands(ratio).addBands(alpha_r).addBands(phi_s).addBands(theta_iRad)
    .addBands(layover).addBands(shadow).addBands(gamma0dB).addBands(ratio_1)

  return image.addBands(
    output.select(['VV', 'VH', 'slope_1', 'slope_2'], ['VV', 'VH', 'layover', 'shadow']),
    null,
    true
  )
}

Answer 2

Code:

var s1 = ee.ImageCollection('COPERNICUS/S1_GRD')
    .filterDate('2019-01-01', '2019-01-31')
    .filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VV'))
    .filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VH'))
    .filter(ee.Filter.eq('instrumentMode', 'IW'))
    .filter(ee.Filter.eq('orbitProperties_pass', 'DESCENDING'))
    .filter(ee.Filter.eq('resolution', 'H'))
    .filter(ee.Filter.eq('resolution_meters', 10))
    .filterBounds(geometry)
    .select('VV','VH','angle');
print('Collection: S1', s1);

var image = ee.Image(
  s1.first())
print('Test image', image);

// Implementation by Andreas Vollrath (ESA), inspired by Johannes Reiche (Wageningen)
 var terrainCorrection= function(image) {
  var imgGeom = image.geometry()
  var srtm = ee.Image('CGIAR/SRTM90_V4').clip(imgGeom) // 30m srtm 
  var sigma0Pow = ee.Image.constant(10).pow(image.divide(10.0))

  // Article ( numbers relate to chapters)
  // 2.1.1 Radar geometry 
  var theta_i = image.select('angle')
  var phi_i = ee.Terrain.aspect(theta_i)
    .reduceRegion(ee.Reducer.mean(), theta_i.get('system:footprint'), 1000)
    .get('aspect')

  // 2.1.2 Terrain geometry
  var alpha_s = ee.Terrain.slope(srtm).select('slope')
  var phi_s = ee.Terrain.aspect(srtm).select('aspect')

  // 2.1.3 Model geometry
  // reduce to 3 angle
  var phi_r = ee.Image.constant(phi_i).subtract(phi_s)

  // convert all to radians
  var phi_rRad = phi_r.multiply(Math.PI / 180)
  var alpha_sRad = alpha_s.multiply(Math.PI / 180)
  var theta_iRad = theta_i.multiply(Math.PI / 180)
  var ninetyRad = ee.Image.constant(90).multiply(Math.PI / 180)

  // slope steepness in range (eq. 2)
  var alpha_r = (alpha_sRad.tan().multiply(phi_rRad.cos())).atan()

  // slope steepness in azimuth (eq 3)
  var alpha_az = (alpha_sRad.tan().multiply(phi_rRad.sin())).atan()

  // local incidence angle (eq. 4)
  var theta_lia = (alpha_az.cos().multiply((theta_iRad.subtract(alpha_r)).cos())).acos()
  var theta_liaDeg = theta_lia.multiply(180 / Math.PI)
  var local=theta_lia.toFloat();
  // 2.2 
  // Gamma_nought_flat
  var gamma0 = sigma0Pow.divide(theta_iRad.cos())
  var gamma0dB = ee.Image.constant(10).multiply(gamma0.log10())
  var ratio_1 = gamma0dB.select('VV').subtract(gamma0dB.select('VH'))

  // Volumetric Model
  var nominator = (ninetyRad.subtract(theta_iRad).add(alpha_r)).tan()
  var denominator = (ninetyRad.subtract(theta_iRad)).tan()
  var volModel = (nominator.divide(denominator)).abs()

  // apply model
  var gamma0_Volume = gamma0.divide(volModel)
  var gamma0_VolumeDB = ee.Image.constant(10).multiply(gamma0_Volume.log10())

  // we add a layover/shadow maskto the original implmentation
  // layover, where slope > radar viewing angle 
  var alpha_rDeg = alpha_r.multiply(180 / Math.PI)
  var layover = alpha_rDeg.lt(theta_i);

  // shadow where LIA > 90
  var shadow = theta_liaDeg.lt(85)

  // calculate the ratio for RGB vis
  var ratio = gamma0_VolumeDB.select('VV').subtract(gamma0_VolumeDB.select('VH'))

  var output = gamma0_VolumeDB.addBands(ratio).addBands(alpha_r).addBands(phi_s).addBands(theta_iRad)
    .addBands(layover).addBands(shadow).addBands(gamma0dB).addBands(ratio_1).addBands(srtm).addBands(local)

  return image.addBands(
    output.select(['VV', 'VH', 'slope_1', 'slope_2'], ['VV', 'VH', 'layover', 'local']),
    null,
    true
  )
}

var test_output= terrainCorrection(image)
print("test_output",test_output)


var s1_all= s1.map(terrainCorrection)
print('s1_all', s1_all);
Map.addLayer(
  s1_all.mean(),
  {bands:'local', min:-20, max:2},
  'Incidence angle'
);

Output:

List (5 elements)
0:"VV", double, EPSG:32631, 28746x21405 px
1:"VH", double, EPSG:32631, 28746x21405 px
2:"angle", float, EPSG:32631, 21x10 px
3:"layover", int ∈ [0, 1], EPSG:4326, 5352x2670 px
4:"local", int ∈ [0, 1], EPSG:4326, 5352x2670 px