Intensity Duration Frequency Equations Research Articles

Equações universais para as distribuições de chuva dos métodos SCS e Huff

ABSTRACT The temporal distribution of design rainfall hyetographs can be obtained through various procedures. One such method involves using temporal distribution curves to disaggregate a rainfall value of longer duration into chronological values within shorter time intervals. This is demonstrated by SCS distribution curves for durations of 6 and 24 hours and the well-known Huff curves. Another approach involves deriving temporal distribution using design hyetograph calculation methods, such as the Chicago and alternating block methods, based on Intensity-Duration-Frequency (IDF) equations. This paper aims to combine these approaches and develop universal equations capable of accurately fitting smooth rainfall time distribution curves. The advantage is the replacement of tables, like SCS and Huff, with analytical equations, enhancing usability in spreadsheets. Furthermore, these universal equations can determine the temporal rainfall distribution using an IDF equation or fitting a specified design hyetograph like Euler type II. Four numerical examples are provided.

Intensity-Duration-Frequency equations for Rio Grande do Sul - Brazil, based on stationary rainfall series

Heavy rainfall information is essential for environmental studies and water engineering. This study therefore aimed to adjust Intensity-Duration-Frequency (IDF) equations for 247 locations in the Rio Grande do Sul (RS) using stationary rainfall series. Mann-Kendall’s test was applied to identify the temporal trends in the Annual Maximum Daily Rainfall (AMDR) series of 271 rain gauges in RS. The Kappa, Generalized Extreme Value (GEV), Gumbel, two-parameters Log-Normal and three-parameters Log-Normal probabilistic distributions were adjusted to the AMDR series without significant temporal trend. The best distribution fit was given by Anderson-Darling’s test, so the AMDR was discretized up to 5 minutes. IDF equations coefficients were adjusted in RStudio, using Nash-Sutcliffe’s Coefficient and the Root-Mean-Square Error to evaluate them. In conclusion: the most suitable distributions for the AMDR were the multiparametric Kappa and GEV; the IDF equations coefficients adjustment was classified as “excellent”; coefficients a and b varied across the RS and are correlated with the AMDR and geographical positions; and the c and d coefficients were practically constant.
 Keywords: goodness of fit test, Kappa probabilistic distribution, trends test.

Development of Intensity-Duration-Frequency (IDF) Models for Manually Operated Rain Gauge Catchment: A Case Study of Port Harcourt Metropolis Using 50years Rainfall Data

Hydraulic structures such as surface drainages and culverts are usually constructed in urban areas with the intention of draining runoff into nearby streams and rivers in order to avoid flooding. However, most of these structures frequently fail to serve the intended use due to the occurrence of high intensity rainfall accompanied with long duration, which produce runoff discharge higher than their designed capacities. This is common in many developing countries as drainages and culverts are most times constructed without considering hydrological analysis of the catchment. Hence, this research considered Port Harcourt city as a case study by utilizing 50years rainfall data to develop rainfall Intensity-Duration-Frequency (IDF) curves that will be used for subsequent design of drainages and culverts within the city and its environs. The IDF curves were developed using Gumbel, Pearson type III and Log-Pearson type III distributions at return periods of 2, 5, 10, 25 and 50years. However, the durations considered were 5, 10, 20, 30, 45, 60, 90, 120, 150, 180, 210, 240, 300, 360 and 420minutes. Results showed that the IDF equations developed for the three frequency distributions highly correlate with the observed intensities since there goodness of fit (R2) ranges from 0.9766 – 0.9865. Also, it was noted that there was no significant difference (p < 0.01) between the predicted rainfall intensities from all the IDF equations and the observed intensities. Notwithstanding, the IDF equation developed for Gumbel distribution was recommended to be given higher priority since it has the highest R2 value.

Development of Intensity-Duration-Frequency (IDF) Models for Manually Operated Rain Gauge Catchment: A Case Study of Port Harcourt Metropolis Using 50 Years Rainfall Data

Hydraulic structures such as surface drainages and culverts are usually constructed in urban areas with the intention of draining runoff into nearby streams and rivers in order to avoid flooding. However, most of these structures frequently fail to serve the intended use due to the occurrence of high intensity rainfall accompanied with long duration, which produce runoff discharge higher than their designed capacities. This is common in many developing countries as drainages and culverts are most times constructed without considering hydrological analysis of the catchment. Hence, this research considered Port Harcourt city as a case study by utilizing 50 years rainfall data to develop rainfall Intensity-Duration-Frequency (IDF) curves that will be used for subsequent design of drainages and culverts within the city and its environs. The IDF curves were developed using Gumbel, Pearson type III and Log-Pearson type III distributions at return periods of 2, 5, 10, 25 and 50 years. However, the durations considered were 5, 10, 20, 30, 45, 60, 90, 120, 150, 180, 210, 240, 300, 360 and 420 minutes. Results showed that the IDF equations developed for the three frequency distributions highly correlate with the observed intensities since there goodness of fit (R2 ) ranges from 0.9766 – 0.9865. Also, it was noted that there was no significant difference (p &lt; 0.01) between the predicted rainfall intensities from all the IDF equations and the observed intensities. Notwithstanding, the IDF equation developed for Gumbel distribution was recommended to be given higher priority since it has the highest R2 value.

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.

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.

Determinação da curva de intensidade-duração-frequência do município de Cruzeiro do Sul – Acre

Information on extreme rainfall events associated with predictability and probabilities, especially in intensity-duration-frequency (IDF) curves, are essential for the development of engineering projects aimed at sanitation, drainage and waterproofing of surfaces, which allow to offer more suitable conditions for dimensioning hydraulic and hydrological works and services. However, much of the North Region of the country does not have this information available or updated. Thus, the objective of this study was to develop the IDF equation for the municipality of Cruzeiro do Sul - AC. A 14-year historical series was used, distributed between 1993 and 2011, such data were analyzed by the Gumbel distribution, the same being related, by means of the daily rain breakdown, for return periods comprising 2 to 100 years and rainfall durations of 5 minutes to 24 hours. In the analysis for the construction of the curve, it was observed that the years 1995 and 2002 corresponded to the years with the highest precipitated height indexes, being 111 mm and 103 mm, respectively, however these events had an estimated return time between 3 and 8 years, which does not denote anomalous events. The IDF curve constructed in the study showed good adherence to the observed data, which proves its use in the region.

Extreme rainfall and IDF equations for Alagoas State, Brazil

Intensity-duration-frequency (IDF) equations have important applications in several engineering areas such as urban drainage designs, hydrological modeling, and soil conservation projects. This study analyzes the annual maximum series and fits IDF equations for 44 rainfall stations in Alagoas State, Brazil. We adjusted parameters of the Gumbel distribution (GD) and the Generalized Extreme Value (GEV) distribution. The fitting of the observed data to the probability distributions, as well as the selection of the best distribution, were based on the Kolmogorov-Smirnov and Anderson-Darling tests at a 5% significance level. The GEV distribution with parameters obtained by the L-moments method was considered the best in 73% of rainfall stations. The estimated IDF equations showed a good fit, with determination coefficients above 0.991. The maximum rainfall intensities have spatial variation following the climatic zones of the state. The fitted equations allow estimating rainfall intensities from 5 minutes to 24 hours with a return period of 2 to 100 years, and standard error of less than 6.83 mm h-1.

Development of Intensity Duration Frequency (IDF) Curves for Rainfall Prediction within the Middle Niger River Basin

Rainfall Intensity-Duration-Frequency (IDF) relationship remains one of the mostly used tools in hydrology and water resources engineering, especially for planning, design and operations of water resource projects. IDF relationship can provide adequate information about the intensity of rainfall at different duration for various return periods. The focus of this research was to develop IDF curves for the prediction of rainfall intensity within the middle Niger River Basin (Lokoja and Ilorin) using annual maximum daily rainfall data. Forty (40) year’s annual maximum rainfall data ranging from 1974 to 2013 was employed for the study. To ascertain the data quality, selected preliminary analysis technique including; descriptive statistics, test of homogeneity and outlier detection test were employed. To compute the three hours rainfall intensity, the ratio of rainfall amount and duration was used while the popular Gumbel probability distribution model was employed to calculate the rainfall frequency factor. To assess the best fit model that can be employed to predict rainfall intensity for various return periods at ungauged locations, four empirical IDF equations, namely; Talbot, Bernard, Kimijima and Sherman equations were employed. The model with the least calculated sum of minimized root mean square error (RMSE) was adopted as the best fit empirical model. Results obtained revealed that the Talbot model was the best fit model for Ilorin and Lokoja with calculated sum of minimized error of 1.32170E-07 and 8.953636E-08. This model was thereafter employed to predict the rainfall intensity for different durations at 2, 5, 10, 25, 50 and 100yrs return periods respectively.

On the Rainfall Intensity–Duration–Frequency Curves, Partial-Area Effect and the Rational Method: Theory and the Engineering Practice

This research evaluates the partial-area effect and its relationship with the rainfall intensity–duration–frequency (IDF) equations. In the Rational Method, if the critical rainfall duration is shorter than the time of concentration, the partial-area effect occurs. We proved that the partial area could exist for the general ID equation i=a/(b+td)c, only when c&gt;1. For these equations, in the application of the Rational Method, the maximum discharge at basin outlet occurs for rainfall duration (td) equal to b/(c−1). Nevertheless, for that case, the Depth Duration Frequency (DDF) has a maximum at that rainfall duration. These situations are present in engineering practice and will be discussed in this paper. Research was done to look for IDF equations with c&gt;1 in hydrologic engineering practice. It found 640 inconsistent IDF equations (c&gt;1) in four countries (Brazil, Mexico, India, and USA), which means that a fundamental principle for building consistent IDF equations (i.e., c&gt;1), published in the scientific literature since 1998, did not reach the hydrologic engineering practice fully. We provided some analysis regarding this gap between theory and engineering practice.

Analysis of rainfall intensity-duration-frequency (IDF) curves of Baghdad city

An appropriate formula of rainfall data is the Intensity Duration Frequency (IDF) relationship. The rainfall IDF relationship is one of the tools used considerably in water resources engineering, either in planning, designing and operating projects of water resources, or in flood control projects. The purpose of this paper is to update rainfall IDF curves of Baghdad city developed in previously. The frequency analysis of available rainfall data is perform by three statistical methods, namely, the Gumbel Distribution Theory, the Log Pearson Type III and Log Normal Distribution to attain rainfall intensities for various short durations (0.25, 0.5, 1, 2, 3, 6, 12 and 24) in hours and return periods (2, 5, 10, 25, 50 and 100) in years. IDF equation was derived based on Bernard equation and the results of three distributions were compared using Kolmogorov-Smirnov goodness of fit test with help of the Easy fit software 5.6. The results of three methods were close and accepted at 10% significant level. The maximum rainfall intensity of 118.052mm/hr was happened at the duration 0.25hr of the return period 100yr, whereas the minimum rainfall intensity of 1.257mm/hr was happened at the duration 24hr of the return period 2yr.

Generation of IDF Equation from Catchment Delineation Using GIS

The study was intended to find out the catchment characteristics of an area and the IDF (Intensity-Duration-Frequency) analysis of rainfall of that area using Gumbel method and Log Pearson type III method. In different studies, the IDF equations are generated for an area without acknowledging the catchment, stream length of the catchment and the time of concentration. In our study the Digital Elevation Map (DEM) of Dhaka was used. The DEM was analyzed using QGIS to find out different catchments, catchment area, catchment slope, stream length etc. The rainfall data of 18 years was collected from BMD (Bangladesh Meteorological Department) at 24 hours’ interval. This rainfall data was analyzed using Gumbel method and Log Pearson Type III method because these methods give accurate prediction for return period more than the range of the acquired data. The return period was taken as 2 years,5 years,10 years,25 years,50 years and 100 years. Finally, the intensity for different return period was plotted against the duration of the rainfall to find out the IDF curve. For any kind of rainfall analysis to find the peak discharge for designing storm sewage lines, small hydraulic structures or calculating surface runoff, infiltration, sub-surface runoff, discharge at rivers or water bodies, the derived IDF equations can be used. Even to find out peak discharge with a return period more than 18 years these set of equation can be used. This method can also be used in other sub urban or urban areas to find out the time of concentration of that catchment and IDF relationships for short duration rainfalls.

Derivation of Design Rainfall and Disaggregation Process of Areas with Limited Data and Extreme Climatic Variability

In a sustainable urbanisation process, the infrastructure has to be designed taking into consideration the hydrological behaviour of the respective catchment. It is mandatory to predict the climatic events accurately to understand the hydrological impacts of urban developments. It is very challenging for hydrologists to model extreme events when there are limited data available. The current study proposed a methodology to calculate the design rainfalls in the coastal region of Sao Paulo, Brazil. The gamma-function distribution used the annual maximum daily rainfalls in a probabilistic approach. The achieved 24-h-design rainfalls were compared to the results from other intensity–duration–frequency equations in different time-series. The rainfall disaggregation used regional and national conversion ratios. The fluctuation of the annual maxima revealed that the study area was affected by the Noah and Joseph erratic processes. Subsequently, the detected extreme event time-series were also used for the derivation of the 24-h-design rainfalls. The outcomes of the study showed that the gamma-function distribution provides reliable results, enhanced by the use of representative disaggregation ratios and proper time-series.

Generic Method for Merging Satellite and Historical Ground Station Data to Design Rainfall Intensity Duration Frequency (IDF) Curves in Recordless Sub-Saharian Countries

The availability of long-term rainfall records is essential to conduct a serious frequency analysis in order to estimate the effective precipitation depth. The development of the process of elaboration of IDF (Intensity-Duration-Frequency) curves for a given location requires very precise data, at least with daily frequency, obtained through the use of rainfall records. The present study presents a method used to merge historical precipitation data with the latest data collected by satellite in order to perform graphs with IDF curves in places where rainfall records are scarce. The homogeneity of the data used is analyzed in order to guarantee its statistical utility and the frequency analysis was performed with the statistical distributions of Extreme Values Type I (Gumbel), Gamma, Pearson Type III and finally with Log-Pearson Type III, in order to verify which one of them applies better to the sites chosen for this analysis: the cities of Benguela and Lobito in the south of Angola. Daily rainfall data from the TRMM mission and historical daily data were used to derive the relationships between the maximum daily precipitation and the sub-daily precipitation values. From the observed daily data, techniques of disaggregation of the collected data were used, in order to generate a synthetic precipitation sequence with the extreme values in periods of time inferior to the daily one, with statistical properties similar to the registered data. Then IDF equations are established, with which the occasional storm depth is calculated for various return periods and various durations and, after them, the IDF curves are drawn for these two geographic stations.

Rainfall Intensity-Duration-Frequency relationship for Trichy and Kumulur

The rainfall Intensity-Duration-Frequency (IDF) relationship is commonly required for planning and designing of various water resource projects. It is a mathematical relationship between the rainfall intensity, duration and return period. This relationship is determined through statistical analysis of recorded rainfall data. The objective of this study is to derive IDF relationship of rainfall at Trichy and Kumulur. A total durations ranging from 10 minutes to 24 hr (10min, 20 min, 30 min, 60 min, 120 min, 180 min, 360 min, 720 min and 1440 min) for return periods of 2, 5, 10, 25, 50 and 100 years were analyzed. In this study, yearly maximum rainfall data for Trichy (1951–2010) and Kumulur (1991–2014) were used. Empirical reduction formula of India Meteorological Department (IMD) has been used to estimate the short duration rainfall intensity from yearly maximum rainfall data. Gumbel and Log Pearson Type III (LPT III) Distribution method was used to develop IDF curves and equations. The results obtained using Gumbel method is somewhat higher than the outcomes obtained using the LPT III distribution method. 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 years) were calculated by using least square method. The results obtained revealed that in all the cases the correlation coefficient is very high representing the goodness of fit of the formulae to estimate IDF in the station of interest.

Determining the Parameters of the Intermediate Duration - Intensity Equation for Mediterranean Region, Turkey

The aim of this study is to determine the parameter estimates of the general intensity-duration-frequency (IDF) formula for the 20 rainfall stations in the Mediterranean Region of Turkey. The maximum annual rainfall data were statistically analyzed for the durations 1, 2, 3, 4, 5, 6, 8, 12, 18 and 24 hours. Generalized Extreme Value (GEV), Gumbel, Normal, two-parameter Lognormal, three-parameter Lognormal, Gamma, Pearson type-III and Log-Pearson type-III distributions were considered and compared using Chi square (χ2) goodness-fit test. Parameters of these distributions were estimated using both maximum likelihood and moment methods. The parameters of the general IDF equation i = (A* TB)/(tC + D) and coefficient of correlation (R) for different return periods (2, 5, 10, 25, 50, 75 and 100 years) were calculated by using nonlinear estimation method. Coefficient of correlation result (R = 0,875) of general IDF equation showed the suitability for intermediate durations in the Mediterranean Region.

Implications of discontinuous IDF equations in generation of runoff hydrographs. Case study: IDF-Porto Alegre (8º DISME)

ABSTRACT The intensity-duration-frequency (IDF) equations establish the relationship between the intensity and the duration of an extreme precipitation associated to the probability of its occurrence. Some studies have fitted multiple IDF equations per rain gauge, valid for certain rain duration ranges. An example is the IDF equation for the 8th District of Meteorology of Porto Alegre rain gauge, established and published by the CPRM in the Pluviometric Atlas Project. The main objective of the present study is to evaluate the implication of using this type of IDF equation, referred to as a “discontinuous IDF equation”, in the generation of runoff hydrographs, using the mentioned IDF as case study. The methodology consisted in comparing the peak flow and the runoff volume of hydrographs generated by the discontinuous IDF equation with the hydrographs obtained by using a single IDF equation. The runoff hydrographs were generated for hypothetical basins with the following characteristics: contribution areas of 5, 20 and 80 km2; CN of 70, 80 and 90; and time of concentration of 20, 40, 60, 100 and 200 minutes. A 24-hour rainfall event was considered with return period of 5, 10, 25, 50 and 100 years. As results, it was observed that, in the case studied, the multiple IDF equation present a better fit to the observed rainfall data than the single IDF equation. However, the discontinuity at the transition point between the equations, depending on its magnitude, may present some influence on the peak flow and on the runoff volume due to occurrence of secondary peaks on the runoff hydrographs. Therefore, it is recommended that a maximum limit of discontinuity must be observed between the multiple equations in order to avoid the occurrence of secondary peaks in the runoff hydrographs.

Estimate of intense rainfall equation parameters for rainfall stations of the Paraíba State, Brazil

ABSTRACT Rainfall is the primary water source for hydrographic basins. Hence, the quantification and knowledge of its temporal and spatial distribution are indispensable in dimensioning hydraulic projects. This study aimed at assessing the fit of a series of rainfall data to different probability models, as well as estimating parameters of the intensity-duration-frequency (IDF) equation for rain stations of the Paraíba State, Brazil. The rainfall data of each station were obtained from the Brazilian Water Agency databanks. To estimate the maximum daily rainfall of each station and return period (5, 10, 15, 25, 50 and 100 years), the following probability distributions were used: Gumbel, Log-Normal II, Log-Normal III, Pearson III and Log-Pearson III. The estimation of rainfall in durations of 5-1,440 min was carried out by daily rainfall disaggregation. The adjustment of the IDF equation was performed via nonlinear multiple regression, using the nonlinear generalized reduced gradient interaction method. When compared to the data observed, the intense rainfall equations for most stations showed goodness of fit with coefficients of determination above 0.99, which supports the methodology applied in this study.

Development of intensity–duration–frequency curves for the Kingdom of Saudi Arabia

ABSTRACTThis paper presents the derivation of the intensity–duration–frequency (IDF) curves for the Kingdom of Saudi Arabia. Such curves were obtained based on rainfall events measured in 28 meteorological stations distributed throughout the Kingdom. For 20–28 years period, 2027 rainfall storms of durations ranging from 10 min to 24 hours were collected and analyzed. Both Institute of Hydrology model (IH-Flood) and Excel-sheet program are used for developing IDF equations for every station. The method of least squares was used to get relationships for the parameters of the IDF formulas. The calculated goodness of fit shows strong correlations range between 0.99 and 0.98 for one of the parameters, and between 0.92 and 0.74 for the other parameters and thence indicating robust IDF formulas for practical use. Regionalization of the IDF parameters for the 13 distinct regions of the Kingdom has been developed. In addition, an average of IDF parameters is made over the Kingdom as a whole to be used in regions of no rainfall records. The resulting IDF curves are usually used for flood estimation in urban/rural watersheds. Using the resulting IDF curves is highly recommended for rigorous, efficient and safe design of hydraulic structures and flood protection works.

DETERMINING IDF EQUATIONS FOR THE STATE OF RONDÔNIA (DETERMINAÇÃO DE EQUAÇÕES IDF PARA O ESTADO DE RONDÔNIA)

This study aimed to estimate the Intensity-Duration-Frequency (IDF) function of extreme pluviometric events for the State of Rondonia in Brazil. This study used forty-one pluviometric stations with over 10 years of historic data. Data were analyzed following the Gumbel distribution and related (through disaggregating of daily rains) to return periods comprising from 2 to 100 years and pluviometric durations from 5 minutes to 24 hours. Furthermore, areas of influence for the applicability of IDF equations were determined by Voronoi diagrams. The IDF equations were validated with the help of the regression coefficient (r²) and the Wilcoxon-Mann-Whitney hypothesis test showed that its use is feasible.