Probabilistic Assessment of Future Drought Characteristics under the Quality Boosted Regional Drought Index

2.1. Study area and data collection

This study presents a thorough investigation of the KCB in Turkey. The central Anatolian semi-arid area in Turkey occupies an area of 53,850 km² and holds special climatic conditions and ecological elements. The KCB region contains multiple drainage basins, while Tuz (Salt) Lake and Beysehir Lake achieve top status as Turkey’s largest freshwater lakes, serving as the region’s main water reservoirs. Drought monitoring tools are helpful for early warnings and mitigation policies. Several authors have suggested numerous drought indicators and monitoring tools to determine drought severity (Citakoglu & Coşkun, 2022; Soylu Pekpostalci et al., 2023). This study developed a new drought index (QBRDI) to assess the spatial-temporal distribution of drought in Turkey’s KCB region. The temporal dataset from nine meteorological stations in Turkey was collected and standardized before. Analyzed data originated from the General Directorate of Meteorology (MGM) of Turkey. Outliers were removed through a weighting scheme, where high weights were given to low values and low weights to high values, among other adjustments. Each station has 696 observations with a time frame of 57 years from 1965 to 2022. The spatial geographical distribution of these stations is provided in Figure 1 with geographic attributes—latitude, longitude, and altitude—while the observational view of these stations is shown in Figure 2. Table 1 presents details about the nine KCB stations in Turkey with geographic attributes—latitude, longitude, and altitude. This spread encompasses the expansive landscapes of the KCB, from vast plains to mountainous regions, in addition to its topographical shapes.

Figure 1

Figure 2

2.2. Probabilistic approach

Fitting an accurate and precise approach is essential for developing standardized drought indicators (Batool et al., 2024). Numerous methodologies have been employed in prior studies to achieve standardization objectives, with the most familiar ones being parametric and non-parametric techniques. In this study, two approaches, parametric and non-parametric, are utilized for standardization. Parametric approaches are the K-Component Gaussian Mixture Model (K-CGMM) (McLachlan & Peel, 2000) and univariate probability models. The univariate probability models are evaluated using the ‘fitDistr’ (Spiess, 2018) function from the Propagate package in R software. Univariate probability models are suitable for unimodal data. Previously, Abbas et al. (2022) used the ‘fitdistrplus’ and ‘Propagate’ package to fit distinct univariate distributions and selected the best one. Univariate probability models are not appropriate for fitting and computing cumulative distribution function (CDF) in the case of multimodal data. K-CGMM is an unsupervised technique utilized for modeling the multimodal data (Batool et al., 2025). K-CGMM is suitable for data that have numerous peaks. K-CGMM splits data into distinct components and fits a Gaussian distribution to each component of the data. It contains two parameters: weights and mean (or variance). For a concise and extensive overview of K-CGMM, see Batool et al. (2023). In some cases, the kth component shows zero variability, causing problems with K-CGMM. Then, determining CDF using a non-parametric technique leads to an accurate inference. The ultimate objective of each approach is to standardize QBRDI data by estimating the CDF from the underlying probability distributions. Hao and AghaKouchak (2014) employed non-parametric techniques to develop a multivariate standardized drought index (MSDI) for assessing drought behavior. Similarly, Ali et al. (2020) deployed the parametric approach in the context of drought assessment. After estimating the CDF using parametric or non-parametric techniques, standardization is performed based on the transformation outlined by Ali et al. (2017).

2.3. Trend analysis

2.4. A framework of the study

The current study generates a drought monitoring index called the Quality Boosted Regional Drought Index (QBRDI) for the Konya region of Turkey, covering nine meteorological stations. The methodology of QBRDI is based on the previous study conducted by Ali et al. (2023). In QBRDI, we used an X-bar chart to identify out-of-control points (OCP). To aggregate regional data, weights are integrated based on the total number of OCP (TOCP). QBRDI is integrated into four different stages. The integration of each stage is presented below.

2.5. Comparative methods and metrics

The weighting procedure in the development of QBRDI undergoes relative assessment within the utilization of the simple model average (SMA) procedure in this research. The cumulative index of the SMA follows this mathematical format:

where S_i represents the ith precipitation observation at the meteorological station. The SMA method serves as a performance assessment approach, utilized by numerous researchers (Jose, Vincent & Dwarakish, 2022; Rhymee et al., 2022; Ombadi et al., 2021). This method is preferred due to its simplicity and ability to combine multiple results into a single index. Previous studies have discussed the limitations of SMA in comparison to more advanced, statistically rigorous methods, highlighting the need for approaches that account for the distribution and variance of the data. Therefore, we justify the use of SMA in this study as a baseline comparison for performance.

In this study, we have utilized the RMSE to determine the relative performance of weighted procedure utilized in QBRDI. Below is the presentation of mathematical expressions that define RMSE:

where P_i is the vector of the original dataset of precipitation, ${\widehat{P}}_i$ is the vector of predicted behavior, and k is the total number of selected stations.

The second performance metric is relative absolute error (RAE), which is also extensively employed in the literature. Mathematically,

where P_i is a vector of an actual data of precipitation and ${\widehat{P}}_i$ is the projection values. When comparing indexes, the lower RAE values indicate the superiority of one index over the other index.

3.1. Implication of weights and the validation of QBRDI

In this section, the results of weights under QBRDI and the validation of this index are defined. QBRDI aims to reduce bias and outliers and increase data reliability. Table 2 shows the monthly weights for all nine stations from January to December. QBRDI gives more weight to stations having lower number of OCP and less weight to stations having larger numbers of OCP and normalizes the dataset to investigate the drought characteristics. Figure 3 shows the temporal variation of all nine station weights QBRDI. It takes time on the x-axis (1965–2022) and weight values on the y-axis and shows the time difference between each model. The results presented in Table 3 demonstrate the superior performance of the deployed weighting procedure (Ali et al., 2023) compared to the SMA method. The RMSE values for the weighting procedure (Ali et al., 2023) are consistently lower across all three statistics—minimum, average, and maximum—indicating more accurate predictions. Specifically, the average RMSE under the weighting procedure (Ali et al., 2023) is 6.282, whereas SMA produces a much higher average RMSE of 15.158. Additionally, the maximum RMSE observed in QBRDI (8.618) is even lower than the minimum RMSE in SMA (7.333), highlighting the substantial improvement in predictive accuracy. Similarly, the RAE values show a significant reduction under the weighting procedure (Ali et al., 2023). The average RAE for the weighting procedure (Ali et al., 2023) is 0.085, while SMA results in an average RAE of 1.409, suggesting that the weighting procedure (Ali et al., 2023) provides more precise estimations and effectively captures variations in observed data. The superior performance of the weighting procedure (Ali et al., 2023) is attributed to its unequal weighting scheme, which assigns larger weights to stations having lower numbers of OCP and less weight to stations having larger numbers of OCP. Unlike SMA, which gives equal importance to all regions regardless of their reliability, QBRDI prioritizes more accurate regional analysis, leading to enhanced predictive accuracy. This dynamic weighting approach ensures that the ensemble is not influenced by poorly performing regions, reducing overall error. The significant reduction in RMSE and RAE validates the effectiveness of this method in improving drought index estimation. Thus, QBRDI emerges as a more robust and reliable alternative to SMA for ensemble modeling by incorporating a refined weighting strategy based on regional observation proximity.

Figure 3

3.2. The implication of K-CGMM and non-parametric technique for standardization

In the present study, parametric and non-parametric approaches are used in the standardization process. The results presented in Table 4 highlight the superior performance of the K-CGMM compared to the univariate probability distributions in terms of the Bayesian Information Criterion (BIC) at various timescales. K-CGMM consistently outperforms univariate probability models, demonstrating its robustness in capturing the underlying behavior across most timescales. For instance, at timescale 1, the BIC for the univariate generalized normal distribution is –143.91, while K-CGMM achieves a significantly lower BIC of –645.13. Similarly, at scale 6, the univariate Johnson SB distribution has a BIC of –336.78, whereas K-CGMM drastically improves the fit with a BIC of –2608.2. These results confirm that K-CGMM provides a more efficient and accurate representation of the data distribution compared to traditional univariate models. However, at timescale 9, K-CGMM does not perform well, as evidenced by its higher BIC value (967.636) compared to the univariate Johnson SU model (–73.06). This suggests that the standard parametric approach for K-CGMM is not suitable at this timescale. To address this limitation, the CDF is determined non-parametrically, ensuring that the model remains flexible and accurately represents the distribution without imposing restrictive parametric assumptions. This adaptive approach allows K-CGMM to maintain its effectiveness across different timescales, even when standard parametric modeling does not provide an optimal fit. Overall, the results demonstrate that K-CGMM is a more effective modeling approach, as it consistently achieves lower BIC values, signifying better goodness-of-fit compared to univariate probability distributions. As depicted in Figure 4, the standardized data illustrate the temporal fluctuations during dry and wet conditions across seven distinct monthly timescales (1, 3, 6, 9, 12, 24, and 48). The y-axis represents standardized values, while the x-axis represents time. It signifies that data values from 0 to –2 show dryness and data values ranging from 0 to 2 show wetness.

Figure 4

3.3. Assessment of long-term probabilities of drought and trend analysis

This section presents an overview of the long-term drought probability in Turkey’s KCB region, using a Markov chain steady-state probability model. The analysis is based on seven distinct classes representing varying drought and wet conditions. Table 5 presents the steady-state probability of seven classes at seven distinct timescales (1, 3, 6, 9, 12, 24, and 48). These values indicate the probability of various events occurring at each timescale. As we examine the probabilities from timescales 1 to 48, it becomes clear that the probabilities of ED and EW fluctuate slightly, with EW generally having lower probabilities.

Meanwhile, MD and MW also exhibit fluctuations, with MD probabilities tending to be slightly higher than MW. NN shows a relatively stable probability of around 0.68 across all timescales. SD and SW exhibit similar patterns; both decrease as monthly timescales increase, and SW decreases continuously. Overall, the probabilities show that distinct timescales have varying impacts on these events, with some showing more stability than others. From these results, it can be concluded that KCB in Turkey may face drought problems in the future. To know the presence of a trend using two non-parametric techniques, Mann–Kendall and Sen’s slope. According to the MK test, a P value above the significance level (0.05) signifies an insignificant trend. Sen’s slope estimates this trend value; its sign indicates the direction of the trend. Table 6 provides trend analysis results for distinct timescales (i.e., 1, 3, 6, 9, 12, 24, and 48). For monthly timescales 1, 3, 6, and 9, the Kendall Z values and slopes are positive, indicating an increasing trend over time. However, these trends are generally relatively weak, as the slope values are small. For the 12- and 24-month timescales, both the Kendall Z values and slopes are negative, indicating a decreasing trend. Interestingly, at the 48-month timescale, the Kendall Z value and slope are positive, suggesting an increasing trend, but this time, the trend appears more prominent as the slope value is higher. These results suggest that there may be some fluctuations in the data, with both weak increasing and decreasing trends, but the most robust trend is observed with a significant positive slope at the 48-month timescale.