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I want to make cloud shadow mask in QGIS. I have raster cloud mask and I have to shift it by X,Y coordinates. Is there any easy solution?

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Yes, there is a very simple solution.

Use either QGIS Translate Raster or GDAL_Translate to create a world-type image (like .bmp, .jpg, .gif or .bil). These rasters don't contain georeference in themselves but rely on a world file with the first/last letters of the image and 'w' on the end, thus a jpg has a jgw file, a bitmap (bmp) has a bpw file.

The world file is just a text format (open in notepad) and you can adjust the coordinates easily stepping until it gets in the right spot (usually 4-6 iterations, depending on how good a guesser you are). Read this to understand the parameters.

BIL/BSQ files are different to worlded files but the concept is the same, the georeference is in a text format, read this to learn more.

Alternately you could georeference the cloud mask to the original but that relies on many points of similarity which may or may not be present.

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