Google Earth Engine: calculating and plotting monthly average NDVI for a region from MODIS data

Question

I am trying to calculate monthly average NDVI for Ukraine the 2010-2020 period using MODIS data and then plot the values onto a graph (averaging all images in each individual month of each year separately across the full period). You can see the code I am using below. However, I keep getting the following error:

From checking the GEE documentation, I assumed this was an casting issue and have fixed those issues so I am not sure why the code is still failing.

//calculate average monthly NDVI for Ukraine
//get MODIS NDVI
var collection = ee.ImageCollection('MODIS/006/MOD13A1').select('NDVI');
//import country boundaries
var countries = ee.FeatureCollection('USDOS/LSIB_SIMPLE/2017');
//Subset Ukraine feature from countries.
var ukr = ee.Feature(
  countries
   .filter(ee.Filter.eq('country_na', 'Ukraine'))
    .first()
);
// Choose a reference period for your baseline
var reference = ee.ImageCollection(collection.filterDate('2010-01-01', '2020-12-31'))
  .sort('system:time_start');
//function to calculate monthly mean
//Get timestamp of first image
var time0 = ee.Image(reference.first().get('system:time_start'));
//Create an empty list (zeros) list to provide a structure into which the NDVI anomalies can be mapped
var first = ee.List([
  ee.Image(0).set('system:time_start', time0).rename('NDVI')
]);
//Use a function to iterate through months and calculate average NDVI
var months = ee.List.sequence(1, 12);
var byMonth = ee.ImageCollection.fromImages(
      months.map(function (m) {
        return ee.Image(reference.filter(ee.Filter.calendarRange(m, m, 'month')))
                    .select(1).mean()
                    .set('month', m);
}));
//Run the iteration
var average = ee.ImageCollection(ee.List(
  reference.iterate(byMonth, first)
));
//Define chart parameters
var chartParam = {
 title: 'Monthly average NDVI',
  hAxis: {title: 'Time'},
  vAxis: {title: 'Average NDVI'},
};
//Plot the chart
var chart = ui.Chart.image.seriesByRegion({
  imageCollection: average,
  regions: ukr,
  reducer: ee.Reducer.mean(),
  scale: 500,
  xProperty: 'system:time_start',
  seriesProperty: 'PROJECT'
});
//Print chart to console
print(chart.setOptions(chartParam));

Answer 1

Looks like you were pretty close, and with the help of Nicholas Clinton's answer here we can arrive at a solution. The main changes I made were:

1. removing unnecessary variable definitions (first and time0)
2. adjust how the function mapped to months is defined
3. added a years variable for the same function mapping technique

All of that said, here's an updated script.

//calculate average monthly NDVI for Ukraine
//get MODIS NDVI
var collection = ee.ImageCollection('MODIS/006/MOD13A1').select('NDVI');
//import country boundaries
var countries = ee.FeatureCollection('USDOS/LSIB_SIMPLE/2017');
//Subset Ukraine feature from countries.
var ukr = ee.Feature(
  countries
   .filter(ee.Filter.eq('country_na', 'Ukraine'))
    .first()
);
print("ukr",ukr);
//Use a function to iterate through months and calculate average NDVI
var months = ee.List.sequence(1, 12);
print("months",months);
var years = ee.List.sequence(2010, 2020);
print("years",years);
// Map filtering and reducing across year-month combinations and convert to ImageCollection
var yrMo = ee.ImageCollection.fromImages(
  years.map(function (y) {
        return months.map(function (m) {
            return collection
              .filter(ee.Filter.calendarRange(y, y, 'year'))
              .filter(ee.Filter.calendarRange(m, m, 'month'))
              .mean()
              .set('year',y)
              .set('month',m);
        });
    }).flatten());
print("yrMo",yrMo);
//Define chart parameters
var chartParam = {
 title: 'Monthly average NDVI',
  hAxis: {title: 'Time'},
  vAxis: {title: 'Average NDVI'},
};
//Plot the chart
var chart = ui.Chart.image.seriesByRegion({
  imageCollection: yrMo,
  regions: ukr,
  reducer: ee.Reducer.mean(),
  scale: 500,
  xProperty: 'system:index',
  seriesProperty: 'PROJECT'
});
//Print chart to console
print(chart.setOptions(chartParam));