What is quantile mapping?
In short: Quantile Mapping (QM) corrects a modeled value by locating its cumulative probability in the model distribution and mapping that probability to the observed distribution. Unlike a mean-only correction, it can adjust multiple parts of the distribution. Its performance depends on the calibration sample, distribution treatment, and handling of values outside the historical range.
The mapping step
Historical GCM data and observations are used to build their cumulative distribution functions. For a model value at probability p, QM returns the observed value associated with the same probability p.
Practical considerations
Precipitation needs special treatment for dry days and very small modeled amounts, while temperature is commonly treated as a continuous variable. Quantile mapping should be calibrated and validated with comparable time steps, seasons, and units.
Apply Quantile Mapping to CMIP5 or CMIP6 series in SD-GCM alongside Delta and EQM.