Add corresponding MODIS LAI band to Sentinel-1 log(VH/VV) data in Google Earth Engine

Question

I am trying to determine the correlation between Sentinel-1 log(VH/VV) data and the corresponding MODIS 4 day LAI product. For the first step, I am trying to add the corresponding LAI data as a band to the Sentinel-1 log(VH/VV) collection. My code so far is provided. I am getting the errors shown below.

var point = ee.Geometry.Point(-96.47664, 41.16506);
var proj = ee.Projection('EPSG:32614');

var reproject = function(image) {
  var reprojected = image.reproject(proj, null, 1000);
  return reprojected};

var LogRatio = function(img) {
  var logVV = img.select('VV');
  var logVH = img.select('VH');
  var logratio = logVH.subtract(logVV).rename('logVH/VV');
  var logratio_float = logratio.toFloat();
  return img.addBands(logratio_float)};

var S1 = ee.ImageCollection('COPERNICUS/S1_GRD');
var S1_TempFilt = S1.filterDate('2017-01-01', '2020-02-20');
var S1_TempFilt_Resamp = S1_TempFilt.map(reproject);
var S1_TempSpatFilt_Resamp = S1_TempFilt_Resamp.filterBounds(point);
var S1_TempSpaceFiltResamp_W_LogCR = S1_TempSpatFilt_Resamp.map(LogRatio);
var S1_Log_VH_VV = S1_TempSpaceFiltResamp_W_LogCR.select('logVH/VV');
print('S1_Log_VH_VV',S1_Log_VH_VV);

var MODIS = ee.ImageCollection('MODIS/006/MCD15A3H');
var MODIS_TempFilt = MODIS.filterDate('2017-01-01', '2020-02-20');
var MODIS_TempFilt_Resamp =  MODIS_TempFilt.map(reproject);
var MODIS_TempSpatFilt_Resamp = MODIS_TempFilt_Resamp.filterBounds(point);
var M_LAI = MODIS_TempSpatFilt_Resamp.select('Lai');
print(M_LAI);

var Find_MODIS_LAI = function(image2) {
  var S1date = ee.Date(image2.get('system:time_start'));
  var LAI_start_date_min = S1date.advance(-1,"day");
  var LAI_start_date_max = S1date.advance(2,"day");
  var MODIS_LAI = M_LAI.filterDate(LAI_start_date_min, LAI_start_date_max);
  return MODIS_LAI};

var MODIS_LAI = S1_Log_VH_VV.map(Find_MODIS_LAI);
print('MODIS_LAI', MODIS_LAI);

var LAI_Band = MODIS_LAI.select('Lai');
print('LAI_Band',LAI_Band);
var LogCR_LAI = S1_Log_VH_VV.addBands(LAI_Band);

Error:

ImageCollection (Error)
Error in map(ID=S1A_IW_GRDH_1SDV_20170108T002112_20170108T002137_014733_017FB8_9BC3):
Image.select, argument 'input': Invalid type. Expected: Image<unknown bands>. Actual: ImageCollection.

S1_Log_VH_VV.addBands is not a function

Answer 1

You can join the two image collections. Something like this:

var s1Lai = ee.ImageCollection(ee.Join.saveAll('lai')
  .apply({
      primary: s1,
      secondary: lai,
      condition: ee.Filter.and(
        ee.Filter.intersects({
          leftField: '.geo',
          rightField: '.geo'
        }),
        ee.Filter.maxDifference({
          // Include LAI within 4 days of s1
          difference: 4 * 24 * 3600 * 1000, 
          leftField: 'system:time_start',
          rightField: 'system:time_start'
        })
      )
  }))
  .map(function (s1) {
    var lai = ee.ImageCollection(
        ee.List(s1.get('lai'))
      )
      .mosaic()
      .rename('LAI')
    return s1
      .addBands(lai)
      .float()
      .set('lai', null)
  })

https://code.earthengine.google.com/dcdd4d8e1c3845ae84ed65a5de9ee828