A simplified storm index method to extrapolate intensity–duration–frequency (IDF) curves for ungauged stations in central Chile

Most of meteorological stations in Chile register rainfall amounts once every 24 h. The creation of intensity–duration–frequency (IDF) curves requires continuous recorded data, and this insufficiency of proper instrumentation has resulted in a lack of IDF curves nationwide. The objective of this study is to further develop and evaluate the feasibility of a new method to estimate IDF curves in ungauged stations under Mediterranean climates of central Chile. A technique used to address this problem is the use of a storm index (S_I), also known as the ‘K’ method, which allows the construction of IDF curves from stations with discontinuous data, by extrapolating data from stations with continuous records, as long as daily rainfall intensities for both stations differ by less than 2 mm h^?1. To test the applicability of this method, S_I values were calculated for 40 meteorological stations located throughout Central Chile (latitudes 30°S to 40°S). The extrapolated IDF curves were then compared with observed data, and the goodness of fit was determined. The results indicate that the storm index method can adequately estimate hourly IDF curve values for stations lacking of continuous rainfall data. Copyright © 2014 John Wiley & Sons, Ltd.     

POTENTIAL OF EXTENDING THE RAINFALL INTENSITY–DURATION–FREQUENCY RELATIONSHIP TO NON-RECORDING RAIN GAUGES

Maximum rainfall intensity–duration–frequency (IDF) curves are commonly applied to determine the design rainfall in water resource projects. Normally, the IDF relationship is derived from recording rain gauges. As the network of non-recording rain gauges (daily rainfall) in Taiwan has a higher density than recording rain gauges, attempts were made in this study to extend the IDF relationship to non-recording rain gauges. Eighteen recording rain gauges and 99 non-recording rain gauges over the Chi-Nan area in Southern Taiwan provide the data sets. The regional IDF formulae were generated for ungauged areas to estimate rainfall intensity for various return periods and rainfall durations larger than or equal to one hour. For rainfall durations less than one hour, a set of adjustment formulae were applied to modify the regional IDF formulae. The method proposed in this study had reasonable application to non-recording rain gauges, which was concluded from the verification of four additional recording rain gauges. © 1997 John Wiley & Sons, Ltd.     

Incorporating uncertainty analysis into a regional IDF formula

A rainfall intensity–duration–frequency (IDF) relationship was generated by pooling annual maximum rainfall series from 14 recording rain gauges in southern Taiwan. Dimensionless frequency curves, plotted by the growth curve method, can be well fitted by regression equations for a duration ranging from 10 mins to 24 hours. As the parameters in regression equations have a good statistical relationship with average annual rainfall, a generalized regional IDF formula was then formulated. The formula, based on average annual rainfall as an index, can be easily applied to non-recording rain gauges. This paper further applies the mean value first-order second moment (MFOSM) method to estimate the uncertainty of the proposed regional IDF formula. From a stochastic viewpoint, the generalized regional IDF formula can accurately simulate the IDF relationship developed using frequency analysis (EV1) at individual stations. The method can provide both rainfall intensity and variance isohyetal maps for various rainfall durations and return periods over the study area. © 1998 John Wiley & Sons, Ltd.     

Regionalization of heavy rainfall to improve climatic design values for infrastructure: case study in Southern Ontario,Canada

Abstract

Southern Ontario, Canada, has been impacted in recent years by many heavy rainfall and flooding events that have exceeded existing historical estimates of infrastructure design rainfall intensity–duration–frequency (IDF) values. These recent events and the limited number of short-duration recording raingauges have prompted the need to research the climatology of heavy rainfall events within the study area, review the existing design IDF methodologies, and evaluate alternative approaches to traditional point-based heavy rainfall IDF curves, such as regional IDF design values. The use of additional data and the regional frequency analysis methodology were explored for the study area, with the objective of validating identified clusters or homogeneous regions of extreme rainfall amounts through Ward's method. As the results illustrate, nine homogeneous regions were identified in Southern Ontario using the annual maximum series (AMS) for daily and 24-h rainfall data from climate and rate-of-rainfall or tipping bucket raingauge (TBRG) stations, respectively. In most cases, the generalized extreme value and logistic distributions were identified as the statistical distributions that provide the best fit for the 24-h and sub-daily rainfall data in the study area. A connection was observed between extreme rainfall variability, temporal scale of heavy rainfall events and location of each homogeneous region. Moreover, the analysis indicated that scaling factors cannot be used reliably to estimate sub-daily and sub-hourly values from 24- and 1-h data in Southern Ontario.

Citation Paixao, E., Auld, H., Mirza, M.M.Q., Klaassen, J. & Shephard, M.W. (2011) Regionalization of heavy rainfall to improve climatic design values for infrastructure: case study in Southern Ontario, Canada. Hydrol. Sci. J. 56(7), 1067–1089.     

Estimation of rainfall intensity–duration–frequency curves at ungauged locations using quantile regression methods

Intensity–duration–frequency (IDF) curves of extreme rainfall are used extensively in infrastructure design and water resources management. In this study, a novel regional framework based on quantile regression (QR) is used to estimate rainfall IDF curves at ungauged locations. Unlike standard regional approaches, such as index-storm and at-site ordinary least-squares regression, which are dependent on parametric distributional assumptions, the non-parametric QR approach directly estimates rainfall quantiles as a function of physiographic characteristics. Linear and nonlinear methods are evaluated for both the regional delineation and IDF curve estimation steps. Specifically, delineation by canonical correlation analysis (CCA) and nonlinear CCA (NLCCA) is combined, in turn, with linear QR and nonlinear QR estimation in a regional modelling framework. An exhaustive comparative study is conducted between standard regional methods and the proposed QR framework at sites across Canada. Overall, the fully nonlinear QR framework, which uses NLCCA for delineation and nonlinear QR for estimation of IDF curves at ungauged sites, leads to the best results.     

How to construct future IDF curves,under changing climate,for sites with scarce rainfall records?

Optimal designs of stormwater systems rely very much on the rainfall Intensity–Duration–Frequency (IDF) curves. As climate has shown significant changes in rainfall characteristics in many regions, the adequacy of the existing IDF curves is called for particularly when the rainfall are much more intense. For data sparse sites/regions, developing IDF curves for the future climate is even challenging. The current practice for such regions is, for example, to ‘borrow’ or ‘interpolate’ data from regions of climatologically similar characteristics. A novel (3‐step) Downscaling‐Comparison‐Derivation (DCD) approach was presented in the earlier study to derive IDF curves for present climate using the extracted Dynamically Downscaled data an ungauged site, Darmaga Station in Java Island, Indonesia and the approach works extremely well. In this study, a well validated (3‐step) DCD approach was applied to develop present‐day IDF curves at stations with short or no rainfall record. This paper presents a new approach in which data are extracted from a high spatial resolution Regional Climate Model (RCM; 30 × 30 km over the study domain) driven by Reanalysis data. A site in Java, Indonesia, is selected to demonstrate the application of this approach. Extremes from projected rainfall (6‐hourly results; ERA40 Reanalysis) are first used to derive IDF curves for three sites (meteorological stations) where IDF curves exist; biases observed resulting from these sites are captured and serve as very useful information in the derivation of present‐day IDF curves for sites with short or no rainfall record. The final product of the present‐day climate‐derived IDF curves fall within a specific range, +38% to +45%. This range allows designers to decide on a value within the lower and upper bounds, normally subjected to engineering, economic, social and environmental concerns. Deriving future IDF curves for Stations with existing IDF curves and ungauged sites with simulation data from RCM driven by global climate model (GCM ECHAM5) (6‐hourly results; A2 emission scenario) have also been presented. The proposed approach can be extended to other emission scenarios so that a bandwidth of uncertainties can be assessed to create appropriate and effective adaptation strategies/measures to address climate change and its impacts. Copyright © 2013 John Wiley & Sons, Ltd.     

Synthetic regional flow duration curve for southern Taiwan

The primary purpose of this study is to develop the regional flow duration curves for southern Taiwan. To define homogeneous regions for developing regional flow duration curves, multivariate statistical analysis (principal component and cluster analysis) was applied to daily flow data from 34 stream-gauged stations in southern Taiwan. Two kinds of clustering variables, the dimensionless flow duration curve and specific flow duration curve, were compared in this study. It was found that three homogeneous regions delineated by specific flow duration curves as clustering variables have more reasonable results. The three homogeneous regions not only have well-defined geographical boundaries, but also correspond to the rainfall and geology characteristics of the regions. It seems that the technique of cluster analysis can reasonably define the homogeneous regions. In each homogeneous region, the synthetic regional flow duration curves were developed by a family of parametric duration curves. This approach has the advantage of being simple and needing only the basin area as an index. The performance of the regional flow duration curve was verified by the comparison of areas under the actual and synthetic flow duration curves; the latter were generated from the regional flow duration curve. Almost all the 34 stream-gauged stations had less than 25% absolute error.     

Design rainfall estimation in Australia: a case study using L moments and Generalized Least Squares Regression

Design rainfall is an important input to rainfall runoff models and is used for many other water resources planning and design applications. The estimation of design rainfall is generally done by applying a regional frequency analysis technique that uses data from a large number of rainfall stations in the region. This paper presents a regional rainfall frequency analysis technique that uses an L moments based index method coupled with Generalized Least Squares Regression (GLSR). The particular advantages of the GLSR method are that it accounts for the differences in record lengths across various sites in the region and inter-station correlation in deriving regional prediction equations. The proposed method has been applied to a data set consisting of 203 rainfall stations across Australia. It has been found that the proposed method can be applied successfully in deriving reasonably accurate design rainfall estimates from 1 to 72 h durations. It has also been found that the proposed method provides quite consistent estimates where a third order polynomial is adequate in smoothing the intensity–frequency–duration (IFD) curves. The method can readily be extended to a larger data set of Australia and other countries to derive generalized IFD data.     

Estimates of changes in design rainfall values for Canada

Annual maximum rainfall data from 51 stations in Canada were analyzed for trends and changes by using the Mann–Kendall trend test and a bootstrap resampling approach, respectively. Rainfall data were analyzed for nine durations ranging from 5 min to 24 h. The data analyzed are typically used in the development of intensity‐duration‐frequency (IDF) curves, which are used for estimating design rainfall values that form an input for the design of critical water infrastructure. The results reveal more increasing than decreasing trends and changes in the data with more increasing changes and larger changes, noted for the longer rainfall durations. The results also indicate that a traditional trend test may not be sufficient when the interest is in identifying changes in design rainfall quantiles. Copyright © 2012 John Wiley & Sons, Ltd.     

Selecting the best IDF model by using the multifractal approach

In this work, the multifractal properties of hourly rainfall data recorded at a location in Southern Spain have been related to the scale properties of the corresponding intensity–duration–frequency (IDF) curves. Four parametric models for the IDF curves have been fitted to the quantiles of rainfall obtained using the generalized Pareto frequency distribution function with the extreme data series obtained for the same place. The scaling of the rainfall intensity moments has been analysed, and the empirical moments scaling exponent function has been obtained. The corresponding values of q₁ and γ₁ have been empirical and theoretically calculated and compared with some characteristics of the different IDF models. Thus, the scaling behaviour of IDF curves has been analysed, and the best model has been selected. Copyright © 2012 John Wiley & Sons, Ltd.     

A multiscaling‐based intensity–duration–frequency model for extreme precipitation

Rainfall intensity–duration–frequency (IDF) curves are a standard tool in urban water resources engineering and management. They express how return levels of extreme rainfall intensity vary with duration. The simple scaling property of extreme rainfall intensity, with respect to duration, determines the form of IDF relationships. It is supposed that the annual maximum intensity follows the generalized extreme value (GEV) distribution. As well known, for simple scaling processes, the location parameter and scale parameter of the GEV distribution obey a power law with the same exponent. Although, the simple scaling hypothesis is commonly used as a suitable working assumption, the multiscaling approach provides a more general framework. We present a new IDF relationship that has been formulated on the basis of the multiscaling property. It turns out that the GEV parameters (location and scale) have a different scaling exponent. Next, we apply a Bayesian framework to estimate the multiscaling GEV model and to choose the most appropriate model. It is shown that the model performance increases when using the multiscaling approach. The new model for IDF curves reproduces the data very well and has a reasonable degree of complexity without overfitting on the data.     

Pooled frequency analysis for intensity–duration–frequency curve estimation

Rainfall intensity–duration–frequency (IDF) curves are used in the design of urban infrastructure. Their estimation is based on rainfall frequency analysis, usually performed on rainfall records from a single gauged station. However, available at‐site record length is often too short to provide accurate estimates for long return periods. In the present study, a general framework for pooled rainfall frequency analysis based on the index‐event model is proposed for IDF estimation at gauged stations. Pooling group formation is defined by the region of influence approach on the basis of the geographical distance similarity measure. Several pooled approaches are defined and evaluated by a procedure through which quantile estimation and uncertainty are assessed. Alternate approaches for the definition of a pooling group are based on different criteria regarding initial pooling group size (and the relationship between size and return period), approaches for assessing pooling group homogeneity, and the use of macroregions in pooling group formation. The proposed framework is applied to identify the preferred approach for pooled rainfall intensity frequency analysis in Canada. Pooled approaches are found to provide more precise estimates than the at‐site approach, especially for long return periods. Pooled parent distribution selection supported the use of the generalized extreme value distribution across the country. Recommendations for pooling group formation include increasing the pooling group size with increases in return period and identifying an appropriate trade‐off between pooling group homogeneity and size for long return periods.     

Derivation of rainfall IDF relations by third-order polynomial normal transform

Establishing the rainfall intensity–duration–frequency (IDF) relations by the conventional method, the use of parametric distribution models has the advantage of automatic compliance of monotonicity condition of rainfall intensity and frequency. However, fitting rainfall data to a distribution separately by individual duration may possibly produce undulation and crossover of IDF curves which does not comply physical reality. This frequently occurs when rainfall record length is relatively short which often is the case. To tackle this problem this study presents a methodological framework that integrates the third-order polynomial normal transform (TPNT) with the least squares (LS) method to establish rainfall IDF relations by simultaneously considering multi-duration rainfall data. The constraints to preserve the monotonicity and non-crossover in the IDF relations can be incorporated easily in the LS-based TPNT framework. Hourly rainfall data at Zhongli rain gauge station in Taiwan with 27-year record are used to establish rainfall IDF relations and to illustrate the proposed methodology. Numerical investigation indicates that the undulation and crossover behavior of IDF curves can be effectively circumvented by the proposed approach to establish reasonable IDF relations.     

Deriving a practical form of IDF formula using transformed rainfall intensities

A general form of formula is presented for the rainfall Intensity–Duration–Frequency (IDF) relationship. This formula is derived from the nearly normal probability distribution function of transformed intensities. In order to transform the raw intensities, a correcting non‐constant spread technique, the Kruskal–Wallis statistic, and the Box–Cox transformation are adopted. These transformations enable to express a simpler model for the IDF formula that agrees well with traditional IDF relationships. Since the proposed method allows the estimation of any percentile value of intensities with a single equation, the intensity percentile at arbitrary duration can be generated easily. The validity of the formula derived by means of the proposed method is assessed using data from major weather stations in Korea. The results show that the percentile intensities produced using the proposed method are in good agreement with those of traditional frequency analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Risk assessment of extreme air pollution based on partial duration series: IDF approach

The occurrences of extreme pollution events have serious effects on human health, environmental ecosystems, and the national economy. To gain a better understanding of this issue, risk assessments on the behavior of these events must be effectively designed to anticipate the likelihood of their occurrence. In this study, we propose using the intensity–duration–frequency (IDF) technique to describe the relationship of pollution intensity (i) to its duration (d) and return period (T). As a case study, we used data from the city of Klang, Malaysia. The construction of IDF curves involves a process of determining a partial duration series of an extreme pollution event. Based on PDS data, a generalized Pareto distribution (GPD) is used to represent its probabilistic behaviors. The estimated return period and IDF curves for pollution intensities corresponding to various return periods are determined based on the fitted GPD model. The results reveal that pollution intensities in Klang tend to increase with increases in the length of time between return periods. Although the IDF curves show different magnitudes for different return periods, all the curves show similar increasing trends. In fact, longer return periods are associated with higher estimates of pollution intensity. Based on the study results, we can conclude that the IDF approach provides a good basis for decision-makers to evaluate the expected risk of future extreme pollution events.     

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.     

Constrained scaling approach for design rainfall estimation

Rainfall depth (or intensity) of the same frequency should follow a non-decreasing relationship with rainfall duration. However, due to the use of finite samples and sampling error, rainfall frequency analysis could yield rainfall intensity (depth)–frequency (IDF, DDF) curves of different durations that might intersect among them. Results of this kind violate physical reality and it is more likely to occur when rainfall record length gets shorter. To ensure the compliance of the physical reality, this paper applied the scale-invariant approach, in conjunction with constrained regression analysis, to circumvent intersections in rainfall IDF or DDF curves. Rainfall data of various durations at rain gauge in Hong Kong are used to demonstrate the procedure. Numerical investigation indicates that the proposed procedure yields more reasonable results than those based on the conventional frequency analysis, especially when only a small sample of data are available.     

Bayesian estimation of intensity–duration–frequency curves and of the return period associated to a given rainfall event

Intensity–duration–frequency (IDF) curves are used extensively in engineering to assess the return periods of rainfall events and often steer decisions in urban water structures such as sewers, pipes and retention basins. In the province of Québec, precipitation time series are often short, leading to a considerable uncertainty on the parameters of the probabilistic distributions describing rainfall intensity. In this paper, we apply Bayesian analysis to the estimation of IDF curves. The results show the extent of uncertainties in IDF curves and the ensuing risk of their misinterpretation. This uncertainty is even more problematic when IDF curves are used to estimate the return period of a given event. Indeed, standard methods provide overly large return period estimates, leading to a false sense of security. Comparison of the Bayesian and classical approaches is made using different prior assumptions for the return period and different estimation methods. A new prior distribution is also proposed based on subjective appraisal by witnesses of the extreme character of the event.     

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.     

重庆市地震预警网络IP地址规划设计解析

重庆预警项目包含有数百个预警监测站,其所获取的观测资料将会越来越丰富,计算测定震中和震级会更加准确,预警成效会显著提升。数百个台站在预警系统中传输数据将巨大地消耗核心路由器的数据传输能力,为提高网络设备路由协议算法效率和网络数据传输性能,规划科学合理的IP地址是一个十分重要的技术环节。本文较详细地阐述了重庆地震预警项目IP地址规划设计的一些基本原则和思路方法,在实践中颇有收效,可为其他网络项目规划设计提供一定的参考。