Is your feature request related to a problem?

I was making sure the test in #6832 failed on main, when it did I wrote a few lines in the what's new file but forgot switching back to the other branch and accidentally pushed directly to main. :(

Describe the solution you'd like

I think it's best if we require a pull request for merging. We seem to pretty much do this anyway.

Seems to be this setting if I understand correctly:

Describe alternatives you've considered

No response

Additional context

No response

Hello,

I would like an option in da.interp()that instead of returning NaNs during extrapolation returns the data corresponding to the end of the breakpoint data set range.

One way to do this is to limit the new coordinates to the array coordinates minimum and maximum value, I did a simple example with this solution down below. I think this is a rather safe way as we are just modifying the inputs to all the various interpolation classes that xarray is using at the moment. But it does look a little weird when printing the extrapolated value, the coordinates shows the limited value instead of the requested coordinates. Maybe this can be handled elegantly somewhere in the source code?

MATLAB uses this quite frequently in their interpolation functions: * https://mathworks.com/help/simulink/ug/methods-for-estimating-missing-points.html * https://mathworks.com/help/simulink/slref/2dlookuptable.html

MCVE Code Sample

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

def interp(da, coords, extrapolation='clip'): """ Linear interpolation that clips the inputs to the coords min and max value.

Parameters
----------
da : DataArray
    DataArray to interpolate.
coords : dict
    Coordinates for the interpolated value.
"""
if extrapolation == 'clip':
    for k, v in da.coords.items():
        coords[k] = np.maximum(coords[k], np.min(v.values))
        coords[k] = np.minimum(coords[k], np.max(v.values))

return da.interp(coords)

Create coordinates:

x = np.linspace(1000, 6000, 4) y = np.linspace(100, 1200, 3)

Create data:

X = np.meshgrid(*[x, y], indexing='ij') data = X[0] * X[1]

Create DataArray:

da = xr.DataArray(data=data, coords=[('x', x), ('y', y)], name='data')

Attempt to extrapolate:

datai = interp(da, {'x': 7000, 'y': 375}) ```

Expected Output

python print(datai) <xarray.DataArray 'data' ()> array(2250000.) Coordinates: x float64 6e+03 y float64 375.0

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