Effect of zero measurements on the spatial correlation structure of rainfall

In this study, the effect of zero measurements on the spatial correlation function of rainfall is analyzed for the quantification of a rainfall field. The use of a bivariate mixed distribution function made it possible to analyze and compare the spatial correlation functions for these three different data sets: only the positive measurements at both gauge locations, positive measurements at either one or both gauge locations, and all measurements including zero at both locations. As an example, the spatial correlation functions are derived for the Geum River Basin, Korea and evaluated for the wet and dry seasons, respectively. Results show that the effect of zero measurements on spatial correlation structures is significant during the wet season, when the inter-station correlations were estimated significantly lower than those during the dry season. It was also found that only the case considering positive measurements are valid for the quantification of rainfall field. Even during the wet season, the inter-station correlation coefficients derived by considering the zero measurements show their high variability along with many abnormally looking high estimates, which made the quantification of the spatial correlation function become very ambiguous.     

Importance of no‐rain measurements on the comparison of radar and rain gauge rain rate

This study evaluated four possible cases of comparing radar and rain gauge rain rate for the detection of mean‐field bias. These four cases, or detection designs, consider in this study are: (1) design 1‐uses all the data sets available, including zero radar rain rate and zero rain gauge rain rate, (2) design 2—uses the data sets of positive radar rain rate and zero or positive rain gauge rain rate, (3) design 3—uses the data sets of zero or positive radar rain rate and positive rain gauge rain rate and (4) design 4—uses the data sets of positive radar rain rate and positive rain gauge rain rate. A theoretical review of these four detection designs showed that only the design 1 causes no design bias, but designs 2, 3 and 4 can cause positive, negative and negative design biases, respectively. This theoretical result was also verified by applying these four designs to the rain rate field generated by a multi‐dimensional rain rate model, as well as to that of the Mt Gwanak radar in Korea. The results from both applications showed that especially the design 4, which is generally used for the detection of mean‐field bias of radar rain rate, causes a serious design bias; therefore, is inappropriate as a design for detecting the mean‐field bias of radar rain rate. Copyright © 2009 John Wiley & Sons, Ltd.     

Applicability of Wakeby distribution in flood frequency analysis: a case study for eastern Australia

Parametric method of flood frequency analysis (FFA) involves fitting of a probability distribution to the observed flood data at the site of interest. When record length at a given site is relatively longer and flood data exhibits skewness, a distribution having more than three parameters is often used in FFA such as log‐Pearson type 3 distribution. This paper examines the suitability of a five‐parameter Wakeby distribution for the annual maximum flood data in eastern Australia. We adopt a Monte Carlo simulation technique to select an appropriate plotting position formula and to derive a probability plot correlation coefficient (PPCC) test statistic for Wakeby distribution. The Weibull plotting position formula has been found to be the most appropriate for the Wakeby distribution. Regression equations for the PPCC tests statistics associated with the Wakeby distribution for different levels of significance have been derived. Furthermore, a power study to estimate the rejection rate associated with the derived PPCC test statistics has been undertaken. Finally, an application using annual maximum flood series data from 91 catchments in eastern Australia has been presented. Results show that the developed regression equations can be used with a high degree of confidence to test whether the Wakeby distribution fits the annual maximum flood series data at a given station. The methodology developed in this paper can be adapted to other probability distributions and to other study areas. Copyright © 2014 John Wiley & Sons, Ltd.     

Identifying individual rain events from pluviograph records: a review with analysis of data from an Australian dryland site

Rainfall is routinely reported as falling in ‘events’ or ‘storms’ whose beginning and end are defined by rainless intervals of a nominated duration (minimum inter‐event time, MIT). Rain events commonly exhibit fluctuations in rain rate as well as periods when rain ceases altogether. Event characteristics such as depth, mean rain rate, and the surface runoff volume generated, are defined in relation to the length of the rain event. These derived properties are dependent upon the value of MIT adopted to define the event, and the literature reveals a wide range of MIT criteria. Surprisingly little attention has been paid to this dependency, which limits the inter‐comparison of results in published work. The diversity in criteria also diminishes the usefulness of historical data on event durations, rain rates, etc., in attempts to document changes in the rainfall climate. This paper reviews the range of approaches used in the recognition of rain events, and a 5 year pluviograph record from an arid location is analysed. Changing MIT from 15 min to 24 h (lying within the range of published criteria) alters the number of rain events from 550 to 118. The mean rain rate declines from 2·04 mm h^?1 to 0·94 mm h^?1, and the geometric mean event duration rises from 0·66 h to 3·98 h. This wide variation in the properties of rain events indicates that more attention needs to be paid to the selection and reporting of event criteria in studies that adopt event‐based data analysis. The selection of a MIT criterion is shown to involve a compromise between the independence of widely‐spaced events and their increasingly variable intra‐event characteristics. Copyright © 2008 John Wiley & Sons, Ltd.     

Impact of wind on the spatial distribution of rain over micro‐scale topography: numerical modelling and experimental verification

The wind‐driven‐rain effect refers to the redistribution of rainfall over micro‐scale topography due to the existence of local perturbed wind‐flow patterns. Rainfall measurements reported in the literature point to the fact that the wind‐driven‐rain distribution can show large variations over micro‐scale topography. These variations should be taken into account in hillslope hydrology, in runoff and erosion studies and in the design of rainfall monitoring networks. In practice, measurements are often not suitable for determining the wind‐driven‐rain distribution. Therefore, a few researchers have employed numerical modelling. In order to provide confidence in using numerical models, experimental verification for a range of different topographic features is imperative. The objective of this study is to investigate the adequacy of a two‐dimensional Computational Fluid Dynamics (CFD) model to predict the wind‐driven‐rain distribution over small‐scale topography. The numerical model is applied to a number of topographic features, including a succession of cliffs, a small isolated hill, a small valley and a field with ridges and furrows. The numerical results are compared with the corresponding measurement results reported in the literature. It is shown that two‐dimensional numerical modelling can provide a good indication of the wind‐driven‐rain distribution over each type of micro‐scale topography that is considered in this study. It is concluded that more detailed verification procedures are currently inhibited due to the lack of available and detailed spatial and temporal rainfall data from field measurements. Copyright © 2005 John Wiley & Sons, Ltd.     

Field experiments constraining the probability distribution of particle travel distances during natural rainstorms on different slope gradients

Rain splash erosion is an important soil transport mechanism on steep hillslopes. The rain splash process is highly stochastic; here we seek to constrain the probability distribution of splash transport distances on natural hillslopes as a function of hillslope gradient and total precipitation depth. Field experiments were conducted under natural precipitation events to observe splash travel on varying slope gradients. The downslope fraction of splash transport on 15°, 25° and 33° gradients were 85%, 96% and 96%, respectively. Maximum splash transport (L_max) was related to the rain splash detachment of soil particles and slope gradient. An empirical relationship of L_max to the precipitation depth and gradient was obtained; it is linearly proportional to hillslope gradient and logarithmically related to precipitation depth. Measured splash distances were calibrated to the fully two‐dimensional (2D) model of splash transport of Furbish et al. (Journal of Geophysical Research 112 : F01001, 2007) that is based on the assumption that radial splash distances are exponentially distributed; calibrated values of mean splash transport distances are an order of magnitude greater than those previously determined in a controlled laboratory setting. We also compared measured data with several one‐dimensional (1D) probability distributions to asses if splash transport distances could be better explained by a heavy‐tailed probability distribution rather than an exponential probability distribution. We find that for hillslopes of 15° and 25°, although a log‐normal probability distribution best describes the data, we find its likelihood is nearly indistinguishable from an exponential distribution based on computing maximum likelihood estimators for all 1D distributions (exponential, log‐normal and Weibull). At 33°, however, we find stronger evidence that measured travel distances are heavy‐tailed. Copyright © 2011 John Wiley & Sons, Ltd.     

Inter-station correlation and estimation errors of areal average rain rate

In this study an equation for estimating the error involved in the areal average rain rate considering the inter-station correlation was derived and applied for two cases: the first compared two storm events with different inter-station correlations, and the second evaluated the seasonal variation of estimation error of monthly rainfall. Similar cases, but without considering the rainfall seasonality, were also investigated for the comparison. This study was applied to the Geum River Basin with 28 rain gauge measurements, each having more than 30 years of rainfall data. A summary of the application results follows: (1) When considering the inter-station correlation, the estimation error involved in the areal average rain rate became significantly decreased proportional to the inter-station correlation. (2) The estimation error of monthly areal average rainfall showed strong seasonality with high ones during the wet season and lower ones during the dry season. (3) The estimation error was well proportional to the areal average rain rate as well as to its standard deviation. The ratio of estimation error to the areal average rain rate itself was estimated to be about 0.1 for the case of assuming no inter-station correlations, but decreased to 0.06 for the case of considering the inter-station correlations between measurements. (4) The relation between the standard deviation of areal average rain rate and the estimation error became much stronger than that between the areal average rain rate itself and the estimation error. The ratio of estimation error to the standard deviations of rain rate amount was estimated to be about 0.2 for the case of assuming no inter-station correlations, but decreased to 0.1 for the case of considering the inter-station correlations. This relation was found to be valid for any case of accumulation time such as in daily, monthly, or annual rainfall data.     

Numerical investigation of apparent multifractality of samples from processes subordinated to truncated fBm

We investigate numerically apparent multi‐fractal behavior of samples from synthetically generated processes subordinated to truncated fractional Brownian motion (tfBm) on finite domains. We are motivated by the recognition that many earth and environmental (including hydrological) variables appear to be self‐affine (monofractal) or multifractal with Gaussian or heavy‐tailed distributions. The literature considers self‐affine and multifractal types of scaling to be fundamentally different, the first arising from additive and the second from multiplicative random fields or processes. It has been demonstrated theoretically by one of us that square or absolute increments of samples from Gaussian/Lévy processes subordinated to tfBm exhibit apparent/spurious multifractality at intermediate ranges of separation lags, with breakdown in power‐law scaling at small and large lags as is commonly exhibited by real data. A preliminary numerical demonstration of apparent multifractality by the same author was limited to Gaussian fields having nearest neighbor autocorrelations and led to rather noisy results. Here, we adopt a new generation scheme that allows us to investigate apparent multifractal behaviors of samples taken from a broad range of processes including Gaussian with and without symmetric Lévy and log‐normal (as well as potentially other) subordinators. Our results shed new light on the nature of apparent multifractality, which has wide implications vis‐a‐vis the scaling of many hydrological as well as other earth and environmental variables. Copyright © 2011 John Wiley & Sons, Ltd.     

Probability prediction of peak break‐up water level through vine copulas

Prediction of the peak break‐up water level, which is the maximum instantaneous stage during ice break‐up, is desirable to allow effective ice flood mitigation, but traditional hydrologic flood routing techniques are not efficient in addressing the large uncertainties caused by numerous factors driving the peak break‐up water level. This research provides a probability prediction framework based on vine copulas. The predictor variables of the peak break‐up water level are first chosen, the pair copula structure is then constructed by using vine copulas, the conditional density distribution function is derived to perform a probability prediction, and the peak break‐up water level value can then be estimated from the conditional density distribution function given the conditional probability and fixed values of the predictor variables. This approach is exemplified using data from 1957 to 2005 for the Toudaoguai and Sanhuhekou stations, which are located in the Inner Mongolia Reach of the Yellow River, and the calibration and validation periods are divided at 1986. The mean curve of the peak break‐up water level estimated from the conditional distribution function can capture the tendency of the observed series at both the Toudaoguai and Sanhuhekou stations, and more than 90% of the observed values fall within the 90% prediction uncertainty bands, which are approximately twice the standard deviation of the observed series. The probability prediction results for the validation period are consistent with those for the calibration period when the nonstationarity of the marginal distributions for the Sanhuhekou station are considered. Compared with multiple linear regression results, the uncertainty bands from the conditional distribution function are much narrower; moreover, the conditional distribution function is more capable of addressing the nonstationarity of predictor variables, and the conclusions are confirmed by jackknife analysis. Scenario predictions for cases in which the peak break‐up water level is likely to be higher than the bankfull water level can also be conducted based on the conditional distribution function, with good performance for the two stations.     

Backward snow depth reconstruction at high spatial resolution based on time‐lapse photography

We report a methodology for reconstructing the daily snow depth distribution at high spatial resolution in a small Pyrenean catchment using time‐lapse photographs and snow depletion rates derived from an on‐site measuring meteorological station. The results were compared with the observed snow depth distribution, determined on a number of separate occasions using a terrestrial laser scanner (TLS). The time‐lapse photographs were projected onto a digital elevation model of the study site, and converted into snow presence/absence information. The melt‐out date (MOD; first occurrence of melt out after peak snow accumulation) was obtained from the projected photograph series. Commencing the backward reconstruction for each grid cell at the MOD, the method uses simulated snow depth depletion rates using a temperature index approach, which are extrapolated to the grid cells of the domain to arrive at the snow distribution of the previous day. Two variants of the reconstruction techniques were applied (1) using a spatially constant degree day factor (DDF) for calculating the daily expected snow depth depletion rate, and (2) allowing a spatially distributed DDF calculated from two consecutive TLS acquisitions compared to the snow depth depletion rate observed at the meteorological station. Validation revealed that both methods performed well (average R² = 0.68; standard RMSE = 0.58), with better results obtained from the spatially distributed approach. Nevertheless, the spatially corrected DDF reconstruction, which requires TLS data, suggests that the constant DDF approach is an efficient, and for most applications sufficiently accurate and easily reproducible method. The results highlight the usefulness of time‐lapse photography for not only determining the snow covered area, but also for estimating the spatial distribution of snow depth. Copyright © 2016 John Wiley & Sons, Ltd.     

Multifractal analysis as a tool for validating a rainfall model

A multifractal analysis was carried out in order to validate the simulation of hourly rainfall records of a local climate model for the Iberian Peninsula. Observed and simulated hourly rainfall data from four locations in Andalusia (southern Spain) were used to carry out the study. In order to detect the influence of the length of the data series on the results, two different sizes were used for the real data: 4 years, and 20 years. The results show that algebraic tails are required to fit the probability distribution of extreme rain event sizes, and rain and dry event durations for both kinds of rainfall data. Similar results are found for the extreme rain event sizes and dry event durations fits when the real and synthetic data are considered. Nevertheless, some differences appear in the cases of rain event durations. The detection of the presence of a first‐order multifractal phase transition associated with a critical moment in the empirical moment scaling exponent function and the results of the extreme rain event sizes fits, reveal that real rainfall is a self‐organized criticality (SOC) process. That behaviour is less evident in the simulated rainfall series. The same ‘synoptic maximum’ value was found for each place with both types of rainfall data. A time clustering analysis was carried out applying the count‐based periodogram and the Fano factor methods. Some periodicities have been detected in the periodograms, especially for the longest real rainfall data series. Copyright © 2007 John Wiley & Sons, Ltd.     

Predicting wetted width in any river at any discharge

Coefficients describing at‐a‐station power‐law relationships between discharge and width were calculated by applying multilevel models to field data collected during routine hydrological monitoring at 326 gauging stations across New Zealand. These hydraulic geometry coefficients were then estimated for each of these stations using standard stepwise multiple‐linear regression models. Analysis was carried out to quantify how the relationship between width and discharge changed in relation to several available explanatory variables. All coefficients describing the at‐a‐station hydraulic geometry were found to have statistically significant relationships with catchment area. Statistically significant relationships between each of the coefficients were also found with the addition of catchment climate as an explanatory variable. Further statistically significant relationships were found when station elevation and channel slope, as well as hydrological source of flow and landcover of the upstream catchment were added to the explanatory variables. The level of confidence that can be associated with estimates of width at ungauged sites, and sites with limited data availability, was then assessed by comparing model predictions with independent paired data on observed width and discharge from 197 sites. When compared against these independent data, model predictions of width were improved with the addition of predictor variables of the hydraulic geometry coefficients. The greatest improvements were made when climate was added to catchment area as predictor variables. Minor improvements were made when all available information was used to predict width at these independent sites. Although the analysis was purely empirical, results describing relationships between hydraulic geometry coefficients and catchment characteristics corresponded well with knowledge of the processes controlling at‐a‐station hydraulic geometry of river width. Copyright © 2010 John Wiley & Sons, Ltd.     

Rainfall network design using kriging and entropy

The spatial distribution of rainfall is related to meteorological and topographical factors. An understanding of the weather and topography is required to select the locations of the rain gauge stations in the catchment to obtain the optimum information. In theory, a well‐designed rainfall network can accurately represent and provide the needed information of rainfall in the catchment. However, the available rainfall data are rarely adequate in the mountainous area of Taiwan. In order to provide enough rainfall data to assure the success of water projects, the rainfall network based on the existing rain gauge stations has to be redesigned. A method composed of kriging and entropy that can determine the optimum number and spatial distribution of rain gauge stations in catchments is proposed. Kriging as an interpolator, which performs linear averaging to reconstruct the rainfall over the catchment on the basis of the observed rainfall, is used to compute the spatial variations of rainfall. Thus, the rainfall data at the locations of the candidate rain gauge stations can be reconstructed. The information entropy reveals the rainfall information of the each rain gauge station in the catchment. By calculating the joint entropy and the transmitted information, the candidate rain gauge stations are prioritized. In addition, the saturation of rainfall information can be used to add or remove the rain gauge stations. Thus, the optimum spatial distribution and the minimum number of rain gauge stations in the network can be determined. The catchment of the Shimen Reservoir in Taiwan is used to illustrate the method. The result shows that only seven rain gauge stations are needed to provide the necessary information. Copyright © 2007 John Wiley & Sons, Ltd.     

Some relationships between lithology,basin form and hydrology: a case study from the Thames basin,UK

The role of lithology in influencing basin form and function is explored empirically by investigating correlations between a range of catchment variables, where the spatial unit of analysis is not surface catchments but lithologically coherent groundwater units. Using the Thames basin, UK, as a case study, nine groundwater units have been identified. Values for 11 hydrological and geomorphological variables, including rainfall, drainage density, Baseflow Index, aquifer porosity, storage coefficient and log‐hydraulic conductivity, aquifer and drainage elevation, river incision, and hypsometric integral have been estimated for each of the groundwater units in the basin, and Pearson correlation coefficients calculated for all pairs of variables. Seven of the correlation coefficients are found to be significant at a confidence level of > 99%. Negative correlations between drainage density and log aquifer hydraulic conductivity, and between drainage density and river incision, and positive correlations between log‐hydraulic conductivity and river incision, log‐hydraulic conductivity and Baseflow Index, and between Baseflow Index and river incision are inferred to have consistent causal explanations. For example, incision of rivers into aquifers leads to relative increases in hydraulic gradients in the vicinity of rivers which, in turn, promotes the development of secondary porosity increasing both aquifer hydraulic conductivity and, hence, Baseflow Index. The implication of this interpretation is that the geomorphological evolution of basins is intimately linked to the evolution of hydraulic conductivity of the underlying aquifers. This is consistent with, and supports the notion of a coupled complexly evolving surface water‐groundwater system. Copyright © 2011 John Wiley & Sons, Ltd.     

Improved Recharge Estimation from Portable,Low‐Cost Weather Stations

Groundwater recharge estimation is a critical quantity for sustainable groundwater management. The feasibility and robustness of recharge estimation was evaluated using physical‐based modeling procedures, and data from a low‐cost weather station with remote sensor techniques in Southern Abbotsford, British Columbia, Canada. Recharge was determined using the Richards‐based vadose zone hydrological model, HYDRUS‐1D. The required meteorological data were recorded with a HOBO^TM weather station for a short observation period (about 1 year) and an existing weather station (Abbotsford A) for long‐term study purpose (27 years). Undisturbed soil cores were taken at two locations in the vicinity of the HOBO^TM weather station. The derived soil hydraulic parameters were used to characterize the soil in the numerical model. Model performance was evaluated using observed soil moisture and soil temperature data obtained from subsurface remote sensors. A rigorous sensitivity analysis was used to test the robustness of the model. Recharge during the short observation period was estimated at 863 and 816 mm. The mean annual recharge was estimated at 848 and 859 mm/year based on a time series of 27 years. The relative ratio of annual recharge‐precipitation varied from 43% to 69%. From a monthly recharge perspective, the majority (80%) of recharge due to precipitation occurred during the hydrologic winter period. The comparison of the recharge estimates with other studies indicates a good agreement. Furthermore, this method is able to predict transient recharge estimates, and can provide a reasonable tool for estimates on nutrient leaching that is often controlled by strong precipitation events and rapid infiltration of water and nitrate into the soil.     

Solar-cycle variation of the daily foF2 and M(3000)F2

Daily values of the ionospheric characteristics foF2 and M(3000)F2 for a given hour and month are correlated with the corresponding daily values of sunspot number using measured data collected at seven European locations. The significance of applying different-order polynomials is considered and the times are confirmed when the higher-order terms are important. Mean correlation coefficients for combined data sets over all hours, months and stations are determined, together with the standard errors of estimates. Comparisons are made with corresponding figures for monthly median values derived from the same data sets.     

Spatial variability and interdependence of rain event characteristics in the Czech Republic

Rain event characteristics are assessed in a 10‐year (1991–2000) record for 122 stations in the Czech Republic. Individual rain events are identified using the minimum interevent time (mit) concept. For each station, the optimal mit value is estimated by examining the distribution of interevent times. In addition, various mit values are considered to account for the effect of mit on rain event characteristics and their interrelationships. The interdependence between rain event characteristics and altitude, average rainfall depth, and geographic location are explored using simple linear models. Most rain event characteristics can be to some extent explained by average total rainfall or altitude, although models including the former significantly outperformed models using the latter. Significant correlation was found among several pairs of monthly mean characteristics often including event rain rate (with event duration, depth, maximum intensity, and fraction of intraevent rainless periods). Moreover, strong correlation was revealed between number of events, interevent time, event depth, and duration. In general, correlation decreases in absolute value with mit. Strong spatial correlation was found for the mean monthly interevent time and number of events. Spatial correlation was considerably smaller for other characteristics. In general, spatial dependence was smaller for larger mit values. Copyright © 2013 John Wiley & Sons, Ltd.     

Grain‐size distribution patterns of a point bar system in the Usri River,India

Grain‐size distribution patterns in a point bar system of the Usri River, India, were critically analysed in the light of log‐normal, log‐hyperbolic and log‐skew‐Laplace distribution models. Sand samples were collected from the cross‐bedding foreset of different sizes of bedform; the objectives were to (i) study whether bedform heights have any role in grain‐size distribution patterns, (ii) offer a best‐fit statistical model, (iii) study the downstream variation of size‐sorting in a point bar system, and (iv) study the mechanism of grain sorting. The results indicate that the bedform heights have no role in grain‐size distribution patterns. Quantitatively when the errors in three distribution models were analysed, it was observed that the log‐normal distribution is the best‐fit statistical model and the next one is the log‐skew‐Laplace. However, in the upper reaches of the river, log‐normal distribution is the best‐fit model in the case of large bedforms, whereas in the lower reaches the log‐normal model is the best‐fit one in the case of small bed forms. It is also observed that within a point bar, for large and small bedforms, there is a tendency for mean grain size to decrease downstream. Between point bars for large bedforms there is no consistency in decreasing grain size downstream, whereas for small bed forms the decrease of grain size downstream is observed except near the confluence at Palkia. With distance of transport, the coarser and finer fractions of sediments are gradually chopped off. The coarser fractions are buried below the advancing bedforms on the lee sides and the finer ones are transported further downstream. Thus the finer admixture giving rise to the fining‐upward sequence overlies a carpet of coarser materials. This mechanism provides a clue to the process of grain sorting in the fluvial environment. An interpretation has been offered for the log‐normality of the grain‐size distribution pattern. During prolonged transportation in a fluvial environment, the larger grain‐size fractions are gradually chopped off and buried below the advancing bedforms on their lee sides. On the other hand, the finer fractions are transported further downstream in suspension. Thus the narrow, intermediate size fraction takes active part in the distribution patterns leading to the generation of unimodality and a symmetric distribution pattern downstream, which are the main criteria for log‐normality. Similarly, increase of bedform size is the effect of increase of stream power and Froude number leading to the selective segregation of bed materials. Thus the intermediate size fractions take a more active part than the coarser and the finer size fractions in developing log‐normality. Besides the hydrodynamic parameters of the Usri, coarsening of grain size downstream has been attributed to (i) the aggrading nature of the Usri downstream, and (ii) the contribution of coarser materials to the Usri by its tributaries and bank erosion. Copyright © 2006 John Wiley & Sons, Ltd.     

Simulation of probability distributions commonly used in hydrological frequency analysis

Random variable simulation has been applied to many applications in hydrological modelling, flood risk analysis, environmental impact assessment, etc. However, computer codes for simulation of distributions commonly used in hydrological frequency analysis are not available in most software libraries. This paper presents a frequency‐factor‐based method for random number generation of five distributions (normal, log–normal, extreme‐value type I, Pearson type III and log‐Pearson type III) commonly used in hydrological frequency analysis. The proposed method is shown to produce random numbers of desired distributions through three means of validation: (1) graphical comparison of cumulative distribution functions (CDFs) and empirical CDFs derived from generated data; (2) properties of estimated parameters; (3) type I error of goodness‐of‐fit test. An advantage of the method is that it does not require CDF inversion, and frequency factors of the five commonly used distributions involves only the standard normal deviate. Copyright © 2006 John Wiley & Sons, Ltd.     

Identification of yield drift deformations and evaluation of the degree of damage through the direct sensing of drift displacements

Inter‐story drift displacement data can provide useful information for story damage assessment. The authors' research group has developed photonic‐based sensors for the direct measurement of inter‐story drift displacements. This paper proposes a scheme for evaluating the degree of damage in a building structure based on drift displacement sensing. The scheme requires only measured inter‐story drift displacements without any additional finite element analysis. A method for estimating yield drift deformation is proposed, and then, the degree of beam end damage is evaluated based on the plastic deformation ratios derived with the yield drift deformation values estimated by the proposed method. The validity and effectiveness of the presented scheme are demonstrated via experimental data from a large‐scale shaking table test of a one‐third‐scale model of an 18‐story steel building structure conducted at E‐Defense. Copyright © 2016 John Wiley & Sons, Ltd.