• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1119-1131
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• 2016

The Neyman-Scott Rectangular Pulses Model (NSRPM) is mainly used to construct hourly rainfall series. This model uses a modest number of parameters to represent the rainfall processes and underlying physical phenomena, such as the arrival of storms or rain cells. In NSRPM, the method of moments has often been used because it is difficult to know the distribution of rainfall intensity. Recently, approximated likelihood function for NSRPM has been introduced. In this paper, we propose a hierarchical model for applying a spatial structure to the NSRPM parameters using the approximated likelihood function. The proposed method is applied to summer hourly precipitation data observed at 59 weather stations (Korea Meteorological Administration) from 1973 to 2011.

• The Korean Journal of Applied Statistics
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• v.29 no.5
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• pp.887-896
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• 2016

The Neyman-Scott Rectangular Pulse (NSRP) model is used to model the hourly rainfall series. This model uses a modest number of parameters to represent the rainfall processes and underlying physical phenomena such as the arrival of a storm or rain cells. In this paper, we proposed approximated likelihood function for the NSRP model and applied the proposed method to precipitation data in Seoul.

• Journal of Korea Water Resources Association
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• v.39 no.4 s.165
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• pp.373-382
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• 2006

In this study a theoretical drought severity-duration-frequency analysis is performed based on a simple Rectangular Pulses Poisson Process Model(RPPM). Data set with various durations are prepared for a given truncation level, whose statistics are then derived to be used for parameter estimation. These parameters are then used for the theoretical drought severity-duration-frequency analysis. The analysis is considered for two cases; one is to consider the overlap probability and the other is not. The drought severity of considering the overlap probability increases more as the return period increases. However, the overlap probability itself decreases as the duration increases, which is because the occurrence probability of events decreases as the duration increases. Also, if the duration increases, the events rarely or even not occur, since parameters of the model cannot be estimated in those cases, so the drought severity may not be computed. This is an obvious limitation of the simple RPPM. In this study the return periods of the important drought events occurred in Seoul are estimated using the results of the study. If the return period of an event is assumed to be the longest one among those with various durations, the return periods of some important event in Seoul are estimated to be between 14 and 35 years. These return periods are not so long to indicate that these droughts can occur frequently.

• Journal of Korea Water Resources Association
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• v.34 no.6
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• pp.577-586
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• 2001

This study proposes a theoretical methodology for deriving a rainfall intensity-duration- frequency (I-D-F) curve using a simple rectangular pulses Poisson process model. As the I-D-F curve derived by considering the model structure is dependent on the rainfall model parameters estimated using the observed first and second order statistics, it becomes less sensitive to the unusual rainfall events than that derided using the annual maxima rainfall series. This study has been applied to the rainfall data at Seoul and Inchon stations to check its applicability by comparing the two I-D-F carves from the model and the data. The results obtained are as followed. (1) As the duration becomes longer, the overlap probability increases significantly. However, its contribution to the rainfall intensity decreases a little. (2) When considering the overlap of each rainfall event, especially for large duration and return period, we could see obvious increases of rainfall intensity. This result is normal as the rainfall intensity is calculated by considering both the overlap probability and return period. Also, the overlap effect for Seoul station is fecund much higher than that for Inchon station, which is mainly due to the different overlap probabilities calculated using different rainfall model parameter sets. (3) As the rectangular pulses Poisson processes model used in this study cannot consider the clustering characteristics of rainfall, the derived I-D-F curves show less rainfall intensities than those from the annual maxima series. However, overall pattern of both I-D-F curves are found very similar, and the difference is believed to be overcome by use of a rainfall model with the clustering consideration.

• Journal of Korea Water Resources Association
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• v.39 no.5 s.166
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• pp.417-430
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• 2006

In this study, the probability density functions (PDFs) of the rainfall generated by PRPM(Poisson Rectangular Pulse Model) and the runoff simulated by SLRM(Single Linear Reservoir Model) and Nash model, were compared to find out the changes of runoff characteristics due to the change of rainfall characteristics. Effect of rainfall frequency, Intensity, and duration on runoff were evaluated using the PDFs derived. Two basin, small and midium-sized ones, were also selected to find out the effect of basin size. As the results, we found that the arrival time, the intensity, and the duration of rainfall differently influence the runoff characteristics, which could be applied to evaluate the effect of climate change.

• Journal of Korea Water Resources Association
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• v.39 no.9 s.170
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• pp.745-754
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• 2006

This study adopted the Rectangular Pulses Poisson Process Model for the drought severity-duration-frequency analysis to characterize the spatial pattern of drought over the Korean peninsula using the rainfall data of the 59 rain gauge stations. First of all, the drought severity in the southern part of the Korean peninsula was found to be generally high for any return period. This result is consistent for both cases with and without considering the overlap probability of rectangular pulses, which is also valid for longer durations. Comparison with those of observed drought frequency and maximum severity also showed that the result in this study has enough reliability.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.341-341
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• 2012

최근 기후변화로 인한 이상호우의 발생으로 도시유역에서의 홍수피해가 급증하고 있으며 이로 인해 도시유역에서의 설계홍수량 산정이 매우 중요시 되고 있다. 지금까지는 도시유역에서의 설계홍수량을 산정하기 위해 I-D-F 곡선을 이용하고 있으나 현실적으로 시간단위 이하의 관측강우량 자료의 부족으로 인해 신뢰성 있는 시간단위 이하의 설계강우량 산정에 많은 불확실성을 지니고 있다. 도시유역의 경우에는 자연유역에 비해 강우발생시 일반적으로 도달시간이 한 시간 이하이기 때문에 극한 강우사상 즉, 단시간에 집중적으로 많은 양의 강우가 발생 할 경우 시간단위 이하의 강우강도를 이용한 유출해석이 필요하다. 따라서 본 연구에서는 추계학적 강우발생기법을 통해 시간단위 강우시계열자료를 확충한 후 분해기법을 통해 시간단위이하강우를 생성하였다. 이를 위해 Bartlett-Lewis rectangular pulse 모형과 Cascade 분해 기법을 이용하여 5분단위 강우량자료를 모의발생 하였다. 또한 모의치와 관측치를 재현기간별로 비교, 분석하여 그 차이를 확인하였다.

• Journal of Korea Water Resources Association
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• v.44 no.2
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• pp.135-144
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• 2011

Direct parameter estimation method is verified with various models based on Neyman-Scott rectangular pulse model (NSRPM). Also, newly modified NSRPM (NMSRPM) that uses normal distribution is developed. Precipitation data observed by Korea Meteorological Administration (KMA) for 47 years is applied for parameter estimation. For model performance verification, we used statistics, wet ratio and precipitation accumulate distribution of precipitation generated. The comparison of statistics indicates that absolute relative error (ARE)s of the results from NSRPM and modified NSRPM (MNSRPM) are increasing on July, August, and September and ARE of NMNSRPM shows 10.11% that is the smallest ARE among the three models. NMNSRPM simulates the characteristics of precipitation statistics well. By comparing the wet ratio, MNSRPM shows the smallest ARE that is 16.35% and by using the graphical analysis, we found that these three models underestimate the wet ratio. The three models show about 2% of ARE of precipitation accumulate probability. Those results show that the three models simulate precipitation accumulate probability well. As the results, it is found that the parameters of NSRPM, MNSRPM and NMNSRPM are able to be estimated by the direct parameter estimation method. From the results listed above, we concluded that the direct parameter estimation is able to be applied to various models based on NSRPM. NMNSRPM shows good performance compared with developed model-NSRPM and MNSRPM and the models based on NSRPM can be developed by the direct parameter estimation method.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.203-207
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• 2009

Neyman-Scott Rectangular Pulse 모형(NSRPM)은 Poisson process에 기초를 둔 모형으로 수자원분야에서는 강수자료를 생성하는데 널리 쓰이고 있다. NSRPM을 구축하기 위해서는 기존에 관측된 강수 자료를 이용하여 NSRPM의 매개변수를 추정하여야 한다. NSRPM의 매개변수를 추정 시 강수자료의 모멘트와 매개변수로 구성된 모멘트식을 비교하여 매개변수를 추정한다. 기존에 사용된 모멘트를 이용한 NSRPM의 매개변수 추정방법의 경우 매개변수로 구성된 모멘트식을 증명하여야지만 NSRPM의 매개변수를 추정할 수 있다. 또한 증명된 모멘트식이 없는 모멘트 값의 경우 매개변수 추정 시 사용하지 못하는 단점이 있다. 이런 한계점으로 인하여 NSRPM 의 수정 및 추정이 어려워 NSRPM은 널리 사용되지 못하고 있다. 본 연구에서는 매개변수 추정방법의 따른 한계점을 극복하고자 직접적인 매개변수 추정방법을 제안하였다. 직접적인 매개변수 추정방법은 모멘트 식을 이용하지 않고 생성된 자료를 이용하여 직접적으로 매개변수를 추정하는 방법이다. 본 연구의 대상지점은 금강유역의 대전으로 선정하였으며, 사용된 자료는 기상청에서 운영하는 대전 지상관측소 강수자료를 사용하였다. 총 39년의 자료를 이용하여 각 방법을 이용하여 매개변수를 추정하였다. 실험결과 직접적인 추정방법이 기존 매개변수 추정방법보다 더 정확한 매개변수를 추정하는 것을 확인 할 수 있었다.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.710-710
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• 2012

구형펄스모형(Rectangular Pulse Model)에서 반영하지 못하는 강우의 군집특성을 잘 반영하는 NSRPM(Neyman-Scott Rectangular Pulse Model) 강우생성 모형은 수자원 분야에 널리 쓰이고 있다. 일반적으로 NSRPM의 5개의 매개변수를 추정하는 최적화기법으로 DFP(Davidon-Fletcher-Powell)과 유전자알고리즘(Genetic Algorithm)을 사용하고 있다. 그러나 DFP는 주어진 초기 값에 따라 민감하며 각 반복 단계마다 헤시안행렬(Hessian Matrix)을 계산하여야 하며 추정된 전체의 해가 국지해에 수렴 할 수 있는 단점이 있다. 유전자 알고리즘을 DFP와 다르게 헤시안 행렬을 사용하지 않고 최적화를 할 수 있다는 장점이 있으나 시간이 오래 걸리는 단점이 있다. 이에 본 연구에서는 이러한 단점을 보완, 강화 하기위해서 최적화 기법으로 반복 단계마다 미분계산이 필요하지 않고 빠른 속도로 계산이 가능한 Nelder-Mead 알고리즘 이용하여 NSRPM매개변수를 추정하고 정확도를 비교하였다. 표 1은 각 기법을 이용하여 추정된 매개변수를 이용하여 생성한 강우의 통계특성과 관측된 통계특성의 상대오차를 나타낸 것이다. 괄호 안 숫자는 중첩되지 않는 누적시간을 나타낸다. 상대오차는 다음과 같다(식 1). 분석결과 Nelder-Mead 기법이 1시간의 평균, 공분산과 6시간 분산 등 전체적으로 GA, DFP보다 높은 정확도를 보였다.