Identifiability of hydrological frequency distributions in L-moment space: correct-selection probability and design-quantile consequence

Abstract Selecting a probability distribution is a routine step in flood and rainfall frequency analysis. However, commonly used three-parameter distributions often overlap in L-moment space and can be difficult to distinguish from typical records. This study examines whether a selected distribution can be identified reliably and whether an incorrect selection leads to a meaningful error in the design estimate. A symmetric Monte Carlo framework was used with five parent and candidate distributions: GEV, GLO, GNO, PE3 and GPA. Four calibration-free selection rules were compared: Anderson–Darling, modified upper-tail Anderson–Darling, Cramér–von Mises and likelihood ranking based on L-moment estimates. Two practical measures were developed: a parent-marginalized identifiability surface and the worst-case design-quantile error due to family confusion. Identifiability is strongly limited by record length. The median probability of correct selection remains below 0.5 until about 150–200 observations, and high-confidence recovery generally requires two to three centuries of record. Identifiability and design consequence are only weakly related. At $$\:n=50$$ and a 100-year return period, 53% of poorly identifiable positions in L-moment space produce errors greater than 10%. The four selection rules differ by less than 3% points in mean correct-selection rate and show the same main failure region, indicating that the limitation is mainly controlled by L-moment geometry and record length rather than by the selection statistic. In a 792-gauge UK river-flow network with a median record length of 54 years, no gauge reaches high-confidence identifiability and only one reaches majority recovery. The longest record in the network (142 years) has an identifiability of 0.496 under Anderson–Darling and the uniform prior, just below majority recovery.