Is your feature request related to a problem?

I need to take centered finite difference of data of length N along the dimension 'X', with boundary conditions (BCs) specified in flexible ways. Before this, we need to pad data with BCs (length becoming N+2) so that the indicing will not be out-of-range.

Commonly used BCs are: 1. fixed - fill with fixed values so derivatives at BCs are (BC - data[-1])/dx and (data[0] - BC)/dx; 2. extend - fill BCs with second outer-most values so that derivatives at BCs are exactly zero; 3. periodic - fill BCs cyclic so that the derivatives are also cyclic.

Describe the solution you'd like

The implementation of differentiate('X') would be like: ```python

padded with BCs into N+2

data_pad = pad_BCs(data, type='periodic')

it is safe to take finite difference

for i in range(len(data)) diff[i] = data_pad [i+1] - data_pad [i-1] ```

The pad_BCs function could be easily implemented with np.pad() function.

Then we can call: python data.differentiate('X', BCs='periodic') We may also specify different kind of BCs at the two boundaries:

python data.differentiate('X', BCs=['extend', 'fixed'], fill_values=0)

Describe alternatives you've considered

No response

Additional context

I am not clear how differentiate() is implemented and just want to know if this can be implemented in a straightforward way.

When I try to iterate over the object grouped returned by groupby_bins, I found that the empty group is missing silently. Here is a simple case: ```python array = xr.DataArray(np.arange(4), dims='dim_0')

one of these bins will be empty

bins = [0,4,5] grouped = array.groupby_bins('dim_0', bins)

for i, group in enumerate(grouped): print(str(i)+' '+group) ``` When a bin contains no samples (bin of (4, 5]), the empty group will be dropped. Then how to iterate over the full bins even when some bins contain nothing? I've read this related issue #1019. But my case here need the correct order in grouped and empty groups need to be iterated over.

What happened?

Given a DataArray da, I try to plot with python da.plot.pcolormesh(shading='flat') and it works well. But if I change shading to 'gouraud', it reports ``` python C:\ProgramData\Anaconda3\lib\site-packages\matplotlib\axes_axes.py in _pcolorargs(self, funcname, shading, args, *kwargs) 5709 else: # ['nearest', 'gouraud']: 5710 if (Nx, Ny) != (ncols, nrows): -> 5711 raise TypeError('Dimensions of C %s are incompatible with' 5712 ' X (%d) and/or Y (%d); see help(%s)' % ( 5713 C.shape, Nx, Ny, funcname))

TypeError: Dimensions of C (256, 512) are incompatible with X (513) and/or Y (257); see help(pcolormesh) ```

Not sure if this relates to xarray or matplotlib.

What did you expect to happen?

python da.plot.pcolormesh(shading='gouraud') should works well as python da.plot.pcolormesh(shading='flat')

Minimal Complete Verifiable Example

```Python import xarray as xr

ds = xr.tutorial.open_dataset('air_temperature') ds.air[0].plot.pcolormesh(shading='gouraud') ```

Relevant log output

```Python C:\ProgramData\Anaconda3\lib\site-packages\matplotlib\axes_axes.py in _pcolorargs(self, funcname, shading, args, *kwargs) 5709 else: # ['nearest', 'gouraud']: 5710 if (Nx, Ny) != (ncols, nrows): -> 5711 raise TypeError('Dimensions of C %s are incompatible with' 5712 ' X (%d) and/or Y (%d); see help(%s)' % ( 5713 C.shape, Nx, Ny, funcname))

TypeError: Dimensions of C (25, 53) are incompatible with X (54) and/or Y (26); see help(pcolormesh) ```

Anything else we need to know?

No

Environment

INSTALLED VERSIONS

commit: None python: 3.8.11 (default, Aug 6 2021, 09:57:55) [MSC v.1916 64 bit (AMD64)] python-bits: 64 OS: Windows OS-release: 10 machine: AMD64 processor: Intel64 Family 6 Model 60 Stepping 3, GenuineIntel byteorder: little LC_ALL: None LANG: None LOCALE: ('Chinese (Simplified)_China', '936') libhdf5: 1.12.1 libnetcdf: 4.8.1

xarray: 0.19.0 pandas: 1.3.1 numpy: 1.20.3 scipy: 1.6.2 netCDF4: 1.5.8 pydap: installed h5netcdf: 0.12.0 h5py: 3.4.0 Nio: None zarr: 2.8.1 cftime: 1.6.0 nc_time_axis: None PseudoNetCDF: None rasterio: None cfgrib: 0.9.9.1 iris: None bottleneck: 1.3.2 dask: 2021.08.0 distributed: 2021.08.0 matplotlib: 3.4.2 cartopy: 0.18.0 seaborn: 0.11.2 numbagg: None pint: None setuptools: 52.0.0.post20210125 pip: 21.0.1 conda: 4.11.0 pytest: 6.2.4 IPython: 7.26.0 sphinx: 4.0.2

Not sure if this has been asked.

I have a sea surface temperature (SST) DataArray (monthly data) and want to use it to define El Nino. An El Nino event is defined by a five consecutive 3-month running mean of SST anomalies in the Niño 3.4 region that is above the threshold of 0.5°C. I know I can use roll object to get the 3-month running mean. But how to meet the requirement of five-consecutive months? Is there a simple way to do this using xarray's API?