I found this HDF5 viewer tool that might be helpful. It looks like those .h5 files from the Earthdata website each contain multiple subdatasets, along with metadata. I’m not sure why ArcGIS isn’t showing it correctly, but GDAL does have a HDF5 driver, so you can access the contents via the command line.
The data appears to have no defined projection, but the HDF5 file contains a
WestBoundingCoordinate under StandardMetadata/. I’m not sure which corner it’s indexed from…
Here’s an example of how you could access the file and convert it to a more typical raster format using Python and GDAL:
Python 3.7.9 (default, Aug 31 2020, 07:22:35)
[Clang 10.0.0 ] :: Anaconda, Inc. on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> import gdal
>>> import numpy
>>> h5_path = '/Users/emily/Downloads/ECOSTRESS_L3_ET_PT-JPL_12208_008_20200831T055358_0601_01.h5'
>>> dataset = gdal.OpenEx(h5_path, gdal.OF_RASTER)
<osgeo.gdal.Dataset; proxy of <Swig Object of type 'GDALDatasetShadow *' at 0x7f8c981e0ed0> >
>>> subdatasets = dataset.GetSubDatasets()
>>> subdataset_path = subdatasets
>>> array = gdal.Open(subdataset_path).ReadAsArray()
>>> raster_driver = gdal.GetDriverByName('GTIFF') # export to GeoTIFF format
>>> y, x = array.shape
>>> new_raster = raster_driver.Create('/Users/emily/Documents/out.tif', x, y, 1, gdal.GDT_Float64)
>>> new_band = new_raster.GetRasterBand(1)
You would still need to figure out how to set the origin, projection and nodata value appropriately. Hope that helps!