“Frequency analyses for stationary and nonstationary hydrological data”
Jun-Haeng HEO
Professor, School of Civil & Environmental Engineering,
Yonsei University, Seoul, Korea
Frequency analysis has been widely used to provide the magnitude of extreme
events and occurrence frequency in hydrologic system and the related fields. In general,frequency analyses can be categorized into four parts depending on the methodology
and characteristics of data as shown in Table. In the conventional at-site and regionalfrequency analyses, the hydrological data are assumed to be independent andstationary. The assumption of independence implies that each random variable has thesame probability distribution as the others and all are mutually independent. And theassumption of stationarity implies that the occurrence of samples and the statisticalcharacteristics (e.g., mean and variance) of the observations do not change over time
irrespective of long-term climatic variability and human-induced change. However,
nowadays the nonstationary problem occurs in hydrological processes because of theinherent variability of the oceanic-atmospheric system and the increasing
anthropogenic influences on the climate and environment. In recent years, there has
been a gradual change with the evidences of nonstationary phenomena (e.g., trends ofobservations and long-term variability of hydrological data) and a recognition of theinfluence of climate change and urbanization on hydrological processes.
MethodData type
Stationary
NonstationaryAt-site frequency analysis(ASFA) Regional frequency analysis (RFA)
Stationary ASFA
Nonstationary ASFA

Stationary RFA
Nonstationary RFA

For nonstationary at-site application, nonstationary frequency analysis employs various
dependent covariates or moments such as time, oceanic-atmospheric components (e.g.
ENSO, SOI, SST, PDO, and NAO) and statistics (e.g. mean and variance). Several
probability distributions such as the Gumbel, GEV, generalized Pareto, generalized
logistic models have been used for nonstationary at-site frequency analysis with severalcovariates. For regional frequency analysis, the index flood method has been widelyused since 1960. And this method can be applied to stationary and nonstationary
cases. For nonstationary cases, three types of nonstationary index flood method are
possible depending on the variabilities of index and growth curve with time.
It is very important to select an appropriate probability model for applied hydrologic data.
As the goodness of fit test, the chi-square, Kolmogorov-Smirnov, Cramer von Mises,
probability plot correlation coefficient, and modified Anderson Darling tests are used forconventional stationary cases. And the Akaike information criterion (AIC), corrected AIC(AICc), Bayesian information criterion (BIC), and likelihood ratio test (LR) have been used
for selecting an appropriate models for nonstationary cases.
In real applications, four types of frequency analyses are applied to stationary andnonstationary annual maximum precipitation data from Korea Meteorological
Administration to figure out the performances of those methods based on thestationary and nonstationary Gumbel and/or GEV models with time as covariate. In
addition, four goodness of fit tests such as AIC, AICc, BIC, and LR for nonstationary
cases are compared with each other based on the several slopes and parameter setsusing the Monte Carlo simulation and then the best goodness of fit test isrecommended depending on the nonstationarity, parameters, and sample sizes.