diff --git a/rio_tiler/io/xarray.py b/rio_tiler/io/xarray.py
index 7541458c..d8916d62 100644
--- a/rio_tiler/io/xarray.py
+++ b/rio_tiler/io/xarray.py
@@ -83,11 +83,14 @@ def __attrs_post_init__(self):
                 "Dataset doesn't have CRS information, please add it before using rio-tiler (e.g. `ds.rio.write_crs('epsg:4326', inplace=True)`)"
             )
 
+        # adds half x/y resolution on each values
+        # https://github.com/corteva/rioxarray/issues/645#issuecomment-1461070634
+        xres, yres = map(abs, self.input.rio.resolution())
         if self.crs == WGS84_CRS and (
-            round(self.bounds[0]) < -180
-            or round(self.bounds[1]) < -90
-            or round(self.bounds[2]) > 180
-            or round(self.bounds[3]) > 90
+            self.bounds[0] + xres / 2 < -180
+            or self.bounds[1] + yres / 2 < -90
+            or self.bounds[2] - xres / 2 > 180
+            or self.bounds[3] - yres / 2 > 90
         ):
             raise InvalidGeographicBounds(
                 f"Invalid geographic bounds: {self.bounds}. Must be within (-180, -90, 180, 90)."
@@ -116,12 +119,16 @@ def maxzoom(self):
     @property
     def band_names(self) -> List[str]:
         """Return list of `band names` in DataArray."""
-        return [str(band) for d in self._dims for band in self.input[d].values]
+        return [str(band) for d in self._dims for band in self.input[d].values] or [
+            "value"
+        ]
 
     def info(self) -> Info:
         """Return xarray.DataArray info."""
-        bands = [str(band) for d in self._dims for band in self.input[d].values]
-        metadata = [band.attrs for d in self._dims for band in self.input[d]]
+        bands = [str(band) for d in self._dims for band in self.input[d].values] or [
+            "value"
+        ]
+        metadata = [band.attrs for d in self._dims for band in self.input[d]] or [{}]
 
         meta = {
             "bounds": self.bounds,
diff --git a/tests/test_io_xarray.py b/tests/test_io_xarray.py
index b6b907f4..85c999b4 100644
--- a/tests/test_io_xarray.py
+++ b/tests/test_io_xarray.py
@@ -485,3 +485,43 @@ def test_xarray_reader_invalid_bounds_crs():
     data.rio.write_crs("epsg:4326", inplace=True)
     with XarrayReader(data):
         pass
+
+
+def test_xarray_reader_no_dims():
+    """test XarrayReader with 2D dataset."""
+    arr = numpy.arange(0.0, 33 * 35).reshape(33, 35)
+    data = xarray.DataArray(
+        arr,
+        dims=("y", "x"),
+        coords={
+            "x": numpy.arange(-170, 180, 10),
+            "y": numpy.arange(-80, 85, 5),
+        },
+    )
+    data.attrs.update({"valid_min": arr.min(), "valid_max": arr.max()})
+
+    data.rio.write_crs("epsg:4326", inplace=True)
+    with XarrayReader(data) as dst:
+        assert dst.minzoom == dst.maxzoom == 0
+        info = dst.info()
+        assert info.bounds == dst.bounds
+        crs = info.crs
+        assert rioCRS.from_user_input(crs) == dst.crs
+        assert info.band_metadata == [("b1", {})]
+        assert info.band_descriptions == [("b1", "value")]
+        assert info.height == 33
+        assert info.width == 35
+        assert info.count == 1
+        assert info.attrs
+
+    with XarrayReader(data) as dst:
+        stats = dst.statistics()
+        assert stats["value"]
+        assert stats["value"].min == 0.0
+
+        img = dst.tile(0, 0, 0)
+        assert img.count == 1
+        assert img.width == 256
+        assert img.height == 256
+        assert img.band_names == ["value"]
+        assert img.dataset_statistics == ((arr.min(), arr.max()),)