Modified Bartlett-Lewis Rectangular Pulse Research Articles

A hybrid stochastic rainfall model that reproduces some important rainfall characteristics at hourly to yearly timescales

Abstract. A novel approach to stochastic rainfall generation that can reproduce various statistical characteristics of observed rainfall at hourly to yearly timescales is presented. The model uses a seasonal autoregressive integrated moving average (SARIMA) model to generate monthly rainfall. Then, it downscales the generated monthly rainfall to the hourly aggregation level using the Modified Bartlett–Lewis Rectangular Pulse (MBLRP) model, a type of Poisson cluster rainfall model. Here, the MBLRP model is carefully calibrated such that it can reproduce the sub-daily statistical properties of observed rainfall. This was achieved by first generating a set of fine-scale rainfall statistics reflecting the complex correlation structure between rainfall mean, variance, auto-covariance, and proportion of dry periods, and then coupling it to the generated monthly rainfall, which were used as the basis of the MBLRP parameterization. The approach was tested on 34 gauges located in the Midwest to the east coast of the continental United States with a variety of rainfall characteristics. The results of the test suggest that our hybrid model accurately reproduces the first- to the third-order statistics as well as the intermittency properties from the hourly to the annual timescales, and the statistical behaviour of monthly maxima and extreme values of the observed rainfall were reproduced well.

A hierarchical Bayesian approach to the modified Bartlett-Lewis rectangular pulse model for a joint estimation of model parameters across stations

Abstract Poisson cluster stochastic rainfall generators (e.g., modified Bartlett-Lewis rectangular pulse, MBLRP) have been widely applied to generate synthetic sub-daily rainfall sequences. The MBLRP model reproduces the underlying distribution of the rainfall generating process. The existing optimization techniques are typically based on individual parameter estimates that treat each parameter as independent. However, parameter estimates sometimes compensate for the estimates of other parameters, which can cause high variability in the results if the covariance structure is not formally considered. Moreover, uncertainty associated with model parameters in the MBLRP rainfall generator is not usually addressed properly. Here, we develop a hierarchical Bayesian model (HBM)-based MBLRP model to jointly estimate parameters across weather stations and explicitly consider the covariance and uncertainty through a Bayesian framework. The model is tested using weather stations in South Korea. The HBM-based MBLRP model improves the identification of parameters with better reproduction of rainfall statistics at various temporal scales. Additionally, the spatial variability of the parameters across weather stations is substantially reduced compared to that of other methods.

포아송 클러스터 가상강우생성 웹 어플리케이션 개발 및 검증 - 우리나라에 대해서

본 연구에서는 포아송 클러스터 강우생성모형의 하나인 MBLRP 모형의 매개변수지도를 우리나라에 대하여 제작하고 이에 기반을 둔 가상강우생성 웹 어플리케이션을 개발 및 검증하였다. 이를 위하여 우리나라의 62개 ASOS 지상 강우 관측소에서 관측된 강우자료를 기반으로 서로 다른 수문모의의 목적(홍수량 모의, 장기 유출량 모의, 일반 모의)에 따른 MBLRP 모형의 매개변수지도를 산정한 후, 이를 Ordinary Kriging 기법을 통해 공간 보간하여 우리나라에 대한 매개변수지도를 제작하였으며, 이에 기반을 두고 가상강우 시계열을 생성하는 웹 어플리케이션을 개발하였다. 검증을 위하여 웹어플리케이션을 사용하여 가상강우를 생성한 후 평균, 분산, 자기상관계수, 무강우 확률, 극한강우량 및 다양한 유역에 대한 극한홍수량과 유출량을 계산하고 이를 관측 강우에 근거하여 산출된 값과 비교하였다. 비교 결과 가상 강우의 각종 통계값은 관측강우에 근거한 값과 매우 유사하게 나타났으나, 극한강우와 극한홍수는 관측치에 근거한 값과 비교하여 16%-40% 정도 과소산정되는 경향을 보였다. 이러한 결과는 교정계수로 활용할 수 있도록 등고선도의 형태로 제공되었다. 본 연구에서 개발한 웹 어플리케이션은 모형의 매개변수 산정부터 가상 강우 시계열 생성까지 일련의 과정을 포함하고 있어 강우자료를 필요로 하는 다양한 수문 분석에 활발히 활용될 것으로 기대된다.

Let-It-Rain: a web application for stochastic point rainfall generation at ungaged basins and its applicability in runoff and flood modeling

We present a web application named Let-It-Rain that is able to generate a 1-h temporal resolution synthetic rainfall time series using the modified Bartlett–Lewis rectangular pulse (MBLRP) model, a type of Poisson stochastic rainfall generator. Let-It-Rain, which can be accessed through the web address http://www.LetItRain.info , adopts a web-based framework combining ArcGIS Server from server side for parameter value dissemination and JavaScript from client side to implement the MBLRP model. This enables any desktop and mobile end users with internet access and web browser to obtain the synthetic rainfall time series at any given location at which the parameter regionalization work has been completed (currently the contiguous United States and Republic of Korea) with only a few mouse clicks. Let-It-Rain shows satisfactory performance in its ability to reproduce observed rainfall mean, variance, auto-correlation, and probability of zero rainfall at hourly through daily accumulation levels. It also shows a reasonably good performance in reproducing watershed runoff depth and peak flow. We expect that Let-It-Rain can stimulate the uncertainty analysis of hydrologic variables across the world.

Application of the Poisson Cluster Rainfall Generation Model to the Urban Flood Analysis

This study examined the applicability of MBLRP (Modified Bartlett-Lewis Rectangular Pulse) rainfall generation model for an urban flood simulation which is a type of Poisson cluster rainfall generation model. This study constructed XP-SWMM model for Namgajwa area of Hongjecheon basin, which is a two-dimensional pipe network-surface flood simulation program and computed a flood discharge and a flooded area with input data of synthetic rainfall time series of 200 years that were generated by the MBLRP model. This study compared the data of flood with synthetic rainfall and flood with corresponding values which were based on design rainfall. The results showed that the flooded area computed with MBLRP model was somewhat smaller than the corresponding values on the basis of the design. A degree of underestimation was from 8% (5 year) to 34% (200 year) and the degree of underestimation increased as a return period increased. This study is meaningful in that it proposes methodology that enables quantifiability of uncertain variables which are related to a flooding through Monte Carlo analysis of urban flooding simulation and applicability and limitations thereof.

Regionalization of the Modified Bartlett–Lewis rectangular pulse stochastic rainfall model across the Korean Peninsula

Abstract The six parameters of the Modified Bartlett–Lewis Rectangular Pulse (MBLRP) model were regionalized across the Korean Peninsula for all 12 calendar months. The parameters of the MBLRP model were estimated at each of the 59 rain gauges and they were spatially interpolated using the Ordinary Kriging method in order to produce maps. The parameter search space used in the parameter estimation process was repetitively narrowed through cross-validation in order to remove the impact of the multi-modality of the MBLRP model. The synthetic rainfall time series generated based on the parameter maps successfully reproduced the various statistical properties of the observed rainfall, such as mean, variance, lag-1 autocorrelation, and probability of zero rainfall at a wide range of time accumulation levels (e.g. hourly through daily). The maps representing the general rainfall characteristics, such as the average rainfall depth per rain storm, the average rain storm duration, the average number of rain cells per rain storm, and the average rain cell duration were also produced based on the estimated parameters. Lastly, some helpful tips in regionalizing the parameters of the Poisson cluster rainfall models are discussed.

극한수문사상의 모의를 위한 포아송 클러스터 강우생성모형의 적용성 평가

본 연구는 우리나라의 극한강우와 극한홍수를 모의하기 위한 MBLRP 포아송 클러스터 강우생성모형의 적용성을 평가하였다. 국내 61개의 기상청 지상기상관측시스템의 강우량 관측지점에 대하여 고립입자 군집화 최적화(ISPSO) 기법을 적용하여 모형의 매개변수를 추정하고, 추정된 매개변수를 바탕으로 각 강우관측지점에서 100년치의 가상 강우시계열을 생성하였다. 생성된 강우시계열을 이용하여 확률강우량 및 확률홍수량을 산정하고 이 값들을 관측치에 근거하여 산정된 값들과 비교하였다. 비교 결과, 모형에 의한 확률강우량은 관측치보다 평균적으로 20~42% 작았으며, 강우의 재현기간이 증가할수록 과소산정되는 정도가 증가하였다. 확률홍수량의 경우, 모형에 의한 값이 관측치에 근거한 값보다 31%에서 50% 작았으며, 이 과소산정량은 홍수의 재현기간의 증가 및 유역의 불투수도의 증가와 함께 증가하였다. This study evaluated the applicability of the Modified Bartlett-Lewis Rectangular Pulse (MBLRP) rainfall generation model for modeling extreme rainfalls and floods in Korean Peninsula. Firstly, using the ISPSO (Isolated Species Particle Swarm Optimization) method, the parameters of the MBLRP model were estimated at the 61 ASOS (Automatic Surface Observation System) rain gauges located across Korean Peninsula. Then, the synthetic rainfall time series with the length of 100 years were generated using the MBLRP model for each of the rain gauges. Finally, design rainfalls and design floods with various recurrence intervals were estimated based on the generated synthetic rainfall time series, which were compared to the values based on the observed rainfall time series. The results of the comparison indicate that the design rainfalls based on the synthetic rainfall time series were smaller than the ones based on the observation by 20% to 42%. The amount of underestimation increased with the increase of return period. In case of the design floods, the degree of underestimation was 31% to 50%, which increases along with the return period of flood and the curve number of basin.

A Poisson Cluster Stochastic Rainfall Generator That Accounts for the Interannual Variability of Rainfall Statistics: Validation at Various Geographic Locations across the United States

A novel approach for a Poisson cluster stochastic rainfall generator was validated in its ability to reproduce important rainfall and watershed response characteristics at 104 locations in the United States. The suggested novel approach, The Hybrid Model (THM), as compared to the traditional Poisson cluster rainfall modeling approaches, has an additional capability to account for the interannual variability of rainfall statistics. THM and a traditional approach of Poisson cluster rainfall model (modified Bartlett-Lewis rectangular pulse model) were compared in their ability to reproduce the characteristics of extreme rainfall and watershed response variables such as runoff and peak flow. The results of the comparison indicate that THM generally outperforms the traditional approach in reproducing the distributions of peak rainfall, peak flow, and runoff volume. In addition, THM significantly outperformed the traditional approach in reproducing extreme rainfall by 2.3% to 66% and extreme flow values by 32% to 71%.

포아송 클러스터 강우생성 모형의 홍수 모의 적용성 평가

본 연구는 우리나라 전역에 대하여 제작된 Modified Bartlett-Lewis Rectangular Pulse (MBLRP) 강우생성 모형의 모수 지도의 적용성을 홍수 재현의 관점에서 평가하였다. MBLRP 모형을 통해 생성된 가상 강우시계열을 사용하여 산정된 확률강우량은 관측치를 사용하여 산정된 확률강우량 보다 약5%에서 40%정도 작았고, 확률강우량의 재현기간이 클수록 과소산정의 정도가 크게 나타났다. 가상의 도시 유역에 MBLRP 모형을 적용하여 산정한 확률홍수량은 관측치를 사용하여 산정한 확률홍수량 보다 약20%에서 45%정도 작게 나타났고, 확률홍수량의 재현기간이 클수록, 그리고 유역의 불투수성이 작을수록 과소산정의 정도가 크게 나타났다. The applicability of the parameter map of the Modified Bartlett-Lewis Rectangular Pulse (MBLRP) model for the Korean Peninsula was assessed from the perspective of flood prediction. The design rainfalls estimated from the MBLRP model were smaller than those from observed values by 5% to 40%, and the degree of underestimation of design rainfall increases with the increase of the recurrence interval of the design rainfall. The design floods at a virtual watershed estimated using the simulated rainfall time series based on MBLRP model were also smaller than those derived from the observed rainfall time series by 20% to 45%. The degree of underestimation of design flood increases with the increase of the recurrence interval of the design flood.

Effect of the inter-annual variability of rainfall statistics on stochastically generated rainfall time series: part 2. Impact on watershed response variables

This study analyzes how the stochastically generated rainfall time series accounting for the inter- annual variability of rainfall statistics can improve the prediction of watershed response variables such as peak flow and runoff depth. The modified Bartlett-Lewis rect- angular pulse (MBLRP) rainfall generation model was improved such that it can account for the inter-annual variability of the observed rainfall statistics. Then, the synthetic rainfall time series was generated using the MBLRP model, which was used as input rainfall data for SCS hydrologic models to produce runoff depth and peak flow in a virtual watershed. These values were compared to the ones derived from the synthetic rainfall time series that is generated from the traditional MBLRP rainfall modeling. The result of the comparison indicates that the rainfall time series reflecting the inter-annual variability of rainfall sta- tistics reduces the biasness residing in the predicted peak flow values derived from the synthetic rainfall time series generated using the traditional MBLRP approach by 26-47 %. In addition, it was observed that the overall variability of the peak flow and run off depth distribution was better represented when the inter-annual variability of rainfall statistics are considered.

Modeling precipitation of short duration by means of the modified Bartlett-Lewis rectangular pulse model

The objective of this work was to evaluate the mathematical modeling of rainfall of duration less than one hour using the modified Bartlett-Lewis model with six parameters. The data used were for the period October 1980 to December 2007, from recording rain gauges (pluviographs) at the meteorological station of Epagri, Urussanga, south of Santa Catarina (latitude 28.31° S, longitude 48.19 ° W). Based on simulations of series with 100 years of data it can be concluded that: the adjustment of the parameters of the modified Bartlett-Lewis model enables the simulation of rain at intervals as small as 5 minutes of duration, preserving the statistical properties of precipitation over various intervals of aggregation in time. In general there was a tendency toward overestimation of the probability of dry periods and underestimation of the covariance for intervals of 24 hours, especially in summer. The total annual rainfall simulated for all time intervals examined remains within the confidence interval of 95%.

Characterization and disaggregation of daily rainfall in the Upper Blue Nile Basin in Ethiopia

In Ethiopia, available rainfall records are mainly limited to daily time steps. Though rainfall data at shorter time steps are important for various purposes like modeling of erosion processes and flood hydrographs, they are hardly available in Ethiopia. The objectives of this study were (i) to study the temporal characteristics of daily rains at two stations in the region of the Upper Blue Nile Basin (UBNB) and (ii) to calibrate and evaluate a daily rainfall disaggregation model. The analysis was based on rainfall data of Bahir Dar and Gonder Meteorological Stations. The disaggregation model used was the Modified Bartlett–Lewis Rectangular Pulse Model (MBLRPM). The mean daily rainfall intensity varied from about 4 mm in the dry season to 17 mm in the wet season with corresponding variation in raindays of 0.4–26 days. The observed maximum daily rainfall varied from 13 mm in the dry month to 200 mm in the wet month. The average wet/dry spell length varied from 1/21 days in the dry season to 6/1 days in the rainy season. Most of the rainfall occurs in the afternoon and evening periods of the day. Daily rainfall disaggregation using the MBLRPM alone resulted in poor match between the disaggregated and observed hourly rainfalls. Stochastic redistribution of the outputs of the model using Beta probability distribution function improved the agreement between observed and calculated hourly rain intensities. In areas where convective rainfall is dominant, the outputs of MBLRPM should be redistributed using relevant probability distributions to simulate the diurnal rainfall pattern.

기후변화가 극한강우와 I-D-F 분석에 미치는 영향 평가

최근 수공시설물의 설계규모를 넘어서는 극한 강우사상이 발생하여 홍수방어를 위하여 구축된 수리구조물이 파괴 되는 등 많은 홍수피해가 발생하고 있다. 따라서 극한 강우사상의 시공간적 발생 특성을 파악하고 미래의 기후변화하에서 극한강우사상이 어떻게 변화하고 설계수명기간(Design period)동안 분포 특성이 어떻게 변화할지를 이해하는 것은 매우 중요하다. 이에 본 논문에서는 미래의 기후변화가 극한 강우에 어떠한 영향을 미치는지를 평가하기 위해 기후변화 시나리오를 이용하여 미래의 극한강우의 특성 분석과 I-D-F 분석을 실시하였다. 본 연구에서는 SRES B2 온난화가스 시나리오와 YONU CGCM 를 이용하여 2030s(2031-2050)를 모의하였으며 통계학적 축소기법을 적용하여 우리나라에 위치한 기상청 산하 관측소별로 일 기상자료를 구축하였다. 또한, 이를 과거 관측 자료와 비교하여 Quantile Mapping 방법으로 편이보정을 실시하였고, 구형펄스(Modified Bartlett Lewis Rectangular Pulse, MBLRP) 모형(Onof과 Wheater, 1993; Onof 2000)과 분해기법(adjust method)을 적용하여 일 강우 시계열자료를 시 강우 시계열 자료로 변환하였으며 지속기간별 빈도별 강우량을 산정하여 I-D-F 곡선을 작성하였다. 본 논문에서는 66개 관측소 중에서 서울, 대구, 전주, 광주 지점의 결과만을 수록하였으며 그 결과 거의 모든 지점에서 현재와 비교하였을 때 지속기간이 길어질수록 강우강도가 증가함을 확인할 수 있었다. Recently, extreme precipitation events beyond design capacity of hydraulic system have been occurred and this is the causes of failure of hydraulic structure for flood prevention and of severe flood damage. Therefore it is very important to understand temporal and spatial characteristics of extreme precipitation events as well as expected changes in extreme precipitation events and distributional characteristics during design period under future climate change. In this paper, climate change scenarios were used to assess the impacts of future climate change on extreme precipitation. Furthermore, analysis of future extreme precipitation characteristics and I-D-F analysis were carried out. This study used SRES B2 greenhouse gas scenario and YONU CGCM to simulate climatic conditions from 2031 to 2050 and statistical downscaling method was applied to establish weather data from each of observation sites operated by the Korean Meteorological Administration. Then quantile mapping of bias correction methods was carried out by comparing the simulated data with observations for bias correction. In addition Modified Bartlett Lewis Rectangular Pulse(MBLRP) model (Onof and Wheater, 1993; Onof 2000) and adjust method were applied to transform daily precipitation time series data into hourly time series data. Finally, rainfall intensity, duration, and frequency were calculated to draw I-D-F curve. Although there are 66 observation sites in Korea, we consider here the results from only Seoul, Daegu, Jeonju, and Gwangju sites in this paper. From the results we found that the rainfall intensity will be increased and the bigger intensity will be occurred for longer rainfall duration when we compare the climate conditions of 2030s with present conditions.