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I would like to get the numpy arrays of some Google Earth Engine collection.

For example here my intent would be to obtain a 4d numpy array with dimensions [timestamp, height, width, bands] (or whatever order) with the Sigma0 data of a given region, defined by its bounds (here in UTM projection).

e.g.

import ee
import geopandas as gpd
from shapely.geometry import box

ee.Initialize()

crs = {'init': 'epsg:32628'}
poly = gpd.GeoSeries(box(578150.0, 1572350.0, 578350.0, 1572550.0), crs=crs)

poly_json = eval(poly.to_json())
gj_geom = poly_json['features'][0]['geometry'] 
geom = ee.Geometry(gj_geom, poly.crs['init'][5:])

collection = (ee.ImageCollection('COPERNICUS/S1_GRD')
              .filter(ee.Filter.date('2019-01-01', '2019-02-1'))
              .filter(ee.Filter.geometry(geom))
             )

How do I obtain the raw data arrays from the filtered collection?

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You can use ee.Image.sampleRectangle() (see this post) for converting GEE images to 2d array. However, there is a limit of 262144 pixels that can be transferred to protect your system from becoming unresponsive.

So for your collection, you can map over a function that applies this sampleRectangle and retrieves the respective array.

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