Comparison Study on the Various Forms of Scale Parameter for the Nonstationary Gumbel Model

Abstract

Most nonstationary frequency models are defined as the probability models containing the time-dependent parameters. For frequency analysis of annual maximum rainfall data, the Gumbel distribution is generally recommended in Korea. For the nonstationary Gumbel models, the time-dependent location and scale parameters are defined as linear and exponential relationship, respectively. The exponentially time-varying scale parameter of nonstationary Gumbel model is generally used because the scale parameter should be positive. However, the exponential form of scale parameter occasionally provides overestimated quantiles. In this study, various forms of time-varying scale parameters such as exponential, linear, and logarithmic forms were proposed and compared. The parameters were estimated based on the method of maximum likelihood. To compare the accuracy of each scale parameter, Monte Carlo simulation was performed for various conditions. Additionally, nonstationary frequency analysis was conducted for the sites which have more than 30 years data with a trend in rainfall data. As a result, nonstationary Gumbel model with exponentially time-varying scale parameter generally has the smallest root mean square error comparing with another forms.

Effect of warming climate on extreme daily rainfall depth using non-stationary Gumbel model with temperature co-variate

“…Several methods have been proposed to deal with time series non-stationarity (Cunha et al 2011;Yilmaz & Perera 2013;Jang et al 2015;Moon et al 2016), and many studies on changes in design rainfall depth or its return level under non-stationary conditions have been conducted (Salvadori & DeMichele 2010;Graler et al 2013;Hassanzadeh et al 2013;Salas & Obeysekera 2013;Shin et al 2014;Choi et al 2019). In order to explain the non-stationary in the frequency analysis and to examine the changes in the extreme rainfall probability distribution with temperature rise, studies have been conducted to express the parameters of the probability distribution using co-variates (Coles et al 2001).…”

Uncertainty in nonstationary frequency analysis of South Korea's daily rainfall peak over threshold excesses associated with covariates

“…Several methods have been proposed to address nonstationarities in the time series (Cunha et al, 2011;Yilmaz and Perera, 2013;Jang et al, 2015;Moon et al, 2016), and many studies have been conducted to examine changes in design rainfall depth or return levels under nonstationary conditions (Salvadori and DeMichele, 2010;Graler et al, 2013;Hassanzadeh et al, 2013;Salas and Obeysekera, 2013;Shin et al, 2014;Choi et al, 2019). Looking at the probability distributions and parameters applied to the above studies, most of the nonstationary frequency analysis is performed by expressing specific parameters of the Gumbel or generalized extreme value (GEV) distribution as a function of the covariate including time (Kim et al, 2017).…”