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
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.
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 joint probability of precipitation and soil moisture is here investigated over Europe with the goal to extrapolate meaningful insights into the potential joint use of these variables for the ...detection of agricultural droughts within a multivariate probabilistic modeling framework. The use of copulas is explored, being the framework often used in hydrological studies for the analysis of bivariate distributions. The analysis is performed for the period 1996–2020 on the empirical frequencies derived from ERA5 precipitation and LISFLOOD soil moisture datasets, both available as part of the Copernicus European Drought Observatory. The results show an overall good correlation between the two standardized series (Kendall's τ= 0.42±0.1) but also clear spatial patterns in the tail dependence derived with both non-parametric and parametric approaches. About half of the domain shows symmetric tail dependence, well reproduced by the Student's t copula, whereas the rest of the domain is almost equally split between low- and high-tail dependences (both modeled with the Gumbel family of copulas). These spatial patterns are reasonably reproduced by a random forest classifier, suggesting that this outcome is not driven by chance. This study stresses how a joint use of standardized precipitation and soil moisture for agriculture drought characterization may be beneficial in areas with strong low-tail dependence and how this behavior should be carefully considered in multivariate drought studies.
•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.
While lung ultrasonography (LUS) has utility for the evaluation of the acute phase of COVID-19 related lung disease, its role in long-term follow-up of this condition has not been well described. The ...objective of this study is to compare LUS and chest computed tomography (CT) results in COVID-19 survivors with the intent of defining the utility of LUS for long-term follow-up of COVID-19 respiratory disease.
Prospective observational study that enrolled consecutive survivors of COVID-19 with acute hypoxemic respiratory failure (HARF) admitted to the Respiratory Intensive Care Unit. Three months following hospital discharge, patients underwent LUS, chest CT, body plethysmography and laboratory testing, the comparison of which forms the basis of this report.
38 patients were enrolled, with a total of 190 lobes analysed: men 27/38 (71.1%), mean age 60.6 y (SD 10.4). LUS findings and pulmonary function tests outcomes were compared between patients with and without ILD, showing a statistically significant difference in terms of LUS score (p: 0.0002), FEV1 (p: 0.0039) and FVC (p: 0.012). ROC curve both in lobe by lobe and in patient's overall analysis revealed an outstanding ILD discrimination ability of LUS (AUC: 0.94 and 0.95 respectively) with a substantial Cohen's coefficient (K: 0.74 and 0.69).
LUS has an outstanding discrimination ability compared to CT in identifying an ILD of at least mild grade in the post COVID-19 follow-up. LUS should be considered as the first-line tool in follow-up programs, while chest CT could be performed based on LUS findings.
•LUS strongly correlates with CT in post COVID-19 ILD assessment.•LUS should be added to follow-up post COVID-19 diagnostic evaluation.•In post COVID-19 ILD evaluation, LUS should be first-line exam.•Chest CT post COVID-19 infection could be performed based on LUS outcomes.
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.
Downscaling and simulating various meteorological variables at different time scales are fundamental topics for making climate change studies in a geographic region. Here, a new approach for ...downscaling the mean daily temperature was implemented using a vine copula‐based approach and considering the best CanESM2 predictors. The accuracy of the copula‐based approach was compared with genetic programming (GP), optimized support vector regression (OSVR), support vector machine (SVM), adaptive neuro‐fuzzy inference system (ANFIS) and artificial neural network (ANN) models at Birjand synoptic station in Iran. In the proposed approach, after examining the different vine copulas, the D‐vine copula was selected as the best copula according to the evaluation statistics and tree sequences. According to the root‐mean‐square error (RMSE) and Nash–Sutcliff efficiency (NSE), the accuracy of the ANN model in downscaling the mean daily temperature data was not acceptable and the other considered models were slightly overestimated. The results indicated that the copula‐based approach outperformed the other models in downscaling the mean daily temperature with NSE = 0.61. However, given the 99% confidence interval of the simulations, a slightly overestimation at temperatures above 20°C was observed for the copula‐based approach, which has better performance than the other considered models. The copula‐based approach was able to reduce RMSE by about 82, 20, 24, 47 and 34% compared to ANN, OSVR, GP, SVM and ANFIS models, respectively. The results also showed that the performance of the support vector regression model optimized by the ant colony algorithm is also acceptable and is in the second rank after the copula‐based approach. The accuracy of the copula‐based approach was also confirmed according to Taylor diagram and violin plot. The proposed approach has a higher accuracy than data‐driven models due to use of the conditional density of vine copulas, and the joint distribution of the mean daily temperature and selected predictors.
Examining the copula‐based approach in four dimensions for downscaling the mean daily temperature. Application of the 4D copula‐based approach to climate change researches as a data‐driven model. Comparison of copula‐based approach with various models to evaluate the accuracy of this approach. Figure shows correlation coefficient, histogram, and empirical contour lines of the observed values of the mean daily temperature at Birjand station and corresponding simulated values by different models.
One, No One, and One Hundred Thousand Ignaccolo, Massimiliano; De Michele, Carlo
Journal of hydrometeorology,
06/2020, Letnik:
21, Številka:
6
Journal Article
Recenzirano
Odprti dostop
The Z–R relationship is a scaling-law formulation, Z = ARb
, connecting the radar reflectivity Z to the rain rate R. However, more than 100 Z–R relationships, with different values of the parameters, ...have been reported in literature. This abundance of relationships is in itself a strong indication that no one “physical” relationship exists, a state of affairs that we find similar to that of the protagonist of Luigi Pirandello’s novel One, No One and One Hundred Thousand. Nevertheless the “elevation” of a simple linear fit in the (logR, logZ) space to the role of “scaling law” is such a widespread tenet in literature that it eclipses the simple realization that the abundance of different intercepts and slopes reflects the inhomogeneous nature of rain, and, in ultimate analysis, the statistical variability existing between the number of drops and drop size distribution. Here, we “eliminate” the contribution of the number of drops by rescaling both reflectivity and rainfall rate to per unit drop variables, (Z, R) → (z, r), so that the remaining variability is due only to the variability of the drop size distribution. We use a worldwide database of disdrometer data to show that for the rescaled variables (z, r) only “one,” albeit approximate, scaling law exists.
Maximum annual daily precipitation does not attain asymptotic conditions. Consequently, the results of classical extreme value theory do not apply to this variable. This issue has raised concerns ...about the frequent use of asymptotic distributions to model the maximum annual daily precipitation and, at the same time, has rekindled interest in deriving and testing its exact (or non-asymptotic) distribution. In this review, we summarize and discuss results to date about the derivation of the exact distribution of maximum annual daily precipitation, with attention on compound/superstatistical distributions.
PDF
