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ABSTRACT We use a multivariate analysis to study droughts in Finland using the Joint Deficit Index (JDI). Subsequently, the joint probability of occurrence of drought characteristics was analysed using Vine copulas. For this purpose, we used monthly precipitation from 22 meteorological stations across Finland in the period 1980–2021. The JDI time series showed that Finland had a normal wetness condition most of the time during the studied period. Trend analysis of the JDI time series using a modified Mann–Kendall test showed that there was no significant trend in the values of this index during the studied period. The drought characteristics, including severity, duration and inter‐arrival time (IAT), were extracted from the JDI time series for each station. The trend analysis of drought characteristics showed that only the Tohmajärvi Kemie station in eastern Finland had a significant negative trend in drought duration and severity. Furthermore, of the 22 stations studied, only two stations showed a significant increasing trend in the duration and severity of drought at the 10% level. The drought characteristics at the remaining stations showed no significant trend at the 10% level of significance. For stations with non‐stationary drought characteristics, generalised additive models for location, scale, and shape (GAMLSS) were used for frequency analysis. The correlation between the three characteristics of severity, duration and IAT was investigated using Kendall's Tau statistic. The results showed a high correlation between the two variables duration and severity and a moderate and acceptable correlation between drought severity and IAT as well as the pair of duration and IAT. In the following, copula functions were used to construct a trivariate distribution of the drought characteristics. Among the copulas tested, the R‐vine copula and its independent mode have the best fit for the variables under study and provide a suitable tree sequence. Finally, using the aforementioned copulas and their conditional density, the frequency analysis of the three drought variables was performed. The results of this study were presented in the form of four‐dimensional graphs to estimate the joint probability of occurrence of drought characteristics based on the JDI. These graphs are presented according to the precipitation conditions of each station, and by having a drought characteristic, other characteristics can be estimated with different probabilities. The proposed method is very efficient in analysing the joint frequency of drought characteristics due to the consideration of the effective parameters and the use of conditional density. [ABSTRACT FROM AUTHOR]

The technology sector serves as a fundamental pillar for all industry sectors in the economy, playing a central role in driving worldwide economic growth. It particularly distinguishes itself in the U.S., representing approximately one-third of the global technology market. However, the technology sector is not a homogenous group of similarly focused companies, its industries vary significantly in their characteristics. This paper analyzes the relationships among U.S. technology industries defined by the Global Industry Classification Standard using Vine copulas and transfer entropy. It spans 1 January 2010–31 January 2024, to clarify intra-sectoral heterogeneity and identify key industries predicting the performance of others. Our findings highlight the predictive power of the semiconductor industry, with significant information transmission to all other industries. Contrarily, the flow in the opposite direction is significant in only 3 of 5 cases. The identification of semiconductors’ central role is particularly valuable for both retail and institutional investors concentrating on technology stocks, as it may indicate future developments in the entire sector. Moreover, due to the industry’s global importance, shocks in the semiconductor industry could propagate across the entire technology sector, leading to broader economic instability. Therefore, the semiconductor industry should be closely monitored by the policymakers too. [ABSTRACT FROM AUTHOR]

In this work, we deal with non-stationary multivariate time series, proposing a method which uses copulas to produce more accurate forecasting. The idea is to apply a copula-based approach to identify change points and then split the time series into consecutive segments based on these change points. In each segment, we define the best-fitting copula family and forecast values of the time series of each segment using the corresponding fitting copula. We apply our model to a financial data set to test the predictive power of our approach. A simulation study is also presented for a detailed illustration and assessment of our proposed methodology. Based on the results of numerical analysis, we observed that our proposed approach will help us to improve the accuracy of forecasting in comparison with other existing methods such as traditional time series forecasting as well as neural network forecasting. [ABSTRACT FROM AUTHOR]

Existing studies on the vulnerability assessment of ecological drought often focus on analyzing vegetation phenotypic characteristics, overlooking the impact of drought on ecosystem services. This study proposes an ecosystem vulnerability assessment method under ecological drought stress from the perspective of ecosystem service value (ESV), considering the characteristics and interactions of hazard-causing factors and hazard-bearing bodies. The spatiotemporal evolution of ecological drought, the spatial characteristics of ecosystem vulnerability, and the vulnerability characteristics of different ecosystem types in the North China region from 1991 to 2021 were evaluated. The results showed that: (1) ecological drought exhibited a trend of intensification followed by alleviation, with the most severe droughts occurring between 2002 and 2011, affecting up to 64.3% of the region; (2) ESV was mainly influenced by vegetation cover and precipitation gradients, displaying a spatial pattern of high values in the southeast and low values in the northwest, with total ESV averaging CNY 18.23 trillion; (3) grasslands exhibited higher sensitivity to drought compared to forests, and the sensitivity was higher in summer and autumn than in winter and spring. This method assessed the vulnerability of ecological drought from the perspective of ecosystem services, providing a new approach for a more comprehensive understanding of the impact of drought on ecosystem service functions. [ABSTRACT FROM AUTHOR]

The growing interest in cryptocurrencies has brought this new means of exchange to the attention of the financial world. This study aims to investigate the effects that a cryptocurrency can have when it is considered as a financial asset. The analysis is carried out from an ex‐post perspective, evaluating the performance achieved in a certain period by three different portfolios. These are the one composed only of equities, bonds and commodities, the second one only of cryptocurrencies, and the third one is a combination of these both ones and thus made up of all considered "traditional" assets and the most performing cryptocurrency of the second portfolio. For these purposes, the classic variance‐covariance approach is applied where the calculation of the risk structure is done via the GARCH‐Copula and GARCH‐Vine Copula approaches. The optimal weights of the assets in the optimized portfolios are determined through Markowitz optimization problem. The analysis mainly showed that the portfolio composed of cryptocurrency and traditional assets has a higher Sharpe index, from an ex‐post perspective, and more stable performances, from an ex‐ante perspective. We justify our selection of the Markowitz approach over conditional VaR and expected shortfall due to their heightened sensitivity to unsystematic extreme events in crypto markets. [ABSTRACT FROM AUTHOR]

With the large-scale development of solar power generation, highly uncertain photovoltaic (PV) power output has an increasing impact on distribution networks. PV power generation has complex correlations with various weather factors, while the time series embodies multiple temporal characteristics. To more accurately quantify the uncertainty of PV power generation, this paper proposes a short-term PV power probabilistic forecasting method based on the combination of decomposition prediction and multidimensional variable dependency modeling. First, a seasonal and trend decomposition using a Loess (STL)-based PV time series feature decomposition model is constructed to obtain periodic, trend, and residual components representing different characteristics. For different components, this paper develops a periodic component prediction model based on TimeMixer for multi-scale temporal feature mixing, a long short-term memory (LSTM)-based trend component extraction and prediction model, and a multidimensional PV residual probability density prediction model optimized by Vine Copula optimized with Q-Learning. These components' results form a short-term PV probabilistic forecasting method that considers both temporal features and multidimensional variable correlations. Experimentation with data from the Desert Knowledge Australia Solar Center (DKASC) demonstrates that the proposed method reduced root mean square error (RMSE) and mean absolute percentage error (MAPE) by at least 14.8% and 22%, respectively, compared to recent benchmark models. In probability interval prediction, while improving accuracy by 4% at a 95% confidence interval, the interval width decreased by 19%. The results show that the proposed approach has stronger adaptability and higher accuracy, which can provide more valuable references for power grid planning and decision support. [ABSTRACT FROM AUTHOR]

This article extends the socially responsible multiobjective problem to (i) estimating optimal portfolios via reward/risk maximization, (ii) including dependence structure between asset returns using vine copulas, and (iii) incorporating enhanced indexation utilizing cumulative zero-order stochastic dominance (CZϵSD). Applying the multiobjective optimal portfolio (MOOP) approach to a sample of EuroStoxx 50 constituents, the results show that the MOOPs provide investors with the flexibility to incorporate different objectives while investing in optimal portfolios. Including social responsibility results in lower portfolio return and economic performance, but at the same time portfolio risk, expected shortfall of portfolio returns below the benchmark, and turnover are reduced. The copula-based predictive models lead to MOOPs with higher returns and reward/risk ratios. Moreover, optimizing environmental scores leads to less risky MOOPs, while optimizing social scores results in higher average return and better risk-adjusted performance. [ABSTRACT FROM AUTHOR]

Abstract It is of practical significance to provide a reference for drought mitigation and water resource enhancement planning in the Henan Province region and to analyze the spatial and temporal evolution characteristics of meteorological agricultural drought in the region. In this study, a multivariate (precipitation, potential evapotranspiration, soil moisture and normalized vegetation index) composite drought index CCDI was constructed based on the D Vine copula model, and the correlations between the CCDI and the standardized precipitation evapotranspiration index (SPEI) and between the CCDI and the standardized soil moisture index (SSI) were analyzed. The ability of the CCDI to evaluate meteorological agricultural drought was assessed, and typical drought events were selected for validation. The spatial and temporal evolution of drought in the Henan region from 1982 to 2022 was characterized using linear trends, M–K mutability tests, and drought centers of gravity, and future trends were analyzed using the Hurst index. The results show that (1) the CCDI correlates well with the SPEI and SSI (P

Copula is a highly flexible joint distribution tool that models its univariate margins and joint dependence separately compared to conventional parametric distribution. The flood can be characterized by multiple interconnected variables, such as peak flow, flood volume, duration, and peak time. This makes a univariate or bivariate joint approach ineffective for risk assessments. Current researchers have worked on trivariate copula modeling, but there are a couple of drawbacks that make this approach unfavourable such as only small number of copula families are applicable for higher dimensional copula modeling. Due to this, only a small number of studies have attempted to predict the flood characteristics using copulas with more than three variables involved. For this reason, the use of vine copula was introduced for the purpose of improving the functionality of higher dimensional copulas, making them a useful and adaptable tool for determining the dependence between complicated paired dependent variables. This study provides an alternative approach to compute the flood characteristics using L-moment method. The results show that the proposed approach is reliable when compared with simulated data. This paper reveals that Gumbel copula successfully employed the vine copula modeling of four-dimensional flood characteristics in Johor River Basin, Malaysia. This study investigates return periods for the first time, taking four important flood variables into account. Based on all scenarios, including bivariate, trivariate, and four-dimensional, the results show that the "OR" joint return period is lower and more likely to occur than the "AND" joint return period. [ABSTRACT FROM AUTHOR]

Local variations in the 3D microstructure can control the macroscopic behavior of heterogeneous porous materials. For example, the permittivity through porous sheets or membranes is governed by local high‐volume pathways or bottlenecks. Due to local variations, unfeasibly large amounts of microstructure data may be needed to reliably predict such material properties directly from image data. Here it is demonstrated that a vine copula approach provides parametric models for local microstructure descriptors that compactly capture the 3D microstructure including its local variations and efficiently probe it with respect to selected, measurable properties. In contrast to common methods of complexity reduction, the proposed approach creates parametric models for the multivariate probability distribution of high‐dimensional descriptor vectors that inherently contain the complex, nonlinear dependencies between these descriptors. Therein, material properties are offered in physically motivated distributions of microstructure descriptors rather than as normally distributed data. Applied to porous fiber networks (paper) before and after unidirectional compression, it is shown that the copula‐based models reveal material‐characteristic relationships between two or more microstructure descriptors. In this way, the presented modeling approach can provide deeper insight into the microscopic origin of effective macroscopic properties of heterogeneous porous materials. [ABSTRACT FROM AUTHOR]

Fatigue load modeling is crucial for optimizing and assessing the lifespan of floating wind turbines. This study addresses the complex characteristics of fatigue loads on floating wind turbines under the combined effects of wind and waves. We propose a fatigue load modeling approach based on Vine copula theory and machine learning. Firstly, we establish an optimal joint probability distribution model using Vine copula theory for the four-dimensional random variables (wind speed, wave height, wave period, and wind direction), with model fit assessed using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Root Mean Square Error (RMSE). Secondly, representative wind and wave load conditions are determined using Monte Carlo sampling based on the established joint probability distribution model. Thirdly, fatigue load simulations are performed using the high-fidelity simulator OpenFAST to compute Damage Equivalent Load (DEL) values for critical components (blade root and tower base). Finally, utilizing measured wind and wave data from the Lianyungang Ocean Observatory in the East China Sea, simulation tests are conducted. We apply five commonly used machine learning models (Kriging, MLP, SVR, BNN, and RF) to develop DEL models for blade root and tower base. The results indicate that the RF model exhibits the smallest prediction error, not exceeding 3.9%, and demonstrates high accuracy, particularly in predicting flapwise fatigue loads at the blade root, achieving prediction accuracies of up to 99.97%. These findings underscore the effectiveness of our approach in accurately predicting fatigue loads under real-world conditions, which is essential for enhancing the reliability and efficiency of floating wind turbines. [ABSTRACT FROM AUTHOR]

Process capability indices (PCIs) are major tools in geometric dimensioning and tolerancing (GD&T) for quantifying the production quality, monitoring production, or prioritizing projects. Initially, PCIs were constructed for studying each characteristic of the process independently. Then, they have been extended to analyze several dependent characteristics simultaneously. Nowadays, with the increasing complexity of the production parts, for example, in aircraft engines, the conformity of one part may rely on the conformity of hundreds of characteristics. Also, because those characteristics are dependent, it may be misleading to make decisions based only on univariate PCIs. However, classical multivariate PCIs in the literature do not allow treating such amount of data efficiently, unless assuming Gaussian distribution, which may be false. Regarding those issues, we advocate for PCI based on some transformation of the conformity rates. This presents the advantage of being free from distributional assumptions, such as the Gaussian distribution. In addition, it has direct interpretation, allowing it to compare different processes. To estimate the PCIs of parts with hundreds of characteristics, we propose to use Vine Copulas. This is a very flexible class of models, which gives precise estimation even in high dimension. From an industrial perspective, the computation of the estimator can be costly. To answer this point, one explains how to compute a lower bound of the proposed PCI, which is faster to calculate. We illustrate our method adaptability with simulations under Gaussian and non-Gaussian distributions. We apply it to compare the production of fan blades of two different factories. [ABSTRACT FROM AUTHOR]

Understanding the lagged correlations between regional precipitation and large scale climate indicators (LCI) is crucial for water management and drought risk assessment. Copula functions are commonly used to quantify the relationship between precipitation and these factors. However, existing studies often neglect monsoon inland areas and lack quantification of the lagged correlations of precipitation at the monthly scale. To address these limitations, this study constructed a 3-dimensional vine copula-based model to assess the impact of large scale climatic change on regional precipitation. The analysis focused on the Hengshao Drought Corridor (HDC), the driest region in Hunan Province, China. The results indicate that precipitation in this region is influenced primarily by the Pacific Ocean’s circulation pattern, particularly the Niño1 + 2 and Niño3 indices, with a 2 ∼ 3 month lag. The R-Vine Copula provided the best fit when identifying lagged correlations, but due to its fitting center, it did not perform as well as the C-Vine Copula in generating stochastic simulated precipitation. The study revealed that the HDC receives more precipitation when the Niño1 + 2 and Niño3 are asynchronous, but less precipitation when they are synchronous, making the area more susceptible to drought events. These findings have implications for the HDC and other monsoon inland regions worldwide, providing insights to cope with climate extremes and develop appropriate strategies.

Aero‐disk is a key component of aero‐engine. Due to its complex working conditions, aero‐disk is prone to structural failures. Therefore, it is essential to analyze the reliability and importance input variables of aero‐disk. In this paper, a framework of aero‐disk reliability analysis and global sensitivity analysis (GSA) was established. First, the hazardous regions of aero‐disk were determined by finite element analysis, and the limit state function of aero‐disk was defined by the life interference model. Then D‐Vine model was utilized to establish the correlation model for aero‐disk hazardous regions to evaluate the reliability of aero‐disk. In addition, two GSA methods based on Copula and space partition were proposed to identify important input random variables considering underlying correlation, and the accuracy of the proposed method was verified by two examples. Finally, the proposed method was applied to the GSA of aero‐disk. The results show that the established framework fills in the gap of uncertainty analysis of aero‐disk, which can be extended to other engineering fields. The proposed GSA methods have both high efficiency and accuracy and can realize multi‐dimensional GSA when the correlation of input variables is considered. [ABSTRACT FROM AUTHOR]

This study proposes an alternative risk assessment approach for evaluating extreme air pollution events through vine copula modeling. Three characteristics of unhealthy air pollution events (i.e., severity, intensity, and duration) in Klang, Malaysia, are examined. The vine copula is fitted using sequential maximum likelihood estimation and joint maximum likelihood estimation, with a subsequent comparison based on criteria such as log-likelihood, Akaike's information criterion, and Bayesian's information criterion. Model fitting and comparison studies demonstrate that the most well-fitted vine copula model, achieved through joint maximum likelihood estimation, comprises the Joe, Rotated Tawn type 2 (180 degrees), and Rotated BB8 (90 degrees) copulas. The positive Kendall's τ correlation coefficient (0.26) for the obtained vine copula indicates that higher values of one characteristic are likely to be associated with higher values of the other characteristics, and vice versa. Furthermore, with the upper tail dependence coefficient (0.31) surpassing the lower tail dependence coefficient (0.18), indicating stronger dependence in the upper tail of their distribution, this underscores the significance of conducting risk assessments for extreme air pollution events characterized by extreme levels of severity, intensity, and duration. A vine copula-based simulation study is conducted to delve deeper into the risk assessment, revealing that extreme air pollution events are not linked to the highest values of joint and conditional probabilities. These findings suggest that extreme values in those distinct characteristics do not consistently occur simultaneously. The return period measures also indicate that extreme air pollution events have long waiting periods. Despite the current status of extreme air pollution events in Klang being controllable, achieving effective control necessitates ongoing efforts, encompassing regulatory actions, industrial controls, robust public transportation programs, and a dedicated transition to cleaner energy sources. This task is crucial for ensuring continuous clean air quality, sustaining our environment, and avoiding negative impacts on the economy and public well-being. [ABSTRACT FROM AUTHOR]

The success of an investment portfolio is not only related to its yield, but is also influenced by market risks, especially the contagion risks that may exist between assets. Therefore, effective portfolio optimization requires first studying the risk contagion relationship between financial assets. We selected a total of six financial assets from different stock and exchange rate markets as the research objects, and explored the risk contagion relationships of various assets in the investment portfolio through Vine Copula. Research has shown that there is often a structural mutation in one or some assets of an investment portfolio, leading to significant fluctuations in investment returns. The Vine Copula model can effectively measure the risk contagion between assets caused by asset structural mutations. [ABSTRACT FROM AUTHOR]

In probabilistic coastal hazard assessments based on the Joint Probability Method, historical storm data is used to build distribution models of tropical cyclone atmospheric parameters (i.e., central pressure deficit, forward velocity, radius of maximum wind, and heading direction). Recent models have used a range of assumptions regarding the dependence structure between these random variables. This research investigates the performance of a series of joint distribution models based on assumptions of parameter independence, partial-dependence (i.e., dependence between only central pressure deficit and radius of maximum wind), and full dependence (i.e., dependence between each pair of tropical cyclone atmospheric parameters). Full dependence models consider a range of copula models, such as the Gaussian copula and vine copulas that combine linear-circular copulas with Gaussian or Frank copulas. The consideration of linear-circular copulas allows for the characterization of correlation between linear variables (e.g., central pressure deficit) and circular variables (e.g., heading direction). The sensitivity of the results to different joint distribution models is assessed by comparing hazard curves at representative locations in New Orleans, LA (USA). The stability of hazard curves generated using a Gaussian copula considering variation in the selection of the zero-degree convention is also assessed. The tail dependence between large central pressure deficit and large radius of maximum wind associated with various copula models are also compared using estimated conditional probability. It is found that the linear-circular Frank vine copula model improve the stability of hazard curves and maximize tail dependence between large central pressure deficit and large radius of maximum wind. However, the meta-Gaussian copula model exhibits performance within this study region that was generally consistent with the tested vine copulas and have the advantage of being easier to implement. [ABSTRACT FROM AUTHOR]

This study employs copula functions to establish the dependency structure of the joint distribution among rainfall intensity, wind speed, and wind direction in Qatar. Based on a Vine Copula, the trivariate distribution between rainfall intensity, wind speed, and wind direction is found to exhibit a root-mean-square error (RMSE) of 0.0072 on the observed vs. modeled cumulative probabilities using ranked normalized observations. It is also found that the winter Shamal winds are most pronounced during rainfall. However, a secondary component of easterly winds known as the Kaus winds is also found to exert an important influence. This wind pattern is observable during rainfall at all the selected stations, albeit with minor variations. It is also found that rainfall stations where the rainfall is obstructed in any way from northwest to north and from east to southeast significantly influence the rainfall measurements. Specific rain gauges in Qatar are found to be situated in disrupted surroundings, such as meteorological stations close to passing traffic, where road spray could infiltrate the rain gauge funnel, impacting the accuracy of rainfall measurements. The study results necessitated the relocation of approximately half of these roadside gauges to mitigate wind-induced biases from road spray. An evaluation of operations is recommended for approximately 80 meteorological stations responsible for measuring rainfall in Qatar. The methodology devised in this study holds potential for application to other Middle Eastern countries and regions with similar climates. [ABSTRACT FROM AUTHOR]

A thorough understanding of the impact of climatic factors on agricultural production is crucial for improving crop models and enhancing predictability of crop prices and yields. Fluctuations in crop yield and price can have significant implications for the market sector and farming community. Given the projected increase in frequency and intensity of extreme events, reliable modelling of cropping patterns becomes essential. Temperature anomalies are expected to play a prominent role in future extreme events, emphasizing the need to comprehend their influence on crop yield. Forecasting extreme yield, which encompasses both the highest and lowest levels of agricultural production within a given time period, along with peak crop prices representing the highest market values, poses greater challenges in forecasting compared to other values. Probability-based predictions, accounting for uncertainty and variability, offer a more accurate approach for extreme value estimation and risk assessment. In this study, we employ a multivariate analysis based on vine copula to explore the interdependencies between temperature anomalies and daily strawberry yield in Santa Maria, California. By considering the maximum and minimum daily yields each month, we observe an increased probability of yield loss with rising temperature anomalies. While we do not explicitly consider the specific impacts of temperature anomalies under individual Representative Concentration Pathway (RCP) scenarios, our analysis is conducted within the broader context of the current global warming scenario. This allows us to capture the overall anticipated effects of regional temperature anomalies on agriculture. The findings of this study have potential impacts and consequences for understanding the vulnerability of agricultural systems and improving crop model predictions. By enhancing our understanding of the relationships between temperature anomalies and crop yield, we can inform decision-making processes related to the impact of climate change on agriculture. This research contributes to the ongoing efforts in improving agricultural sustainability and resilience in the face of changing climatic conditions. [ABSTRACT FROM AUTHOR]

Design flood hydrographs are often used to project safe and cost-effective hydraulic structures. This study proposes a system based on a combination of empirical and statistical approaches for constructing synthetic design flood hydrographs, that practitioners can easily apply. The system uses scaled observed seasonal flood hydrographs and respects the dependence structure among the flood peaks, volumes, and durations deduced from the set of seasonal flood hydrographs observed. The method was developed and tested based on data from the Horné Orešany reservoir in Slovakia. [ABSTRACT FROM AUTHOR]

In the context of large-scale development and clustering integration of offshore wind power， fairly and equitably recovering the transmission costs of offshore wind power integration systems and allocating them to wind farms has become a pressing issue in the offshore wind power industry. To address this challenge， a method for allocating fixed costs in offshore wind power integration systems， taking into account the correlation of wind power output， is proposed. Firstly， the Vine copula function is employed to construct a correlation model for the output of multiple offshore wind farms. Additionally， it is assumed that the system’s load demand model follows a normal distribution， and the generators follow a ［0，1］ probability distribution. Then， using a combination of Monte Carlo sampling and the probability flow power flow tracking method， the fixed cost allocation for each integrated offshore wind farm is calculated. Finally， through case simulation analysis， the reasonableness and effectiveness of the proposed method are validated.

Existing studies on the vulnerability assessment of ecological drought often focus on analyzing vegetation phenotypic characteristics, overlooking the impact of drought on ecosystem services. This study proposes an ecosystem vulnerability assessment method under ecological drought stress from the perspective of ecosystem service value (ESV), considering the characteristics and interactions of hazard-causing factors and hazard-bearing bodies. The spatiotemporal evolution of ecological drought, the spatial characteristics of ecosystem vulnerability, and the vulnerability characteristics of different ecosystem types in the North China region from 1991 to 2021 were evaluated. The results showed that: (1) ecological drought exhibited a trend of intensification followed by alleviation, with the most severe droughts occurring between 2002 and 2011, affecting up to 64.3% of the region; (2) ESV was mainly influenced by vegetation cover and precipitation gradients, displaying a spatial pattern of high values in the southeast and low values in the northwest, with total ESV averaging CNY 18.23 trillion; (3) grasslands exhibited higher sensitivity to drought compared to forests, and the sensitivity was higher in summer and autumn than in winter and spring. This method assessed the vulnerability of ecological drought from the perspective of ecosystem services, providing a new approach for a more comprehensive understanding of the impact of drought on ecosystem service functions.

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Vegetation is one of the key components in terrestrial ecosystems, particularly in climate, carbon balance, and water cycling. The healthy growth of vegetation can depend mainly on the context of climate change, such as more frequent occurrences of droughts and heat waves. Moreover, the degradation of vegetation can cause irreversible damage to the structure and functionality of terrestrial ecosystems. Compound hot and dry events can further exacerbate their impact on the vegetation, due to the positive feedback between droughts and heatwaves. Therefore, it is very necessary to evaluate the response relationship between vegetation and compound hot and dry events, in order to clarify the ecosystem response to climate change for effective mitigation and adaptation strategies. The correlation between vegetation and drought or hot indices has been commonly used to determine their relationship in recent years. However, the overall correlation coefficient is often insufficient to capture the tail dependence between extreme events and vegetation conditions. In this study, a Vine Copula-based model was constructed to assess the vulnerability of vegetation using the detrended and standardized normalized vegetation index (SNDVI), standardized precipitation and evapotranspiration index (SPEI), and standardized temperature index (STI). The probability of vegetation loss was determined for the different land use and climatic regions in the Loess Plateau from 1982 to 2015. The results show: 1) There was a positive correlation between SNDVI and SPEI in most areas of the Loess Plateau, whereas, a negative correlation was found between SNDVI and STI. Grasslands shared the highest correlation between SNDVI and SPEI, followed by cropland, and the forests with the lowest correlation. There was no significant difference in the correlation distribution between grassland and cropland SNDVI with SPEI from June to August. However, there was a gradual decrease in the correlation between forest and shrub SNDVI with SPEI. The correlation distribution between grassland and cropland SNDVI with STI remained relatively unchanged, while the correlation between forest and shrub SNDVI with STI gradually increased. 2) The vulnerability values of vegetation to extreme compound dry and hot conditions were 0.51, 0.57, and 0.55 respectively, in June, July, and August, which was significantly higher than those to single drought or high-temperature events. Regions with higher vulnerability were concentrated in the northern part of Shaanxi, Ningxia, eastern Gansu, and Inner Mongolia. 3) The vegetation exhibited a significantly higher vulnerability to extreme compound dry and hot conditions in arid and semi-arid regions, compared with the single extreme drought or high-temperature events. In humid and semi-humid regions, vegetation vulnerability to extreme compound dry and hot conditions was generally comparable or slightly lower than that to single drought or high-temperature events. 4) There was a great variation in the vulnerability of different vegetation types. The vulnerability was ranked in the descending order of grassland, cropland, shrub, forest. The vulnerability of grassland to extreme compound dry and hot conditions increased by 26% to 56% during summer, compared with single drought or high temperature events, while the cropland vulnerability increased by 11% to 24% and 19% to 48%, respectively. Since the SNDVI can only represent the vegetation cover, more vegetation indices (such as gross primary productivity (GPP) and net primary productivity (NPP)) can be expected to assess the vegetation dynamics and their response to extreme events, in order to reduce some uncertainties in the future research. [ABSTRACT FROM AUTHOR]

High-dimensional data sets are often available in genome-enabled predictions. Such data sets include nonlinear relationships with complex dependence structures. For such situations, vine copula-based (quantile) regression is an important tool. However, the current vine copula-based regression approaches do not scale up to high and ultra-high dimensions. To perform high-dimensional sparse vine copula-based regression, we propose 2 methods. First, we show their superiority regarding computational complexity over the existing methods. Second, we define relevant, irrelevant, and redundant explanatory variables for quantile regression. Then, we show our method's power in selecting relevant variables and prediction accuracy in high-dimensional sparse data sets via simulation studies. Next, we apply the proposed methods to the high-dimensional real data, aiming at the genomic prediction of maize traits. Some data processing and feature extraction steps for the real data are further discussed. Finally, we show the advantage of our methods over linear models and quantile regression forests in simulation studies and real data applications. [ABSTRACT FROM AUTHOR]

AbstractDeep-seabed polymetallic nodules have been recognized as a potential solution to the depletion of many metals that are produced by terrestrial minerals. Mineral resources obtained by deep-seabed mining vehicles significantly affect the economic viability of underwater mining activities. Therefore, an accurate prediction of the harvested mineral resources is significantly important. Probabilistic approach-based prediction, which enhances the accuracy of the economic evaluation, requires a statistical model of the variability of each metal element in the harvested polymetallic nodules. However, the probability distribution of the metal elements in the polymetallic nodules has rarely been studied thus far. A multivariate joint probability distribution must be adopted because the variabilities of these metal elements is correlated with each other. However, multivariate statistical approaches have not been actively studied owing to their highly sophisticated theories. The objective of this study was to establish a systematic framework for modeling a multivariate joint probability distribution of correlated random variables. A case study was performed to characterize the metal elements of the polymetallic nodules using the proposed approach. [ABSTRACT FROM AUTHOR]

Contaminated air is unhealthy for people to breathe and live in. To maintain the sustainability of clean air, air pollution must be analyzed and controlled, especially after unhealthy events. To do so, the characteristics of unhealthy events, namely intensity, duration, and severity are studied using multivariate modeling. In this study, the vine copula approach is selected to study the characteristics data. Vine copula is chosen here because it is more potent than the standard multivariate distributions, and multivariate copulas, especially in modeling the tails related to extreme events. Here, all nine different vine copulas are analyzed and compared based on model fitting and the comparison of models. In model fitting, the best model obtained is Rv123-Joint-MLE, a model with a root nodes sequence of 123, and optimized using the joint maximum likelihood. The components for the best model are the Tawn type 1 and Rotated Tawn type 1 180 degrees representing the pair copulas of (intensity, duration), and (intensity, severity), respectively, with the Survival Gumbel for the conditional pair copula of (duration, severity; intensity). Based on the best model, the tri-variate dependence structure of the intensity, duration, and severity relationship is positively correlated, skewed, and follows an asymmetric distribution. This indicates that the characteristic's, including intensity, duration, and severity, tend to increase together. Using comparison tests, the best model is significantly different from others, whereas only two models are quite similar. This shows that the best model is well-fitted, compared to most models. Overall, this paper highlights the capability of vine copula in modeling the asymmetric dependence structure of air pollution characteristics, where the obtained model has a better potential to become a tool to assess the risks of extreme events in future work. [ABSTRACT FROM AUTHOR]

Purpose: Estimating the joint probability of occurrence and joint return period of suspended sediment load (SSL) is necessary for the design and operation of hydraulic structures. The amount of SSL is closely related to the amount of runoff, which is highly dependent on the amount of rainfall. Therefore, the purpose of this study is to estimate the joint probability of occurrence and the joint return period of SSL values given rainfall and river discharge values. Methods: The vine copula family was used in this study to trivariate frequency analyses of SSL associated with rainfall and stream flow in Allah Basin, Iran. We used daily data of 140 events recorded at Jokanak station during 1975–2020. To create the probabilistic model, the structures of D-vine, C-vine, and R-vine copula functions, as well as rotational, Gaussian, and independent modes, were examined based on log-likelihood, AIC, and BIC criteria. Results: The results of examining the marginal distributions showed that the generalized Pareto (RMSE=3.91, NSE=0.98, MAPE=3.91), log-normal (RMSE=2.69, NSE=0.99, MAPE=7.69), and GEV (RMSE=2.16, NSE=0.99, MAPE=5.43) are the best-fitted distributions on rainfall, river flow, and SSL data, respectively. By examining the various vine structures, the D-vine was chosen as a suitable copula (AIC=−727.8, BIC=−714.3, and log-likelihood=366.9) for modeling the dependency structure among rainfall (R), river flow (Q), and SSL. Examining the tree structure of considered copulas revealed that the D-vine copula maintains the dependency of the pairs of variables by selecting the best edges until the last tree. Frank and Clayton's 180-degree copulas were chosen as the best internal copula functions. The conditional return period of suspended sediment load in the study area was calculated and presented as contour curves based on rainfall and corresponding discharge. The return period provided is given by the occurrence of runoff and rainfall values. Compared to the univariate method, the presented return period includes a range of data. For example, in the 2-year return period, changes in SSL values provide a range of 0.46 to 1,395,579 tons per day, given the corresponding rainfall and runoff values with probabilities of 0.0031 to 0.50. Conclusions: Using this model, SSL values can be estimated by having the amounts of rainfall and river flow at different probability levels. The results showed that using the rotated copulas can describe the correlation in all directions, and therefore provide more reliable results. [ABSTRACT FROM AUTHOR]

Fatigue load modeling is crucial for optimizing and assessing the lifespan of floating wind turbines. This study addresses the complex characteristics of fatigue loads on floating wind turbines under the combined effects of wind and waves. We propose a fatigue load modeling approach based on Vine copula theory and machine learning. Firstly, we establish an optimal joint probability distribution model using Vine copula theory for the four-dimensional random variables (wind speed, wave height, wave period, and wind direction), with model fit assessed using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Root Mean Square Error (RMSE). Secondly, representative wind and wave load conditions are determined using Monte Carlo sampling based on the established joint probability distribution model. Thirdly, fatigue load simulations are performed using the high-fidelity simulator OpenFAST to compute Damage Equivalent Load (DEL) values for critical components (blade root and tower base). Finally, utilizing measured wind and wave data from the Lianyungang Ocean Observatory in the East China Sea, simulation tests are conducted. We apply five commonly used machine learning models (Kriging, MLP, SVR, BNN, and RF) to develop DEL models for blade root and tower base. The results indicate that the RF model exhibits the smallest prediction error, not exceeding 3.9%, and demonstrates high accuracy, particularly in predicting flapwise fatigue loads at the blade root, achieving prediction accuracies of up to 99.97%. These findings underscore the effectiveness of our approach in accurately predicting fatigue loads under real-world conditions, which is essential for enhancing the reliability and efficiency of floating wind turbines.

Abstract Estimation of instantaneous peak discharge is important in the design of hydraulic structures and reservoir management. In this study, a new approach called CEEMD-Copula-GARCH is presented for simulating instantaneous peak discharge in the Qale Shahrokh basin, upstream of Zayanderood Dam, Iran. In the developed method, the Complementary ensemble empirical mode decomposition (CEEMD) algorithm was used to analyze the observed values and generate the intrinsic mode function values and residual series. For this purpose, the intrinsic mode function values were simulated based on vine copula and its tree sequence (C-vine, D-vine, R-vine and their independent and Gaussian modes), and the residual series of the CEEMD algorithm were simulated by the GARCH model. The results of simulating instantaneous peak discharge values (m3/s) using the CEEMD-Copula-GARCH approach in the study area showed that the amount of simulation error based on the RMSE statistic compared to the CEEMD-Copula model and simulation without decomposition has improved by about 20 and 70%, respectively. The model’s efficiency was also estimated based on the Nash–Sutcliffe efficiency in the proposed approach of 0.99, and the certainty of the proposed approach was also confirmed based on the presented violin plot. According to the presented results, the proposed approach has high accuracy and efficiency in the simulation of instantaneous peak discharge (m3/s), which can be used in the flood control system design and flood management. Using the methodology proposed in this study, multivariable models can be used in simulating univariate series with high accuracy.

Ridge regression estimators can be interpreted as a Bayesian posterior mean (or mode) when the regression coefficients follow multivariate normal prior. However, the multivariate normal prior may not give efficient posterior estimates for regression coefficients, especially in the presence of interaction terms. In this paper, the vine copula-based priors are proposed for Bayesian ridge estimators under the Cox proportional hazards model. The semiparametric Cox models are built on the posterior density under two likelihoods: Cox's partial likelihood and the full likelihood under the gamma process prior. The simulations show that the full likelihood is generally more efficient and stable for estimating regression coefficients than the partial likelihood. We also show via simulations and a data example that the Archimedean copula priors (the Clayton and Gumbel copula) are superior to the multivariate normal prior and the Gaussian copula prior. [ABSTRACT FROM AUTHOR]

We employ and examine vine copulas in modeling symmetric and asymmetric dependency structures and forecasting financial returns from 2001 to 2022, a period that includes the 2008 financial crisis, the 2011 European sovereign debt crisis, the 2020 COVID‐19 pandemic crisis, and the 2022 Russian invasion of Ukraine with the resulting energy crisis. We analyze the asset allocations performed and test different portfolio strategies, such as maximum Sharpe ratio, minimum variance, and minimum conditional value at risk. Using international financial market indices, we specify the regular, drawable, and canonical vine copulas, such as the Gaussian, Student's t, Clayton, Frank, Joe, Gumbel, and mixed copulas, and analyze both in‐sample and out‐of‐sample portfolio performances. Out‐of‐sample portfolio back‐testing shows that vine copulas reduce portfolio risk better than the benchmark portfolio strategies and also better than simple multivariate copulas. Overall, we find that mixed vine copula models perform best with regard to risk reduction, both for the entire period 2001–2022 and during financial crises periods. Thus, a mixture of symmetric and asymmetric copula families works best in terms of portfolio risk reduction irrespective of the chosen optimization approach. [ABSTRACT FROM AUTHOR]

We analyze the properties of the Maximum Likelihood (ML) estimator when the underlying log-likelihood function is numerically maximized with the so-called zig-zag algorithm. By splitting the parameter vector into sub-vectors, the algorithm maximizes the log-likelihood function alternatingly with respect to one sub-vector while keeping the others constant. For situations when the algorithm is initialized with a consistent estimator and is iterated sufficiently often, we establish the asymptotic equivalence of the zig-zag estimator and the "infeasible" ML estimator being numerically approximated. This result gives guidance for practical implementations. We illustrate how to employ the algorithm in different estimation problems, such as in a vine copula model and a vector autoregressive moving average model. The accuracy of the estimator is illustrated through simulations. Finally, we demonstrate the usefulness of our results in an application, where the Bitcoin heating 2017 is analyzed by a dynamic conditional correlation model. [ABSTRACT FROM AUTHOR]

The success of an investment portfolio is not only related to its yield, but is also influenced by market risks, especially the contagion risks that may exist between assets. Therefore, effective portfolio optimization requires first studying the risk contagion relationship between financial assets. We selected a total of six financial assets from different stock and exchange rate markets as the research objects, and explored the risk contagion relationships of various assets in the investment portfolio through Vine Copula. Research has shown that there is often a structural mutation in one or some assets of an investment portfolio, leading to significant fluctuations in investment returns. The Vine Copula model can effectively measure the risk contagion between assets caused by asset structural mutations.

Estimation of instantaneous peak discharge is important in the design of hydraulic structures and reservoir management. In this study, a new approach called CEEMD-Copula-GARCH is presented for simulating instantaneous peak discharge in the Qale Shahrokh basin, upstream of Zayanderood Dam, Iran. In the developed method, the Complementary ensemble empirical mode decomposition (CEEMD) algorithm was used to analyze the observed values and generate the intrinsic mode function values and residual series. For this purpose, the intrinsic mode function values were simulated based on vine copula and its tree sequence (C-vine, D-vine, R-vine and their independent and Gaussian modes), and the residual series of the CEEMD algorithm were simulated by the GARCH model. The results of simulating instantaneous peak discharge values (m3/s) using the CEEMD-Copula-GARCH approach in the study area showed that the amount of simulation error based on the RMSE statistic compared to the CEEMD-Copula model and simulation without decomposition has improved by about 20 and 70%, respectively. The model's efficiency was also estimated based on the Nash–Sutcliffe efficiency in the proposed approach of 0.99, and the certainty of the proposed approach was also confirmed based on the presented violin plot. According to the presented results, the proposed approach has high accuracy and efficiency in the simulation of instantaneous peak discharge (m3/s), which can be used in the flood control system design and flood management. Using the methodology proposed in this study, multivariable models can be used in simulating univariate series with high accuracy. [ABSTRACT FROM AUTHOR]

Abstract Ridge regression was originally proposed as an alternative to ordinary least-squares regression to address multicollinearity in linear regression and was later extended to logistic and Cox regressions. The ridge estimator is interpreted as the Bayesian posterior mean or median in the Bayesian framework when the regression coefficients have multivariate normal priors. We previously proposed using vine copula-based joint priors on regression coefficients in linear and Cox regressions, including an interaction that promotes the use of ridge regression because the interaction term can result in multicollinearity. We showed that vine copula-based priors improve the estimation accuracy over the multivariate normal prior, and they would be a promising approach in other regression types, such as logistic regression. In this study, we focus on a case involving two covariates and their interaction terms, and propose a vine copula-based prior for Bayesian ridge estimators under a logistic model. Simulation and data analysis results show that Archimedean (Clayton and Gumbel) copula priors are superior to other priors (the Gaussian copula and trivariate normal priors) in the presence of multicollinearity. [ABSTRACT FROM AUTHOR]

It is crucial in industrial processes to consider key variables to ensure safe operation and high product quality. Moreover, these variables are difficult to obtain using traditional measurement methods; hence, it makes sense to develop soft sensor regression models to process the variable prediction. However, there are numerous variables integrating noisy and redundant information in complex industrial processes. Using such variables in traditional regression models may result in reducing the model's efficiency and performance. Thus, this paper proposes a multi‐layer feature ensemble soft sensor regression method using a stacked auto‐encoder (SAE) and vine copula (ESAE–VCR) to address these problems. To do so, the number of neurons in the hidden layer of the SAE is determined by the principal component analysis (PCA). The multi‐layer features of the process variables are extracted using a stacked AE, and the regression models are established for each feature layer. A linear regression ensemble method is used to combine the regression models with the multi‐layer features to obtain the final predictive model that will estimate the values of the key variables. The effectiveness and practicality of the ESAE–VCR are validated by comparing them with several common soft measurement methods in two examples. In the numerical example, the ESAE–VCR yields an accuracy of prediction (R2) of 0.9898 and a root mean square error (RMSE) of 0.1804. In the industrial example, the ESAE–VCR yields an R2 of 0.9908 and an RMSE of 0.1205. [ABSTRACT FROM AUTHOR]

Current practice in predicting future weather is the use of numerical weather prediction (NWP) models to produce ensemble forecasts. Despite of enormous improvements over the last few decades, they still tend to exhibit bias and dispersion errors and, consequently, lack calibration. Therefore, these forecasts may be improved by statistical postprocessing. In this work, we propose a D‐vine‐copula‐based postprocessing for 10 m surface wind speed ensemble forecasts. This approach makes use of quantile regression related to D‐vine copulas, which is highly data driven and allows one to adopt more general dependence structures as the state‐of‐the‐art zero‐truncated ensemble model output statistic (tEMOS) model. We compare local and global D‐vine copula quantile regression (DVQR) models to the corresponding tEMOS models and their gradient‐boosting extensions (tEMOS‐GB) for different sets of predictor variables using one lead time and 60 surface weather stations in Germany. Furthermore, we investigate which types of training periods can improve the performance of tEMOS and the D‐vine‐copula‐based method for wind speed postprocessing. We observe that the D‐vine‐based postprocessing yields a comparable performance with respect to tEMOS if only wind speed ensemble variables are included and to substantial refinements if additional meteorological and station‐specific weather variables are integrated. As our main result, we note that, in the global setting, DVQR is able to provide better scores than tEMOS‐GB in general, whereas the local DVQR is able to substantially outperform the local tEMOS‐GB at particular stations admitting nonlinear relationships among the variables. In addition, we remark that training periods capturing seasonal patterns perform the best. Last but not least, we adapt a criterion for calculating the variable importance in D‐vine copulas and we outline which predictor variables are due to this approach the most important for the correction of wind speed ensemble forecasts. [ABSTRACT FROM AUTHOR]

Dependence among different cyber risk classes is a fundamentally underexplored topic in the literature. However, disregarding the dependence structure in cyber risk management leads to inconsistent estimates of potential unintended losses. To bridge this gap, this article adopts a regulatory perspective to develop vine copulas to capture dependence. In quantifying the solvency capital requirement gradient for cyber risk measurement according to Solvency II, a dangerous paradox emerges: an insurance company does not tend to provide cyber risk hedging products as they are excessively expensive and would require huge premiums that it would not be possible to find policyholders. [ABSTRACT FROM AUTHOR]

We consider structural breaks and use vine copulas to hierarchically model the underlying assets' dependence structure of the portfolio of G7 equity market indices (1998–2019). This framework is noticed for its flexibility in capturing asymmetry and non-linearity in a time-varying style. We compare the portfolio performance in terms of the minimum Conditional Value-at-risk (CVaR) and the maximum return-to-CVaR ratio criteria with the traditional mean-variance framework and the equal-weighted strategy. The outcomes show the outperformance of our method across subperiods. Canonical vine copula marginally outperforms drawable vine copula in terms of return-to-risk ratio. Our proposed vine copula models better capture the risk-return tradeoff especially during critical market moments. [ABSTRACT FROM AUTHOR]

This research investigates the utilization of copula functions in the water resources field, encompassing meteorological and hydrological aspects. A review of the Web of Sciences archive revealed 15143 studies featuring copula keywords. Notably, 40% of these studies pertain to copula-based simulation within this field. Groundwater studies were the least conducted, accounting for only 3% of all studies in the field. Regarding copula functions, studies were generally divided into two parts: frequency analysis and simulation, encompassing all dimensions of copula functions. Researchers confirmed the performance of copula functions in both parts. Studies in copula functions have revealed a new approach in joint frequency analysis and conditional probability estimation, based on the marginal distribution of data and their conditional density. The results indicate that in more than 2 dimensions, the tree sequence of vine copula has reduced computational complications and allows for the determination of different structures based on independent and dependent variables. Various studies have shown that the use of copula functions has been successful due to its lack of assumptions and restrictions and has good performance. For this reason, this approach is considered. The approach has been increasingly utilized in 2-dimensions and multi-variables, and continues to progress and develop.

To use energy generated in wind farms (WFs), which contain uncertainty in their output, as a primary power source in a power system, a sophisticated balancing operation scheme is required. This study focuses on a balancing group (BG) scheme combining WFs and a variable-speed pumped-storage hydro generator (PSHG), which has a large capacity to compensate for the WF output. The proposed BG operational scheduling approach aims to maximize the expected revenue obtained in the day-ahead power market under the uncertainty in WF output and market price by considering the operational constraints of the PSHG, i.e., the water storage capacity and frequency of operation for switching pump-up/-down. In such a BG scheme, it is crucial to consider time-varying and time-dependent uncertainties in WF output to manage PSHG capacity constraints, as well as to derive a reasonable plan in practical computation time. The proposed BG operational scheduling scheme derives a set of WF output scenarios that represents the heterogeneous and time-dependent characteristics of real-world WF output behavior from probability density distributions derived by a cutting-edge prediction approach and implements the expected revenue maximization problem with scenario-based chance constraints of water storage transition by introducing computationally effective iterative optimization algorithm based on surrogate functions. Simulation results suggest that the proposed scheme provides an effective BG operation by considering the uncertainty in the WF output.

Reliable and easy-to-implement predictions of hydrometeorological variables are important for policymaking and public security. In this study, we developed a probabilistic framework for the description of hydrometeorological high-dimensional dependence and prediction by first-time coupling the principle of maximum entropy (POME) with C-vine copulas (PC). Two case studies with different emphases were investigated to evaluate the application of the PC framework. In the first case, we tested the PC framework based on a one-month-ahead streamflow forecast at the outlet station of the Jinsha River Basin. Results indicated that: (1) the marginal probability distributions or margins derived from optimal-moment-based POME best represented the current state of knowledge compared with those from traditional parametric distributions, and (2) the PC framework produced more skillful forecasts than did the traditional parametric C-vine (TC) and three data-driven models. The second case verified the performance of the PC framework in nationwide summer drought identification. Results of visual comparison of two typical historical summer drought events indicated that the PC framework captured the spatio-temporal characteristics of droughts. The PC framework combines the respective advantages of POME and C-vine copulas, ensuring its potential in higher-dimensional hydrometeorological modeling and flexibility in extending to other fields. [ABSTRACT FROM AUTHOR]