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Item type:Publication, Access status: without files , Revisiting long-range dependence in annual precipitation(Elsevier, 2018); ; ; Long-range dependence (LRD), the so-called Hurst–Kolmogorov behaviour, is considered to be an intrinsic characteristic of most natural processes. This behaviour manifests itself by the prevalence of slowly decaying autocorrelation function and questions the Markov assumption, often habitually employed in time series analysis. Herein, we investigate the dependence structure of annual rainfall using a large set, comprising more than a thousand stations worldwide of length 100 years or more, as well as a smaller number of paleoclimatic reconstructions covering the last 12,000 years. Our findings suggest weak long-term persistence for instrumental data (average H = 0.59), which becomes stronger with scale, i.e. in the paleoclimatic reconstructions (average H = 0.75).Publicationtype: Journal Article7 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfallGenerating fine-scale time series of intermittent rainfall that are fully consistent with any given coarse-scale totals is a key and open issue in many hydrological problems. We propose a stationary disaggregation method that simulates rainfall time series with given dependence structure, wet/dry probability, and marginal distribution at a target finer (lower-level) time scale, preserving full consistency with variables at a parent coarser (higher-level) time scale. We account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths. This approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean, variance, and autocorrelation function (ACF) for a mixed-type stochastic process in terms of mean, variance, and ACFs of both continuous and discrete components, respectively. To achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse-scale totals, the generated lower-level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model. To assess model performance, we study rainfall process as intermittent with both independent and dependent occurrences, where dependence is quantified by the probability that two consecutive time intervals are dry. In either case, we provide analytical formulations of main statistics of our mixed-type disaggregation model and show their clear accordance with Monte Carlo simulations. An application to rainfall time series from real world is shown as a proof of concept.Publicationtype: Journal Article4 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A global survey on the seasonal variation of the marginal distribution of daily precipitationTo characterize the seasonal variation of the marginal distribution of daily precipitation, it is important to find which statistical characteristics of daily precipitation actually vary the most from month-to-month and which could be regarded to be invariant. Relevant to the latter issue is the question whether there is a single model capable to describe effectively the nonzero daily precipitation for every month worldwide. To study these questions we introduce and apply a novel test for seasonal variation (SV-Test) and explore the performance of two flexible distributions in a massive analysis of approximately 170,000 monthly daily precipitation records at more than 14,000 stations from all over the globe. The analysis indicates that: (a) the shape characteristics of the marginal distribution of daily precipitation, generally, vary over the months, (b) commonly used distributions such as the Exponential, Gamma, Weibull, Lognormal, and the Pareto, are incapable to describe "universally" the daily precipitation, (c) exponential-tail distributions like the Exponential, mixed Exponentials or the Gamma can severely underestimate the magnitude of extreme events and thus may be a wrong choice, and (d) the Burr type XII and the Generalized Gamma distributions are two good models, with the latter performing exceptionally well.Publicationtype: Journal Article4 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A quick gap filling of missing hydrometeorological dataData gaps are ubiquitous in hydrometeorological time series, and filling these values still remains a challenge. Since data sets without missing values may be a prerequisite in performing many analyses, a quick and efficient gap-filling methodology is required. In this study the problem of filling sporadic, single-value gaps using time-adjacent observations from the same location is investigated. The applicability of a local average (i.e., based on few neighboring in time observations) is examined and its advantages over the sample average (i.e., using the whole data set) are illustrated. The analysis reveals that a quick and very efficient (i.e., minimum mean-squared estimation error) gap filling is achieved by combining a strictly local average (i.e., using one observation before and one after the missing value) with the sample mean.Publicationtype: Journal Article2 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Just two moments! A cautionary note against use of high-order moments in multifractal models in hydrologyThe need of understanding and modelling the space-time variability of natural processes in hydrological sciences produced a large body of literature over the last thirty years. In this context, a multifractal framework provides parsimonious models which can be applied to a widescale range of hydrological processes, and are based on the empirical detection of some patterns in observational data, i.e. a scale invariant mechanism repeating scale after scale. Hence, multifractal analyses heavily rely on available data series and their statistical processing. In such analyses, high order moments are often estimated and used in model identification and fitting as if they were reliable. This paper warns practitioners against the blind use in geophysical time series analyses of classical statistics, which is based upon independent samples typically following distributions of exponential type. Indeed, the study of natural processes reveals scaling behaviours in state (departure from exponential distribution tails) and in time (departure from independence), thus implying dramatic increase of bias and uncertainty in statistical estimation. Surprisingly, all these differences are commonly unaccounted for in most multifractal analyses of hydrological processes, which may result in inappropriate modelling, wrong inferences and false claims about the properties of the processes studied. Using theoretical reasoning and Monte Carlo simulations, we find that the reliability of multifractal methods that use high order moments (> 3) is questionable. In particular, we suggest that, because of estimation problems, the use of moments of order higher than two should be avoided, either in justifying or fitting models. Nonetheless, in most problems the first two moments provide enough information for the most important characteristics of the distribution.Publicationtype: Journal Article4 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Battle of extreme value distributions : a global survey on extreme daily rainfallTheoretically, if the distribution of daily rainfall is known or justifiably assumed, then one could argue, based on extreme value theory, that the distribution of the annual maxima of daily rainfall would resemble one of the three limiting types : (a) type I, known as Gumbel; (b) type II, known as Frechet; and (c) type III, known as reversed Weibull. Yet, the parent distribution usually is not known and often only records of annual maxima are available. Thus, the question that naturally arises is which one of the three types better describes the annual maxima of daily rainfall. The question is of great importance as the naive adoption of a particular type may lead to serious underestimation or overestimation of the return period assigned to specific rainfall amounts. To answer this question, we analyze the annual maximum daily rainfall of 15,137 records from all over the world, with lengths varying from 40 to 163 years. We fit the generalized extreme value (GEV) distribution, which comprises the three limiting types as special cases for specific values of its shape parameter, and analyze the fitting results focusing on the behavior of the shape parameter. The analysis reveals that (a) the record length strongly affects the estimate of the GEV shape parameter and long records are needed for reliable estimates ; (b) when the effect of the record length is corrected, the shape parameter varies in a narrow range ; (c) the geographical location of the globe may affect the value of the shape parameter; and (d) the winner of this battle is the Frechet law.Publicationtype: Review Article10 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , How extreme is extreme? An assessment of daily rainfall distribution tailsThe upper part of a probability distribution, usually known as the tail, governs both the magnitude and the frequency of extreme events. The tail behaviour of all probability distributions may be, loosely speaking, categorized into two families: heavy-tailed and light-tailed distributions, with the latter generating "milder" and less frequent extremes compared to the former. This emphasizes how important for hydrological design it is to assess the tail behaviour correctly. Traditionally, the wet-day daily rainfall has been described by light-tailed distributions like the Gamma distribution, although heavier-tailed distributions have also been proposed and used, e.g., the Lognormal, the Pareto, the Kappa, and other distributions. Here we investigate the distribution tails for daily rainfall by comparing the upper part of empirical distributions of thousands of records with four common theoretical tails: those of the Pareto, Lognormal, Weibull and Gamma distributions. Specifically, we use 15 029 daily rainfall records from around the world with record lengths from 50 to 172 yr. The analysis shows that heavier-tailed distributions are in better agreement with the observed rainfall extremes than the more often used lighter tailed distributions. This result has clear implications on extreme event modelling and engineering design.Publicationtype: Journal Article7 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Entropy based derivation of probability distributions: a case study to daily rainfallThe principle of maximum entropy, along with empirical considerations, can provide consistent basis for constructing a consistent probability distribution model for highly varying geophysical processes. Here we examine the potential of using this principle with the Boltzmann-Gibbs-Shannon entropy definition in the probabilistic modeling of rainfall in different areas worldwide. We define and theoretically justify specific simple and general entropy maximization constraints which lead to two flexible distributions, i.e., the three-parameter Generalized Gamma (GG) and the four-parameter Generalized Beta of the second kind (GB2), with the former being a particular limiting case of the latter. We test the theoretical results in 11,519 daily rainfall records across the globe. The GB2 distribution seems to be able to describe all empirical records while two of its specific three-parameter cases, the GG and the Burr Type XII distributions perform very well by describing the 97.6% and 87.7% of the empirical records, respectively.Publicationtype: Journal Article3 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Can a simple stochastic model generate rich patterns of rainfall events?Several of the existing rainfall models involve diverse assumptions, a variety of uncertain parameters, complicated mechanistic structures, use of different model schemes for different time scales, and possibly classifications of rainfall patterns into different types. However, the parsimony of a model is recognized as an important desideratum as it improves its comprehensiveness, its applicability and possibly its predictive capacity. To investigate the question if a single and simple stochastic model can generate a plethora of temporal rainfall patterns, as well as to detect the major characteristics of such a model (if it exists), a data set with very fine timescale rainfall is used. This is the well-known data set of the University of Iowa comprising measurements of seven storm events at a temporal resolution of 5-10. s. Even though only seven such events have been observed, their diversity can help investigate these issues. An evident characteristic resulting from the stochastic analysis of the events is the scaling behaviors both in state and in time. Utilizing these behaviors, a stochastic model is constructed which can represent all rainfall events and all rich patterns, thus suggesting a positive reply to the above question. In addition, it seems that the most important characteristics of such a model are a power-type distribution tail and an asymptotic power-type autocorrelation function. Both power-type distribution tails and autocorrelation functions can be viewed as properties enhancing randomness and uncertainty, or entropy.Publicationtype: Journal Article1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A probabilistic approach to the concept of Probable Maximum PrecipitationThe concept of Probable Maximum Precipitation (PMP) is based on the assumptions that (a) there exists an upper physical limit of the precipitation depth over a given area at a particular geographical location at a certain time of year, and (b) that this limit can be estimated based on deterministic considerations. The most representative and widespread estimation method of PMP is the so-called moisture maximization method. This method maximizes observed storms assuming that the atmospheric moisture would hypothetically rise up to a high value that is regarded as an upper limit and is estimated from historical records of dew points. In this paper, it is argued that fundamental aspects of the method may be flawed or inconsistent. Furthermore, historical time series of dew points and "constructed" time series of maximized precipitation depths (according to the moisture maximization method) are analyzed. The analyses do not provide any evidence of an upper bound either in atmospheric moisture or maximized precipitation depth. Therefore, it is argued that a probabilistic approach is more consistent to the natural behaviour and provides better grounds for estimating extreme precipitation values for design purposes.Publicationtype: Journal Article7