Temporal and spatial response of agricultural drought to meteorological drought in inner Mongolia plateau inland river basin

Abstract

Meteorological drought is the primary cause of agricultural drought. Studying how agricultural drought responds to meteorological drought is crucial for understanding drought evolution. This paper takes the inland river basin of the Inner Mongolia Plateau as the research object, characterizes meteorological drought and agricultural drought respectively by the standardized precipitation evapotranspiration Index (SPEI) and the standardized Soil Water Index (SSMI), analyzes the spatio-temporal continuous dynamic evolution characteristics of drought in the study area from 1961 to 2021, explores the spatio-temporal response characteristics of meteorological and agricultural drought, and establishes a drought characteristic response model. The results show that: (1) The three dimensional (3D) identification method can accurately and comprehensively understand the dynamic evolution process of drought events and regional drought development law; (2) A total of 28 drought event pairs were successfully matched from 1961 to 2021, and the matching results can ensure that the complex relationship between the two types of droughts on the temporal and spatial scale is closer to reality; (3) The optimal response models for duration, area and severity of drought in the study area are Gaussian Copula function, Clayton Copula function and Clayton Copula function, respectively. This study provides a new method for accurately assessing the spatio-temporal variation and response of drought.

Introduction

In the context of climate change and rapid economic and social progress, drought has become one of the major disasters facing countries around the world, posing a threat to health and stable development^1,2. With the gradual rise of global temperature, water shortage situation is aggravated, and human beings are facing more severe drought situation^3,4. Since the 21 st century, the problem of drought is worsening, leading to reduced crop yields, irreversible impacts on the ecological environment, and directly threatening the realization of the United Nations’ Sustainable Development Goals^5,6. Therefore, drought has become the focus of common attention of experts in different fields.

Luo et al. calculated the standardized precipitation evapotranspiration index (SPEI) for Henan Province from 1987 to 2020, and analyzed the evolution of multi-year meteorological drought in the region⁷. Johnson et al. calculated the 1981–2021 SPEI based on station data in coastal Ghana to analyze drought events in the region⁸. Based on the meteorological drought Composite Index (MCI), other scholars have revealed the temporal and spatial variation characteristics of drought in this region⁹. It is worth noting that the above studies only consider the temporal characteristics while ignoring the spatial linkage when identifying drought events. But in fact, drought is a wet and dry anomaly involving a three-dimensional (3D) scale. Therefore, it is more accurate and reasonable to reveal the evolution law of drought events in spatio-temporal scale from the 3D perspective¹⁰.

At present, the international drought classification method has been generally recognized, including meteorological drought, agricultural drought, hydrological drought, socio-economic drought¹¹. The formation and evolution of drought are influenced by meteorology, hydrology, geomorphology, human activities, social economy and other aspects. The time and mechanism of various kinds of drought are different, but there are certain interrelation and response relationship between them¹². The results of a researcher show that the propagation time of meteorological drought to hydrological drought has obvious seasonal characteristics, and the propagation time of four seasons is different¹³. Another study showed that the propagation time from meteorological drought to hydrological drought was 3–12 months¹⁴. Vicente-Serrano calculated the correlation coefficient between drought and standardized runoff and reservoir storage, revealing that surface runoff has a short response time to meteorological drought (1–4 months), while reservoir storage has a longer response time to meteorological drought (7–10 months)¹⁵. Based on the meteorological drought index and agricultural drought index, Sun et al. calculated the drought response time and its influence in different climatic regions, vegetation and irrigation conditions¹⁶. In 2024, Palagiri researched the transmission mechanism of meteorological drought to agricultural drought from 1991 to 2022 based on the copula method, and determined that drought transmission speed was different in different time periods through 12-year moving average analysis¹⁷. With the deepening of the research, some scholars began to try to build statistical models between drought characteristic variables, so that meteorological drought data can be used to simulate, monitor and warn agricultural and hydrological drought. Edossa et al. established the linear relationship between different drought characteristic variables¹⁸. Another study showed that there were obvious nonlinear relationships between different drought characteristics¹⁹.

Current research mostly focuses on the temporal characteristics of drought but fails to fully consider its spatial evolution features, making it difficult to comprehensively reveal the response processes among different types of drought. In essence, drought response is a spatio-temporal continuous three-dimensional dynamic process. From the 3D perspective, the spatio-temporal response process between different drought types is very complex. For example, a large meteorological drought induces several small agricultural droughts or several small meteorological droughts simultaneously trigger one agricultural drought²⁰. Feng et al. showed that the study of drought propagation mechanism based on a 3D perspective can more intuitively and effectively describe the drought propagation process²¹. Therefore, this paper first matches meteorological and agricultural drought events with spatio-temporal connections to ensure that the complex relationship between meteorology and agricultural drought on the spatio-temporal scale is closer to the actual situation, thereby more accurately constructing the response relationship model between meteorological drought and agricultural drought and the optimal response relationship model among different drought characteristic variables.

In view of this, this study selected the Inner Mongolia Plateau inland river basin (IMPIRB) as the research object, using SPEI and standardized soil moisture index (SSMI) to measure meteorological drought and agricultural drought. Using 3D recognition method and spatio-temporal matching criteria, we extract and match the corresponding meteorological and agricultural drought events. Then, from the perspective of Copula function, the optimal response model between drought characteristic variables was established, and the probability curves of different drought characteristic variables were constructed using the selected optimal Copula function. This study analyzed the characteristics of drought response from spatiotemporal multi-scale system, aiming to provide scientific basis for formulating drought prevention and resistance strategies and agricultural drought early warning.

Study region

Located at the northern foot of Yinshan Mountain in northern China, IMPIRB covers parts of Xilin Gol League, Ulanqab, Chifeng, Baotou, Bayannur and Hohhot, covering an area of about 316,600 km², mainly composed of grassland and cultivated land. The terrain of the study area is high in the southwest and low in the northeast, with an elevation of 760–2332 m. The ecological environment in this region is relatively fragile, and drought will cause grassland degradation, grassland desertification and crop reduction, and the drought degree is also increasing. Figure 1 shows the map of study area, elevation and land use type.

Fig. 1

Map of study area, elevation and land use type. It was drawn by ArcGIS 10.6.1 (https://desktop.arcgis.com/zh-cn/desktop/index.html).

Materials and methods

Materials

Due to the limited measured data of soil water content in the study area, which could not meet the research needs, the Global Terrestrial Assimilation System (GLDAS) data product was selected. The Noah model in this product provides soil moisture content for a more accurate assessment of agricultural drought^22,23. In this study, the monthly data of soil water content provided by Noah model was used to calculate the standardized soil moisture index (SSMI). The time series was 1961–2021, and the spatial resolution was 0.25°×0.25°, which could be obtained by NASA. The standardized precipitation evapotranspiration index (SPEI) was calculated using the monthly precipitation and evapotranspiration data from 1961 to 2021 provided by the CRU TS v.4.07 dataset with a spatial resolution of 0.5°×0.5°. To ensure consistent spatial resolution of raster data, the spatial resolution of SSMI is resampled to 0.5°×0.5°.

Methods

The workflow of this study is shown in Fig. 2. Firstly, extract the precipitation, potential evapotranspiration and soil moisture observation data of IMPIRB from 1961 to 2021, and calculate the SPEI and SSMI of IMPIRB. Secondly, meteorological drought events and agricultural drought events from 1961 to 2021 were extracted based on three-dimensional recognition methods. Then, the matching criteria of drought events were adopted to match the meteorological and agricultural drought events with spatio-temporal correlations from 1961 to 2021. The matched pairs of meteorological and agricultural drought events were classified in response, and the spatio-temporal response characteristics of various responses were analyzed. Finally, the Copula function is used to infer the joint distribution probability of different drought characteristic variables, and the optimal Copula function is determined by model accuracy evaluation.

Fig. 2

Workflow diagram.

Drought index

In this paper, SPEI and SSMI were selected to characterize meteorological drought and agricultural drought respectively. The main calculation steps of SPEI are as follows: calculate the series of difference between monthly precipitation and evapotranspiration A; Using Log⁃logistic probability distribution function to fit A sequence, f(x) is obtained. The SPEI value is obtained by converting f(x) to the standard normal distribution²⁴. The calculation steps of SSMI are slightly different from SPEI. The difference is that it is necessary to use the optimal distribution function of soil moisture, normal distribution, to fit and merge it to obtain the cumulative probability distribution function, and finally to obtain the SSMI value²⁵.

The sensitivity of standardized drought index in different time scales to drought event identification is different²⁶. Research shows that the meteorological drought index with a 3-month time scale can more accurately analyze the impact of drought on agriculture, while the agricultural drought index with a 1-month time scale can quickly respond to the recent climate change, which is very important for agricultural producers who need to timely understand and cope with drought conditions²⁷. Therefore, SPEI on a 3-month scale (SPEI-3) was used for meteorological drought identification, and SSMI on a 1-month scale (SSMI-1) was used for agricultural drought identification. Both SPEI and SSMI were obtained after standardized treatment, and their drought grades could be divided according to existing research results, and − 1 was selected as the threshold, as shown in Table 1²⁸.

Table 1 Drought division description Table²⁹.

3D identification method

The 3D identification method of drought events is to extract spatiotemporal continuous drought events from three-dimensional space, which mainly includes three steps: drought patch recognition, drought patch time-history connection, and drought characteristic variable extraction. For detailed steps, see reference³⁰.

Drought event matching

According to the results of 3D drought identification, the drought response characteristics can be described more vividly from multiple levels by matching the drought events with genetic links from the spatio-temporal scale. The matching steps are as follows:

(1) Sequence of drought events. According to the 3D recognition results of meteorological and agricultural drought events (assuming M-field meteorological drought events and N-field agricultural drought events), an m×n matrix X is formed by ordering different types of drought events according to the occurrence time, and the element ($\:{X}_{mn}$) in the matrix is the matching pair of drought events to be detected.

(2) If the matching pair of drought events has an intersection in time, the corresponding position of the matrix is marked with 1, otherwise marked with 0. The judging formula of whether there is a successful match on the time scale is as follows:

$${X_{mn}} = \left\{ {\begin{array}{*{20}{c}} { = 1,{D_{overlap}} \ne \:\varphi \:\:\:if\left\{ {\begin{array}{*{20}{c}} {{M_{st}} \leqslant \:{A_{st}} \leqslant \:{M_{et}}} \\ {\:or} \\ {\:{A_{st}} \leqslant \:{M_{st}} \leqslant \:{A_{et}}?{D_{overlap}} \geqslant \:min(MD/3,AD/3)} \end{array}} \right.} \\ {\: = 0,{D_{overlap}} = \varphi \:\:if\left\{ {\begin{array}{*{20}{c}} {{A_{st}}> {M_{et}}} \\ {\:or} \\ {\:{A_{et}}> {M_{st}}} \end{array}} \right.} \end{array}} \right.$$

(1)

Where Φ represents the empty set; $\:{D}_{overlap}$ represents the intersection of duration, and $\:{M}_{st}$ and $\:{M}_{et}$ represent the start time and end time of meteorological drought respectively. $\:{A}_{st}$ and $\:{A}_{et}$ represent the start time and end time of agricultural drought respectively. In the special case ($\:{A}_{st}$ ≤ $\:{M}_{st}$ ≤ $\:{A}_{et}$), meteorological drought occurs later than agricultural drought, which needs further judgment. If the meteorological and agricultural drought only have an accidental intersection in time, and there is no substantial corresponding relationship, they should be abandoned.

(3) If the drought event pair with time intersection also has space intersection and is larger than the drought area threshold, it is considered that the drought event pair is successfully matched.

(4) On the basis of the third step, the matching pairs of drought events are coded based on the sequence of drought event numbering.

Classification of drought response relationships

According to Feng et al. ‘s study on drought transmission characteristics in northwest China, drought response relationships can be divided into four categories: A consecutive meteorological drought causes an agricultural drought event (labeled C1), a meteorological drought causes multiple agricultural droughts (labeled C2), multiple meteorological drought causes an agricultural drought (labeled C3), and more complex multiple meteorological drought causes multiple agricultural droughts (labeled C4)²¹.

Nonlinear relationship simulation based on copula function

The correlative research shows that the nonlinear probability relationship between predictor and prediction object can be established based on the conditional probability of Copula function^31,32. X and Y are used to represent a characteristic variable corresponding to meteorological and agricultural drought, and $\:{F}_{x\left(x\right)}$ and $\:{F}_{y\left(y\right)}$ are edge distribution functions of X and Y respectively. Let u=$\:{F}_{x\left(x\right)}$, v=$\:{F}_{y\left(y\right)}$, then the joint distribution function of X and Y can be expressed as:

$$\:\text{F}\left(\text{x},\text{y}\right)=\text{C}\left[{F}_{x}\left(x\right),{F}_{y}\left(y\right)\right]=\text{C}(\text{u},\text{v})$$

(3)

Where, C is the Copula function.

Model accuracy evaluation

Using RMSE, AIC and BIC to judge the accuracy of the response relationship model among drought characteristic variables. Generally, the smaller the RMSE, AIC and BIC, the higher the representation accuracy³³.

Results

Spatio-temporal evolution characteristics of drought

Previous studies have shown that the average response time of agricultural drought to meteorological drought is three months. Therefore, SPEI-3 is selected for meteorological drought identification, and SSMI-1 is selected for agricultural drought identification. Based on SPEI-3 and SSMI-1, 104 meteorological drought events and 85 agricultural drought events were identified by 3D identification method. Table 2 shows the five most severe meteorological and agricultural drought events. According to the data shown in Table 2, typical meteorological drought (No.96) began in April 2017 and ended in December, lasting 9 months. The typical agricultural drought (No.36) began in October 2000 and ended in May 2002, lasting 20 months.

Table 2 The five most severe meteorological and agricultural drought events.

Taking typical meteorological drought and typical agricultural drought as examples, the time and space continuous evolution of a single drought event was analyzed. As shown in Fig. 3 (a), the evolution characteristics of typical meteorological drought are as follows: the meteorological drought began in April 2017, and the drought center was located in the middle of Xilin Gol; From May to August 2017, the drought center moved southwest to the southwest of Xilin Gol, and the drought was the most severe in the whole river basin in June. From September to October 2017, the drought center continued to migrate to the southwest, and the drought intensity decreased slightly. In November, the drought intensity increased, and the drought center was located in the west of Xilinhot. In December, the drought subsided and the drought was lifted. All in all, the drought in the northern part of Xilin Gol is the most serious.

As shown in Fig. 3 (b), the specific evolution characteristics of typical agricultural drought are as follows: From October 2000 to May 2001, the drought center of this agricultural drought was concentrated in the southwest of Xilin Gol; From June to September 2001, the drought area increased and the drought intensity was stronger. In November 2001, both the area and intensity of drought decreased, and the center shifted to the southeast. From January to March 2002, the drought intensity became more intense, mainly concentrated in the west of Xilin Gol; In May 2002, the drought intensity decreased and the drought ended.

Fig. 3

Evolution process of typical meteorological drought and agricultural drought events (a) Meteorological drought (b) Agricultural drought.

Drought event matching

According to the spatiotemporal scale drought event matching criteria, 104 meteorological droughts and 85 agricultural droughts were matched in time and space, and 28 meteorological and agricultural drought events were successfully matched, as shown in Fig. 4. The same colors in the picture represent the same pair of drought events.

Fig. 4

Matching results of meteorological-agricultural drought event pairs.

The 28 meteorological and agricultural drought event pairs successfully matched included 15 C1-responsive drought event pairs, 4 C2-responsive drought event pairs, 4 C3-responsive drought event pairs and 5 C4 responsive drought event pairs. The number of drought event pairs of C1 type is relatively large, accounting for more than 50%. The statistical results of the characteristic variables of drought events contained in each response type drought event pair are shown in Fig. 5. All the successfully matched drought event pairs contain 42 meteorological droughts and 54 agricultural droughts. Among them, C4 responsive drought events included the largest number of drought events, with 15 meteorological drought events and 24 agricultural drought events respectively. Overall, the duration, severity and area of meteorological and agricultural drought events included in the C1, C2 and C3 response types are all relatively small. Specifically, the drought characteristic variables in C1 and C4 response types showed similar conditions, that is, compared with meteorological drought, agricultural drought had a larger duration mean and a smaller severity and area mean. The average drought area, severity and duration of agricultural drought events included in C2 response type are all smaller than those of meteorological drought. According to the characteristic variable values of each drought event involved in the analysis, this is because the response type is manifested as a long-duration, high-severity and large-area meteorological drought triggering two small-scale agricultural drought events in different regions. For the C3 response type, this type of drought event triggered a larger agricultural drought for multiple meteorological droughts, so the average drought duration of agricultural drought events was longer and the severity was stronger.

Fig. 5

Box plots of the number of drought events, duration, severity and area in each drought response type.

Since the response characteristics of C1 response types are relatively simple, the complex spatio-temporal response characteristics of meteorological-agricultural drought events are analyzed in detail by taking C2 response types, C3 response types and C4 response types as examples. Taking the 16th drought event pair successfully matched as an example, the No.73 (May 2005 - January 2006) meteorological drought matched No.44 (July 2005) and No.45 (September 2005 - May 2006) two agricultural drought events, as shown in Fig. 6. No.73 meteorological drought that occurred from May 2005 to January 2006 covered more than 90% of IMPIRB, and the drought in eastern Bayannur was more serious. The No.73 meteorological drought event caused the No.44 agricultural drought event located in the northwest of Xilin Gol and the No.45 agricultural drought event concentrated in the west of Xilin Gol in the middle period of development (July 2005), and the spatial distribution of drought situation had a good consistency.

Fig. 6

Spatio-temporal response characteristics of agricultural drought No.44 and No.45 to meteorological drought No.73.

Take the matching of the third drought event pair as the representative, the two meteorological droughts No.8 (February 1966) and No.9 (January 1967) matched the agricultural drought event No.9 (November 1966 - May 1967), as shown in Fig. 7. The spatio-temporal response characteristics of this meteorological and agricultural drought event pair are mainly as follows: The No.8 meteorological drought in the central part of IMPIRB in February 1966 and the No.9 meteorological drought in the southern part of IMPIRB in January 1967 jointly triggered the No.9 agricultural drought event concentrated in the southwest of Ulanqab from November 1966 to May 1967. The whole response process showed obvious combined effect of meteorological drought events.

Fig. 7

Temporal and spatial responses of No.9 agricultural droughts to No.8 and No.9 meteorological droughts.

Taking the 24th drought event pair successfully matched as the representative, the spatio-temporal response characteristics of multiple agricultural droughts to multiple meteorological droughts were analyzed. First, the temporal evolution of the drought events included in the 24th drought event pair were analyzed. The 24th drought event pair includes 5 meteorological droughts, starting and ending from November 2013 to May 2016. No.89 meteorological drought was the most serious (lasting 7 months, drought severity is 1.93 month*10⁶km²), followed by No.91 meteorological drought event, lasting 5 months. The drought severity was 1.19 month*10⁶km². The 24th drought event pair included four agricultural droughts, which started and ended from February 2014 to June 2016. Agricultural drought events were continuously affected by several meteorological drought events, and the drought duration was long, showing obvious prolongation effect, while the drought severity was weakened, among which No.74 agricultural drought events had the largest scale. According to the development process of the 24th drought event, it can be divided into three stages, as shown in Fig. 8. In the first stage, from November 2013 to June 2014, one meteorological drought induced the same agricultural drought, which was specifically manifested as No.89 meteorological drought (November 2013 to May 2014) covering the whole study area triggered No.73 agricultural drought events (February 2014) distributed in Bayannur. The second stage was from July 2014 to June 2015, which included two meteorological droughts and two agricultural droughts. The No.89 meteorological drought, No.90 meteorological drought and No.91 meteorological drought in the late development period caused the No.74 agricultural drought (July 2014 -- September 2015) and No.75 agricultural drought (August 2015), and the spatial distribution characteristics of the severe drought region had a good consistency. The third stage was from July 2015 to June 2016, including 2 meteorological droughts and 1 agricultural drought event. The specific temporal and spatial response characteristics were as follows: The No.92 meteorological drought (July 2015), which occurred in the western parts of IMPIRB, and the No.93 meteorological drought (April to May 2016), which almost covered the whole area of the study area, jointly triggered the No.93 agricultural drought (October 2015 to June 2016) concentrated in the northwest of Ulanqab.

Fig. 8

Characteristics of spatio-temporal response to the 24th drought event (a) Phase I: November 2013 - June 2014 (b) Phase II: July 2014 - June 2015 (c) Phase III: July 2015 - June 2016.

The matched drought events were projected onto the corresponding drought centers, and the spatial distribution pattern of drought event centers was obtained, as shown in Fig. 9. The distribution characteristics of the centers of meteorological and agricultural drought events successfully matched are basically the same in space, and they are mainly concentrated in the west of Xilin Gol in general. In addition, some meteorological drought events were distributed in the northeast of Xilin Gol, the southwest of Ulanqab and the south of Bayannur, while some agricultural drought events were distributed in the west of Bayannur and the northwest of Ulanqab.

Fig. 9

Spatial distribution characteristics of drought centers with successful matching.

Response relationship of drought characteristic variables

Table 3 shows the optimal selection results of the marginal distribution function between the characteristic variables of meteorological drought and agricultural drought. The optimal marginal distribution functions of the combined meteorological and agricultural drought duration were Exp distribution and Wb distribution, respectively, the drought severity was Gam distribution, and the drought area was normal distribution and LogN distribution, respectively.

Table 3 Optimal marginal distribution functions for drought characteristic variables.

Table 4 shows the goodness-fit test results of the joint distribution function for different combinations of drought characteristic variables based on AIC, BIC and RMSE and the optimal Copula function. The optimal joint distribution function of meteorological and agricultural drought duration is Gaussian Copula function, and the optimal joint distribution function of meteorological and agricultural drought area and severity is Clayton Copula function.

Table 4 Goodness of fit test of copula function.

After selecting the optimal Copula function, we use this function to infer the joint distribution probability between meteorological drought and agricultural drought, as shown in Fig. 10. From the contour line in Fig. 9, we can get the probability that any drought characteristic variable is less than a certain value, and the possible combination of different variables under a certain probability. The joint distribution probability characteristics of different characteristic variables (duration, severity and area) between meteorological and agricultural droughts successfully matched are basically the same. As can be seen from Fig. 10 (a), when the duration of meteorological drought and agricultural drought is less than 10 months, 15 months and 20 months at the same time, the probability is 10%, 40% and 65% respectively. As shown in Fig. 10 (b), when meteorological drought severity and agricultural drought severity are simultaneously less than 1 month*10⁶km² and 2 month*10⁶km², the probability is 20%, and 74%, respectively. When the meteorological drought severity is less than 2 month*10⁶km², the probability that the agricultural drought severity is less than 1 month*10⁶km² is 50%. As can be seen from Fig. 10 (c), when the meteorological drought area and agricultural drought area are simultaneously less than 10⁵km²2*10⁵km² and 3*10⁵km², the probability is 10%, 44% and 65%, respectively; when the meteorological drought area is less than 4 *10⁵km², the probability of agricultural drought area is less than 3*10⁵km² is 68%.

Fig. 10

Drought characteristic variables joint distribution probability results.(a) Duration (b) Severity (c) Area.

Discussion

Characteristics of drought lag time

Meteorological drought will have an impact on soil moisture, and then lead to agricultural drought resulting in crop reduction. Drought monitoring results based on agricultural drought index have a certain lag compared with meteorological drought³⁴. The method to determine the response lag time is to calculate the correlation coefficient between SSMI and SPEI of each time scale, and select the time scale with the greatest correlation. The response delay characteristics of agricultural drought to meteorological drought in different months were quantitatively discussed according to the calculation results. The correlation coefficients between monthly scale SSMI of different IMPIRB partitions and SPEI of different time scales are shown in Fig. 11.

Fig. 11

correlation coefficient between SSMI at the October scale and SPEI at different time scales.

As shown in Fig. 11 (a), the correlation coefficient between SPEI and SSMI of IMPIRB is large from June to August, and reaches the maximum in autumn (> 0.8). The average lag time, as determined by the monthly maximum correlation coefficient, is 5 months in summer and 4 months in autumn. The maximum correlation coefficient of winter and spring decreased and mostly concentrated in 0.6–0.7. It can be seen that the average lag time of winter and spring was 7 months and 10 months respectively, which was longer than that of autumn. In conclusion, agricultural drought in autumn had the fastest response and the shortest lag time. The drought response delay from 1961 to 2021 was quantified according to Pearson correlation coefficients between monthly scale SSMI and different time scales SPEI, as shown in Fig. 11 (b). As can be seen from Fig. 11 (b), in the study area, the correlation coefficient between monthly SSMI and SPEI of different time scales first increased and then decreased in fluctuation, the maximum correlation coefficient was 0.844, and the corresponding response lag time was 3 months. That is, the maximum time-lag correlation coefficient of agricultural drought to meteorological drought was 3-month, indicating that the response of meteorological drought on 3-month time scale was very close to that of agricultural drought on month scale.

Multi-angle response of drought time and space

There is an intrinsic relationship between the occurrence and development of agricultural drought and meteorological drought. Some scholars have studied and discussed the response process between the two drought types^35,36. In previous studies, the matching of drought event pairs mainly focused on the temporal variation of different drought types, but ignored their spatial relationship^37,38.

Based on the 3D recognition method, the matching process between droughts is discussed in this paper. The spatio-temporal response relationship between different droughts is described comprehensively by considering the characteristics of time and space. Considering the spatial characteristics of drought response, the complexity of drought response is increased. For example, a large meteorological drought event covering a large area may trigger several small-scale agricultural drought events, showing decomposition effect, indicating that the degree of drought is weakened during the response process. An agricultural drought event may be triggered by several small-scale meteorological drought events, showing a combined effect. In addition, the results show that the response of agricultural drought has a lag characteristic, which is consistent with the existing research results^39,40. According to the spatio-temporal matching criteria, there were 42 meteorological drought events and 54 agricultural drought events paired in IMPIRB from 1961 to 2021, indicating a strong spatio-temporal correlation between the two types of droughts. Matching meteorological and agricultural drought events from the perspective of time and space can ensure that their complex relationship on the scale of space-time is closer to the actual situation, and the response relationship between them is more three-dimensional.

Advantages and limitations

Compared with the drought response method that only focuses on time characteristics, this study overcomes the application limitation of traditional methods by responding between meteorological and agricultural drought events from the perspective of space-time, and can perform more reliable analysis in the area with a wide spatial range³⁹. Based on Copula function, the response relationship between different drought characteristic variables is established, which can accurately describe the nonlinear covariant relationship between droughts^41,42,43. In this paper, extreme drought events are incorporated into the optimal response relationship model, which improves the reliability of agricultural drought event prediction to some extent²⁰. These quantitative response relationships can be directly applied to local drought risk management. By real-time monitoring of meteorological drought indicators, the possible agricultural drought risk levels can be predicted 1 to 3 months in advance, providing a critical time buffer for decisions such as adjusting the planting structure of crops and optimizing the allocation of irrigation water. The research results have certain reference value for the early warning of agricultural drought in the study area and can also provide theoretical references for actual agricultural production activities and the formulation of drought resistance and disaster reduction plans.

However, there are still some aspects in this article that need improvement. Firstly, the resolution of the dataset is relatively coarse and cannot meet the accuracy requirements of hundreds of meters. It is difficult to capture the changes in small-scale drought and can only roughly identify the drought conditions at various locations in the study area, which may deviate from the actual situation^44,45. Secondly, due to the limitations of the physical and parametric schemes of the assimilation system model, GLDAS soil moisture products may lead to errors in soil moisture data. Although the data assimilation process reduces these errors to a certain extent, there is still a deviation of 5–10% compared with field observations⁴⁶. Therefore, future research can combine higher-resolution datasets to enhance the accuracy and applicability of the data. At the same time, multi-model integration methods can be adopted for cross-validation to reduce the systematic errors caused by the physical parameterization of a single model, so as to understand and monitor drought events more comprehensively.

Furthermore, previous studies have shown that factors such as human activities, underlying surface characteristics, and climate types all have significant impacts on drought responses^47,48,49,50. Human activities are significant in the transmission of meteorological drought to agricultural drought, for example, by influencing soil moisture through irrigation, and thus agricultural drought response^51,52. Different underlying surface characteristics also play an important role in drought response⁵³. Pena-Angulo et al. showed that different land use types had different vegetation types and coverage, which led to different distribution of precipitation between soil water and evapotranspiration, thus affecting drought response⁵⁴. In addition, different climate types also influence drought response by systematically influencing the water cycle^49,55. Therefore, it is necessary to consider the influence of multiple factors in order to more fully and accurately clarity the mechanism of drought response.

Conclusions

This paper uses the 3D drought identification method to extract the spatio-temporal continuous drought events in IMPIRB from 1961 to 2021. Through spatio-temporal scale matching and characteristic variable analysis, the dynamic evolution laws and spatio-temporal response characteristics of meteorological and agricultural drought events are revealed. The established spatio-temporal response model can accurately predict the occurrence probability of agricultural drought. It provides a scientific basis for formulating a zoned and differentiated drought early warning system and drought resistance dispatching plan, significantly enhancing the accuracy and predictability of regional drought risk management. The main conclusions of this article are as follows:

(1) Using the 3D identification method, 104 meteorological drought events and 85 agricultural drought events were identified in the study area from 1961 to 2021. Typical meteorological drought events and agricultural drought duration were 9 months and 20 months respectively. The distribution of drought centers in typical meteorological droughts is scattered and the evolution characteristics are obvious.

(2) From 1961 to 2021, 28 drought event pairs were successfully matched in the study area, among which C1 response type was more common. With the increase of the scale of drought events, the response relationship between droughts becomes more complex. Among the response types, agricultural drought and meteorological drought have obvious response relationship in spatio-temporal scale. The distribution characteristics of drought centers in space are basically the same, mainly concentrated in the west of Xilin Gol.

(3) The optimal marginal distribution functions of the matched drought duration were Exp distribution and Wb distribution, the drought severity was Gam distribution, and the drought area was normal distribution and LogN distribution, respectively. The optimal response models of meteorological-agricultural drought duration, area and severity were Gaussian Copula, Clayton Copula and Clayton Copula, respectively. The joint probability characteristic curve of agricultural drought characteristic variables and meteorological drought characteristic variables was established, which can provide theoretical reference for practical agricultural production activities and the formulation of drought prevention and relief programs.