An examination of the fluctuation and long-term persistence of drought regimes in the Jing River basin using the PDSI–SWAT model

A drought occurs when precipitation significantly decreases, evaporation increases, or melting is insufficient. Drought disasters occur when droughts reach an intensity that disturbs the usual demand for water resources in human civilization, the economy, and the environment's usual demand for water resources. According to several studies (Wu et al. 2020, 2023; Lee et al. 2022; Samantaray et al. 2022), it is clear that droughts have become increasingly common due to the coupled influences of human activity and climate change. Previous research has demonstrated that changes in air circulation, land use, and land cover affect precipitation, evaporation, river runoff (RO), and groundwater RO, further affecting the watershed's water cycle and increasing the frequency of droughts (Hoerling et al. 2006; Poshyvailo-Strube et al. 2022). However, due to the limitations of science and technology, it is impossible to fully understand how changes in the spatiotemporal pattern and process of water circulation affect the regional drought regime and intensify the regional drought catastrophe. Therefore, understanding the evolution of the drought regime in the context of a changing environment is vital and urgent at the current stage, as is developing practical strategies to deal with the environmental shift and rising pattern of drought disasters.

Researchers have performed extensive research to evaluate whether environmental changes over the last decade have altered the drought regime. The study categorizes them into two groups: trend detection and variability analysis. Trend identification is the technique of analyzing the trend change of a given drought indicator to anticipate the future drought regime. For example, Dai (2013) found that the likelihood of drought has increased since 1950 in parts of Africa, southern Asia, eastern Australia, and southern Europe by evaluating the Palmer drought severity index (PDSI) and the potential evapotranspiration index (PET). Drought would also worsen and expand over the next 30–90 years, as precipitation decreased and evaporation increased. McCabe & Wolock (2015) investigated the global drought trend from 1901 to 2009 using the monthly precipitation (P) and the PET. They came to a different conclusion from Dai (2013): despite rising temperatures and potential evapotranspiration (ET), greater precipitation kept the worldwide drought regime relatively stable. Ficklin et al.’s (2015) study of fluctuations in the PET and PDSI in the United States discovered that the drought regime shifted geographically significantly between 1979 and 2013. Gudmundsson & Seneviratne (2015) found that the frequency of drought in Europe varied greatly by geography, with droughts reducing in the north and increasing in the south, using the standardized precipitation index (SPI). In addition, several studies have investigated the characteristics and spatial distribution of drought regime change. Sheffield & Wood (2008), for example, studied soil-moisture levels around the world from 1950 to 2000. They discovered that the soil moisture was slightly damp due to increased precipitation but got drier after the 1970s.

As is widely acknowledged, drought variability has a substantial influence on efforts to prevent regional disasters and guarantee water security. Thus, many studies on drought evolution in response to changing environmental conditions are making substantial progress (Yan et al. 2022; Zhao et al. 2022; Elias et al. 2023; Zhu et al. 2023a). However, few studies have investigated the variability of the drought regime as a result of climate change and human activities, with the majority focusing on a small number of variables that drive the drought event, such as precipitation, temperature, and RO. As a result, this study will concentrate on the unexpected nature of the drought regime in order to increase our understanding of dealing with drought disasters in a changing environment.

Many drought indices have been developed and used to describe the trend and variability of the regional drought regime, including soil moisture indices, crop physical–ecological indices, meteorological indices (precipitation, temperature, and so on), and other comprehensive or hybrid indices (Komuscu 1999; Heim 2002; Narasimhan & Srinivasan 2005). The PDSI is well known and widely utilized because it provides information regarding drought's influence on water supply and duration. In reality, when W. C. Palmer introduced the PDSI in 1965 (Palmer 1965), his primary goal was to quantify the amount and consumption of soil water at the time; however, the PDSI has evolved into a semiofficial drought index in the United States after more than 50 years (Hu & Willson 2000). In comparison with the SPI, precipitation anomaly percentage index, and other indices (Abushandi & Al Ajmi 2022; Raziei & Miri 2023; Xu et al. 2023), the PDSI can include more information such as actual ET, water supply, water requirement, and previous precipitation. In summary, it has the following three potential advantages: (1) the PDSI can efficiently investigate long-term droughts, particularly in low- and middle-latitude regions; (2) the PDSI is a tool for investigating the fundamental implications of global warming using surface air temperature and physical water-balance models; and (3) the PDSI can take into account previous months' situations. Because of these properties, the PDSI is often utilized for comparing drought research across several spatiotemporal scales in response to changing climate conditions.

Many scholars have used the PDSI to analyze drought, with numerous insightful findings. Zuzulová & Šiška (2017) analyzed the PDSI values from three gauges in western Slovakia: Bratislava, Piešťany, and Hurbanovo. This was done each month from 1981 to 2010, 2021 to 2050, and 2071 to 2100, aiming to establish the frequency with which droughts occur across time and across space. After utilizing the PDSI to investigate the temporal and geographical variability of drought in the upper Tana River basin, Wambua et al. (2017) discovered that the southeast Tana River basin is more prone to drought than the northwest. Dai et al. (2004) used a monthly PDSI dataset from 1870 to 2000, combined with empirical orthogonal function analysis, to investigate ENSO's impact on dry and wet areas worldwide. Ye et al. (2013) used trend detection, comparison analysis, and statistics of the PDSI data and monthly precipitation data from 160 Chinese sites to investigate how droughts and floods vary across time and space. The findings clearly indicate that the PDSI accurately reflects the regional drought regime in China and serves as a representative indicator to investigate its geographical variance.

Numerous studies have found that human activities have exacerbated droughts, with low precipitation being the primary cause of droughts in China's river basins, particularly the Jing River basin on the Loess Plateau (Zheng et al. 2019; Han et al. 2021; Wang et al. 2022). Drought attribution research, whether based on mathematical statistics theory or distributed hydrological models, has the following characteristics: time-series analysis is primarily used to determine the relationship between drought occurrence and factors such as temperature, precipitation, and human activity. However, the extent of their impact remains unknown, despite the overly simplistic selection of drought-driving factors, which fails to account for their overall impact on drought.

The study's research region is China's Jing River basin, and the primary targets are to address the following issues: (1) Are there any regional or temporal variations in drought events in the Jing River basin? (2) How has the drought event changed in terms of space and time? (3) Will the observed spatiotemporal trends persist? To answer them, the modified PDSI was used in this study to depict the drought regime, the moving cut data-rescaled variance analysis (MC-V/S) method for finding change points, and the range of variability approach (RVA) to rate changes in the drought regime and zone. Additionally, detrended fluctuation analysis (DFA) was used to assess the drought regime's persistence across multiple zones. The study generally aims to complete the basin's drought division and provide direction for planning decision-making during drought monitoring and disaster warning by determining the spatiotemporal variability of the drought regime in the Jing River basin.

The Jing River basin's industrial development is distinguished by its heavy-industry-dominant structure, which requires a significant amount of water (Du et al. 2022). It worsens the lack of water resources in the Jing River basin, resulting in drastically reduced regional agricultural production. The Jing River basin's unique climatic characteristics cause frequent droughts, which have a significant impact on the region's economic development (Huang et al. 2014). As a result, it is vital to investigate drought occurrences in the Jing River basin, as this will provide better technical assistance for water resource management and drought response in the Loess Plateau.

Despite its widespread usage for drought diagnosis and evaluation in the Loess Plateau, the PDSI index has numerous limitations (Liu, Y. et al. 2016, 2017; Liu, Y. R. et al. 2017). For example, the use of a simple two-layer bucket-type soil-moisture water-balance model (Yan et al. 2013; Ma et al. 2016) frequently results in inaccurate hydrological predictions. Fortunately, several researchers have enhanced the PDSI calculation findings by employing hydrological models, resulting in improved drought characterization and detection performance (Zou et al. 2017). Thus, this study used the distributed Soil and Water Assessment Tool (SWAT) model to simulate the water balance, guaranteeing that the PDSI accurately reflects drought differences on a large scale.

The major data required for this investigation are mostly geographical and meteorological data. Geographic data are generally divided into three types: (1) digital elevation data (Figure 1(b)), which can be collected from the USGS/NASA shuttle radar topography mission with a spatial resolution of 90 m, available for download from http://srtm.csi.cgiar.org; (2) land-use data with a resolution of 30 m (Figure 1(c)), which can be downloaded from the National Tibetan Plateau Data Centre of China (https://data.tpdc.ac.cn/en/data/a75843b4-6591-4a69-a5e4-6f94099ddc2d/); and (3) soil distribution type data at a 1 km resolution (Figure 1(d)), which can be obtained from the World Data Centre for Soils (https://data.isric.org/geonetwork/srv/eng/catalog.search#/metadata/2919b1e3-6a79-4162-9d3a-e640a1dc5aef). Daily observations from 17 meteorological stations located throughout the basin, as shown in Figure 1(b), include daily precipitation, maximum and minimum temperatures, wind speed, solar radiation, and relative humidity from 1961 to 2013, which can be obtained from China's daily surface climate data (V3.0). In addition, the Yellow River Conservancy Commission's Hydrological Yearbook provides observational RO data at the Zhangjiashan gauge.

This study first created the SWAT model for hydrological simulation in the Jing River basin in order to calculate the PDSI variables such as ET, recharge to soils (R), RO, water loss to soil layers (L), and potential values (PET, PR, PRO, and PL), as well as to replace a simple two-layer bucket-type soil-moisture water-balance model. Currently, efforts are underway to develop the PDSI–SWAT model and determine its index.

The USDA's Agricultural Research Service developed the SWAT model, a distributed hydrological model, in the early 1990s. Its main components are the hydrological process, soil erosion, and water quality sub-modules. It is a distributed hydrological model that is well suited to understanding water and sediment (Francesconi et al. 2016). The study goals may dictate the use of different modules for simulation. This study primarily uses the hydrological module to simulate the hydrological cycle of the Jing River basin.

This module includes four calculation modules: soil flow, surface RO, subsurface RO, and evaporation.

• (1) Surface RO estimates. The two calculation models are employed, i.e., the SCS curve approach and the Green and Ampt infiltration method. The SCS curve approach is a prominent tool for simulating multi-scale RO processes in a variety of soil and land-use scenarios. The calculated equation is as follows:

  

  (2)

  where Q_surf indicates the cumulative RO (mm); R_day indicates the rain depth of a certain day (mm); I_a represents initial loss (mm); and S stands for retention coefficient (mm), which is related to soil, land-use type and slope within the watershed, and can be calculated as follows:

  

  (3)

  where CN represents the number of curves on a certain day, which is generally equal to 0.2S. According to Equation (2), surface RO can be generated in the basin only when R_day > I_a.

• (2) Calculating soil flow. The model uses the dynamic storage method for management and fully accounts for topographic features, soil permeability, and soil effective water content.

• (3) Calculating groundwater. According to the model, there are two types of groundwater in the basin: confined water and diving water. The confined water is thought to go outside the basin, whereas only the diving water flows straight into the river channel. The following is the diving water balance equation:

  

  (4)

  where aq_sh,i represents the diving volume of the i day (mm); aq_sh,i−1 indicates the diving volume of the i − 1 day (mm); w_rchrg,sh represents the groundwater recharge of the river on the i day; w_revap represents the amount of water that enters the soil on the day i due to insufficient soil moisture (mm); w_pump,sh indicates the amount of diving pumped on the day i (zero by default) (mm); and Q_gw represents the underground water flow into the channel on the day i (mm), which can be replenished to the channel only when the diving exceeds the specified water-level threshold.

Furthermore, the SWAT model was designed to simulate monthly-scale hydrological phenomena in the Jing River basin from 1961 to 2013. The streamflow data at Zhangjiashan gauge is used to calibrate and validate the SWAT model in the Jing River basin, with calibration and validation periods spanning 1987–1992 and 1993–1995, respectively. According to previous research findings (Rodrigues et al. 2014; Yen et al. 2016; Liu, Y. et al. 2017; Liu, Y. R. et al. 2017), the calibration parameters are presented in Table 1.

The computational procedure for the PDSI–SWAT is as follows:

• (1) Data are required. Potential ET and the Sub1-SUB27 sub-basin precipitation were added to the PDSI as inputs, along with local soil parameters found by the SWAT hydrological model. These soil parameters included the distribution of soil layers, the effective field water capacity, the soil's initial effective water content, and more. Additionally, the local historical record of the drought was used, including its beginning and ending dates and intensity, to adjust the weight factor K.

• (2) Calculation step. Essentially, the construction of the PDSI–SWAT consists of seven parts (Zou et al. 2017; Choi et al. 2019): (a) create a statistical hydrological account; (b) find the coefficients for ET, recharge, RO, and water loss for each climate factor; (c) find climate-appropriate values for all water-balance factors, including ET, RO, water loss, recharge, and precipitation; (d) calculate the water anomaly index: surplus and shortage values; (e) formulate the PDSI calculation; (f) adjust the weight factor K; and (g) calculate the final PDSI to ascertain the duration and intensity of the drought.

The moving cut data-rescaled variance analysis (MC-V/S) is a modified method for detecting abrupt dynamic change based on the moving cut data-rescaled range analysis (He et al. 2010), which can effectively identify the variation range of time series without omitting change points and has a better application in hydrological alteration detection. The primary purpose of this study is to identify the change point in the PDSI–SWAT series of each sub-basin in the Jing River basin, with comprehensive descriptions provided below.

• (1) Choose the sliding removal data window length M.

• (2) Starting from the i (i= 1, 2, …, N−M+ 1; N is the total number of records in the time series) data of the time-series to be analyzed, M data are removed continually, and the remaining N−M data are connected to obtain a new time-series.

• (3) Use V/S to determine the new time-series' scaling index. The precise computational procedure is as follows:

Determination of the V/S analysis scaling exponent: plot n and (V/S)_n on a log(_n)–log(V/S)_n graph, then use least squares regression to get the straight line's slope. The scaling exponent γ is equal to half of the slope. The sequence demonstrates anti-correlation qualities when 0 < γ < 0.5, random-walk characteristics when γ = 0.5, and positive correlation characteristics when 0.5 < γ < 1.

• (4) Repetition of steps (2) and (3) is necessary until the original sequence is completed. Keeping the removal window length M constant, and move the window progressively using the sliding step size M.

• (5) A scaling index sequence of length N − M + 1 can be constructed by repeating steps (1) through (4).

• (6) After performing variance analysis on the obtained scaling-index sequence, the original sequence's mutation point or mutation interval is first estimated using the variance contribution size interval. The outcome is then confirmed by combining the mean mutations at a predetermined confidence level.

DFA is a method for analyzing fractal scaling behavior and highlighting self-similarity in time series. It keeps false correlation detection from happening, which is helpful for studying how long-term memories change over time in noisy, nonstationary time-series (Kantelhardt et al. 2001). Thus, this study uses the DFA to explain long-range persistence, aiming to explore future changes in the PDSI sequences in each sub-basin of the Jing River. Here is a summary of the procedure:

• (1) Starting with a bounded PDSI–SWAT time-series with a length of N, where t= 1,…, N, the equation of the integral series R(t) of the PDSI–SWAT sequence is as follows:

  

  (14)

  where denotes the mean value of the time series.

• (2) The integrated series R(t) is divided into n non-overlapping segments or boxes with a length of s, where, ⁠. To make full use of the data, the same procedure is repeated starting from the opposite end so that 2n segments can be obtained.

• (3) A least squares straight-line fit is calculated by minimizing the squared errors within each segment, and the local trend is obtained. Then, the PDSI–SWAT sequence is detrended by subtracting the polynomial fits from the original sequence, and the detrended sequence is obtained:

  

  (15)

  where denotes the fitting polynomial in segment i. Linear, quadratic, cubic, or higher-order polynomials can be used in the fitting procedure.
• (4) The variance of each segment of the detrended sequence is computed:

  

  (16)
• (5) All equal-length segments are averaged to calculate the standard DFA fluctuation function:

  

  (17)

• (6) The scaling behavior of the fluctuation functions is determined by analyzing log–log plots of F(s) versus h, i.e., F(s) ∼sh. If the PDSI–SWAT time series r_t is long-range power law correlated, F(s) increases, for large values of s, as a power-law. Here, the h denotes the well-known generalized Hurst exponent, called the scale index (0 <h< 1), and is generally calculated by the least squares method, as the slope of the straight line. When h > 0.5, it is explained that the trend of the PDSI–SWAT sequence is persistent and has a positive long-range correlation, which indicates that the future trend of the PDSI–SWAT sequence is almost the same as the past. When 0 < h < 0.5, it indicates the trend of the PDSI–SWAT sequence has a negative long-range correlation, that is, the future trend of the PDSI sequence is opposite to that of the past. When h= 0.5, it reveals the PDSI sequence has scale invariance, i.e., the future change of the PDSI–SWAT sequence is an independent random process and has irrelevant or short-range correlation.

If there exists a time t that satisfies ⁠, and ⁠, then it is considered that the mean of the sequence at this point has undergone a significant variation.

The land-use transition matrix is a two-dimensional matrix constructed based on the changes in land cover over time within a specific region. We can identify the transformations between different land-use categories over two time-periods by analyzing this matrix, which illustrates changes in various land-use types, their locations, and the areas affected over time. The transition matrix not only reflects static area data for each land category within fixed regions and time periods but also reveals more nuanced information, including the areas that transitioned out of each category initially and the areas that transitioned into each category by the end. This analysis, based on changes in area, helps to capture regional land-use dynamics. The variation in area primarily reflects changes in the total area for each land-use type, enabling an understanding of overall trends and structural shifts in land-use patterns.

Markov (1907) introduced the Markov model, which serves as the theoretical basis for this analysis. The model operates on the principle that an ordered stochastic process (X₁ < X₂ < …< X_n), where each state X_i depends only on the preceding state X_i−1, is termed a Markov process. In studies of land-use change, this process can be interpreted as a Markov process.

According to the evaluation criteria, the simulation effect improves with higher correlation coefficients (R²), lower relative errors (R_e), and lower RMSE. Table 8 shows the error analysis results from the model's calibration and validation periods. The table shows that the fitting effect is good, with R_e, R², and RMSE at the model's calibration period being 15.8%, 0.91, and 32.87 m³/s, respectively. The relative errors of R² and R_e throughout the validation period were 0.81 and 1.6%, respectively, which were within acceptable limits, and the validation effect was satisfactory. As a result, we can infer that the model fits the model requirements and is applicable in this study area.

The statistical analysis of each Jing River sub-basin's PDSI mutation sites reveals that most of the change years happened before 1980, with the PDSI modifications occurring largely between May and August. In Figure 10, the sub-basins are color-coded based on similar mutation time points. The graphic shows that the PDSI adjustments for Sub1 ∼ Sub5 in the northern basin occurred in June 1979, while Sub8, Sub11, Sub12, and Sub16 were concentrated in June 1966. The PDSI modifications for Sub6, Sub7, Sub9, Sub10, Sub13 ∼ Sub15, and Sub17 ∼ Sub23 occurred in August 1975. Sub24, Sub25, and Sub26, all in the lower parts of the Jing River, differ significantly from the places in terms of the PDSI changes in August 1982, May 1986, and August 2011. Since Sub27 has not changed, future research will focus on the first 26 sub-basins.

As shown in Figure 12, all 26 sub-basins are decentralized, with a significant drop in the amount of spot data in the central area compared with the pre-change point. Even though there are no irregularities in the percentage distributions of the three graphics, Sub24's variation range grows a lot, which suggests that this sub-basin is very likely to experience either severe drought or flooding.

It is clear from this figure that the PDSI divergence distributions in Sub1, Sub2, Sub3, Sub4, Sub5, and Sub25 are equivalent in terms of the decentralization trend. The upper part has more divergence points, the middle part less, and the lower part is almost constant compared with before the mutation point. It reveals that the frequency of droughts in these sub-basins has decreased, and there is a weak humidification trend overall.

The scatter distribution of the PDSI in Sub8, Sub11, Sub12, and Sub16 is similar, showing an increase in the proportion of lower scattered points, a decrease in the middle part, and no change in the upper part. This suggests that the frequency of drought may increase after a change point in these sub-basins, with an overall weak drought trend.

Sub6, Sub7, Sub9, Sub10, Sub14, and Sub26 have seen the most significant change, with the proportion of upper scattered points more than doubling before the change point, while the middle and lower parts have decreased. This indicates a significant decrease in the frequency of drought in these sub-basins after the change point, and overall, there is a strong humidification trend.

The PDSI scatter distribution in the remaining sub-basins (Sub13, Sub15, Sub17, Sub18, Sub19, Sub20, Sub21, Sub22, and Sub23) falls between the weak and strong humidification trends, with a rise in scatter points in the upper half, a significant drop in the middle, and an increase in the lower half. This implies a slight rise in drought events in these sub-basins, while flood frequency has decreased considerably. Overall, the basin has a strong rainy inclination, but dryness is sometimes probable.

Furthermore, the RVA approach was employed to evaluate and analyze the degree of the PDSI variation in 26 sub-basins of the Jing River basin between 1961 and 2013. Figure 12 shows the results. The PDSI variation degrees of Sub8, Sub11, Sub12, and Sub16 are all 0.13, suggesting that these four sub-basins have modest variations, but the remaining 22 sub-watersheds have medium variations ranging from 0.34 to 0.5.

Each sub-basin in the Jing River basin is currently experiencing a drought, as is evident. At this point, the key to foreseeing and assessing future drought development trends is to determine whether there is a consistent change. In other words, understanding how the area's drought pattern changes over time is crucial for drought prevention or mitigation. This study uses DFA to find the long-term or persistent link between the drought in each sub-basin using the scale index h (0 < h < 1), which was discussed in the last section. Figure 14 shows the results. Except for Sub27, all other sub-basins have a scale index h > 0.5, indicating that their PDSIs show positive continuity, implying that the current drought pattern will continue in the future. When combined with zoning data, the PDSI of Sub8, Sub11, Sub12, and Sub16 in weak dry areas will continue to drop in the future, accompanied by an accelerating aridification trend. Therefore, it is critical to plan for drought resilience in this area. In contrast, the other sub-basins' PDSI will climb further, and the drought will improve.

The Jing River basin in China, where drought is prevalent, is used as an example in this study. We analyzed meteorological and hydrological data from the Jing River basin from 1961 to 2013, used the PDSI to identify the drought's characteristics, employed moving cut data-rescaled variance analysis to determine the spatiotemporal changes in regional drought conditions, and introduced the variation range technique to partition the Jing River basin according to the evaluation and ranking of drought conditions. Finally, this study used DFA to evaluate drought conditions' endurance and determine whether these changes will persist in the future. The statistical analysis results reveal significant changes in each sub-basin's PDSI sequences, with the majority occurring between 1960 and 1970. In the four regions of the Jing River basin, the first has a tiny decline in the PDSI, namely weak dry areas; the second is constant, namely stable areas; the third has a slight increase in the PDSI, namely weak wet areas; and the fourth has a significant increase in the PDSI, namely strong wet areas. The results of the persistence analysis indicate that the current drought situation will continue, potentially intensifying the drought in the arid area and alleviating the dryness in the humid area. These incidents suggest that the sub-basins of the Jing River basin may experience varying drought conditions, necessitating careful consideration. We should prioritize places with decreases and provide drought warning and relief efforts.

Several scientists are currently investigating the pattern of drought changes on a global scale, utilizing PDSI data and hydrological models. For example, Dai (2011) combined temperature and precipitation data from 1850 to 2010 to build a worldwide land monthly average PDSI dataset with 2.5° precision. Wang et al. (2011) used a coupled land surface model to assess soil moisture content and reconstruct droughts in China and the United States. Narasimhan & Srinivasan (2005) also used SWAT modeling data to obtain soil moisture and potential evapotranspiration for agricultural drought monitoring. In this study, we developed the Jing River basin drought index, which is superior to previous studies since it estimates the water balance using the SWAT model based on physical principles rather than the two-layer soil model. The proposed SWAT–PDSI takes into account various drought-related meteorological and hydrological variables, such as precipitation, present and predicted ET, surface RO, and soil moisture. Simultaneously, this study uses variation zoning to analyze how long droughts last in different areas, the law of temporal variation of drought indicators, and the degree of variation in these indicators. However, this work has a few issues. For example, while this study uses data from 1987 to 1995, which provides a solid foundation for model calibration and validation, the time-frame selection has various limitations and influencing factors. (1) Using older data may not fully reflect current climate and environmental changes, such as significant shifts in global and regional climates and an increase in the frequency of extreme weather events. (2) These changes, combined with significant land-use changes such as growing urbanization, agricultural expansion, and deforestation, have an impact on RO patterns that have not been fully investigated in this work. Furthermore, modern human activities like irrigation, dam construction, and groundwater extraction have a significant impact on hydrological processes that may not be fully reflected due to outdated data. (3) Previous climate conditions may differ from current and future scenarios, impacting the accuracy of model predictions. Data acquired between 1987 and 1995 may lack the precision and spatial resolution of more recent data, which is crucial for improving model simulation accuracy. Thus, model parameters based on historical data may not accurately reflect current conditions, necessitating a sensitivity analysis to better understand model uncertainty. To address these limits, future research should use current data for recalibration, model a variety of land use and climate scenarios, and incorporate data on human activities to improve the realism and utility of simulation results.

As has been seen, droughts, particularly those affecting agriculture, are caused by both human activity and natural oscillations. Thus, a thorough assessment of the involvement of both natural and human causes in agricultural droughts is highly speculative and requires additional research. As a result, several options for further analysis and inquiry emerge. For example, a more in-depth analysis of regional differences in RO patterns should give information about local factors that influence hydrological processes, such as soil types, vegetation cover, and microclimatic variables. Tarasova et al. (2018) observed regional patterns in the characteristics of rainfall-RO episodes in Germany and their spatial controls. They identified hydrologically related variables for each catchment area using 115 climate, topography, geomorphology, soil, land-use, hydrogeology, and geological descriptors to characterize the mean, variability, and seasonality of event RO coefficients, time scales, rise times, and multi-peak event occurrences. In addition, Zhu et al. (2023b) created a large-scale spatiotemporal deep-learning rainfall-RO forecast model for hydrological stations in the upper reaches of the Yangtze River and evaluated the effectiveness of using three satellite-based precipitation products' spatial information in reducing RO forecast errors. Chen et al. (2023) enhanced the SWAT model by accurately representing phenological dates in the vegetation-growth module, which is crucial for increasing the SWAT model's performance when computing terrestrial water and energy balances. Wang et al. (2023) tested the patch generation land-use simulation model in the Shiyang River basin and determined its suitability in arid conditions. These findings indicate that future research should widen its scope to include more current data and longer time-periods in order to identify emerging trends and better understand the effects of accelerated climate change on water supplies. To begin, sophisticated remote-sensing technology can improve the accuracy of land-use data and may be incorporated into better RO predictions. Second, scenario-based modeling can simulate a wide range of land-use and climate-change scenarios and should be strengthened since it is useful for predicting future circumstances and developing sustainable water resource management plans. Third, quantifying the impact of human activities on RO patterns, such as irrigation, dam construction, and groundwater extraction, is crucial for understanding the factors influencing hydrological changes (He et al. 2023; Zheng et al. 2023) and should be paid more attention. Furthermore, sensitivity and uncertainty evaluations of model parameters should be increased in order to help adjust the model and improve forecast accuracy. We believe that future studies can build on this study's findings to develop more effective and sustainable water management policies in the Jing River basin by exploring these research avenues.

This study's research object is PDSI data from 27 sub-basins of the Jing River basin. In this study, the moving cut data-rescaled variance analysis was used to determine the PDSI change point in each sub-basin, and the mean and scatter distribution of the PDSI before and after the change point were statistically analyzed. The degree of the PDSI alteration was then determined using the RVA. Finally, the long-term persistence of the PDSI in each sub-basin was examined using DFA, with the goal of discussing the future drought regime in the Jing River basin. In-depth research and discussion produced the following results:

• (1) The PDSI demonstrates significant change and clear geographic distribution discrepancies. This illustrates that the evolution of drought in the Jing River basin is not consistent and fluctuates.

• (2) The mean and scatter distribution of the PDSI before and after the change point categorize the Jing River basin into four zones: weak wet, weak dry, strong wet, and stable. Different subdivisions illustrate the spatial heterogeneity of drought characteristics. During the investigation period, humidification was the basin's most significant regional distribution characteristic.

• (3) The PDSI in the Jing River basin has a long-term positive correlation, meaning that future droughts will follow a similar pattern to the previous period. As a result, it is proposed that the management department pay close attention to the development of drought in the basin's western area, strengthen construction for persistent drought, and insist on drought prevention and relief simultaneously.

• (4) This study examined the drought regime variation in the Jing River basin using the PDSI, which can be used as a data foundation and decision-support tool for regional drought-relief initiatives. Future research should focus on recalibration using current data, increasing remote-sensing data use, modeling a variety of land-use and climatic scenarios, and including data on human activities to improve the realism and utility of PDSI results.

This study was supported by the National Natural Science Foundation of China (Grant No. 51979005), the National Natural Science Foundation of China (Grant No. 52379003), the Natural Science Basic Research Program of Shaanxi (2022 JC-LHJJ-03) and the Special Fund for Basic Research Funds of Central Universities (300102293201).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.