Intensity-duration-frequency Curves Research Articles

Future extreme heat wave events using Bayesian heat wave intensity-persistence day-frequency model and their uncertainty

Heat wave events are occurring more often and over a wider area around the world, and in the coming era of global warming, their intensity will intensify and their persistence days will be longer. In this study, the relationship between the occurrence probability, intensity, and persistency days of future extreme heat wave events is explained using the concept of IDF (rainfall intensity-duration-frequency) curves for extreme rainfall events. The uncertainty of the non-stationary heat wave intensity-persistence day-frequency (HPF) model is analyzed using Bayesian inference. Non-stationary HPF curves were applied to a total of 16 future daily maximum surface air temperature ensembles projected at six major sites in Korea. From the ensemble of future climate information, it was found that the intensity of the extreme heat wave event for persistence day of 2-day estimated in 2050 would be more likely to rise in the range of 1.23–1.69 °C (under RCP 4.5) and 1.15–1.96 °C (under RCP 8.5) than that estimated in 2010. It was also found that the uncertainty resulting from parameter estimation of the HPF model was greater than the uncertainty resulting from the inter-model variability of various climate model combinations. When reflecting the uncertainty resulting from the estimation of model parameters, the 95% confidence interval of the delta change for the heat wave intensity projected in 2050 from 2010 was estimated to be 0.53–4.94 °C (under RCP 4.5) and 0.89–5.57 °C (under RCP 8.5).

Kajian Kesesuaian Rumus Intensitas Hujan dan Kurva Intensitas Durasi Frekuensi (IDF) di Wilayah Kampus Universitas Brawijaya, Malang

Rainfall intensity known as an essential variable in rainfall-runoff transformation. Flood events occurred in 2017 at Brawijaya University campus caused by high intensity and landuse change in campus's internal and external environment. The study aims to examine performance of several empirical formulas in estimating rainfall intensity, investigating characteristic of each empirical formula’s contant due to varying return period (Tr), and determining appropriate Intensity Duration Frequency (IDF) curve. The formula of Sherman, Talbot, and Ishiguro was employed to obtain empirical intensity, while intensity on varying return period was calculated using Log Pearson Type III. The proposed rainfall intensity formula was selected through comparison between empirical intensity with those from observation according to criteria of relative error (KR), Nash Sutcliffe Efficiency (NSE), and Peak Weight Root Mean Square Error (PWRMSE). The Sherman formula showed best performance in estimating rainfall intensity as indicated by low value of KR and PWRMSE, followed by NSE close to one. The constant of empirical formula “a” was directly proportional with increasing of Tr; conversely, constant “b” and “n” were inverse with Tr. The validation result of Sherman formula demonstrated that the formula showed good reliability, thus recommended to estimate intensity and IDF curve in the study area.

Estimates of Precipitation IDF Curves and Design Discharges for Road-Crossing Drainage Structures: Case Study in Four Small Forested Watersheds in the Southeastern US

AbstractWe compared precipitation intensity-duration-frequency (PIDF) curves developed for four small forested watersheds to spatially interpolated estimates from the National Oceanic and Atmospher...

Water management in Saudi Arabia: a case study of Makkah Al Mukarramah region

In the hydrologic design of water management infrastructures, rainfall characteristics are often used and the available historical rainfall events in the form of intensity–duration–frequency (IDF) curves are essential. However, due to the rise in the emission of greenhouse gases, the magnitude and frequency of future extreme rainfalls will be changed. Therefore, the current study aims to develop the IDF curves models in the region of Makkah Al Mukarramah, Saudi Arabia. In this study, five models were developed to estimate the rainfall intensity for the different durations and return periods, using three statistical parameters e, m, and C, calculated from the rainfall intensity data for the time series in each station. The results showed that the rainfall intensity average is ranged between 15.4 mm/10 min and 25.9 mm/60 min for Al Karr Sufli station from 1966 to 2005, and 29.8 mm/120 min and 49.6 mm/720 min for Baqrane station during the period of 1971–2005. Besides, the KGE, R2, and Theil’s U performance tests of the probability distribution models revealed that the exponential model is the best for the Al-Barzah, Ain Al Azizia and Al Karr Sufli, and Humma Syssed stations, and the log Pearson III model is the best model for Baqrane station. The outcomes of this research reveal the potential of this approach in projecting upcoming climate situations for urban catchment where long-term hourly rainfall data are not easily available.

A robust method to develop future rainfall IDF curves under climate change condition in two major basins of Iran

Current rainfall Intensity-Duration-Frequency (IDFs) curves generally were developed based on stationary extreme value assumption. However, climate change is expected to alter extreme rainfalls and invalidate the stationary assumption. So, it is crucial to develop future rainfall IDFs taking into account the impacts of climate change. Difficulty in preparing reliable rainfall time series with fine time step and capturing extremes for future climate scenarios has led to limited studies aimed at investigating the change of IDF curves due to climate change. In this paper, a robust stochastic rainfall model (NSRP) is employed to produce future rainfall IDFs for five stations across Karkheh and Karun basins in Iran. NSRP can generate long-term realistic rainfall series containing extremes. Moreover, it applies changes in different rainfall statistical characteristics, projected by GCMs, in the downscaling procedure. For each station, the model was calibrated using observed rainfalls series. Then, 3000-year daily rainfall series were generated, and historical IDFs were developed. Consequently, NSRP parameters were perturbed based on GCM projections. Then, 3000-year future rainfall series were generated, and future IDFs were developed. The climate change uncertainties were represented by employing two GCM (CanESM2 and HadGem2) and three emission scenarios (RCP2.6, RCP4.5, and RCP8.5). The results showed NSRP is able to reproduce observed extreme rainfalls in a wide range of time scales. Also, climate change will lead to a considerable increase in future extreme rainfall intensity in the study basins. As averages of all considered scenarios, rainfall intensities will increase between 22 and 206% in the future.

Development of Intensity Duration Frequency Curves for Wolkite Town

One of the major challenges faced by engineer and hydrologist is insufficient or non-availability of hydrological and meteorological data to appropriately design, operate and plan water resources against extreme rainfall event. Such data would be needed for the development of Rainfall _Intensity _Duration-Frequency (IDF) curves for design of culverts, ditches, storm drainage and different hydraulic structures in urban area systems. The main objectives of this paper is to compare and contrast the existed IDF Curve for the study area which is prepared by Ethiopian Road Authority and the one which is calculated and organized specifically for the town by this researchers, and to derive the IDF curve relationship of the rainfall data which is found in Wolkite metrological station of Ethiopia. This study analyzed the daily rainfall data collected from Ethiopian Meteorological Agency (EMA) Addis Ababa, for five (5) stations in the southern nation, nationalities and peoples of Ethiopia. But only one of the stations which founds in Wolkite towns has adequate daily rainfall recorded for about 33 years (1987-2019). The data was processed and analyzed using Microsoft Excel spread sheet to generate series of peak annual rainfall. The rainfall intensity values were calculated for different duration of (10-200) minutes to estimate returns period of (2, 5, 10, 20, 50, and 100 years) using Gumbel Distribution Methods and Log Pearsons III Distribution Methods. The R2 test was used to confirm the appropriateness of the fitted distributions for the locations the two distribution methods. The result shows that Gumbels distribution methods has larger R2 values and the best fit from the two distributions, and the two distribution methods deliver almost all similar results, however the Log Pearsons method has greater results than Gumbles distribution methods. The developed IDF curve delivers larger amount of intensity than that of IDF curve developed by ERA for similar time of duration in minutes. Finally IDF curves were developed for the towns and recommended for the design of storm drainage system.

An Efficient Statistical Approach to Develop Intensity-Duration-Frequency Curves for Precipitation and Runoff under Future Climate.

Ongoing and potential future changes in precipitation will affect water management infrastructure. Urban drainage systems are particularly vulnerable. Design standards for many stormwater practices rely on precipitation intensity-duration-frequency (IDF) curves based on extreme value analysis. General Circulation Models (GCMs) project increases in future average temperature but are less clear on changes in precipitation. In many areas, climate projections suggest relatively small changes in total precipitation volume, but also suggest increased magnitude of extreme events. Model skill in predicting extreme precipitation events, however, is limited. We develop an approach for estimating future IDF curves that is efficient, uses widely available statistically downscaled GCM output, and is consistent with published IDF curves for the United States that are often incorporated into local stormwater regulations and design guides (and are GCM model agnostic). The method provides a relatively simple way to develop scenarios in a format directly useful to assessing risk to stormwater management infrastructure. Model biases are addressed through equidistant quantile mapping, in which the modeled change in the cumulative distribution of storm events from historical to future conditions is used to adjust the extreme value fit used for IDF curve development. The approach is efficient because it requires only annual maxima and is readily automated, allowing rapid examination of results across projections. We estimate future IDF curves at locations throughout the United States and link IDF-derived design storms to a rainfall-runoff model to evaluate the potential change in storage volume requirements for capture-based stormwater management practices by 2065.

Estimation of Regional Sub-Daily Rainfall Ratios Using SKATER Algorithm and Logistic Regression

Developing Intensity-Duration-Frequency (IDF) curves is a paramount input in stormwater systems design. To construct these IDF curves, rainfall records at sub-daily durations, provided by continuous rainfall recorders, are required; however, these recorders are seldom available in many locations of interest. To fill this gap, available meteorological and topographical information for a study area in Saudi Arabia are investigated to get an estimate of the ratios of sub-daily rainfall depths to the 24-h depths (sub-daily ratios or SDRs), via applying the following methodology. A spatially constrained regionalization approach is implemented, using the SKATER algorithm, based on 60 gauging stations, to form regions of contiguous stations, based on the similarities of their SDRs. Four different regions are formed, where each region shows consistent SDRs; yet distinctly different from other regions. Subsequently, a multinomial logistic regression model is built and trained, with commonly available meteorological and topographical information as explanatory variables, to determine to which region a specific location belongs. The model is validated based on a hold-out validation method and assessed through confusion matrix statistics to evaluate the model performance. The model shows high performance in predicting the correct regional SDR and it is extended to produce a gridded map covering ungauged areas. Based on this procedure, one can develop the IDF curve for any location within the study area, even if there is no rainfall recorder in that location.

Global mapper 15.0 - uporedni programski alat za dizajn otvorenih kanalskih sistema za odvodnjavanje

This research aimed at computing peak flow discharge using state-of-theart technology for watershed analysis to design a suitable open channel to minimize the effects of flood hazard during and after rainfall in an environment. A comprehensive topographical survey data obtained by Shuttle Radar Topographic Mission was employed in this study. The result of the survey shows that both the maximum and minimum elevation at 61.9 m and 51.1 m, respectively, and the mean slope of the area was 0.012. Watershed analysis of the study area was carried out using the Global Mapper15.0. The result shows that the parameters obtained such as the mean area of the sub-catchments is 1.43 ha, the mean length of channel flow is 99.33 m, the mean length of overland flow is 111.81 m, mean upstream elevation for overland flow is 63.30 m, mean downstream elevation for overland flow is 62.37 m and mean downstream elevation for channel flow is 61.12 m. The intensity duration frequency curve of the catchment was developed and a return period of 25 years was used to obtain an average rainfall intensity of 218.81 mm/hr. The peak discharge was obtained as 2.01 m3 /s using rational formula due to the area of the watershed being less than 80 hectares. Finally, several design parameters for the modeled rectangular channel were calculated. The result indicated that the width of the channel is 0.80 m and the depth of the channel is 1.0 m. The developed modeled channel has a design capacity of 2.03 m3 /s which is greater than watershed peak discharge 2.01 m3 /s. The size of the modeled channel was compared with the size of the existing channel and the result revealed that the existing drain was insufficient to carry the discharge from the catchment area due to its design capacity of 0.91m3 /s. It is recommended that the dimension of the existing drain should be increased to meet with the dimension of the modeled drain and a discharge point (safe outlet) should be provided.

Developing Rainfall Intensity Duration Curve for Selected Towns in Western Part of Ethiopia

Rainfall and Its Intensity is needed for planning and designing of various water resource projects including infrastructure such as the design of urban drainage works, Storm Sewers, Culverts and etc. The main aim of this research was to develop Rainfall intensity duration curve for the selected towns in western part of Ethiopia. Gumbel and the Log Pearson Type III Probability distribution (LPT III) were used to develop rainfall intensity duration curves for the selected towns in western part of Ethiopia. The IDF curves developed by Gumbel’s Extreme value distribution shows, the pattern similarity for all return period, duration and all considered stations but the rainfall intensity shows an increasing with increase in the return period and decrease with rainfall duration increase in all return periods and also show high Rainfall intensity (mm/hr.) so that it was used to derive Empirical equation using Logarithmic transformation method to determine the constants (C, m, a) considered to derive the equation. Then the comparison was made between rainfall developed by using Gamble’s Probability distribution and computed by Empirical equation. In all return period and duration of time it shows good relation which approximately equal to unity (R2) but for 1000 return period differs which is still acceptable without any uncertainty for further application. So, the developed Rainfall intensity duration curves and derived empirical equations can be used for the planning and design of any Water Resources projects and infrastructure in the towns related to water resources.

Intensity-duration-frequency curves in the municipality of Belo Horizonte from the perspective of non-stationarity

ABSTRACT The study of changes in hydrological data series is of great scientific and practical importance for water resources systems, since these are normally projected based on the assumption that time series is statistically stationary. However, such assumption may not be verified when aspects as changes or climatic variability are considered. In this sense, the present study sought to identify trends in maximum rainfall intensities in Belo Horizonte (MG) and propose, in view of the observed results, a new intensity-duration-frequency (IDF) curve from the perspective of non-stationarity. For the trend analysis, statistical tests were applied, and an adaptation of the concept “Minimax Design Life Level” was proposed to quantify rainfall intensities and fit a non-stationary IDF curve. As a result, different trends were detected, with an increase in rainfall intensities for durations equal to or less than 1 hour starting in 2000. Regarding the IDF relationships, the obtained rain intensities were up to 48% higher than current estimates. Our results emphasize the need to periodically review IDF relationships in order to avoid under or overestimation in the design of hydraulic structures.

Development of a General Equation for Intensity-Duration-Frequency (IDF): Iraq

In the field of water resource management, rainfall intensity-duration-frequency (IDF) curves are of great importance, especially in the design of hydraulic structures and the assessment of flash-flood risks. The aim of this study is to obtain IDF curves and find empirical equations for rain duration for Al-Najaf city in the southwest of Iraq. Rainfall data for 30 years, from 1989 to 2018, were collected. The practical reduction equation of the Indian Meteorological Department (IMD), with six methods of probability distribution, was used for short intervals (0.25, 0.5, 1, 2, 3, 6, 12, and 24 hours) with a specified recurrence period (100, 50, 25, 10, 5, and 2 years). The Kolmogorov-Smirnov, chi-squared, and Anderson-Darling goodness of fit tests were used with the help of EasyFit 5.6 software. The findings revealed that the highest intensity of rainfall occurs during a repeated cycle of 100 years with a duration of 0.25 hours, while the lowest intensity of rainfall occurs during a repeated cycle of 2 years with a duration of 24 hours. In the results obtained from the six methods, as well as the superiority of the log Pearson type III method, the consistency of the fit tests showed some convergence.

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

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

Next-Generation Intensity-Duration-Frequency Curves for Climate-Resilient Infrastructure Design: Advances and Opportunities

National and international security communities (e.g., U.S. Department of Defense) have shown increasing attention for innovating critical infrastructure and installations due to recurring high-profile flooding events in recent years. The standard infrastructure design approach relies on local precipitation-based intensity-duration-frequency (PREC-IDF) curves that do not account for snow process and assume stationary climate, leading to high failure risk and increased maintenance costs. This paper reviews the recently developed next-generation IDF (NG-IDF) curves that explicitly account for the mechanisms of extreme water available for runoff including rainfall, snowmelt, and rain-on-snow under nonstationary climate. The NG-IDF curve is an enhancement to the PREC-IDF curve and provides a consistent design approach across rain- to snow-dominated regions, which can benefit engineers and planners responsible for designing climate-resilient facilities, federal emergency agencies responsible for the flood insurance program, and local jurisdictions responsible for developing design manuals and approving subsequent infrastructure designs. Further, we discuss the recent advances in climate and hydrologic science communities that have not been translated into actional information in the engineering community. To bridge the gap, we advocate that building climate-resilient infrastructure goes beyond the traditional local design scale where engineers rely on recipe-based methods only; the future hydrologic design is a multi-scale problem and requires closer collaboration between climate scientists, hydrologists, and civil engineers.

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

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

Estimating IDF Curves Consistently over Durations with Spatial Covariates

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.

IDF Curves and Maximum Rainfall in 24 hours in the Subregions of La Mojana and San Jorge in Northern Colombia

IDF Curves and Maximum Rainfall in 24 hours in the Subregions of La Mojana and San Jorge in Northern Colombia

Current and Future Intensity-Duration-Frequency Curves based on Weighted Ensemble GCMs and Temporal Dissagregation

Hydrological events are expected to increase in both magnitude and frequency in tropical areas due to climate variability. The Intensity – Duration – Frequency (IDF) curves are important means of evaluating the efficiency of irrigation and drainage systems. The necessity to update IDF curves arises from the need to gain better understanding of the impacts of climate change. This study explores an approach based on weighted Global Circulation Models (GCMs) and temporal disaggregation method to develop future IDFs under Representative Concentration Pathways (RCP) emission scenarios. The work consists of 20 ensemble GCMs, three RCPs (2.6, 4.5, and 8.5) and two projection periods (2050s and 2080s). The study compared three statistical distributions and selected Generalized Extreme Value (GEV) being the best fitting distribution with baseline rainfall series and therefore used for IDF projection. The result obtained shows that, the highest rainfall intensities of 19.32, 35.07 and 39.12 mm/hr occurred under 2-, 5-, and 20 years return periods, respectively. IDFs from the multi-model ensemble GCMs have shown increasing intensity in the future for all the return periods. This study indicated that the method could produce promising results which can be extended to other catchments.

Rainfall Intensity Analysis for Synoptic Stations in Northern Nigeria

With the large inter-annual variability of rainfall in Northern Nigeria, a zone subject to frequent dry spells which often result in severe and widespread droughts, the need for intense study of rainfall and accurate forecast of rainfall intensity duration frequency (IDF) curves cannot be over emphasized. The Intensity Duration Frequency relationship is a mathematical relationship between the rainfall intensity and rainfall duration for given return periods. Using a subset of the network of fifteen continuous auto recording rain gauges available in Northern Nigeria, a total of seven different time durations ranging from 12 minutes to 24 hours were developed for return periods of 2, 5, 10, 25, 50 and 100 years. The maximum data series so obtained was fitted to Gumbel’s Extreme Value Type 1 distribution. Linear Regression Analysis was then used to obtain the intensity-duration relationships for the various locations from which Intensity-Duration Frequency (IDF) curves were generated using Microsoft Excel for various return periods.
 Keywords: Extreme rainfall, intensity, duration, frequency, Northern Nigeria

Intensity-duration-frequency curve derivation from different rain gauge records

Development of Intensity-Duration-Frequency (IDF) Curves is important for the design of various hydraulic structures such as culverts, dams, and stormwater drainage systems. In this paper, rainfall analyses are conducted to evaluate the effect of using rainfall records from different rain gauge types on IDF Curves construction. Rainfall data are collected from two recording rain gauges at Namman catchment in western Saudi Arabia. Using the available 13 years rainfall data of the two gauges, annual maxima rainfall series values are extracted and used for IDF curves computations. The rainfall gauge which is equipped with a siphon produced IDF curves with higher precipitation intensities in comparison with the other gauge. This indicates that the siphon mechanism plays an important role in decreasing the under-catchment amount of the tipping bucket gauges during heavy rainfall storms. The current study shows that the under-catchment amount of tipping-bucket rain gauges can have a significant impact on the IDF curves and the characteristics of the design storm. A correction relationship to adjust rain intensity data sets of recording rain gauges that are not furnished with siphons is proposed in this paper. The adjusted rainfall intensity values are utilized to construct reliable IDF curves.