[Questions] Seasonal QuantileDeltaMapping adjustment with linear interpolation leads to jumps in the timeseries

[saschahofmann]

Setup Information

• Xclim version: 0.54.0

Context

Moved from PR #2019 and best summarised by @coxipi:

Basic interpolation of EmpiricalQuantileMapping (EQM): Discrete data {sim_q, af_q} -> Interp to continuous function: af = f(sim).
Basic interpolation of QuantileDeltaMapping: Discrete data {q, af_q} -> Interp to continuous function: af = f(rank).
After we add a time grouping index in the mix, e.g. for EQM the discrete data is {season, sim_q,af_q}. The idea is to interpolate this to a bivariate function af = f(dayofyear, sim). In this case, it makes sense to think of the sim values as being distributed along dayofyear, we have the orginal timeseries for these values.
If we try this in QDM, the final function will look like af = f(dayofyear, rank). But the notion of rank is dependent on the time grouping. Saying that we want a mix of the adjustment of season-1 and season-2 when we are the boundary of the two seasons is a bit weird, since the ranks were computed for season-1 or season-2, but not the period in between.
To give a concrete example, consider tasmax on Feb.28. Its rank is computed in DJF. But if we included it in MAM, it would be a lower rank. We are saying that we have an interpolated continuous function that we want to apply on those ranks, but these values are still segmented, there are four groups of ranks in a year. Say Feb.28 of year 20XX is rank=0.9, but in MAM would be rank=0.3. Should apply the transformation for a rank in-between?

Steps To Reproduce

No response