How to copy over date (system time index) variable from first image within a function

Question

I have calculated the monthly total rainfall for a region using CHIRPS data and would like to add this data onto a graph. At the moment it works for one single year, when I set "month" as the xProperty. However, when I sum the images by month in this function below, the system:time_start variable is lost, meaning I cannot add images from multiple years to a graph whilst showing the date correctly along the x-axis. I believe I need to copy over the system:time_start variable from the first image of the month to the summed image in this function but I am not sure how to do this.

var lt_precip = ee.ImageCollection.fromImages(
      years.map(function (y) {
        return months.map(function (m) {
          return precipitation.filter(ee.Filter.calendarRange(y, y, 'year'))
                    .filter(ee.Filter.calendarRange(m, m, 'month'))
                    .sum()
                    .set('year', y)
                    .set('month', m)
          });
      }).flatten());
print("lt_precip",lt_precip); 

Please find a full link to the code here: https://code.earthengine.google.com/43c0eebd26ac7a22c33f7a6ef2160ee4.

Answer 1

You are right about the need to copy the 'system:time_start' from the first image. This is one way to do it:

var lt_precip = ee.ImageCollection.fromImages(
      years.map(function (y) {
        return months.map(function (m) {
          var collection = precipitation.filter(ee.Filter.calendarRange(y, y, 'year'))
                    .filter(ee.Filter.calendarRange(m, m, 'month'));
          return collection
                    .sum()
                    .set('year', y)
                    .set('month', m)
                    .copyProperties(collection.first(),['system:time_start'])
          });
      }).flatten());

https://code.earthengine.google.com/27c369fd5e45b99a405f88189170caa9