Neyman-Scott Rectangular Pulses Model Research Articles

Development and Application of a Rainfall Temporal Disaggregation Method to Project Design Rainfalls

A climate model is essential for hydrological designs considering climate change, but there are still limitations in employing raw temporal and spatial resolutions for small urban areas. To solve the temporal scale gap, a temporal disaggregation method of rainfall data was developed based on the Neyman–Scott Rectangular Pulse Model, a stochastic rainfall model, and future design rainfall was projected. The developed method showed better performance than the benchmark models. It produced promising results in estimating the rainfall quantiles for recurrence intervals of less than 20 years. Overall, the analysis results imply that extreme rainfall events may increase. Structural/nonstructural measures are urgently needed for irrigation and the embankment of new water resources.

Modeling the response of soil moisture to climate variability in the Mediterranean region

Abstract. Future climate scenarios for the Mediterranean region indicate a possible decrease in annual precipitation associated with an intensification of extreme rainfall events in the coming years. A major challenge in this region is to evaluate the impacts of changing precipitation patterns on extreme hydrological events such as droughts and floods. For this, it is important to understand the impact of climate change on soil moisture since it is a proxy for agricultural droughts, and the antecedent soil moisture condition plays a key role on runoff generation. This study focuses on 10 sites, located in southern France, with available soil moisture, temperature, and precipitation observations for a 10-year time period. Soil moisture is simulated at each site at the hourly time step using a model of soil water content. The sensitivity of the simulated soil moisture to different changes in precipitation and temperature is evaluated by simulating the soil moisture response to temperature and precipitation scenarios generated using a delta change method for temperature and a stochastic model (the Neyman–Scott rectangular pulse model) for precipitation. Results show that soil moisture is more impacted by changes in precipitation intermittence than precipitation intensity and temperature. Overall, increased temperature and precipitation intensity associated with more intermittent precipitation leads to decreased soil moisture and an increase in the annual number of days with dry soil moisture conditions. In particular, a temperature increase of +4 ∘C combined with a decrease of annual rainfall between 10 % and 20 %, corresponding to the current available climate scenarios for the Mediterranean, lead to a lengthening of the drought period from June to October with an average of +28 d of soil moisture drought per year.

PERFORMANCE OF MIXED EXPONENTIAL AND EXPONENTIAL DISTRIBUTION REPRESENTING RAIN CELL INTENSITY IN NEYMANSCOTT RECTANGULAR PULSE (NSRP) MODEL

Sub-daily timescale data such as hourly data are needed for modeling urban systems. However such series are not readily available as compared to daily rainfall series. Stochastic rainfall models are useful in estimating input for design work. One of the models that applies the clustered point process theory is the Neyman-Scott Rectangular Pulses (NSRP) model. The model uses a flexible model fitting procedure which involves matching approximately a chosen set of historical statistics which exceeds in number of set of parameters to be estimated. An optimization technique called Shuffle Complex Evolution (SCE-UA) was used to estimate the parameters. The performance of NSRP model was evaluated using 10 years hourly data taken from a station in Wilayah Persekutuan. Two distributions, namely exponential (EXP) and mixed exponential (MEXP) were used to model the cell intensities in the model. The models were evaluated on a monthly basis regarding their ability to preserve the statistical properties as well as the physical properties of the rainfall time-series over timescales of 1 h, 6 h and 24 h. The performance of the models with the two different distributions was evaluated and compared. The model with the mixed exponential (MEXP) distribution perform better in preserving most of the statistical and physical properties of the observed data

Continuous rainfall generation for a warmer climate using observed temperature sensitivities

Continuous rainfall sequences are often used as inputs in hydrologic modeling, particularly where a probabilistic assessment is required. Continuous rainfall sequences provide a means for accounting of all aspects of rainfall that produce flooding, for example, not just the design rainfall event but also the rainfall prior to the extreme rainfall event. With the advent of climate change, higher temperatures have been associated with changes in rainfall, in particular intensifying rainfall extremes with less uniform temporal patterns. Given these demonstrated changes to extreme rainfall with temperature rise, there is a need to modify continuous rainfall generators to account for current and likely future changes in temperature.In this work we propose a novel method for simulating continuous rainfall sequences for a future warmer climate by conditioning parameters on their historical sensitivity with temperature. To demonstrate the proposed technique we use a one-dimensional Neyman-Scott Rectangular Pulses model at two locations across Australia. The statistics used in the parameter estimation are conditioned on their historical sensitivity to average monthly temperature to simulate rainfall for a change in temperature. The results are validated by comparing the simulated rainfall against observations originating from differing temperatures and it is shown that the model captures the relative difference in the mean monthly rainfall and monthly maxima. Encouraged by these results we simulate rainfall for higher temperatures and capture expected changes to annual maxima and design temporal patterns for a warmer climate. While we demonstrate our methodology in the simulation of sub-daily rainfall using a specific model, the approach presented here can be applied to all weather generation schemes for projection in a warmer climate.

A development of multisite hourly rainfall simulation technique based on neyman-scott rectangular pulse model

A development of multisite hourly rainfall simulation technique based on neyman-scott rectangular pulse model

A development of multisite hourly rainfall simulation technique based on neyman-scott rectangular pulse model

A development of multisite hourly rainfall simulation technique based on neyman-scott rectangular pulse model

Neyman Scott Rectangular Pulse Modeling for Storm Rainfall Analysis in Peninsular Malaysia

The objective of this study is to evaluate the application Neyman-Scott Rectangular Pulse (NSRP) modeling in describing the storm rainfall in Peninsular Malaysia. Hourly rainfall data for the periods of 1970 to 2008 from 50 rain-gauge stations in Peninsular Malaysia is used in this study. The rain-gauge stations are divided into four sub regions, namely northwest, west, southwest and east. The goodness of fit of the NSRP model to the observation is tested first before further application of the model. The results showed the NSRP model is able to represent the rainfall data in Peninsular Malaysia.

추계학적 강우모형의 매개변수 변동을 통한 서울지역 여름철 강우 변동특성 분석

본 연구에서는 강우의 변동특성 분석에 있어 기존의 접근법인 지속기간별 강우량의 변화 분석을 통하여 얻는 데 한계가 있는 강우의 구조적 변동특성을 분석하기 위하여 추계학적 강우모형을 이용하였다. Neyman-Scott 구형펄스 모형(Neyman-Scott Rectangular Pulse Model, NSRPM)은 점 과정을 이용한 추계학적 강우생성 모형으로 시간단위 강우를 생성함으로써 수문학 분야에서 널리 쓰이고 있으며 강우특성과 관련한 5개의 매개변수로 구성되어있다. 각 매개변수는 물리적인 의미를 가지고 있으므로 서울지점의 1973~2011년 여름철 시강우자료를 이용하여 NSRPM의 매개변수를 추정하고 추정된 매개변수의 변화를 분석하여 강우의 구조적인 변화를 분석하고 기존연구와 비교 분석하였다. In this study a stochastic rainfall generation model is used to analyze the structural variability of rainfall events since it has limitations in the traditional approach of measuring rainfall variability according to different durations. The NSRPM(Neyman-Scott Rectangular Pulse Model) is a stochastic rainfall generation model using a point process with 5 model parameters which is widely used in hydrologic fields. The five model parameters have physical meaning associated with rainfall events. The model parameters were estimated using hourly rainfall data from 1973 to 2011 at Seoul stations. The variability of model parameter estimates was analyzed and compared with results of traditional analysis.

A comparative study of mixed exponential and Weibull distributions in a stochastic model replicating a tropical rainfall process

A stochastic rainfall model is presented for the generation of hourly rainfall data in an urban area in Malaysia. In view of the high temporal and spatial variability of rainfall within the tropical rain belt, the Spatial–Temporal Neyman–Scott Rectangular Pulse model was used. The model, which is governed by the Neyman–Scott process, employs a reasonable number of parameters to represent the physical attributes of rainfall. A common approach is to attach each attribute to a mathematical distribution. With respect to rain cell intensity, this study proposes the use of a mixed exponential distribution. The performance of the proposed model was compared to a model that employs the Weibull distribution. Hourly and daily rainfall data from four stations in the Damansara River basin in Malaysia were used as input to the models, and simulations of hourly series were performed for an independent site within the basin. The performance of the models was assessed based on how closely the statistical characteristics of the simulated series resembled the statistics of the observed series. The findings obtained based on graphical representation revealed that the statistical characteristics of the simulated series for both models compared reasonably well with the observed series. However, a further assessment using the AIC, BIC and RMSE showed that the proposed model yields better results. The results of this study indicate that for tropical climates, the proposed model, using a mixed exponential distribution, is the best choice for generation of synthetic data for ungauged sites or for sites with insufficient data within the limit of the fitted region.

Analysis of the Applicability of Parameter Estimation Methods for a Stochastic Rainfall Model

추계학적 강우모형 NSRPM (Neyman-Scott Rectangular Pulse Model)은 RPM (Rectangular Pulse Model)에서 반영하지 못하는 강우의 군집특성을 잘 반영하여 시간 스케일의 강우를 생성함으로서 수문학적 적용성이 뛰어난 강우모형이다. NSRPM은 5개의 모형 매개변수로 이루어져 있으며 매개변수 추정을 위하여 최적화 기법으로 널리 쓰이고 있는 수치해석 기법인 DFP (Davidon-Fletcher-Powell)기법, 직접적 탐색 기법인 유전자 알고리즘을 사용하고 있다. 그러나 DFP 기법은 입력 초기값에 민감하며 국소 최저치에 수렴하는 확률이 높은 단점이 있으며 유전자 알고리즘기법은 탐색에 소요되는 시간이 많이 걸린다는 단점이 있다. 본 연구에서 사용된 Nelder-Mead기법은 순차적 탐색기법으로 연산 속도가 빠르며 입력 초기값이 필요하지 않아 사용하기 쉬운 장점을 가지고 있다. 본 연구는 전국 지상기상관측소 59개소를 대상으로 1973-2011년 39년 동안의 시간강우 자료를 수집하고 최적화 기법 DFP 기법, 유전자 알고리즘, Nelder-Mead 기법을 이용하여 NSRPM의 매개변수를 추정하여 지속시간 1시간, 6시간, 12시간, 24시간 별 평균, 분산, 공분산에 대해서 각 기법의 정확성을 평가하였다. 본 연구결과 전반적으로 Nelder-Mead기법이 가장 높은 정확도를 보였으며 유전자 알고리즘, DFP 기법 순으로 나타났다. A stochastic rainfall model, NSRPM (Neyman-Scott Rectangular Pulse Model), is able to reflect the cluster characteristics of rainfall events which is unable in the RPM (Rectangular Pulse Model). Therefore NSRPM has advantage in the hydrological applications. The NSRPM consists of five model parameters and the parameters are estimated using optimization techniques such as DFP (Davidon-Fletcher-Powell) method and genetic algorithm. However the DFP method is very sensitive in initial values and is easily converge to local minimum. Also genetic algorithm has disadvantage of long computation time. Nelder-Mead method has several advantages of short computation time and no need of a proper initial value. In this study, the applicability of parameter estimation methods was evaluated using rainfall data of 59 national rainfall networks from 1973-2011. Overall results demonstrated that accuracy in parameter estimation is in the order of Nelder-Mead method, genetic algorithm, and DFP method.

Stochastic downscaling of climate model precipitation outputs in orographically complex regions: 2. Downscaling methodology

[1] A new methodology of stochastic downscaling of climate model precipitation outputs to subdaily temporal resolution and in a multisite framework is presented. The methodology is based on the reparameterization for future climate of the Spatiotemporal Neyman-Scott Rectangular Pulses model. The reparameterization is carried out by estimating the model parameters as done for the calibration of the model for the historical climate and using future statistics that are obtained: (i) applying to the daily historical statistics a factor of change computed from the control and future climate model outputs and (ii) by rescaling the altered daily statistics according to the scaling properties exhibited by the historical raw moments, in order to generate the future statistics at the temporal resolutions required by the reparameterization procedure. The downscaled scenarios are obtained in a multisite framework accounting for cross correlations among the stations. The methodology represents a robust, efficient, and unique approach to generate multiple series of spatially distributed subdaily precipitation scenarios by Monte Carlo simulation. It presents thus a unique alternative for addressing the internal variability of the precipitation process at high temporal and spatial resolution, as compared to other downscaling techniques, which are affected by both computational and resolution problems. The application of the presented approach is demonstrated for a region of complex orography where the model has proved to provide good results, in order to analyze potential changes in such vulnerable areas.

Stochastic downscaling of precipitation to high-resolution scenarios in orographically complex regions: 1. Model evaluation

[1] The simulation of space-time precipitation has been studied since the late 1980s. However, there are still many open issues concerning the most appropriate approach to simulate it, specially in highly heterogeneous areas, such as in mountain environments. For this reason, we present here a comprehensive investigation of the Space-Time Neyman-Scott Rectangular Pulses model, with the purpose of analyzing its performance in a challenging Alpine environment of Switzerland and identifying weaknesses that can drive future improvements. The results point at the suitability of the model in reproducing not only the basic statistics at different temporal aggregations, but also the more challenging distributional and scaling properties. The intrinsic stationarity of the model in space, induced by the parameter estimation procedure, poses occasional limitations with regard to the accurate simulation of the variability of the observed climate characteristics, which are strongly influenced by local microclimates. However, the model is able, even in the complex Alpine environment, to preserve the spatial patterns observed in the actual precipitation process. The study allowed (i) to conclude about the robustness of the model and its suitability for multisite downscaling of precipitation estimated from climate model simulations, as reported in the companion paper, and (ii) to put in evidence some limitations that require further consideration to improve space-time rainfall generation.

Comparison of drought projections using two UK weather generators

Possible changes in drought under future climate scenarios may pose unprecedented challenges for water resources, as well as other environmental and societal issues, and need assessment to quantify their associated risk. Two weather generators, based upon (a) the Neyman-Scott Rectangular Pulses (NSRP) model as implemented by the United Kingdom Climate Projections 09 (UKCP09) study, and (b) the generalized linear model (GLM) approach, are used to investigate potential variations in drought conditions for six catchments in the UK under climate projections. The results show that both weather generators provide rainfall simulations having satisfactory monthly statistics. However, the rainfall series from the UKCP09 weather generators lack inter-annual variability, whereas the GLM simulations, which include non-stationary global circulation model (GCM) outputs as driving variables, seem to have a more appropriate representation of the observed drought conditions. For drought projections in the 2080s, the UKCP09 simulations provide repetitive patterns without much temporal variation, similar to the results in the control period. This study suggests that for the drought index considered here (a 3-month drought severity index) the GLM approach appears to be a more appropriate model for drought study on inter-annual scales in comparison with the UKCP09 weather generator. Editor D. Koutsoyiannis Citation Chun, K.P., Wheater, H.S., and Onof, C., 2013. Comparison of drought projections using two UK weather generators. Hydrological Sciences Journal, 58 (2), 295–309.

A simple approach for stochastic generation of spatial rainfall patterns

Summary Rainfall scenarios are of considerable interest for design flood and flood risk analysis. To this end, the stochastic generation of continuous rainfall sequences is often coupled with the continuous hydrological modelling. In this context, the spatial and the temporal rainfall variability represents a significant issue, especially for basins in which the rainfall field cannot be approximated through the use of a single station. Therefore, methodologies for the spatially and temporally correlated rainfall generation are welcome. An example of such a methodology is the well-established Spatial–Temporal Neyman-Scott Rectangular Pulse (STNSRP), a modification of the single-site Neyman-Scott Rectangular Pulse (NSRP) approach, designed to incorporate specific features to reproduce the rainfall spatial cross-correlation. In order to provide a simple alternative to the STNSRP, a new method of generating synthetic rainfall time series with pre-set spatial–temporal correlation is proposed herein. This approach relies on the single-site NSRP model, which is used to generate synthetic hourly independent rainfall time series at each rain gauge station with the required temporal autocorrelation (and several other appropriately selected statistics). The rank correlation method of Iman and Conover (IC) is then applied to these synthetic rainfall time series in order to introduce the same spatial cross-correlation that exists between the observed time series. This combination of the NSRP model with the IC method consents the reproduction of the observed spatial–temporal variability of a rainfall field. In order to verify the proposed procedure, four sub-basins of the Upper Tiber River basin are investigated whose basin areas range from 165 km2 to 2040 km2. Results show that the procedure is able to preserve both the rainfall temporal autocorrelation at single site and the rainfall spatial cross-correlation at basin scale, and its performance is comparable with that of the STNSRP model for rainfall field generation. Given its simple formal structure (based on well established methods: i.e. NSRP and IC), we believe that the proposed approach can be conveniently utilized to generate spatially and temporally correlated rainfall scenarios.

Neyman-Scott-based water distribution network modelling

Residential water demand is one of the most difficult parameters to determine when modelling drinking water distribution networks. It has been proven to be a stochastic process which can be characterised as a series of rectangular pulses having set intensity, duration and frequency. Such parameters can be determined using stochastic models such as the Neyman-Scott rectangular pulse model (NSRPM). NSRPM is based on resolving a non-linear optimisation problem involving theoretical moments of the synthetic demand series (equiprobable) and of the observed moments (field measurements) statistically establishing the measured demand series. NSRPM has been applied to generating local residential demand. However, this model has not been validated for a real distribution network with residential demand aggregation, or compared to traditional methods (which is dealt with here). This paper compares the results of synthetic stochastic demand series (calculated using NSRPM applied to determining pressure and flow rate) to results obtained using traditional simulation methods using the curve of hourly variation in demand and to actual pressure and flow rate measurements. The Humaya sector of Culiacan, Sinaloa, Mexico, was used as study area.

Differential Evolution 기법을 이용한 Neyman-Scott Rectangular Pulse 모형의 매개변수 추정

The NSRPM(Neyman-Scott Rectangular Pulse Model), a stochastic rainfall generation model using clustered point process theory, is widely used in hydrology since it is able to reflect the cluster characteristics of rainfall events but the RPM(Rectangular Pulse Model) is not able to handle that. DFP(Davidon-Flectcher-Powell) and GA(Genetic Algorithm) are generally used to estimate 5 model parameters of the NSRPM. However DFP is sensitive to initial value and has tendency to get not global solution but local minimization. GA has an advantage of optimizing without Hessian matrix, but it needs relatively long computing time. In this study, a DE(Differential Evolution) method applied in model parameter estimation in order to overcome those drawbacks. The rainfall model parameters during the summer season (June-August) at Seoul, Pusan, Daegu, Mokpo, Gangrung, which have more than 30 year long hourly precipitation data, were estimated using hourly rainfall data from 1961 to 2011. Results were compared to those using DFP and GA. The performance of the DE method was evaluated using test statistics and demonstrated better performance in preserving physical and statistical properties of observed rainfall data.

Further developments of a transient Poisson-cluster model for rainfall

Stochastic point processes for rainfall are known to be able to preserve the temporal variability of rainfall on several levels of aggregation (e.g. hourly, daily), especially when the cluster approach is used. One major assumption in most of the applications todate is the stationarity of the rainfall properties in time, which must be reconsidered under a climate change hypothesis. Here, we propose new theoretical developments of a Poisson-based model with cluster, namely the Neyman–Scott Rectangular Pulses Model, which treats storm frequency as a nonstationary function. In this paper, storm frequency is modelled as a linear function of time in order to reproduce an increase (or decrease) of the mean annual precipitation. The basic theory is reconsidered and the moments are derived up to the third order. Then, a calibration method based on the generalized method of moments is proposed and discussed. An application to a rainfall time series from Uccle illustrates how this model can reproduce a trend for the average rainfall. This work opens new avenues for future developments on transient stochastic rainfall models and highlights the major challenges linked to this approach.

Modeling of Drinking Water Distribution Networks Using Stochastic Demand

Residential water demand is one of the most difficult parameters to determine when modeling drinking water distribution networks. It has been proven to be a stochastic process that can be characterized as a series of rectangular pulses with a set intensity, duration and frequency. These parameters can be determined using stochastic models such as the Neyman-Scott Rectangular Pulse (NSRP) model. The NSRP model is based on the solution of a non-linear optimization problem. This solution involves theoretical moments that represent the synthetic demand series (equiprobable) and the observed moments (field measurements) that statistically establish the measured demand series. The NSRP model has been applied for residential demand, and the results have been published. However, this model has not been validated for a real distribution network or compared with traditional methods. The present study compared the results of synthetic stochastic demand series, which were calculated using the NSRP model, applied to the determination of pressures, flow rates and leaks; to the results obtained using traditional simulation methods, which use the curve of hourly variation in demand, and to actual pressure and flow rate measurements. The Humaya sector of Culiacan, Sinaloa, Mexico, was used as the study area.

직접적인 매개변수 추정방법을 이용한 새로운 수정된 Neyman-Scott 구형펄스모형 개발 연구

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.

Neyman-Scott 구형 펄스모형의 직접적인 매개변수 추정연구

SRPM (Neyman-Scott Rectangular Pulse Model)은 수문학분야에서 널리 쓰이고 있는 강수생성모형이다. NSRPM을 구축하기 위해서는 총 5개의 매개변수를 추정하여야 한다. 일반적으로 사용되는 모멘트를 이용하여 매개변수를 추정할 경우, 사용되는 목적함수의 증가에 따라 추정되는 매개변수의 결과가 평탄해지고 목적함수를 추가하거나 조정하기 위해서는 복잡한 수식을 다시 계산해야 하며 추정된 매개변수가 무작위변수 생성 모형에 따라 상이한 결과를 나타내는 단점이 있다. 본 연구에서는 직접적인 매개변수 추정방법을 제시하여 모멘트를 이용한 매개변수 추정의 단점을 극복하고자 하였다. 직접적인 추정방법을 적용하기 위하여 NSRPM의 강수 생성 개수에 따른 통계치 변화를 모의하여 직접적인 추정을 위한 모형을 구축하였다. 기상청 청주 지상관측소의 관측 강수 자료를 사용하여 모멘트를 이용하여 추정된 매개변수와 직접적인 방법을 이용하여 매개변수를 추정하였다. 총 4 개의 무작위변수 알고리즘을 적용하여 강수를 생성하였고, 관측 강수 시계열을 이용하여 정확도를 비교하였다. 비교 결과 직접적인 추정방법이 모멘트를 이용한 매개변수 추정방법보다 안정적이고 높은 정확도를 보이는 매개변수를 추정하는 것으로 나타났다. NSRPM (Neyman-Scott Rectangular Pulse Model) is one of the common model for generating future precipitation time series in stochastical hydrology. There are 5 parameters to compose the NSRPM model for generating precipitation time series. Generally parameter estimation using moment has some problems related with increased objective functions and shows different results in accordance with random variable generating models. In this study, direct parameter estimation method was proposed to cover with disadvantages of parameter estimation using moment. To apply the direct parameter estimation, generating stochastical data variance in accordance with numbers of precipitation events of NSRPM was done. Both kinds of methods were applied at the Cheongju gauge station data. Precipitation time series were generated using 4 different random variable generator, and compared with observed time series to check the accuracies. As a results, direct method showed more stable and better results.