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

Versions

Output of `xr.show_versions()`

INSTALLED VERSIONS ------------------ commit: None python: 3.7.7 (default, Mar 23 2020, 23:19:08) [MSC v.1916 64 bit (AMD64)] python-bits: 64 OS: Windows OS-release: 10 machine: AMD64 processor: Intel64 Family 6 Model 58 Stepping 9, GenuineIntel byteorder: little LC_ALL: None LANG: en LOCALE: None.None libhdf5: 1.10.4 libnetcdf: None xarray: 0.15.0 pandas: 1.0.3 numpy: 1.18.1 scipy: 1.4.1 netCDF4: None pydap: None h5netcdf: None h5py: 2.10.0 Nio: None zarr: None cftime: None nc_time_axis: None PseudoNetCDF: None rasterio: None cfgrib: None iris: None bottleneck: 1.3.2 dask: 2.13.0 distributed: 2.13.0 matplotlib: 3.1.3 cartopy: None seaborn: 0.10.0 numbagg: None setuptools: 46.1.3.post20200330 pip: 20.0.2 conda: 4.8.3 pytest: 5.4.1 IPython: 7.13.0 sphinx: 2.4.4