Intensity Duration Frequency Relationships Research Articles

Bayesian estimation of rainfall intensity–duration–frequency relationships

Summary Rainfall intensity–duration–frequency (IDF) curves are one of the most commonly used tools in water resources engineering. They give an idea of how return levels of extreme rainfall intensities vary with duration over a range of return periods. It is assumed that the annual maximum intensity follows the generalised extreme value (GEV) distribution. Conventional methods of estimating IDF relationships do not provide estimates of uncertainty. We propose a Bayesian framework for handling uncertainties in IDF models. Firstly, we collect annual maximum intensity data over a relevant range of rainfall durations. Secondly, we define an approximate likelihood, the “independence” likelihood, in which the correlations have been ignored between maximum intensity data of different durations. Finally, we apply Bayesian inference to obtain the adjusted posterior, which accounts for likelihood misspecification. A comparison with earlier methods, without any adjustment amongst others, shows that the adjusted posteriors are considerably wider.

Comparison of Annual Maximum and Partial Duration Series for Derivation of Rainfall Intensity-Duration-Frequency Relationships in Peninsular Malaysia

AbstractThe use of partial duration series (PDS) with generalized Pareto (GPA) distribution in hydrological frequency analysis has been popular during the last few decades because PDS is capable of including more extreme events than annual maximum series (AMS). In Malaysia, the most updated rainfall intensity-duration-frequency (IDF) relationships that serve as the official hydrological design guideline are based on the fitting of AMS to the generalized extreme value (GEV) distribution. The purpose of this paper is to identify the statistical model that best represent Peninsular Malaysia for deriving rainfall IDF relationships. Besides GEV and GPA distributions, other distributions such as generalized logistic (GLO), Gumbel (EV1), lognormal (LN3), and log-Pearson Type III (LP3) are also included in this study. Rainfall data with record length varying between 10 and 41 years from 60 rainfall stations in Peninsular Malaysia are computed into AMS and PDS, and fitted to the selected distributions. The L-momen...

Multiparameter probability distributions for heavy rainfall modeling in extreme southern Brazil

Abstract Study region The study was conducted in the Rio Grande do Sul state – Brazil. Study focus Studies about heavy rainfall events are crucial for proper flood management in river basins and for the design of hydraulic infrastructure. In Brazil, the lack of runoff monitoring is evident, therefore, designers commonly use rainfall intensity–duration–frequency (IDF) relationships to derive streamflow-related information. In order to aid the adjustment of IDF relationships, the probabilistic modeling of extreme rainfall is often employed. The objective of this study was to evaluate whether the GEV and Kappa multiparameter probability distributions have more satisfying performance than traditional two-parameter distributions such as Gumbel and Log-Normal in the modeling of extreme rainfall events in southern Brazil. Such distributions were adjusted by the L-moments method and the goodness-of-fit was verified by the Kolmogorov–Smirnov, Chi-Square, Filliben and Anderson–Darling tests. New hydrological insights for the region The Anderson–Darling and Filliben tests were the most restrictive in this study. Based on the Anderson–Darling test, it was found that the Kappa distribution presented the best performance, followed by the GEV. This finding provides evidence that these multiparameter distributions result, for the region of study, in greater accuracy for the generation of intensity–duration–frequency curves and the prediction of peak streamflows and design hydrographs. As a result, this finding can support the design of hydraulic structures and flood management in river basins.

Downscaling approach to develop future sub-daily IDF relations for Canberra Airport Region, Australia

Abstract. Downscaling of climate projections is the most adopted method to assess the impacts of climate change at regional and local scale. In the last decade, downscaling techniques which provide reasonable improvement to resolution of General Circulation Models' (GCMs) output are developed in notable manner. Most of these techniques are limited to spatial downscaling of GCMs' output and still there is a high demand to develop temporal downscaling approaches. As the main objective of this study, combined approach of spatial and temporal downscaling is developed to improve the resolution of rainfall predicted by GCMs. Canberra airport region is subjected to this study and the applicability of proposed downscaling approach is evaluated for Sydney, Melbourne, Brisbane, Adelaide, Perth and Darwin regions. Statistical Downscaling Model (SDSM) is used to spatial downscaling and numerical model based on scaling invariant concept is used to temporal downscaling of rainfalls. National Centre of Environmental Prediction (NCEP) data is used in SDSM model calibration and validation. Regression based bias correction function is used to improve the accuracy of downscaled annual maximum rainfalls using HadCM3-A2. By analysing the non-central moments of observed rainfalls, single time regime (from 30 min to 24 h) is identified which exist scaling behaviour and it is used to estimate the sub daily extreme rainfall depths from daily downscaled rainfalls. Finally, as the major output of this study, Intensity Duration Frequency (IDF) relations are developed for the future periods of 2020s, 2050s and 2080s in the context of climate change.

Sub-daily extreme events distribution and changes in Northeastern Brazil in the 20th century

Abstract. The regional analysis of extreme hydrological events is connected with the availability of a dense network of rainfall data that is absent or inaccessible in Brazil, especially for sub-daily information. In engineering, extreme events rainfall information is represented by intensity–duration–frequency (IDF) relationships which are the most commonly used tools in water resources engineering for planning and design. Even if the sub-daily information that is included in the relationships is not available, the extreme rainfall information rest in the fundamentals of the IDF. This paper analyzes spatial distribution and track changes in sub-daily precipitation over Northeastern (NE) Brazil. Precipitation was estimated from IDF relationships information in Brazil based in rainfall measured from 1920's to 1950's (but still used in engineering projects) and information from the last half of the 20th century obtained from several IDFs gathered from municipalities' manuals, local symposia and books in many cases not easily obtainable. Results showed an intensification of extreme events in recent years, especially in shorter duration rainfall (less than 12 h). Hourly rainfall is bigger in almost all the Brazilian region, but especially in littoral and Northern portion, however, 12 and 24 h rainfall exhibit increases in the North, but, lower values in the Southern half of the region in concordance with flood changes reported by Milly et al. (2005). Analyzing the ratio between 1 and 24 h rainfall is possible to confirm its increase in all the region, with up to 35% in some areas. These results were able to show insight of sub-daily extreme events changes during 20th century in NE Brazil were previous reports were not found. The results also alerts for the necessity of engineering projects review, as outdated information is still being used for design purposes.

A More Efficient Rainfall Intensity-Duration-Frequency Relationship by Using an “at-site” Regional Frequency Analysis: Application at Mediterranean Climate Locations

Intensity-duration-frequency (IDF) relationships are the tools for obtaining design rainfall estimation. Their calculation requires rainfall data not commonly available in time. The scarce spatial information makes it difficult to perform a Regional Frequency Analysis (RFA). The objective of this paper was to establish a new method to obtain more efficient IDF relationships than those traditionally applied, by using at-site regional frequency analysis. An application to rainfall datasets from two Mediterranean climate locations (Spain and Chile) has been set up. Nine annual maximum rainfall data series (AMS) of duration from 10 min to 24 h were analyzed. The tests of Mann–Whitney for homogeneity, Wald-Wolfowitz for independence and Mann-Kendall for stationarity, were conducted to test the underlying assumptions in frequency analyses. The RFA tests identified the nine considered datasets from each location as a homogeneous region, and the suitable regional frequency distribution to establish the regional growth curves. Considering the regional index flood model, the regional growth curves were used to obtain the rainfall quantiles for the return periods and durations considered at each location Their combination with the equations obtained after correlating the mean values from the AMS and their durations permitted the obtainment of the new power-type IDF relationships.. The efficiency of the new model was evaluated by using several efficiency indexes, being more efficient and giving a better performance compared to traditional IDF models. The proposed method offers great application possibilities in Mediterranean climate areas located in the Mediterranean Catchment, California, Mexico, Central Chile, Australia and South Africa.

Model and parameter uncertainty in IDF relationships under climate change

Quantifying distributional behavior of extreme events is crucial in hydrologic designs. Intensity Duration Frequency (IDF) relationships are used extensively in engineering especially in urban hydrology, to obtain return level of extreme rainfall event for a specified return period and duration. Major sources of uncertainty in the IDF relationships are due to insufficient quantity and quality of data leading to parameter uncertainty due to the distribution fitted to the data and uncertainty as a result of using multiple GCMs. It is important to study these uncertainties and propagate them to future for accurate assessment of return levels for future. The objective of this study is to quantify the uncertainties arising from parameters of the distribution fitted to data and the multiple GCM models using Bayesian approach. Posterior distribution of parameters is obtained from Bayes rule and the parameters are transformed to obtain return levels for a specified return period. Markov Chain Monte Carlo (MCMC) method using Metropolis Hastings algorithm is used to obtain the posterior distribution of parameters. Twenty six CMIP5 GCMs along with four RCP scenarios are considered for studying the effects of climate change and to obtain projected IDF relationships for the case study of Bangalore city in India. GCM uncertainty due to the use of multiple GCMs is treated using Reliability Ensemble Averaging (REA) technique along with the parameter uncertainty. Scale invariance theory is employed for obtaining short duration return levels from daily data. It is observed that the uncertainty in short duration rainfall return levels is high when compared to the longer durations. Further it is observed that parameter uncertainty is large compared to the model uncertainty.

Analysis of hourly rainfall data for the development of IDF relationships using the order statistics approach of probability distributions

Rainfall intensities of various frequencies and durations are important parameters for the hydrologic design of storm sewers, culverts and other hydraulic structures. This can be achieved by the rainfall Intensity–Duration–Frequency (IDF) relationship, which is determined through rainfall frequency analysis. This paper exemplifies the use of the Gumbel and Fréchet distributions for modeling annual n-hourly maximum rainfall over different durations ‘n’ such as 1, 2, 3, 6, 12, 18, 24, 48, and 72 h (hr) recorded at Kanyakumari and Mandla rain-gauge stations. The order statistics approach is applied for the determination of distributional parameters in order to estimate rainfall and develop IDF relationships for different return periods. Goodness-of-Fit (GoF) tests such as the Anderson–Darling and Kolmogorov–Smirnov tests are employed for checking the adequacy of fitting the distributions to the recorded data. A diagnostic test involving the D-index is applied in order to select whether the Gumbel or the Fréchet is the most suitable distribution for the rainfall estimation. Model Performance Indicators (MPIs) such as the root mean square error and the correlation coefficient are used to analyse the performance of IDF relationships given by the Gumbel and Fréchet distributions. Based on the GoF and diagnostic test results, and MPI values, the study suggests that the IDF relationships developed using the Gumbel distribution are better suited for the estimation of rainfall intensity for Kanyakumari and Mandla.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada): an evaluation of regional climate model simulation with respect to two gridded datasets

This study proposes an assessment procedure to compare two gridded (Cubic Spline, CS, and ANUSPLIN) datasets and one regional climate model simulation series (CRCM 4.1.1) of seasonal maximum precipitation (SMP) over southern Quebec (Canada). This study consists of: (1) identifying the appropriate models that could provide the most accurate SMP estimates at a particular grid point; (2) delineating the climatic homogeneous regions; and (3) providing sub-regional intensity–duration–frequency (IDF) estimates. More specifically, five popular probability distributions (Generalized Extreme Value, Generalized Logistic, Weibull, Gamma, Log-Normal) are compared; cluster analysis was employed to delineate a set of homogeneous sub-regions and one empirical model (Montana) was used to represent IDF relationships. From the results, it was found that: (1) CS product is more compatible with mean and maximum observed SMP time series than that of ANUSPLIN and CRCM 4.1.1 datasets, especially in summer; (2) Generalized Extreme Value represents the primary distribution pattern for the study area; (3) southern Quebec can be delineated into two distinct homogeneous sub-regions, especially in winter; and (4) Montana equation provides an accurate IDF model. This study can be viewed as an initial step towards the development of IDF curves under non-stationary conditions within the context of seasonal features in the regional precipitation regime.

Intra and inter-annual variability of runoff and sediment yield of an olive micro-catchment with soil protection by natural ground cover in Southern Spain

Despite the fact that the microcatchment scale allows us to evaluate the real complexity of soil protection in fields, few studies have been carried out in olive groves. This paper explores, on annual and event scales, the hydrological and erosive patterns observed in an olive microcatchment of about 6ha under non-tillage with spontaneous grass cover, where data series of runoff and sediment load have been measured in a contrasting hydrological period of over 5years. Firstly, the features of the data series acquired in the study station and its temporal context were explored through statistical analysis (statistics, histograms and correlation test), the intensity–duration–frequency relationships and the annual values of MOPREDAS dataset (1946–2005). In addition, annual and seasonal patterns were checked through Principal Components Analysis (PCA) to characterize the impact of rainfall variability and management techniques. Events with return periods of under 3years caused sediment loads between 7.2 and 17.0Mg., which implies that very high soil losses can be expected from frequent events. Although the contribution of a few events to the annual runoff and sediment load is substantial, a different distribution characterized by prolonged rainfall periods and very high soil losses was observed for a “rainy year” 2009–2010 (with an accumulated frequency of annual rainfall close to 79%). The PCA illustrated a seasonal pattern of events where low values of soil losses and sediment concentration were observed in spring. This is probably associated to lower soil moisture and to sediment being trapped by the grass cover. Finally, the minimal cost of the spontaneous cover for soil protection encourages its use, despite the fact that could be inefficient when inter-rill erosion is either not the main source of sediment in the catchment or it is not well-established.

Influence of climate change on IDF curves for the metropolitan area of Barcelona (Spain)

ABSTRACTThe evaluation of the possible climate change influence on extreme precipitation is very interesting in the Mediterranean area due to the usual and characteristic high intensities of its rainfall pattern. This analysis is also very important in urban zones, especially those densely populated with complex sewer systems, generally vulnerable to torrential rainfall. In this work, a total of 114 simulated daily rainfall series, 84 for the period 2000–2099 and 30 for the control period 1951–1999, have been analysed. These series were obtained for six thermo‐pluviometric stations located in the metropolitan area of Barcelona using the information provided by five general circulation models under four future climate scenarios of greenhouse gas emissions and applying statistical downscaling methods. The potential changes in the intensity–duration–frequency relationships due to climate change have been investigated. For the last third of the 21st century, under A1B, A2 and B2 climate scenarios, an increase of at least 4% has been found on the expected daily rainfall with return period longer than 20 years. Using a temporal downscaling based on scaling properties of rainfall, future hourly extreme rainfall has been estimated. For almost all the scenarios and periods considered, the increase on the expected hourly rainfall has resulted slightly higher than the corresponding daily rainfall. The greatest differences between the future hourly and daily rainfall estimated have been found in the second third of the century under scenarios A1B (8%) and A2 (9%). © 2013 Royal Meteorological Society

Deriving a practical form of IDF formula using transformed rainfall intensities

A general form of formula is presented for the rainfall Intensity–Duration–Frequency (IDF) relationship. This formula is derived from the nearly normal probability distribution function of transformed intensities. In order to transform the raw intensities, a correcting non-constant spread technique, the Kruskal–Wallis statistic, and the Box–Cox transformation are adopted. These transformations enable to express a simpler model for the IDF formula that agrees well with traditional IDF relationships. Since the proposed method allows the estimation of any percentile value of intensities with a single equation, the intensity percentile at arbitrary duration can be generated easily. The validity of the formula derived by means of the proposed method is assessed using data from major weather stations in Korea. The results show that the percentile intensities produced using the proposed method are in good agreement with those of traditional frequency analysis. Copyright © 2013 John Wiley & Sons, Ltd.

RainIDF: automated derivation of rainfall intensity–duration–frequency relationship from annual maxima and partial duration series

RainIDF, a software tool for derivation of rainfall intensity–duration–frequency (IDF) relationship is developed as an Excel add-in by using Visual Basics for Applications (VBA). The tool is integrated with two of the most widely used statistical distributions for determination of IDF relationship: the generalized extreme value (GEV) distribution for annual maxima series, and the generalized Pareto (GPA) distribution for partial duration series (PDS). It provides automated distribution fitting for rainfall data in the form of annual maxima or PDS for multiple intervals, solving and plotting of rainfall IDF curves. RainIDF uses the Solver add-in function in Excel to solve the coefficients of the empirical IDF formula in one step. The methodology built into RainIDF is discussed and rainfall IDF relationships for several stations in Peninsular Malaysia are derived and compared. RainIDF is available for download on GitHub (http://github.com/kbchang/rainidf) as an Excel add-in.

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.

Simple generalization approach for intensity-duration-frequency relationships

Rainfall intensity–duration–frequency (IDF) relationships describe rainfall intensity as a function of duration and return period, and they are significant for water resources planning, as well as for the design of hydraulic constructions. In this study, the two-parameter lognormal (LN2) and Gumbel distributions are used as parent distribution functions. Derivation of the IDF relationship by this approach is quite simple, because it only requires an appropriate function of the mean of annual maximum rainfall intensity as a function of rainfall duration. It is shown that the monotonic temporal trend in the mean rainfall intensity can successfully be described by this parametric function which comprises a combination of the parameters of the quantile function a(T) and completely the duration function b(d) of the separable IDF relationship. In the case study of Aegean Region (Turkey), the IDF relationships derived through this simple generalization procedure (SGP) may produce IDF relationships as successfully as does the well-known robust estimation procedure (REP), which is based on minimization of the nonparametric Kruskal–Wallis test statistic with respect to the parameters θ and η of the duration function. Because the approach proposed herein is based on lower-order sample statistics, risks and uncertainties arising from sampling errors in higher-order sample statistics were significantly reduced. The authors recommend to establish the separable IDF relationships by the SGP for a statistically favorable two-parameter parent distribution, because it uses the same assumptions as the REP does, it maintains the observed temporal trend in the mean additionally, it is easy to handle analytically and requires considerably less computational effort. Copyright © 2012 John Wiley & Sons, Ltd.

Rainfall spatial organization and areal reduction factors in the metropolitan area of Barcelona (Spain)

The rainfall spatial organization in the metropolitan area of Barcelona (Spain) has been studied from records of an urban rain gauge network in the period 1994–2009. Using statistical and regional analysis techniques, correlation between data recorded by the different rain gauges has been calculated, and the effective number of independent stations (n eq) equivalent to the used network has been determined. It has been found out that for durations longer than 20 min, the areal rainfall return period observed for a storm registered by the network approximately decreases by a factor of 1/n eq in relation to the current point rainfall intensity–duration–frequency relationships for the metropolitan area of Barcelona. Using objective analysis techniques, continuous precipitation fields have been generated on a regular grid with a spatial resolution of 300 × 300 m for the storms registered by the rain gauges from 1994 to 2009, for durations from 10 min to 24 h. The precipitation fields obtained have been useful to estimate the characteristic areal reduction factors in the metropolitan area of Barcelona. A direct relationship has been found between the areal reduction factor for all the area corresponding to the urban rainfall network of Barcelona and the effective number of n eq for every duration considered.

IDF relationships using bivariate copula for storm events in Peninsular Malaysia

► We derive IDF points of convective storms by using the copula method. ► The correlation between storm intensity and duration is negative and moderate. ► The Frank and Gaussian copula are suitable for storms in Peninsular Malaysia. ► We compare the results with the IDF curves from the univariate approach. ► The IDF points from both methods are in agreement with each other. Intensity–duration–frequency (IDF) curves are used in many hydrologic designs for the purpose of water managements and flood preventions. The IDF curves available in Malaysia are those obtained from univariate analysis approach which only considers the intensity of rainfalls at fixed time intervals. As several rainfall variables are correlated with each other such as intensity and duration, this paper aims to derive IDF points for storm events in Peninsular Malaysia by means of bivariate frequency analysis. This is achieved through utilizing the relationship between storm intensities and durations using the copula method. Four types of copulas; namely the Ali–Mikhail–Haq (AMH), Frank, Gaussian and Farlie–Gumbel–Morgenstern (FGM) copulas are considered because the correlation between storm intensity, I , and duration, D , are negative and these copulas are appropriate when the relationship between the variables are negative. The correlations are attained by means of Kendall’s τ estimation. The analysis was performed on twenty rainfall stations with hourly data across Peninsular Malaysia. Using Akaike’s Information Criteria (AIC) for testing goodness-of-fit, both Frank and Gaussian copulas are found to be suitable to represent the relationship between I and D . The IDF points found by the copula method are compared to the IDF curves yielded based on the typical IDF empirical formula of the univariate approach. This study indicates that storm intensities obtained from both methods are in agreement with each other for any given storm duration and for various return periods.

Rainfall Intensity-Duration-Frequency Relationships for Andhra Pradesh, India: Changing Rainfall Patterns and Implications for Runoff and Groundwater Recharge

Accurate and current rainfall characterization is an important tool for water-related system design and management. Updated rainfall intensity-duration-frequency (IDF) relationships in peninsular India were developed; impacts on runoff and groundwater recharge attributable to changes in rainfall characteristics are discussed. Two data sets were used from gage in Hyderabad city, the capital of Andhra Pradesh: hourly rainfall data for the 19 years from 1993–2011 and daily rainfall data for the 30 years from 1982–2011. Hourly data were used to develop updated rainfall IDF relationships; daily data were used for trend analysis of threshold-based rainfall events. IDF curves were developed for return periods of 2, 5, 10, 15, 25, 50, 75, and 100 years for 1-, 2-, 4-, 8-, and 24-h durations. The updated IDF relationships showed a significant change in rainfall characteristics compared with older relationships for the region surrounding Hyderabad, India; they showed greater rainfall intensities across all durations and return periods. Greater intensity storms may reduce groundwater recharge and increase runoff, making the surface storage of runoff increasingly important to enhance recharge and reduce flooding risks.

Intense rainfalls prediction models for the state of Mato Grosso, Brazil (Portuguese)

A ausência de equações de chuvas intensas para o Estado do Mato Grosso e a necessidade de maior segurança na elaboração de projetos e dimensionamento de obras hidráulicas, objetivou este estudo na obtenção das relações de intensidade-duração-frequência (IDF) e do modelo de Bell. Utilizou-se, então, da metodologia da desagregação da chuva de 24 h para as observações diárias de 136 estações pluviométricas do Estado do Mato Grosso disponíveis no banco de dados da Agência Nacional de Águas. Empregando a distribuição de Gumbel foram estimadas para cada tempo de duração, as chuvas intensas para os períodos de retorno de 2, 5, 10, 25, 50 e 100 anos e, posteriormente, para cada estação, ajustaram-se as relações IDF e os modelos de Bell. Os coeficientes das relações IDF e dos modelos de Bell ajustados pelo método dos mínimos quadrados, para todas as estações avaliadas, apresentaram coeficientes de determinação e o índice de concordância de Willmott superiores a 0,98 e 0,85, respectivamente, o que classifica o ajustamento como ótimo.

Developing rainfall intensity–duration–frequency relationship for two regions in Saudi Arabia

Intensity–duration–frequency (IDF) relationship of rainfall amounts is one of the most commonly used tools in water resources engineering for planning, design and operation of water resources projects. The objective of this research is to derive IDF relationship of rainfall at Najran and Hafr Albatin regions in the kingdom of Saudi Arabia (KSA). These relationships are useful in the design of urban drainage works, e.g. storm sewers, culverts and other hydraulic structures. Two common frequency analysis techniques were used to develop the IDF relationship from rainfall data of these regions. These techniques are: Gumbel and the Log Pearson Type III distribution (LPT III).An equation for estimating rainfall intensity for each region was derived using both techniques. The results obtained using Gumbel distribution are slightly higher than the results obtained using the LPT III distribution. Rainfall intensities obtained from these two methods showed good agreement with results from previous studies on some parts of the study area. The chi-square goodness-of-fit test was used to determine the best fit probability distribution. The parameters of the IDF equations and coefficient of correlation for different return periods (2, 5, 10, 25, 50 and 100) are calculated by using non-linear multiple regression method. The results obtained showed that in all the cases the correlation coefficient is very high indicating the goodness of fit of the formulae to estimate IDF curves in the region of interest.