The default download resolution of ERA-Interim data is 0.75x0.75 degrees. If you specify a higher resolution the data will be interpolated.
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When you download ERA-interim data, the grid points are projected into a Cartesian lat/long grid. The default horizontal resolution of the output is 0.75x0.75 degrees, approximating the irregular grid spacing on the Gaussian grid.
If you specify a different output resolution, the system does not use more input points, it merely interpolates the same data to a higher resolution. This makes the output look smoother, but does not increase the accuracy or the precision of the data.