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I'm using MODIS satellite data that I've converted into GeoTIFFs (using extract subdataset). ArcMap automatically sets the geographic coordinate system to GCS_Unknown_datum_based_upon_the_Clarke_1866_ellipsoid. After some digging around on the MODIS site, I think, but am not entirely sure, that the starting coordinate system is supposed to be GCS WGS 1984. My goal is to get these into Lambert Azimuthal Equal Area projection and ultimately clip them to show the arctic region. I've tried a few different methods, but when the full image is projected, I always get the inconsistent extent error. For the record, I'm using ArcMap 10.3.1.

What I've tried:
- Project raster as is
- Define projection (set to GCS WGS 1984) and then project raster (Define projection gives me a warning that it already has a projection since ArcMap has technically given the images a coordinate system)
- Project raster into GCS WGS 1984 and then project raster into LAEA
- Going into ArcCatalog to manually change the spatial reference (no way to edit it)

For projecting into LAEA, I've done it both specifying an output cell size and using the default output cell size.

The images always look correct once they're clipped (all of the land area looks to be there and in the general shape it should be) and I don't get the error when I add the clipped images to the data frame, but I'm assuming there's some small distortion or issue with these final images.

I'm processing upwards of 800 images so I'm trying to find a solution that can be done either through batch processing or model builder.

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Both of the datasets that you are using rely on special projection systems used by the MODIS system. While it is possible to use ArcGIS etc to read the data, it will often cause projection issues at various stages. Instead, you should convert the data to GeoTIFF and project it into a more suitable projection system, such as GCS WGS84 using the MODIS Reprojection Tool - the MRT can be downloaded here.

It is reasonably simple to use this tool, and also pretty straight forward to implement a batch solution that can help you process all 800 images in one go.

You can also use a polar coordinate system for better results in arctic regions.

In retracing your steps, it seems as if there is a bug in the input datalayers, resulting in MRT being unable to read them.

As for your work flows, going through 'Define Projection' into 'GCS WGS84' followed by 'Project Raster' into 'LAEA' the results come out as expected. The warning that ArcGIS provides makes sense, given how ill suited the LAEA projection is for global data, and thus, if you were to reproject the dataset back into lat/lon, you would get significant distortions. However, if you keep the data in LAEA, it should be okay. However, using global data that originates in a 0.05 degree climate modelling grid in a arctic application is not a good approach, due to how ill suited 'degrees-as-pixel-size' is in the arctic. Instead, you should rely on swath data and calculate derived layers yourself.

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You can do a batch process for mosaic, reproject and crop your MODIS data easily, but out of ArcGIS.

Use MODIS Reprojection Tool and read MODIS Reprojection Tool User’s Manual. In my opinion, by far the best option to preprocess MODIS data.

Create a .Batch file using a master parameter file. You can set bands to extract, projection, dates to mosaic, extent, and so on. Run .Batch file in cmd or terminal. As an advise, put all .hdf files into a single folder.

With ModelBuilder, you will spend a lot of time for the same process.

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