Hydrological frequency analysis of large-ensemble climate simulation data using control density as a statistical control

Uncertainty in hydrological statistics estimated with finite observations, such as design rainfall, can be quanti‐ fied as a confidence interval using statistical theory. Ensemble climate data also enables derivation of a confi‐ dence interval. Recently, the database for policy decision making for future climate change (d4PDF) was developed in Japan, which contains dozens of simulated extreme rain‐ fall events for the past and 60 years into the future, allow‐ ing the uncertainty of design rainfall to be quantified as a confidence interval. This study applies an order statistics distribution to evaluate uncertainty in the order statistics of extreme rainfall from the perspective of mathematical theory, while a confidence interval is used for uncertainty evaluation in the probability distribution itself. An advan‐ tage of the introduction of an order statistics distribution is that it can be used to quantify the goodness-of-fit between observation and ensemble climate data under the condition that the extreme value distribution estimated from observa‐ tions is a true distribution. The order statistics distribution is called the control density distribution, which is derived from characteristics that order statistics from standard uni‐ form distribution follows beta distribution. The overlap ratio of the control density distribution and frequency dis‐ tributions derived from ensemble climate data is utilized for evaluation of the degree of goodness-of-fit for both data.