What happened?

When aggregating a dataset over specified dimensions I don't expect variables which don't have those dimensions to be aggregated.

What did you expect to happen?

When a weighting is applied to the aggregation, variables which do not have the aggregation dimensions are nevertheless aggregated. Presumably because the weights get broadcast across those variables. Perhaps this is the intended behavior but it seems surprising to me and should at least be documented I think.

Minimal Complete Verifiable Example

```Python import xarray as xr import numpy as np

var1 = np.ones((2, 2, 3))

var2 = np.ones((3))

lon = np.arange(4).reshape(2, 2) lat = np.arange(4).reshape(2, 2)

ds = xr.Dataset( { "temperature": (["x", "y", "time"], var1), "precipitation": (["time"], var2), }, coords={ "lon": (["x", "y"], lon), "lat": (["x", "y"], lat), "time": np.arange(3), }, )

print(ds.sum(['x', 'y']))

Precipitation (with no x or y dimension) is not summed over, leading to values [1. 1. 1.]

print(ds.weighted(xr.ones_like(ds['temperature'])).sum(['x', 'y']))

Precipitation is now summed over, leading to values [4. 4. 4.]

```

MVCE confirmation

• [X] Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
• [X] Complete example — the example is self-contained, including all data and the text of any traceback.
• [X] Verifiable example — the example copy & pastes into an IPython prompt or Binder notebook, returning the result.
• [X] New issue — a search of GitHub Issues suggests this is not a duplicate.
• [X] Recent environment — the issue occurs with the latest version of xarray and its dependencies.

Relevant log output

No response

Anything else we need to know?

No response

Environment

Closes #1790

This is a bit empty at the moment so feel free to add any snippets you think would be useful :-)

Would there be interest in adding a 'cookbook' section to the docs a-la Pandas? The current Recipes section might then be better renamed as Gallery?

It's useful for the kind of thing which isn't a full-fledged example, but might be useful nonetheless. I'll hapily put together a pull-request if there's interest.

Code Sample, a copy-pastable example if possible

```python import xarray as xr import numpy as np

da = xr.DataArray(np.random.rand(15), dims=['latitude'], coords={'latitude':np.linspace(90, -90, 15)})

This gives an empty latitude slice

print(da.sel(latitude=slice(20, 60)))

After converting the DataArray to dask...

da=da.chunk()

...this throws a ValueError due to 'conflicting sizes'

print(da.sel(latitude=slice(20, 60))) ```

Problem description

I would expect the dask based DataArray to return an empty slice just as the numpy one does.

Although arguably it would be nicer if both returned the latitude values between 20 and 60 - regardless of the direction of the coordinate. Perhaps the sel method could check whether the coordinate is increasing or decreasing?

Output of xr.show_versions()

```python ds = xr.Dataset({"test": np.arange(0, 5, dtype='float16')}) ds.to_netcdf('test.nc')

```

This fails because the float16 type doesn't exist for NetCDF files, throwing an TypeError: illegal primitive data type.

It might be nice if the xarray netCDF engine promoted this to float32 instead.

Output of xr.show_versions()

• [x] Closes #621 and #37 - finishes #814
• [x] Tests added / passed
• [x] Passes git diff upstream/master **/*py | flake8 --diff
• [x] Fully documented, including whats-new.rst for all changes and api.rst for new API

Code Sample, a copy-pastable example if possible

```python

Create basic Dataset

import numpy as np import pandas as pd import xarray as xr

temp = 15 + 8 * np.random.randn(2, 2, 3)

precip = 10 * np.random.rand(2, 2, 3) lon = [[-99.83, -99.32], [-99.79, -99.23]] lat = [[42.25, 42.21], [42.63, 42.59]]

for real use cases, its good practice to supply array attributes such as

units, but we won't bother here for the sake of brevity

ds = xr.Dataset({'temperature': (['x', 'y', 'time'], temp), 'precipitation': (['x', 'y', 'time'], precip)}, coords={'lon': (['x', 'y'], lon), 'lat': (['x', 'y'], lat), 'time': pd.date_range('2014-09-06', periods=3), 'reference_time': pd.Timestamp('2014-09-05')})

Both of these throw attribute errors

ds.notnull()

ds.isnull()

```

Problem description

The above methods throw AttributeError: 'Variable' object has no attribute '_constructor' errors when called on Datasets. It's not clear if this operation is currently supported, but if it's not then it probably shouldn't be exposed through the API.

Expected Output

Dataset of boolean DataArrays indicating null-ness.

Output of xr.show_versions()