1,721,008 research outputs found
Multifractal rainfall extremes: Theoretical analysis and practical estimation.
No full textWe study the extremes generated by a multifractal model of temporal rainfall and propose a practical method to estimate the Intensity–Duration–Frequency (IDF) curves. The model assumes that rainfall is a sequence of independent and identically distributed multiplicative cascades of the beta-lognormal type, with common duration D. When properly fitted to data, this simple model was found to produce accurate IDF results [Langousis A, Veneziano D. Intensity–duration–frequency curves from scaling representations of rainfall. Water Resour Res 2007;43. doi:10.1029/2006WR005245]. Previous studies also showed that the IDF values from multifractal representations of rainfall scale with duration d and return period T under either d! 0 or T!1, with different scaling exponents in the two cases. We determine the regions of the (d,T)-plane in which each asymptotic scaling behavior applies in good approximation, find expressions for the IDF values in the scaling and non-scaling regimes, and quantify the bias when estimating the asymptotic power-law tail of rainfall intensity from finite-duration records, as was often done in the past. Numerically calculated exact IDF curves are compared to several analytic approximations. The approximations are found to be accurate and are used to propose a practical IDF estimation procedure
Comparison of different approaches in evaluating extreme rainfall distributions from empirical records
No full textMultifractality and rainfall extremes: A review
No full textThe multifractal representation of rainfall and its use to predict rainfall extremes have advanced significantly in recent years. This paper summarizes this body of work and points at some open questions. The need for a coherent overview comes in part from the use of different terminology, notation, and analysis methods in the literature and in part from the fact that results are dispersed and not always readily available. Two important trends have marked the use of multifractals for rainfall and its extremes. One is the recent shift of focus from asymptotic scaling properties (mainly for the intensity-durationfrequency curves and the areal reduction factor) to the exact extreme distribution under
nonasymptotic conditions. This shift has made the results more relevant to hydrologic applications. The second trend is a more sparing use of multifractality in modeling, reflecting the limits of scale invariance in space-time rainfall. This trend has produced
models that are more consistent with observed rainfall characteristics, again making the results more suitable for application. Finally, we show that rainfall extremes can be
analyzed using rather rough models, provided the parameters are fitted to an appropriate range of large-deviation statistics
A critical analysis of the shortcomings in spatial frequency analysis of rainfall extremes based on homogeneous regions and a comparison with a hierarchical boundaryless approach
Full text linkWe investigate and discuss limitations of the approach based on homogeneous regions (hereafter referred to as regional approach) in describing the frequency distribution of annual rainfall maxima in space, and compare its performance with that of a boundaryless approach. The latter is based on geostatistical interpolation of the at-site estimates of all distribution parameters, using kriging for uncertain data. Both approaches are implemented using a generalized extreme value theoretical distribution model to describe the frequency of annual rainfall maxima at a daily resolution, obtained from a network of 256 raingauges in Sardinia (Italy) with more than 30 years of complete recordings, and approximate density of 1 gauge per 100 km2. We show that the regional approach exhibits limitations in describing local precipitation features, especially in areas characterized by complex terrain, where sharp changes to the shape and scale parameters of the fitted distribution models may occur. We also emphasize limitations and possible ambiguities arising when inferring the distribution of annual rainfall maxima at locations close to the interface of contiguous homogeneous regions. Through implementation of a leave-one-out cross-validation procedure, we evaluate and compare the performances of the regional and boundaryless approaches miming ungauged conditions, clearly showing the superiority of the boundaryless approach in describing local precipitation features, while avoiding abrupt changes of distribution parameters and associated precipitation estimates, induced by splitting the study area into contiguous homogeneous regions
A simple approximation to multifractal rainfall maxima using a generalized extreme value distribution model
No full textAmong different approaches that have been proposed to explain the scaling structure of temporal rainfall, a significant body belongs to models based on sequences of independent pulses with internal multifractal structure. Based on a standard asymptotic result from extreme value theory, annual rainfall maxima are typically modelled using a generalized extreme value (GEV) distribution. However, multifractal rainfall maxima converge slowly to a GEV shape, with important shape-parameter estimation issues, especially from short samples. The present work uses results from multifractal theory to propose a solution to the GEV shape-parameter estimation problem, based on an iterative numerical procedure
A nonparametric procedure to assess the accuracy of the normality assumption for annual rainfall totals, based on the marginal statistics of daily rainfall: an application to the NOAA/NCDC rainfall database
Full text linkWe develop a nonparametric procedure to assess the accuracy of the normality assumption for annual rainfall totals (ART), based on the marginal statistics of daily rainfall. The procedure is addressed to practitioners and hydrologists that operate in data-poor regions. To do so we use 1) goodness-of-fit metrics to conclude on the approximate convergence of the empirical distribution of annual rainfall totals to a normal shape and classify 3007 daily rainfall time series from the NOAA/NCDC Global Historical Climatology Network database, with at least 30 years of recordings, into Gaussian (G) and non-Gaussian (NG) groups; 2) logistic regression analysis to identify the statistics of daily rainfall that are most descriptive of the G/NG classification; and 3) a random-search algorithm to conclude on a set of constraints that allows classification of ART samples on the basis of the marginal statistics of daily rain rates. The analysis shows that the Anderson–Darling (AD) test statistic is the most conservative one in determining approximate Gaussianity of ART samples (followed by Cramer–Von Mises and Lilliefors’s version of Kolmogorov–Smirnov) and that daily rainfall time series with fraction of wet days fwd < 0.1 and daily skewness coefficient of positive rain rates skwd > 5.92 deviate significantly from the normal shape. In addition, we find that continental climate (type D) exhibits the highest fraction of Gaussian distributed ART samples (i.e., 74.45%; AD test at α = 5% significance level), followed by warm temperate (type C; 72.80%), equatorial (type A; 68.83%), polar (type E; 62.96%), and arid (type B; 60.29%) climates
Marginal methods of intensity-duration-frequency estimation in scaling and nonscaling rainfall
No full textPractical methods for the estimation of the intensity-duration-frequency (IDF) curves are usually based on the observed annual maxima of the rainfall intensity I(d) in intervals of different duration d. Using these historical annual maxima, one estimates the IDF curves under the condition that the rainfall intensity in an interval of duration d with return period T is the product of a function a(T) of T and a function b(d) of d (separability condition). Various parametric or semiparametric assumptions on a(T) and b(d) produce different specific methods. As alternatives we develop IDF estimation procedures based on the marginal distribution of I(d). If the marginal distribution scales in a multifractal way with d, this condition can be incorporated. We also consider hybrid methods that estimate the IDF curves using both marginal and annual maximum rainfall information. We find that the separability condition does not hold and that the marginal
and hybrid methods perform better than the annual maximum estimators in terms of accuracy and robustness relative to outlier rainfall events. This is especially true for long return periods and when the length of the available record is short. Marginal and hybrid methods produce accurate IDF estimates also when only a few years of continuous rainfall data are available
A parametric approach for simultaneous bias correction and high-resolution downscaling of climate model rainfall
Full text linkDistribution mapping has been identified as the most efficient approach to bias-correct climate model rainfall, while reproducing its statistics at spatial and temporal resolutions suitable to run hydrologic models. Yet its implementation based on empirical distributions derived from control samples (referred to as nonparametric distribution mapping) makes the method's performance sensitive to sample length variations, the presence of outliers, the spatial resolution of climate model results, and may lead to biases, especially in extreme rainfall estimation. To address these shortcomings, we propose a methodology for simultaneous bias correction and high-resolution downscaling of climate model rainfall products that uses: (a) a two-component theoretical distribution model (i.e., a generalized Pareto (GP) model for rainfall intensities above a specified threshold u*, and an exponential model for lower rainrates), and (b) proper interpolation of the corresponding distribution parameters on a user-defined high-resolution grid, using kriging for uncertain data. We assess the performance of the suggested parametric approach relative to the nonparametric one, using daily raingauge measurements from a dense network in the island of Sardinia (Italy), and rainfall data from four GCM/RCM model chains of the ENSEMBLES project. The obtained results shed light on the competitive advantages of the parametric approach, which is proved more accurate and considerably less sensitive to the characteristics of the calibration period, independent of the GCM/RCM combination used. This is especially the case for extreme rainfall estimation, where the GP assumption allows for more accurate and robust estimates, also beyond the range of the available data
Threshold detection for the generalized Pareto distribution: review of representative methods and application to the NOAA NCDC daily rainfall database
Full text linkIn extreme excess modeling, one fits a generalized Pareto (GP) distribution to rainfall excesses above a properly selected threshold u. The latter is generally determined using various approaches, such as nonparametric methods that are intended to locate the changing point between extreme and nonextreme regions of the data, graphical methods where one studies the dependence of GP-related metrics on the threshold level u, and Goodness-of-Fit (GoF) metrics that, for a certain level of significance, locate the lowest threshold u that a GP distribution model is applicable. Here we review representative methods for GP threshold detection, discuss fundamental differences in their theoretical bases, and apply them to 1714 overcentennial daily rainfall records from the NOAA-NCDC database. We find that nonparametric methods are generally not reliable, while methods that are based on GP asymptotic properties lead to unrealistically high threshold and shape parameter estimates. The latter is justified by theoretical arguments, and it is especially the case in rainfall applications, where the shape parameter of the GP distribution is low; i.e., on the order of 0.1-0.2. Better performance is demonstrated by graphical methods and GoF metrics that rely on preasymptotic properties of the GP distribution. For daily rainfall, we find that GP threshold estimates range between 2 and 12 mm/d with a mean value of 6.5 mm/d, while the existence of quantization in the empirical records, as well as variations in their size, constitute the two most important factors that may significantly affect the accuracy of the obtained results
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