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Acosta-Castellanos, Pedro Mauricio, Yuddy Alejandra Castro Ortegón, and Nestor Rafael Perico Granados. "Regionalization of IDF Curves by Interpolating the Intensity and Adjustment Parameters: Application to Boyacá, Colombia, South America." Water 15, no. 3 (January 31, 2023): 561. http://dx.doi.org/10.3390/w15030561.
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Intensity, duration and frequency (IDF) curves are necessary tools for the design and construction of hydraulic projects. However, the pluviographic records needed to determine the IDF curves do not exist or are scarce. This research presents the regionalization of the IDF curves for the department of Boyacá, Colombia, which is made up of 16 municipalities including the provincial capital, Tunja. For the regionalization, the adjustment parameters (u and α) of the IDF curve stations in the study area were used. In the case of regionalization by the parameters found for the construction of the IDF curves, estimation methods with ordinary moments means and maximum likelihood were used. The regionalization and interpolation of the data were performed with Arcgis software. The resulting isoline maps were made in the case of regionalization intensities, and each map is associated with a different return period and duration to construct the IDF curves in the studied area. In the case of the regionalization maps, the parameters associated with each individual parameter were performed last. The results show that the use of IDF curve data is more accurate and reduces errors in the design. With the methods proposed in this study, IDF curves can be constructed for any site of interest that does not have rainfall stations.
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Ariff, Noratiqah Mohd, Abdul Aziz Jemain, and Mohd Aftar Abu Bakar. "Potential of plotting positions for intensity-duration-frequency curves with short rainfall records." Malaysian Journal of Fundamental and Applied Sciences 13, no. 4-1 (December 5, 2017): 394–99. http://dx.doi.org/10.11113/mjfas.v13n4-1.814.
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Intensity-duration-frequency (IDF) curves represent the relationship between storm intensity, storm duration and return period. The IDF curves available are mostly done by fitting series of annual maximum rainfall intensity to parametric distributions. However, the length of annual rainfall records, especially for small scaled data, are not always enough. Rainfall records of less than 50 years are usually deemed insufficient to unequivocally identify the probability distribution of the annual rainfall. Thus, this study introduces an alternative approach that replaces the need for parametric fitting by using empirical distribution based on plotting positions to represent annual maximum rainfall series. Subsequently, these plotting positions are used to build IDF curves. The IDF curves found are then compared to the IDF curves yielded from the parametric GEV distribution which is a common basis for IDF curves. This study indicates that IDF curves obtained using plotting positions are similar to IDF curves found using GEV distribution for storm events. Hence, researchers could model and subsequently build IDF curves for annual rainfall records of less than 50 years by using plotting positions and avoid any probability distribution fitting of insufficient data.
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de Souza Costa, Carlos Eduardo Aguiar, Claudio José Cavalcante Blanco, and José Francisco de Oliveira-Júnior. "IDF curves for future climate scenarios in a locality of the Tapajós Basin, Amazon, Brazil." Journal of Water and Climate Change 11, no. 3 (January 16, 2019): 760–70. http://dx.doi.org/10.2166/wcc.2019.202.
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Abstract Changes in the global climate are attributed to the levels of greenhouse gases. Thus, future scenarios (Representative Concentration Pathways – RCPs) have been developed to explore the impact of different climate policies on the world. The RCPs are essential tools for General Circulation Models (GCMs) to simulate future climate changes. Curves that associate Intensity, Duration and Frequency (IDF) are used in forecasts and are fundamental for the design of hydraulic projects and risk management. The objective of this study was to design IDF curves for the RCP 4.5 and 8.5, using data from the HadGEM2-ES, CanESM2 and MIROC5 models. The Equidistance Quantile Matching Method was used to design the IDF curves. The simulated curves presented differences when related to the existing curve. The largest differences were for the MIROC5 (146% in RCP 8.5) and the smallest differences were for the CanESM2 (−20.83% for RCP 8.5). This result demonstrates that the method incorporates changes in future climate variability. The spatial resolutions of each model influenced their IDF curves, which led the CanESM2 curves to not present satisfactory results that are different from the MIROC5 curves, which were the ones that best represented the possible future differences.
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Nandalal, K. D. W., and P. Ghnanapala. "Development of IDF Curves for Colombo." Engineer: Journal of the Institution of Engineers, Sri Lanka 50, no. 1 (February 9, 2017): 33. http://dx.doi.org/10.4038/engineer.v50i1.7242.
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Alsumaiti, Tareefa S., Khalid A. Hussein, Dawit T. Ghebreyesus, Pakorn Petchprayoon, Hatim O. Sharif, and Waleed Abdalati. "Development of Intensity–Duration–Frequency (IDF) Curves over the United Arab Emirates (UAE) Using CHIRPS Satellite-Based Precipitation Products." Remote Sensing 16, no. 1 (December 20, 2023): 27. http://dx.doi.org/10.3390/rs16010027.
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The recent flooding events in the UAE have emphasized the need for a reassessment of flood frequencies to mitigate risks. The exponential urbanization and climatic changes in the UAE require a reform for developing and updating intensity–duration–frequency (IDF) curves. This study introduces a methodology to develop and update IDF curves for the UAE at a high spatial resolution using CHIRPS (Climate Hazards Group InfraRed Precipitation with Station) data. A bias correction was applied to the CHIRPS data, resulting in an improved capture of extreme events across the country. The Gumbel distribution was the most suitable theoretical distribution for the UAE, exhibiting a strong fit to the observed data. The study also revealed that the CHIRPS-derived IDF curves matched the shape of IDF curves generated using rain gauges. Due to orographic rainfall in the northeastern region, the IDF intensities were at their highest there, while the aridity of inland regions resulted in the lowest intensities. These findings enhance our understanding of rainfall patterns in the UAE and support effective water resource management and infrastructure planning. This study demonstrates the potential of the CHIRPS dataset for IDF curve development, emphasizes the importance of performing bias corrections, and recommends tailoring adjustments to the intended application.
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Schardong, Andre, Slobodan P. Simonovic, Abhishek Gaur, and Dan Sandink. "Web-Based Tool for the Development of Intensity Duration Frequency Curves under Changing Climate at Gauged and Ungauged Locations." Water 12, no. 5 (April 27, 2020): 1243. http://dx.doi.org/10.3390/w12051243.
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Rainfall Intensity–Duration–Frequency (IDF) curves are among the most essential datasets used in water resources management across the globe. Traditionally, they are derived from observations of historical rainfall, under the assumption of stationarity. Change of climatic conditions makes use of historical data for development of IDFs for the future unreliable, and in some cases, may lead to underestimated infrastructure designs. The IDF_CC tool is designed to assist water professionals and engineers in producing IDF estimates under changing climatic conditions. The latest version of the tool (Version 4) provides updated IDF curve estimates for gauged locations (rainfall monitoring stations) and ungauged sites using a new gridded dataset of IDF curves for the land mass of Canada. The tool has been developed using web-based technologies and takes the form of a decision support system (DSS). The main modifications and improvements between version 1 and the latest version of the IDF_CC tool include: (i) introduction of the Generalized Extreme value (GEV) distribution; (ii) updated equidistant matching algorithm (QM); (iii) gridded IDF curves dataset for ungauged location and (iv) updated Climate Models.
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Mohymont, B., G. R. Demarée, and D. N. Faka. "Establishment of IDF-curves for precipitation in the tropical area of Central Africa - comparison of techniques and results." Natural Hazards and Earth System Sciences 4, no. 3 (May 28, 2004): 375–87. http://dx.doi.org/10.5194/nhess-4-375-2004.
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Abstract. The establishment of Intensity-Duration-Frequency (IDF) curves for precipitation remains a powerful tool in the risk analysis of natural hazards. Indeed the IDF-curves allow for the estimation of the return period of an observed rainfall event or conversely of the rainfall amount corresponding to a given return period for different aggregation times. There is a high need for IDF-curves in the tropical region of Central Africa but unfortunately the adequate long-term data sets are frequently not available. The present paper assesses IDF-curves for precipitation for three stations in Central Africa. More physically based models for the IDF-curves are proposed. The methodology used here has been advanced by Koutsoyiannis et al. (1998) and an inter-station and inter-technique comparison is being carried out. The IDF-curves for tropical Central Africa are an interesting tool to be used in sewer system design to combat the frequently occurring inundations in semi-urbanized and urbanized areas of the Kinshasa megapolis.
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Thanh, Son Tran, and Anh Ha Xuan. "Deriving of Intensity–Duration–Frequency (IDF) curves for precipitation at Hanoi, Vietnam." E3S Web of Conferences 403 (2023): 06002. http://dx.doi.org/10.1051/e3sconf/202340306002.
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The rainfall Intensity-Duration-Frequency (IDF) relationship is one of the most commonly used tools in establishing rain intensity formulas for urban stormwater drainage design. Currently, the rain formulas being applied in Vietnam according to the design standard TCVN 7957-2008 are mostly Soviet formulas with climate parameters dating back to the 80s of the twentieth century. Therefore, it is no longer suitable for the calculation of the current stormwater drainage system, especially in the context of climate change. In this paper, we used statistical methods to process rain gauge data from 1960 to 2021 to build the IDF curve for the inner city of Hanoi (Vietnam). The results show that the new IDF curves are more suitable for the current climate situation than the IDF curves according to TCVN 7957-2008.
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Mohammed, Abdulrasheed, Salisu Dan’Azumi, Abubakar Ahmed Modibbo, and Abubakar Abbas Adamu. "DEVELOPMENT OF RAINFALL INTENSITY DURATION FREQUENCY (IDF) CURVES FOR DESIGN OF HYDRAULIC STRUCTURES IN KANO STATE, NIGERIA." Platform : A Journal of Engineering 5, no. 2 (June 30, 2021): 10. http://dx.doi.org/10.61762/pajevol5iss2art12706.
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Rainfall intensity is an essential parameter in the design of any hydraulic structure. The IDF curves are used to design hydraulic structures such as culverts, bridges, roads, urban drainage systems, and many more. Colonial masters developed the first IDF curve for Kano State based on records of 1938 - 1944 (6 years) followed by Oyenbade (1982), and since then, it has not been reviewed or updated. As a result of changes in rainfall patterns that have taken place over time and the climate change, the Oyenbade IDF curves might no longer be suitable for hydraulics design in Kano State. Therefore, this research aims to develop the new IDF curves and establish empirical equations of rainfall intensity that can be used for safe and economic hydraulics design in Kano State. India Meteorological Department (IMD) reduction formula was used to disaggregate maximum daily rainfall of Kano gauge station into the rainfall of shorter durations. Lognormal probability distribution was found to fit best the data set of all the durations using Easyfit 5.0 software and estimate rainfall intensities for 2, 5, 10, 25, 50, and 100 years return periods. It was found out that rainfall intensities increase with the increase in return periods but decreases with an increase in duration. The coefficient of determination ‘R2’ for all return periods indicated a strong relationship in IDF models developed. Hence, the new IDF curves developed should estimate rainfall intensities for hydraulics design in Kano State. The derived IDF models could be used for better results and accuracy.
Keywords: Probability distributions, IMD reduction formula, return periods, rainfall duration, easy fit software 5.0
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Singh, Vijay P., and Lan Zhang. "IDF Curves Using the Frank Archimedean Copula." Journal of Hydrologic Engineering 12, no. 6 (November 2007): 651–62. http://dx.doi.org/10.1061/(asce)1084-0699(2007)12:6(651).
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Parding, Kajsa Maria, Rasmus Emil Benestad, Anita Verpe Dyrrdal, and Julia Lutz. "A principal-component-based strategy for regionalisation of precipitation intensity–duration–frequency (IDF) statistics." Hydrology and Earth System Sciences 27, no. 20 (October 20, 2023): 3719–32. http://dx.doi.org/10.5194/hess-27-3719-2023.
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Abstract. Intensity–duration–frequency (IDF) statistics describing extreme rainfall intensities in Norway were analysed with the purpose of investigating how the shape of the curves is influenced by geographical conditions and local climate characteristics. To this end, principal component analysis (PCA) was used to quantify salient information about the IDF curves, and a Bayesian linear regression was used to study the dependency of the shapes on climatological and geographical information. Our analysis indicated that the shapes of IDF curves in Norway are influenced by both geographical conditions and 24 h precipitation statistics. Based on this analysis, an empirical model was constructed to predict IDF curves in locations with insufficient sub-hourly rain gauge data. Our new method was also compared with a recently proposed formula for estimating sub-daily rainfall intensity based on 24 h rain gauge data. We found that a Bayesian inference of a PCA representation of IDF curves provides a promising strategy for estimating sub-daily return levels for rainfall.
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Kareem, Dalshad Ahmed, Aumed Rahman M Amen, Andam Mustafa, Mehmet Ishak Yüce, and Michał Szydłowski. "Comparative Analysis of Developed Rainfall Intensity–Duration–Frequency Curves for Erbil with Other Iraqi Urban Areas." Water 14, no. 3 (January 29, 2022): 419. http://dx.doi.org/10.3390/w14030419.
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Rainfall Intensity–Duration–Frequency (IDF) relationships are widely used in water infrastructure design and construction. IDF curves represent the relationship between rainfall intensity, duration, and frequency, and are obtained by analyzing observed data. These relationships are critical for the safe design of flood protection structures, storm sewers, culverts, bridges, etc. In this study, the IDF curves and empirical IDF formulas for the city of Erbil were developed for the first time by employing the annual maximum rainfall data for a period of 39 years (1980–2018), which is the only available recorded data. Statistical techniques such as Gumbel and Log-Pearson Type III (LPT III) were utilized to determine the IDF curves and empirical equations from daily rainfall data for several standard durations and return periods. The correlation between the rainfall intensities obtained from IDF curves and the empirical formula presented a reliable match, with a coefficient of determination of (R2 = 1). The results were compared to previously developed IDF curves and empirical formulas in Iraqi cities to show their reliability. Moreover, the results can be an initial step for authorities to establish required guidelines in the studied area, and in the design process of the storm water infrastructure of urban basins in the future.
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Minh, Huynh Vuong Thu, Kim Lavane, Le Thi Lanh, Lam Van Thinh, Nguyen Phuoc Cong, Tran Van Ty, Nigel K. Downes, and Pankaj Kumar. "Developing Intensity-Duration-Frequency (IDF) Curves Based on Rainfall Cumulative Distribution Frequency (CDF) for Can Tho City, Vietnam." Earth 3, no. 3 (August 1, 2022): 866–80. http://dx.doi.org/10.3390/earth3030050.
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Information on the relationship between rainfall intensity, duration and accumulation frequency or return period (IDF) is commonly utilized in the design and management of urban drainage systems. Can Tho City, located in the Vietnamese Mekong Delta, is a city which has recently invested heavily in upgrading its stormwater drainage systems in the hope of preventing reoccurring flood events. Yet, much of these works were designed based on obsolete and outdated IDF rainfall curves. This paper presents an updated IDF curve for design rainfall for Can Tho City. For each duration and designated return period, a cumulative distribution function (CDF) was developed using the Pearson III, Log-Pearson III, and Log-Normal distribution functions. In order to choose the best IDF rainfall curve for Can Tho City, the CDF rainfall curve and empirical formulas used in Vietnam and Asia (Vietnamese standard 7957:2008, Department of Hydrology, Ministry of Transportation, Talbot, Kimijima, and Bermard) were compared. The goodness of fit between the IDF relationship generated by the frequency analysis (CDF curve), and that predicted by the IDF empirical formulas was assessed using the efficiency index (EI), and the root mean squared error (RMSE). The IDF built from Vietnam’s standard TCVN 7957:2008 with new parameters (A = 9594, C = 0.5, b = 26, n = 0.96) showed the best performance, with the highest values of EI (0.84 ≤EI≤ 0.93) and the lowest values of RMSE (2.5 ≤RMSE≤ 3.2), when compared to the other remnants.
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Ulrich, Jana, Felix S. Fauer, and Henning W. Rust. "Modeling seasonal variations of extreme rainfall on different timescales in Germany." Hydrology and Earth System Sciences 25, no. 12 (December 2, 2021): 6133–49. http://dx.doi.org/10.5194/hess-25-6133-2021.
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Abstract. We model monthly precipitation maxima at 132 stations in Germany for a wide range of durations from 1 min to about 6 d using a duration-dependent generalized extreme value (d-GEV) distribution with monthly varying parameters. This allows for the estimation of both monthly and annual intensity–duration–frequency (IDF) curves: (1) the monthly IDF curves of the summer months exhibit a more rapid decrease of intensity with duration, as well as higher intensities for short durations than the IDF curves for the remaining months of the year. Thus, when short convective extreme events occur, they are very likely to occur in summer everywhere in Germany. In contrast, extreme events with a duration of several hours up to about 1 d are conditionally more likely to occur within a longer period or even spread throughout the whole year, depending on the station. There are major differences within Germany with respect to the months in which long-lasting stratiform extreme events are more likely to occur. At some stations the IDF curves (for a given quantile) for different months intersect. The meteorological interpretation of this intersection is that the season in which a certain extreme event is most likely to occur shifts from summer towards autumn or winter for longer durations. (2) We compare the annual IDF curves resulting from the monthly model with those estimated conventionally, that is, based on modeling annual maxima. We find that adding information in the form of smooth variations during the year leads to a considerable reduction of uncertainties. We additionally observe that at some stations, the annual IDF curves obtained by modeling monthly maxima deviate from the assumption of scale invariance, resulting in a flattening in the slope of the IDF curves for long durations.
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Zeri, Sarah Jabbar, Mohammed Magdy Hamed, Xiaojun Wang, and Shamsuddin Shahid. "Utilizing Satellite Data to Establish Rainfall Intensity-Duration-Frequency Curves for Major Cities in Iraq." Water 15, no. 5 (February 22, 2023): 852. http://dx.doi.org/10.3390/w15050852.
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This study generates intensity-duration-frequency curves for three important cities in Iraq using Global Precipitation Measurement Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG), Global Satellite Mapping of Precipitation near real-time (GSMaP NRT), and gauge corrected (GSMaP GC) satellite precipitation datasets. Many probability distribution functions were used to fit the maximum yearly rainfall data. The Sherman equation was used to create intensity-duration-frequency (IDF) curves for rainfall intensities with 2-, 5-, 10-, 25-, 50-, and 100-year return periods, with the estimated coefficients of the best-fit distribution serving as the fitting parameters. The discrepancy between the IDF curves produced from the satellites and the observed data was used to bias correct the satellite IDF curves. The Generalized Extreme Value Distribution model best describes the hourly rainfall distribution of satellite data. GSMaP GC was the best option for creating IDF curves with higher correlations with observed data at Baghdad, Basra, and Mosul. The study indicates the necessity of gauge correction of satellite rainfall data to reduce under- and over-estimating observed rainfall. GSMaP GC can reasonably estimate rainfall in a predominantly arid climate region like Iraq. The generated IDF curves may be an important step toward achieving sustainable urban stormwater management in the country.
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Abu Arra, Ahmad, and Eyüp Şişman. "Characteristics of Hydrological and Meteorological Drought Based on Intensity-Duration-Frequency (IDF) Curves." Water 15, no. 17 (September 1, 2023): 3142. http://dx.doi.org/10.3390/w15173142.
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As a catastrophic phenomenon, drought has destructive impacts on water resources, the environment, and the ecosystem. Consequently, drought plays a vital role in risk assessment, water resources management, and drought mitigation plans. The main aim of this research is to obtain critical intensity-duration-frequency (IDF) drought curves and to provide a comprehensive understanding of the drought characteristics by considering the meteorological Standardized Precipitation Index (SPI), Standardized Precipitation Evapotranspiration Index (SPEI), and hydrological Standardized Streamflow Index (SSI). Critical IDF curves for the drought index and return period selection are identified. Also, new terms are defined as the specific drought duration, the maximum drought duration, and the critical intensity based on drought IDF curves. The results show that the SPI3 based on run theory for 500 years return period has higher drought intensity compared with other drought indices. In some IDF curves, the 2-year return period of a 12-month duration timescale is not provided. Regarding the maximum drought duration, the SPEI12 gave a longer duration. With the new concepts in this research, the presented IDF drought methodology has a novel additional practice to identify the critical intensity and maximum drought duration. Using this methodology for any drought index will contribute to converting data with mathematical calculations into IDF curves for design and risk assessment purposes.
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Elsebaie, Ibrahim H., Mohamed El Alfy, and Atef Qasem Kawara. "Spatiotemporal Variability of Intensity–Duration–Frequency (IDF) Curves in Arid Areas: Wadi AL-Lith, Saudi Arabia as a Case Study." Hydrology 9, no. 1 (December 27, 2021): 6. http://dx.doi.org/10.3390/hydrology9010006.
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In arid areas, flashflood water management is a major concern due to arid climate ambiguity. The examining and derivation of intensity–duration–frequency (IDF) curves in an urban arid area under a variety of terrain patterns and climatic changes is anticipated. Several flood events have been reported in the Al-Lith region of western Saudi Arabia that took away many lives and caused disruption in services and trade. To find and examine the extremities and IDF curves, daily rainfall data from 1966 to 2018 is used. The IDF curves are created for a variety of return periods and climate scenarios in three terrain variabilities. This research examines various distributions to estimate the maximum rainfall for several metrological stations with varying return periods and terrain conditions. Three main zones are identified based on ground elevation variability and IDF distributions from upstream in the eastern mountainous area to downstream in the western coastal area. These IDF curves can be used to identify vulnerable hotspot areas in arid areas such as the Wadi AL-Lith, and flood mitigation steps can be suggested to minimize flood risk.
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Galiatsatou, Panagiota, and Christos Iliadis. "Intensity-Duration-Frequency Curves at Ungauged Sites in a Changing Climate for Sustainable Stormwater Networks." Sustainability 14, no. 3 (January 21, 2022): 1229. http://dx.doi.org/10.3390/su14031229.
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Intensity-duration-frequency (IDF) curves representing the variation of the magnitude of extreme rainfall events with a return period and storm duration are widely used in hydrologic infrastructure design, flood risk management projects, and climate change impact studies. However, in many locations worldwide, short-duration rainfall-observing sites with long records do not exist. This paper introduces a new methodological framework for extracting IDF curves at ungauged sites transferring information from gauged ones with a relatively homogeneous extreme rainfall climate. This methodology is grounded on a simple scaling concept based on the multifractal behaviour of rainfall. A nonstationary Generalized Extreme Value (GEV) distribution fitted to annual rainfall monthly maxima at the ungauged site using a moving-time window approach is also applied to consider effects of a changing climate on IDF curve construction. An application is presented at the study site of Fourni, Crete, to derive IDF curves under changing climate conditions and present implications of the proposed methodology in the design of a sustainable stormwater network. The methodology introduced in this work results in increased rainfall extremes up to 20.5%, while the newly designed stormwater network is characterised by increased diameters of its primary conduits, compared to the ones resulting under fully stationary conditions.
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Hamed, Mohammed Magdy, Sarah Jabbar Zeri, and Shamsuddin Shahid. "Establishing rainfall intensity-duration-frequency curves for Baghdad, Iraq using satellite data." IOP Conference Series: Earth and Environmental Science 1369, no. 1 (June 1, 2024): 012046. http://dx.doi.org/10.1088/1755-1315/1369/1/012046.
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Abstract Rainfall intensity-duration-frequency (IDF) curves were generated for Baghdad by utilising three satellite precipitation datasets: Global Satellite Mapping of Precipitation Near Real-Time (GSMaP NRT), gauge-corrected (GSMaP GC) and Global Precipitation Measurement Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG). Maximum annual rainfall data was fitted using several probability distribution methods. The calculated coefficients from the best-fit distribution were used as fitting parameters to generate IDF curves for return periods of 2, 5, 10, 25, 50 and 100 years using the Sherman equation. To address discrepancies between the satellite-derived IDF curves and observed data, bias correction was performed based on the differences. The analysis revealed that the Generalized Extreme Value Distribution model accurately described the hourly rainfall distribution. GSMaP GC exhibited the highest correlation with the observed data, making it the preferred option for generating IDF curves. The study highlighted the importance of gauge correction for satellite rainfall data to minimise the underestimation or overestimation of rainfall. GSMaP GC demonstrated reasonable accuracy in estimating rainfall in Iraq’s mainly arid climate area. By assisting in the creation of efficient methods for dealing with rainstorm events, the created IDF curves are a major step towards advancing sustainable urban stormwater management in the country.
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Noor, Muhammad, Tarmizi Ismail, Eun-Sung Chung, Shamsuddin Shahid, and Jang Sung. "Uncertainty in Rainfall Intensity Duration Frequency Curves of Peninsular Malaysia under Changing Climate Scenarios." Water 10, no. 12 (November 28, 2018): 1750. http://dx.doi.org/10.3390/w10121750.
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This study developed a methodological framework to update the rainfall intensity-duration-frequency (IDF) curves under climate change scenarios. A model output statistics (MOS) method is used to downscale the daily rainfall of general circulation models (GCMs), and an artificial neural network (ANN) is employed for the disaggregation of projected daily rainfall to hourly maximum rainfall, which is then used for the development of IDF curves. Finally, the 1st quartiles, medians, and 3rd quartiles of projected rainfall intensities are estimated for developing IDF curves with uncertainty level. Eight GCM simulations under two radiative concentration pathways (RCP) scenarios, namely, RCP 4.5 and RCP 8.5, are used in the proposed framework for the projection of IDF curves with related uncertainties for peninsular Malaysia. The projection of rainfall revealed an increase in the annual average rainfall throughout the present century. The comparison of the projected IDF curves for the period 2006–2099 with that obtained using GCM hindcasts for the based period (1971–2005) revealed an increase in rainfall intensity for shorter durations and a decrease for longer durations. The uncertainty in rainfall intensity for different return periods for shorter duration is found to be 2 to 6 times more compared to longer duration rainfall, which indicates that a large increase in rainfall intensity for short durations projected by GCMs is highly uncertain for peninsular Malaysia. The IDF curves developed in this study can be used for the planning of climate resilient urban water storm water management infrastructure in Peninsular Malaysia.
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Sane, Youssouph, Geremy Panthou, Ansoumana Bodian, Theo Vischel, Thierry Lebel, Honore Dacosta, Guillaume Quantin, et al. "Intensity–duration–frequency (IDF) rainfall curves in Senegal." Natural Hazards and Earth System Sciences 18, no. 7 (July 5, 2018): 1849–66. http://dx.doi.org/10.5194/nhess-18-1849-2018.
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Abstract. Urbanization resulting from sharply increasing demographic pressure and infrastructure development has made the populations of many tropical areas more vulnerable to extreme rainfall hazards. Characterizing extreme rainfall distribution in a coherent way in space and time is thus becoming an overarching need that requires using appropriate models of intensity–duration–frequency (IDF) curves. Using a 14 series of 5 min rainfall records collected in Senegal, a comparison of two generalized extreme value (GEV) and scaling models is carried out, resulting in the selection of the more parsimonious one (four parameters), as the recommended model for use. A bootstrap approach is proposed to compute the uncertainty associated with the estimation of these four parameters and of the related rainfall return levels for durations ranging from 1 to 24 h. This study confirms previous works showing that simple scaling holds for characterizing the temporal scaling of extreme rainfall in tropical regions such as sub-Saharan Africa. It further provides confidence intervals for the parameter estimates and shows that the uncertainty linked to the estimation of the GEV parameters is 3 to 4 times larger than the uncertainty linked to the inference of the scaling parameter. From this model, maps of IDF parameters over Senegal are produced, providing a spatial vision of their organization over the country, with a north to south gradient for the location and scale parameters of the GEV. An influence of the distance from the ocean was found for the scaling parameter. It is acknowledged in conclusion that climate change renders the inference of IDF curves sensitive to increasing non-stationarity effects, which requires warning end-users that such tools should be used with care and discernment.
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Ghebreyesus, Dawit T., and Hatim O. Sharif. "Development and Assessment of High-Resolution Radar-Based Precipitation Intensity-Duration-Curve (IDF) Curves for the State of Texas." Remote Sensing 13, no. 15 (July 23, 2021): 2890. http://dx.doi.org/10.3390/rs13152890.
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Conventionally, in situ rainfall data are used to develop Intensity Duration Frequency (IDF) curves, which are one of the most effective tools for modeling the probability of the occurrence of extreme storm events at different timescales. The rapid recent technological advancements in precipitation sensing, and the finer spatio-temporal resolution of data have made the application of remotely sensed precipitation products more dominant in the field of hydrology. Some recent studies have discussed the potential of remote sensing products for developing IDF curves. This study employs a 19-year NEXRAD Stage-IV high-resolution radar data (2002–2020) to develop IDF curves over the entire state of Texas at a fine spatial resolution. The Annual Maximum Series (AMS) were fitted to four widely used theoretical Extreme Value statistical distributions. Gumble distribution, a unique scenario of the Generalized Extreme Values (GEV) family, was found to be the best model for more than 70% of the state’s area for all storm durations. Validation of the developed IDFs against the operational Atlas 14 IDF values shows a ±27% difference in over 95% of the state for all storm durations. The median of the difference stays between −10% and +10% for all storm durations and for all return periods in the range of (2–100) years. The mean difference ranges from −5% for the 100-year return period to 8% for the 10-year return period for the 24-h storm. Generally, the western and northern regions of the state show an overestimation, while the southern and southcentral regions show an underestimation of the published values.
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Tayşi, H., and M. Özger. "Disaggregation of future GCMs to generate IDF curves for the assessment of urban floods." Journal of Water and Climate Change 13, no. 2 (October 29, 2021): 684–706. http://dx.doi.org/10.2166/wcc.2021.241.
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Abstract Urbanization and industrialization cause an increase in greenhouse gas emissions, which in turn causes changes in the atmosphere. Climate change is causing extreme rainfalls and these rainfalls are getting stronger day after day. Floods are threatening urban areas, and short-duration rainfall and outdated drainages are responsible for urban floods. Intensity–Duration–Frequency (IDF) curves are crucial for both drainage system design and assessment of flood risk. Once IDF curves are determined from historical data, they are assumed to be stationary. However, IDF curves must be non-stationary and time varying based on preparation for extreme events. This study generates future IDF curves with short-duration rainfalls under climate change. To represent future rainfall, an ensemble of four Global Climate Models generated under Representative Concentration Pathways (RCP) 4.5 and 8.5 were used in this study. A new approach to the HYETOS disaggregation model was applied to disaggregate daily future rainfall into sub-hourly using disaggregation parameters of hourly measured rainfalls. Hence, sub-hourly future rainfalls will be obtained capturing historical rainfall patterns instead of random rainfall characteristics. Finally, historical and future IDF curves were compared. The study concludes that increases in short-duration rainfalls will be highly intensified in both the near and distant futures with a high probability.
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Doan Thi, Noi, and Tien Thanh Nguyen. "Bias-Corrected IDF Curves From Satellite-Based Rainfall for HoaBinh Province, Vietnam." Asian Journal of Water, Environment and Pollution 19, no. 5 (September 16, 2022): 1–9. http://dx.doi.org/10.3233/ajw220065.
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Satellite-based rainfall is extremely valuable data to quantify the probability of occurrence of rainfall events but is still uncertain to a certain extent. Therefore, this study firstly evaluates the performance of the satellite-based rainfall, PERSIANN-CCS, with rain gauge rainfall. The power transformation method is then applied to correct the satellite-based rainfall. Importantly, the Intensity-Duration-Frequency (IDF) curves are then constructed with the return periods of 5, 10, 25, 50, 100 and 200 years using the Gumbel probability distribution. The results show an efficiency of power transformation on satellite-based rainfall for both rainfall amount and events. It is especially noticed that it is well matched between bias-corrected satellite-based and rain gauge IDF curves duration 12-, 24-, 48- and 72-hour as a particular. For the duration of less than 12-hour, satellite-based IDF curves without bias correction significantly fit the rain-gauge IDF curves within the considered periods.
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Failla, Giulia, Marcella Lo Bianco, Gabriele Freni, and Gaetano Beninati. "Rainfall variability assessment in the hydrological catchment of Addis Ababa." IOP Conference Series: Earth and Environmental Science 1136, no. 1 (January 1, 2023): 012022. http://dx.doi.org/10.1088/1755-1315/1136/1/012022.
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Abstract The Intensity-Duration-Frequency (IDF) relationship is a key input for defining the hydrograph and peak flow discharge required for the hydraulic design. The IDF curves describe the relationship between rainfall intensity, rainfall duration, and return period. The objective of this study was to develop an accurate rainfall analysis in the Addis Ababa catchment. To compute reliable IDF curves, long rainfall data at fine time step scale and uniformly distributed are necessary. In Ethiopia, there is limited availability of data at sub-hourly and at spatial scales. To cope with these issues, (1) stochastic disaggregation techniques have been employed to disaggregate daily observed data into sub-hourly data and (2) to guarantee homogeneity in the project area, the merge of satellite data and observed gauged data have been considered. In this study, IDF curves have been computed for the entire hydrological catchment of Addis Ababa (~1430 km2). The results of the study include tabular and graphical presentation of IDF curves under changed climatic conditions, for return periods of 2, 5, 10, 25, 50 and 100 years for the durations of 15,30 min and 1, 3, 6, 12 and 24 hours.
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Jurado, Oscar E., Jana Ulrich, Marc Scheibel, and Henning W. Rust. "Evaluating the Performance of a Max-Stable Process for Estimating Intensity-Duration-Frequency Curves." Water 12, no. 12 (November 25, 2020): 3314. http://dx.doi.org/10.3390/w12123314.
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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.
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Sangüesa, Claudia, Roberto Pizarro, Ben Ingram, Alfredo Ibáñez, Diego Rivera, Pablo García-Chevesich, Juan Pino, Felipe Pérez, Francisco Balocchi, and Francisco Peña. "Comparing Methods for the Regionalization of Intensity−Duration−Frequency (IDF) Curve Parameters in Sparsely-Gauged and Ungauged Areas of Central Chile." Hydrology 10, no. 9 (August 28, 2023): 179. http://dx.doi.org/10.3390/hydrology10090179.
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Estimating intensity−duration−frequency (IDF) curves requires local historical information of precipitation intensity. When such information is unavailable, as in areas without rain gauges, it is necessary to consider other methods to estimate curve parameters. In this study, three methods were explored to estimate IDF curves in ungauged areas: Kriging (KG), Inverse Distance Weighting (IDW), and Storm Index (SI). To test the viability of these methods, historical data collected from 31 rain gauges distributed in central Chile, 35° S to 38° S, are used. As a result of the reduced number of rain gauges to evaluate the performance of each method, we used LOOCV (Leaving One Out Cross Validation). The results indicate that KG was limited due to the sparse distribution of rain gauges in central Chile. SI (a linear scaling method) showed the smallest prediction error in all of the ungauged locations, and outperformed both KG and IDW. However, the SI method does not provide estimates of uncertainty, as is possible with KG. The simplicity of SI renders it a viable method for extrapolating IDF curves to locations without data in the central zone of Chile.
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Escobar-González, Diego, Mélany S. Singaña-Chasi , Juan González-Vergara , Bolívar Erazo , Miguel Zambrano, Darwin Acosta , Marcos Villacís , Mario Guallpa , Braulio Lahuatte, and Diego H. Peluffo-Ordóñez. "Intensity-Duration-Frequency Curve for Extreme Rainfall Event Characterization, in the High Tropical Andes." Water 14, no. 19 (September 23, 2022): 2998. http://dx.doi.org/10.3390/w14192998.
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In fields such as hydrology, meteorology, and civil engineering, the study of extreme precipitation events is useful to prevent rainfall related disasters. A widely-used practice to address such a problem is by using statistical inferences about precipitation intensity, duration and frequency (IDF). Despite of its great usefulness, the selection of the adequate data and methodology to characterize precipitation’s IDF in the urban area of high-altitude Andean cities remains an open issue for practitioners and decision makers. In this sense, the present paper develops an approach to schematically build the IDF curves for a sub-basin of the study case Andean city, Quito–Ecuador. The here-used data holds information from 12 meteorological stations. Then, the IDF curves are obtained by using both a parametrization followed by a Gamma distribution and a 3-parameter cumulative distribution function, also called mnp. Finally, the curve-fitting process is estimated numerically by adjusting the Sherman equation. Results (average R2=0.9) demonstrated that the framework is well-suited for the high-altitude regime. As a noticeable outcome, a novel spatial interpolation-based analysis is introduced, which enabled the identification of extreme rainfall events according to its duration.
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Cruz, Josias Da Silva, Igor Henrique Coelho Alves, Cleidson Da Silva Alves, Nélio Moura de Figueiredo, Evanice Pinheiro Gomes, and Carlos Eduardo Aguiar de Souza Costa. "EQUAÇÕES DE CHUVAS INTENSAS COM DADOS CPC MORPHING TECHNIQUE (CMORPH) PARA O MUNICÍPIO DE ALTAMIRA - PA." IRRIGA 24, no. 1 (March 29, 2019): 192–207. http://dx.doi.org/10.15809/irriga.2019v24n1p192-207.
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EQUAÇÕES DE CHUVAS INTENSAS COM DADOS CPC MORPHING TECHNIQUE (CMORPH) PARA O MUNICÍPIO DE ALTAMIRA - PA
JOSIAS DA SILVA CRUZ1; IGOR HENRIQUE COELHO ALVES1; CLEIDSON DA SILVA ALVES1; NELIO MOURA DE FIGUEIREDO2; EVANICE PINHEIRO GOMES1 E CARLOS EDUARDO AGUIAR DE SOUZA COSTA1
1Programa de Pós-Graduação de Engenharia de Civil, Universidade Federal do Pará, Rua Augusto Corrêa, 1 - Guamá, 66075-110, Belém – Pará – Brasil. E-mail: josias.cruz75@gmail.com, igor_alves12@yahoo.com.br, cleidsonalves.eng.mecanica@gmail.com, vava51.gomes@gmail.com, eduardoaguiarsc@hotmail.com
2Faculdade de Engenharia Naval, Universidade Federal do Pará, Rua Augusto Corrêa, 1 - Guamá, 66075-110, Belém – Pará – Brasil. E-mail: neliomfigueiredo@outlook.com
1 RESUMO
As equações de chuvas intensas são fundamentais para o dimensionamento de projetos hidráulicos, porém, na Amazônia, há dificuldade na obtenção de séries históricas consistentes para a geração dessas equações. Assim, o objetivo deste estudo foi utilizar dados de precipitação obtidos por satélite como uma nova alternativa para gerar equações de chuvas intensas. Além dos dados de pluviômetro, utilizou-se os dados de precipitação obtidos como produtos da Climate Prediction Center Morphing Technique (CMORPH) para o município de Altamira, PA. A partir desses últimos, foram escolhidos três pontos de leitura no município, chamados de estações sintéticas 1, 2 e 3. Usou-se a distribuição de extremo tipo I (Gumbel) para gerar curvas IDFs para diferentes tempos de retorno (TR) e durações. As estações sintéticas 1 e 3 tiveram bons ajustes às curvas teóricas geradas, porém a sintética 2 subestimou os valores, sendo esta com a menor média de precipitação extrema. As curvas IDF derivadas das equações tiveram coeficiente de ajustes satisfatórios. Deste modo, é possível afirmar que os dados de satélite são alternativas viáveis na geração de curvas IDF, sendo essenciais para locais onde não existem registros históricos de precipitação.
Palavras-Chave: Curvas IDF, Distribuição de Gumbel, Obras Hidráulicas.
CRUZ, J. S.; ALVES, I. H. C.; ALVES, C. S.; FIGUEIREDO, N. M.; GOMES, E. P.; COSTA, C. E. A. S. C.
INTENSE RAINFALL EQUATIONS IN THE AMAZON REGION WITH DATA CPC MORPHING TECHNIQUE (CMORPH)
2 ABSTRACT
Intense rainfall equations are fundamental for the design of hydraulic projects, however, in Amazon, it is difficult to obtain consistent historical series to generate these equations. Thus, the objective of this study was to use precipitation data obtained by satellite as a new alternative to generate intense rainfall equations. In addition to rain gauge data, precipitation data obtained as products of the Climate Prediction Center Morphing Technique (CMORPH) for the municipality of Altamira, PA were used. From the latter, three reading points were chosen in the municipality, called synthetic stations 1, 2 and 3. The I-type distribution (Gumbel) was used to generate IDF curves for different return times (TR) and durations. Synthetic stations 1 and 3 had good adjustments to the theoretical curves generated, but synthetic 2 underestimated the values, and presented the lowest average of extreme precipitation. IDF curves derived from the equations had a satisfactory coefficient of adjustment. In this way, it is possible to affirm that satellite data are viable alternatives in the generation of IDF curves, being essential for places where there are no historical records of precipitation.
Keywords: IDF curves, Gumbel distribution, Hydraulic Works.
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Doulabian, Shahab, Erfan Ghasemi Tousi, Amirhossein Shadmehri Toosi, and Sina Alaghmand. "Non-Stationary Precipitation Frequency Estimates for Resilient Infrastructure Design in a Changing Climate: A Case Study in Sydney." Hydrology 10, no. 6 (May 24, 2023): 117. http://dx.doi.org/10.3390/hydrology10060117.
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The intensity–duration–frequency (IDF) curve is a commonly utilized tool for estimating extreme rainfall events that are used for many purposes including flood analysis. Extreme rainfall events are expected to become more intense under the changing climate, and there is a need to account for non-stationarity IDF curves to mitigate an underestimation of the risks associated with extreme rainfall events. Sydney, Australia, has recently started experiencing flooding under climate change and more intense rainfall events. This study evaluated the impact of climate change on altering the precipitation frequency estimates (PFs) used in generating IDF curves at Sydney Airport. Seven general circulation models (GCMs) were obtained, and the best models in terms of providing the extreme series were selected. The ensemble of the best models was used for comparing the projected 24 h PFs in 2031–2060 with historical values provided by Australian Rainfall and Runoff (ARR). The historical PFs consistently underestimate the projected 24 h PFs for all return periods. The projected 24 h 100 yr rainfall events are increased by 9% to 41% for the least and worst-case scenario compared to ARR historical PFs. These findings highlight the need for incorporating the impact of climate change on PFs and IDF curves in Sydney toward building a more prepared and resilient community. The findings of this study can also aid other communities in adapting the same framework for developing more robust and adaptive approaches to reducing extreme rainfall events’ repercussions under changing climates.
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Pizarro, Roberto, Ben Ingram, Fernando Gonzalez-Leiva, Rodrigo Valdés-Pineda, Claudia Sangüesa, Nicolás Delgado, Pablo García-Chevesich, and Juan Valdés. "WEBSEIDF: A Web-Based System for the Estimation of IDF Curves in Central Chile." Hydrology 5, no. 3 (August 4, 2018): 40. http://dx.doi.org/10.3390/hydrology5030040.
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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.
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Ritschel, Christoph, Uwe Ulbrich, Peter Névir, and Henning W. Rust. "Precipitation extremes on multiple timescales – Bartlett–Lewis rectangular pulse model and intensity–duration–frequency curves." Hydrology and Earth System Sciences 21, no. 12 (December 20, 2017): 6501–17. http://dx.doi.org/10.5194/hess-21-6501-2017.
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Abstract. For several hydrological modelling tasks, precipitation time series with a high (i.e. sub-daily) resolution are indispensable. The data are, however, not always available, and thus model simulations are used to compensate. A canonical class of stochastic models for sub-daily precipitation are Poisson cluster processes, with the original Bartlett–Lewis (OBL) model as a prominent representative. The OBL model has been shown to well reproduce certain characteristics found in observations. Our focus is on intensity–duration–frequency (IDF) relationships, which are of particular interest in risk assessment. Based on a high-resolution precipitation time series (5 min) from Berlin-Dahlem, OBL model parameters are estimated and IDF curves are obtained on the one hand directly from the observations and on the other hand from OBL model simulations. Comparing the resulting IDF curves suggests that the OBL model is able to reproduce the main features of IDF statistics across several durations but cannot capture rare events (here an event with a return period larger than 1000 years on the hourly timescale). In this paper, IDF curves are estimated based on a parametric model for the duration dependence of the scale parameter in the generalized extreme value distribution; this allows us to obtain a consistent set of curves over all durations. We use the OBL model to investigate the validity of this approach based on simulated long time series.
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Ghimire, Binita, Gehendra Kharel, Esayas Gebremichael, and Linyin Cheng. "Evaluating Non-Stationarity in Precipitation Intensity-Duration-Frequency Curves for the Dallas–Fort Worth Metroplex, Texas, USA." Hydrology 10, no. 12 (December 2, 2023): 229. http://dx.doi.org/10.3390/hydrology10120229.
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Extreme precipitation has become more frequent and intense with time and space. Infrastructure design tools such as Intensity-Duration-Frequency (IDF) curves still rely on historical precipitation and stationary assumptions, risking current and future urban infrastructure. This study developed IDF curves by incorporating non-stationarity trends in precipitation annual maximum series (AMS) for Dallas–Fort Worth, the fourth-largest metropolitan region in the United States. A Pro-NEVA tool was used to develop non-stationary IDF curves, taking historical precipitation AMS for seven stations that showed a non-stationary trend with time as a covariate. Four statistical indices—the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Root Mean Square Error (RMSE), and Nash–Sutcliffe Efficiency (NSE)—were used as the model goodness of fit evaluation. The lower AIC, BIC, and RMSE values and higher NSE values for non-stationary models indicated a better performance compared to the stationary models. Compared to the traditional stationary assumption, the non-stationary IDF curves showed an increase (up to 75%) in the 24 h precipitation intensity for the 100-year return period. Using the climate change adaptive non-stationary IDF tool for the DFW metroplex and similar urban regions could enable decision makers to make climate-informed choices about infrastructure investments, emergency preparedness measures, and long-term urban development and water resource management planning.
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Agbazo, Médard Noukpo, Gabin Koto N'Gobi, Basile Kounouhewa, Eric Alamou, Abel Afouda, and Aristide Akpo. "Estimation of IDF Curves of Extreme Rainfall by Simple Scaling in Northern Oueme Valley, Benin Republic (West Africa)." Earth Sciences Research Journal 20, no. 1 (April 30, 2016): 1–7. http://dx.doi.org/10.15446/esrj.v20n1.49405.
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<p>Rainfall intensity-duration-frequency (IDF) curves are of particular importance in water resources management, for example, in urban hydrology, for the design of hydraulic structures and the estimation of the flash flood risk in small catchments. IDF curves 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 and structures. In this study, scaling properties of extreme rainfall are examined to establish the scaling behavior of statistical non-central moment over different durations. IDF curves and equations are set up for all stations by using the parameter obtained from scaling behavior, the location and scale parameters μ24 and σ24 of the Gumbel distribution (EVI) sample of annual maximum 1440 min rainfall data. In another hand, we have established the IDF curves for ten selected rain gauge stations in the Northern (Oueme Valley) parts of Benin Republic, West Africa by using the simple scaling approach. Analysis of rainfall intensities (5 min and 1440 min rainfall data) from the ten rainfall stations shows that rainfall in north-Benin displays scales invariance property from 5 min to 1440 min. For time scaling, the statistical properties of rainfall follow the hypothesis of simple scaling. Therefore, the simple scaling model applies to the rainfall in (Oueme Valley). Hence, the simple scaling model is thought to be a viable approach to estimate IDF curves of hourly and sub-hourly rainfall form rainfall projections. The obtained scaling exponents are less than 1 and range from 0.23 to 0.59. The empirical model shows that the scaling procedure is a good estimator as it is more efficient and gives more accurate estimates compared with the observed rainfall than the traditional method which only consists the Gumbel model in all stations for lower return periods (T<5 years) but not for higher return periods.</p><p> </p><p><strong>Estimación de las Curvas IDF de Extrema Precipitación por Escala Simple en el Valle Oueme, al Norte de la República de Benín (Africa occidental)</strong></p><p> </p><p><strong>Resumen</strong></p><p>Las curvas de precipitación Intensidad-Duración-Frecuencia (IDF) son de particular importancia en el manejo de los recursos hídricos, como es el caso de la hidrología urbana o para el diseño de estructuras hidráulicas y la estimación del riesgo de crecidas en pequeñas captaciones. Las curvas IDF describen la intensidad de las precipitaciones como una función con períodos de duración y recurrencia, lo que las hace significativas en la planeación de recursos hídricos así como en el diseño de construcciones y estructuras hidráulicas. Este estudio examina las propiedades de escala en precipitaciones extremas para establecer un comportamiento en momentos estadísticos marginales en diferentes períodos de duración. Se establecieron las curvas IDF y las ecuaciones para todas las estaciones a partir del parámetro obtenido del comportamiento de escala, la ubicación y los parámetros de escala μ24 and σ24 de la muestra de información de precipitación máxima anual de 1440 minutos de la distribución de Gumbel (EVI). Por otro lado, se establecieron las curvas IDF para 10 estaciones pluviométricas seleccionadas en el Valle Oueme, al norte de la República de Benín (África occidental), con el uso de aproximación simple de escala. El análisis de las intensidades de precipitación en las diez estaciones pluviométricas muestra que la precipitación en el norte de Benín expone propiedades de poca variación en la escala 5 min y 1440. En el tiempo de escala, las propiedades estadísticas de precipitación confirman la hipótesis de escala simple; además, este modelo so corresponde a la precipitación del Valle Oueme. Por lo tanto, el modelo de escala simple se considera una aproximación viable para estimar las curvas IDF en las proyecciones de precipitación de cada hora y sub-hora. Los exponentes de escala obtenidos son menores a 1 y oscilan de 0,23 a 0,59. El modelo empírico muestra que el procedimiento de escala es un buen estimativo, más eficiente y con cálculos más exactos que el método tradicional, el cual consiste solamente en el modelo Gumbel aplicado en todas las estaciones pluviométricas en períodos de menor recurrencia (T<5 años) pero no en lapsos de mayor recurrencia.</p>
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Panthou, G., T. Vischel, T. Lebel, G. Quantin, and G. Molinié. "Characterizing the space–time structure of rainfall in the Sahel with a view to estimating IDAF curves." Hydrology and Earth System Sciences Discussions 11, no. 7 (July 23, 2014): 8409–41. http://dx.doi.org/10.5194/hessd-11-8409-2014.
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Abstract. Intensity–duration–area–frequency (IDAF) curves are increasingly demanded for characterizing the severity of storms and for designing hydraulic structures. Their computation requires inferring areal rainfall distributions over the range of space–time scales that are the most relevant for hydrological studies at catchment scale. In this study, IDAF curves are computed for the first time in West Africa, based on the data provided by the AMMA-CATCH Niger network, composed of 30 recording rain gauges having operated since 1990 over a 16 000 km2 area in South West Niger. The IDAF curves are obtained by separately considering the time (IDF) and space (Areal Reduction Factor – ARF) components of the extreme rainfall distribution. Annual maximum intensities are extracted for resolutions between 1 and 24 h in time and from point (rain-gauge) to 2500 km2 in space. The IDF model used is based on the concept of scale invariance (simple scaling) which allows the normalization of the different temporal resolutions of maxima series to which a global GEV is fitted. This parsimonious framework allows using the concept of dynamic scaling to describe the ARF. The results show that coupling a simple scaling in space and time with a dynamical scaling relating space and time allows modeling satisfactorily the effect of space–time aggregation on the distribution of extreme rainfall.
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Ulrich, Jana, Oscar E. Jurado, Madlen Peter, Marc Scheibel, and Henning W. Rust. "Estimating IDF Curves Consistently over Durations with Spatial Covariates." Water 12, no. 11 (November 6, 2020): 3119. http://dx.doi.org/10.3390/w12113119.
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Given that long time series for temporally highly resolved precipitation observations are rarely available, it is necessary to pool information to obtain reliable estimates of the distribution of extreme precipitation, especially for short durations. In this study, we use a duration-dependent generalized extreme value distribution (d-GEV) with orthogonal polynomials of longitude and latitude as spatial covariates, allowing us to pool information between durations and stations. We determine the polynomial orders with step-wise forward regression and cross-validated likelihood as a model selection criterion. The Wupper River catchment in the West of Germany serves as a case study area. It allows us to estimate return level maps for arbitrary durations, as well as intensity-duration-frequency curves at any location—also ungauged—in the research area. The main focus of the study is evaluating the model performance in detail using the Quantile Skill Index, a measure derived from the popular Quantile Skill Score. We find that the d-GEV with spatial covariates is an improvement for the modeling of rare events. However, the model shows limitations concerning the modeling of short durations d≤30min. For ungauged sites, the model performs on average as good as a generalized extreme value distribution with parameters estimated individually at the gauged stations with observation time series of 30–35 years available.
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Mirhosseini, Golbahar, Puneet Srivastava, and Amirreza Sharifi. "Developing Probability-Based IDF Curves Using Kernel Density Estimator." Journal of Hydrologic Engineering 20, no. 9 (September 2015): 04015002. http://dx.doi.org/10.1061/(asce)he.1943-5584.0001160.
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Marra, Francesco, Efrat Morin, Nadav Peleg, Yiwen Mei, and Emmanouil N. Anagnostou. "Intensity–duration–frequency curves from remote sensing rainfall estimates: comparing satellite and weather radar over the eastern Mediterranean." Hydrology and Earth System Sciences 21, no. 5 (May 9, 2017): 2389–404. http://dx.doi.org/10.5194/hess-21-2389-2017.
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Abstract. Intensity–duration–frequency (IDF) curves are widely used to quantify the probability of occurrence of rainfall extremes. The usual rain gauge-based approach provides accurate curves for a specific location, but uncertainties arise when ungauged regions are examined or catchment-scale information is required. Remote sensing rainfall records, e.g. from weather radars and satellites, are recently becoming available, providing high-resolution estimates at regional or even global scales; their uncertainty and implications on water resources applications urge to be investigated. This study compares IDF curves from radar and satellite (CMORPH) estimates over the eastern Mediterranean (covering Mediterranean, semiarid, and arid climates) and quantifies the uncertainty related to their limited record on varying climates. We show that radar identifies thicker-tailed distributions than satellite, in particular for short durations, and that the tail of the distributions depends on the spatial and temporal aggregation scales. The spatial correlation between radar IDF and satellite IDF is as high as 0.7 for 2–5-year return period and decreases with longer return periods, especially for short durations. The uncertainty related to the use of short records is important when the record length is comparable to the return period ( ∼ 50, ∼ 100, and ∼ 150 % for Mediterranean, semiarid, and arid climates, respectively). The agreement between IDF curves derived from different sensors on Mediterranean and, to a good extent, semiarid climates, demonstrates the potential of remote sensing datasets and instils confidence on their quantitative use for ungauged areas of the Earth.
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Cannon, Alex J., and Silvia Innocenti. "Projected intensification of sub-daily and daily rainfall extremes in convection-permitting climate model simulations over North America: implications for future intensity–duration–frequency curves." Natural Hazards and Earth System Sciences 19, no. 2 (March 1, 2019): 421–40. http://dx.doi.org/10.5194/nhess-19-421-2019.
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Abstract. Convection-permitting climate models have been recommended for use in projecting future changes in local-scale, short-duration rainfall extremes that are of the greatest relevance to engineering and infrastructure design, e.g., as commonly summarized in intensity–duration–frequency (IDF) curves. Based on thermodynamic arguments, it is expected that rainfall extremes will become more intense in the future. Recent evidence also suggests that shorter-duration extremes may intensify more than longer durations and that changes may depend on event rarity. Based on these general trends, will IDF curves shift upward and steepen under global warming? Will long-return-period extremes experience greater intensification than more common events? Projected changes in IDF curve characteristics are assessed based on sub-daily and daily outputs from historical and late 21st century pseudo-global-warming convection-permitting climate model simulations over North America. To make more efficient use of the short model integrations, a parsimonious generalized extreme value simple scaling (GEVSS) model is used to estimate historical and future IDF curves (1 to 24 h durations). Simulated historical sub-daily rainfall extremes are first evaluated against in situ observations and compared with two high-resolution observationally constrained gridded products. The climate model performs well, matching or exceeding performance of the gridded datasets. Next, inferences about future changes in GEVSS parameters are made using a Bayesian false discovery rate approach. Large portions of the domain experience significant increases in GEVSS location (>99 % of grid points), scale (>88 %), and scaling exponent (>39 %) parameters, whereas almost no significant decreases are projected to occur (<1 %, <5 %, and <5 % respectively). The result is that IDF curves tend to shift upward (increases in location and scale), and, with the exception of the eastern US, steepen (increases in scaling exponent), which leads to the largest increases in return levels for short-duration extremes. The projected increase in the GEVSS scaling exponent calls into question stationarity assumptions that form the basis for existing IDF curve projections that rely exclusively on simulations at the daily timescale. When changes in return levels are scaled according to local temperature change, median scaling rates, e.g., for the 10-year return level, are consistent with the Clausius–Clapeyron (CC) relation at 1 to 6 h durations, with sub-CC scaling at longer durations and modest super-CC scaling at sub-hourly durations. Further, spatially coherent but small increases in dispersion – the ratio of scale and location parameters – of the GEVSS distribution are found over more than half of the domain, providing some evidence for return period dependence of future changes in extreme rainfall.
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Panthou, G., T. Vischel, T. Lebel, G. Quantin, and G. Molinié. "Characterising the space–time structure of rainfall in the Sahel with a view to estimating IDAF curves." Hydrology and Earth System Sciences 18, no. 12 (December 11, 2014): 5093–107. http://dx.doi.org/10.5194/hess-18-5093-2014.
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Abstract. Intensity–duration–area–frequency (IDAF) curves are increasingly demanded for characterising the severity of storms and for designing hydraulic structures. Their computation requires inferring areal rainfall distributions over the range of space scales and timescales that are the most relevant for hydrological studies at catchment scale. In this study, IDAF curves are computed for the first time in West Africa, based on the data provided by the AMMA-CATCH Niger network, composed of 30 recording rain gauges having operated since 1990 over a 16 000 km2 area in south-western Niger. The IDAF curves are obtained by separately considering the time (intensity–duration–frequency, IDF) and space (areal reduction factor, ARF) components of the extreme rainfall distribution. Annual maximum intensities are extracted for resolutions between 1 and 24 h in time and from point (rain gauge) to 2500 km2 in space. The IDF model used is based on the concept of scale invariance (simple scaling) which allows the normalisation of the different temporal resolutions of maxima series to which a global generalised extreme value (GEV) is fitted. This parsimonious framework allows one to use the concept of dynamic scaling to describe the ARF. The results show that coupling a simple scaling in space and time with a dynamical scaling that relates to space and time allows one to satisfactorily model the effect of space–time aggregation on the distribution of extreme rainfall.
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Ologhadien, I., and G. O. Esebene. "Model Selection and Design of Storm Water Drainage Systems at Oleh, Delta State, Nigeria." European Journal of Engineering and Technology Research 7, no. 1 (February 22, 2022): 70–77. http://dx.doi.org/10.24018/ejeng.2022.7.1.2728.
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Rainfall Intensity-Duration-Frequency curves and equations present the exceedance probability of a given rainfall intensity and storm duration expected to occur at a particular location, for the design of storm water drainage systems and hydraulic structures. The aim of this study was to develop IDF curves/equations aim for Oleh, a municipality situated in the low-lying and flood prone region of Nigeria. The study was conducted using annual maxima rainfall series (ARMS) of 28 years obtained from Nigeria Meteorological Agency (NiMet). The AMRS were extracted into 15 Nos. storm durations between 10minutes and 600 minutes. The AMRS of each duration was fitted to Gumbel (EV1), LN2 and Normal (N) distributions using the K-S and A-D goodness-of-fit module of Easyfit software, Version 5.6. The graphical plots, development of IDF models and computations of performance measures of R2 NSE and RSR, were executed in Microsoft Excel, 2010. The results of GOF tests show that for K-S tests, Gumbel (EVI) is best-fit distribution in four durations, LN2 was best –fit in Nine out of fifteen durations, and Normal distribution durations scored 2. Similarly, for A-D GOF test, Gumbel (EVI) scored three (3), LN2 scored eleven (11), while Normal distribution scored one (1). Consequently, LN2 is the best-fit distribution, seconded by Gumbel (EVI). Accordingly, LN2 and Gumbel (EVI) distributions have been adopted in the development of the IDF models for Oleh municipality, while the performances of the IDF models may be presented the inequality; 0.984 ? R2 ? 0.998; 0.990 ? NSE ? 0.998 and 0.045 ? RSR ? 0.096. The graphical plots, IDF curves and models exhibited the peculiar attributes of IDF curves/equations reported in literature. The performance measures show that the equations are robust for practical application in the design of storm water drainage systems and hydraulic structures.
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Ewea, Hatem A., Amro M. Elfeki, Jarbou A. Bahrawi, and Nassir S. Al-Amri. "Modeling of IDF curves for stormwater design in Makkah Al Mukarramah region, The Kingdom of Saudi Arabia." Open Geosciences 10, no. 1 (December 31, 2018): 954–69. http://dx.doi.org/10.1515/geo-2018-0076.
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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.
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Tien Thanh, Nguyen, and Luca Dutto Aldo Remo. "Projected Changes of Precipitation IDF Curves for Short Duration under Climate Change in Central Vietnam." Hydrology 5, no. 3 (July 13, 2018): 33. http://dx.doi.org/10.3390/hydrology5030033.
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In future years, extreme weather events are expected to frequently increase due to climate change, especially in the combination of climate change and events of El Niño–Southern Oscillation. This pays special attention to the construction of intensity–duration–frequency (IDF) curves at a tempo-spatial scale of sub-daily and sub-grid under a context of climate change. The reason for this is that IDF curves represent essential means to study effects on the performance of drainage systems, damps, dikes and reservoirs. Therefore, the objective of this study is to present an approach to construct future IDF curves with high temporo-spatial resolutions under climate change in central Vietnam, using the case of VuGia-ThuBon. The climate data of historical and future from a regional climate model RegCM4 forced by three global models MPI-ESM-MR, IPSL-CM5A-LR and ICHEC-EC-EARTH are used to re-grid the resolution of 10 km × 10 km grid spacing from 25 km × 25 km on the base of bilinear interpolation. A bias correction method is then applied to the finest resolution of a hydrostatic climate model for an ensemble of simulations. Furthermore, the IDF curves for short durations of precipitation are constructed for the historical climate and future climates under two representative concentration pathway (RCP) scenarios, RCP4.5 and RCP8.5, based on terms of correlation factors. The major findings show that the projected precipitation changes are expected to significantly increase by about 10 to 30% under the scenarios of RCP4.5 and RCP8.5. The projected changes of a maximum of 1-, 2-, and 3-days precipitation are expected to increase by about 30–300 mm/day. More importantly, for all return periods (i.e., 10, 20, 50, 100, and 200 years), IDF curves completely constructed for short durations of precipitation at sub-daily show an increase in intensities for the RCP4.5 and RCP8.5 scenarios.
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Nguyen, Quan Trong, Nhi Thi Thao Pham, and Khoi Nguyen Dao. "Developing IDF curve of extreme rainfall at Tan Son Hoa station for the period 1980-2015." Science & Technology Development Journal - Science of The Earth & Environment 1, no. M2 (December 31, 2017): 73–81. http://dx.doi.org/10.32508/stdjsee.v1im2.447.
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Recently, the Intensity – Duration – Frequency (IDF) relationship of extreme rainfalls in a local area is usually investigated to provide accurate required data for calculating, planning, and developing urban drainage systems, especially in the context of climate change. Traditionally, IDF curves are computed based on a statistical method for analyzing the frequency of occurrence or non-occurrence of annual extreme rainfall events over a return period; or based on a probability distribution function of these events. However, these traditional methods do not take into consideration the relationship between extreme rainfalls of different durations as they only simulate the intensity of extreme rainfall events at each individual duration after generated a large number of parameter sets. Therefore, the results of these methods are inaccurate and much depend on the actual observed data. In this study, a new approach to develop IDF relations was proposed based on the scale-invariance nature of extreme rainfalls at different durations. This method will be examined and compared with traditional methods based on the IDF curves of extreme rainfalls at Tan Son Nhat gauge station (HCMC) from 1980 to 2015. Results have indicated that there is a linear relationship between extreme rainfalls at different time scales and showed that the proposed method is appropriate for estimating the IDF curves with many prominent advantages rather than traditional method.
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El Hannoun, Wafaa, Anas Boukili Makhoukhi, Abdelhak Zoglat, and Salah-Eddine El Adlouni. "Intensity–Duration–Frequency Curves for Dependent Datasets." Water 15, no. 14 (July 20, 2023): 2641. http://dx.doi.org/10.3390/w15142641.
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Intensity–duration–frequency (IDF) curves of precipitation are a reference decision support tool used in hydrology. They allow the estimation of extreme precipitation and its return periods. Typically, IDF curves are estimated using univariate frequency analysis of the maximum annual intensities of precipitation for different durations. It is then assumed that the annual maxima of different durations are independent to simplify the parameter estimation. This strong hypothesis is not always verified for every climatic region. This study examines the effects of the independence hypothesis by proposing a multivariate model that considers the dependencies between precipitation intensities of different durations. The multivariate model uses D-vine copulas to explore the intraduration dependencies. The generalized extreme values distribution (GEV) is considered a marginal model that fits a wide range of tail behaviors. An illustration of the proposed approach is made for historical data from Moncton, in the province of New Brunswick (Eastern Canada), with climatic projections made through three scenarios of the Representative Concentration Pathway (RCP).
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Hu, Huiling, and Bilal M. Ayyub. "Machine Learning for Projecting Extreme Precipitation Intensity for Short Durations in a Changing Climate." Geosciences 9, no. 5 (May 9, 2019): 209. http://dx.doi.org/10.3390/geosciences9050209.
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Climate change is one of the prominent factors that causes an increased severity of extreme precipitation which, in turn, has a huge impact on drainage systems by means of flooding. Intensity–duration–frequency (IDF) curves play an essential role in designing robust drainage systems against extreme precipitation. It is important to incorporate the potential threat from climate change into the computation of IDF curves. Most existing works that have achieved this goal were based on Generalized Extreme Value (GEV) analysis combined with various circulation model simulations. Inspired by recent works that used machine learning algorithms for spatial downscaling, this paper proposes an alternative method to perform projections of precipitation intensity over short durations using machine learning. The method is based on temporal downscaling, a downscaling procedure performed over the time scale instead of the spatial scale. The method is trained and validated using data from around two thousand stations in the US. Future projection of IDF curves is calculated and discussed.
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Schwandt, Peter, Thomas Bertsch, Evelyn Liepold, and Gerda-Maria Haas. "Age- and Gender-Specific Components of the Metabolic Syndrome in 2228 First Graders: The PEP Family Heart Study." Scientifica 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/394807.
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Because first graders are critical for excess weight gain, we assessed components of the metabolic syndrome (MetS) using the pediatric definition of the International Diabetes Federation (IDF). We compared four MetS components as defined by the IDF with age- and gender-specific components in 2228 first graders at the age of 6. The growth curves were derived from 22113 children and adolescents who participated in the PEP Family Heart Study. The aim was to determine in first graders precise values of waist circumference (WC), blood pressure (BP), triglycerides (TG), and HDL-Cholesterol (HDL-C) based on growth curves that were developed for a large German population of youths and to assess the prevalence in terms of both definitions at this critical age. The prevalence of high blood pressure for age was 13% compared with only 2% according to IDF. Because of this considerable divergence, we propose to define MetS components based on national growth curves.
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Collalti, Dino, Nekeisha Spencer, and Eric Strobl. "Flash flood detection via copula-based intensity–duration–frequency curves: evidence from Jamaica." Natural Hazards and Earth System Sciences 24, no. 3 (March 14, 2024): 873–90. http://dx.doi.org/10.5194/nhess-24-873-2024.
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Abstract. Extreme rainfall events frequently cause hazardous floods in many parts of the world. With growing human exposure to floods, studying conditions that trigger floods is imperative. Flash floods, in particular, require well-defined models for the timely warning of the population at risk. Intensity–duration–frequency (IDF) curves are a common way to characterize rainfall and flood events. Here, the copula method is employed to model the dependence between the intensity and duration of rainfall events flexibly and separately from their respective marginal distribution. Information about the localization of 93 flash floods in Jamaica was gathered and linked to remote-sensing rainfall data, and additional data on location-specific yearly maximum rainfall events were constructed. The estimated normal copula has Weibull and generalized extreme value (GEV) marginals for duration and intensity, respectively. Due to the two samples, it is possible to pin down above which line in the intensity duration space a rainfall event likely triggers a flash flood. The parametric IDF curve with an associated return period of 216 years is determined as the optimal threshold for flash flood event classification. This methodology delivers a flexible approach to generating rainfall IDF curves that can directly be used to assess flash flood risk.
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Cavus, Yonca, Kerstin Stahl, and Hafzullah Aksoy. "Drought intensity–duration–frequency curves based on deficit in precipitation and streamflow for water resources management." Hydrology and Earth System Sciences 27, no. 18 (September 27, 2023): 3427–45. http://dx.doi.org/10.5194/hess-27-3427-2023.
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Abstract. Drought estimates in terms of physically measurable variables such as precipitation deficit or streamflow deficit are key knowledge for an effective water management. How these deficits vary with the drought event severity indicated by commonly used standardized indices is often unclear. Drought severity calculated from the drought index does not necessarily correspond to the same amount of deficit in precipitation or streamflow at different regions, and it is different for each month in the same region. We investigate drought to remove this disadvantage of the index-based drought intensity–duration–frequency (IDF) curves and develop IDF curves in terms of the associated deficit. In order to study the variation of deficits, we use the link between precipitation and streamflow and the associated indices, the Standardized Precipitation Index (SPI) and the Standardized Streamflow Index (SSI). More specifically, the analysis relies on frequency analysis combined with the total probability theorem applied to the critical drought severity. The critical drought has varying durations, and it is extracted from dry periods. IDF curves in terms of precipitation and streamflow deficits for the most severe drought of each drought duration in each year are then subject to comparison of statistical characteristics of droughts for different return periods. Precipitation and streamflow data from two catchments, the Seyhan River (Türkiye) and the Kocher River (Germany), provide examples for two climatically and hydrologically different cases. A comparison of the two cases allows a similar method to be tested in different hydrological conditions. We found that precipitation and streamflow deficits vary systematically, reflecting seasonality and the magnitude of precipitation and streamflow characteristics of the catchments. Deficits change from one month to another at a given station. Higher precipitation deficits were observed in winter months compared to summer months. Additionally, we assessed observed past major droughts experienced in both catchments on the IDF curves, which show that the major droughts have return periods at the order of 100 years at short durations. This coincides with the observation in the catchments and shows the applicability of the IDF curves. The IDF curves can be considered a tool for using in a range of specific activities of agriculture, ecology, industry, energy and water supply, etc. This is particularly important to end users and decision-makers to act against the drought quickly and precisely in a more physically understandable manner.
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Alemaw, Berhanu F., and Ron T. Chaoka. "Regionalization of Rainfall Intensity-Duration-Frequency (IDF) Curves in Botswana." Journal of Water Resource and Protection 08, no. 12 (2016): 1128–44. http://dx.doi.org/10.4236/jwarp.2016.812088.
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