Bartlett-Lewis Rectangular Pulse Model Research Articles

Deriving rainfall IDF curves using modified Bartlett-Lewis rectangular pulses (BLRP) model for Babylon City, Iraq

In this study, daily rainfall data spanning 32 years, from 1991 to 2022, were collected from the Babylon City Meteorological Station (BCMS). The modified Bartlett-Lewis Rectangular Pulses (BLRP) model with seven parameters was used to generate the intensity-duration-frequency (IDF) curve for durations of 2, 5, 10, 25, 50, and 100 years. The estimated extreme values obtained from BCMS were fitted with EasyFit software using three statistical continuous distributions: the Gumbel (EV-1), Generalized Extreme Value (GEV), and Log-Pearson type III (LP-3) to determine the optimal distribution model for the IDF curve. The AIC and BIC criteria were employed to rank the generated IDF curves for each duration to select the optimal distribution model. The results of the AIC criteria ranked the PDFs as LP-3 first model, EV-1 second model, and GEV third model with sums of weighted rank values as 16, 17, and 27, respectively. In contrast, the BIC criteria ranked the PDFs as EV-1 first model, LP-3 second model, and GEV third model with sums of weighted rank values as 16, 17, and 27, respectively. The EV-1 and LP-3 models were selected as the most suitable results for simulating the maximum rainfall in Babylon City for various return periods. This decision was based on the total score of the special rankings of the two tests, with EV-1 and LP-3 having the lowest values of AIC and BIC.

Bartlett–Lewis Model Calibrated with Satellite-Derived Precipitation Data to Estimate Daily Peak 15 Min Rainfall Intensity

Temporal variability of rainfall is extreme in the rangelands of northern Australia and occurs at annual, decadal, and even longer timescales. To maintain long-term productivity of the rangelands of northern Australia under highly variable rainfall conditions, suitable land management practices are assessed using rangeland biophysical models, e.g., GRASP (GRASs Production). The daily maxima of the 15 min rainfall intensity (I15) are used to predict runoff and moisture retention in the model. The performance of rangeland biophysical models heavily relies on the I15 estimates. As the number of pluviograph stations is very limited in northern Australian rangelands, an empirical I15 model (Fraser) was developed using readily available daily climate variables, i.e., daily rainfall total, daily diurnal temperature range, and daily minimum temperature. The aim of this study is to estimate I15 from daily rainfall totals using a well-established disaggregation scheme coupled with the Bartlett–Lewis rectangular pulse (BLRP) model. In the absence of pluviograph data, the BLRP models (RBL-E and RBL-G) were calibrated with the precipitation statistics estimated using the Integrated Multi-satellitE Retrievals for GPM (global precipitation measurement) (IMERG; 30 min, 0.1° resolution) precipitation product. The Fraser, RBL-E, and RBL-G models were assessed using 1 min pluviograph data at a single test site in Darwin. The results indicated that all three models tended to underestimate the observed I15, while a serious underestimation was observed for RBL-E and RBL-G. The underestimation by the Fraser, RBL-E, and RBL-G models consisted of 23%, 38%, and 50% on average, respectively. Furthermore, the Fraser model represented 29% of the variation in observed I15, whereas RBL-E and RBL-G represented only 7% and 11% of the variation, respectively. A comparison of RBL-E and RBL-G suggested that the difference in the spatial scales of IMERG and pluviograph data needs to be addressed to improve the performance of RBL-E and RBL-G. Overall, the findings of this study demonstrate that the BLRP model calibrated with IMERG statistics has the potential for estimating I15 for the GRASP biophysical model once the scale difference between IMERG and point rainfall data is addressed.

A Multi criteria Decision Making based nonparametric method of fragments to disaggregate daily precipitation

This study addresses the issue of scant availability of sub-daily precipitation data by introducing a novel selection methodology named ‘Pattern Mapping’ (PM) within the existing Method of Fragments (MOF) framework for the disaggregation of daily precipitation. PM introduces multiple statistics based criterion in the selection of fragments thus enhancing accuracy of the selection process. The performance of deterministic and stochastic versions of PM-MOF is compared with three widely used disaggregation methods, namely K Nearest Neighbour based MOF (KNN-MOF), Bartlett-Lewis Rectangular Pulse model (using HYETOS software package) and Micro-Canonical Cascade (MCC) using reanalysis data at 14 global locations spanning various climatic zones. It is seen that the PM-MOF method has considerably lower percentage error in replicating the standard statistics (−50.2 to 50.3% for stochastic PM-MOF and −7.4 to 13.2% for deterministic PM-MOF) when compared to existing methods (KNN-MOF (−65.4 to 76.2%), HYETOS (−78.3 to 69.4%) and MCC (−63.1 to 72%)). The comparison of densities using skill score show that skill score of PM-MOF is 0.97 which is higher than other methods (0.94 for KNN-MOF, 0.83 for HYETOS and 0.85 for MCC). Control experiments designed around varying length of training data and stochastic/deterministic mode (of PM-MOF) ascertain the contribution of the novel methodological improvements in the superior performance of PM-MOF. The robustness of the methodology and geography independent performance of PM-MOF makes it a potent candidate for wider application in hydrological and climate studies.

Coupling of satellite-derived precipitation products with Bartlett-Lewis model to estimate intensity-frequency-duration curves for remote areas

Intensity-frequency-duration (IFD) curves (also known as intensity-duration-frequency (IDF) curves in some regions) are widely used to take into consideration the probability of occurrence of extreme precipitation for the design of water related infrastructure. Derivation of IFD curves is based on statistical analysis of observed extreme precipitation events and thus the reliability of the curves mostly depends on the record length of observations. At sub-hourly timescales however, ground-based precipitation observations are often absent or very limited in terms of spatial coverage and record length, particularly in remote areas around the world. Given the availability of satellite-derived precipitation products (SPPs) with finer spatiotemporal resolution and near-global coverage, there is great potential to use these products in the planning and design of infrastructure. This paper proposes a novel framework, SIFD (Satellite-derived IFD curves) to combine long-term daily gauge data and sub-hourly SPP to estimate IFD curves for time intervals from 0.5 to 24 h. A recent variant of the Random Parameter Bartlett-Lewis Rectangular Pulse model (RPBLRPX) was used to disaggregate daily gauge data to derive IFD curves. In the absence of sub-daily rain gauge data, the statistics required for the RPBLRPX model were obtained using the Integrated Multi-satellitE Retrievals for GPM (IMERG; 30-min, 0.1° resolution) product derived from the Global Precipitation Measurement (GPM) mission. Performance of the SIFD framework was tested against gauge data from seven Australian sites across a wide range of climatologies. The disaggregation scheme coupled with the RPBLRPX model was capable of reproducing the wet-period mean intensity, wet-period standard deviation, and wet-period fraction with reasonable accuracy across the sub-daily timescales. The coefficient of determination (r2) values were 0.39 (mean intensity), 0.38 (standard deviation), and 0.87 (wet-period fraction) at 0.5 h timescale. Furthermore, despite some differences in methodology and record length, the IFD estimates computed using the SIFD framework were fairly close to those of the Bureau of Meteorology (BoM). The skill metrics for Sydney were the best with a bias ratio (BR) of 1.01, root mean square error (RMSE) of 13% of the mean of the BoM estimates, and a Nash-Sutcliffe coefficient of efficiency (NSE) of 0.97. The worst case was found at Hobart (BR = 1.43, RMSE = 66%, and NSE = 0.26). Overall, the results indicate that the proposed SIFD framework could provide a viable alternative to estimate unbiased IFD curves at the sub-hourly timescale in the absence of adequate sub-hourly ground-based observations.

A stochastic rainfall model that can reproduce important rainfall properties across the timescales from several minutes to a decade

A stochastic rainfall model that can reproduce various rainfall characteristics at timescales between 5 min and one decade is introduced. The model generates the fine-scale rainfall time series using a randomized Bartlett-Lewis rectangular pulse model. Then the rainstorms are shuffled such that the correlation structure between the consecutive storms are preserved. Finally, the time series is rearranged again at the monthly timescale based on the result of the separate coarse-scale monthly rainfall model. The method was tested using the 69 years of 5-minute rainfall data recorded at Bochum, Germany. The mean, variance, covariance, skewness, and rainfall intermittency were well reproduced at the timescales from 5 min to a decade without any systematic bias. The extreme values were also well reproduced at timescales from 5 min to 3 days. The past-7-day rainfall before an extreme rainfall event, which is highly associated with the extreme flow discharge was reproduced well too. The rainstorm shuffling approaches introduced here may be adopted as a standard procedure in combination with any Poisson cluster rainfall model. The methods are simple and parsimonious, yet significantly reduce the systematic underestimation of rainfall variance at coarse scales, and improve the reproduction of skewness, and extreme rainfall depths values at a range of time-scales, thereby addressing well-known shortcomings of Poisson cluster rainfall models.

Improved reliability of stormwater detention basin performance through water quality data-informed real-time control

Stormwater detentions basins are designed to capture stormwater to reduce and delay peak flows and to improve water quality. A novel technology proposed to improve basin performance is real-time, active control of the basin outflow, in so-called “smart” stormwater systems. Existing studies demonstrate the performance of active controls that respond in real-time to basin water level, detention time, and rainfall forecast for one or a small number of rainfall events. We hypothesize that the performance of these active controls can be improved by incorporating real-time water quality data into the control algorithm. In addition, we hypothesize that active control performance depends on hydrologic variability, specifically the frequency and intensity of runoff inputs. In this paper, we test these hypotheses using a numerical modeling framework for systems-level reliability analysis of active and passive stormwater basin outflow control using a Monte Carlo method. The analysis is performed using the urban hydrology model EPA-SWMM driven by stochastic rainfall time-series generated from the Modified Bartlett-Lewis Rectangular Pulses Model. Water quality-informed real-time active control algorithms are developed, tested, and shown to display an improvement over traditional, passive (no control) systems and other storage-based active controls for water and pollutant capture. Seasonal and duration curve analysis showed that water level- and water quality- informed control performance varied for different storm return periods and this variability could partly be attributed to the fraction of time the valve is closed. In addition, control performance was sensitive to rainfall variability, generally decreasing as storms become less frequent and more intense. Therefore, control system performance may depend on seasonal and longer time-scale variability in climate and rainfall-runoff processes. We anticipate this study to be a starting point to incorporate theories of reliability to assess detention basin and conveyance network performance under more complex real-time control algorithms and failure modes.

Precipitation extremes on multiple timescales – Bartlett–Lewis rectangular pulse model and intensity–duration–frequency curves

Abstract. For several hydrological modelling tasks, precipitation time series with a high (i.e. sub-daily) resolution are indispensable. The data are, however, not always available, and thus model simulations are used to compensate. A canonical class of stochastic models for sub-daily precipitation are Poisson cluster processes, with the original Bartlett–Lewis (OBL) model as a prominent representative. The OBL model has been shown to well reproduce certain characteristics found in observations. Our focus is on intensity–duration–frequency (IDF) relationships, which are of particular interest in risk assessment. Based on a high-resolution precipitation time series (5 min) from Berlin-Dahlem, OBL model parameters are estimated and IDF curves are obtained on the one hand directly from the observations and on the other hand from OBL model simulations. Comparing the resulting IDF curves suggests that the OBL model is able to reproduce the main features of IDF statistics across several durations but cannot capture rare events (here an event with a return period larger than 1000 years on the hourly timescale). In this paper, IDF curves are estimated based on a parametric model for the duration dependence of the scale parameter in the generalized extreme value distribution; this allows us to obtain a consistent set of curves over all durations. We use the OBL model to investigate the validity of this approach based on simulated long time series.

Usability of the BLRP model for hydrological applications in arid and semi-arid regions with limited precipitation data

In this study, Hydrological Simulation Program-FORTRAN (HSPF) is used to investigate rainfall-runoff process in Taleghan watershed, northern Iran. Despite the high accuracy of the model, the lack of rainfall data at short time scales (hour and less than hour) restricted implementation of the model especially for long time simulations. Some studies use simple division for daily rainfall disaggregation into the hourly values to provide data requirements of HSPF model. In simple division, each rainfall event is divided into 24 pulse stochastically and the peak flows may not properly being simulated due to the lower rainfall intensities. In this study, random parameter Bartlett–Lewis rectangular pulse (BLRP) model was implemented to disaggregate daily rainfall time series into the hourly values and the results compared with that of simple division. In BLRP model, parameters of the model calibrated against the 1, 24 and 48 h mean, variance, lag1 auto covariance and proportion dry of observed rainfall. The calibrated model was then implemented to disaggregate daily rainfall data into the hourly values. To compare two disaggregation approaches, daily stream flow simulation by HSPF model is initialized in 2 scenarios by applying the hourly rainfall data resulted from two disaggregation methods. The results indicated that while using the simple division method leads to the underestimation of peak flows, using the BLRP model improved peak flow simulations. This study indicated usability of the BLRP model for rainfall disaggregation in arid and semi-arid regions with limited fine scale precipitation data availability.

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

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.

BLRPM을 이용한 서울지점 시단위 강우의 월별 경년변화 연구

본 논문에서는 공간상의 한 점에 대한 연속시간 강우모델로 시간단위의 통계특성을 재현하는데 유용하다고 알려진 BLRPM(Bartlett-Lewis Rectangular Pulse Model)을 이용하여, 측우기 자료를 포함하는 서울지점의 일강우 자료를 분해하고 지속시간별로 집성하여 모의된 시단위 단기 강우의 정량적 장기변화 특성을 분석해 보았다. 모의자료의 전이확률과 발생빈도 분석결과, 측우기 관측계열(CWK)에 비해 근대 우량계 관측계열(MRG)의 무강우 지속기간은 길어지고 강우지속기간은 짧아졌음을 알 수 있다. 이는 과거에 비해 근래의 강우지속기간이 짧아졌음을 의미하고, 근래 강우량의 양적증가와 같이 고려해 보면 근래의 강우강도가 과거보다 매우 높아졌음을 증명해 준다. 1960년대 전후로 구분한 자료계열(BCC와 ACC)에 대하여 지속시간별 모의 강우량의 평균과 분산의 비(증감률)를 월별로 비교한 결과, 전반적으로 9월이 증가의 정도가 가장 컸고 8월도 비교적 큰 증가 경향을 보였다. 그러나 6월은 오히려 약간 감소한 경향을 나타냈다. In this study, Quantative long-term change characteristics of generated hourly short-term rainfall were analyzed through the disaggration of daily rainfall which are include Chukwooki rainfall of Seoul into hourly rainfall and then re-aggragation of the hourly rainfall by duration. From the analysis of transition probabilities and occurance fequencies of generated rainfall, modern rain gage data set(MRG)'s mean lengths of dry spells are increased and mean lengths of wet spells are decreased compared to Chukwooki data set(CWK). this means that rainfall durations of these days are shorter than past. And rainfall intensities of these days are much increased than past when considered with quantative increment of rainfall. From results of comparisons for the ratios of means and variances of generated durational rainfall which are classified with pre- and post- A.D. 1960, Increasing rates of September are greastest over all and August also shows the great Increasing rate relatively. But June shows the decreasing trend.

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.

Application of the stochastic model for temporal rainfall disaggregation for hydrological studies in north western England

Assessment of climate change on any hydrological system requires higher temporal resolution at hourly or less in terms of time scale. This paper implements the Bartlett–Lewis Rectangular Pulses (BLRP) model coupled with a proportional adjusting procedure to disaggregate daily rainfall to hourly rainfall in order to demonstrate the reliability of this method. Three stations in northwestern England have been selected that represent different climates in the region. Parameters estimation of the BLRP model has been performed under different levels of hourly rainfall aggregation for a combination of rainfall statistics. The HYETOS model, which applies BLRP, reproduced standard statistics such as mean, variance, Lag-1, autocorrelation as well as dry proportions. Moreover, the model was proven to have the capability to disaggregate the rainfall extremes. The fitted BLRP model could then be used to disaggregate future daily rainfall in order to investigate the climate change impact of different rainfall intensities.

A fine-scale point process model of rainfall with dependent pulse depths within cells

A cluster point process model is considered for the analysis of fine-scale rainfall time series. The model is based on three Poisson processes. The first is a Poisson process of storm origins, where each storm has a random (exponential) lifetime. The second is a Poisson process of cell origins that occur during the storm lifetime, terminating when the storm finishes. Each cell has a random lifetime that follows an exponential distribution (or terminates when the storm terminates, whichever occurs first). During cell lifetimes, a third Poisson process of instantaneous pulses occurs. The model is essentially an extension of the well-known Bartlett-Lewis rectangular pulses model, with the rectangular profiles replaced with a Poisson process of instantaneous pulse depths to ensure more realistic rainfall profiles for fine-scale series. Model equations, derived in Cowpertwait et al. (2007), are used to fit different sets of properties to a 60 year record of 5-min data taken from Kelburn, New Zealand. As in the previous work, two superposed processes are used to account for two main and distinct precipitation types (convective and stratiform). By treating the within-cell pulses as dependent random variables, it is found, by simulation, that improved fits to extreme values and the proportion of dry intervals are obtained. Citation Cowpertwait, P. S. P., Xie, G., Isham, V., Onof, C. & Walsh, D. C. I. (2011) A fine-scale point process model of rainfall with dependent pulse depths within cells. Hydrol. Sci. J. 56(7), 1110–1117.

Mathematical modeling and simulation of hourly precipitation through rectangular pulses

The recorded historical series of precipitation are usually available for short periods of time and with many failures. The use of mathematical modeling to simulate rainfall is a tool used to circumvent this problem and to simulate the operation of water systems in different scenarios. The present study applies mathematical modeling to the hourly pluviometric precipitation data simulation. A pluviographical data set from October 1980 to December 2007 was used in the study. Precipitation data sets were obtained through daily pluviometric digitalization from the Meteorologic Station of Epagri at Urussanga, in southern Santa Catarina, Brazil (latitude 28º 31’ S and longitude 48º 19’ W). To simulate the hourly rain series, the stochastic model was modified based on the Bartlett-Lewis rectangular pulses model with six parameters. Those parameters were fitted by minimizing a function related to the analytical expressions that define the average, variance, and autocorrelation coefficient at lag 1 and the probability of a dry period related to the estimated values from the observed data. Ten series were simulated for 100 years of data. Data analyses and results showed that fitting Bartlett-Lewis model parameters makes it possible to simulate hourly rainfall while preserving precipitation statistical properties at several temporal aggregation levels. In general, the probability of dry periods tended to be overestimated.

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.

Quantification of anticipated future changes in high resolution design rainfall for urban areas

Good performance of sewer systems is of paramount importance in modern cities. The last decades have shown an increase in the frequency of large storms, leading to flooding of urban areas, implying large direct and indirect costs to society. It is becoming necessary to assess to what extent changes in extreme rainfall will continue due to anthropogenic greenhouse gas emissions and socio-economic development paths. Changes in rainfall are usually predicted using General Circulation Models. However, these models cannot be used directly to predict changes in extreme point rainfall because the temporal and spatial resolution is too coarse. This paper presents an approach to overcoming the scale problem by constructing a model of rainfall based on the Random Parameter Bartlett–Lewis rectangular pulse model in combination with a multi-scaling disaggregator. The model performs well and indicates that an increase of 2–15% in extreme rainfall can be expected in Denmark the next 80 years.

Scenarios of extreme daily precipitation for Norway under climate change

Based on downscaled daily precipitation values from the global climate model of the Max Planck Institute in Hamburg, time series of 20 years have been generated to describe the current climate of 1980–1999 (control data) and the future climate of 2030–2049 (scenario data) for Norway. These time series serve as training data for the Randomised Bartlett-Lewis Rectangular Pulse Model (RBLRPM), a precipitation simulation model, and time series of 1000 years length have been generated to assess possible changes in the extreme precipitation regime due to climate change. The analysis of changes in extreme value patterns for annual and seasonal values in the scenario and control data sets shows tendencies towards increased extreme values and seasonal shifts for the scenario period. A general increase in mean and standard deviation of the extreme value sample and for values of 10 and 100 years return period is found, although the regional variability is significant. For some regions the increase is in the order of 10 to 50 % for both annual and seasonal values.

On the representation of hyetograph characteristics by stochastic rainfall models

Two stochastic models of the rainfall process, belonging to different categories, are compared in terms of how well they reproduce certain hyetograph characteristics. The first is the scaling model of storm hyetograph, which belongs to the category of storm-based models. The second is the Bartlett–Lewis rectangular pulse model, the most widespread among the category of point process models. The scaling model is further developed introducing one more parameter to better-fit historical data. The Bartlett–Lewis model is theoretically studied to extract mathematical relationships for the intra-storm structure. The intercomparison is based on the storm hyetographs of a data set from Greece and another one from USA. The different storms are identified in each data set and classified according to their duration. Both models are fitted using the characteristics of storms. The comparison shows that the scaling model of storm hyetograph agrees well with the structure of historical hyetographs whereas the Bartlett–Lewis rectangular pulse model exhibits some discrepancies in either its original version or its random parameter version. However, it is shown that the performance of the Bartlett–Lewis model is significantly improved, and becomes comparable to that of the scaling model, by introducing a power-law dependence of its cell related parameters (duration and rate of arrivals) on the storm duration.