I am working with multiple raster files that cover all of united states. The file format of the rasters - GeoTIFF. I have around 100 geotiffs that I need to process. Then I have another shapefile with polygons. What I need to do is extract information (SUM of all values) from the raster files by using the polygon shapes and get data in a table format. I have tried ArcMap 10.3 Spatial Analyst extension's Zonal Statistics (Table) for the SUM, but I was not satisfied with the results - there are way too many 0s in places where there should be some values even if they are small.
I am asking for a good way to extract values in ArcMap, QGIS, possible R or other software. The GeoTIFFS dimensions are 3600 pixels to 859 pixels and they are around 25mb in size (each).
If there any model builder suggestions with functions information that would be great!