The command line programs in this repository use the bias adjustment and downscaling functionality in xclim.
A typical quantile delta change workflow using xclim starts by calculating the adjustment factors for each quantile:
from xclim import sdba
QDM = sdba.QuantileDeltaMapping.train(
da_sim, da_hist, nquantiles=100, group="time.month", kind="+"
)The group determines the timescale for the adjustment factors
(see grouping for options)
and the kind can be additive or multiplicative.
In this case adjustment factors for each month are calculated by
taking the difference between the quantiles from a future experiment (da_sim)
and an historical experiment (da_hist).
The resulting xarray Dataset (QDM.ds) contains the adjustment factors (af).
It can be useful to plot these adjustment factors to understand the climate signal
between the two experiments.
The next step is to apply the adjustment factors to a dataset of interest.
da_qq = QDM.adjust(da_ref, interp="nearest") For each value in the observational dataset (da_ref),
a corresponding quantile is calculated
(e.g. a 20C day might be the 0.6 quantile)
and then xclim looks up the nearest (interp="nearest") adjustment factor to that quantile in af
and applies it to that observational value.
It is also possible to use linear or cubic interpolation (e.g. interp="linear")
instead of just picking the nearest adjustment factor,
although often it makes very little difference to the end result.
(See Wang and Chen (2013) for an explanation of why
non-parametric methods like linear and cubic interpolation are preferred to
fitting a parametric distribution.)
According to the documentation,
the interpolation is done between quantiles (i.e. if a data value falls between two quantiles)
and also between adjustment factors to avoid discontinuities.
With respect to the latter, the adjustment factor interpolation is performed by
xclim.sdba.utils.interp_on_quantiles,
which in the two dimensional case (e.g. with time.month grouping) uses
scipy.interpolate.griddata
to smooth out the two dimensional (quantile, month) af field.
From playing around with the different interpolation options,
it appears that the two dimensional interpolation is cyclic
(e.g. January values are aware of nearby December values).