I have a program where I open a .nc file, do something with it, and want to reopen it later, after an external program has been modifying it, and my issue is that the caching mechanism will give me the already opened version of the file, and not the refreshed version on the disk. To demonstrate this behavior, let's say you have two files: bla.nc and bla_mod.nc, with different content:

```python import shutil import xarray as xr

a = xr.open_dataset("bla.nc")

Simulate external process modifying bla.nc while this script is running

shutil.copy("bla_mod.nc", "bla.nc")

a.close() # this is the only thing that WOULD make it work!

b = xr.open_dataset("bla.nc")

Here I would expect b to be different than a, but it is not

```

I understand that the file SHOULD be closed (or that I should use a context manager) in an ideal world, and that if so it would work but let's say it is not (perhaps we forgot, or we're simply being lazy).

At first I thought that I could use the cache parameter to open_dataset for that purpose, but after studying the code, I discovered that it is connected to a different caching mechanism than the one that is at play here.

After some experiments to better understand the code, I came to the conclusion that the only way my particular use case could be supported (that is, without using an explicit close or a context manager, which is, in itself, debatable, I admit) is that if the underlying netCDF4._netCDF4.Dataset file object is explicitly closed, like it is when flushed out of the cache:

https://github.com/pydata/xarray/blob/5735e163bea43ec9bc3c2e640fbf25a1d4a9d0c0/xarray/backends/file_manager.py#L222

Given that I cannot really see how, in the particular case where the user calls open_dataset for a second time, she wouldn't want the fresh version on disk, it made me think that a fix for that behavior would be to simply explicitly flush the cache immediately after the CachingFileManager for a particular dataset has been created, as I do here:

https://github.com/pydata/xarray/compare/master...cjauvin:netcdf-caching-bug

Because I admit that this looks weird at first sight (why close an object immediately after having created it?), I imagine that a better option would probably be to add a boolean option to the CachingFileManager, in order to make it optional (something like flush_and_close_file_if_already_present).

I think this subtle change would result in a more coherent experience with the exact use case that I present, but admittedly, I didn't study the overall code deeply enough to be certain that it couldn't result in unwanted side effects for some other backends.

• [x] Tests added
• [x] Passes pre-commit run --all-files
• [x] User visible changes (including notable bug fixes) are documented in whats-new.rst
• [x] New functions/methods are listed in api.rst

This is a follow-up to https://github.com/pydata/xarray/pull/5870/, which adds a weighted quantile function.

The question of how to precisely define the weighted quantile function is surprisingly complex, and this implementation offers a compromise in terms of simplicity and compatibility:

• The only interpolation method supported is the so-called "Type 7", as explained in https://aakinshin.net/posts/weighted-quantiles/, which proposes an R implementation, that I have adapted
• It turns out that Type 7 is apparently the most "popular" one, at least in the Python world: it corresponds to the default linear interpolation option of numpy.quantile (https://numpy.org/doc/stable/reference/generated/numpy.quantile.html) which is also the basis of xarray's already existing non-weighted quantile function
• I have taken care in making sure that the results of this new function, with equal weights, are equivalent to the ones of the already existing, non-weighted function (when used with its default interporlation option)

The interpolation question is so complex and confusing that entire articles have been written about it, as mentioned in the blog post above, in particular this one, which establishes the "nine types" taxoxomy, used, implicitly or not, by many software packages: https://doi.org/10.2307/2684934.

The situation seems even more complex in the NumPy world, where many discussions and suggestions are aimed toward trying to improve the consistency of the API. The current non-weighted situation has the 9 options, as well as 4 extra legacy ones: https://github.com/numpy/numpy/blob/376ad691fe4df77e502108d279872f56b30376dc/numpy/lib/function_base.py#L4177-L4203

This PR cuts the Gordian knot by offering only one interpolation option, but.. given that its implementation is based on apply_ufunc (in a very similar way to xarray's already existing non-weighted quantile function, which is also using apply_ufunc with np.quantile), in the event that np.quantile ever gains a weights keyword argument, it would be very easy to swap it. That way, xarray's weighted quantile could lose a little bit of code, and gain a plethora of interpolation options.

• [x] Tests added
• [x] User visible changes (including notable bug fixes) are documented in whats-new.rst
• [x] New functions/methods are listed in api.rst

This follows https://github.com/pydata/xarray/pull/2922 to add var, std and sum_of_squares to DataArray.weighted and Dataset.weighted. I would also like to add weighted quantile, eventually.