Annual Maximum Rainfall Intensity Research Articles

Artificial neural network-empowered projected future rainfall intensity-duration-frequency curves under changing climate

With the increasing trend of greenhouse gases in the atmosphere, by 2052 the temperature is expected to rise by 1.5 °C from the Pre-industrial Period, affecting future extreme rainfall events. This necessitates quantifying extreme hydrologic events to plan and design hydrologic and hydraulic structures using rainfall Intensity-Duration-Frequency (IDF) curves to adapt to future climate scenarios. This study developed future projected IDF curves for the Southeast United States using disaggregated sub-hourly (15-, 30-, and 45-min) monthly maximum rainfall from 2030 to 2059 using five climate models under the Representative Concentration Pathway 8.5 scenario. A computationally efficient feed-forward back-propagation Artificial Neural Network (ANN)-based approach was found to be significantly superior for disaggregating rainfall to a stochastic model with an average Nash–Sutcliffe efficiency (NSE) ranging from 0.67 to 0.84. The study found that there is an increasing rate of future projected annual maximum rainfall intensities in the range of 7% to 36% with reference to the historical period. The spatial variation in future projected extreme rainfall depths showed that the Gulf-Atlantic coast and the Appalachian Mountains are expected to receive more extreme rainfalls.

The intensification of short-duration rainfall extremes due to climate change – Need for a frequent update of intensity–duration–frequency curves

Numerous studies have investigated future changes in extreme precipitation by employing climate models. However, trends in extreme short-duration (20–180 min) rainfall intensities, that is, design storm rainfall intensities used for stormwater infrastructure design, have received considerably less attention despite their importance. This study quantified the effect of climate change on design storm intensity based on observations. Trends were investigated for diverse short-term rainfall durations, ranging from 20 to 180 min, at 11 meteorological stations in Northern Europe, Estonia. The Mann-Kendall test and Sen’s slope estimator were used to detect trends and calculate the trend magnitudes by analyzing a 70 year period of high-resolution temporal observed rainfall data. The Sen’s slope indicated a positive magnitude of slopes for all the durations and stations investigated, and two stations in Northeast Estonia showed significantly increasing trends (p < 0.05). Unsurprisingly, the spatial distribution of trends revealed notable variations from station to station, as extreme rainfall events are heavily localized due to cloudburst. Despite this variety, it can be generalized that the annual maximum rainfall intensities in Estonia have increased at an average rate of 4 % per decade due to changing climate conditions, invariant of the rainfall duration analyzed. The use of decades enables to easily keep the intensity–duration–frequency curves updated, and it is more practical and relatable for engineers as well. The findings of this study provide critical knowledge for urban water management decision-makers, indicating the need to frequently update urban design criteria to design climate resilient urban infrastructure.

Homogeneity Analysis of Turkish Rainfall Intensity Series

In this study, homogeneity checking the annual maximum rainfall intensity series for periods ranging from 30 to 78 years were obtained from 103 stations operated by the Turkish State Meteorological Service. Absolute homogeneity tests namely Standard Normal Homogeneity Test (SNHT), Buishand Range Test (BRT), Pettitt Test (PT), and Von Neumann Ratio Test (VNRT) were applied at a confidence level of 95%. Stations were classified inhomogeneous if at least one of the standard durations data classified suspect or doubtful. Assuming that the factor destabilizing the homogeneity is the trend, a detrended methodology (DFA) was performed. After the implementation of DFA, absolute homogeneity tests were reapplied to the series of rainfall intensity. As a result of this study 49 of 103 stations called useful all 14 standard durations. 45 of the remaining 54 stations classified useful all standard durations after trend components separated from rainfall intensity series. As a result of the analysis, it was determined that the remaining 8 of 103 stations had inhomogeneous values after the trend components were separated.

A temporal downscaling approach for sub-daily gridded extreme rainfall intensity estimation under climate change

Study regionCanada. Study focusIntensity-duration-frequency curves need to be updated to account for the potential effect of climate change. However, sub-daily regional climate model (RCM) simulations required for this purpose are commonly unavailable. The scaling approach is often applied for temporal downscaling of point daily precipitation; nevertheless, difference in spatial scale between simulations and observations may complicate its application at the grid scale. This study proposes a grid-scale temporal downscaling approach for estimating sub-daily gridded extreme rainfall intensity under climate change at regions with a relatively high station density. The approach uses daily annual maximum rainfall intensity series from RCM simulations and grid-scale scaling properties from observations. The study evaluates two methods for estimating gridded scaling exponents needed in temporal downscaling. The assessment is performed on observation-based and RCM-based temporally downscaled quantiles. The effect of temporal downscaling and bias correction on sub-daily quantiles and relative changes is also analysed. The approach is applied to three case studies across Canada. New hydrological insights for the regionPiecewise simple scaling is found over the study domains, indicating caution in using simple scaling. The performance of the approach in estimating sub-daily observation-based gridded rainfall intensity quantiles is suitable, with preference for point to grid transfer at the annual maximum series stage. Bias correction is necessary for properly estimating sub-daily RCM-based quantiles, presenting less impact on relative changes.

Comportamiento espacial y temporal de las intensidades máximas anuales subhorarias de precipitación para duraciones desde los 15 minutos a 24 horas en Chile Central

Maximum rainfall intensity is an interesting factor to analyze when determining whether temporal and spatial changes have occurred. Data gathered from 11 rain gauges were used to determine annual maximum rainfall intensities for the Maule Region (central Chile), for durations from 15-minute to 24-hour durations, between 1974 and 2009. Statistical tests of position and dispersion were applied to this dataset, along with the non-parametric Mann-Kendall test to identify tendencies. Results showed that the highest intensities occurred at gauging stations with greater orographic influence and in areas near bodies of water. Additionally, the statistical analysis revealed that maximum rainfall intensities did not seem to show spatial or temporal tendencies through time. Instead, results suggest that intensities have remained stable within historic ranges and have not manifested important changes.

Defining rainfall intensity clusters in Turkey by using the fuzzy c-means algorithm

Turkey has seven traditionally accepted climatic zones that are defined primarily by maritime and topographic influences. Across these zones, the annual amount of rainfall, including its intensity and its seasonal distribution, vary considerably. These variations, which impact on both urban and rural communities, including the occurrence of water shortages and flash flooding events, are increasing in both frequency and magnitude due to global warming and climate change. Several types of climate occur in Turkey where climate zones have been defined with various methodologies. To better understand rainfall intensity patterns across Turkey, this study used the Fuzzy C-Means (FCM) algorithm to define their spatial distribution. In the first stage, the annual maximum rainfall intensity records for periods ranging from 30 to 78 years were obtained from 95 stations operated by the Turkish State Meteorological Service, and the longitude, latitude and altitude data for the stations were compiled for cluster analysis. Secondly, all rainfall intensities and geographical values were normalized, and in the third stage, the FCM algorithm was applied. The comparison of annual maximum rainfall intensities revealed five clusters. Four clusters were identified as discrete zones and one was identified as a transitional zone. Weather stations located in different geographical regions sometimes fell into the same clusters. In other words, rainfall events of similar intensity can occur in different climatic zones. This study, which brought a different perspective to clustering studies, showed that rainfall intensity values can be successfully analyzed at a national scale with the FCM technique.

Rainfall Intensity-Duration-Frequency Relationship. Case Study: Depth-Duration Ratio in a Semi-Arid Zone in Mexico

Intensity–Duration–Frequency (IDF) curves describe the relationship between rainfall intensity, rainfall duration, and return period. They are commonly used in the design, planning and operation of hydrologic, hydraulic, and water resource systems. Considering the intense rainfall presence with flooding occurrences, limited data used to develop IDF curves, and importance to improve the IDF design for the Ensenada City in Baja California, this research study aims to investigate the use and combinations of pluviograph and daily records, to assess rain behavior around the city, and select a suitable method that provides the best results of IDF relationship, consequently updating the IDF relationship for the city for return periods of 10, 25, 50, and 100 years. The IDF relationship is determined through frequency analysis of rainfall observations. Also, annual maximum rainfall intensity for several duration and return periods has been analyzed according to the statistical distribution of Gumbel Extreme Value (GEV). Thus, Chen’s method was evaluated based on the depth-duration ratio (R) from the zone, and the development of the IDF relationship for the rain gauges stations was focused on estimating the most suitable (R) ratio; chosen from testing several methods and analyzing the rain in the region from California and Baja California. The determined values of the rain for one hour and return period of 2 years (P12) obtained were compared to the values of some cities in California and Baja California, with a range between 10 and 16.61 mm, and the values of the (R) ratio are in a range between 0.35 and 0.44; this range is close to the (R) ratio of 0.44 for one station in Tijuana, a city 100 km far from Ensenada. The values found here correspond to the rainfall characteristics of the zone; therefore, the method used in this study can be replicated to other semi-arid zones with the same rain characteristics. Finally, it is suggested that these results of the IDF relationship should be incorporated on the Norm of the State of Baja California as the recurrence update requires it upon recommendation. This study is the starting point to other studies that imply the calculation of a peak flow and evaluation of hydraulic structures as an input to help improve flood resilience in the city of Ensenada.

Update of intensity–duration–frequency curves for Kuwait due to extreme flash floods

Flash floods have devastating power due to their high rainfall intensities and short durations, causing serious damage to infrastructure and human life. Recent observations in the desert environment of Kuwait witnessed an increase in rainfall extremes, and the currently adopted intensity–duration–frequency (IDF) curves constructed three decades ago did not produce reliable design frequencies for existing stormwater drainage systems in residential areas. In this study, the IDF curves for the urban zone of the State of Kuwait were updated with recent records of annual maximum rainfall intensity from January 2006 to December 2017, and the Extreme Value type-I probability distribution was implemented to perform frequency analysis and estimate the design storm. The study concluded that frequent updating of IDF curves is necessary for the examined rainfall data to account for harmonic climatic variations in compliance with sunspot cycles. The updated IDF curves confirmed the pronounced increase in rainfall intensities within short durations of 5–15 min, thereby affecting water-related infrastructure in small urban catchments. Here we call for urgent action to be taken to adopt flood mitigation plans in residential areas to avoid the catastrophic impacts of extreme flash floods.

A Rainfall Intensity Data Rescue Initiative for Central Chile Utilizing a Pluviograph Strip Charts Reader (PSCR)

To develop intensity-duration-frequency (IDF) curves, it is necessary to calculate annual maximum rainfall intensities for different durations. Traditionally, these intensities have been calculated from the analysis of traces recorded by rain gauges on pluviograph strip charts (PSCs). For many years, these charts have been recorded and analyzed by the personnel who operate and maintain the pluviograph gauges, thus the reliability of the observational analysis depends exclusively on the professional experience of the person performing the analysis. Traditionally, the analyzed PSCs are physically stored in data repository centers. After storing rainfall data on aging paper for many years, the risk of losing rainfall records is very high. Therefore, the conversion of PSC records to digital format is crucial to preserve and improve the historical instrumental data base of these records. We conducted the first “Data Rescue Initiative” (DRI) for central Chile using a pluviograph strip charts reader (PSCR), a tool that uses a scanner-type device combined with digital image processing techniques to estimate maximum rainfall intensities for different durations for each paper band (&gt;80,000 paper bands). On the paper bands, common irregularities associated with excess ink, annotations, or blemishes can affect the scanning process; this system was designed with a semi-automatic module that allows users to edit the detected trace to improve the recognition of the data from each PSC. The PSCR’s semi-automatic characteristics were designed to read many PSCs in a short period of time. The tool also allows for the calculation of rainfall intensities in durations ranging between 15 min to 1 h. This capability improves the value of the data for water infrastructure design, since intense storms of shorter duration often have greater impacts than longer but less intense storms. In this study, the validation of the PSCR against records obtained from observational analysis showed no significant differences between maximum rainfall intensities for durations of 1 h, 6 h, and 24 h.

Modelling of Intensity-Duration Frequency curves for Upper Cauvery Karnataka through Normal Distribution

The IDF Curves accessible are for the most part done by fitting arrangement of yearly greatest precipitation force to parametric dispersions. Intensity-duration-frequency (IDF) curves represent the relationship between storm intensity, storm duration and return period. Environmental change is relied upon to intensify the boundaries in the atmosphere factors. Being prone to harsh climate impacts, it is very crucial to study extreme rainfall-induced flooding for short durations over regions that are rapidly growing. One way to approach the extremes is by the application of the Intensity-Duration-Frequency (IDF) curves. The annual maximum rainfall intensity (AMRI) characteristics are often used to construct these IDF curves that are being used in several infrastructure designs for urban areas. Thus, there is a necessity to obtain high temporal and spatial resolution rainfall information. Many urban areas of developing countries lack long records of short-duration rainfall. The shortest duration obtained is normally at a daily scale/24 h. Thus, it is very crucial to find a methodology to construct IDF curves for short-duration rainfall (sub-daily) for these urban areas. The fast extension of urban area that does not have adequate preparedness to cope with climate change is certainly a big risk to life and economy. The study region lies in Karnataka India. The sub-daily IDF curves for current and future climate for the region were constructed from 1 to 24 h based on the Normal Distribution approach. Rainfall data of 23 (Twenty three) hydrological years of all stations were used. Maximum rainfall frequency analysis was made by Normal Distribution method. Finally Equations were developed for different return periods.

Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes

The goal of quantile regression is to estimate conditional quantiles for specified values of quantile probability using linear or nonlinear regression equations. These estimates are prone to “quantile crossing”, where regression predictions for different quantile probabilities do not increase as probability increases. In the context of the environmental sciences, this could, for example, lead to estimates of the magnitude of a 10-year return period rainstorm that exceed the 20-year storm, or similar nonphysical results. This problem, as well as the potential for overfitting, is exacerbated for small to moderate sample sizes and for nonlinear quantile regression models. As a remedy, this study introduces a novel nonlinear quantile regression model, the monotone composite quantile regression neural network (MCQRNN), that (1) simultaneously estimates multiple non-crossing, nonlinear conditional quantile functions; (2) allows for optional monotonicity, positivity/non-negativity, and generalized additive model constraints; and (3) can be adapted to estimate standard least-squares regression and non-crossing expectile regression functions. First, the MCQRNN model is evaluated on synthetic data from multiple functions and error distributions using Monte Carlo simulations. MCQRNN outperforms the benchmark models, especially for non-normal error distributions. Next, the MCQRNN model is applied to real-world climate data by estimating rainfall Intensity–Duration–Frequency (IDF) curves at locations in Canada. IDF curves summarize the relationship between the intensity and occurrence frequency of extreme rainfall over storm durations ranging from minutes to a day. Because annual maximum rainfall intensity is a non-negative quantity that should increase monotonically as the occurrence frequency and storm duration decrease, monotonicity and non-negativity constraints are key constraints in IDF curve estimation. In comparison to standard QRNN models, the ability of the MCQRNN model to incorporate these constraints, in addition to non-crossing, leads to more robust and realistic estimates of extreme rainfall.

Potential of plotting positions for intensity-duration-frequency curves with short rainfall records

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.

Trends in extreme rainfall in the state of New South Wales, Australia

ABSTRACTThe trends in annual maximum rainfall (AMR) intensity data in New South Wales, Australia, were examined. Data from 60 stations were used covering three study periods, 1955–2010, 1965–2010 and 1978–2010. Mann-Kendall (MK) and Spearman’s rho (SR) tests were applied to assess trends at local stations. Pre-whitening (PW), trend-free pre-whitening (TFPW) and the variance correction (VC) tests were used to assess the effects of serial correlation on trend results. For regional trend analysis, the regional MK test was employed. The impacts of climatic variability modes on the observed trends in AMR intensity and seasonal maximum rainfall data were investigated. It was found that positive trends were more frequent than the negative ones. The PW, TFPW and VC tests resulted in a slight reduction in the count of stations exhibiting significant positive trends. The number of stations exhibiting significant trends decreased when the impact of climate variability modes was considered.

Multiscale Spatial and Temporal Statistical Properties of Rainfall in Central Arizona

Abstract The statistical properties of the rainfall regime in central Arizona are investigated using observations from the early 1980s of the Flood Control District of Maricopa County (FCDMC) network, currently consisting of 310 gauges ranging in elevation from 220 to 2325 m MSL. A set of techniques is applied to analyze the properties across a wide range of temporal scales (from 1 min to years) and the associated spatial variability. Rainfall accumulation is characterized by (i) high interannual variability, which is partially explained by teleconnections with El Niño–Southern Oscillation; (ii) marked seasonality, with two distinct maxima in summer (July–September) and winter (November–March); (iii) significant orographic control; and (iv) strong diurnal cycle in summer, peaking in early afternoon at higher elevations and at nighttime in lower desert areas. The annual maximum rainfall intensities occur in the summer months and increase with elevation, suggesting that higher terrain enhances the strength of thermal convective activity. The intergauge correlation of wintertime rainfall is high even at short aggregation times (&amp;lt;1 h) because of the widespread nature of the weather systems, while summer monsoonal thunderstorms are more localized in space and time. Spectral and scale invariance analyses show the presence of different scaling regimes in summer and winter, which are related to the typical meteorological phenomena of the corresponding time scales (frontal systems and isolated convective cells). Results of this work expand previous studies on the dominant meteorological features in the region and support the development of rainfall downscaling models from coarse products of climate, meteorological, or other statistical models.

Deriving short-duration rainfall IDF curves from a regional climate model

Climate change is expected to exacerbate the extremes in the climate variables. Being prone to harsh climate impacts, it is very crucial to study extreme rainfall-induced flooding for short durations over regions that are rapidly growing. One way to study the extremes is by the application of the Intensity-Duration-Frequency (IDF) curves. The annual maximum rainfall intensity (AMRI) characteristics are often used to construct these IDF curves that are being used in several infrastructure designs for urban areas. Thus, there is a need to obtain high temporal and spatial resolution rainfall information. Many urban areas of developing countries lack long records of short-duration rainfall. The shortest duration obtained is normally at a daily scale/24 h. Thus, it is very crucial to find a methodology to construct IDF curves for short-duration rainfall (sub-daily) for these urban areas. Vietnam is a developing country with rapidly increasing population as well as urbanization. The fast extension of urban area that does not have adequate preparedness to cope with climate change is certainly a big risk to life and economy. The limitation in studying impacts over many regions of Vietnam is the need for robust and sufficient data, both spatial and temporal. To overcome this limitation, this paper describes constructing IDF curves using 6 hourly rainfall AMRI output from a regional climate model (RCM) that downscaled a global climate model (GCM) output at high spatial and temporal resolutions. The study region is Hanoi, the capital city of Vietnam. The sub-daily IDF curves for current and future climate for Hanoi were constructed from 1 to 24 h based on the simple scaling approach. The findings indicate that it is likely that Hanoi might experience more flooding conditions in the future with the AMRI increasing between 34 and 48% for all return periods from 10 to 200 years. The methodology adopted in this paper is suitable for similar ungauged areas elsewhere and will provide useful information in devising adequate planning strategies for drainage designs.

Estimation of intensity-duration-frequency relationships according to the property of scale invariance and regionalization analysis in a Mediterranean coastal area

Usually, networks of daily rainfall raingauges have a higher spatial cover than tippet bucket raingauges networks. Consequently, it would be of high interest to make use of daily rainfall information to asses IDF curves for unobserved locations. The present work proposes achieving this goal by using the assumption of simple scaling invariance. Indeed, series observed over sufficiently long periods for 10 tippet bucket raingauge, allowed us to test the hypothesis of simple scaling of annual maximum rainfall intensities in northern Tunisia. This assumption, combined with Gumbel model of maximum rainfall intensities allowed us to develop a methodology to estimate IDF curves from the daily rainfall totals. In fact, a regionalization formula which involves the percentile 90% of the annual maximum daily rainfall was developed and validated. This regionalization formula applied to daily data of 25 rainfall stations in the sub area of Tunis region, combined with the assumption of simple scaling has enabled us to develop Intensity Duration Area Frequency (IDAF) curves for Tunis area.

Impact of Global Warming on Intensity-Duration-Frequency (IDF) Relationship of Precipitation: A Case Study of Toronto, Canada

Annual maximum rainfall intensity for several duration and return periods has been analyzed according to the Gumbel distribution. The Intensity-Duration-Frequency (IDF) curves before and after 1980 have been computed and compared. For the city of Toronto, it is shown that the rainfall intensities after 1980 are lower than those from before this date. This is especially clear for those of short duration. Comparing our results with those of other authors, it appears that, for the moment, no general law on the impact of global warming on the curves intensity duration frequency cannot be made. It appears that the impact of global warming on rainfall varies with geographic location and that it is not possible to draw some general conclusions across the planet.

Simple generalization approach for intensity-duration-frequency relationships

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

연최대치 계열과 연최대치 독립 호우사상 계열의 비교

본 연구에서는 강우 지속기간이 짧은 경우와 긴 경우에 대한 연최대치 계열과 연최대치 독립 호우사상 계열의 차이를 살펴보았다. 연최대치 독립호우사상은 1961년부터 2010년까지의 서울지점 시강우 자료에 다양한 IETD와 절단값을 적용하여 추출하였다. 결정된 연최대치 독립호우사상 계열은 기존의 연최대치 계열과 비교하였다. 그 결과를 요약하면 다음과 같다. 첫째, IETD와 절단값의 영향은 예상할 수 있는 수준을 벗어나지 않았다. 예를 들어, IETD의 증가에 따라 짧은 지속기간 및 긴 지속기간을 갖는 독립 호우사상의 발생 빈도는 유사한 감소비율을 갖으나, 절단값의 증가에 따라서는 특히 지속기간이 긴 호우사상의 발생빈도가 급격히 감소하는 것으로 나타났다. 둘째, 추출된 독립 호우사상의 평균 강우강도는 강우 지속기간에 관계없이 거의 일정한 것으로 나타났다. 이는 연 최대치 강우강도가 주로 지속기간이 긴 호우사상에서 결정될 가능성이 크다는 것을 의미한다. 마지막으로, 강우지속기간이 짧은 경우, 연 최대치 계열과 연 최대치 독립 호우사상 계열의 차이가 매우 큰 것으로 확인되었다. 그러나 이러한 차이는 강우 지속기간이 증가함에 따라 현저히 줄어들었다. 이러한 결과는 특히 매우 짧은 집중시간을 고려하는 작은 유역의 경우, 전통적인 자료 분석방법을 통해 결정된 설계강우가 실제 발생 가능성이 없는 비현실적인 경우가 될 가능성이 매우 큼을 의미한다. This study investigated the differences between annual maximum series and annual maximum independent rainfall event series with relatively short and long rainfall durations. Annual maximum independent rainfall events were selected by applying various IETDs and thresholds to the hourly rainfall data in Seoul for the duration from 1961 to 2010. Annual maximum independent rainfall event series decided were then compared with the conventional annual maximum series. Summarizing the results is as follows. First, the effect of IETD and threshold was not beyond the expected level. For example, as the IETD increases, the frequencies of independent rainfall events decreased similarly in their rate for both with short and long durations. However, as the threshold increases, the frequency of those with rather long durations decreased much higher. Second, The mean rainfall intensity of the independent rainfall events was found to remain constant regardless of their duration. This indicates that the annual maximum rainfall intensity could be found in a rainfall event with longer durations. Lastly, the difference between the annual maximum rainfall series and the annual maximum independent rainfall event series with rather short rainfall durations was found significantly large, which decreases with longer durations. This result indicates that the conventional data analysis method, especially for small basins with short concentration time, could lead an unrealistic design rainfall with little possibility of occurrence.

파괴확률과 다중파괴유형을 이용한 우수관의 안전성 분석

우수관의 성능이 한계상태(performance limit state)에 도달할 확률을 정량적으로 산정할 수 있는 FORM(First-Order Reliability Model)의 AFDA(Approximate Full Distribution Approach) 신뢰성 모형을 개발하였다. 우수관망에서 각각의 관으로 유입하는 유량이 그 관의 허용 가능 배출량을 초과하여 성능한계상태에 도달할 때 이를 파괴상태(failure state)라 정의하여 신뢰함수를 수립하였다. 우수관거로의 유입량은 합리식, 유출량은 Manning의 공식을 적용하였다. 또한 신뢰성 해석을 위한 관련 확률변수들에 대한 통계적 특성과 분포함수에 대한 해석이 수행되었다. 강우자료의 불확실성 해석에서 우리나라 여러 중소도시에 대한 연 최대강우강도의 확률분포가 Gumbel 극치분포함수와 일치함을 확인하였다. 개발된 신뢰성 모형을 Y자형 우수관망에 적용하여 성능한계상태가 발생할 확률, 즉 파괴확률(probability of failure)을 정량적으로 산정하였다. Manning의 공식을 이용하여 우수관의 직경 변화에 따른 파괴확률의 거동특성을 분석하였다. 특히 문경과 대전의 50년 재현기간을 갖는 설계 강우강도에 대한 우수관의 파괴확률을 산정한 결과에 의하면, 관의 직경이 특정수치 이하일 경우 파괴확률이 급격히 커지는 것을 확인할 수 있었다. 이는 실제 우수관의 유효직경이 설계직경에 가깝도록 항상 관내 불순물을 제거하는 것이 파괴확률을 줄이는 최선의 방법임을 의미하는 것이다. 또한 우수관 시스템의 경우 여러 개의 관이 모여 하나의 관으로 흘러 들어가는 경우가 많으며 이 경우 다중파괴유형(multiple failure mode)을 적용하여 시스템이 파괴상태에 도달할 확률을 정량적으로 산정하였다. 본 연구에서 개발된 신뢰성 모형은 우수관의 운용, 관리, 감독은 물론 설계에 활용이 가능 할 것이다. AFDA (Approximate Full Distribution Approach) model of FORM (First-Order Reliability Model) which can quantitatively calculate the probability that storm sewer reach to performance limit state was developed in this study. It was defined as a failure if amount of inflow exceed the capacity of storm sewer. Manning's equation and rational equation were used to determine the capacity and inflow of reliability function. Furthermore, statistical characteristics and distribution for the random variables were analyzed as a reliability analysis. It was found that the statistical distribution for annual maximum rainfall intensity of 10 cities in Korea is matched well with Gumbel distribution. Reliability model developed in this study was applied to Y shaped storm sewer system to calculate the probability that storm sewer may exceed the performance limit state. Probability of failure according to diameter was calculated using Manning's equation. Especially, probability of failure of storm sewer in Mungyeong and Daejeon was calculated using rainfall intensity of 50-year return period. It was found that probability of failure can be significantly increased if diameter is decreased below the original diameter. Therefore, cleaning the debris in sewer pipes to maintain the original pipe diameter should be one of the best ways to reduce the probability of failure of storm sewer. In sewer system, two sewer pipes can flow into one sewer pipe. For this case, probability of system failure was calculated using multiple failure mode. Reliability model developed in this study can be applied to design, maintenance, management, and control of storm sewer system.