boundary conditions for differentiate()

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:

# 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:

data.differentiate('X', BCs='periodic')

We may also specify different kind of BCs at the two boundaries:

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.

[dcherian]

+1 for xgcm.

On the xarray side, I think we should just recommend composing pad with diff or differentiate. We’ll need to add a “extrapolate” option for the padded coordinate variables for this to work.

[jbusecke]

yes all of the grid methods (grid.diff etc) are now internally using grid_ufuncs. The axis methods are still going through the old code path, but will be deprecated soon! Please let us know how you get along with the new functionality, we are very curious for user feedback!