Intensity-Duration-Frequency Models Research Articles

Bias‐Adjustment Methods for Future Subdaily Precipitation Extremes Consistent Across Durations

AbstractModel output from climate projections often requires bias‐adjustment to compensate for systematic model errors. A bias‐adjustment method for extreme precipitation intensity is proposed that preserves the scaling equation for different accumulation levels from hourly to daily, using intensity‐duration‐frequency (IDF) modeling. A validation is performed within a pseudo‐reality setting, based on hourly precipitation from 28 regional climate model projections of the EURO‐CORDEX ensemble over Belgium. The scaling‐based adjustment methods improve upon previous methods, an optimal method is identified, and, analytical quantile mapping methods must be avoided due to three identified problems. The ensemble mean of the adjusted extreme precipitation intensity obeys the above‐mentioned scale‐invariance property, which is consistent with observed extreme intensities. We thus show that IDF modeling provides added value in the context of bias‐adjustment, and, that the particular IDF model proposed balances well between accuracy and the preservation of desired properties such as scale invariance and consistency among rainfall durations.

Modeling Rainfall Intensity-Duration-Frequency (IDF) and Establishing Climate Change Existence in Uyo-Nigeria Using Non-Stationary Approach

This study aims at establishing if climate change exists in the Niger Delta environment using non-stationary rainfall Intensity-Duration-Frequency (IDF) modelling incorporating time-variant parameters. To compute the intensity levels, the open-access R-studio software was used based on the General Extreme Value (GEV) distribution function. Among the four linear parameter models adopted for integrating time as a covariate, the fourth linear model incorporating scale and location with the shape function constant produced the least corrected Akaike Information Criteria (AICc), varying between 306.191 to 101.497 for 15 and 1440 minutes, respectively, selected for calibration of the GEV distribution equation. The non-stationary intensities yielded higher values above those of stationary models, proving that the assumption of stationary IDF models underestimated extreme events. The difference of 13.71 mm/hr (22.71%) to 14.26 mm/hr (17.0%) intensities implies an underestimation of the peak flood from a stationary IDF curve. The statistical difference at a 95% confidence level between stationary and non-stationary models was significant, confirming evidence of climatic change influenced by time-variant parameters. Consequently, emphasis should be on applying shorter-duration storms for design purposes occurring with higher intensities to help reduce the flood risk and resultant infrastructural failures.

Deriving rainfall intensity–duration–frequency (IDF) curves and testing the best distribution using EasyFit software 5.5 for Kut city, Iraq

Abstract The intensity of rainfall can be considered as an essential factor in designing and operating hydraulic structures. The intensity–duration–frequency (IDF) curve is used for designing hydraulic projects such as drainage networks, road culverts, bridges, and many other hydraulic structures. In the field of water resources engineering, IDF curve is dependent widely on the plan, designing, and operating the project. Additionally, it can be used for different flood engineering structures. The purpose of this research is to get the frequency of the intensity of rain duration for Al KUTcity, Iraq, and find curves. Three essential techniques of frequency analysis (Gumbel distribution, lognormal, and log Pearson Type III) were depended to formulate this relationship based on data of rainfall intensity during the period between 1992 and 2019. Distribution methods involving lognormal, Gumbel, and log Pearson Type III were applied by Indian Meteorological Department (IMD) for short periods of 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 12, and 24 h with 2, 5, 10, 25, 50, and 100 years return periods. The results showed that rainfall intensity reduced as the duration of the storm increased, and if the return period of the rainfall was large, rainfall of any specific duration showed a higher intensity. Using EasyFit 5.5 software, for all durations, the lognormal probability distribution showed the best fit for the data group and estimated intensities of precipitation for return periods of 2, 5, 10, 25, 50, and 100 years. According to the obtained results, one can notice that the intensity of rainfall increased with the increment in return periods, but decreased with the increment in duration. The resulting IDF models could be used to improve accuracy and results.

The tales that the distribution tails of non-Gaussian autocorrelated processes tell: efficient methods for the estimation of the k-length block-maxima distribution

ABSTRACT The focal point of this work is the estimation of the distribution of maxima without the use of classic extreme value theory and asymptotic properties, which may not be ideal for hydrological processes. The problem is revisited from the perspective of non-asymptotic conditions, and regards the so-called exact distribution of block-maxima of finite-sized k-length blocks. First, we review existing non-asymptotic approaches/models, and introduce an alternative and fast model. Next, through simulations and comparisons (using asymptotic and non-asymptotic models), involving intermittent processes (e.g. rainfall), we highlight the capability of non-asymptotic approaches to model the distribution of maxima with reduced uncertainty and variability. Finally, we discuss an alternative use of such models that concerns the theoretical estimation of the multi-scale probability of obtaining a zero value. This is a useful finding when the scope is the multi-scale modelling of intermittent hydrological processes (e.g. intensity–duration–frequency models). The work also provides step-by-step recipes and an R package.

Evaluation of Generalized Extreme (GEV), Log-Pearson Type 3 (LP3), Pearson Type 3(P3) and Gumbel (EV1) Distributions for Development of IDF Equations for Warri, Nigeria

The application of Gumbel (EVI) to the development of rainfall intensity– duration – frequency (IDF) curves has often been criticized on theoretical and empirical grounds as it may underestimate the largest extreme rainfall amounts. The consequences of underestimation are economic losses, property damages, and loss of life. Therefore, it is important that water resources engineering infrastructure be accurately design to avoid these consequences. This paper evaluates the performances of four probability distributions; GEV, EV1, LP3 and P3 using the annual maxima precipitation series of 26 years for Warri Metropolis obtained from Nigerian Meteorological Agency (NiMet). The strength and weakness of the four probability distributions were examined with the goodness of fit (GOF) module of Easyfit software which implemented Kolmogorov - Smirnov (KS) and Anderson - Darling (AD) tests at 5% significance level. The Easyfit software fitted the precipitation series data to the four probability distributions and ranked the four probability distributions across the fifteen rainfall durations. Results show that for both KS and AD tests, GEV distribution was found to be best-fit distribution and it was applied to the development of IDF curves in Warri Metropolis, Nigeria. Furthermore, the IDF values obtained were applied in the development of three-parameter IDF models for return periods of 10 - , 15 -, 20 -, 25 - , 50 -, and 100-years. The mean absolute error, Nash – Sutcliffe Efficiency (NSE) and Root Mean Square Error (RMSE) indices computed for the IDF models increase with increasing return periods. The IDF curves and models depicted the general attributes of IDF curves and models. This study could be of significant academic value and improvement to professional practice in the design of storm water drainage systems. Therefore, the developed IDF curves and models are recommended to the Warri Urban Authority for inclusion in her stormwater handbooks and manuals.

Climate change-induced variations in future extreme precipitation intensity-duration-frequency in flood-prone city of Adama, central Ethiopia.

The influences of climate change on the features of extreme rainfall events have become unprecedented that needs improved understanding at all levels for planning effective management strategies of the potential risks. This study aims to assess the potential influences of climate change on extreme rainfall characteristics in flood-vulnerable city of Adama. Daily precipitation records of 1967-2016 and projection of global circulation models (GCMs): CanESM2 and HadCM3 for 2021-2070 were disaggregated into shorter time resolutions using the Hyetos model. Gumbel type I probability distribution and power-regression model ([Formula: see text] were used for deducing intensity-duration-frequency (IDF) curves and for describing their functions, respectively. The extreme rainfall intensity of the historical and future periods for a range of storm durations and return periods were compared and contrasted. A close agreement is obtained between the observed and the modeled rainfall intensity with high values of coefficient of determination (> 0.996) and Nash-Sutcliffe efficiency (> 0.850). Besides, statistically significant (p < 0.05) direct linear relationship is found between the return periods and the coefficient parameter of the IDF models. Moreover, the intensity of extreme precipitation over 2021-2070 in Adama city would increase up to 49.5%, depending on storm duration and return period considered. This could have consequences of the way the city's drainage infrastructures are designed, operated, and sustained. Hence, flood-prone areas should be recognized in order to formulate effective strategies for mitigation and adaption of potential impacts. The standards for designing future drainage infrastructures should also be updated aiming to reflect the effects of climatic change.

A Review Study on Stationary and Non-Stationary IDF Models Used in Rainfall Data Analysis around the World from 1951-2020

This article focuses on an overview of the processes of generating rainfall intensity-duration-frequency (IDF) models, the different types and applications. IDF model is an important tool applied in the design of either hydrologic or hydraulic design such as prediction of rainfall intensities to estimate peak runoff volumes for mitigation of flooding. IDF models evolved from stationary – parametric (empirical) and non-parametric (stochastic) models, to non-stationary models in which variables vary with time. Each category controls the ways models predict rainfall intensities, and reveals their strength and weaknesses. IDF models must therefore, be chosen in terms of the project objective, data availability, size of the study, location, output needed, and the desired simplicity. For instance, while the parametric model predicts better for shorter durations and return periods only, the non-parametric models predict better for both shorter and longer durations and return periods. For projects requiring change of input data over time and evaluation of uncertainty bounds, risk assessment, including incorporation of changes in extreme precipitation, the non-stationary model approach must be selected. Also, of importance for catchments without rainfall amount and corresponding duration records but has daily (24-hourly) record of rainfall depth, the Indian Meteorological Department (IMD) method of shorter duration disaggregation can be adopted to generate in-put data for the development of IDF curves for such a location. Therefore, each model type has limitations that may make it unsuitable for some projects. Reviewing input data and output requirements, and simplicity are all necessary to decide on which model type should be selected.

Evaluating the Performance of a Max-Stable Process for Estimating Intensity-Duration-Frequency Curves

To explicitly account for asymptotic dependence between rainfall intensity maxima of different accumulation duration, a recent development for estimating Intensity-Duration-Frequency (IDF) curves involves the use of a max-stable process. In our study, we aimed to estimate the impact on the performance of the return levels resulting from an IDF model that accounts for such asymptotical dependence. To investigate this impact, we compared the performance of the return level estimates of two IDF models using the quantile skill index (QSI). One IDF model is based on a max-stable process assuming asymptotic dependence; the other is a simplified (or reduced) duration-dependent GEV model assuming asymptotic independence. The resulting QSI shows that the overall performance of the two models is very similar, with the max-stable model slightly outperforming the other model for short durations (d≤10h). From a simulation study, we conclude that max-stable processes are worth considering for IDF curve estimation when focusing on short durations if the model’s asymptotic dependence can be assumed to be properly captured.

Development of Models for Rainfall Intensity- duration-frequency for Akure, South-west, Nigeria

The rainfall Intensity-Duration-Frequency (IDF) relationship is widely used for adequate estimation of rainfall intensity over a particular catchment. A 25 year daily rainfall data were collected from Nigerian Meteorological Agency (NIMET) Abuja for Akure station. Twenty five year annual maximum rainfall amounts with durations of 5, 10, 15, 20, 30, 45, 60, 90, 120, 180, 240, 300 and 420 minutes were extracted and subjected to frequency analysis using the excel solver software wizard. A total of six (6) return period specific and one (1) general IDF models were developed for return periods of 2, 5, 10, 25, 50 and 100 years using Gumbel Extreme Value Type-1 and Log Pearson Type -3 distributions. Anderson Darling goodness of fit test was used to ascertain the best fit probability distribution. The R2 values range from 0.982 to 0.985 for GEVT -1 and 0.978 to 0.989 for Log Pearson type -3 while the Mean Squared Error from 33.56 to 156.50 for GEVT -1 and 43.01 to 150.63 Log Pearson Type III distributions respectively. The probability distribution models are recommended for the prediction of rainfall intensities for Akure metropolis.

Rainfall intensity-duration-frequency models for Lokoja Metropolis, Nigeria

Intensity-Duration-Frequency (IDF) relationship is one of the most commonly used tools in water resources engineering. The purpose of this study was to develop rainfall intensity-duration-frequency models/curves for Lokoja Metropolis, Kogi State, Nigeria. Rainfall data was obtained from Nigeria Meteorological Agency (NIMET) and sorted for frequency analysis. Five different frequency analysis techniques namely; Normal, Log-Normal, Gumbel, Pearson Type III and Log-Pearson Type III distributions were used to develop the IDF relationships for Lokoja. Storm durations of 5, 10, 20, 30, 45, 60, 90 and 120 minutes, and return periods of 2, 5, 10, 25, 50 and 100 years were adopted for the derivation of the models. Kolmogorov-Smirnov and Anderson Darling goodness of fit tests were conducted using Easy Fit software to ascertain the best distribution that fits the data. A power-law model was adopted in developing the desired IDF models/ curves for the study area. The results of the goodness of fit showed that all the five distributions were not rejected both at 5% and 1% significance levels except Pearson Type III which recorded Anderson-Darling value of 3.0814 at 30 minutes’ duration which is above the critical value of 2.5018 at 5% level of significance. Although, all the distributions gave good results, Log-Pearson Type III distribution was adjudged the best for the study area because of its best ranking. It is recommended that the IDF models/curves derived in this study should be used as tools for prediction of rainfall events for design of hydraulic structures in the study area. Also, more meteorological stations should be created in the country and properly equipped to generate requisite data for planning and design of water resources systems. Keywords: Rainfall-Intensity-Duration-frequency models, Log-Pearson Type III distribution, Power model, rainfall events, hydraulic structures

Modeling of IDF curves for stormwater design in Makkah Al Mukarramah region, The Kingdom of Saudi Arabia

Abstract Reducing the negative impacts of flooding in Makkah AL Mukarramah region in the Kingdom of Saudi Arabia (KSA) is of utmost importance. In the last decade, there are huge mega infrastructure projects in KSA in general and in Makkah AL Mukarramah region in particular. These projects require adequate stormwater drainage systems. Since, the availability of rainfall and runoff data are scarce, engineers and hydrologists rely on models developed in temperature regions that are not hydrologically similar from temperate regions. This leads to inaccurate designs of stormwater facilities. Therefore, deveoping in situ Intensity-Duration-Frequency (IDF) curves is a must in this arid region. This paper aims at modeling IDF curves for Makkah Al-Mukarramah region. Maximum annual daily rainfall series of 80 storms (with sub-hourly and hourly data) from four stations are investigated through six different probability distributions. Consequently, rainfall depth-duration-frequency models and curves are derived. Results revealed that the Gumbel Type I is the optimal one. Thus, it is used to deduce the IDF curves and relations for each station and for the region as a whole. The R2 value for fitting power-lawfunction (i = a Db) to the data is very high for the IDF parameters. The R2 for the coefficient parameter, a, is between 0.9999 and 0.9988 while it ranges between 0.8754 and 0.8039 for exponent parameter, b. High correlation coefficient (more than 0.95) has been obtained. The resulting IDF models are strongly recommended for rigorous, effective and safe design of the stormwater systems in Makkah Al-Mukarramah region.

WEBSEIDF: A Web-Based System for the Estimation of IDF Curves in Central Chile

The lack of reliable continuous rainfall records can exacerbate the negative impact of extreme storm events. The inability to describe the continuous characteristics of rainfall from storm events increases the likelihood that the design of hydraulic structures will be inadequate. To mitigate extreme storm impacts and improve water governance at the catchment scale, it is vital to improve the availability of data and the array of tools used to model and forecast hydrological processes. In this paper, we describe and discuss the implementation of a web-based system for the estimation of intensity–duration–frequency (IDF) curves (WEBSEIDF) in Chile. The web platform was constructed using records from 47 pluviographic gauges available in central Chile (30–40° S), with at least 15 years of reliable records. IDF curves can be generated for durations ranging from 15 min to 24 h. In addition, the extrapolation of rainfall intensity from pluviograph to pluviometric gauges (i.e., 24-h rainfall accumulation) can be carried out using the storm index (SI) method. IDF curves can also be generated for any spatial location within central Chile using the ordinary Kriging method. These procedures allow the generation of numerical and graphical displays of IDF curves, for any selected spatial location, and for any combination of probability distribution function (PDF), parameter estimation method, and type of IDF model. One of the major advantages of WEBSEIDF is the flexibility of its database, which can be easily modified and saved to generate IDF curves under user-defined scenarios, that is, changing climate conditions. The implementation and validation of WEBSEIDF serves as a decision support system, providing an important tool for improving the ability of the Chilean government to mitigate the impact of extreme hydrologic events in central Chile. The system is freely available for students, researchers, and other relevant professionals, to improve technical decisions of public and private institutions.

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.

Orographic Effects on Extreme Rainfall at Different Durations: A Case Study in Campania Region (Southern Italy)

Long-term probabilistic prediction of extreme rainfall at the regional scale is a significant tool in the mitigation of hydro-geological disasters: it actually provides the starting point in the design of strategic hydraulic infrastructures and emergency plans. A crucial task of regional estimation of extreme rainfall is how to include the complex effects of orographic barriers in a mathematical model for Intensity-Duration-Frequency (IDF) curves. Here, an analysis of how orography can affect extreme rainfall at different durations is presented for three orographic systems that are very relevant for hydrological risk assessment in the Campania Region in Southern Italy. Then, we introduce a power law model to link the amplification factor to the duration, thus allowing a simple and effective enhancement of the IDF model in mountainous areas.

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.

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.

Development of a method of robust rain gauge network optimization based on intensity-duration-frequency results

Abstract. Based on rainfall intensity-duration-frequency (IDF) curves, fitted in several locations of a given area, a robust optimization approach is proposed to identify the best locations to install new rain gauges. The advantage of robust optimization is that the resulting design solutions yield networks which behave acceptably under hydrological variability. Robust optimization can overcome the problem of selecting representative rainfall events when building the optimization process. This paper reports an original approach based on Montana IDF model parameters. The latter are assumed to be geostatistical variables, and their spatial interdependence is taken into account through the adoption of cross-variograms in the kriging process. The problem of optimally locating a fixed number of new monitoring stations based on an existing rain gauge network is addressed. The objective function is based on the mean spatial kriging variance and rainfall variogram structure using a variance-reduction method. Hydrological variability was taken into account by considering and implementing several return periods to define the robust objective function. Variance minimization is performed using a simulated annealing algorithm. In addition, knowledge of the time horizon is needed for the computation of the robust objective function. A short- and a long-term horizon were studied, and optimal networks are identified for each. The method developed is applied to north Tunisia (area = 21 000 km2). Data inputs for the variogram analysis were IDF curves provided by the hydrological bureau and available for 14 tipping bucket type rain gauges. The recording period was from 1962 to 2001, depending on the station. The study concerns an imaginary network augmentation based on the network configuration in 1973, which is a very significant year in Tunisia because there was an exceptional regional flood event in March 1973. This network consisted of 13 stations and did not meet World Meteorological Organization (WMO) recommendations for the minimum spatial density. Therefore, it is proposed to augment it by 25, 50, 100 and 160% virtually, which is the rate that would meet WMO requirements. Results suggest that for a given augmentation robust networks remain stable overall for the two time horizons.

Assessment of design rainfall uncertainty for hydrologic engineering applications in Hong Kong

Hydrologic engineering designs and analyses often require the specification of design storm which involves rainfall amount, duration and hyetograph. In practice, the determination of design rainfall in hydrologic engineering applications involves the frequency analysis of extreme rainfalls of different durations and the establishment of rainfall hyetograph for the design event under consideration. Sampling errors exist in the estimation of rainfall depth (or intensity) quantiles from frequency analysis, which will be transmitted in the process of determining the design rainfall hyetograph. This paper presents a practical methodological framework based on the bootstrap resampling scheme to assess the uncertainty features associated with the magnitude of estimated rainfall depth/intensity quantiles and the corresponding design hyetographs. The procedure is implemented to quantify uncertainty of design rainfall hyetograph following the Stormwater Drainage Manual of Hong Kong involving the use of rainfall intensity–duration–frequency (IDF) model. Of particular interesting is that the bootstrap resampling scheme implemented herein is modified to handle unequal record period of annual maximum rainfall data series of different durations and to account for their intrinsic correlations. According to the adopted rainfall IDF model, the design rainfall hyetograph is a function of the IDF model coefficients. Due to the correlation among rainfall quantiles of different durations, the IDF coefficients are found to be strongly related in a nonlinear fashion which should not be ignored in the establishment of the design hyetographs.

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.

Selecting the best IDF model by using the multifractal approach

AbstractIn this work, the multifractal properties of hourly rainfall data recorded at a location in Southern Spain have been related to the scale properties of the corresponding intensity–duration–frequency (IDF) curves. Four parametric models for the IDF curves have been fitted to the quantiles of rainfall obtained using the generalized Pareto frequency distribution function with the extreme data series obtained for the same place.The scaling of the rainfall intensity moments has been analysed, and the empirical moments scaling exponent function has been obtained. The corresponding values ofq1andγ1have been empirical and theoretically calculated and compared with some characteristics of the different IDF models. Thus, the scaling behaviour of IDF curves has been analysed, and the best model has been selected. Copyright © 2012 John Wiley &amp; Sons, Ltd.