Regional Intensity–duration–frequency Research Articles

Regional non-stationary future extreme rainfall under changing climate over Asian Monsoon Region

An increase in the Intensity-Duration-Frequency (IDF) of rainfall extremes questions the assumption of stationarity in the design and planning of water infrastructures under changing climate. To address this, non-stationary-based approaches are widely used for assessing the extremes over time. However, the trends associated with future extreme rainfall would differ from that of the historical dataset. Therefore, the main objective of this study is to develop a non-stationary modelling approach to generate future regional IDF curves by incorporating the trend in the rainfall over Asian Monsoon Region (AMR). Daily rainfall data from (i) APHRODITE and (ii) baseline period (1951–2005) and future projections (2020−2100) simulated from 27 GCMs are used in this study. The proposed framework includes (i) selection of GCM models, (ii) Stationary (S) and Non-Stationary (NS) Generalized Extreme Value Distribution (GEVD) Models, (iii) delineation of extreme precipitation zones, (iv) performance evaluation of zone-wise models, and (v) estimation of future regional IDF curves for near-future (2020–2060), and far-future (2061–2100). Results show that the eight models and their corresponding GCM covariates cover around 90% of grids across the AMR compared to S-GEVD models among the 27 GCMs. Six extreme precipitation zones were obtained, and fitted regional models could mimic the individual station models. The change in extreme rainfall intensity for the future climate is higher for zone-1 (low extreme rainfall region), with an increase of 87–98% across different emission scenarios using the non-stationary models, whereas for zone-6 (higher extreme rainfall region) has a 60–68% increase from its stationary counterparts. For high and low emission scenarios, intensity increases up to 98% and 87% respectively for a lower return period (5-year), and 65% and 58% for a higher return period (100-year) by the end of the century.

Regionalization of rainfall intensity–duration–frequency (IDF) curves with L-moments method using neural gas networks

Floods are one of the most frequent and destructive natural events which lead to lots of human and financial losses with damage to the houses, farms, roads, and other buildings. Intensity–duration–frequency (IDF) curves are the main and practical tools that have been used for flood control studies, including the design of the water structures. In many cases, there is no measuring device at the desired place, or their information is not helpful if there is any available. In this case, it is not possible to extract these curves through conventional methods. Regionalizing the IDF curves is a method that has solved the issues mentioned in the common methods. In this research, the regionalized IDF curves are extracted in Khuzestan province, Iran using 21 rain gauge stations through L-moments and neural gas networks. Clustering is one of the most effective steps and a prerequisite for regional frequency analysis (RFA) that divides the region and existing stations into hydrologically homogenous regions. In this study, clustering is done using two new models named neural gas (NG) and growing neural gas (GNG) network. Comparing the regional IDF curves with at-site curves, it was found that neural gas network models had a more accurate performance and higher efficiency, so they had the lowest estimate error amount among other models. Also, due to the acceptable difference between regional and at-site curves, the efficiency of L-moments in RFA was evaluated as appropriate.

Avaliação de equações de intensidade-duração-frequência e técnicas de espacialização na Bacia do Rio Grande no estado da Bahia, Brasil

ABSTRACT Understanding the probabilistic behavior of extreme rainfall on a fine temporal and spatial scales is crucial for design and risk assessment of hydraulic structures. However, information at appropriate resolutions is frequently limited or unavailable at the locations of interest, thereby requiring the estimation of Intensity-Duration-Frequency (IDF) curves at the regional scale. In this paper, we resort to simplified approaches for rainfall disaggregation and spatialization for deriving a regional IDF equation for the Grande River catchment, in the Brazilian state of Bahia. Our results suggest that, at the daily time scale, the maximum rainfall amounts can be reasonably described by the light-tailed Gumbel distribution in the study region. The spatialization procedures indicated that, whereas both the Inverse Distance Weighting (IDW) and the ordinary kriging techniques could capture the spatial variability of rainfall quantiles, for several durations of practical interest, only the former was able to model the spatial variability of the IDF parameters. Finally, despite the simplifying assumptions, we were able to derive smooth spatial surfaces for the aforementioned quantities, which might be useful for the design of hydraulic structures at ungauged sites.

Quantitative assessment of annual maxima, peaks-over-threshold and multifractal parametric approaches in estimating intensity-duration-frequency curves from short rainfall records

The present study uses hourly rainfall measurements from 36 raingauge stations in the northeastern United States with more than 55 years of recordings, to assess the accuracy and robustness of three conceptually different parametric approaches to produce intensity-duration-frequency (IDF) curves from rainfall records: (a) the well celebrated parametric IDF model based on annual maxima (AM) series, initially introduced by Rossi and Villani (1994) and later extended by Koutsoyiannis et al. (1998), (b) a peaks-over-threshold (PoT) model based on proper fitting of a reparametrized generalized Pareto (GP) distribution to the scaled excesses of the average rainfall intensity over various durations d, and (c) the analytical approximation introduced by Langousis et al. (2009) for estimation of multifractal (MF) rainfall maxima. Since its development, the third approach has never been tested in real world applications, and/or compared to routinely used approaches for IDF curve estimation. The obtained results show that the MF approach may constitute an important tool for hydrological applications, as it produces more accurate and robust IDF estimates than the other two approaches, irrespective of the duration d and return period T of interest, especially in cases where rainfall records exhibit significant length limitations. In addition, the parameters of the MF analytical approximation are found to be descriptive of the local topography and rainfall climatology of the region, providing a physically meaningful modeling setting that is particularly suited for regional frequency analysis and IDF estimation at ungauged locations.

Automatic feature selection and weighting for the formation of homogeneous groups for regional IDF estimation

The intensity-duration frequency (IDF) curve has been used as an effective tool to quantify the risk associated with the impact of extreme rainfall on civil infrastructure. However, recent changes in the rainfall climatology caused by climate change and urbanization have made estimates in the stationary environment provided by the traditional regional IDF approach increasingly inaccurate. This inaccuracy is mainly caused by the lack of consideration for the temporal and spatial differences in the selection of similarity indicators (attributes that are used to measure similarity of extreme rainfall patterns among different stations), resulting in ineffective formation of homogeneous groups (group of stations that share similar extreme rainfall patterns) at various regions. To consider the temporal differences of similarity indicators, including meteorological factors, topographic features and urban impact indicators, a three-layer design is proposed based on the three stages in extreme rainfall formation: cloud formation, rainfall generation and change of rainfall intensity over an urban surface. During the process, the impacts from climate change and urbanization on extreme rainfall patterns are considered through the inclusion of potential features that relate to the rainfall mechanism at each layer. The spatial differences of similarity indicators for Homogeneous Group Formation (HGF) at various regions is resolved by using an automatic feature selection and weighting algorithm, specifically the hybrid searching algorithm of Tabu Search, Lagrange Multiplier and Fuzzy C-means clustering, to select the optimal combination of features for HGF based on the uncertainty in the regional estimates of the rainfall quantiles for a specific site. The proposed methodology fills the gap of including the urbanization impacts on the extreme rainfall patterns during HGF process and challenges the traditional assumption that the same set of features can be equally effective in generating the optimal homogeneous group in regions with different geographic and meteorological characteristics.

A local-regional scaling-invariant Bayesian GEV model for estimating rainfall IDF curves in a future climate

Future changes in rainfall patterns induced by climate changes will affect society and ecosystems, and quantifying these changes is of utmost importance for the management of hydroclimate risk. In particular, the estimation of intensity-duration-frequency (IDF) curves for rainfall data is a routine procedure in urban hydrology and hydraulic studies and should be revisited to reflect future changes in rainfall variability. In this work, we propose a novel methodology based on the scaling-invariant property of rainfall duration versus intensity to estimate parameters of a generalized extreme value (GEV) distribution at sub-daily scales. A Bayesian inference framework is developed so that uncertainties are reduced and can be easily propagated to IDF curves. The proposed model can be employed to: (i) improve local (at-site) GEV estimates for sites with limited rainfall records; (ii) estimate GEV parameters at sub-daily scales and construct IDF curves for sites where only daily rainfall records are available (partially gauged sites); (iii) construct regional IDF curves for homogeneous hydrologic regions; and (iv) update local and regional IDF curves from simulations of future daily rainfall. The model is tested using historical rainfall data from 18 gauges located in the Han River Watershed in South Korea, and projected climate change scenarios RCP 6 and RCP 8.5 from the Met Office Hadley Centre HadGEM2-AO model. When considering historical data, the results show that the model satisfactorily estimate IDF curves for both gauged and partially gauged sites. In future scenarios, the model reveals a substantial increase in rainfall events of rare intensity (large return periods), mostly due to changes in the rainfall variability rather than changes in the average rainfall. Particularly, for a 100-year return period event, we expect an increase of about 23% in scenario RCP 6 and about 30% under scenario RCP 8.5 when projected using regional IDF curves. To the best of our knowledge, this is the first statistical approach in the literature to assess future changes in regional IDF curves, which in our opinion is more suitable than evaluating local estimates only.

Development of Monsoonal Rainfall Intensity-Duration-Frequency (IDF) Relationship and Empirical Model for Data-Scarce Situations: The Case of the Central-Western Hills (Panchase Region) of Nepal

Intense monsoonal rain is one of the major triggering factors of floods and mass movements in Nepal that needs to be better understood in order to reduce human and economic losses and improve infrastructure planning and design. This phenomena is better understood through intensity-duration-frequency (IDF) relationships, which is a statistical method derived from historical rainfall data. In Nepal, the use of IDF for disaster management and project design is very limited. This study explored the rainfall variability and possibility to establish IDF relationships in data-scarce situations, such as in the Central-Western hills of Nepal, one of the highest rainfall zones of the country (~4500 mm annually), which was chosen for this study. Homogeneous daily rainfall series of 8 stations, available from the government’s meteorological department, were analyzed by grouping them into hydrological years. The monsoonal daily rainfall was disaggregated to hourly synthetic series in a stochastic environment. Utilizing the historical statistical characteristics of rainfall, a disaggregation model was parameterized and implemented in HyetosMinute, software that disaggregates daily rainfall to finer time resolution. With the help of recorded daily and disaggregated hourly rainfall, reference IDF scenarios were developed adopting the Gumbel frequency factor. A mathematical model [i = a(T)/b(d)] was parameterized to model the station-specific IDF utilizing the best-fitted probability distribution function (PDF) and evaluated utilizing the reference IDF. The test statistics revealed optimal adjustment of empirical IDF parameters, required for a better statistical fit of the data. The model was calibrated, adjusting the parameters by minimizing standard error of prediction; accordingly a station-specific empirical IDF model was developed. To regionalize the IDF for ungauged locations, regional frequency analysis (RFA) based on L-moments was implemented. The heterogeneous region was divided into two homogeneous sub-regions; accordingly, regional L-moment ratios and growth curves were evaluated. Utilizing the reasonably acceptable distribution function, the regional growth curve was developed. Together with the hourly mean (extreme) precipitation and other dynamic parameters, regional empirical IDF models were developed. The adopted approach to derive station-specific and regional empirical IDF models was statistically significant and useful for obtaining extreme rainfall intensities at the given station and ungauged locations. The analysis revealed that the region contains two distinct meteorological sub-regions highly variable in rain volume and intensity.

Regionalization of Rainfall Intensity-Duration-Frequency using a Simple Scaling Model

Design storm is one of the most important tools to design hydraulic structures, hydrologic system and watershed management, mostly extracted by intensity- duration - frequency (IDF) curves for a given specific duration and return period. As for conventional methods to calculate IDF curves, the precipitation should be recorded for different durations so that foregoing curves can be extracted. Such data can be collected from rain gauge stations. In many areas, just daily precipitation data are available by which IDF curves cannot be extracted as per conventional methods. The aim of this research is to make IDF curves for short-term durations according to time scaling model as well as daily rainfalls. The relationships of this method are characterized with three variables including mean (μ 24) and standard deviation (σ 24) of daily rainfall intensity, and scaling exponent (H) by which all IDF curves might be drawn. The method used in present paper entails for less computational steps than conventional methods and by far has low parameters considerably than others in turn increases reliability. Scaling method is used to extract the IDF curves in rain-gauge stations in Khuzestan province located in southwest Iran and results proved the efficiency and robustness of the scaling method. Also ability of scaling concept method was examined in constructing of regional IDF.

극치자료계열의 Scaling 특성과 Bayesian GLM Model을 이용한 지역빈도해석

확률강수량 산정은 하천관리, 수공구조물 설계 및 위험도 분석에 있어 중요한 기초적인 자료 중 하나이다. 실무에서는 대표지속시간에 대해서 지점빈도해석을 통해 확률강수량을 추정하고 이를 지속시간에 대해서 회귀분석을 실시하여 IDF (intensity-duration-frequency) 곡선을 작성한다. 이들 IDF곡선을 활용하여 기타 지속시간에 대해서는 내삽 또는 외삽으로 보간 하여 확률강수량 추정이 이루어지고 있다. 우리나라의 경우 상대적으로 자료 연한이 짧은 점을 고려한다면, 보다 정확하고 신뢰성 있는 확률강수량 산정 기법의 필요성이 대두되고 있다. 이러한 이유로 본 연구에서는 Bayesian GLM 모형을 통하여 자료의 확률분포 매개변수의 Scaling 특성을 고려할 수 있는 지역빈도해석 모형을 개발하였다. 모형 적용결과 개별지점에서 효과적인 매개변수 추정뿐만 아니라, 유역전체의 특성을 대표하는 매개변수 추정이 가능하였다. 본 연구결과를 통해 도출된 IDF 곡선은 향후 다양한 수자원분야의 기초자료로 활용될 수 있을 것으로 기대되며, 미계측유역 또는 지속시간별 자료가 불충분한 지역에 대해서도 활용이 가능할 것으로 판단된다. Design rainfalls are one of the most important hydrologic data for river management, hydraulic structure design and risk analysis. The design rainfalls are first estimated by a point frequency analysis and the IDF (intensity-duration-frequency) curve is then constructed by a nonlinear regression to either interpolate or extrapolate the design rainfalls for other durations which are not used in the frequency analysis. It has been widely recognised that the more reliable approaches are required to better account for uncertainties associated with the model parameters under circumstances where limited hydrologic data are available for the watershed of interest. For these reasons, this study developed a hierarchical Bayesian based GLM (generalized linear model) for a regional frequency analysis in conjunction with a scaling function of the parameters in probability distribution. The proposed model provided a reliable estimation of a set of parameters for each individual station, as well as offered a regional estimate of the parameters, which allow us to have a regional IDF curve. Overall, we expected the proposed model can be used for different aspects of water resources planning at various stages and in addition for the ungaged basin.

Analysis of Rainfall Intensity-Duration-Frequency Relationship for Rwanda

Global atmospheric and oceanic perturbations and local weather variability induced factors highly alter the rainfall pattern of a region. Such factors result in extreme events of devastating nature to mankind. Rainfall Intensity Duration Frequency (IDF) is one of the most commonly used tools in water resources engineering particularly to identify design storm event of various magnitude, duration and return period simultaneously. In light of this, the present study is aimed at developing rainfall IDF relationship for entire Rwanda based on selected twenty six (26) rainfall gauging stations. The gauging stations have been selected based on reliable rainfall records representing the different geographical locations varying from 14 to 83 years of record length. Daily annual maximum rainfall data has been disaggregated into sub-daily values such as 0.5 hr, 1 hr, 3 hr, 6 hr and 12 hr and fitted to the probability distributions. Quantile estimation has been made for different return periods and best fit distribution is identified based on least square standard error of estimate. At-site and regional IDF parameters were computed and subsequent curves were established for different return period. The moment ratio diagram (MRD) and L-moment ratio diagram (LMRD) methods have been used to fit frequency distributions and identify homogeneous regions for observed 24-hr maximum annual rainfall. The rainfall stations have been divided into five homogeneous rainfall regions for all 26 stations. The results of present analysis can be used as useful information for future water resources development planning purposes.

Regional frequency analysis of extreme rainfall events in Jakarta

Jakarta is vulnerable to flooding and extreme rainfall events are always the main cause of the occurrence of heavy flood events with loss of life and property. The flood in February 2007 is one of the most devastating events with the total rainfall during the 2-week period amounted to almost one-fourth of the total rainfall in 2007 at some stations. The huge scale of the loss due to this event as well as a series of big consecutive events the following years draw the attention to understand the flood risk in detail for Jakarta region. The study aimed to (1) estimate the return period for the February 2007 event in Jakarta, (2) develop intensity–duration–frequency (IDF) curves as well as the corresponding confidence intervals for Jakarta region up to 7-day duration and (3) understand the uncertainty of developed IDF curves induced with at-site and regional approaches. Daily rainfall data from 11 stations within Jakarta region with record lengths ranging from 15 to 22 years were collected. As the reliability of the frequency analysis is influenced by record length available, the frequencies and magnitudes of extreme rainfall events in the Jakarta region were analyzed by regional frequency analysis (RFA) based on the method of L-moments. One station (Darmaga) was removed from 11 stations after the data quality and homogenization check. The annual maximum rainfall series of duration of 1, 2, 3, 4, 5, 6, and 7 day at the 10 stations in Jakarta were then aggregated for the investigation. Because the value of discordancy measure exceeded the critical value, station Tangerang was subsequently removed from the group. Annual maximum series at these 9 stations were finally combined as the study region and passed the discordancy measure and heterogeneity measures of RFA. The accuracy of at-site rainfall quantile estimates by at-site and RFA was assessed and compared by error bounds at the confidence level of 90 %, based on Monte Carlo simulations by fitting generalized extreme value probability distributions to the regional average sample L-moment ratios. The results showed that the return period of the February 2007 extreme event in Jakarta is over 300 year for 3-day duration at Halim station; close to 200 and 150-year return periods for 7-day duration at Halim and Pdk Betung stations, respectively. For the first time, the Jakarta regional multi-day IDF curves together with the corresponding 90 % confidence intervals for 2, 5, 10, 30, 50, 100, 200, and 300 year were developed. For effective flood risk mapping/mitigation in Jakarta, duration of longer than 1-day design storm should be considered. Also frequent re-visit of the IDF curves is indeed important if severe storms occurred after the IDF curves are established. Finally, the study suggested that more stations/data should be acquired for the region so that the estimation is more robust and reliable.

Precipitation frequency analysis based on regional climate simulations in Central Alberta

Summary A Regional Climate Model (RCM), MM5 (the Fifth Generation Pennsylvania State University/National Center for Atmospheric Research mesoscale model), is used to simulate summer precipitation in Central Alberta. MM5 was set up with a one-way, three-domain nested framework, with domain resolutions of 27, 9, and 3 km, respectively, and forced with ERA-Interim reanalysis data of ECMWF (European Centre for Medium-Range Weather Forecasts). The objective is to develop high resolution, grid-based Intensity–Duration–Frequency (IDF) curves based on the simulated annual maximums of precipitation (AMP) data for durations ranging from 15-min to 24-h. The performance of MM5 was assessed in terms of simulated rainfall intensity, precipitable water, and 2-m air temperature. Next, the grid-based IDF curves derived from MM5 were compared to IDF curves derived from six RCMs of the North American Regional Climate Change Assessment Program (NARCCAP) set up with 50-km grids, driven with NCEP-DOE (National Centers for Environmental Prediction-Department of Energy) Reanalysis II data, and regional IDF curves derived from observed rain gauge data (RG-IDF). The analyzed results indicate that 6-h simulated precipitable water and 2-m temperature agree well with the ERA-Interim reanalysis data. However, compared to RG-IDF curves, IDF curves based on simulated precipitation data of MM5 are overestimated especially for IDF curves of 2-year return period. In contract, IDF curves developed from NARCCAP data suffer from under-estimation and differ more from RG-IDF curves than the MM5 IDF curves. The over-estimation of IDF curves of MM5 was corrected by a quantile-based, bias correction method. By dynamically downscale the ERA-Interim and after bias correction, it is possible to develop IDF curves useful for regions with limited or no rain gauge data. This estimation process can be further extended to predict future grid-based IDF curves subjected to possible climate change impacts based on climate change projections of GCMs (general circulation models) of IPCC (Intergovernmental Panel on Climate Change).

Probabilistic Modelling of Hourly Rainfall Data for Development of Intensity-Duration-Frequency Relationships

The rainfall Intensity-Duration-Frequency (IDF) relationship is commonly required for planning and designing of various water resources projects. The IDF relationship is a mathematical relationship between the rainfall intensity, duration and return period. This relationship is determined through statistical analysis of recorded rainfall data. In this paper, annual n-hourly maximum rainfall for different duration of 'n' such as 1-hour (hr), 2-hr, 3-hr, 6-hr, 12-hr, 18-hr, 24-hr, 48-hr and 72-hr are extracted from hourly rainfall data recorded at Hissar and Kalingapatnam; and further used for estimation of rainfall for different return periods. Order statistics approach is applied for determination of parameters of Gumbel distribution. Regional IDF relationships to estimate rainfall intensity for different return periods for Hissar and Kalingapatnam regions are developed and presented in the paper.

Regional Intensity-Duration-Frequency Curves Derived from Ensemble Empirical Mode Decomposition and Scaling Property

This paper proposes deriving regional intensity-duration-frequency (IDF) curves for Edmonton, Canada, based on the scaling property of precipitation data using ensemble empirical mode decomposition (EEMD). Selected sets of annual maximum precipitation data were decomposed by the EEMD to intrinsic mode functions (IMFs), and the scaling property was investigated. Next, representative scale exponents were extracted. The results show that quantiles derived from general extreme value (GEV) probability distribution (PD) with parameters derived by the probability-weighted moment (PWM) are more accurate than those derived from the extreme value type I (EVI) PD with parameters derived by the method of moment (MOM), whose underestimation of rainfall intensity becomes obvious for high return period (greater than 25 years) and short duration (less than 1 h). The results also show that for Edmonton, generally three of four IMFs of the precipitation data showed a simple scaling property, and regional IDF curves derived from the scaling IDF and EEMD approach predict accurate storm intensities for rain-gauging sites at both the calibration and validation stages, but there could be errors associated with predicted storms of high return periods (100 year). DOI: 10.1061/(ASCE)HE.1943-5584.0000612. © 2013 American Society of Civil Engineers.

Regionalization of heavy rainfall to improve climatic design values for infrastructure: case study in Southern Ontario, Canada

Southern Ontario, Canada, has been impacted in recent years by many heavy rainfall and flooding events that have exceeded existing historical estimates of infrastructure design rainfall intensity–duration–frequency (IDF) values. These recent events and the limited number of short-duration recording raingauges have prompted the need to research the climatology of heavy rainfall events within the study area, review the existing design IDF methodologies, and evaluate alternative approaches to traditional point-based heavy rainfall IDF curves, such as regional IDF design values. The use of additional data and the regional frequency analysis methodology were explored for the study area, with the objective of validating identified clusters or homogeneous regions of extreme rainfall amounts through Ward's method. As the results illustrate, nine homogeneous regions were identified in Southern Ontario using the annual maximum series (AMS) for daily and 24-h rainfall data from climate and rate-of-rainfall or tipping bucket raingauge (TBRG) stations, respectively. In most cases, the generalized extreme value and logistic distributions were identified as the statistical distributions that provide the best fit for the 24-h and sub-daily rainfall data in the study area. A connection was observed between extreme rainfall variability, temporal scale of heavy rainfall events and location of each homogeneous region. Moreover, the analysis indicated that scaling factors cannot be used reliably to estimate sub-daily and sub-hourly values from 24- and 1-h data in Southern Ontario. Citation Paixao, E., Auld, H., Mirza, M.M.Q., Klaassen, J. & Shephard, M.W. (2011) Regionalization of heavy rainfall to improve climatic design values for infrastructure: case study in Southern Ontario, Canada. Hydrol. Sci. J. 56(7), 1067–1089.

Developing Intensity-Duration-Frequency Curves in Scarce Data Region: An Approach using Regional Analysis and Satellite Data

The availability of data is an important aspect in frequency analysis. This paper explores the joint use of lim- ited data from ground rainfall stations and TRMM data to develop Intensity Duration Frequency (IDF) curves, where very limited ground station rainfall records are available. Homogeneity of the means and variances are first checked for both types of data. The study zone is assumed to be belonging to the same region and checked using the Wiltshire test. An Index Flood procedure is adopted to generate the theoretical regional distribution equation. Rainfall depths at various return periods are calculated for all stations and plotted spatially. Regional patterns are identified and discussed. TRMM data are used to develop ratios between 24-hr rainfall depth and shorter duration depths. The regional patterns along with the developed ratios are used to develop regional IDF curves. The methodology is applied on a region in the North-West of Angola.

Development of isopluvial map using L-moment approach for Tehri-Garhwal Himalaya

Estimation of design rainfall intensity is crucial for design and planning of water resources engineering projects. The intent of the present study is to develop regional IDF curves for Tehri-Garhwal Himalayan region in India, wherein numbers of hydropower projects are in planning and execution stage. Self Recording Rain Gauge (SRRG) stations are generally not so frequent in the project locations. Under this situation, the engineers are forced to use regional intensity duration frequency (IDF) curves. Under this study, four stations viz. Tehri M.T.Lab, Mukhim, Pilkhi and Dhuttu were available with SRRG data. These data are used to develop the regional IDF curve for entire Tehri-Garwal region. After selection of the most intensive storms, return periods has been determined using regionalized L-moment method. After developing IDF curves for above four raingauge stations, Thiessen Ploygon method is applied to find out average IDF curve. To show the spatial variability, Isopluvial maps have been generated using ArcGIS and a relation equation has been developed.

Assessment of future change in intensity–duration–frequency (IDF) curves for Southern Quebec using the Canadian Regional Climate Model (CRCM)

Intensity–duration–frequency curves are used extensively in engineering to assess the return periods of rainfall events. The estimation and use of IDF curves rely on the hypothesis of rainfall series stationarity, namely that intensities and frequencies of extreme hydrological events remain unchanged over time. It is however expected that global warming will modify the occurrence of extreme rainfall events. In order to assess how extreme rainfall events will be modified in a future climate, an analysis of the Canadian Regional Climate Model (CRCM) simulations under control (1961–1990) and future (2041–2070) climates was performed. May to October annual maximum (MOAM) rainfall for 2-, 6-, 12- and 24-h durations were extracted and analyzed using regional frequency analysis for grid boxes covering the Southern Quebec region. Comparison with available rainfall records shows that CRCM estimates are consistent with those based on observed data considering the different spatial scales related to observed data (meteorological stations) and to simulated ones (grid boxes). Comparison of regional estimates in control and future climate at the grid box scale reveals that return periods of 2- and 6-h events will approximately halve in future climate while they will decrease by a third for 12- and 24-h events. Regional IDF curves at the grid box and the station scales are proposed. The analysis of spatial correlation of simulated MOAM series in control and future climates for the region under study suggests that, for a given duration, spatial correlations will decrease in a future climate suggesting that annual extreme rainfall events may result from more convective (and thus more localized) weather systems. Multi-model ensemble systems (different GCMs with different RCMs) as well as multi-member ensembles (investigation of possible sensitivity to initial conditions) are needed to investigate the impact of model structures on future change in extreme rainfalls.

Regional rainfall intensity formulas based on scaling property of rainfall

This work developed regional Intensity–Duration–Frequency (IDF) formulas for non-recording sites based on the scaling theory. Forty-six recording raingauges over northern Taiwan provide the data set for analysis. The temporal scaling properties of annual maximum rainfall series for various durations were first investigated. The hypothesis of piecewise simple scaling combined with Gumbel distribution was used to develop the IDF scaling formulas. Since most of parameters in IDF scaling formulas can be estimated from the annual 1-day maximum series, these parameters were regionalized based on the relationship between the scaling exponent and the average of annual 1-day maximum rainfall. Three scaling homogeneous regions were classified by different scaling regimes and regional IDF scaling formulas were developed in each region. The analyzed results reveal that the regional IDF scaling formulas proposed herein resulted in reasonable simulations and verifications.

Incorporating uncertainty analysis into a regional IDF formula

A rainfall intensity–duration–frequency (IDF) relationship was generated by pooling annual maximum rainfall series from 14 recording rain gauges in southern Taiwan. Dimensionless frequency curves, plotted by the growth curve method, can be well fitted by regression equations for a duration ranging from 10 mins to 24 hours. As the parameters in regression equations have a good statistical relationship with average annual rainfall, a generalized regional IDF formula was then formulated. The formula, based on average annual rainfall as an index, can be easily applied to non-recording rain gauges. This paper further applies the mean value first-order second moment (MFOSM) method to estimate the uncertainty of the proposed regional IDF formula. From a stochastic viewpoint, the generalized regional IDF formula can accurately simulate the IDF relationship developed using frequency analysis (EV1) at individual stations. The method can provide both rainfall intensity and variance isohyetal maps for various rainfall durations and return periods over the study area. © 1998 John Wiley & Sons, Ltd.