What is empirical quantile mapping?
In short: Empirical Quantile Mapping (EQM) maps modeled quantiles to observed quantiles using cumulative distributions estimated directly from the data. It does not require a named theoretical distribution such as Normal or Gamma. This flexibility can represent irregular distributions, although estimates near the tails are limited by the available historical sample.
How EQM differs from general QM
Quantile mapping is the broader method family; implementations may use fitted parametric distributions or empirical distributions. EQM specifically uses ranked observations and model values, with interpolation between empirical quantiles.
When to use it
EQM is useful when a simple theoretical distribution does not describe the variable well. Validation remains essential because sparse extremes, nonstationarity, wet-day handling, and extrapolation choices can influence future corrected values.
SD-GCM includes Empirical Quantile Mapping for downscaling and bias-correcting CMIP5 and CMIP6 data.