Development of an analytical probabilistic model to estimate runoff event volumes in South Korea

Abstract

• A lognormal distribution best represents the rainfall characteristics of South Korea. • An analytical probabilistic model (APM) for lognormal distribution is developed. • The return period of APM is overestimated due to the seasonal rainfall distribution. • The APM adjustment magnitudes and the seasonal rainfall distributions are correlated. This study showed that the complex rainfall characteristics of South Korea, where rainfall is concentrated during a specific period, are poorly represented with a simple single parameter distribution. Thus, a two-parameter lognormal distribution that best represents the rainfall characteristics of South Korea was proposed by comparing four different distributions. Using this distribution, this study developed a suitable analytical probabilistic model (APM) to simulate runoff event volumes in South Korea and suggested an APM parameter-adjustment method based on rainfall characteristics. Thirty-year rainfall data recorded at ten stations were grouped based on the interevent time definition (IETD) of each station. With the grouped rainfall events, the probability density function (PDF) of the lognormal distribution was confirmed to best fit the rainfall event characteristic histograms in South Korea, including those of the rainfall event volume, duration, and interevent time. The APM was developed by deriving the PDF of the runoff event volume with a lognormal distribution, and a frequency analysis was performed based on the runoff event volume obtained by the APM and the Storm Water Management Model (SWMM) to verify the suitability of the derived model. The runoff event volumes output by the APM were compared with the runoff event volumes simulated by the SWMM. The exceedance probabilities and return periods output by the developed APM with a lognormal distribution were very close to the SWMM results. However, the return periods output by the APM were overestimated, and adjustment parameters were needed to match the outputs to the SWMM results. This study found a strong correlation between the adjustment parameters and the coefficients of variation in the average monthly rainfall. This result suggested that model parameter adjustments are necessary before applying an APM to rainfall datasets with large coefficients of variation in average monthly rainfall data.