Replace polynomial in CRU downscaling with piecewise linear

[fabern]

The CRU dataset is downscaled from the monthly observations to daily observations.
Some variables (e.g. temperature) use polynomial interpolation for that.
This can give rise to strange patterns, e.g. see below the seasonal patterns of daily minimum temperature for the years 1901 to 2023 at a Swiss site.

The differences might be too small to be relevant for vegetation simulations.
Nevertheless, I am wondering whether a simple piecewise linear interpolation would not be better behaved.
Is there a strong justification of the polynomial approach? Otherwise, I would suggest to change this to something linear.

Furthermore, a linear interpolation would have the advantage that the interpolated values are guaranteed to lie within the extremes of the observed ones. This could help avoid potential numerical issues.

[stineb]

Could you plot the time series (all years)?

[fabern]

This is the time series 1901 to 2023.

Details get a bit lost. What we can see however, is that the down-scaled, interpolated time series is not bounded by the extremes of the monthly averages.

This extensions is not a problem per se. After all, the down-scaled data should be more varying than the average. But the shape in the first plot just looks strange.