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.     

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.     

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.     

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.     

An analytical method of stage–fall–discharge rating

This paper presents an analytical method for establishing a stage–fall–discharge rating using hydraulic performance graphs (HPG). The rating curves derived from the HPG are used as the basis to establish the functional relation of stage, fall and discharge through regression analysis following the USGS procedure. In doing so, the conventional trial‐and‐error process can be avoided and the associated uncertainties involved may be reduced. For illustration, the proposed analytical method is applied to establish stage–fall–discharge relations for the Keelung River in northern Taiwan to examine its accuracy and applicability in an actual river. Based on the data extracted from the HPG for the Keelung River, one can establish a stage–fall–discharge relation that is more accurate than the one obtained by the conventionally used relation. Furthermore, the discharges obtained from the proposed rating method are verified through backwater analysis for measured high water level events. The results indicate that the analytical stage–fall–discharge rating method is capable of circumventing the shortcomings of those based on single‐station data and, consequently, enhancing the reliability of flood estimation and forecasting. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Extreme precipitation time trends in Ontario, 1960–2010

The impact of climate change on the behaviour of intensity–duration–frequency curves is critical to the estimation of design storms, and thus to the safe design of drainage infrastructure. The present study develops a regional time trend methodology that detects the impact of climate change on extreme precipitation from 1960 to 2010. The regional time trend linear regression method is fitted to different durations of annual maximum precipitation intensities derived from multiple sites in Ontario, Canada. The results show the relationship between climate change and increased extreme precipitation in this province. The regional trend analysis demonstrates, under nonstationary conditions arising from climate change, that the intensity of extreme precipitation increased decennially between 1.25% for the 30‐min storm and 1.82% for the 24‐h storm. A comparison of the results with a regional Mann–Kendall test validates the found regional time‐trend results. The results are employed to extrapolate the intensity–duration–frequency curves temporally and spatially for future decades across the province. The results of the regional time trend assessment help with the establishment of new safety margins for infrastructure design in Ontario. Copyright © 2016 John Wiley & Sons, Ltd.     

Analytical solution for frequency response of equipment in laterally loaded multistorey buildings

An analytical and closed-form frequency response of equipment mounted on multistorey buildings subjected to horizontal ground motion is proposed. In this study, the dynamics of the equipment and the building is expressed as a state-flow graph model, in which the interaction effect between the equipment and the building is considered. Based on the graph model, the analytical results for the frequency response of the acceleration of the equipment and the internal force in the support are derived. One of the advantages of this method is that the closed-form solutions of the frequency response expressed by polynomial form will be easily examined by analytical and numerical computations without complex operation. Moreover, the dynamic of the primary and secondary systems and their dynamic interaction are expressed separately in the derived formula. Thus most of the items in the formula need not be computed repeatedly for different supports of the equipment in design. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Wavefield interpolation in 3D large‐step Fourier wavefield extrapolation

Extrapolating wavefields and imaging at each depth during three‐dimensional recursive wave‐equation migration is a time‐consuming endeavor. For efficiency, most commercial techniques extrapolate wavefields through thick slabs followed by wavefield interpolation within each thick slab. In this article, we develop this strategy by associating more efficient interpolators with a Fourier‐transform‐related wavefield extrapolation method. First, we formulate a three‐dimensional first‐order separation‐of‐variables screen propagator for large‐step wavefield extrapolation, which allows for wide‐angle propagations in highly contrasting media. This propagator significantly improves the performance of the split‐step Fourier method in dealing with significant lateral heterogeneities at the cost of only one more fast Fourier transform in each thick slab. We then extend the two‐dimensional Kirchhoff and Born–Kirchhoff local wavefield interpolators to three‐dimensional cases for each slab. The three‐dimensional Kirchhoff interpolator is based on the traditional Kirchhoff formula and applies to moderate lateral velocity variations, whereas the three‐dimensional Born–Kirchhoff interpolator is derived from the Lippmann–Schwinger integral equation under the Born approximation and is adapted to highly laterally varying media. Numerical examples on the three‐dimensional salt model of the Society of Exploration Geophysicists/European Association of Geoscientists demonstrate that three‐dimensional first‐order separation‐of‐variables screen propagator Born–Kirchhoff depth migration using thick‐slab wavefield extrapolation plus thin‐slab interpolation tolerates a considerable depth‐step size of up to 72 ms, eventually resulting in an efficiency improvement of nearly 80% without obvious loss of imaging accuracy. Although the proposed three‐dimensional interpolators are presented with one‐way Fourier extrapolation methods, they can be extended for applications to general migration methods.     

Displacement–acceleration control via stiffness–damping collaboration

An approach is presented to stiffness–damping simultaneous optimization for displacement–acceleration simultaneous control. To make a shear building model stiffer, the sum of mean-square interstorey drifts to stationary random excitations is minimized or the mean-square top-floor absolute acceleration is maximized subject to the constraints on total storey stiffness capacity and total damper capacity. Optimality conditions are derived and a two-step optimization method using the optimality conditions is devised. In the first step, the optimal design is found for a specified set of total storey stiffness capacity and total damper capacity. In the second step, a series of optimal designs is found with respect to a varied set of total storey stiffness capacity and total damper capacity. While increase of total stiffness capacity and increase of total damper capacity are both effective in reduction of deformation, only increase of total damper capacity is effective in reduction of acceleration. Acceleration control is carried out in the second step via increase of total damper capacity. It is shown through numerical examples that the proposed method is efficient and reliable. Copyright © 1999 John Wiley & Sons, Ltd.     

Dynamic analysis of flexible rectangular fluid containers subjected to horizontal ground motion

In this paper, an analytical method is proposed to determine the dynamic response of 3‐D rectangular liquid storage tanks with four flexible walls, subjected to horizontal seismic ground motion. Fluid–structure interaction effects on the dynamic responses of partially filled fluid containers, incorporating wall flexibility, are accounted for in evaluating impulsive pressure. The velocity potential in which boundary conditions are satisfied is solved by the method of separation of variables using the principle of superposition. The impulsive pressure distribution is then computed. Solutions based on 3‐D modeling of the rectangular containers are obtained by applying the Rayleigh–Ritz method using the vibration modes of flexible plates with suitable boundary conditions. Trigonometrical functions that satisfy boundary conditions of the storage tank such that the flexibility of the wall is thoroughly considered are used to define the admissible vibration modes. The analysis is then performed in the time domain. Moreover, an analytical procedure is developed for deriving a simple formula that evaluates convective pressure and surface displacements in a similar rigid tank. The variation of dynamic response characteristics with respect to different tank parameters is investigated. A mechanical model, which takes into account the deformability of the tank wall, is developed. The parameters of such a model can be obtained from developed charts, and the maximum seismic loading can be predicted by means of a response spectrum characterizing the design earthquake. Accordingly, a simplified but sufficiently accurate design procedure is developed to improve code formulas for the seismic design of liquid storage tanks. Copyright © 2013 John Wiley & Sons, Ltd.     

Rigid–plastic approximation to predict plastic motion under strong earthquakes

The paper shows that the rigid–plastic oscillator can be used to evaluate the maximum plastic displacement of any elastic–plastic oscillator under any earthquake. Motivated by this result a rigid–plastic response spectrum is introduced, which provides an easy method to calculate the maximum plastic displacement of a rigid–plastic oscillator for any given earthquake. Such a spectrum is easier to construct than the elastic–plastic response spectrum or the classical elastic one. By means of appropriate formulas presented in the paper, the rigid–plastic response spectrum can be used to determine a realistic upper bound to the maximum plastic displacement of any elastic–plastic oscillator under the given earthquake. Copyright © 2001 John Wiley & Sons, Ltd.     

Catchment chemostasis revisited: Water quality responds differently to variations in weather and climate

Solute concentrations in streamflow typically vary systematically with stream discharge, and the resulting concentration–discharge relationships are important signatures of catchment biogeochemical processes. Solutes derived from mineral weathering often exhibit decreasing concentrations with increasing flows, suggesting dilution of a kinetically limited weathering flux by a variable flux of water. However, previous work showed that concentration–discharge relationships of weathering‐derived solutes in 59 headwater catchments were much weaker than this simple dilution model would predict. Instead, catchments behaved as chemostats, with rates of solute production and/or mobilization that were nearly proportional to water fluxes, on both event and interannual timescales. Here, we re‐examine these findings using data for a wider range of solutes from 2,186 catchments, ranging from ~10 to >1,000,000 km² in drainage area and spanning a wide range of lithologic and climatic settings. Concentration–discharge relationships among this much larger set of larger catchments are broadly consistent with the previously described chemostatic behaviour, at least on event and interannual timescales for weathering‐derived solutes. Among these same catchments, however, site‐to‐site variations in mean concentrations of weathering‐derived solutes exhibit strong negative correlations with long‐term average precipitation and discharge, reflecting strong climatic control on long‐term leaching of the critical zone. We use multiple regression of site characteristics including discharge to identify potential controls on long‐term mean concentrations and find that lithologic and land cover controls are significant predictors for many analytes. The picture that emerges is one in which, on event and interannual timescales, weathering‐derived stream solute concentrations are chemostatically buffered by groundwater storage and fast chemical reactions, but each catchment's chemostatic “set point” reflects site‐to‐site differences in climatically driven evolution of the critical zone. In contrast to these weathering products, some nutrients and particulates are often near‐chemostatic across all timescales, and their long‐term mean concentrations correlate more strongly with land use than climatic characteristics.     

Estimating evapotranspiration for a temperate salt marsh,Newcastle, Australia

Evapotranspiration was studied at a salt marsh site in the Hunter River estuary, NSW, Australia, during 1996–8. Estimates of actual evapotranspiration (E_a) were obtained for three sites using the eddy correlation method. These values were compared with results obtained with the Penman and Penman–Monteith equations, and with pan evaporation. The Penman–Monteith method was found to be most reliable in estimating daily and hourly evapotranspiration. Surface resistance values averaging 12 s m^?1 were derived from the eddy correlation estimates. Recent tidal flooding and rainfall were found to decrease surface resistance and increase E_a/E_p ratios. Estimates of evapotranspiration obtained using the Penman–Monteith method were shown to be sensitive to changes in surface resistance, canopy height and the method used to estimate net radiation from incoming solar radiation. These results underline the importance of accurately estimating such parameters based on site‐specific data rather than relying on empirical equations, which are derived primarily for crops and forests. Copyright © 2001 John Wiley & Sons, Ltd.     

Zircon fission‐track and U–Pb double dating using femtosecond laser ablation–inductively coupled plasma–mass spectrometry: A technical note

We present a new LA–ICP–MS system for zircon fission‐track (FT) and U–Pb double dating, whereby a femtosecond laser combined with galvanometric optics simultaneously ablates multiple spots to measure average surface U contents. The U contents of zircon measured by LA–ICP–MS and standardized with the NIST SRM610 glass are comparable to those measured by the induced FT method, and have smaller analytical errors. LA–ICP–MS FT dating of seven zircon samples including three IUGS age standards is as accurate as the external detector method, but can give a higher‐precision age depending on the counting statistics of the U content measurement. Double dating of the IUGS age standards gives FT and U–Pb ages that are in agreement. A chip of the Nancy 91500 zircon has a homogeneous U content of 84 ppm, suggesting the possibility of using this zircon as a matrix‐matched U‐standard for FT dating. When using the Nancy 91500 zircon as a U‐standard, a zeta calibration value of 42–43 year cm² for LA–ICP–MS FT dating is obtained. While this value is strictly valid only for the particular session, it can serve as a reference for other studies.     

Construction of Intensity–Duration–Frequency (IDF) curves for precipitation at Lubumbashi,Congo, under the hypothesis of inadequate data

Abstract

Intensity–Duration–Frequency (IDF) curves for precipitation constitute a probabilistic tool and have proven useful in water resources management. In particular, IDF curves for precipitation enable questions on the extreme character of precipitation to be answered. The construction of IDF curves for precipitation is difficult or impossible in tropical areas due to the lack of long-term extreme precipitation data. A technique is proposed to overcome this shortcoming by combining limited high-frequency information on rainfall extremes with long-term daily rainfall information. It may be regarded as an extension of Koutsoyiannis' approach. Using this technique, IDF curves for precipitation are produced for Lubumbashi in Congo.

Citation Van de Vyver, H. & Demarée, G. R. (2010) Construction of Intensity–Duration–Frequency (IDF) curves for precipitation at Lubumbashi, Congo, under the hypothesis of inadequate data. Hydrol. Sci. J. 55(4), 555–564.     

Ground motion directionality in the 2010–2011 Canterbury earthquakes

This paper examines the observed directionality of ground motions in the Christchurch urban area during the 2010–2011 Canterbury, New Zealand earthquakes. A dataset of ground motions recorded at 20 strong motion stations over 10 different earthquake events is utilized to examine the ratios of various response spectral directionality definitions and the orientation of the maximum direction. Because the majority of previous related studies have utilized overlapping ground motion datasets from the NGA database, the results of this study provide a largely independent assessment of these ground motion aspects. It is found that the directionality ratio between the maximum (100th percentile) and 50th percentile orientation‐independent spectral acceleration is similar to that obtained from recent studies. Ground motions from the 4 September 2010 Darfield earthquake are shown to exhibit strong directionality for source‐to‐site distances up to R_rup = 30 km, notably further than results from a previous study, which suggests that such effects are generally limited to R_rup < 5 km. The adopted dataset also offers the unique potential to consider site‐specific effects on directionality ratios and maximum direction orientations; however, in both cases, site‐specific effects are found not to be significant in the observed empirical results. Copyright © 2014 John Wiley & Sons, Ltd.