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.

     

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.     

Projected Changes of Future Extreme Drought Events under Numerous Drought Indices in the Heilongjiang Province of China

Effective drought prediction methods are essential for the mitigation of adverse effects of severe drought events. This study utilizes the Reconnaissance Drought Index, Standardized Precipitation Index and Standardized Precipitation Evapotranspiration Index to assess the occurrence of future drought events in the study area of the Heilongjiang province of China over a period of 2016–2099. The drought indices were computed from the meteorological data (temperature, precipitation) generated by the global climate model (HadCM3A2). Moreover, Mann-Kendall trend test was applied for the assessment of future climatic trends and detecting probable differences in the behaviour of various drought indices. Drought forecasting periods has been divided into three categories: the early phase (1916–2030), middle phase (2031–2060) and late phase (2061–2099). The occurrence of future droughts is also ranked according to their intensity (mild, moderate, severe and extreme drought). Based on the drought results, more number of drought events are expected to occur during 12-month drought analysis are, RDI during 2084–2098 (DD = 14, DS = ?1.38), SPEI during 2084–2098 (DD = 14, DS = ?1.33) and SPI during 2084–2095 (DD = 12, DS = ?1.19). The 1st and 2nd months of the years studied predicted a warming trend, while the 7th, 8th, and 9th months predicted a wetter trend. Finally, it was observed that RDI is more sensitive to drought and indicated a high percentage of years under severe and extreme drought conditions during the drought frequency analysis. Conclusively, this study provides a strategies for water resources management and monitoring of droughts, in which drought indices like RDI can play a central role.     

A Novel Multi-Scalar Drought Index for Monitoring Drought: the Standardized Precipitation Temperature Index

Nowadays human beings are facing many environmental challenges because of frequently occurring drought hazards. Several adverse impacts of drought hazard are continued in many parts of the world. Drought has a substantial influence on water resources and irrigation. It may effect on the country’s environment, communities, and industries. Therefore, it is important to improve drought monitoring system. In this paper, we proposed a novel method – Standardized Precipitation Temperature Index (SPTI) for drought monitoring that utilize the regional tempreature. We compared the performance of our proposed drought index – SPTI with commonly used drought indices (i.e., Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI)) for 17 meteorological stations of Khyber Pakhtunkhwa (KPK) province (Pakistan) that have both extreme (arid and humid) climatic environment. We found that SPTI is strongly correlated with SPI and performed better than SPEI in low temperature regions for drought monitoring. In summary, SPTI is recommended for detecting and monitoring the drought conditions over different time scales.     

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.     

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.     

Regional Drought Assessment Based on the Reconnaissance Drought Index (RDI)

Regional drought assessment is conventionally based on drought indices for the identification of drought intensity, duration and areal extent. In this study, a new index, the Reconnaissance Drought Index (RDI) is proposed together with the well known Standardized Precipitation Index (SPI) and the method of deciles. The new index exhibits significant advantages over the other indices by including apart from precipitation, an additional meteorological parameter, the potential evapotranspiration. The drought assessment is achieved using the above indices in two river basins, namely Mornos and Nestos basins in Greece. It is concluded that although the RDI generally responds in a similar fashion to the SPI (and to a lesser extent to the deciles), it is more sensitive and suitable in cases of a changing environment.     

Comparison of Meteorological,Hydrological and Agricultural Drought Responses to Climate Change and Uncertainty Assessment

A comparison study of meteorological, hydrological and agricultural drought responses to climate change resulting from different General Circulation Models (GCMs), emission scenarios and hydrological models is presented. Drought variations from 1961–2000 to 2061–2100 in Huai River basin above Bengbu station in China are investigated. Meteorological drought is recognized by the Standardized Precipitation Index (SPI) while hydrological drought and agricultural drought are indexed with a similar standardized procedure by the Standardized Runoff Index (SRI) and Standardized Soil Water Index (SSWI). The results generally approve that hydrological and agricultural drought could still pose greater threats to local water resources management in the future, even with a more steady background to meteorological drought. However, the various drought responses to climate change indicate that uncertainty arises in the propagation of drought from meteorological to hydrological and agricultural systems with respect to alternative climates. The uncertainty in hydrological model structure, as well as the uncertainties in GCM and emission scenario, are aggregated to the results and lead to much wider variations in hydrological and agricultural drought characteristics. Our results also reveal that the selection of hydrological models can induce fundamental differences in drought simulations, and the role of hydrological model uncertainty may become dominating among the three uncertainty sources while recognizing frequency of extreme drought and maximum drought duration.     

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.

     

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.

     

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.     

Drought Occurrence Probability Analysis Using Multivariate Standardized Drought Index and Copula Function Under Climate Change

This study aims to investigate the effect of climate change on the probability of drought occurrence in central Iran. To this end, a new drought index called Multivariate Standardized Drought Index (MSDI) was developed, which is composed of the Standardized Precipitation Evapotranspiration Index (SPEI) and the Standardized Soil Moisture Index (SSI). The required data included precipitation, temperature (from CRU TS), and soil moisture (from the ESA CCA SM product) on a monthly time scale for the 1980–2016 period. Moreover, future climate data were downloaded from CMIP6 models under the latest SSPs-RCPs emission scenarios (SSP1-2.6 and SSP5-8.5) for the 2020–2056 period. Based on the normalized root mean square error (NRMSE), Cramer-von mises statistic (S_n), and Nash Sutcliffe (NS) evaluation criteria, the Galambos and Clayton functions were selected to derive copula-based joint distribution functions in both periods. The results showed that more severe and longer droughts will occur in the future compared to the historical period and in particular under the SSP5-8.5 scenario. From the derived joint return period, a drought event with defined severity or duration will happen in a shorter return period as compared with the historical period. In other words, the joint return period indicated a higher probability of drought occurrence in the future period. Moreover, the joint return period analysis revealed that the return period of mild droughts will remain the same, while it will decrease for extreme droughts in the future.

     

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.     

Assessment of Hydrological Drought Revisited

A variety of indices for characterising hydrological drought have been devised which, in general, are data demanding and computationally intensive. On the contrary, for meteorological droughts very simple and effective indices such as the Standardised Precipitation Index (SPI) have been used. A methodology for characterising the severity of hydrological droughts is proposed which uses an index analogous to SPI, the Streamflow Drought Index (SDI). Cumulative streamflow is used for overlapping periods of 3, 6, 9 and 12 months within each hydrological year. Drought states are defined which form a non-stationary Markov chain. Prediction of hydrological drought based on precipitation is also investigated. The methodology is validated using reliable data from the Evinos river basin (Greece). It can be easily applied within a Drought Watch System in river basins with significant storage works and can cope with the lack of streamflow data.     

基于VIC模型的滦河流域综合干旱指数的构建与应用

干旱频发已成为严重制约社会经济可持续发展的重要因素,但由于干旱形成机理复杂,影响因素众多,目前尚无公认普遍适用的干旱指数,因此寻找并构建适用于研究区的综合干旱指数成为当前研究的热点和重点。本文以滦河流域为研究对象,选取1960-1979年为研究期,通过对降水距平百分数、相对湿润度和由VIC模型的中间变量-土壤含水量计算得到的土壤相对湿度指数进行主成分分析,构建了适用于该流域的综合干旱指数,对研究期的旱情进行了评价,并与标准化降水指数(SPI)、帕默尔指数(PDSI)的评价结果进行比较,验证其适用性。结果表明:基于VIC模型的综合干旱指数能较好地评价滦河流域历史旱情。该研究在提升海河流域干旱监测和评价能力方面具有一定的理论与实用价值,也为其它流域的干旱评价具有参考价值。     

Assessment of Probabilistic Multi-Index Drought Using a Dynamic Naive Bayesian Classifier

The proper consideration of all plausible feature spaces of the hydrological cycle and inherent uncertainty in preceding developed drought indices is inevitable for comprehensive drought assessment. Therefore, this study employed the Dynamic Naive Bayesian Classifier (DNBC) for multi-index probabilistic drought assessment by integrating various drought indices (i.e., Standardized Precipitation Index (SPI), Streamflow Drought Index (SDI), and Normalized Vegetation Supply Water Index (NVSWI)) as indicators of different feature spaces (i.e., meteorological, hydrological, and agricultural) contributing to drought occurrence. The overall results showed that the proposed model was able to account for various physical forms of drought in probabilistic drought assessment, to accurately detect a drought event better than (or occasionally equal to) any single drought index, to provide useful information for assessing potential drought risk, and to precisely capture drought persistence in terms of drought state transition probability in drought monitoring. This easily produced an alternative method for comprehensive drought assessment with combined use of different drought indices.     

Spatial Patterns and Temporal Variability of Drought in Western Iran

An analysis of drought in western Iran from 1966 to 2000 is presented using monthly precipitation data observed at 140 gauges uniformly distributed over the area. Drought conditions have been assessed by means of the Standardized Precipitation Index (SPI). To study the long-term drought variability the principal component analysis was applied to the SPI field computed on 12-month time scale. The analysis shows that applying an orthogonal rotation to the first two principal component patterns, two distinct sub-regions having different climatic variability may be identified. Results have been compared to those obtained for the large-scale using re-analysis data suggesting a satisfactory agreement. Furthermore, the extension of the large-scale analysis to a longer period (1948–2007) shows that the spatial patterns and the associated time variability of drought are subjected to noticeable changes. Finally, the relationship between hydrological droughts in the two sub-regions and El Niño Southern Oscillation events has been investigated finding that there is not clear evidence for a link between the two phenomena.     

Analysis of Drought from Humid,Semi-Arid and Arid Regions of India Using DrinC Model with Different Drought Indices

The study aims at evaluating the various drought indices for the humid, semi-arid and arid regions of India using conventional indices, such as rainfall anomaly index, departure analysis of rainfall and other indices such as Standard Precipitation Index (SPI) and Reconnaissance Drought Index (RDI) that were analyzed using the DrinC software. In SPI, arid region has seven drought years, whereas humid and semi-arid regions have four. In case of RDI, the humid and semi-arid regions have 11 drought years, whereas arid regions have 10 years. The difference in SPI and RDI was due to the fact that RDI considered potential evapotranspiration, and hence, correlation with plants would be better in case of RDI. Humid region showed a decreasing trend in initial value of RDI during the drought as compared to semiarid and arid regions and indicated possible climate change impact in these regions. Among all the indices, RDI was considered as an effective indicator because of implicit severity and high prediction matches with the actual drought years. SPI and RDI were found to be well correlated with respect to 3 months rainfall data and SPI values led to prediction of annual RDI. The results of our study established that this correlation could be used for developing disaster management plan well in advance to combat the drought consequences.

     

Evaluation and Assessment of Meteorological Drought by Different Methods in Trarza Region,Mauritania

Drought Indexes (DIs) are commonly used for assessing the effect of drought such as the duration and severity. In this study, long term precipitation records (monthly recorded for 44 years) in three stations (Boutilimit (station 1), Nouakchott (station 2), and Rosso (station 3)) are employed to investigate the drought characteristics in Trarza region in Mauritania. Six DI methods, namely normal Standardized Precipitation Index (normal-SPI), log normal Standardized Precipitation Index (log-SPI), Standardized Precipitation Index using Gamma distribution (Gamma-SPI), Percent of Normal (PN), the China-Z index (CZI), and Deciles are used for this purpose. The DI methods are based on 1-, 3-, 6-, and 12 month time periods. The results showed that DIs produce almost the same results for the Trarza region. The droughts are detected in the seventies and eighties more than the 1990s. Twelve drought years might be experienced in station 2 and six in stations 1 and 3 in every 44 years, according to reoccurrence probability of the gamma-SPI and log-SPI results. Stations 1 and 3 might experience fewer drought years than station 2, which is located right on the coast. In station 1, which is located inland, when the annual rainfall is less than 123 mm, it is likely that severe drought would occur. This is 63 mm/year for station 2 and 205 mm/year for station 3 which is located in the south west on the Senegal River. DI results indicate that the CZI and the gamma-SPI methods make similar predictions and the log-SPI makes extreme drought predictions for the monthly period for all the stations. For longer periods (3-, 6-, and 12 month period), for all the stations, the log-SPI and the gamma-SPI produce similar results, making severe drought predictions while the normal-SPI and the CZI methods predict more wet and fewer drought cases. The log-SPI, the gamma-SPI, PN and Deciles were able to capture the historical extreme and severe droughts observed in early 1970s and early 1980s.