In the present study, a method based on the conditional density of vine copulas was used to drought monitoring and predicting the rainfall deficiency signature for a 60‐day duration in Dashband, ...sub‐basin of Lake Urmia basin. The annual rainfall and rainfall deficiency signatures at 10‐, 30‐ and 60‐day durations were considered as variables. D‐, C‐ and R‐vine copulas were used to represent the dependence among the variables, finding that D‐vine copula results to be more accurate for the case of interest. We found that, if the rainfall is less than the long‐term mean in the region, the rainfall deficiency signature for near future can be estimated by acceptable accuracy. Moreover, the results of the conditional probability analysis of rainfall deficiency signature for a 60‐day duration respect to the other variables showed that, on average, the probability of the occurrence of rainfall deficiency signature of 250 mm compared to the long‐term mean in the study area is more than 50% per year. The results showed that the proposed approach may facilitate the meteorological drought management in the considered sub‐basin.
A 4‐D method due to the conditional density of vine copulas was proposed to provide predictive equations and simulate the values of rainfall deficiency signatures for meteorological drought management. The diagonal section of copulas was used to reduce the complexity of the conditional density of pairwise variables. While, examining the accuracy of C‐, D‐, and R‐vine copulas, the proposed method was used to predict short‐term rainfall deficiency signatures in the studied basin.
The development of satellite sensors and interferometry synthetic aperture radar (InSAR) technology has enabled the exploitation of their benefits for long-term structural health monitoring (SHM). ...However, some restrictions cause this process to provide a small number of images leading to the problem of small data for SAR-based SHM. Conversely, the major challenge of the long-term monitoring of civil structures pertains to variations in their inherent properties by environmental and/or operational variability. This article aims to propose new hybrid unsupervised learning methods for addressing these challenges. The methods in this work contain three main parts: (i) data augmentation by the Markov Chain Monte Carlo algorithm, (ii) feature normalization, and (iii) decision making via Mahalanobis-squared distance. The first method presented in this work develops an artificial neural network-based feature normalization by proposing an iterative hyperparameter selection of hidden neurons of the network. The second method is a novel unsupervised teacher–student learning by combining an undercomplete deep neural network and an overcomplete single-layer neural network. A small set of long-term displacement samples extracted from a few SAR images of TerraSAR-X is applied to validate the proposed methods. The results show that the methods can effectively deal with the major challenges in the SAR-based SHM applications.
Abstract
Extremal dependence describes the strength of correlation between the largest observations of two variables. It is usually measured with symmetric dependence coefficients that do not depend ...on the order of the variables. In many cases, there is a natural asymmetry between extreme observations that cannot be captured by such coefficients. An example for such asymmetry is large discharges at an upstream and a downstream stations on a river network: an extreme discharge at the upstream station will directly influence the discharge at the downstream station, but not vice versa. Simple measures for asymmetric dependence in extreme events have not yet been investigated. We propose the asymmetric tail Kendall's
τ
as a measure for extremal dependence that is sensitive to asymmetric behavior in the largest observations. It essentially computes the classical Kendall's
τ
but conditioned on the extreme observations of one of the two variables. We show theoretical properties of this new coefficient and derive a formula to compute it for existing copula models. We further study its effectiveness and connections to causality in simulation experiments. We apply our methodology to a case study on river networks in the United Kingdom to illustrate the importance of measuring asymmetric extremal dependence in hydrology. Our results show that there is important structural information in the asymmetry that would have been missed by a symmetric measure. Our methodology is an easy but effective tool that can be applied in exploratory analysis for understanding the connections among variables and to detect possible asymmetric dependencies.
Plain Language Summary
Compound events describe situations where the simultaneous behavior of two or more variables lead to severe impacts. For instance, the dependence between climate or hydrological variables can lead to particular conditions that result in extreme events at the same time in different locations. Since the physical processes behind these phenomena are very complex, there can be a stronger influence from one variable on another than the other way around. In such cases, there is asymmetry in the dependence between the extreme observations of the two variables. The traditional measures of dependence are symmetric and cannot detect any asymmetries. We propose a new measure that is sensitive to asymmetric behavior in extremes. It is based on an extension of the Kendall's
τ
coefficient, a classical dependence measure. We derive evidence from theory and simulation experiments for the effectiveness of our new methodology. We then apply it to a case study on river networks in the United Kingdom where we show that our measure detects asymmetric behavior of extreme discharges with a preferred direction from upstream to downstream stations. Our work points out the importance of considering proper tools for analyzing the connections between different variables in particular in the presence of asymmetry in extreme observations.
Key Points
Coefficients that can detect asymmetry in dependence among extremes are crucial since traditional methods rely on assumption of symmetry
We propose a conditional version of Kendall's tau that allows to detect asymmetries between extremes, conditioning on one variable at a time
This new measure can be used for exploratory analysis, model assessment, and to detect directional asymmetries or causal structures in extremes
Environmental variability is a major challenging issue in bridge health monitoring because bridges are more prone to such variability than other civil structures. To deal with this challenge, this ...article proposes a new machine-learning method for early damage detection under environmental variability by means of the
k
-medoids clustering, a new damage indicator, and an innovative approach for selecting a proper cluster number. Estimation of a reliable alarming threshold is another important challenge for early damage detection via most of the machine-learning methods. On this basis, a novel probabilistic approach using the theory of extreme value and a goodness-of-fit measure is proposed to estimate an alarming threshold. The major contributions of this article include proposing a new damage indicator suitable for decision making by clustering-based algorithms, an innovative cluster selection algorithm for dealing with the problem of environmental variability and increasing damage detectability, and a novel probabilistic method for threshold estimation. Modal-based features of the well-known Z24 Bridge are considered to verify the accuracy and effectiveness of the proposed approaches along with several comparative studies. Results show that the methods presented here are highly able to detect early damage even under strong environmental variations and estimate a reliable threshold.
Maximum annual daily precipitation is a fundamental hydrologic variable that does not attain asymptotic conditions. Thus the classical extreme value theory (i.e., the Fisher-Tippett's theorem) does ...not apply and the recurrent use of the Generalized Extreme Value distribution (GEV) to estimate precipitation quantiles for structural-design purposes could be inappropriate. In order to address this issue, we first determine the exact distribution of maximum annual daily precipitation starting from a Markov chain and in a closed analytical form under the hypothesis of stochastic independence. As a second step, we formulate a superstatistics conjecture of daily precipitation, meaning that we assume that the parameters of this exact distribution vary from a year to another according to probability distributions, which is supported by empirical evidence. We test this conjecture using the world GHCN database to perform a worldwide assessment of this superstatistical distribution of daily precipitation extremes. The performances of the superstatistical distribution and the GEV are tested against data using the Kolmogorov-Smirnov statistic. By considering the issue of model's extrapolation, that is, the evaluation of the estimated model against data not used in calibration, we show that the superstatistical distribution provides more robust estimations than the GEV, which tends to underestimate (7-13%) the quantile associated to the largest cumulative frequency. The superstatistical distribution, on the other hand, tends to overestimate (10-14%) this quantile, which is a safer option for hydraulic design. The parameters of the proposed superstatistical distribution are made available for all 20,561 worldwide sites considered in this work.
Developing statistical period and simulating the required values in case of data shortage increases certainty and reliability of simulations and statistical analyses, which is very important in ...studies on hydrology and water resources. Therefore, in this study, for simulating values of potential evapotranspiration at Birjand Station located in eastern Iran, contemporaneous autoregressive moving average (CARMA), CARMA-generalized autoregressive conditional heteroskedasticity (GARCH), and Copula-GARCH models were used in statistical period of 1984–2019. The potential evapotranspiration and relative humidity time series were simulated using these three models. CARMA model has acceptable accuracy for simulating potential evapotranspiration values due to the effect of the second parameter on simulations. Nash–Sutcliffe efficiency (NSE) coefficient of CARMA model for simulating potential evapotranspiration values was estimated as 0.85. NSE coefficient of CARMA-GARCH model was obtained as 0.87 through extracting residuals of CARMA model and simulating variance of data using GARCH model. Comparing the CARMA and CARMA-GARCH models with each other, it was concluded that a combination of two linear and non-linear time series models increases simulation accuracy to some extent. Using Clayton copula (the selected copula from the studied copulas), the mentioned values were simulated by Copula-GARCH model. The results showed that among the three models used, Copula-GARCH model reduced root mean square error of bivariate simulation compared to CARMA and CARMA-GARCH models by 15 and 13%, respectively. The results also showed that the proposed model simulates the average, first, and third quarters and range of changes in the data by 5 and 95% better than the two CARMA and CARMA-GARCH models.
In this study, a new method was proposed to model the occurrence of related variables based on the conditional density of copula functions. The proposed method was adopted to investigate the dynamics ...of meteorological and hydrological droughts in the Zarinehroud basin, southeast of Lake Urmia, during the period 1994–2015. For this purpose, the modified precipitation anomaly percentage and streamflow drought indices were extracted. Finally, the joint frequency analysis of duration-duration and severity-severity characteristics of meteorological and hydrological droughts was analyzed. Analysis of 7 different copulas used to create the joint distribution in the Zarinehroud basin indicated that the Frank copula had the best performance in describing the relationship between the meteorological and hydrological drought severities and durations. By examining the results of the bivariate analysis of duration-duration of meteorological and hydrological droughts at different stations, the expected meteorological and hydrological drought durations were estimated in the years ahead. For example, at Chalkhmaz station, 4- to 7-month duration for the hydrological drought and 9- to 12-month duration for the meteorological drought is expected in the years ahead. The joint frequency analysis of drought characteristics allows to determine the meteorological and hydrological drought characteristics at a single station at the same time using joint probabilities. Also, the results indicated that by knowing the conditional density, the hydrological drought characteristics can be easily estimated for the given meteorological drought characteristics. This could provide users and researchers useful information about the probabilistic behavior of drought characteristics for optimal operation of surface water.
The extrapolation of quantiles beyond or below the largest or smallest observation plays an important role in hydrological practice, design of hydraulic structures, water resources management, or ...risk assessment. Traditionally, extreme quantiles are obtained using parametric methods that require to make an a priori assumption about the distribution that generated the data. This approach has several limitations mainly when applied to the tails of the distribution. Semiparametric or nonparametric methods, on the other hand, allow more flexibility and they may overcome the problems of the parametric approach. Therefore, we present here a comparison between three selected semi/nonparametric methods, namely the methods of Hutson (Stat and Comput, 12(4):331–338, 2002) and Scholz (Nonparametric tail extrapolation. Tech. Rep. ISSTECH-95-014, Boeing Information and Support Services, Seattle, WA, United States of America, 1995) and kernel density estimation. While the first and third methods have already applications in hydrology, Scholz (Nonparametric tail extrapolation. Tech. Rep. ISSTECH-95-014, Boeing Information and Support Services, Seattle, WA, United States of America, 1995) is proposed in this context for the first time. After describing the methods and their applications in hydrology, we compare their performance for different sample lengths and return periods. We use synthetic samples extracted from four distributions whose maxima belong to the Gumbel, Weibull, and Fréchet domain of attraction. Then, the same methods are applied to a real precipitation dataset and compared with a parametric approach. Eventually, a detailed discussion of the results is presented to guide researchers in the choice of the most suitable method. None of the three methods, in fact, outperforms the others; performances, instead, vary greatly with distribution type, return period, and sample size.
•Seasonality patterns are a key aspect of the energy-water nexus.•Changes in streamflow seasonality slightly affect future revenue.•Changes in price seasonality may significantly affect the losses of ...revenue.•Price seasonality brings about more uncertainty on revenue than climate change.
The energy-water nexus presents important implications at seasonal scale. For instance, electricity prices and streamflow have complex seasonal patterns and changes in both may adversely impact hydropower plant revenue. In order to quantify the effect of changes in price and water seasonality on future revenue distribution and its related uncertainty, we consider the case of a run-of-the-river plant. To this end, we integrate a hydrologic model, a hydropower model, two glacier inventories, six climate scenarios and five electricity price seasonal scenarios. Our results show that the impact of climate change on streamflow of the considered run-of-the-river plant will decrease the revenue by 20% in a business-as-usual price scenario. This decrease is mostly driven by a reduction of the annual streamflow due to glacier shrinkage rather than by the evolution of seasonality. From this perspective, the difference between the various climate scenarios is low. In contrast, change in electricity price seasonality induces a marked uncertainty in revenue. According to our scenarios, which assume no change in the mean annual electricity price, a change in price seasonality may indeed exacerbate or mitigate the impact of climate by 50 or 33% respectively, compared to the business-as-usual scenario. Our analysis highlights the need for considering intra-annual dynamics when investigating the energy-water nexus.
Climate models' outputs are affected by biases that need to be detected and adjusted to model climate impacts. Many climate hazards and climate-related impacts are associated with the interaction ...between multiple drivers, i.e. by compound events. So far climate model biases are typically assessed based on the hazard of interest, and it is unclear how much a potential bias in the dependence of the hazard drivers contributes to the overall bias and how the biases in the drivers interact. Here, based on copula theory, we develop a multivariate bias-assessment framework, which allows for disentangling the biases in hazard indicators in terms of the underlying univariate drivers and their statistical dependence. Based on this framework, we dissect biases in fire and heat stress hazards in a suite of global climate models by considering two simplified hazard indicators: the wet-bulb globe temperature (WBGT) and the Chandler burning index (CBI). Both indices solely rely on temperature and relative humidity. The spatial pattern of the hazard indicators is well represented by climate models. However, substantial biases exist in the representation of extreme conditions, especially in the CBI (spatial average of absolute bias: 21 ∘C) due to the biases driven by relative humidity (20 ∘C). Biases in WBGT (1.1 ∘C) are small compared to the biases driven by temperature (1.9 ∘C) and relative humidity (1.4 ∘C), as the two biases compensate for each other. In many regions, also biases related to the statistical dependence (0.85 ∘C) are important for WBGT, which indicates that well-designed physically based multivariate bias adjustment procedures should be considered for hazards and impacts that depend on multiple drivers. The proposed compound-event-oriented evaluation of climate model biases is easily applicable to other hazard types. Furthermore, it can contribute to improved present and future risk assessments through increasing our understanding of the biases' sources in the simulation of climate impacts.
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