modis - Reclassifying NDWI using Google Earth Engine?

I'm trying to reclassify a NDWI raster into 1 for values >0.4 and 0 for <0.4. I understand that its possible to use .remap in case of discrete values, but not sure how to reclassify NDWI raster using a threshold. Ideally, I need a function which will reclassify each image in a collection.

Attached is the earth engine code I used (and struck)

// Import MODIS 8 day reflectance collection.
var collection = ee.ImageCollection('MODIS/006/MYD09A1')
                   .filterBounds(roi);


//roi refers to an area of interest
//start data and end date 
var iniDate = ee.Date.fromYMD(2016,1,1);
var endDate = ee.Date.fromYMD(2017,12,31);
print('MODIS', collection);

// MODIS bands
var modisBands = 
['sur_refl_b03','sur_refl_b04','sur_refl_b01','sur_refl_b02', 

'sur_refl_b06', 'sur_refl_b07'];
var lsBands = ['blue','green','red','nir','swir1','swir2'];

// helper function to extract the QA bits
function getQABits(image, start, end, newName) {
// Compute the bits we need to extract.
var pattern = 0;
for (var i = start; i <= end; i++) {
pattern += Math.pow(2, i);
}


// Return a single band image of the extracted QA bits, giving the band
// a new name.
return image.select([0], [newName])
            .bitwiseAnd(pattern)
            .rightShift(start);
}

// A function to mask out cloudy pixels.
function maskQuality(image) {

// Select the QA band.
var QA = image.select('StateQA');
// Get the internal_cloud_algorithm_flag bit.
var internalQuality = getQABits(QA,8, 13, 'internal_quality_flag');
// Return an image masking out cloudy areas.
return image.updateMask(internalQuality.eq(0));
}

// create cloud free composite
var noCloud = collection.filterDate(iniDate,endDate)

                        .map(maskQuality)
                        .select(modisBands,lsBands);

// Function to calculate and add an NDWI band
var addNDWI = function(image) {
return image.addBands(image.normalizedDifference(['green', 'swir1']));
};

// Add NDWI band to image collection
var noCloud = noCloud.map(addNDWI);


// create NDWI image collection
var NDWI = noCloud.select(['nd']);

// Reclassify each image in NDWI collection and calculate yearly composite

Answer

What about values equal to 0.4?

.gt(): greater than

.gte(): greater or equal than

Then:

// Reclassify each image in NDWI collection and calculate yearly composite
var reclassified = NDWI.map(function(img){
  return img.gte(0.4) // or gt()
})