Drought Characterisation Based on Water Surplus Variability Index

Drought assessment, characterisation and monitoring increasingly requires considering not only precipitation but also the other meteorological parameters such as an evapotranspiration. Thus, some new drought indices based on precipitation and evapotranspiration have been developed. This study introduces a new drought index named the water surplus variability index (WSVI). The procedure to estimate the index involves accumulation water surplus at different time scales. To approve the proposed procedure, the WSVI is compared with the standardized precipitation index (SPI), the reconnaissance drought index (RDI) and the standardized precipitation evapotranspiration index (SPEI) based on 1-, 3-, 6- and 12-month timescales using data from several weather stations located in regions with different aridity index. Near perfect agreement (d?~?1) between WSVI and SPI, RDI and SPEI was indicated in humid and sub-humid locations. The results also showed that the correlation coefficients between WSVI and SPI, RDI and SPEI were higher for semi-arid stations than for arid ones.     

基于双源蒸散与混合产流的Palmer 旱度模式构建及应用

选取半干旱地区老哈河流域为研究对象,基于双源蒸散发能力计算模型和混合产流模块,依据palmer旱度模式的思路,构建适用于我国北方半干旱地区的机理性旱度模式。利用该模式计算15个代表站点1957—2008年的旱度值,并与实际旱情记载以及降水距平百分率进行了对照检验。结果表明,该旱度模式计算的各地区的Palmer干旱指标与文献描述的干湿情况较为一致,能够反映所研究区域干旱程度的变化情况;与降水距平百分率相比,该模式综合考虑了水分亏缺量和持续时间因子对干旱强度的影响,可以反映流域下垫面特性及植被生理物候特性对干旱的影响机制,能够更好地表现干旱过程的持续性。此外,该模式还能合理给出旱情在空间上的发生和发展的变化情况。     

Fitting Drought Duration and Severity with Two-Dimensional Copulas

This study aims to model the joint drought duration and severity distribution using two-dimensional copulas. The method of inference function for margins (IFM method) is employed to construct copulas. Two separate maximum likelihood estimations of univariate marginal distributions are performed first, then followed by a maximization of the bivariate likelihood as a function of the dependence parameters. The drought duration and severity are assumed to be exponential and gamma distributions, respectively. Several copulas are tested to determine the best data fitted copula. Droughts, defined using the Standardized Precipitation Index (SPI), of Wushantou (Taiwan) are employed as an example to illustrate the proposed methodology. The copula fitting results for drought duration and severity are quite satisfactory. The bivariate drought analyses, including the joint probabilities and bivariate return periods, based on the derived copula-based joint distribution are also investigated to demonstrate the advantages of bivariate modeling of droughts.     

Evaluation of changes in RDI<Subscript>st</Subscript> index effected by different Potential Evapotranspiration calculation methods

Investigation of drought event has a great importance in the natural erctt management and water resources management planning. One of the important indexes of drought severity assessment is RDIst index, this index is B35based on ratio of precipitation (P) and potential evapotranspiration (PET) factors. Many different methods have been introduced for PET calculation. In this study results of monthly RDIst index (1 month) based on some popular PET calculation methods include: Jensen-Haise, Modified Jensen-Haise, Thornthwaite, Hargreaves-Samani, Blaney-Criddle and FAO Penman-Monteith (this method was used as reference method) with minimum data requirements were compared. In this research climatic data of 17 synoptic stations (with different climate conditions) in Iran during 1967–2014 were used to estimate PET and monthly RDIst index. Results of this paper showed that different methods of PET calculation had significant impact on RDIst index. According to results based on RMSE index Hargreaves- Samani had the most similarities with FAO Penman-Monteith method. Based on means comparison test, Blaney-Criddle and Modified Jensen-Haise methods had the most similarities with FAO Penman-Monteith (mean of RDIst index in 58.8% of stations in Thornthwaite method, 52.9% of stations in Jensen-Haise and Hargreaves-Samani methods and 71% of stations in Blaney-Criddle and Modified Jensen- Haise methods had not different by FAO Penman-Monteith).     

基于Copula函数的水文干旱联合概率分布研究

双变量联合分布及重现期计算是水文干旱研究的重要内容。根据游程理论确定水文干旱事件,利用Copula函数建立干旱历时和烈度的联合分布,计算不同干旱事件的重现期。实例分析结果表明,联合分布可以考虑干旱历时与烈度不同组合情况,计算的联合重现期大于边际分布计算结果,泾河和北洛河最长历时干旱事件联合重现期为480 a和342 a。     

Temporal Hydrologic Alterations Coupled with Climate Variability and Drought for Transboundary River Basins

Climate change (CC) and drought episode impacts linked with anthropogenic pressure have become an increasing concern for policy makers and water resources managers. The current research presents a comprehensive methodology but simple approach for predicting the annual streamflow alteration based on drought indices and hydrological alteration indicators. This has been achieved depending on the evaluation of drought severity and CC impacts during the human intervention periods to separate the influence of climatic abnormality and measure the hydrologic deviations as a result of streamflow regulation configurations. As a representative case study, the Lesser Zab River Basin in northern Iraq has been chosen. In order to analyse the natural flow regime, 34 hydrological years of streamflow (1931–1965) prior to the main dam construction were assessed. The Indicators of Hydrologic Alteration (IHA) method has been applied to quantify the hydrological alterations of various flow characteristics. In addition, an easy approach for hydrological drought prediction in relatively small basins grounded on meteorological parameters during the early months of the hydrological year has been presented. The prediction was accomplished by implementing the one-dimensional drought examination and the reconnaissance drought index (RDI) for evaluating the severity of meteorological drought. The proposed methodology is founded on linear regression relations connecting the RDI of 3, 6, and 12 months and the streamflow drought index (SDI). The results are critical for circumstances where an early exploration of meteorological drought is obtainable. Outcomes assist water resources managers, engineers, policy makers and decision-makers responsible for mitigating the effects of CC.     

Analysing Drought Severity and Areal Extent by 2D Archimedean Copulas

Droughts can be considered as multidimensional hazardous phenomena characterised by three attributes: severity, duration and areal extent. Conventionally, drought events are assessed for their severity, using drought indices such as SPI (Standardised Precipitation Index), RDI (Reconnaissance Drought Index), PDSI (Palmer Drought Severity Index) and many others. This approach may be extended to incorporate the modelling of an additional dimension, the duration or the areal extent. Since the marginal distributions describing these dimensions of drought are often different, no simple mixed probability distribution can be used for the bivariate frequency analysis. The copula approach seems to be sufficiently general and suitable for this type of analysis. It is the aim of this paper to analyse droughts as two-dimensional phenomena, including drought severity and areal extent. In this paper, the Gumbel-Hougaard copula from the Archimedean family is used for this two-dimensional frequency analysis. Annual data on historical droughts from Eastern Crete are analysed for their severity and areal extent, producing copula-based probability distributions, incorporating Gumbel marginal probability functions. Useful conclusions are derived for estimating the «OR» return period of drought events related to both severity and areal extent.     

Drought Monitoring by Reconnaissance Drought Index (RDI) in Iran

Drought is one of the most important natural hazards in Iran and frequently affects a large number of people, causing tremendous economic losses, environmental damages and social hardships. Especially, drought has a strong impact on water resources in Iran. This situation has made more considerations toward the study and management of drought. The present study is focused on two important indices; SPI and RDI, for 3, 6, 9, 12, 18 and 24 months time scales in 40 meteorological synoptic stations in Iran. In the case of RDI computation, potential evapotranspiration was an important factor toward drought monitoring. So, evapotranspiration was calculated by Penman-Monteith equation. The correlation of RDI and SPI was also surveyed. Drought severity maps for SPI and RDI were also presented in the driest year (1999–2000). The present results have shown that the correlation of SPI and RDI was more considerable in the 3, 6 and 9 months than longer time scales. Furthermore, drought severity maps have shown that during 1999–2000, the central, eastern and south-eastern parts of Iran faced extremely dry conditions. While, according to SPI and RDI trends, other parts of the country suffered from severe drought. The SPI and RDI methods showed approximately similar results for the effect of drought on different regions of Iran. Since, RDI resolved more climatic parameters, such as evapotranspiration, into account which had an important role in water resource losses in the Iranian basins, it was worthwhile to consider RDI in drought monitoring in Iran, too.     

Using the Fuzzy Clustering and Principle Component Analysis for Assessing the Impact of Potential Evapotranspiration Calculation Method On the Modified RDI Index

The modified reconnaissance drought index (RDIe) which is a modified version of RDI is presented for assessing drought conditions with an emphasis on agricultural drought. The potential evapotranspiration (PET) and effective rainfall are required climatic variables to calculate RDIe. Although the FAO Penman–Monteith (FPM) equation is the reference method for determining the PET, due to the need for data of a large number of climatic variables it is difficult to use in areas with shortage climatic data. Therefore, in this research, using the fuzzy clustering (FC) and principle component analysis (PCA) methods, the influence of PET calculation methods including FPM (used as reference method), FAO Penman (FP), Hargreaves-Samani (HS), Blaney-Criddle (BC), Turc (Tu), Jensen-Haise (JH), Priestley–Taylor (PT) and FAO24 Radiation (Ra) methods on the RDIe (in 1, 3 and 12-month time scales) was assessed. In this study the climatic data series of 5 stations in Fars province, Iran from 1989 to 2018 was used. Based on the results of PCA model, in short-term time scales (1 and 3-month), the calculated RDIe values based on the HS method (at 100% of stations) and in long-term time scale (annual) based on the FP method (at 60% of stations) had the highest correlation with RDIe based on the FPM method. According to the results of FC method, in 1-month time scale, the values of RDIe using PT and HS methods (at 100% and 80% of selected stations, respectively), in 3-month time scale, the values of RDIe using PT, HS and Ra methods (at 100% of stations) and in annual time scale, the values of RDIe using FP method (at 60% of stations) had the highest similarities with the values of RDIe using FPM. Therefore, it is recommended to replace the FPM method with HS (in 1 and 3-month time scales) and FP (in 12-month time scales) methods in areas with minimum available meteorological data.

     

Comparing SPI and RDI Applied at Local Scale as Influenced by Climate

Drought and wetness events were studied in the Northeast Algeria with SPI and RDI. The study area includes a variety of climatic conditions, ranging from humid in the North, close to the Mediterranean Sea, to arid in the South, near the Sahara Desert. SPI only uses precipitation data while RDI uses a ratio between precipitation and potential evapotranspiration (PET). The latter was computed with the Thornthwaite equation, thus using temperature data only. Monthly precipitation data were obtained from 123 rainfall stations and monthly temperature data were obtained from CFSR reanalysis gridded temperature data. Both data sets cover the period 1979–80 to 2013–14. Using ordinary kriging, the gridded temperature data was interpolated to all the locations having precipitation data, thus providing to compute SPI and RDI with the same observed rainfall data for the 3-, 6- and 12-month time scales. SPI and RDI were therefore compared at station level and results and have shown that both indices revealed more sensitive to drought when applied in the semi-arid and arid zones. Differently, more wetness events were detected by RDI in the more humid locations. Comparing both indices, they show a coherent and similar behavior, however RDI shows smaller differences among climate zones and time-scales, which is an advantage relative to the SPI and is likely due to including PET in RDI.     

Characterisation of Drought Properties with Bivariate Copula Analysis

Drought severity and duration are usually modelled independently. However, these two characteristics are known to be related. To model this relationship, a joint distribution of drought severity and duration using a bivariate copula model is proposed and applied to daily rainfall data (1976–2007) of 30 rain gauge stations in Peninsular Malaysia. The drought characteristics are classified using the standardized precipitation index (SPI) and their univariate marginal distributions are further identified by fitting exponential, gamma, generalized extreme value, generalized gamma, generalized logistics, generalized pareto, gumbel max, gumbel min, log-logistic, log-pearson3, log-normal, normal, pearson 5, pearson 6 and weibull distributions. The three-parameter log-normal distribution is identified as the best fitting distribution for drought severity while the generalized pareto distribution is determined as the most appropriate distribution for drought duration with respect to the application of the Anderson-Darling procedure. The dependency among the drought properties is analysed using Kendall’s τ method. The maximum likelihood estimation of the univariate marginal distributions and the maximisation of the bivariate likelihood are employed to compute the Akaike Information Criterion (AIC) values in verifying the best fitting copula distribution. The Galambos distribution is recognised as the most appropriate copula distribution for describing the relationship between drought severity and duration. The conditional drought probability and drought return period are further described to explain the drought properties comprehensively. The probabilities of drought occurrences under certain circumstances with a specific seriousness or duration can be determined in order to verify the possibility of drought episodes. The return period of a recurrent drought has also been investigated to identify the time-interval for repeated drought occurrences under similar situation.     

A Non-Stationary Reconnaissance Drought Index (NRDI) for Drought Monitoring in a Changing Climate

Traditionally, drought indices are calculated under stationary condition, the assumption that is not true in a changing environment. Under non-stationary conditions, it is assumed the probability distribution parameters vary linearly/non-linearly with time or other covariates. In this study, using the GAMLSS algorithm, a time-varying location parameter of lognormal distribution fitted to the initial values (α₀) of the traditional Reconnaissance Drought Index (RDI) was developed to establish a new index called the Non-Stationary RDI (NRDI), simplifying drought monitoring under non-stationarity. The fifteen meteorological stations having the longest records (1951–2014) in Iran were chose to evaluate the NRDI performances for drought monitoring. Trend analysis of the α₀ series at multiple time windows was tested by using the Mann-Kendall statistics. Although all stations detected decreasing trend in the α₀ series, eight of them were significant at the 5% probability level. The results showed that the time-dependent relationship is adequate to model the location parameter at the stations with the significant temporal trend. There were remarkable differences between the NRDI and the RDI, especially for the time windows larger than 6 months, implying monitoring droughts using the NRDI under non-stationarity. The study suggests using the NRDI where the significant time trend appears in the initial values of RDI due to changing climate.     

干旱事件重现期计算问题研究

干旱重现期大小是用于评价干旱事件严重程度的重要指标。干旱重现期的计算涉及给定阈值下干旱过程划分(识别)、样本系列分布函数拟合等关键环节,其中干旱阈值的确定是前提。提出以干旱事件的最长调查期为约束条件确定干旱阈值的思路,即根据样本计算的干旱事件最大重现期不应超过最长调查期,以此为据确定干旱阈值并从样本序列中识别干旱事件。同时,针对因干旱历时样本经验点据"平台式"过度集中而导致的频率曲线适线困难问题,建议采用基于游程理论的游程长度分布函数估计干旱历时概率分布。以青海民和县1932年-2010年的月降雨资料为例,对上述方法进行了应用研究,结合Copula函数计算了干旱事件的重现期。     

Risk Assessment of Droughts in Gujarat Using Bivariate Copulas

This study presents risk assessment of hydrologic extreme events droughts in Saurashtra and Kutch region of Gujarat state, India. Drought is a recurrent phenomenon and risk assessment of droughts can play an important role in proper planning and management of water resources in the study region. In the study, drought events are characterized by severity and duration, and drought occurrences are modeled by Standardized Precipitation Index (SPI) computed on mean areal precipitation, aggregated at a time scale of 6?months for the period 1900?C2008. After evaluating several distribution functions, drought variable??severity is best described by non-parametric kernel density, whereas duration is best fitted by exponential distribution. Considering the extreme nature of drought variables, the upper tail dependence copula families including two Archimedean??Gumbel-Hougaard, BB1 and one elliptical??Student??s t copulas are evaluated for modeling joint distribution of drought variables. On evaluating their performance using various goodness-of-fit measures, Gumbel-Hougaard copula is found to be the best performing copula in modeling the joint dependence structure of drought variables. Also, while comparing with traditional bivariate distributions, the copula based distributions are resulted in better performance as compared to bivariate log-normal and the logistic model for bivariate extreme value distributions. Then joint and conditional return periods of drought characteristics are derived, which can be helpful for risk based planning and management of water resources systems in the study region.     

Analysis of Irrigation Needs Using an Approach Based on a Bivariate Copula Methodology

The problem of drought probability has been investigated by several authors, who have usually analysed droughts using various drought indices such as the Standard Precipitation Index. Various aspects of time series of such indices (intensity, severity and duration) were investigated by several authors using a copula method. Because such analysis is based on only one basic climatic variable, this paper addresses a different approach, i.e., joint analysis of the severity and duration of the most demanding potential annual irrigation periods by a bivariate copula method. Characteristics of these periods are derived from both temperature and precipitation. Maximum annual duration of the potential irrigation period and corresponding rainfall deficit were inferred from these basic variables as inputs to two-dimensional probability analysis by the copula method, because this offers more direct answers to questions of irrigation needs. Results indicate the suitability of the proposed method for analysis of irrigation needs, with greater benefits than the typical one-dimensional analysis of individual climatic variables. A case study for testing the method was done for southwestern Slovakia, for which the frequency of irrigation needs was estimated. Example results indicate that every second year, a one-month period can be expected in which temperatures are >25^°C and there is a moisture deficit of ～30 mm. Even more significant periods of drought can be expected, for example, with a 5 or 10-year return period. These phenomena significantly damage agriculture yields, so requirements for irrigation structures in the study area are indicated by the proposed method.     

Spatial and Time Variability of Drought Based on SPI and RDI with Various Time Scales

The spatial and temporal variability of droughts were studied for the Northeast Algeria using SPI and RDI computed with monthly precipitation data from 123 rainfall stations and CFSR reanalysis monthly temperature data covering the period 1979–80 to 2013–14. The gridded temperature data was interpolated to all the locations having precipitation data, thus providing to compute SPI and RDI with the time scales of 3-, 6- and 12-month with the same observed rainfall data. Spatial and temporal patterns of droughts were obtained using Principal Component Analysis in S-Mode with Varimax rotation applied to both SPI and RDI. For all time scales of both indices, two principal components were retained identifying two sub-regions that are similar and coherent for all SPI and RDI time scales. Both components explained more than 70% and 74% of drought spatial variability of SPI and RDI, respectively. The identified sub-regions are similar and coherent for all SPI and RDI time scales. The Modified Mann-Kendall test was used to assess trends of the RPC scores, which have shown non-significant trends for decreasing drought occurrence and severity in both identified drought sub-regions and all time scales. Both indices have shown a coherent and similar behavior, however with RDI likely showing to identify more severe and moderate droughts in the southern and more arid sub-region which may be due to its ability to consider influences of global warming. Results for RDI are quite uniform relative to time scales and show smaller differences among the various climates when compared with SPI. Further assessments covering the NW and NE of Algeria using longer time series should be performed to better understand the behavior of both indices.     

Development of Drought Indices for Semi-Arid Region Using Drought Indices Calculator (DrinC) – A Case Study from Madurai District,a Semi-Arid Region in India

Drought is considered as a major natural hazard/ disaster, affecting several sectors of the economy and the environment worldwide. Drought, a complex phenomenon can be characterised by its severity, duration, and areal extent. Drought indices for the characterization and the monitoring of drought simplify the complex climatic functions and can quantify climatic anomalies for their severity, duration, and frequency. With this as background drought indices were worked out for Madurai district of Tamil Nadu using DrinC (Drought Indices Calculator) software. DrinC calculates the drought indices viz., deciles, Standard Precipitation Index (SPI), Reconnaissance Drought Index (RDI), Streamflow Drought Index (SDI) by providing a simple, though flexible interface by considering all the factors. The drought of 3, 6 and 9 months as time series can also be estimated. The results showed that drought index of Madurai region by decile method revealed that among the 100 years, 20 years were affected by drought and it is cyclic in nature and occurring almost every 3 to 7 years once repeatedly, except for some continuous period, i.e., 1923, 1924 and 1985, 1986, etc. During the last five decades, the incidence is higher with 13 events, whereas in the first five decades it was only 7. The SPI and RDI index also followed the similar trend of deciles. However, under SPI and RDI, the severely dry and extremely dry category was only seven years and all other drought years of deciles were moderately dry. Our study indicated that SPI is a better indicator than deciles since here severity can be understood. SDI did not follow the trend similar to SPI or RDI. Regression analysis showed that the SPI and RDI are significantly correlated and if 1st 3 months rainfall data is available one can predict yearly RDI drought index. The results demonstrated that these approaches could be useful for developing preparedness plan to combat the consequences of drought. Findings from such studies are useful tools for devising strategic preparedness plans to combat droughts and mitigate their effects on the activities in the various sectors of the economy.     

The Effect of Temperature Adjustment on Reference Evapotranspiration and Reconnaissance Drought Index (RDI) in Iran

The reference evapotranspiration (ET₀) is necessary to calculate Reconnaissance Drought Index (RDI). To estimate ET₀, FAO56 Penman-Monteith method which needs reference stations data is commonly used. Most of the meteorological stations in Iran are classified as non-reference satations and The use of their data in ET₀ calculation can affect the RDI. The objective of the present study is to evaluate the effect of temperature adjustment based on the reference condition on ET₀ and RDI values in non-reference stations of Iran. For this purpose, the meteorological data, recorded during 1960–2014 in 27 non-reference stations located in arid and semi-arid regions, were used. First, the values of ET₀ were determined using observed values of temperature. Using these values, RDI were computed by Log-Normal and Gamma distributions at annual and 6-month scales. Then the values of minimum, maximum and dew point temperatures were adjusted on the basis of the reference condition. The values of ET₀ and consequently RDI were calculated using adjusted data. On the basis of obtained results, at annual and 6-month scales, using observed values of temperature instead of adjusted values in non-reference stations cause to overestimate the value of ET₀. Also, using observed data with no adjustment can change the drought class which was determined on the basis of RDI. According to these results, temperature adjustment based on reference condition can change the values of ET₀ and RDI which was calculated by using Log-Normal or Gamma distributions at annual and 6-month scales.     

Trend Detection of Drought in Arid and Semi-Arid Regions of Iran Based on Implementation of Reconnaissance Drought Index (RDI) and Application of Non-Parametrical Statistical Method

Drought is known as one of the main natural hazards especially in arid and semi-arid regions where there are considerable issues in regard to water resources management. Also, climate changes has been introduced as a global concern and therefore, under conditions of climate change and global warming, the investigation of drought severity trend in regions such as Iran which is mainly covered by arid and semi-arid climate conditions is in the primary of importance. Therefore, in this study, based on the application of Reconnaissance Drought Index (RDI) for assessment drought severities, and also the implementation of non-parametric Mann- Kendall statistics and Sen’s slope estimator, the trends in different time series of RDI (3, 6, 9, 12, 18 and 24 monthly time series) were investigated. Results indicated the frequent decreasing trends in RDI time series particularly for long term time series (12, 18 and 24 monthly time series) than short term ones. Decreasing trend in RDI time series means the increasing trend in drought severities. Since the water resources especially ground water in most cases are affected by long term droughts, therefore, increasing trend in drought intensities in long term ones can be a threat for water resources management in surveyed areas.     

Evaluation of Drought Condition in Arid and Semi- Arid Regions,Using RDI Index

Investigation of drought event has a great importance in the natural resources management and planning water resources management. One strategy to manage drought is to predict drought conditions by probabilistic tools. In this study climate data of 11 synoptic stations in south of Iran during 1980–2014 were used to estimate of seasonal drought based on RDI index. To prediction of drought (from 2015 to 2020) and analysis of changes trend of it, time series model, first-order Markov Chain model and parametric and non- parametric statistical methods were used. Results showed that MA (5), MA (10), AR (12) and AR (15) were the best time series models that fitted in data of all stations. According to results of prediction of drought classes, classes with normal and moderate dry condition had allocated the most frequency of seasonal drought classes from 2015 to 2020 based on time series model and Markov Chain method. Analysis of changes trend of drought classes showed that based on observed data (1980–2014) and predicted data (1980–2020) changes trend of drought classes in all stations had increasing trend based on parametric and non- parametric statistical methods but increasing trend in about 27% of stations include: Bandar Abbas, Bandar Lengeh, Jask and Shiraz had significant level of 5%. Finally result showed that the study area in 2020 compared to 2014 will be drier.