The finding of the optimal radius of influence makes assumption on the ordering of the dimensions in the longitude array

Code Sample, a minimal, complete, and verifiable piece of code

The problem is well illustrated by reading and trying to remap the AWS tesdata:

>>> from satpy import Scene
>>> FILENAMES = ["/home/a000680/data/aws_testdata_from_nigel/W_XX-OHB-Stockholm,SAT,AWS1-MWR-1B-RAD_C_OHB_20230816120142_G_D_20240115111111_20240115125434_T_B____radsim.nc"]
>>> AREAID = 'eurol'
>>> scn = Scene(filenames=FILENAMES, reader='aws_l1b_nc')
>>> scn.load(['1'])
>>> local = scn.resample(AREAID)
>>> local.show('1')
Could not calculate source definition resolution

See the comments in the Satpy PR here: https://github.com/pytroll/satpy/pull/2565

In the method to determine the optimal radius of influence to be used when reampping data (https://github.com/pytroll/pyresample/blob/6a8afc0085e0b4269f00991ab79fe1b3766bb817/pyresample/geometry.py#L664) the assumption is that the first dimension on the longitude array dscribes the scanlines/rows of the (e.g. channel) dataset.

The specific code lines that should be adapted in case that self.lons is an xarray.DataArray is this part I believe:

        rows = self.shape[0]
        start_row = rows // 2  # middle row
        src = CRS('+proj=latlong +datum=WGS84')
        if radius:
            dst = CRS("+proj=cart +a={} +b={}".format(radius, radius))
        else:
            dst = CRS("+proj=cart +ellps={}".format(ellps))
        # simply take the first two columns of the middle of the swath
        lons = self.lons[start_row: start_row + 1, :2]
        lats = self.lats[start_row: start_row + 1, :2]

I would propose something like this instead:

        rows = self.lons['y'].shape[0]
        start_row = rows // 2  # middle row
        src = CRS('+proj=latlong +datum=WGS84')
        if radius:
            dst = CRS("+proj=cart +a={} +b={}".format(radius, radius))
        else:
            dst = CRS("+proj=cart +ellps={}".format(ellps))
        # simply take the first two columns of the middle of the swath
        lons = self.lons.sel(y=start_row)[:2]
        lats = self.lats.sel(y=start_row)[:2]

Problem description

[this should also explain why the current behaviour is a problem and why the
expected output is a better solution.]

Expected Output

Actual Result, Traceback if applicable

Versions of Python, package at hand and relevant dependencies