Enhancing Drought Forecasting Accuracy: A Wavelet-ARIMA Modelling Approach for Standardized Precipitation Index Data

This study introduces ensemble empirical mode decomposition (EEMD) coupled with the autoregressive integrated moving average (ARIMA) model for drought prediction. In the realm of drought forecasting, we assess the EEMD-ARIMA model against the traditional ARIMA approach, using monthly precipitation data from January 1970 to December 2019 in Herat province, Afghanistan. Our evaluation spans various timescales of standardized precipitation index (SPI) 3, SPI 6, SPI 9, and SPI 12. Statistical indicators like root-mean-square error, mean absolute error (MAE), mean absolute percentage error (MAPE), and R2 are employed. To comprehend data features thoroughly, each SPI series initially computed from the original monthly precipitation time series. Subsequently, each SPI undergoes decomposition using EEMD, resulting in intrinsic mode functions (IMFs) and one residual series. The next step involves forecasting each IMF component and residual using the corresponding ARIMA model. To create an ensemble forecast for the initial SPI series, the predicted outcomes of the modeled IMFs and residual series are finally added. Results indicate that EEMD-ARIMA significantly enhances drought forecasting accuracy compared to conventional ARIMA model.

Standard Precipitation Index (SPI) and, its variant, Standard Precipitation and Evapotranspiration Index (SPEI) are among the most commonly used drought assessment indices worldwide. SPI uses precipitation as its only input to assess drought. Unlike SPI, SPEI uses both precipitation and temperature, thereby considering the influence of global warming to some extent. Assessments of performance between SPI and SPEI is well addressed. However, no adequate literature was found on the assessment of the degree of agreement between SPI and SPEI at different time scales. Hence, this research focused on examining the level of agreement between SPI and SPEI as drought assessment tools at 1-month, 3-month, 6-month, 12-month and 24-month time scales. The test of agreement between SPI and SPEI was conducted using Cohen’s Kappa statistics and the Bland–Altman method. Gridded monthly precipitation and temperature Climatic Research Unit time-series data version 4.01 were used to calculate SPI and SPEI for the period 1901 to 2016. The results of Cohen’s Kappa statistics indicate that there existed a fair degree of agreement between SPI and SPEI at all time scales. A positive linear correlation (r > 0.7, p < 0.001) was also observed between SPI and SPEI ratings at all time scales. Small mean difference (bias) in the Bland and Altman analyses result indicated for the presence of agreement between the assessment tools. This study has found that there is an acceptable level of agreement between SPI and SPEI ratings in the study area, at all timescales.

Drought forecasting plays an important role in the planning and management of water resources systems. In this paper, a hybrid wavelet and adaptive neuro-fuzzy inference system (WANFIS) is proposed for drought forecasting. The WANFIS model was developed by combining two methods, namely a discrete wavelet transform and adaptive neuro-fuzzy inference system (ANFIS) model. To assess the effectiveness of this model, the standardised precipitation index (SPI) was applied for meteorological drought analysis at five rainfalls gauging stations located around the Klang River basin, Malaysia. The SPI drought forecasting capability performance of the WANFIS model is compared with the autoregressive integrated moving average (ARIMA) and ANFIS models using various statistical measures. Comparison of the results reveals that the WANFIS model performs better than the traditional ANFIS and ARIMA models.

Water resources have always been a major concern, particularly in arid and semiarid parts of the world. Low precipitation and its uneven distribution in Algeria, along with fast population and agriculture activity increase and, particularly, recent droughts, have made water availability one of the country’s most pressing issues. The objectives of the studies reported in this article are to investigate and forecast the meteorological and hydrological drought in Wadi Ouahrane basin (270 km2) using linear stochastic models known as Autoregressive Integrated Moving Average (ARIMA) and multiplicative Seasonal Autoregressive Integrated Moving Average (SARIMA). In particular, data from 6 precipitation stations and 1 hydrometric station for the period 1972–2018 were used to evaluate the Standardized Precipitation Index (SPI) and the Standardized Runoff Index (SRI) for 12 months. Then, the multiplicative ARIMA model was applied to forecasting drought based on SPI and SRI. As a result, the ARIMA model (1,0,1)(0,0,1)12 for SPI and (1,0,1)(1,0,1)12 for SRI were shown to be the best models for drought forecast. In fact, both models exhibited high quality for SPI and SRI of 0.97 and 0.51 for 1-month and 12-month lead time, respectively, based on validation R2. In general, prediction skill decreases with increase in lead time. The models can be used with reasonable accuracy to forecast droughts with up to 12 months of lead time.

Unlike other natural disasters, drought events evolve slowly in time and their impacts generally span a long period of time. Such features do make possible a more effective drought mitigation of the most adverse effects, provided a timely monitoring of an incoming drought is available. Among the several proposed drought monitoring indices, the Standardized Precipitation Index (SPI) has found widespread application for describing and comparing droughts among different time periods and regions with different climatic conditions. However, limited efforts have been made to analyze the role of the SPI for drought forecasting. The aim of the paper is to provide two methodologies for the seasonal forecasting of SPI, under the hypothesis of uncorrelated and normally distributed monthly precipitation aggregated at various time scales k. In the first methodology, the auto-covariance matrix of SPI values is analytically derived, as a function of the statistics of the underlying monthly precipitation process, in order to compute the transition probabilities from a current drought condition to another in the future. The proposed analytical approach appears particularly valuable from a practical stand point in light of the difficulties of applying a frequency approach due to the limited number of transitions generally observed even on relatively long SPI records. Also, an analysis of the applicability of a Markov chain model has revealed the inadequacy of such an approach, since it leads to significant errors in the transition probability as shown in the paper. In the second methodology, SPI forecasts at a generic time horizon M are analytically determined, in terms of conditional expectation, as a function of past values of monthly precipitation. Forecasting accuracy is estimated through an expression of the Mean Square Error, which allows one to derive confidence intervals of prediction. Validation of the derived expressions is carried out by comparing theoretical forecasts and observed SPI values by means of a moving window technique. Results seem to confirm the reliability of the proposed methodologies, which therefore can find useful application within a drought monitoring system.

Drought is one of the most significant hazards in Sri Lanka. Status of drought in Sri Lanka was assessed using Standardized Precipitation Index (SPI) at 3, 6, and 12 months’ time scales using monthly rainfall (1970 to 2017) data of 54 weather stations. The frequency of drought events was evaluated using SPI, and trend of SPI was also detected using the Mann–Kendall (MK) test and Sen’s slope estimator. The result based on SPI identified hydrological years 1975-76, 1982-83, 1986-87, 1988-89, 2000-01, 2001-02, 2013-14, and 2016-17 as drought years for 52, 32, 35, 33, 33, 31, 31, and 31% of tested stations (54), respectively, at annual time scale. Comparison of the SPI at different time scales revealed that more drought events (SPI ≤ −1) occurred during Yala season than Maha cropping season. Considering the Thiessen polygon average rainfall, more frequent drought events occurred in the dry zone (57%) than the wet (49%) and intermediate zone (47%) at the annual time scale. SPI trend results showed greater increase in drought (59% of stations) during Yala seasons as compared to the Maha cropping season (15% of stations) in Sri Lanka.

Global climate change, temperature rise and some kinds of extreme meteorological disaster, such as the drought, threaten the development of the natural ecosystem and human society. Forecasting in drought is an important step toward developing a disaster mitigation system. In this study, we utilized the statistical, autoregressive integrated moving average (ARIMA) model to predict drought conditions based on the standardized precipitation index (SPI) and standardized precipitation evapotranspiration index (SPEI) in a major tributary in the lower reaches of Nu River. We employed data from 2001 to 2010 to fit the model and data from 2011 to 2013 for model validation. The results showed that the coefficients of determination (R2) was over 0.85 in each index series, and the root-mean-square error and mean absolute error were low, implying that the ARIMA model is effective and adequate for this region.

The objective of this study is to analyze drought patterns in the Tano River Basin (TRB) of Ghana using Standardized Precipitation Index (SPI) and Reconnaissance Drought Index (RDI). Precipitation data from 1981 to 2019 for the TRB was accessed from Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS), extracted into time Series using Python to four locations within the basin and used for the analysis together with the National Aeronautics and Space Administration (NASA) POWER (Prediction Of Worldwide Energy Resource) Temperature data. Anderson-Darling test was performed to check for the normality of the precipitation. Two separate station data sets from TAHMO and Earth Observation Research Innovation Centre (EORIC) were used to validate the CHIRPS data. The Scaler Index (SI) from the two data sets are respectively 0.383 and 0.016. This indicates the CHIRPS data extracted is sufficiently accurate. The SPI and RDI on the time scales of 1, 3, 6 and 12 months were calculated using the Drought Indices Calculator (DrinC) software and characterized into the magnitude, duration, and severity of the drought. Regression analysis was performed to compare RDI and SPI values. The results show that the coefficient of regression R2 is 0.9789, 0.9689 and 0.8799 for 1, 6 and 12 months respectively. This indicates a stronger correlation between SPI and RDI values. However, R2 is observed to decreases with increasing time scale, which means for shorter time scales, SPI and RDI are more similar than for longer time scales. To further examine the possible impacts of climate change on the drought profile of the basin, the Mann-Kendall trend test was conducted to compare the trends in SPI and RDI for 1, 6 and 12 timescales. Apart from RDI 6 for Tanoso which recorded a decrease in trend of – 0.17 as against 0.14 of SPI 6, all other timescales recorded an increase in trend for RDI as compared to SPI. Although most of these increases in trend is not significant at 10% significance level, a trend of 1.95 and 1.71 of RDI 1 for Buako and Sepremboi respectively were significant compared to that of SPI 1 for same stations. These increases in trend of RDI as compared to SPI suggests the possible impact of climate change since RDI estimation takes into consideration potential evapotranspiration (PET), which is a factor of temperature. This could have negative implications on agricultural production and drinking water supply within the basin considering that the basin solely relies on surface water for crop production and drinking water supply.

Drought is a slow‐onset, creeping natural hazard and a recurrent phenomenon in the arid and semi‐arid regions of Gujarat (India). In Asia, the standardized precipitation index (SPI) has gained wider acceptance in the detection and the estimation of the intensity, magnitude and spatial extent of droughts. The main advantage of the SPI, in comparison with other indices, is that the SPI enables both determination of drought conditions at different time scales and monitoring of different drought types. This index captures the accumulated deficit (SPI &lt; 0) or surplus (SPI &gt; 0) of precipitation over a specified period, and provides a normalized measure (i.e. spatially invariant Z score) of relative precipitation anomalies at multiple time scales. In the present study, monthly time series of rainfall data (1981–2003) from 160 stations were used to derive SPI, particularly at 3‐month time scales. This 3‐month SPI was interpolated to depict spatial patterns of meteorological drought and its severity during typical drought and wet years. Correlation analysis was also done to evaluate usefulness of SPI to quantify effects of drought on food grain productivity. Further, time series of SPI were exploited to assess the drought risk in Gujarat. Copyright © 2007 Royal Meteorological Society

In this study the capability of two advanced hybrid artificial intelligence-based methods is investigated in modelling meteorological droughts based on the standardized precipitation index (SPI) for various time windows. The outcomes are compared with adaptive neuro-fuzzy inference system (ANFIS), support vector regression (SVR), autoregressive integrated moving average (ARIMA) and seasonal autoregressive integrated moving average (SARIMA). The best-fitted distribution functions are found to vary with respect to stations and time windows. For Canakkale, Istanbul and Tekirdag stations, the correlation coefficients (CC) of hybridized method of ANFIS with gray wolf optimization (ANFIS-GWO) and ARIMA are in the range of 0.88–0.94, 0.88–0.96 and 0.86–0.94, respectively. The performance index also showed that the ANFIS-GWO provides superior accuracy in modelling droughts, with the minimum value (PI = 0.78) for SPI12 of Canakkale station. Forward-chaining cross-validation and the P value of the Chi-squared test also confirm that ANFIS-GWO is the superior model, in which there is not a significant difference between the trend of the predicted categories and that of the real categories for all stations and SPIs.

The study of floods and droughts requires the knowledge of wet and dry event sequences. They are the two important extreme conditions which directly or indirectly affects every field of environmental science. These extreme conditions are due to the change in one, of the many but most important parameter, rainfall. The standardized precipitation index is designed to quantify the rainfall for multiple time scales. These time scales reflect the impact of drought/floods on the availability of the different water resources. The modified classification by Agnew is referred for the classification of wet and dry events during the 20th Century for Surat district. The monthly rainfall data from 1901 to 2000 is utilized to determine the SPI values. SPI was calculated for 4, 6, 12, 24 and 48 months time scales. The area experienced more than 20% years of dry and wet events for the 20th Century. It is observed that the years 1942, 1945 and 1959 are identified as severe wet events for all the time scale. Year 1998 is identified as moderate wet event for all time scale. Years 1936 and 1987 are identified as severe dry events and year 1935 is identified as moderate dry event for all the time scales. No extreme wet event was observed. For extreme dry scenario all the years identified for different time scales are different.

Standardised Precipitation Index (SPI) data for Integrated Hydrological Units (IHU) Hydrometric Areas (Kral et al. [1]). SPI is a drought index based on the probability of precipitation for a given accumulation period as defined by McKee et al. [2]. SPI is calculated for different accumulation periods: 1, 3, 6, 12, 18, 24 months. Each of these is in turn calculated for each of the twelve calendar months. Note that values in monthly (and for longer accumulation periods also annual) time series of the data therefore are likely to be autocorrelated. The standard period which was used to fit the gamma distribution is 1961-2010. The dataset covers the period from 1862 to 2015. NOTE: the difference between this dataset with the previously published dataset 'Standardised Precipitation Index time series for IHU hydrometric areas (1961-2012)' [SPI_IHU_HA] (Tanguy et al., 2015 [3]), apart from the temporal extent, is the underlying rainfall data from which SPI was calculated. In the previously published dataset, CEH-GEAR (Keller et al., 2015 [4], Tanguy et al., 2014 [5]) was used, whereas in this new version, Met Office 5km rainfall grids were used (see supporting documentation for more details). Within Historic Droughts project (grant number: NE/L01016X/1), the Met Office has digitised historic rainfall and temperature data to produce high quality historic rainfall and temperature grids, which motivated the change in the underlying data to calculate SPI. The methodology to calculate SPI is the same in the two datasets. [1] Kral, F., Fry, M., Dixon, H. (2015). Integrated Hydrological Units of the United Kingdom: Hydrometric Areas without Coastline. NERC-Environmental Information Data Centre https://doi.org/10.5285/3a4e94fc-4c68-47eb-a217-adee2a6b02b3 [2] McKee, T. B., Doesken, N. J., Kleist, J. (1993). The Relationship of Drought Frequency and Duration to Time Scales. Eighth Conference on Applied Climatology, 17-22 January 1993, Anaheim, California. [3] Tanguy, M.; Kral., F.; Fry, M.; Svensson, C.; Hannaford, J. (2015). Standardised Precipitation Index time series for Integrated Hydrological Units Hydrometric Areas (1961-2012). NERC Environmental Information Data Centre. https://doi.org/10.5285/5e1792a0-ae95-4e77-bccd-2fb456112cc1 [4] Keller, V. D. J., Tanguy, M., Prosdocimi, I., Terry, J. A., Hitt, O., Cole, S. J., Fry, M., Morris, D. G., and Dixon, H.: CEH-GEAR: 1 km resolution daily and monthly areal rainfall estimates for the UK for hydrological use, Earth Syst. Sci. Data Discuss., 8, 83-112, https://doi.org/10.5194/essdd-8-83-2015, 2015. [5] Tanguy, M.; Dixon, H.; Prosdocimi, I.; Morris, D. G.; Keller, V. D. J. (2014). Gridded estimates of daily and monthly areal rainfall for the United Kingdom (1890-2012) [CEH-GEAR]. NERC Environmental Information Data Centre. https://doi.org/10.5285/5dc179dc-f692-49ba-9326-a6893a503f6e

Standardised Precipitation Index (SPI) data for Integrated Hydrological Units (IHU) groups (Kral et al. [1]). SPI is a drought index based on the probability of precipitation for a given accumulation period as defined by McKee et al. [2]. SPI is calculated for different accumulation periods: 1, 3, 6, 12, 18, 24 months. Each of these is in turn calculated for each of the twelve calendar months. Note that values in monthly (and for longer accumulation periods also annual) time series of the data therefore are likely to be autocorrelated. The standard period which was used to fit the gamma distribution is 1961-2010. The dataset covers the period from 1862 to 2015. NOTE: the difference between this dataset with the previously published dataset 'Standardised Precipitation Index time series for IHU Groups (1961-2012)' [SPI_IHU_groups] (Tanguy et al., 2015 [3]), apart from the temporal extent, is the underlying rainfall data from which SPI was calculated. In the previously published dataset, CEH-GEAR (Keller et al., 2015 [4], Tanguy et al., 2014 [5]) was used, whereas in this new version, Met Office 5km rainfall grids were used (see supporting information for more details). Within Historic Droughts project (grant number: NE/L01016X/1), the Met Office has digitised historic rainfall and temperature data to produce high quality historic rainfall and temperature grids, which motivated the change in the underlying data to calculate SPI. The methodology to calculate SPI is the same in the two datasets. [1] Kral, F., Fry, M., Dixon, H. (2015). Integrated Hydrological Units of the United Kingdom: Groups. NERC-Environmental Information Data Centre doi:10.5285/f1cd5e33-2633-4304-bbc2-b8d34711d902 [2] McKee, T. B., Doesken, N. J., Kleist, J. (1993). The Relationship of Drought Frequency and Duration to Time Scales. Eighth Conference on Applied Climatology, 17-22 January 1993, Anaheim, California. [3] Tanguy, M.; Kral., F.; Fry, M.; Svensson, C.; Hannaford, J. (2015). Standardised Precipitation Index time series for Integrated Hydrological Units Groups (1961-2012). NERC Environmental Information Data Centre. https://doi.org/10.5285/dfd59438-2170-4472-b810-bab33a83d09f [4] Keller, V. D. J., Tanguy, M., Prosdocimi, I., Terry, J. A., Hitt, O., Cole, S. J., Fry, M., Morris, D. G., and Dixon, H.: CEH-GEAR: 1 km resolution daily and monthly areal rainfall estimates for the UK for hydrological use, Earth Syst. Sci. Data Discuss., 8, 83-112, doi:10.5194/essdd-8-83-2015, 2015. [5] Tanguy, M.; Dixon, H.; Prosdocimi, I.; Morris, D. G.; Keller, V. D. J. (2014). Gridded estimates of daily and monthly areal rainfall for the United Kingdom (1890-2012) [CEH-GEAR]. NERC Environmental Information Data Centre. https://doi.org/10.5285/5dc179dc-f692-49ba-9326-a6893a503f6e

Meteorological drought is one of the inseparable climatic phenomena in sub-tropical countries such as Iran. In these areas, which encompass the vastest deserts of the world, the effects of precipitation scarcity on water resources manifest themselves promptly. This study employed the standardized precipitation index (SPI), as a meteorological drought assessment tool, over 3- and 12-month time scales during the years 1970 to 2014. We compared the accuracy of the neuro-fuzzy model (as a non-linear model) with time-series models for modeling of drought. Time-series analysis was conducted according to the Box–Jenkins method. ARIMA (3, 0, 4) and ARIMA (2, 0, 1) were selected as the best-fitting time-series models for modeling SPI at time scales of 3 and 12 months, respectively. The results indicated that the neuro-fuzzy model significantly outperforms the time-series models. The Nash–Sutcliffe efficiency (NSE) coefficients are equal to 0.12 and 0.60 respectively for SPI3 and SPI12 estimated by ARIMA model, while NSE coefficients for neuro-fuzzy model are equal to 0.52 and 0.80 respectively for SPI3 and SPI12 in validation period. Also, the violin plots demonstrated that the neuro-fuzzy model (unlike the ARIMA model) is well-suited to estimate the volatility of SPI values for wet and dry periods, which is a very important prerequisite for efficient water resources’ management.

The Standardized Precipitation Index (SPI) was developed to detect drought and wet periods at different time scales, an important characteristic that is not accomplished with typical drought indices. More and more users employ the SPI to monitor droughts. Although calculation of the SPI is easier than other drought indices, such as the Palmer Drought Index, it is still relatively complex. In China, an index called the China‐Z Index (CZI) has been used since 1995 by the National Climate Centre of China to monitor moisture conditions across the country. The calculation of this index is easier than the SPI. A third index, the statistical Z‐Score, can also be used to monitor droughts. This paper evaluates the SPI, CZI and Z‐Score on 1‐, 3‐, 6‐, 9‐ and 12‐month time scales using monthly precipitation totals for four locations in China from January 1951 to December 1998 representing humid and arid climates, and cases of drought and flood. Advantages and disadvantages for the application of each index are compared. Study results indicate that the CZI and Z‐Score can provide results similar to the SPI for all time scales, and that the calculations of the CZI and Z‐Score are relatively easy compared with the SPI, possibly offering better tools to monitor moisture conditions. Copyright © 2001 Royal Meteorological Society