Search

• The temporal patterns of extreme hydrometeorological events in the Hanjiang River Basin (HRB) were revealed. • The joint occurrence probability of bivariate extreme hydrometeorological events was analyzed. • An analysis framework for the coincidence probability of extreme hydrometeorological events was proposed. Extreme hydrometeorological events are often highly destructive and can cause huge damage to the natural environment and social economy. As climate change and human activities intensify, the frequency and intensity of such extreme events continue to increase. This phenomenon is also shown in the Hanjiang River Basin (HRB) in recent decades. In this study, we focus on the coincidence occurrence patterns of extreme hydrometeorological events. First, we used the standardized index method to extract the annual maximum and minimum values of runoff, precipitation, maximum and minimum temperatures from 1961 to 2019 in the control area of the Baihe (BH) hydrological station, with time scales from 1 month to 12 months. Then through the Copula and nested structure Copula functions, the joint occurrence probability of bivariate and multivariate were analyzed. The results show that too high a maximum temperature will inhibit runoff, while an increase in minimum temperature will promote an increase in runoff to a certain extent. Both the maximum and minimum temperatures in the basin shown a significant increasing trend, and the intensity of hydrological drought also shows an increasing trend. An increase in maximum temperature will aggravate hydrological drought, as the combined joint occurrence probability of them is the greatest. Analysis through the nested structure Copula functions show that when extreme hydrometeorological events both occurred at the median of their intervals, their coincidence occurrence probability is the maximum, and when the time scale is eight months, their coincidence occurrence probability is the highest. This study can provide a reference for joint probability analysis of extreme hydrometeorological events. [ABSTRACT FROM AUTHOR]

• The integrated framework can reveal joint encounter and state evolution of short-duration rainstorms. • It's more sensitive to the changes in their probability of 0.2–0.7 and the JRPRE of 15-30freq. • The probability of synchronous F-L between P and R is greater. • The transition probability and limit probability of the F/H and F-H are large. • The P and R usually appear in the evolutionary state with the highest risk. In this study, in order to reveal the joint encounter and state evolution characteristics of urban short-duration rainstorms, a case study is conducted in Zhengzhou city, China. The joint probability distribution model of total rainfall (P) and peak rainfall (R) is constructed by using the Copula function, and their joint encounter and joint return period are analyzed. Additionally, the state evolution characteristics of P and R are explored by incorporating with the Markov chain. The results show that: (1) there is a good correlation between P and R under different rainfall durations. The Clayton Copula function is found suitable for 0.5 h and 1 h rainfall durations, while the Frank Copula function is selected for the 1.5 h rainfall duration. The P and R are more densely distributed in the joint probability interval of 0.2–0.7 and the joint return period of rainfall events (JRPRE) of 15-30freq, which are particularly sensitive to the changes in the corresponding intervals. (2) The probability of synchronous rich (F)-low (L) between P and R is greater than that of asynchronous F-L. The probability of synchronous F-L increases with longer rainfall durations, reaching the highest value of 74.92 % for the 1.5 h rainfall duration. (3) The transition probability and limit probability of the F/high (H) state and F-H combination state are relatively large, indicating that P and R exhibit strong self-conservation. These states are associated with the highest risk and tend to occur more frequently with shorter average return periods of rainfall events (ARPRE). The findings are valuable in uncovering the occurrence patterns of short-duration rainstorms and facilitating measures to mitigate waterlogging, thereby supporting urban sustainable development. [ABSTRACT FROM AUTHOR]

• The nonstationarity is incorporated into drought propagation analysis. • 20% is the optimal conditional probability to determine the propagation threshold. • The nonstationarity framework improves the accuracy of hydrological drought identification. Accurate drought warnings in changing environments remain challenging since the nonstationary behaviors of drought propagation. The novelty of this study is the presentation of a nonstationary framework for drought propagation analysis and the objective determination of drought propagation thresholds. The calculated propagation probabilities and thresholds are responsive to changing environments. The Generalized Addictive Models in Location, Scale and Shape (GAMLSS) and time-varying Clayton copula function were adopted to establish the nonstationary joint distribution between meteorological and hydrological drought indices. Several indices reflecting the climatic and anthropic impacts on hydrological process were selected as covariates. Combined with the conditional probability distribution function, the time-varying drought propagation probabilities can be estimated to describe the watershed drought tolerance variations. The receiver operator characteristic (ROC) curves were utilized to determine the propagation thresholds for drought warnings. The upper Yellow River Basin (UYRB) was selected as the study area. Results indicate that the nonstationary models show better fitting performance for two drought indices series. The Clayton copula function with dynamic parameters offers a more accurate description of the linkages between two types of drought. The analysis of watershed drought tolerance reveals a declining trend from June to October, contrasting with an increasing trend during other months. In comparison to the stationary approach, the hit rates of the proposed method improve by 0.18, reaching 0.88, while the false alarm rates decrease by 0.11, reaching 0.24. The criteria for propagation threshold determination in the UYRB is established as a conditional probability of 20%. These findings can provide a foundation for drought warning management in a changing environment. [ABSTRACT FROM AUTHOR]

The copula functions have been widely applied as an advance technique to create joint probability distribution of drought duration and severity. The approach of data collection as well as the amount of data and dispersion of data series can last a significant impact on creating such joint probability distribution using copulas. Usually, such traditional analyses have shed an Unconnected Drought Runs (UDR) approach towards droughts. In other word, droughts with different durations would be independent of each other. Emphasis on such data collection method causes the omission of actual potentials of short-term extreme droughts located within a long-term UDR. Meanwhile, traditional method is often faced with significant gap in drought data series. However, a long-term UDR can be approached as a combination of short-term Connected Drought Runs (CDR). Therefore this study aims to evaluate systematically two UDR and CDR procedures in joint probability of drought duration and severity investigations. For this purpose, rainfall data (1971–2013) from 24 rain gauges in Lake Urmia basin, Iran were applied. Also, seven common univariate marginal distributions and seven types of bivariate copulas were examined. Compared to traditional approach, the results demonstrated a significant comparative advantage of the new approach. Such comparative advantages led to determine the correct copula function, more accurate estimation of copula parameter, more realistic estimation of joint/conditional probabilities of drought duration and severity and significant reduction in uncertainty for modeling. [ABSTRACT FROM AUTHOR]

Cost-benefit analysis and flood frequency analysis have been integrated into a comprehensive framework to estimate cost effective design values. However, previous cost-benefit based extreme flood estimation is based on stationary assumptions and analyze dependent flood variables separately. A Non-Stationary Cost-Benefit based bivariate design flood estimation (NSCOBE) approach is developed in this study to investigate influence of non-stationarities in both the dependence of flood variables and the marginal distributions on extreme flood estimation. The dependence is modeled utilizing copula functions. Previous design flood selection criteria are not suitable for NSCOBE since they ignore time changing dependence of flood variables. Therefore, a risk calculation approach is proposed based on non-stationarities in both marginal probability distributions and copula functions. A case study with 54-year observed data is utilized to illustrate the application of NSCOBE. Results show NSCOBE can effectively integrate non-stationarities in both copula functions and marginal distributions into cost-benefit based design flood estimation. It is also found that there is a trade-off between maximum probability of exceedance calculated from copula functions and marginal distributions. This study for the first time provides a new approach towards a better understanding of influence of non-stationarities in both copula functions and marginal distributions on extreme flood estimation, and could be beneficial to cost-benefit based non-stationary bivariate design flood estimation across the world. [ABSTRACT FROM AUTHOR]

This paper highlights the usefulness of the minimum information and parametric pair-copula construction (PCC) to model the joint distribution of flood event properties. Both of these models outperform other standard multivariate copula in modeling multivariate flood data that exhibiting complex patterns of dependence, particularly in the tails. In particular, the minimum information pair-copula model shows greater flexibility and produces better approximation of the joint probability density and corresponding measures have capability for effective hazard assessments. The study demonstrates that any multivariate density can be approximated to any degree of desired precision using minimum information pair-copula model and can be practically used for probabilistic flood hazard assessment. [ABSTRACT FROM AUTHOR]

• A deep convolutional generative adversarial network (DCGAN) combined with Wasserstein generative adversarial network (WGAN) called DC-WGAN is proposed as a runoff generation model. • A runoff generation method based on Copula function is developed. • The applicability of DC-WGAN in the field of runoff stochastic generation for a reservoir system is verified. • The spatial–temporal correlation of runoff samples of DC-WGAN compared with the Copula function is analyzed. The implicit stochastic optimization (ISO) model is a methodology that has been extensively employed in the mid-long term optimal operation of a reservoir system. The generation of runoff series is the key technology to make up for the poor representativeness and reliability of historical runoff samples and is the premise to guarantee the accuracy of the ISO model. However, the traditional methods are not suitable for the stochastic generation of runoff series, among reservoirs with spatial–temporal correlation. In this work, the generative adversarial network called DC-WGAN is developed as a runoff generation model. DC-WGAN is based on a data-driven model and can capture the correlation of runoff series in time and space dimensions simultaneously. The proposed method is applied to the downstream Jinsha river cascade and Three Gorges cascade reservoirs in China to generate ten-day runoff series and is compared with the stochastic generation method based on Copula function. The focus of this paper is the model's performance in replicating the spatial–temporal correlation of ten-day runoff series. Results are as follows. (1) DC-WGAN has strong learning and generalization ability, which can learn the correct distribution of original runoff samples and generate runoff series similar to that from the validation set. (2) The runoff series among reservoirs with spatial–temporal correlation can be generated through DC-WGAN without assuming the probability distribution of samples in advance. (3) DC-WGAN is better than Copula function in capturing the spatial–temporal correlation, especially the moderate and weak correlation. The proposed methodology has a high practical value and application prospect for the stochastic generation of runoff series with spatial–temporal correlation. [ABSTRACT FROM AUTHOR]

Highlights: [•] The method of deriving copula-based low flow distributions is proposed. [•] Statistical dependence is detected among the characteristics of low flow event. [•] Copula-based derived distributions can perform well against observations. [•] Choice of marginal distributions is important in copula-based derived distribution. [•] It is useful to study the impacts of climate change/human activities on low flows. [ABSTRACT FROM AUTHOR]

• Drought risk framework is adopted based on a nonstationary drought index and multivariate copulas. • Drought encounter risks among three GPZs were fully evaluated at different situations. • The Songnen Plain is least likely to encounter drought with other two GPZs. • The joint probabilities of droughts occur in the three GPZs could provide strategies for food security. Better understanding for the likelihood of drought occur in the main grain production zones of China is key to minimize the risk for food security, especially in a changing climate. In an attempt to encompass the climate variability in the assessment of drought, a nonstationary standardized precipitation index (NSPI) was established for three major grain production zones (Songnen Plain (SN), North China Plain (NC), and Sichuan Basin (SC), hereinafter referred to GPZs) by means of using the climate indices as covariates. Then three commonly used Archimedean copulas (i.e., Clayton, Frank, and Gumbel-Hougaard) were adopted to determine the joint drought probability model. Using the joint probability distribution, the risk of drought in different degree occurring among the three GPZs, conditional joint probability, and conditional return period of different drought combinations of GPZs were analyzed. The results show that NSPI reflected the drought conditions well in three GPZs, and the copula-based joint probability distributions of different drought situations among the three GPZs were reasonable. For the situation of droughts encounter in two GPZs, synchronous droughts in different degree are more prone to encounter in NC & SC, and the conditional joint drought probability (return period) is also higher (lower) in the combination of SC and NC. For the situation of droughts encounter in three GPZs, the probability of synchronous droughts in the three GPZs is decreasing with increase of drought degree. If a specifically drought (NSPI ≤ -1) occurred in two GPZs, the conditional joint drought probability is highest in NC, then followed by SC, and SN. The findings of this study could provide important implications of decision-making for food security. [ABSTRACT FROM AUTHOR]

Summary: Design storms with standardized hyetograph shapes and selected combinations of storm depths and durations are widely used in engineering hydrology. The key distinguishing feature between equal-duration design storms is their distinct intensity distributions. Differences in design storm hyetographs do not affect storm frequency, since only the frequency of the combination of storm depth and duration are determined through the use of Depth–Duration–Frequency curves. Probability distributions of peak intensity within rainfall events are not determined in current practice. Some current research applies copulas to joint distributions of rainstorm variables, but most of these are limited to bivariate distributions, and those that are developed for trivariate distributions do not address key variables important to everyday practice, or are limited by complexity of analysis. An alternative approach to characterizing peak storm intensity, intensity peak factor, together with its probability distribution is developed in this paper. An Archimedean copula is applied to describe the joint probability distribution of storm duration with intensity peak factor. That joint distribution is combined with the probability distribution of storm depth, to produce a joint probability distribution for storm depth, duration, and peak intensity. The result is a simple approach to fully characterizing the storm variables of direct interest to practitioners, thereby providing a complete probabilistic description of the return period or frequency of a selected design storm. [Copyright &y& Elsevier]

Summary: In hydrology, one often needs to model two dependent variables; regardless of the marginal distribution that each of them follows, while still taking account of the dependence structure that exists between them. In this respect, the use of copulas to model the dependence between the two variables has been found to be attractive. However, the use of copulas for bivariate modeling in previous applications has been restrictive, in the sense that it has focused exclusively on copulas expressible by a simple mathematical form, while ignoring a wide class of other bivariate models that are available to the practitioner. These other models were not given the attention that they deserve, because it was wrongly assumed that they are not flexible enough to allow for different marginal distribution families to be chosen for the two variables that are being modeled. In this article, we shed more light on this class of models, by presenting three specific members of this class, and showing their usefulness through hydrological applications. The results of these applications show that the suggested models have their own dependence structures, and need to be given the same level of consideration in hydrology as the more popular copula models. There is in fact a need in hydrology to consider a wide variety of bivariate models, especially if each model has its own distinctive dependence structure, and given the wide variety of dependence structures that the hydrologist might encounter. The main purpose of this paper is therefore to encourage the exploration of a wider class of potentially useful bivariate models that hydrologists need to consider. [Copyright &y& Elsevier]

Summary: Current drought information is based on indices that do not capture the joint behaviors of hydrologic variables. To address this limitation, the potential of copulas in characterizing droughts from multiple variables is explored in this study. Starting from the standardized index (SI) algorithm, a modified index accounting for seasonality is proposed for precipitation and streamflow marginals. Utilizing Indiana stations with long-term observations (a minimum of 80 years for precipitation and 50 years for streamflow), the dependence structures of precipitation and streamflow marginals with various window sizes from 1- to 12-months are constructed from empirical copulas. A joint deficit index (JDI) is defined by using the distribution function of copulas. This index provides a probability-based description of the overall drought status. Not only is the proposed JDI able to reflect both emerging and prolonged droughts in a timely manner, it also allows a month-by-month drought assessment such that the required amount of precipitation for achieving normal conditions in future can be computed. The use of JDI is generalizable to other hydrologic variables as evidenced by similar drought severities gleaned from JDIs constructed separately from precipitation and streamflow data. JDI further allows the construction of an inter-variable drought index, where the entire dependence structure of precipitation and streamflow marginals is preserved. [Copyright &y& Elsevier]