Multivariate Frequency Analysis of Meteorological Drought Using Copula

The multivariate frequency analysis of droughts for Agartala (India) was carried out in the present study. The meteorological drought was modelled using Standardised Precipitation Index(SPI) at the time scale of 1, 3, 6 and 12 months. Three droughts variables i.e., duration, severity, interval were determined for SPI at the time scale of 1, 3, 6 and 12 months. For the construction of bivariate and trivariate joint distributions Archimedean and metaelliptical copulas were used. Upper tail dependence test was also carried out. The best copula was selected based on minimum value Akaike’s information criteria (AIC)) and Schwarz information criterion(SIC). The drought risk was estimated using joint probabilities and return period for the study area.     

Comparison of the Calculated Drought Return Periods Using Tri-variate and Bivariate Copula Functions Under Climate Change Condition

Water Resources Management - Concerning the various effects of climate change on intensifying extreme weather phenomena all around the world, studying its possible consequences in the following...     

Drought Monitoring Using the Multivariate Standardized Precipitation Index (MSPI)

One major characteristic of the Standardized Precipitation Index (SPI) is its flexibility to be calculated in a variety of time scales and hence being aware of different types of droughts. However, various time scales may result in confusion of the water resources’ researchers, decision makers and users in identifying and specifying drought periods in a certain region. To solve this problem in this article, a multivariate approach has been utilized having the ability to aggregate a variety of the SPI time series into a new time series called the Multivariate Standardized Precipitation Index (MSPI). The MSPI is based on the principal components analysis (PCA) of the SPI time series in a certain location. Having specified the first principal component’s (PC₁’s) scores, the MSPI would be simply attained by dividing PC₁’s values by the monthly standard deviation. In this article, MSPI’s capability in depicting the variability of the SPI time series (in five ranges of time scales, including 3–6, 6–12, 3–12, 12–24, and 24–48 months) was studied at four weather stations representing the four different climates in Iran from the driest to the wettest climates. The results showed that the PC₁ is able to justify more than 74 % of the variability for the selected sets of the SPI time scales in the studied climates. Also, it became clear that the drought and wet severity classes monitored by MSPIs matched very satisfyingly to those of the five sets of the SPI time scales. Therefore, in cases where the aggregation time scales for calculating the SPI are not previously known, this study recommends the researchers use the MSPI.     

Multivariate Flood Frequency Analysis Using Bivariate Copula Functions

Water Resources Management - Multivariate analysis of flood frequency was used extensively in water resources research. Often the only flood peak or volume is analyzed with statistical...     

Multivariate Drought Frequency Analysis using Four-Variate Symmetric and Asymmetric Archimedean Copula Functions

In drought frequency analysis, as the number of drought variables increases, the joint behavior between these variables needs to be studied. Therefore, this study aims to develop a flexible four-variate joint distribution function of the regional stochastic nature of drought. Using run theory, drought duration, severity, peak, and inter-arrival time were abstracted from the Standardized Precipitation Evapotranspiration Index (SPEI) aggregated at six months, observed in mainland China between 1961 and 2013. As these drought variables showed significant dependence properties and followed different marginal distributions, we employed and compared six four-variate symmetric and asymmetric Archimedean copulas (i.e., Frank, Clayton, Gumbel–Hougaard). The best-fitting model for each region was carefully selected using RMSE, AIC, and BIAS goodness-of-fit tests. Results revealed that the empirical and theoretical probabilities of the symmetric Clayton in regions NE (Northeast), CS (Central and Southern China), EMC (Entire China), and symmetric Frank in regions NC (North China), SC (South China), IM (Inner Mongolia), NW (Northwest), TP (Tibet Plateau) agreed well. Symmetric Frank copula was considered the best-fit for station-based drought analysis in EMC. Based on these copulas, the drought probabilities and return periods for the occurrence of drought events over the next 5, 10, 20, 50, and 100 years in each region were hereby comprehensively explained, and the results shown here could be helpful in the appraisal of the adequacies of water supply systems under drought conditions in all regions. This study showed that a four-variate copula approach is a vital tool for probabilistic interpretation of hydrological and meteorological data in the different climatic region of mainland China.

     

基于Copula函数的鄱阳湖都昌站枯水多变量频率分析

以鄱阳湖湖区都昌水文站1958—2007年长系列日平均水位资料为基础,采用干旱分析中应用广泛的游程理论进行湖泊枯水的识别,提取枯水历时、平均枯水强度和最大枯水强度作为湖泊枯水特征变量;采用Archimedean Copula函数构造了变量的联合分布,分析了枯水事件出现的概率,计算了枯水事件的联合重现期和条件重现期。结果表明Weibull分布、Logistic分布和GEV分布分别适于作为干旱历时、平均枯水强度和最大枯水程度的边缘分布函数;Clayton Copula函数适于都昌站枯水多变量联合分布的拟合;联合分布考虑了枯水事件多个变量之间的相关性,能提供更多的湖泊枯水特征信息,更能全面揭示湖泊枯水的概率统计特征。     

The Impact of Climate Change on Hydro-Meteorological Droughts Using Copula Functions

Climate change has made many alterations to the climate of earth, including hydro-climatic extreme events. To investigate the impact of climate change on hydro-meteorological droughts in the Kamal-Saleh dam basin in Markazi province, Iran, proportional to future climate conditions, a new and comprehensive index was developed with the aim of accurately estimating drought in a more realistic condition. This aggregate drought index (ADI) represented the main meteorological and hydrological characteristics of drought. Temperature and precipitation projections for future climates were simulated by five CMIP5 models and downscaled over the study area during 2050s (2040–2069) and 2080s (2070–2099) relative to the baseline period (1976–2005). By fitting five univariate distribution functions on drought severity and duration, proper marginal distributions were selected. The joint distribution of drought severity and duration was chosen from five types of copula functions. The results revealed that in future, severe droughts are expected to frequently occur in a shorter period.

     

Uncertainty-Driven Characterization of Climate Change Effects on Drought Frequency Using Enhanced SPI

The Standardized Precipitation Index (SPI) is a well-established drought index that is based on transforming the interannual distribution of precipitation to a standard normal distribution. Because of its robust statistical basis, SPI is readily applicable to different regions making comparisons between locations and time windows possible. Nevertheless, the usability of SPI results is undermined by shortcomings that are partly resultant from data and model uncertainties. One such shortcoming is the inability of the existing SPI model to include change in variability of interannual precipitation from non-stationary normal – mostly caused by climate change. In addition, epistemic uncertainty in the form of incompleteness in station-wide precipitation records results in heterogeneity and inconsistency in SPI results. The effects of such epistemic uncertainty on the accuracy of estimations of long-term changes in drought frequency are mostly unknown. Given such deficiency, SPI’s procedure and subsequent results remain deterministic and inadequately informative. Here, we introduce modifications to the traditional SPI using Dempster-Shafer theory (DST) to enable modeling and propagation of variability and epistemic uncertainty with the regular SPI procedure. By generalizing the SPI model from a deterministic setting to an “uncertainty-driven setting” provided by DST, this work makes possible: (a) efficiently propagating data uncertainty in interpolation of station-wide precipitation and SPI, and (b) modeling the effects of shift in precipitation normals (due to e.g., climate change) on drought frequency. In addition, the significance of this shift may then be evaluated with respect to the epistemic uncertainty by measuring how much of the surrounding epistemic uncertainty this shift encloses (i.e., “probability of enclosing”). The latter is especially important due to large unknowns already associated with climate change modeling. We implement the model on summer extreme drought for the Okanagan Basin, BC, Canada. For a single general circulation model and scenario (CGCM3 A2) a maximum 7 % increase in summer extreme drought (for 2080s, as per current definition) is estimated with a maximum probability of enclosing of 36 %.     

Scenario Assessment of Streamflow Simulation and its Transition Probability in Future Periods Under Climate Change

The effect of climate change on water resources is an important challenge. To analyze the negative effects of this phenomenon and recommend adaptive measures, it is necessary to assess streamflow simulation scenarios and streamflow transition probabilities in future periods. This paper employs the HadCM3 (Hadley Centre Coupled Model, version 3) model to generate climate change scenarios in future periods (2010–2039, 2040–2069, and 2070–2099) and under A2 emission scenarios. By introducing climatic variable time series in future periods to the IHACRES (Identification of unit Hydrographs And Component flows from Rainfall, Evaporation and Streamflow data) hydrological model, long-term streamflow simulation scenarios are produced. By fitting statistically different distributions on runoff produced by using goodness-of-fit tests, the most appropriate statistical distribution for each month is chosen and relevant statistical parameters are extracted and compared with statistical parameters of runoff in the base period. Results show that long-term annual runoff average in the three future periods compared to the period 2000–1971 will decrease 22, 11, and 65 %, respectively. ?Despite the reduction in total runoff volume in future periods compared to the baseline period, the decrease is related to medium and high flows. In low flows, total runoff volumes for future periods compared to the baseline period will increase 47, 41, and 14 %, respectively. To further assess the impact of annual average runoff on flows, it is necessary to examine the correlation of time series using streamflow transition probabilities. To compare the streamflow transition probability in each of the future periods with base period streamflow in each month, streamflow is discretized and performance criteria are used. Results show a low coefficient of correlation and high error indicators.     

Valuation of Drainage Infrastructure Improvement Under Climate Change Using Real Options

Valuation of infrastructure systems under climate change is a challenging issue because climate changes constantly and the influence of climate change is hardly predictable. Serious climate change effects can often be represented by frequent heavy rainfall events and floods. In response, municipalities should improve existing drainage systems to adapt to climate change. However, it is difficult to properly determine when or how to improve these systems because different investment strategies could result in entirely different outcomes. This study proposes a decision framework that can assist municipalities in identifying an optimal infrastructure investment strategy under climate change using a real option approach. The framework considers the uncertainties of climate change based on the volatility of flood damage and estimates the value of wait option for the improvement investment using binomial model. A case study is conducted to verify the proposed framework and assess how different investment strategies affect the value of a drainage system. The results showed that the system improvement with 100 year-flood design in 2019 was the most beneficial among available alternatives.     

Development of a Non-stationary Standardized Precipitation Evapotranspiration Index (NSPEI) for Drought Monitoring in a Changing Climate

In a changing climate, drought indices as well as drought definitions need to be revisited because some statistical properties, such as the long-term mean, of climate series may change over time. This study aims to develop a Non-stationary Standardized Precipitation Evapotranspiration Index (NSPEI) for reliable and robust quantification of drought characteristics in a changing climate. The proposed indicator is based on a non-stationary log-logistic probability distribution, assuming the location parameter of the distribution is a multivariable function of time and climate indices, as covariates. The optimal non-stationary model was obtained using a forward selection method in the framework of the Generalized Additive Models in Location, Scale, and Shape (GAMLSS) algorithm. The Non-stationary and Stationary forms of SPEI (i.e., NSPEI and SSPEI) were calculated using the monthly precipitation and temperature data of 32 weather stations in Iran for the common period of 1964–2014. The results showed that almost at all the stations studied, the non-stationary log-logistic distributions outperformed the stationary ones. The AICs of the non-stationary models for 97% of the stations were lower than those of the stationary models. The non-stationary models at 90% of the stations were statistically significant at the 5% significance level. While SSPEI identified the long-term and continuous drought and wet events, NSPEI revealed the short-term and frequent drought/wet periods at almost all the stations of interest. Finally, it was revealed that NSPEI, compared to SSPEI, was a more reliable and robust indicator of drought duration and drought termination in vegetation cover during the severest drought period (the 2008 drought). Therefore, it was suggested as a suitable drought index to quantify drought impacts on vegetation cover in Iran.

     

基于多尺度SPI指数的哈巴河地区近53 a的干旱分析

为了对新疆哈巴河地区开展最新的旱情研究,以期全面了解该地区干旱特征及演变规律,基于不同时间尺度下的标准化降水指数(SPI)方法,分析了哈巴河地区1962—2014年间的干旱演变特征。结果表明①近53 a来,SPI指数方法在哈巴河地区有较高的适用性,不同时间尺度SPI皆可监测旱情变化,且与记载的流域实际旱情相符。②从SPI₁,SPI₃,SPI₆指数过程线可以看出,哈巴河地区发生不同干旱等级事件的概率为20%左右;SPI₃指数较SPI₁,SPI₆指数评价的旱情程度要重;SPI₁₂呈现显著的上升趋势,长时间尺度说明地区气候在逐步变湿,有助于减轻地区干旱。③不同季节SPI的年际过程差异显著,其中年SPI最小值为1963年的-1.97,53 a间发生轻旱、中旱、重旱等不同等级干旱事件的年份分别为9,4,0 a。④四季SPI发生轻旱级别以上干旱的年份约占26%~28%,平均约11 a。⑤冬季SPI呈增加趋势,其余季节及年SPI变化趋势不明显,且夏季SPI与年SPI过程较为相似。研究结果可为区域旱情监测与预警、风险管理提供科学依据。     

Assessing Socioeconomic Drought Based on a Standardized Supply and Demand Water Index

Socioeconomic drought occurs when a water shortage is caused by an imbalance between the supply and demand of water resources in natural and human socioeconomic systems. Compared with meteorological drought, hydrological drought, and agricultural drought, socioeconomic drought has received relatively little attention. Hence, this study aims to construct a universal and relatively simple socioeconomic drought assessment index, the Standardized Supply and Demand Water Index (SSDWI). Taking the Jianjiang River Basin (JJRB) in Guangdong Province, China, as an example, we analyzed the socioeconomic drought characteristics and trends from 1985 to 2019. The return periods of different levels of drought were calculated. The relationships among socioeconomic, meteorological, and hydrological droughts and their potential drivers were discussed. Results showed that: (1) SSDWI can assess the socioeconomic drought conditions well at the basin scale. Based on the SSWDI, during the 35-year study period, 29 socioeconomic droughts occurred in the basin, with an average duration of 6.16 months and average severity of 5.82. Socioeconomic droughts mainly occurred in autumn and winter, which also had more severe droughts than other seasons. (2) In the JJRB, the joint return periods of “∪” and “∩” for moderate drought, severe drought, and extreme drought were 8.81a and 10.81a, 16.49a and 26.44a, and 41.68a and 91.13a, respectively. (3) Because of the increasing outflow from Gaozhou Reservoir, the occurrence probability of socioeconomic drought and hydrological drought in the JJRB has declined significantly since 2008. Reservoir scheduling helps alleviate hydrological and socioeconomic drought in the basin.

     

An Analysis of Non-stationary Drought Conditions in Parana State Based on Climate Change Scenarios

Water Resources Management - Climate change affects the hydrological cycle and has a significant influence on water resources, which can lead to environmental and socioeconomic damage caused by...     

Accounting for Climate Change and Drought in Implementing Sustainable Groundwater Management

Groundwater provides close to 40% of California’s overall water supply under average hydrologic conditions. It is a critical source of backup during drought when increased pumping occurs to compensate for reduced surface supplies and decreased soil moisture. The conundrum is that in regions of the state where groundwater dependence is already high and rates of recharge are low, over the long term the volume withdrawn, particularly during droughts, generally exceeds replenishment in many regions. The result is overdraft - ongoing declines in groundwater levels over the long-term. To facilitate the reduction or cessation of long-term groundwater overdraft, this paper proposes that sustainable groundwater management must include the development of a drought reserve. The reserve, ideally sourced, sited and used locally, would encompass sufficient water for use during a drought such that the increased withdrawals during a drought do not result in unrecoverable groundwater declines and concomitant negative impacts. The objective is to reduce vulnerability to the state’s periodic droughts, as opposed to mitigating seasonal variations in precipitation. This paper first summarizes the issues associated with developing drought reserves, and then examines in detail how two California groundwater management agencies approach establishing and implementing a drought reserve.     

Quantifying the Contributions of Climate Change and Human Activities to Drought Extremes,Using an Improved Evaluation Framework

Water Resources Management - An increasing amount of studies have emphasized that more frequent and extensive extreme events have occurred around the world. The effects of climate change and...     

A New Non-stationary Hydrological Drought Index Encompassing Climate Indices and Modified Reservoir Index as Covariates

Due to accelerating climate variability and intensified anthropogenic activities, the hypothesis of stationarity of data series is no longer applicable, questioning the reliability of the traditional drought index. Thus, it is critical to develop a non-stationary hydrological drought index that takes into account the joint impacts of climate and anthropogenic changes in a drought assessment framework. In this study, using the Generalized Additive Model for Location, Scale and Shape (GAMLSS), a new Non-stationary Standardized Runoff Index (NSRI) was developed combining climate indices (CI) and modified reservoir index (MRI) as explanatory variables. This novel index was applied to the hydrological drought assessment of the Hanjiang River basin (HRB) in China, and its reliability was assessed by comparing with the traditional Standardized Runoff Index (SRI). Results indicated that the optimal non-stationary model with CI and MRI as covariates performed better than did other models. Furthermore, NSRI was more robust in identifying extreme drought events and was more effective in the study region than the conventional SRI. In addition, based on the method of Breaks for Additive Seasonal and Trend (BFAST), it was found that there were two change points in 1981 and 2003 for the NSRI series at four hydrological stations in the HRB, which indicated that hydrological drought in the basin had a prominent non-stationary behavior. Our findings may provide significant information for regional drought assessment and water resources management from a changing environment perspective.

     

基于PDSI指数的三江源干旱气候特征分析

根据三江源地区12个气象站点1971—2004年的气象资料,利用修正的Palmer旱度模式,计算分析了三江源地区PDSI指数的时空变化特征,并采用Morlet小波变换系数分析了PDSI指数的变化周期。结果表明:三江源地区有变干趋势,但变化趋势不显著,其中黄河源显著变干对三江源变干影响较大;三江源地区干旱发生年份与厄尔尼诺现象出现的年份基本相近;三江源地区西北较干旱、东南较湿润;经小波分析,三江源PDSI指数大约有20 a的第一主变化周期,与太阳双黑子活动周期相近,在20 a周期内还包括11～12 a和6 a的小周期;三江源干旱化与气候变暖、降水减少密切相关,尤其是夏、秋两季。     

Streamflow Forecast and Reservoir Operation Performance Assessment Under Climate Change

This study attempts to investigate potential impacts of future climate change on streamflow and reservoir operation performance in a Northern American Prairie watershed. System Dynamics is employed as an effective methodology to organize and integrate existing information available on climate change scenarios, watershed hydrologic processes, reservoir operation and water resource assessment system. The second version of the Canadian Centre for Climate Modelling and Analysis Coupled Global Climate Model is selected to generate the climate change scenarios with daily climatic data series for hydrologic modeling. Watershed-based hydrologic and reservoir water dynamics modeling focuses on dynamic processes of both streamflow generation driven by climatic conditions, and the reservoir water dynamics based on reservoir operation rules. The reliability measure describes the effectiveness of present reservoir operation rules to meet various demands which are assumed to remain constant for the next 100 years in order to focus the study on the understanding of the structure and the behaviour of the water supply. Simulation results demonstrate that future climate variation and change may bring more high-peak-streamflow occurrences and more abundant water resources. Current reservoir operation rules can provide a high reliability in drought protection and flood control.     

水文变异条件下基于Copula函数的非一致性干旱频率分析方法——以鄱阳湖为例

受环境变化的影响,时间序列的非一致性已对干旱频率分析造成越来越多的影响。针对目前干旱频率分析对时间序列“非一致性”考虑不足的问题,提出通过对时间序列的变异诊断、分时段干旱特征变量提取、Copula联合分布函数构建等过程,对水文变异条件下的非一致性干旱频率进行分析。以鄱阳湖为研究对象,采用非一致性干旱频率计算方法对湖口站1955—2015年的水位序列进行分析。结果显示:湖口站水位序列于2003年出现了跳跃向下的变异,水位变异后的干旱历时和干旱烈度比变异前均有所增大,同频率干旱事件的重现期存在较大幅度的缩减。鄱阳湖区有关水资源管理部门应尽快对干旱应对措施作出相应的调整,以适应水文变异带来的挑战。