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A Generalized Framework for Deriving Nonparametric Standardized Drought Indicators

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Abstract

This paper introduces the Standardized Drought Analysis Toolbox (SDAT) that offers a generalized framework for deriving nonparametric univariate and multivariate standardized indices. Current indicators suffer from deficiencies including temporal inconsistency, and statistical incomparability. Different indicators have varying scales and ranges and their values cannot be compared with each other directly. Most drought indicators rely on a representative parametric probability distribution function that fits the data. However, a parametric distribution function may not fit the data, especially in continental/global scale studies. SDAT is based on a nonparametric framework that can be applied to different climatic variables including precipitation, soil moisture and relative humidity, without having to assume representative parametric distributions. The most attractive feature of the framework is that it leads to statistically consistent drought indicators based on different variables.

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... SPEI features an intensity scale that calculates both negative and positive values, indicating dry and wet episodes. SPEI calculation uses the difference between the PET and P. Further, various procedures have been employing to standardize observed P to quantify the SPI values and the difference between the PET and P to quantify SPEI values [37,54]. However, in the current assessment, we implemented the transformation technique [52,54,55] of SPI and SPEI is as follows: ...
... SPEI calculation uses the difference between the PET and P. Further, various procedures have been employing to standardize observed P to quantify the SPI values and the difference between the PET and P to quantify SPEI values [37,54]. However, in the current assessment, we implemented the transformation technique [52,54,55] of SPI and SPEI is as follows: ...
... For a complete definition of the function βðhÞ: , refer to [29,54,56]. When 0<β hÞ ð ≤ 0:5; ð2Þ ...
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This research aims to find the best model for predicting the Standardized Precipitation Index (SPI) and the Standardized Precipitation and Evapotranspiration Index (SPEI) in the future. The study estimates SPI and SPEI at different time scales, ranging from 1 to 48 months. To predict drought, Random Forest (RF) models are used based on lag times of 1–12 months for the estimated drought indices (SPI and SPEI). Accuracy and error metrics like Nash–Sutcliffe efficiency (NSE), root-mean-square error (RMSE), producer accuracy (PA), user accuracy (UA), and Choen’s kappa are used to assess the models. The NSE values for the SPI at varying time scales (1, 3, 6, 9, 12, and 48 months) indicate that Bahawalpur, Rawalpindi, Murree, and Sargodha stations have the highest NSE values of 0.1148, 0.5868, 0.8302, 0.9196, 0.9516, 0.9801, and 0.9845, respectively. Similarly, the RMSE values for SPI at these time scales show that Bahawalpur, Rawalpindi, Murree, and Sargodha stations have the lowest RMSE values of 0.6187, 0.6094, 0.4091, 0.2865, 0.2275, 0.1594, and 0.1106, respectively. The NSE and variance explained for SPI and SPEI at a 1-month time scale were found to be poor, but they improved as the time scale increased. On the other hand, the RMSE values for SPI and SPEI at a 1-month time scale were found to be high but decreased with longer time scales. The stations that exhibit the highest values of the NSE for the SPEI at various time scales (1, 3, 6, 9, 12, and 48 months) are Rawalpindi, Jhelum, Murree, Mianwali, Rawalpindi, and Sargodha, respectively. These stations have NSE values of 0.0784, 0.6074, 0.8353, 0.9225, 0.9542, 0.9760, and 0.9896, respectively. Similarly, the stations with the lowest RMSE values for SPEI at these time scales are Sargodha, Murree, Murree, Murree, Murree, and Sargodha, with RMSE values of 1.002, 0.5909, 0.3993, 0.2626, 0.2132, 0.1546, and 0.0941, respectively. The analysis reveals a distinct pattern indicating that stations situated at higher elevations exhibit a more pronounced correlation between the SPI and SPEI indices in comparison to stations at lower elevations. Notably, Murree, Jhelum, Sialkot, and Rawalpindi demonstrate a statistically significant and strong correlation between the SPI and SPEI. Overall, the results show that SPEI is a better drought index for classifying and monitoring meteorological drought in stations with lower elevations. However, in stations with higher elevations, the selected indices provide similar information, but with some differences.
... The parametric approach relies on the frequency distribution of precipitation using a theoretical statistical distribution, typically the two-parameter gamma distribution. On the other hand, the non-parametric approach employs the derivation of the marginal probability of precipitation based on empirical plotting positions [20]. As a result, with the non-parametric approach, the SPI can be relatively easily computed directly from observed precipitation data without assuming any underlying distribution. ...
... Farahmand and AghaKouchak [20] presented a non-parametric framework, called the Standardized Drought Analysis Toolbox (SDAT), offering a versatile and robust approach for the assessment of drought conditions across diverse geographical regions and climatic regimes. For the estimation of SPI, they used the Gringorten plotting position. ...
... Under the non-parametric approach, it is proposed to use an empirical plotting position instead of a parametric distribution [20]. Based on the nature and behavior of the data, many authors have proposed new and/or modified existing probability plotting formulas (e.g., [30][31][32][33][34][35]). ...
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Accurate drought identification is important for both scientists and decision-makers to be able to make informative decisions. In this study, parametric and non-parametric approaches for analyzing meteorological drought are compared, aiming at simplifying the calculation of the Standardized Precipitation Index (SPI). The comparison is performed across various meteorological stations covering the entire territory of Greece, using monthly rainfall data spanning from 1961 to 2021. Meteorological drought is assessed through the SPI for the 12-month reference period. A two-parameter gamma distribution, with parameters estimated using the maximum likelihood estimation method, is employed for the estimation of the SPI drought index as the parametric classic approach. For the non-parametric approach, the SPI drought index is estimated using six empirical probability plotting positions: Beard, Blom, Cunnane, Gringorten, Hazen, and Weibull. Results indicate that the empirical approach can effectively identify drought events in comparison to the classic approach. However, caution is advised, particularly when different drought classes are identified, as the non-parametric approaches may underestimate drought severity. In addition, for the Greek meteorological conditions, the results revealed that in the case of extreme drought events, the estimation of SPI employing the classic approach is to be preferred.
... There are two well-established methods for the potential evapotranspiration (PET) calculation: the Thornthwaite method [47], which considers only temperature, and the Penman-Monteith method [48], which is physics-based. The Penman-Monteith method was recommended by the Food and Agriculture Organization of the United Nations (FAO) in 1988 as the standard for PET calculation [49]. This method allows for accurate and reliable PET estimation using weather data, avoiding the challenges of field measurements, and is widely used globally. ...
... Additionally, parametric distribution functions require a minimum period of 30 years to provide accurate estimates of drought conditions. To address these limitations, Farahmand et al. (2015) proposed a non-parametric framework known as the Standardized Drought Analysis Toolbox (SDAT) [49]. SDAT was chosen to calculate the SPEI. ...
... Additionally, parametric distribution functions require a minimum period of 30 years to provide accurate estimates of drought conditions. To address these limitations, Farahmand et al. (2015) proposed a non-parametric framework known as the Standardized Drought Analysis Toolbox (SDAT) [49]. SDAT was chosen to calculate the SPEI. ...
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Amid global climate change, recurrent drought events pose significant challenges to regional water resource management and the sustainability of socio-economic growth. Thus, understanding drought characteristics and regional development patterns is essential for effective drought monitoring, prediction, and the creation of robust adaptation strategies. Most prior research has analyzed drought events independently in spatial and temporal dimensions, often overlooking their dynamic nature. In this study, we employ a three-dimensional methodology that accounts for spatiotemporal continuity to identify and extract meteorological drought events based on a 3-month standardized precipitation evapotranspiration index (SPEI3). Measured by the SPEI3 index, the incidence of drought increased in the middle part of the basin, especially in some parts of Sichuan and Yunnan province, and the frequency of drought events decreased in the upper reaches. We evaluate drought events within the Yangtze River basin from 1980 to 2016 by examining five variables: chronology, extent, severity, duration, and epicenter locations. The results show that a total of 97 persisting drought events lasting at least 3 months have been identified in Yangtze River basin. Most events have a duration between 4 and 7 months. The findings indicate that while the number of drought events in the Yangtze River basin has remained unchanged, the intensity, duration, and severity of these events have shown a slight increase from 1980 to 2016. The drought events gradually moved from the western and southeastern parts of the basin to the central region. The most severe drought event occurred between January 2011 and October 2011, with a duration of 10 months and an affected area of 0.94 million km2, impacting over fifty percent of the basin. Changes in wetness and dryness in the Yangtze River basin are closely related to El Niño/Southern Oscillation (ENSO) events, with a positive correlation between the intensity of cold events and the probability of extreme drought. This study enhances our understanding of the dynamics and evolution of drought events in the Yangtze River basin, providing crucial insights for better managing water resources and developing effective adaptation strategies.
... There are many other alternatives in the growing literature for drought monitoring, and a recent comprehensive review of various indices can be found in (Alahacoon and Edirisinghe, 2022). In a nutshell, the concept of standardised drought indices is generally summarised with the Standardised Drought Analysis Toolbox (SDAT), which includes the possibility of extending the idea of SPI to bivariate data using non-parametric estimates (Farahmand and AghaKouchak, 2015). Afterwards, this process is generalized and expanded for higher dimensional data so that it is possible to construct any standardized index by flexibly embedding the relationship between weather variables (Erhardt and Czado, 2018). ...
... To begin with, the SDAT mentioned above relies on a non-parametric framework that can be applied to different climatic variables including precipitation, soil moisture and relative humidity, without assuming typical parametric distributions. (Farahmand and AghaKouchak, 2015). In a similar vein, the multivariate tool introduced by Erhardt and Czado allows non-parametric distribution estimates for the climatic variables for the index construction (Erhardt and Czado, 2018). ...
... In a different setting, considering different threshold levels while deriving the drought characteristics can quantify the changes across different drought levels in depth. The generation of multiple drought indices relying on multiple sources can add more novelty to the drought characteristics analysis by following the work of Farahmand and AghaKouchak (2015) and the corresponding references therein. It is possible to explore the application of these indices in different climatic regions and consider integrating other relevant variables, such as soil moisture or vegetation indices, to further refine drought assessments. ...
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Drought, which has harmful impacts both environmentally and economically, is one of the most devastating natural phenomena. In order to better understand and monitor the effects of drought, various methods have been developed in recent decades to quantify drought characteristics, with a primary focus on univariate drought indices. Mainly, drought characteristics are crucial to examine the impacts of drought in-depth on any specific area. This study endeavours to investigate univariate and bivariate drought indices using both parametric and non-parametric copula techniques. For that purpose, drought characteristics, such as duration, severity, mean intensity and peak intensity are analysed relying on different drought indices. The dependence among the main characteristics is evaluated and corresponding bivariate return period calculations are investigated. The data set used in this study is retrieved from monthly meteorological observations collected at five different Stations in Konya, located in the Central Anatolia Region of Turkey. Main numerical findings indicate the importance of using multiple drought indices for different geographical reasons for extreme dry periods.
... Many researchers have been focusing on assessing the accuracy of SSI from a statistical approach [22,31]. However, few studies compare the SSI with fixed-or variablethreshold methods for identifying drought events and their characteristics. ...
... (accessed on 17 August 2023) [33]. It calculates the SSI based on a non-parametric approach using the empirical Gringorten plotting position rather than fitting with parametric functions [31]. ...
... The empirical probability equation used in this study is as follows [31]: ...
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Climate change is increasing air temperatures and altering the precipitation and hydrological regime on a global scale. Challenges arise when assessing the impacts of climate change on the local scale for water resource management purposes, especially for low-mountain headwater catchments that not only serve as important water towers for local communities but also have distinct hydrological characteristics. Until now, no low-flow or hydrological drought studies had been carried out on the Lauter River. This study is unique in that it compares the Lauter River, a transboundary Rhine tributary, with a nearby station on the Rhine River just below its confluence at the French–German border. The Lauter catchment is a mostly natural, forested catchment; however, its water course has been influenced by past and present cultural activities. Climate change disturbances cascade through the hydrologic regime down to the local scale. As we are expecting more low-flow events, the decrease in water availability could cause conflicts between different water user groups in the Lauter catchment. However, the choice among different methods for identifying low-flow periods may cause confusion for local water resource managers. Using flow-rate time series of the Lauter River between 1956 and 2022, we compare for the first time three low-flow identification methods: the variable-threshold method (VT), the fixed-threshold method (FT), and the Standardized Streamflow Index (SSI). Similar analyses are applied and compared to the adjacent Maxau station on the Rhine River for the same time period. This study aims at (1) interpreting the differences amongst the various low-flow identification methods and (2) revealing the differences in low-flow characteristics of the Lauter catchment compared to that of the Rhine River. It appears that FT reacts faster to direct climate or anthropogenic impacts, whereas VT is more sensitive to indirect factors such as decreasing subsurface flow, which is typical for small headwater catchments such as the Lauter where flow dynamics react faster to flow disturbances. Abnormally low flow during the early spring in tributaries such as the Lauter can help predict low-flow conditions in the Rhine River during the following half-year and especially the summer. The results could facilitate early warning of hydrological droughts and drought management for water users in the Lauter catchment and further downstream along some of the Rhine.
... Many researchers have been focusing on assessing the accuracy of SSI from a statistical approach [19,28] . However, few studies compare the SSI with fixed or variable threshold methods for identifying drought events and their characteristics. ...
... (accessed on 17 August 2023) [30] . It calculates the SSI based on a non-parameter approach using empirical Gringorten plotting position other than fitting with parametric functions [28] . ...
... The empirical probability equation used in this study is as below [28] , ...
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Climate change is increasing air temperatures and altering the precipitation and hydrological re-gime on a global scale. Challenges arise when assessing the impacts of climate change on the local scale for water resources management proposes, especially for low mountain headwater catch-ments that not only serve as important water towers for local communities, but also have distinct hydrological characteristics. Until now, no low flow or hydrological drought studies have been carried out on the Lauter River. This study is unique in that it compares the Lauter River, a transboundary Rhine tributary with a nearby station on the River Rhine just below its confluence at the French-German border. The Lauter catchment is a mostly natural, forested catchment, however, its water course has been influenced by past and present cultural activities. Climate change disturbances cascade through the hydrologic regime right down to the local scale. As we are expecting more low flow events, the decrease in water availability could cause conflicts be-tween different water user groups in the Lauter catchment. However, the choice of different methods for identifying low flow periods may cause confusion for local water resources manag-ers. Using flow rate time series of the Lauter River between 1956 and 2022 we compare for the first time three low flow identification methods: the variable threshold method (VT), the fixed threshold method (FT), and the Standardized Streamflow Index (SSI). Similar analyses are applied and compared to the adjacent Maxau station on the Rhine River for the same time period. This study aims at 1) interpreting the differences amongst the various low flow identification methods and 2) revealing the differences in low flow characteristics of the Lauter catchment compared to the Rhine River. It appears that the FT reacts faster to direct climate or anthropogenic impacts whereas VT is more sensitive to indirect factors such as decreasing subsurface flow which is typical for small headwater catchments, such as the Lauter where flow dynamics react faster to flow disturbances. Abnormally low flow during the early Spring in tributaries such as the Lauter can help predict low flow conditions of the Rhine River during the following half year and espe-cially for the summer. The results could facilitate Early Warning of hydrological droughts and drought management for water users in the Lauter catchment and further downstream along some of the Rhine.
... In this study, we utilized SPI and SSI to examine the spatial and temporal characteristics of meteorological and hydrological droughts in the PLB. The SPI is derived by initially fitting a gamma probability distribution to the precipitation data, followed by transforming the accumulated gamma probability into the Cumulative Distribution Function (CDF) of the standard normal distribution, with zero representing the mean value (Farahmand and AghaKouchak, 2015). A ...
... We also applied this process to derive seasonal SSI. Here, based on the observed monthly precipitation data and simulated monthly soil water moisture, we employed the Standardized Drought Analysis Toolbox (SDAT) software package in MATLAB (Farahmand and AghaKouchak, 2015) to calculate the SPI and standardized SSI at a three-month scale (medium-term periods), such as in the spring (March-May) and summer (June-August), etc. The classification of the two drought indices is shown in Table 3. ...
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The Poyang Lake Basin (PLB) has a long-standing history of drought, which has been intensified by global warming, posing significant risks to water security and agriculture. However, the specific patterns of drought, particularly seasonal variations, remain poorly understood, making it crucial to investigate these dynamics for effective water management and resilience planning. We employed calibrated SWAT model to simulate monthly soil moisture in five sub-basins to analyze drought characteristics across the PLB over the past six decades. A Multivariate Standardized Drought Index (MSDI) was then developed with simulated Standardized Soil Moisture Index (SSI) and Standardized Precipitation Index (SPI) based on copula functions. We found that (1) The SWAT can simulate monthly streamflow well with NS being 0.76–0.92 for validation data over the sub-basins in the PLB. (2) The MSDI index indicated that there were more drought events during 1960–1979 and 2000–2019, highlighting a cyclical pattern of drought events in the PLB. (3) The Xiushui River Basin encountered the most extreme drought conditions since 2000, indicating the basin faced a high risk of dry conditions. Additionally, our wavelet period analysis showed an increase in drought frequency after the year 2000, with less distinct periodicity. These findings contribute to our understanding of drought dynamics in the Poyang Lake Basin and offer valuable insights for developing sustainable water resource management and climate adaptation strategies in the region.
... For instance, the 6-month SPI is advantageous for identifying seasonal droughts, the 12-month SPI is adequate for assessing annual droughts and the 24-month SPI is suitable for long-term drought analysis (Łabędzki, 2007). This study used the Standardized Drought Analysis Toolbox (SDAT) to calculate generalized univariate DI (Farahmand & AghaKouchak, 2015). The method derives nonparametric standardized drought indices using empirical probabilities. ...
... SPI relies solely on precipitation data for its computation. In this study, a nonparametric approach proposed by Farahmand and AghaKouchak (2015) is utilised to estimate the SPI. This method diverges from the traditional two-parameter gamma distribution (McKee et al., 1993) and employs empirical probabilities for SPI derivation instead. ...
Article
Climate change and anthropogenic influences amplify drought complexity, entangle non‐stationarity (NS) and further challenge drought comprehension. This study aims to understand the dynamic evolution of drought propagation patterns due to climatic and anthropogenic pressures by assessing the non‐stationary linkages between hydrological variables and drought characteristics. It employs four standardized drought indicators to comprehensively examine the spatio‐temporal evolution of meteorological (MD) and hydrological (HD) drought characteristics. Data from 29 semi‐arid catchments from six river basins in Peninsular India, are analyzed to uncover distinct drought propagation patterns. This study utilizes a novel Non‐overlapping Block‐stratified Random Sampling (NBRS) approach to detect NS in drought characteristics and hydrological variables, shedding light on the underlying drivers of this dynamic behavior. The results indicate similarities in drought behavior for the Sabarmati, Mahi and Tapi (SMT) basins compared with the Godavari, Krishna and Pennar (GKP) basins, with shorter (longer) propagation times noted for SMT (GKP) basins. While HD severity decreases over time in SMT basins, it intensifies in GKP basins, which are linked to intensive anthropogenic interventions such as river regulation and reservoir operations, thus resulting in prolonged and intensified droughts. Rainfall primarily exhibits time‐invariance, while significant NS is observed in potential evapotranspiration (particularly in the Krishna and Pennar basins), streamflow and baseflow across all basins. The study also identified three distinct drought propagation patterns in these basins, highlighting cases where MD did not transition to HD, instances of HD occurring without preceding MD and synchronous propagation of MD to HD. The study outcomes provide profound insights into the evolution of drought dynamics under climatic and anthropogenic pressures, which will aid policymakers and stakeholders in formulating strategies for drought preparedness and response.
... The past few decades have been accompanied by a transformation in methods for developing drought indices, shifting from single input variables (e.g., standardized precipitation index (SPI) (McKee et al. 1993) and soil moisture index (SSI) (Hao and AghaKouchak 2013)) to multi-variate indices (e.g., standardized precipitation evapotranspiration index (SPEI) (Vicente-Serrano et al. 2010), standardized precipitation temperature index (SPTI) (Wable et al. 2019), and new multivariate standardized drought index (MSDI) (Hao and AghaKouchak 2013)). Additionally, indices based on parametric probability distribution functions have been replaced by nonparametric frameworks that describe drought more effectively (Hao and Aghakouchak 2014;Farahmand and AghaKouchak 2015;Alizadeh and Nikoo 2018). Furthermore, the development of combined condition indices (CCIs) such as vegetation health index (VHI) (Kogan 1995), scaled drought condition index (SDCI) (Rhee et al. 2010b), microwave integrated drought index (MIDI) (Zhang and Jia 2013), and integrated drought monitoring index (IDMI) (Arun Kumar et al. 2021) has been widely advanced using single condition indices (SCIs) such as precipitation condition index (PCI) (Rhee et al. 2010a), temperature condition index (TCI) (Kogan 1995), potential evapotranspiration condition index (PETCI) (Allen et al. 2007), soil moisture condition index (SMCI) (Zhang and Jia 2013), and vegetation condition index (VCI) (Kogan 1995). ...
... So far, several studies have used standardized indices at multiple timescales, especially SPI (Zhang et al. 2017;Alkaraki and Hazaymeh 2023b;Yin and Zhang 2023) and SPEI (Tian et al. 2020;Ali et al. 2022;Yang et al. 2023), to evaluate the newly developed indices. To avoid probability distribution function fitting, which may not always be the best selection of a distribution function, a nonparametric approach was proposed for deriving SIs (Farahmand and AghaKouchak 2015;Fooladi et al. 2021). The SIs including SPI, SPEI, and SSI were assumed for target selection. ...
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This study aims to determine the crucial variables for predicting agricultural drought in various climates of Iran by employing feature selection methods. To achieve this, two databases were used, one consisting of ground-based measurements and the other containing six reanalysis products for temperature (T), root zone soil moisture (SM), potential evapotranspiration (PET), and precipitation (P) variables during the 1987–2019 period. The accuracy of the global database data was assessed using statistical criteria in both single- and multi-product approaches for the aforementioned four variables. In addition, five different feature selection methods were employed to select the best single condition indices (SCIs) as input for the support vector regression (SVR) model. The superior multi-products based on time series (SMT) showed increased accuracy for P, T, PET, and SM variables, with an average 47%, 41%, 42%, and 52% reduction in mean absolute error compared to SSP. In hyperarid climate regions, PET condition index was found to have high relative importance with 40% and 36% contributions to SPEI-3 and SPEI-6, respectively. This suggests that PET plays a key role in agricultural drought in hyperarid regions because of very low precipitation. Additionally, the accuracy results of different feature selection methods show that ReliefF outperformed other feature selection methods in agricultural drought modeling. The characteristics of agricultural drought indicate the occurrence of drought in 2017 and 2018 in various climates in Iran, particularly arid and semi-arid climates, with five instances and an average duration of 12 months of drought in humid climates.
... This approach eliminates the need to assume the existence of representative parametric distributions (Hao et al., 2014;Vo and Liou, 2024). The process begins by calculating the empirical probability for each value, which are then transformed using the inverse normal distribution function, ensuring the data is normalized to follow a standard (Farahmand and AghaKouchak, 2015). The SDAT package for MATLAB was used to calculate the GWI for this paper. ...
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Study region: The Haouz aquifer, situated in central Morocco, a data-scarce region. Study focus: Groundwater resources in semi-arid regions face increasing threats from climate change, particularly due to warming and overexploitation. However, data scarcity limits the ability to monitor and predict groundwater changes accurately. This study addresses this challenge by predicting future drought conditions in the Haouz aquifer using SPI and SPEI climatic drought indices, Machine Learning models, and Med-CORDEX regional climate models under RCP 4.5 and 8.5 scenarios. New Hydrological Insights for the Region: This study is the first in the region to predict groundwater drought based on precipitation and temperature data, relying on the principle of drought propagation. The comparative analysis of the machine learning models shows that Random Forest stands out for its superior predictive performance, influenced by annual trends and long-term climatic indices, with significant contributions from geographical variables. The results indicate a combined influence of land use and natural characteristics on the drought of the Haouz aquifer, following a longitudinal variation and showing a trend towards decreasing variability from the mid-to long-term. Additionally, extreme drought conditions are expected to intensify in most study points particularly under RCP 8.5. The eastern area of the aquifer remains the least impacted by this future trend, continuing to reflect normal drought conditions even in the long term under RCP 8.5.
... These indices are favored in the literature for their simplicity, broad applicability across regions, and their capacity to accurately represent drought conditions (Çavuş et al. 2023;Gümüş, 2023;Lorenzo et al. 2024;Sun et al. 2023). In addition to univariate drought indices, multivariate drought indices that combine multiple drought types, typically by determining the joint probability between hydrometeorological variables, have also been developed and utilized in past studies (Hao and AghaKouchak 2013;Farahmand and AghaKouchak 2015;Li et al. 2021;Zhang et al. 2019). ...
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The significance of drought monitoring and prediction systems has grown substantially due to the escalating impacts of climate change. However, existing tools for drought analysis face several limitations, including restricted functionality to single-variable indices, reliance on predefined probability distributions, lack of flexibility in choosing distributions, and the need for advanced programming expertise. These constraints hinder comprehensive and accurate drought assessments. This study introduces DroughtStats, a novel, user-friendly software designed to overcome these challenges and enhance drought analysis capabilities. DroughtStats integrates advanced statistical tools to analyze hydrometeorological data, compute both single-variable and multivariable drought indices using empirical and parametric methods, and evaluate drought characteristics with improved accuracy. Notably, it supports a broader range of probability distributions, performs copula-based analyses, and estimates potential evapotranspiration using multiple methods, including Penman–Monteith. Additionally, DroughtStats can analyze the relationship between different datasets using techniques like copula-based Kendall’s tau. By addressing the limitations of existing tools, DroughtStats provides a more flexible and comprehensive approach to drought monitoring. Its versatility and global applicability are demonstrated through a case study in Turkey’s Çoruh River Basin (CRB), where drought indices based on precipitation and streamflow are calculated to characterize drought conditions. The results show that DroughtStats can successfully identify and characterize drought events at various time scales, providing valuable insights into drought severity, frequency, and recovery, and offering a reliable tool for ongoing drought monitoring and management.
... Bivariate indices, such as SPEI and SMRI, are derived from differences in precipitation-evapotranspiration and the sum of snowmelt and rainfall, respectively. Univariate indices, including SPI, SRI, and SSI, standardize cumulative distribution functions (CDFs) of precipitation, runoff, and soil moisture, using Gringorten plotting positions for consistency with methods by [42]). ...
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Recent above-normal temperatures, which exacerbated the impacts of precipitation deficits, are recognized as the primary driver of droughts in the Upper Colorado River Basin (UCRB), USA. This research aims to enhance drought prediction models by addressing structural changes in non-stationary temperature time series and minimizing drought misclassification through the ES-CBS-SVR model, which integrates ESSVR and CBS-SVR. The research investigates whether this coupling improves prediction accuracy. Furthermore, the model’s performance will be tested in a region distinct from those originally used to evaluate its generalizability and effectiveness in forecasting drought conditions. We used a change point detection technique to divide the non-stationary time series into stationary subsets. To minimize the chances of drought mis-categorization, category-based scoring was used in ES-CBS-SVR. In this study, we tested and compared the ES-CBS-SVR and SVR models in the Upper Colorado River Basin (UCRB) using data from the Global Land Data Assimilation System (GLDAS), where the periods 1950–2004 and 2005–2014 were used for training and testing, respectively. The results indicated that ES-CBS-SVR outperformed SVR consistently across of the drought indices used in this study in a higher portion of the UCRB. This is mainly attributed to variable hyperparameters (regularization constant and tube size) used in ES-CBS-SVR to deal with structural changes in the data. Overall, our analysis demonstrated that the ES-CBS-SVR can predict drought more accurately than traditional SVR in a warming climate.
... The main limitation of the SPI is that (i) it relies solely on a single input parameter, precipitation, and (ii) it fails to account for the influence of temperature, a critical factor in a region's overall water balance and water usage. We used the Standardised Drought Analysis Toolbox (SDAT) function by [36,37] to compute the SPI in MATLAB. ...
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Drought consequences depend on its type and class and on the preparedness and resistance of communities, which, in turn, depends on the knowledge and capacity to manage this climate disturbance. Therefore, this study aims to assess the drought regime in Southern Africa based on vegetation and meteorological indices. The SPI and SPEI were calculated at different timescales, using ERA5 data for the 1971–2020 period. The results revealed the following: (i) droughts of various classes at different timescales occurred throughout the study period and region; (ii) a greater Sum of Drought Intensity and Number, in all classes, but lower duration and severity of droughts with the SPI than with the SPEI; (iii) drought frequency varies from 1.3 droughts/decade to 4.5 droughts/decade, for the SPI at 12- to 3-month timescales; (iv) the number, duration, severity and intensity of drought present high spatial variability, which tends to decrease with the increasing timescale; (v) the area affected by drought increased, on average, 6.6%/decade with the SPI and 9.1%/decade with the SPEI; and (vi) a high spatial-temporal agreement between drought and vegetation indices that confirm the dryness of vegetation during drought. These results aim to support policymakers and managers in defining legislation and strategies to manage drought and water resources.
... Positive values of the SPEI indicate wet conditions relative to the long-term climatology, whereas negative values identify dry conditions. The standardization step is based on a nonparametric approach in which the probability distributions of the data samples are empirically estimated (Hao et al., 2014;Farahmand and AghaKouchak, 2015). ...
Preprint
In this paper, we assess and develop a climate service focused on the production of seasonal predictions for summer wildfires in a Mediterranean region through a participatory approach with end-users. We start by building a data-driven model that links a drought indicator (Standardised Precipitation Evapotranspiration Index; SPEI) with a series of burned areas in Catalonia (northeastern Spain). Afterwards, we feed this model with SPEI forecasts obtained through a combination of the antecedent observed conditions and climatology. Finally, we assess the forecasting skill of the system by using cross-validation to evaluate the predictions as if they had been made operationally. Our fire forecasting system reveals an untapped and useful burned area predictive ability. We argue that this source of predictability is mostly attributable to the effect of observed initial conditions on summer drought conditions. This system was conceived with the stakeholders, merging climate-driven predictions with information that is of interests to the users, including the identification of climate variables, thresholds and models. The co-production of this customized system allows fire-risk outlooks to be translated into usable information for fire management. This fire forecasting ability plays a crucial role in developing proactive fire management practices such as long-term fuel assessment and other fire-risk planning, thus minimising the impact of adverse climate conditions on summer burned area.
... One of the major limitations of the study is that it considered SPI for drought classification, which relies on two parametric distributions; hence, ignores the non-parametric drought indices (as proposed by Farahmand & AghaKouchak, 2015). We note that IMD monitors droughts primarily based on SPI-3, and rainfall anomaly. ...
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The natural variability in the occurrence of concurrent extremes of droughts and heatwaves is frequently attributed to climate change and anthropogenic causes, disregarding its association with large-scale global tel econnections. This study explores this association by demonstrating how concurrent droughts and heatwaves (CDHW) in India are temporally and spatially connected to multiple global teleconnections (referred to as climate variability modes). Composite and wavelet coherence analyses are implemented for the univariate evaluation of droughts and heatwaves—measured using the standardized precipitation index (SPI) and the standardized heat index (SHI), respectively—in relation to the climate variability modes. Furthermore, an attribution table framework is employed to examine the extremal dependence of concurrent heatwaves and droughts in India on the climate variability modes during 1951–2018. The results exhibit a higher probability of CDHW events when they are preceded by a large-scale global teleconnection. Overall, the insights drawn from this study suggest the possibility of relying on the climate variability modes to issue season-ahead forecasts of CDHW.
... This index is the most widely used drought index with physical significance, constructed on the basis of historical soil moisture time series, which has the advantages of simple and easy calculation, taking into account the characteristics of data distribution, etc., and is able to provide a basis for regional agricultural drought monitoring as well as drought impact assessment. The standardized soil moisture index (SSI) is calculated with reference to the standardized precipitation index (SPI) drought indicator 43 . ...
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It is of practical significance to provide a reference for drought mitigation and water resource enhancement planning in the Henan Province region and to analyze the spatial and temporal evolution characteristics of meteorological agricultural drought in the region. In this study, a multivariate (precipitation, potential evapotranspiration, soil moisture and normalized vegetation index) composite drought index CCDI was constructed based on the D Vine copula model, and the correlations between the CCDI and the standardized precipitation evapotranspiration index (SPEI) and between the CCDI and the standardized soil moisture index (SSI) were analyzed. The ability of the CCDI to evaluate meteorological agricultural drought was assessed, and typical drought events were selected for validation. The spatial and temporal evolution of drought in the Henan region from 1982 to 2022 was characterized using linear trends, M–K mutability tests, and drought centers of gravity, and future trends were analyzed using the Hurst index. The results show that (1) the CCDI correlates well with the SPEI and SSI (P < 0.01) and is able to characterize both meteorological and agricultural drought conditions in a better integrated way. (2) The fluctuation frequencies of the CCDI were obviously different at different time scales, indicating the different sensitivities of drought time scales to precipitation, potential evapotranspiration, soil moisture and the NDVI. All four seasons showed increasing trends at different rates. (3) During the study period of 1982–2022, the frequency of drought in Henan Province was mainly in the range of 21.95%-41.46%, and the intensity of drought occurrence was mainly dominated by light to moderate drought. (4) Based on the migration characteristics of the center of gravity of drought determined by ArcGIS, the center of gravity of drought during the study period is mostly concentrated in several cities in the central part of Henan, and the migration trajectory is mostly in the north‒south north–south direction, which is in line with the characteristics of the distribution of the data expressed by the standard deviation ellipse. (5) To analyze future drought trends in Henan, the mean values of the Hurst index in spring, summer, autumn and winter were 0.578, 0.766, 0.62 and 0.596, respectively, all of which showed persistent trends, while spring and winter Most areas may still have a dry trend in the future, the future dry trend in summer is mainly concentrated in the area around Henan, and the wet trend is distributed in the central-eastern part of the country and individual areas in the north and south. In the fall, most of the areas are wet trend, and individual areas have arid trend.The comprehensive drought index constructed in this paper can provide a new reference for drought prevention and drought relief in Henan Province.
... where Φ is the standard normal distribution function, and is the probability derived from Eq. (1). Farahmand and AghaKouchak (2015) provided detailed descriptions of deriving non-parametric SPEI. In this study, SPEI-3 was used to evaluate the performance of clustering in the SP region. ...
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Droughts may exhibit spatiotemporal heterogeneity at regional scale. Effective drought assessment and management necessitates identifying homogeneous areas. However, previous studies often simplified clustering analysis by focusing only on a single variable. In this study, we present a novel drought risk map for the Southern Plains (SP) region of the United States by integrating the wavelet-entropy approach with k -means clustering algorithm to capture spatio-temporal patterns of drought-related variables across various resolutions while eliminating redundant information. We considered multiple drought indicators and indices including gridded precipitation (P), potential evapotranspiration (PET), normalized difference vegetation index (NDVI), and Standardized Precipitation Evapotranspiration Index (SPEI) as well as geographical coordinates and topography map. Through evaluating five different combinations of input datasets, we selected the one demonstrating optimal results based on Davies-Bouldin and Calinski-Harabasz criteria. In addition to P, PET, and NDVI, including the coordinates and elevation as secondary variables significantly enhanced the clustering performance. Using these variables, the region was subdivided into 21 clusters. The Pearson’s correlation coefficients for the SPEI between centroid members and corresponding cells within clusters averaged between 0.84 to 0.94. Comparison with an existing cluster map (DRA) for the region revealed that our proposed cluster map showed higher variability between clusters for P, PET, and NDVI, confirming the robustness of the clustering results for drought conditions in the SP. The new clustering framework is expected to provide valuable insights for understanding and addressing drought dynamics in the SP region.
... In addition, it considers spatial heterogeneity for regions with highly different climates compared with the Palmer Drought Severity Index (Zargar et al. 2011). However, the SPEI value depends on the Probability Distribution Function of meteorological variables (Paulo et al. 2016); a parametric distribution function may not always fit the data, especially in continental/global scale studies (Farahmand and AghaKouchak 2015). Therefore, a nonparameter 3-month SPEI is used in this study. ...
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Analyzing spatiotemporal patterns of dryness/wetness is important for measures and strategy development for the resulting disasters. This research explores projected dryness/wetness patterns and influence factors in China under two Shared Socioeconomic Pathway (SSP)-based scenarios (SSP245 and SSP585). The dryness/wetness is evaluated by a non-parameter Standardized Precipitation Evapotranspiration Index, and the influence is analyzed by the GeoDetector method. The result shows that under SSP245, dryness is more likely to increase in autumn. It is primarily located in North-China, South-China, and Middle-lower Yangtze in summer and autumn and in South-China and Huang-Huai-Hai in other seasons. Wetness is more likely to be enhanced in winter, and simultaneous precipitation has more influence, especially in semiarid regions. Under SSP585, the dryness is enhanced throughout China except in winter, and the wetness is enhanced except in autumn. The enhanced wetness in spring and winter is located in North-China and in summer in Southwest China. Temperature has a greater influence in spring and autumn, and precipitation has a greater influence in winter on dryness. The interaction influence is enhanced in almost all regions and seasons under two scenarios. The results could be useful for land managers to develop strategies and mitigate the effects of climate change.
... If these distributions were used to fit precipitation time series with many zeros, zero and small rainfall amounts (usually indicating dry conditions) would not be well accounted for, which might affect the drought analysis. To resolve this issue, we split the precipitation values into zero values and positive values and estimate their probabilities separately (Naresh Kumar et al., 2009;Farahmand and AghaKouchak, 2015), as expressed in Eq. (2.5). In this way, we calculate SPI values for each day as follows: we calculate SPI values includes three steps. ...
... They do not require adopting a specific probability distribution for reference variables like SM, precipitation, and PET. This lack of assumption about a representative probability distribution eliminates the need to estimate parameters and assess goodness-of-fit, providing a computational advantage (Farahmand and AghaKouchak, 2015). However, as previously mentioned, non-parametric methods struggle with extrapolation when faced with new extremes. ...
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The European Space Agency (ESA) under the Climate Change Initiative (CCI) has developed a multi-satellite global, daily Soil Moisture (SM) dataset that has paved the ways for agricultural drought studies. To evaluate the performance of this ESACCI SM, two SM-based indices i.e. parametric distribution-based Standardized Soil Moisture Index (SSMI) and non-parametric distribution-based Empirical Standardized Soil Moisture Index (ESSMI) are computed to characterize agricultural drought in the Southern Plateau and Hills (SPH) in India from 1991 to 2020. SSMI and ESSMI are then compared with the Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI). The yearly temporal analysis revealed a consistent pattern among all the four indices with 2003 and 2020 marked as the driest and wettest years, respectively. On the other hand, monthly temporal analysis indicated SSMI and ESSMI lagged behind SPI and ESSMI suggesting a delayed response of SM to precipitation. Spatial distributions of indices showed that the SM-based indices effectively capture temporal variations of dryness or wetness across seasons. The near normal and mild to moderate droughts predominated (both spatially and temporally) the SPH and SSMI better captured the extreme drought areas compared to ESSMI. Further, Dynamic Threshold Run Theory (DTRT) is introduced to identify and characterize drought events based on their duration, frequency, intensity and peak. The findings revealed a resemblance in spatial distribution between the duration and frequency. The drought peak and intensity revealed a moderate nature of drought conditions. Overall, this study highlights the effectiveness of ESACCI SM product to characterize the agricultural droughts.
... Long-term extreme hydrometeorological events are analyzed using the nonparametric Standardized Precipitation Index (SPI; Farahmand and AghaKouchak 2015;Hao and Agha-Kouchak 2014). The SPI serves as a standardized metric for assessing precipitation anomalies, specifically designed to quantify both deficits and excesses of rainfall across diverse temporal scales. ...
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Southeastern South America is particularly vulnerable to extreme hydrometeorological events (EHEs). This study presents a multi-hazard analysis of long-term and short-term EHEs and their changes across southeastern South America for the 1961–1990 and 1991–2020 periods, using daily to monthly ERA5 data. Long-term EHEs are studied using the standardized precipitation index at 3- and 18-month timescales. Short-term EHEs are characterized by heatwaves, heavy precipitation, and flash droughts. Individual hazard components are derived by multiplying the frequency, duration, and intensity of the identified EHEs. The long-term and short-term EHE multi-hazard indices are formulated by aggregating these individual hazard components. Long-term multi-hazards prevail in the southwest and central west of the study region, including Argentina’s core crop region. A substantial water excess hazard hotspot is found in the southern areas, while the hotspot of seasonal to hydrological drought hazard is in northern and western areas. Short-term multi-hazards are more common in the north and central east, primarily impacting northeastern Argentina, southern Brazil, and southeastern Paraguay. In this hotspot region, heatwave hazard has increased by 30% in the last decades and flash drought and heavy precipitation frequencies are the highest. The current total multi-hazard, combining long-term and short-term multi-hazard indices, is higher and more widespread than between 1960 and 1990. Short-term hazards are more likely to co-occur, while long-term hazards tend to alternate. The study region is one of the most productive agricultural areas worldwide, so high EHE hazards can impact crop yields, threaten food security, and affect human well-being.
... The SPI has the advantages of using only precipitation data, to characterise drought at different scales, can be used to consistently monitor the characteristics of extreme events of precipitation and drought, and be applied to any region or type of climate conditions [7,41]. We used the Standardized Drought Analysis Toolbox (SDAT) function provided by [42,43] to calculate the SPI in MATLAB. ...
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Drought affects human and natural systems, human and animal life and health, and socioeconomic activities. Drought consequences depend on its type and class, but also on the preparedness and resistance of communities to this climate disturbance. In the last decades, droughts accounted for about 16% of the total number of disasters but were responsible for 95% of the number of deaths and 26% of economic losses in Africa. This study aims to assess the drought regime in Southern Africa based on drought and vegetation indices. The SPI and SPEI were calculated at different timescales, using ERA5 data for the 1971 – 2020 period. The spatiotemporal distribution of drought descriptors was analyzed and compared with the patterns of the NDVI, EVI and VCI vegetation indices. The results reveal (i) the occurrence of droughts of various classes and at different timescales throughout the study period and region, (ii) high spatial variability in the number, duration, severity and intensity of drought, which tends to decrease with increasing timescale, (iii) high spatial-temporal agreement between drought and vegetation indices that confirm the dryness of vegetation during drought. These results aim to support policymakers in defining legislation to manage drought and water resources.
... The standardized soil moisture index (SSMI) was generated by transforming the soil moisture information using a nonparametric empirical distribution. The approach of empirical distribution was adopted by Farahmand and AghaKouchak (2015) for the effective transformation of any time-series hydrological and climate data into standardized indices. In this research the empirical Gringorten plotting position (Gringorten 1963) was utilized to derive the marginal distribution of soil moisture. ...
Article
The soil moisture drought is an intermediate event between meteorological and agricultural droughts. The information on soil moisture droughts provides an indication about the resilience of the agricultural systems. In the present study, a comparative assessment of the monthly soil moisture gridded data products of Modern Era Retrospective analysis for Research and Applications, i.e., MERRA-2 (0.5° × 0.5°), Climate Prediction Center, i.e., CPC (0.5° × 0.5°), Global Land Data Assimilation System, i.e., GLDAS (0.25° × 0.25°), and European Space Agency Climate Change Initiative, i.e., ESA CCI (0.25° × 0.25°) during 2000 to 2019 was carried out in terms of drought occurrence and severity. The long-term soil moisture information was transformed into standardized soil moisture index (SSMI) using nonparametric distribution, followed by computation of drought duration and magnitude using thresholding approach. The long-term trends of drought parameters, i.e., duration and magnitude, were extracted using Mann–Kendall test and Sen’s Slope method, respectively. It was interesting to note that irrespective of zones, the SSMI derived from MERRA-2 and CPC have maximum coherence in terms of both pattern and intensity, followed by GLDAS. The trends of drought duration and magnitude differ based on the data products; however, frequent droughts were observed over parts of peninsular India and Indo-Gangetic plains irrespective of data products. The increased drought duration and magnitude were found over major parts of central and peninsular India, western parts of north-eastern India and eastern parts of north-western India.
... techniques such as remote sensing, statistical analysis, and machine learning have provided profound insights on the temporal and spatial dynamics of droughts globally (Dorjsuren et al., 2016;Han et al., 2022;Hargrove et al., 2023;Liou and Mulualem, 2019;Soomro et al., 2021;Wu et al., 2024). When these methodologies are adapted to the context of Taiwan, they could significantly enhance the accuracy and applicability of drought forecasts and assessments. ...
... We therefore use a non-parametric method for the calculation of the drought indices, following ref. 79. ...
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Globally, droughts are becoming longer, more frequent, and more severe, and their impacts are multidimensional. These impacts typically extend beyond the water balance, as long-term, cumulative changes in the water balance can lead to regime shifts in land cover. Here, we assess the effects of temporal changes in water supply and demand over multiple time scales on vegetation productivity and land cover changes in continental Chile, which has experienced a severe drought since 2010. Across most of continental Chile, we observed a persistent negative trend in water supply and a positive trend in atmospheric water demand since 2000. However, in water-limited ecoregions, we have observed a negative temporal trend in the water demand of vegetation, which intensified over longer time scales. This long-term decrease in water availability and the shift in water demand have led to a decrease in vegetation productivity, especially for the Chilean Matorral and the Valdivian temperate forest ecoregions. We found that this decrease is primarily associated with drought indices associated with soil moisture and actual evapotranspiration at time scales of up to 12 months. Further, our results indicate that drought intensity explains up to 78% of temporal changes in the area of shrublands and 40% of the area of forests across all ecoregions, while the burned area explained 70% of the temporal changes in the area of croplands. Our results suggest that the impacts of long-term climate change on ecosystems will extend to drought-tolerant vegetation types, necessitating the development of context-specific adaptation strategies for agriculture, biodiversity conservation and natural resource management.
... These indices were initially developed based on a parametric probability distribution function, which requires fitting hydroclimatic data to the distribution function. In many cases, however, the data do not fit this distribution function, resulting in a "statistically inconsistent and incomparable" method (Farahmand and AghaKouchak, 2015). To solve these problems, a non-parametric method was introduced by Farahmand and AghaKouchak (2015) that ensures statistical consistency and comparability of the standardized indices. ...
... Various standardized drought indices are used to assess the characteristics of drought events such as onset, cessation, duration and intensity (e.g., Chen et al., 2018Chen et al., , 2019Farahmand & AghaKouchak, 2015;Heim, 2002;Kwon et al., 2019;Mishra, 2020;Rivera et al., 2017;WMO, 2012;Zhao et al., 2017). These standardized drought indices facilitate the comparison of droughts across different regions and timescales. ...
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A reliable understanding of linkages between meteorological, hydrological and agricultural droughts (MD, HD, and AD respectively) is crucial to building resilience and planning for future climate changes. Despite Australia being prone to severe droughts, lagtimes of propagation (and recovery), from meteorological to hydrological and agricultural droughts across its large hydroclimatic regions, are poorly understood. Therefore, we investigate the characteristics of drought propagation and recovery time lags for droughts of four timescales and a combination of drought onset and cessation criteria in 407 unregulated catchments within six major precipitation zones across the country. We find that the propagation and recovery lags depend on climatic conditions, drought criteria and timescales. The median of catchment average propagation times from MD to HD across Australia varied from 0.8 to 1.7 months for 1‐month timescales, increasing to 2.2–5.0 months for 12‐month timescales. The corresponding recovery lagtimes were 1.3–3.7 and 1.7–7.0 months respectively. Similarly, the median of catchment average propagation times from MD to AD ranged from 0.8 to 1.9 months for 1‐month timescales, increasing to 0.6–5.0 months for 12‐month. The corresponding recovery lagtimes were 0.7–2.8 and 0.3–8.7 months respectively. For droughts of smaller timescales, propagation and recovery lags are linearly correlated with recovery lagtimes consistently greater than propagation times. However, as the timescale increases, these relationships weaken suggesting effects of other catchment attributes (e.g., groundwater contributions) on lag relationships.
... If the parametric method fails to provide complete coverage of the scatter plot, the implementation of a non-parametric approach is necessary. The application of non-parametric probability plotting approaches in hydrology has been extensively demonstrated, as exemplified in the research conducted by Farahmand and AghaKouchak (2015), where a comprehensive framework was presented for the modeling of non-parametric drought indices. In this research, standardization of the CDF is carried out according to the following set of equations: ...
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Climate changes and global warming increase risk of recurrent extreme and complex climatic features. It necessitates accurate modeling and forecasting of climate phenomena for sustainable development goals. However, machine learning algorithms and advanced statistical models are extensively employed to analyze complex data and make predictions related to climate phenomena. It is important to have comprehensive knowledge to use these models and consider their potential implications. This study aims to evaluate and compare some popular machine learning and probabilistic methods by analyzing various time series indices associated with precipitation and temperature. For application, time series data of Standardized Precipitation Temperature Index (SPTI), Standardized Temperature Index (STI), Standardized Compound Drought and Heat Index (SCDHI), and Biased Diminished Weighted Regional Drought Index (BDWRDI) are used from various meteorological regions of Pakistan. The performance of each algorithm is compared using Residual Mean Square Error (RMSE) and Mean Average Error (MAE). The outcomes associated with this research indicate a higher preference of neural networks over machine learning methods in the training sets. However, the efficiency varies from model to model, indicator to indicator, time scale to time scale, and location to location during the testing phase. The most appropriate models are found by considering a list of candidates forecasting models and investigating the performance of each model.
... The standardised snow water equivalent index (SWEI; Huning and AghaKouchak, 2020) aims to quantify snow drought conditions. To compute this index we followed Huning and AghaKouchak (2020), who used a non-parametric approach (Farahmand and AghaKouchak, 2015) to standardise SWE time series. In general, instead of fitting a specific distribution function to the data, the SWEI computes the probabilities associated with the SWE time series using the empirical Gringorten plotting position (Gringorten, 1963): ...
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There is a wide variety of drought indices, yet a consensus on suitable indices and temporal scales for monitoring streamflow drought remains elusive across diverse hydrological settings. Considering the growing interest in spatially distributed indices for ungauged areas, this study addresses the following questions: (i) What temporal scales of precipitation-based indices are most suitable to assess streamflow drought in catchments with different hydrological regimes? (ii) Do soil moisture indices outperform meteorological indices as proxies for streamflow drought? (iii) Are snow indices more effective than meteorological indices for assessing streamflow drought in snow-influenced catchments? To answer these questions, we examined 100 near-natural catchments in Chile with four hydrological regimes, using the standardised precipitation index (SPI), standardised precipitation evapotranspiration index (SPEI), empirical standardised soil moisture index (ESSMI), and standardised snow water equivalent index (SWEI), aggregated across various temporal scales. Cross-correlation and event coincidence analysis were applied between these indices and the standardised streamflow index at a temporal scale of 1 month (SSI-1), as representative of streamflow drought events. Our results underscore that there is not a single drought index and temporal scale best suited to characterise all streamflow droughts in Chile, and their suitability largely depends on catchment memory. Specifically, in snowmelt-driven catchments characterised by a slow streamflow response to precipitation, the SPI at accumulation periods of 12–24 months serves as the best proxy for characterising streamflow droughts, with median correlation and coincidence rates of approximately 0.70–0.75 and 0.58–0.75, respectively. In contrast, the SPI at a 3-month accumulation period is the best proxy over faster-response rainfall-driven catchments, with median coincidence rates of around 0.55. Despite soil moisture and snowpack being key variables that modulate the propagation of meteorological deficits into hydrological ones, meteorological indices are better proxies for streamflow drought. Finally, to exclude the influence of non-drought periods, we recommend using the event coincidence analysis, a method that helps assessing the suitability of meteorological, soil moisture, and/or snow drought indices as proxies for streamflow drought events.
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Extreme hydrometeorological events (EHEs) pose significant risks to central-northeastern Argentina, requiring a nuanced understanding of subnational-level vulnerability and risk. This study integrates physical and socio-economic data to evaluate individual and multi-hazard risks across long-term and short-term time scales. Vulnerability is analyzed through exposure, sensitivity, and adaptive capacity. Risk is assessed as the interaction between EHE hazards and vulnerability. The analysis reveals a medium average vulnerability across the region, with marked spatial differences. Central Argentina— encompassing southern Santa Fe, eastern Córdoba, and northern Buenos Aires—shows medium vulnerability due to high exposure, counterbalanced by low sensitivity and high adaptive capacity. In contrast, northwest and central-western regions—including Formosa, eastern Salta, and eastern Santiago del Estero—exhibit high vulnerability driven by high sensitivity and low adaptive capacity despite low exposure. Heatwave risk is the highest and most widespread, particularly in northern Argentina. Risks from long-term dry and wet extreme precipitation display distinct regional patterns. Heavy precipitation risks are locally high in the northeast. Flash drought risk remains comparatively low across the region. The findings highlight that long-term multi-hazard risk is the most extensive and severe, while short-term multi-hazard risk is less widespread but dominated by heatwaves. Despite limitations, including uncertainties in input data and a constrained set of indicators, these results underscore the need for tailored adaptation strategies. Efforts should focus on reducing exposure in the south through improved infrastructure and agricultural practices and enhancing adaptive capacity in the north. Future research should explore compound risks and identify practical adaptation measures.
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Global warming will lead to strong drought challenges in China. Exploring the spatiotemporal patterns of and changes in meteorological drought in China in the future is therefore of great significance for minimizing drought risks and for mitigating agricultural losses. It is crucial to consider the drought seasonality and aggregation while exploring the spatiotemporal patterns of and changes in meteorological drought in China. This study applied the ST-Moran scatterplot method to identify the drought spatiotemporal aggregation areas (DSTAAs) in China during 2021–2100 under three shared socioeconomic pathways (SSP1-2.6, SSP2-4.5, and SSP5-8.5 emission scenarios). Based on the identification results, we further analyzed the spatiotemporal patterns of and changes in drought in different seasons, agricultural regions, and time periods in China, and the detailed drought conditions on the Northeast China Plain. The results highlight that (1) the drought will abate, become slightly worse, and become significantly worse over time under the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios. (2) Seasonally, the main drought seasons exhibit a transition trend from spring-winter to summer-autumn over time. As the emission level increases, this transition trend becomes increasingly evident. Detailed results in the Northeast China Plain confirm this seasonal transition trend in China and indicate that droughts in the major grain-producing areas in summer require more attention for preparedness and mitigation. (3) Spatially, the Northeast China Plain, Qinghai Tibet Plateau, and the northern arid and semiarid region have the largest number of significant DSTAAs. These results will support relevant institutions in formulating strategies for drought preparedness and mitigation.
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Drought is a significant natural disaster with adverse effects on both social and ecological systems. Unlike other natural disasters, drought develops slowly and gradually, complicating its early detection and often resulting in severe impacts on affected regions. Consequently, accurate and dependable drought monitoring is essential for devising effective mitigation strategies. Standardized drought indices are vital tools in drought monitoring, providing a means to quantify and characterize drought events. Most standardized drought indices utilize the Standardized Precipitation Index (SPI) method, which is valued for its simplicity and flexibility. However, this study contends that the SPI method lacks several critical elements, particularly in practice, such as determining the most suitable probability distribution for hydrometeorological variables. Therefore, this study proposes a novel methodology for calculating standardized drought indices and assesses its performance against conventional and nonparametric standardized indices, employing various methods capable of capturing complex dependencies. The novel methodology involves identifying the best-fit probability distributions for each data group through various goodness-of-fit tests. This approach ensures that each group is modeled optimally, considering the seasonal variations inherent to each group. The Seyhan River Basin has been chosen as a case study for the proposed methodology. The drought characteristics of the basin are analyzed using indices derived from the new methodology, the conventional SPI method, and the nonparametric method. Additionally, trend analyses were performed on the calculated indices to identify any directional changes in drought patterns within the Seyhan River Basin. The performance of the proposed methodology was evaluated by analyzing its relationship with nonparametric standardized indices and comparing it to the relationship between conventional standardized indices and nonparametric standardized indices. The results show that the newly proposed methodology outperforms the conventional SPI method across various dependence measures, suggesting it captures the underlying data structure more effectively than the SPI method.
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Las sequías son un fenómeno de escala regional que afecta la seguridad alimentaria, la provisión de agua y energía, cuya severidad, duración y frecuencia se espera aumenten en un contexto de cambio climático. En el presente trabajo se estudió la tendencia en la precipitación anual y estacional en la provincia de Santa Cruz; la ocurrencia de sequías meteorológicas y las proyecciones climáticas hasta el año 2100. Para el cálculo de las sequías se utilizó el Índice Estandarizado de Precipitación (SPI) en una escala de 6 meses (SPI6) para un periodo pasado reciente (1961-2020) y dos periodos futuros (2041-2060 y (2081-2100). Se pudo observar que más de un 70% de la superficie de la provincia presentó una tendencia negativa en la precipitación anual para el periodo 1961-2020. Este efecto fue más acentuado al estudiarlo de forma estacional, donde se observó que durante el otoño e invierno se presentaron las tendencias más negativas, ubicadas hacia la región noroeste de la provincia. La frecuencia de eventos totales de sequía (ES) para el pasado reciente se presentaron entre 2,6 a 4,5 eventos/década, no coincidiendo las zonas más afectadas por sequías con las regiones de tendencias negativas en la precipitación. Con respecto al cambio climático, al analizar los escenarios de mayor emisión de gases de efecto invernadero (GEI), (SSP2-4.5 y SSP5-8.5) para el periodo 2081-2100, se pudo observar que una mayor superficie del territorio provincial será afectada por una disminución en la precipitación anual de hasta un 30% para SSP5-8.5. Analizando las sequías proyectadas, se determinó que la región oeste de la provincia presentará una menor cantidad de eventos de sequía, pero de mayor duración y severidad que en el periodo de referencia acentuándose en el escenario SSP5-8.5.
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Global climate models (GCMs) are extensively used to calculate standardized drought indices. However, inaccuracies in GCM simulations and uncertainties inherent in the standardization methodology limit the precision of drought evaluations. The objective of this research is to remove bias in GCMs for improving drought monitoring and assessment. Consequently, this article proposes a new framework for drought index under the ensemble of GCMs—Multi‐Model Quantile Mapped Standardized Precipitation Index (MMQMSPI). In accordance of Standardized Precipitation Index (SPI), the second stage derives a new index by assessing the feasibility of parametric and nonparametric models during standardization. In the application, we used 18 GCMs from the Coupled Model Intercomparison Project Phase 6 (CMIP6) data of precipitation across 32 grid points within the Tibetan Plateau region. The comparative findings reveal that the integration of KCGMD is the most suitable choice compared to other best‐fitted univariate distributions in both features of the proposed framework. In this research, we assess the implications of evaluating future patterns of drought for the years 2015–2100 using seven different time periods and three different future scenarios. Temporal behavior clearly shows monthly variations in the pattern of MMQMSPI, and these variations differ on each time scale, but a drastic change can be seen over the long term, i.e., extreme dry and wet conditions, with a higher probability in all scenarios.
Chapter
In the first step of analysis, the observed and grid precipitation and relative soil moisture data were compared for the reference period 2008–2016. The study utilized the (IDW) interpolation method to map the spatial distribution of annual averaged observed and grid precipitation as well as relative soil moisture across China from 2008 to 2016.
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Drought is one of the most important meteorological disasters. Many results of meteorological droughts in the Yunnan-Guizhou Plateau (YGP) are currently being studied, however, fewer results have been integrated to analyze the hydro-meteorological droughts. Therefore, the hydro-meteorological drought characteristics and their relationships with the sea surface temperature (SST) and climate indexes were studied using the reanalysis dataset and the non-parametric standardized precipitation evapotranspiration runoff index (SPERI). The results showed that (1) The YGP mainly exhibited drought in annual, winter, and drought season, and drought in spring (summer, autumn, and rain season) mainly occurred in the west (east). Moreover, the YGP drought was dominated by a decreasing trend. (2) The SPERIs in annual, spring, and drought season were positively correlated with longitude, and the other seasons were negatively correlated. (3) Except for the spring, winter and drought season, the area of the mild drought in the other time scales, as well as the area of the moderate, severe, and extreme drought at all time scales (except for summer), showed an increasing trend. (4) The drought duration was longer in some regions of the west, the drought severity was stronger in some regions of the southwest, and the drought intensity was higher in some regions of the east. (5) The regions where the YGP drought area had a significant positive correlation with SSTs were mainly located in the Atlantic, Indian, Western Pacific, and Arctic Ocean. The best relationships with SPERI were the North Atlantic-Eurasia teleconnection and the Central Indian Precipitation.
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The Standardized Precipitation Index (SPI) is widely used as drought meteorological index, to identify the duration and/or severity of a drought. The SPI is usually computed by fitting the gamma probability distribution to the observed precipitation data. In this work, the possibility to calculate SPI by fitting to the precipitation data the normal and the log-normal probability distributions was studied. For this purpose, 19 time series of monthly precipitation of 76 years were used, and the assumption that the gamma probability distribution would provide better representation of the precipitation data than log-normal and normal distributions, at various time scales (1, 3, 6, 12 and 24 months) was tested. It is concluded that for SPI of 12 or 24 months, the log-normal or the normal probability distribution can be used for simplicity, instead of gamma, producing almost the same results.
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Droughts are difficult to detect and monitor. Drought indices, most commonly the Palmer Drought Severity Index (PDSI), have been used with limited success as operational drought monitoring tools and triggers for policy responses. Recently, a new index, the Standardized Precipitation Index (SPI), was developed to improve drought detection and monitoring capabilities. The SPI has several characteristics that are an improvement over previous indices, including its simplicity and temporal flexibility, that allow its application for water resources on all timescales. In this article, the 1996 drought in the southern plains and southwestern United States is examined using the SPI. A series of maps are used to illustrate how the SPI would have assisted in being able to detect the onset of the drought and monitor its progression. A case study investigating the drought in greater detail for Texas is also given. The SPI demonstrated that it is a tool that should be used operationally as part of a state, regional, or national drought watch system in the United States. During the 1996 drought, the SPI detected the onset of the drought at least 1 month in advance of the PDSI. This timeliness will be invaluable for improving mitigation and response actions of state and federal government to drought-affected regions in the future.
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This paper investigates the impact of climate change on drought by addressing two questions: (1) How reliable is the assessment of climate change impact on drought based on state-of-the-art climate change projections and downscaling techniques? and (2) Will the impact be at the same level from meteorological, agricultural, and hydrologic perspectives? Regional climate change projections based on dynamical downscaling through regional climate models (RCMs) are used to assess drought frequency, intensity, and duration, and the impact propagation from meteorological to agricultural to hydrological systems. The impact on a meteorological drought index (standardized precipitation index, SPI) is first assessed on the basis of daily climate inputs from RCMs driven by three general circulation models (GCMs). Two periods and two emission scenarios, i.e., 1991-2000 and 2091-2100 under B1 and A1Fi for Parallel Climate Model (PCM), 1990-1999 and 2090-2099 under A1B and A1Fi for Community Climate System Model, version 3.0 (CCSM3), 1980-1989 and 2090-2099 under B2 and A2 for Hadley Centre CGCM (HadCM3), are undertaken and dynamically downscaled through the RCMs. The climate projections are fed to a calibrated hydro-agronomic model at the watershed scale in Central Illinois, and agricultural drought indexed by the standardized soil water index (SSWI) and hydrological drought by the standardized runoff index (SRI) and crop yield impacts are assessed. SSWI, in particular with extreme droughts, is more sensitive to climate change than either SPI or SRI. The climate change impact on drought in terms of intensity, frequency, and duration grows from meteorological to agricultural to hydrological drought, especially for CCSM3-RCM. Significant changes of SSWI and SRI are found because of the temperature increase and precipitation decrease during the crop season, as well as the nonlinear hydrological response to precipitation and temperature change.
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The occurrence of widespread, severe drought in Africa, India, North America, China, the USSR, Australia, and western Europe has once again underscored the vulnerability of developed and developing societies to drought The occurrence of severe drought during 1982-83 is shown in Fig. 1. These recent droughts have emphasized the need for more research on the causes as well as the impacts of drought and the need for additional planning to help mitigate the possible worst effects of future droughts. Drought has been the subject of a great deal of systematic study, particularly reconstructions of drought history, computations of drought frequency, and, to a lesser extent, investigations of first-, second-, and even third-order impacts of drought on society.
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Chapter
Despite the fact that drought is an inevitable feature of climate for nearly all climatic regimes, progress on drought preparedness has been extremely slow. Many nations now feel a growing sense of urgency to move forward with a more proactive, risk-based drought management approach (ISDR, 2003; Wilhite, 2000). Certainly the widespread occurrence of this insidious natural hazard in recent years has contributed to the sense of urgency. But, drought occurs in many parts of the world and affects portions of many countries on an annual basis. For example, the average area affected by severe and extreme drought in the United States each year is 14%. This figure has been as high as 65% (1934) and has hovered in the 35–40% range in recent years. So, does the widespread occurrence of drought in the United States over the last 5–6 years explain the emergence of several national initiatives centered on drought monitoring and preparedness, given that events of this magnitude have not motivated policy makers to act in the past? Our experience would suggest that this is only one of the factors contributing to the increased attention being directed to this subject in the United States and in other drought-prone countries.
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A multi-institutional partnership, the US Agency for International Development's Famine Early Warning System Network (FEWS NET) provides routine monitoring of climatic, agricultural, market, and socioeconomic conditions in over 20 countries. FEWS NET supports and informs disaster relief decisions that impact millions of people and involve billions of dollars. In this chapter, we focus on some of FEWS NET's hydrologic monitoring tools, with a specific emphasis on combining low frequency and high frequency assessment tools. Low frequency assessment tools, tied to water and food balance estimates, enable us to evaluate and map long-term tendencies in food security. High frequency assessments are supported by agrohydrologic models driven by satellite rainfall estimates, such as the Water Requirement Satisfaction Index (WRSI). Focusing on eastern Africa, we suggest that both these high and low frequency approaches are necessary to capture the interaction of slow variations in vulnerability and the relatively rapid onset of climatic shocks.
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Adapting the usual manual methods of computing Kendall's tau to automatic computation result in a running time of order N . A method is described with running time of order N log N.
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Adapting the usual manual methods of computing Kendall's tau to automatic computation result in a running time of order N2. A method is described with running time of order N log N.
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S ummary This paper is concerned with the non‐parametric estimation of a distribution function F , when the data are incomplete due to grouping, censoring and/or truncation. Using the idea of self‐consistency, a simple algorithm is constructed and shown to converge monotonically to yield a maximum likelihood estimate of F. An application to hypothesis testing is indicated.
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Drought chokes ecosystems, strangles economies, and threatens human health [Wilhite, 2005]. In the United States, drought has recently forced states, including economic powerhouses like California and Texas, to declare a state of emergency. Complications such as an increase in fires, rising food prices, and water scarcity further compound the effects of drought [Pozzi et al., 2013; Hao et al., 2014].
Article
This paper analyzes changes in areas under droughts over the past three decades and alters our understanding of how amplitude and frequency of droughts differ in the Southern Hemisphere (SH) and Northern Hemisphere (NH). Unlike most previous global-scale studies that have been based on climate models, this study is based on satellite gauge-adjusted precipitation observations. Here, we show that droughts in terms of both amplitude and frequency are more variable over land in the SH than in the NH. The results reveal no significant trend in the areas under drought over land in the past three decades. However, after investigating land in the NH and the SH separately, the results exhibit a significant positive trend in the area under drought over land in the SH, while no significant trend is observed over land in the NH. We investigate the spatial patterns of the wetness and dryness over the past three decades, and we show that several regions, such as the southwestern United States, Texas, parts of the Amazon, the Horn of Africa, northern India, and parts of the Mediterranean region, exhibit a significant drying trend. The global trend maps indicate that central Africa, parts of southwest Asia (e.g., Thailand, Taiwan), Central America, northern Australia, and parts of eastern Europe show a wetting trend during the same time span. The results of this satellite-based study disagree with several model-based studies which indicate that droughts have been increasing over land. On the other hand, our findings concur with some of the observation-based studies.
Article
A monthly dataset of Palmer Drought Severity Index (PDSI) from 1870 to 2002 is derived using historical precipitation and temperature data for global land areas on a 2.58 grid. Over Illinois, Mongolia, and parts of China and the former Soviet Union, where soil moisture data are available, the PDSI is significantly correlated (r 5 0.5 to 0.7) with observed soil moisture content within the top 1-m depth during warm-season months. The strongest correlation is in late summer and autumn, and the weakest correlation is in spring, when snowmelt plays an important role. Basin-averaged annual PDSI covary closely (r 5 0.6 to 0.8) with streamflow for seven of world's largest rivers and several smaller rivers examined. The results suggest that the PDSI is a good proxy of both surface moisture conditions and streamflow. An empirical orthogonal function (EOF) analysis of the PDSI reveals a fairly linear trend resulting from trends in precipitation and surface temperature and an El Nino- Southern Oscillation (ENSO)-induced mode of mostly interannual variations as the two leading patterns. The global very dry areas, defined as PDSI ,2 3.0, have more than doubled since the 1970s, with a large jump in the early 1980s due to an ENSO-induced precipitation decrease and a subsequent expansion primarily due to surface warming, while global very wet areas (PDSI .1 3.0) declined slightly during the 1980s. Together, the global land areas in either very dry or very wet conditions have increased from ;20% to 38% since 1972, with surface warming as the primary cause after the mid-1980s. These results provide observational evidence for the increasing risk of droughts as anthropogenic global warming progresses and produces both increased temperatures and increased drying.
Article
The Palmer Drought Severity Index (PDSI) has been calculated for about 30 years as a means of providing a single measure of meteorological drought severity. It was intended to retrospectively look at wet and dry conditions using water balance techniques. The Standardized Precipitation Index (SPI) is a probability index that was developed to give a better representation of abnormal wetness and dryness than the Palmer indices. Before the user community will accept the SPI as an alternative to the Palmer indices, a standard method must be developed for computing the index. Standardization is necessary so that all users of the index will have a common basis for both spatial and temporal comparison of index values. If different probability distributions and models are used to describe an observed series of precipitation, then different SPI values may be obtained. This article describes the effect on the SPI values computed from different probability models as well as the effects on dry event characteristics. It is concluded that the Pearson Type III distribution is the `best' universal model, and that the reliability of the SPI is sample size dependent. It is also concluded that because of data limitations, SPIs with time scales longer than 24 months may be unreliable. An internet link is provided that will allow users to access Fortran 77 source code for calculating the SPI.
Article
A new global index used operational satellite remote sensing as primary inputs and enhances near real-time drought monitoring and mitigation efforts. A DSI algorithm was developed using satellite-derived ET, PET, and NDVI products to detect and monitor droughts on a global basis. The DSI algorithm was developed to overcome several limitations and to exploit the relative volume of operational satellite records and associated vegetation indicators. The input datasets and the DSI model were introduced and DSI patterns and anomalies in relation to alternative global PDSI information and documented regional drought events. The MODIS operational net primary production (NPP) product was used as an indicator of vegetation productivity changes under documented severe droughts in the Amazon, Europe, and Russia, and to evaluate corresponding DSI- and PDSI-based vegetation drought responses.
Article
Defining droughts based on a single variable/index (e.g., precipitation, soil moisture, or runoff) may not be sufficient for reliable risk assessment and decision-making. In this paper, a multivariate, multi-index drought-modeling approach is proposed using the concept of copulas. The proposed model, named Multivariate Standardized Drought Index (MSDI), probabilistically combines the Standardized Precipitation Index (SPI) and the Standardized Soil Moisture Index (SSI) for drought characterization. In other words, MSDI incorporates the meteorological and agricultural drought conditions for overall characterization of drought. In this study, the proposed MSDI is utilized to characterize the drought conditions over several Climate Divisions in California and North Carolina. The MSDI-based drought analyses are then compared with SPI and SSI. The results reveal that MSDI indicates the drought onset and termination based on the combination of SPI and SSI, with onset being dominated by SPI and drought persistence being more similar to SSI behavior. Overall, the proposed MSDI is shown to be a reasonable model for combining multiple indices probabilistically.