A method and system for evaluating the dynamic propagation process of drought in a river basin

Abstract

The application discloses a kind of method and system for evaluating the process of drought dynamic propagation in drainage basin, including obtaining drought data and collating, abnormal value detection is carried out to drought data;Multiple types of drought index are calculated, and multi-scale calculation is carried out;Drought event is identified based on three-dimensional connectivity;Drought characteristic parameter is calculated to quantify the effective drought event identified, while the migration track of drought event is quantified, the space-time evolution characteristics of drought event are obtained;According to the time series of multiple types of drought index, Granger causality test is carried out;Drought propagation rate between any two types of droughts is calculated;The correlation of two two drought types under multi-scale is calculated, the drought propagation time is quantified, and the key season and spatial distribution sign of the propagation between droughts are identified.The application realizes the accurate identification and quantitative characterization of the propagation process, response time and spatial difference of basin drought by tracking the dynamic track of drought event and analyzing the interaction between multiple types of drought.

Description

Technical Field

[0001] This invention relates to drought monitoring and hydrological process analysis technology, specifically to a method and system for assessing the dynamic propagation process of drought within a watershed. Background Technology

[0002] Drought formation is primarily driven by variability within the climate system and influenced by factors at multiple spatiotemporal scales, making it one of the most complex types of meteorological disasters. To deepen our understanding of drought evolution patterns and accurately identify and extract drought events, subsequent multi-feature analysis is essential. Assessing the dynamic propagation process of drought within a watershed, tracking the dynamic trajectory of drought events, and analyzing the interactions among different types of drought enabled the precise identification and quantitative characterization of drought propagation processes, response times, and spatial differences within the watershed. A better understanding of the spatiotemporal dynamics of drought is crucial for early warning systems and the development of reliable resilience strategies to ensure food security.

[0003] Despite the availability of satellite remote sensing data and advancements in spatiotemporal analysis, methodologies for assessing drought dynamics are still under development. Currently, drought duration, intensity, spatial extent, migration paths, and origin and end points are used to describe drought dynamics, but the methods for describing the spatiotemporal behavior of drought events are not yet systematic. Furthermore, the propagation order between different drought types remains controversial, and drought propagation paths may vary depending on regional and environmental factors.

[0004] The three-dimensional framework integrates spatial, temporal, and intensity dimensions, enabling a comprehensive analysis of drought propagation mechanisms and their impacts. The resulting connectivity-based approach provides a novel method for assessing drought characteristics and tracking its dynamic evolution, and has been successfully applied in hydrometeorological research. However, existing research largely focuses on unidirectional propagation relationships between different drought types, with limited exploration of bidirectional correlation mechanisms. Systematic studies on the bidirectional dependence and propagation characteristics among different drought types remain insufficient. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a method and system for assessing the dynamic propagation process of drought within a watershed, in order to expand the identification of three-dimensional connectivity drought, quantify the migration characteristics of multiple types of drought events within a watershed, systematically study the bidirectional dependence between different drought types, and study the propagation characteristics of drought and its driving processes among various types of drought.

[0006] Technical solution: The method described in this invention includes the following steps:

[0007] S1. Select a representative watershed as the study area, obtain data on drought in the study area, including precipitation data, runoff data and soil moisture data, and organize the runoff data and soil moisture data.

[0008] S2. Perform outlier detection on the drought data affecting the study area. If outliers are found, process them; otherwise, proceed directly to step S3.

[0009] S3. Calculate multiple types of drought indices, including standardized precipitation index, standardized runoff index and standardized soil moisture index, and perform multi-scale calculations on the drought indices.

[0010] S4. Identifying drought events based on three-dimensional connectivity, including: setting a drought index threshold, aggregating continuous drought areas into discrete patches through neighborhood connectivity analysis, obtaining drought patches, and screening drought patches with an area greater than the area threshold and a duration exceeding the threshold time as valid drought events;

[0011] S5. Based on the identified effective drought events, calculate four drought characteristic parameters—drought duration, drought area, drought intensity, and drought centroid—to quantify the identified effective drought events. At the same time, quantify the migration trajectory of the drought events to obtain the spatiotemporal evolution characteristics of the drought events.

[0012] S6. Based on the time series of multiple drought indices, perform Granger causality tests to quantify the bidirectional dependency between any two of the three drought types: meteorological drought, hydrological drought, and agricultural drought.

[0013] S7. Calculate the drought propagation rate among meteorological, hydrological, and agricultural droughts;

[0014] S8. Based on the maximum cross-correlation coefficient method, calculate the pairwise correlations between meteorological, hydrological and agricultural drought at multiple scales, quantify drought propagation time, and identify key seasonal and spatial distribution characteristics of the propagation between meteorological-hydrological-agricultural drought.

[0015] Furthermore, in step S1, the runoff data and soil moisture data are processed, including: calculating the total runoff data based on surface runoff, groundwater runoff and snowmelt, and converting the surface moisture content into volumetric soil moisture content.

[0016] Furthermore, in step S2, outliers are defined as values ​​in the time series that deviate from the mean by more than three standard deviations. The criteria involve scanning the time series pixel by pixel and variable by variable to check for outliers. The specific method for handling outliers is to delete them and then fill in the missing values ​​using linear interpolation.

[0017] Furthermore, the calculation method for the multiple drought indices in step S3 is as follows:

[0018] First, the historical sequence of each variable is sorted by A sliding cumulative processing method is applied over several months to construct a cumulative value series at the corresponding scale. Based on this cumulative value series, its long-term mean is calculated as a climate baseline value, and a probability distribution model suitable for this variable is fitted. This model is then used to calculate the cumulative values ​​observed within a specific time period. The monthly cumulative value is placed in this probability distribution to obtain the cumulative probability of the cumulative value occurring in the historical climate background, thereby quantitatively assessing the degree of deviation of the current water conditions from the long-term average state and its probability of occurrence.

[0019] Secondly, the inverse function of the cumulative distribution function of the standard normal distribution is used to convert the cumulative probability value into the corresponding Z score;

[0020] Finally, the final standardized index is calculated based on the standardized deviation.

[0021] Furthermore, the specific method in step S4 is as follows:

[0022] First, drought areas are determined based on drought index thresholds;

[0023] Secondly, different discrete patches are divided into arid patches based on the spatial characteristics of the arid region.

[0024] The third step is to further screen drought patches based on their area. If a drought patch is smaller than the area threshold, it is eliminated.

[0025] Finally, drought patches were divided and screened at different times. When the duration of a drought patch exceeded the time threshold, consecutive spatiotemporal drought patches were considered as valid drought events.

[0026] Furthermore, the definition and calculation method of the drought characteristic parameters in step S5 are as follows:

[0027] Drought duration refers to the interval from the occurrence of an event to its end;

[0028] The drought area is defined as the union of the projected areas of drought patches at different time periods:

[0029] ;

[0030] in, For the drought area, It refers to the duration of the drought event. Indicates the first Projected area of ​​drought patches in each time period .

[0031] Drought intensity is quantified as the absolute value of the product of the drought index and the area of ​​the grid cell, resulting in an intensity unit of square kilometers.

[0032] The drought centroid is defined as the weighted center during a drought event;

[0033] The migration trajectory of a drought event includes both the migration distance and the migration direction, calculated as follows:

[0034] The migration distance of a drought event is defined as the distance between the initial and final centroids of the drought event, and is calculated using a half-sine equation:

[0035] ;

[0036] The formula for calculating the direction of drought migration is:

[0037] ;

[0038] in, The migration distance of the drought event. For the Earth's radius, and These represent the geographic coordinates of the centroids at the start and end points of the drought event, respectively. Let be the initial azimuth angle from the start point to the end point of the drought event. .

[0039] Furthermore, step S6 specifically involves:

[0040] For any combination of drought type A and drought type B, the null hypothesis is tested in two separate tests:

[0041] First test of the null hypothesis The lag value of drought type A has no predictive effect on drought type B, therefore it is included. The earlier sequence cannot improve the effect on The accuracy of predictions for subsequent changes, among which, This represents the corresponding drought index sequence. This represents the corresponding drought index sequence;

[0042] Second test of the null hypothesis The lag value of drought type B has no predictive effect on drought type A, therefore it is included. The earlier sequence cannot improve the effect on The accuracy of predictions for subsequent changes;

[0043] Based on the vector autoregression framework, construct separate structures containing only... Restricted models and containing early sequences For the unrestricted model of the early sequence, the prediction errors of the two types of models are compared using the F-test:

[0044] If you refuse ,but The hysteresis value can be significantly reduced The prediction error indicates that drought type A has a one-way dependent driving force on drought type B.

[0045] If you refuse ,but The hysteresis value can be significantly reduced The prediction error indicates that drought type B has a one-way dependent driving force on drought type A.

[0046] If both are rejected and If the preceding sequences of the two types of drought mutually enhance each other's prediction accuracy, then there is a bidirectional dependency between type A drought and type B drought.

[0047] If neither can be refused and If the condition is met, then it can be determined that there is no significant Granger dependency between the two types of drought.

[0048] Furthermore, the formula for calculating the drought propagation rate in step S7 is as follows:

[0049] ;

[0050] in, For the rate of drought spread, This represents the duration of overlap between the source drought event and the target drought event on the timeline. The duration of the drought event itself.

[0051] Furthermore, the formulas for calculating the pairwise correlations between meteorological, hydrological, and agricultural drought at multiple scales in step S8 are as follows:

[0052] ;

[0053] in, The correlation coefficient, and They represent the first The first time scale Drought-like index and the first The first time scale Drought-like index, Indicates the first Drought-like index types, These correspond to the standardized precipitation index, standardized runoff index, and standardized soil moisture index, respectively. Indicates the first Drought-like index types, These correspond to the standardized precipitation index, standardized runoff index, and standardized soil moisture index, respectively. and Different values; Indicates the first A time scale , Indicates the first A time scale . The covariance of the rank variable. For the first At the first time scale, the first The original sequence of the drought-like index, before being rank-transformed into a hierarchical variable. For the first At the first time scale, the first The original sequence of the drought-like index, before being rank-transformed into a hierarchical variable. Representing rank, Indicates the first Drought-like index in the 1st rank variable sequence at each time scale standard deviation Indicates the first Drought-like index in the 1st rank variable sequence at each time scale The standard deviation.

[0054] The system used in the method includes:

[0055] The data processing unit is used to select representative watersheds as study areas, acquire data on drought affecting the study areas, including precipitation data, runoff data, and soil moisture data, and organize the runoff data and soil moisture data.

[0056] The outlier detection unit is used to detect outliers in the drought data affecting the study area. If outliers are found, they are processed; if no outliers are found, the multi-scale drought index calculation unit is executed directly.

[0057] The multi-scale drought index calculation unit is used to calculate various types of drought indices, including standardized precipitation index, standardized runoff index and standardized soil moisture index, and to perform multi-scale calculations on drought indices.

[0058] The drought event identification unit is used to identify drought events based on three-dimensional connectivity, including: setting a drought index threshold, aggregating continuous drought areas into discrete patches through neighborhood connectivity analysis to obtain drought patches, and screening drought patches with an area greater than the area threshold and a duration exceeding the threshold time as valid drought events;

[0059] The spatiotemporal evolution feature acquisition unit is used to quantify the identified effective drought events by calculating four drought feature parameters: drought duration, drought area, drought intensity, and drought centroid, and at the same time quantify the migration trajectory of the drought events to obtain the spatiotemporal evolution features of the drought events.

[0060] The causality test unit is used to perform Granger causality tests based on the time series of multiple drought indices, quantifying the bidirectional dependency between any two of the three drought types: meteorological drought, hydrological drought, and agricultural drought.

[0061] The drought propagation rate calculation unit is used to calculate the drought propagation rate among meteorological, hydrological, and agricultural droughts.

[0062] The drought identification unit is used to calculate the correlation between meteorological, hydrological and agricultural droughts at multiple scales based on the maximum cross-correlation coefficient method, quantify the drought propagation time, and identify the key seasonal and spatial distribution characteristics of the propagation between meteorological-hydrological-agricultural droughts.

[0063] Invention Principle: The three types of drought exhibit temporal propagation relationships and spatial correlation characteristics. Three-dimensional connectivity identification methods can effectively identify drought events and describe the spatial evolution of drought patches. The Granger causality test is an ideal tool for analyzing the bidirectional dependence between drought types, while drought propagation rate and maximum cross-correlation methods effectively assess drought response time and seasonal characteristics. This invention combines spatiotemporal dynamic analysis and causal relationship analysis to develop a technique for assessing the dynamic propagation process of drought within a watershed.

[0064] Beneficial effects: Compared with the prior art, the significant technical effects of this invention are as follows: It expands the three-dimensional connectivity identification method, quantifies the migration direction and distance between the initiation and termination centroids of drought, and improves the tracking and measurement of typical drought event trajectories; Based on Granger causality test analysis and correlation analysis, it systematically studies the bidirectional dependence and propagation characteristics between different drought types, deepening the understanding of drought propagation dynamics; It makes up for the shortcomings of existing technologies in the study of bidirectional propagation of multiple types of drought, and provides a scientific basis for drought early warning and water resource management. Attached Figure Description

[0065] Figure 1 This is a flowchart of the method described in this invention;

[0066] Figure 2The diagram shows the spatial distribution of the area, intensity, and duration of drought events, where (a) represents the spatial distribution of the area of ​​meteorological drought events, (b) represents the spatial distribution of the intensity of meteorological drought events, (c) represents the spatial distribution of the duration of meteorological drought events, (d) represents the spatial distribution of the area of ​​hydrological drought events, (e) represents the spatial distribution of the intensity of hydrological drought events, (f) represents the spatial distribution of the duration of hydrological drought events, (g) represents the spatial distribution of the area of ​​agricultural meteorological drought events, (h) represents the spatial distribution of the intensity of agricultural drought events, and (i) represents the spatial distribution of the duration of agricultural drought events.

[0067] Figure 3 The spatial distribution of the migration trajectories of drought events and the directional distribution of the number of drought events in the Yellow River Basin are shown. (a) shows the spatial distribution of the migration trajectories of meteorological drought events and the directional distribution of the number of drought events from 1981 to 1989; (b) shows the spatial distribution of the migration trajectories of hydrological drought events and the directional distribution of the number of drought events from 1981 to 1989; (c) shows the spatial distribution of the migration trajectories of agricultural drought events and the directional distribution of the number of drought events from 1981 to 1989; (d) shows the spatial distribution of the migration trajectories of meteorological drought events and the directional distribution of the number of drought events from 1990 to 1999; (e) shows the spatial distribution of the migration trajectories of hydrological drought events and the directional distribution of the number of drought events from 1990 to 1999; and (f) shows the spatial distribution of the migration trajectories of agricultural drought events from 1990 to 1999. The spatial distribution and directional distribution of the number of drought events are as follows: (g) is the spatial distribution of the migration trajectory of meteorological drought events from 2000 to 2009 and the directional distribution of the number of drought events; (h) is the spatial distribution of the migration trajectory of hydrological drought events from 2000 to 2009 and the directional distribution of the number of drought events; (i) is the spatial distribution of the migration trajectory of agricultural drought events from 2000 to 2009 and the directional distribution of the number of drought events; (j) is the spatial distribution of the migration trajectory of meteorological drought events from 2010 to 2022 and the directional distribution of the number of drought events; (k) is the spatial distribution of the migration trajectory of hydrological drought events from 2010 to 2022 and the directional distribution of the number of drought events; (l) is the spatial distribution of the migration trajectory of agricultural drought events from 2010 to 2022 and the directional distribution of the number of drought events.

[0068] Figure 4 The two-way dependence spatial distribution of various drought indices in the Yellow River Basin is shown, where (a) is the two-way dependence spatial distribution of SPI-SRI, (b) is the two-way dependence spatial distribution of SPI-SMI, and (c) is the two-way dependence spatial distribution of SRI-SMI.

[0069] Figure 5The map shows the spatial distribution of drought propagation ratios among different drought types in the Yellow River Basin. (a) shows the spatial distribution of meteorological-hydrological drought propagation ratios, (b) shows the spatial distribution of meteorological-agricultural drought propagation ratios, (c) shows the spatial distribution of hydrological-agricultural drought propagation ratios, and (d) shows the spatial distribution of agricultural-hydrological drought propagation ratios.

[0070] Figure 6 The spatial distribution maps of the maximum correlation coefficient (MCC) among various drought indices in the Yellow River Basin are shown below. (a) shows the spatial distribution map of the maximum correlation coefficient (MCC) between SPI and SRI, (b) shows the spatial distribution map of the maximum correlation coefficient (MCC) between SPI and SMI, and (c) shows the spatial distribution map of the maximum correlation coefficient (MCC) between SRI and SMI.

[0071] Figure 7 The map shows the spatial distribution of drought propagation time and season among drought types in the Yellow River Basin. (a) represents the spatial distribution of meteorological-hydrological drought propagation time, (b) represents the spatial distribution of meteorological-hydrological drought propagation season, (c) represents the spatial distribution of meteorological-agricultural drought propagation time, (d) represents the spatial distribution of meteorological-agricultural drought propagation season, (e) represents the spatial distribution of hydrological-agricultural drought propagation time, (f) represents the spatial distribution of hydrological-agricultural drought propagation season, (g) represents the spatial distribution of agricultural-hydrological drought propagation time, and (h) represents the spatial distribution of agricultural-hydrological drought propagation season. Detailed Implementation

[0072] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0073] like Figure 1 As shown, the method for assessing the dynamic propagation process of drought within a watershed proposed in this invention includes the following steps:

[0074] S1. Select a representative watershed as the study area and obtain data on drought in the study area, including precipitation data, runoff data, and soil moisture data. Runoff data includes surface runoff, groundwater runoff, and snowmelt. Soil moisture data is the water content of the surface layer (0-10cm). The obtained runoff data and soil moisture data are processed, including: calculating the total runoff data based on surface runoff, groundwater runoff, and snowmelt, and converting the water content of the surface layer (0-10cm) into volumetric soil moisture content.

[0075] The selected study area in this embodiment is the Yellow River Basin. The main factors affecting drought in the Yellow River Basin are precipitation, runoff, and soil moisture. Precipitation data were obtained from the Climate Hazards Infrared Precipitation and Station Data (CHIRPS). Surface runoff, groundwater runoff, snowmelt, and soil moisture data were obtained from the Global Land Data Assimilation System (GLDAS). Total runoff data was calculated by adding the three components of surface runoff, groundwater runoff, and snowmelt. In the soil moisture data, the moisture content of the surface layer (0-10cm) was expressed in kg / m² and converted to volumetric soil moisture content (mm / mm) by dividing by 100.

[0076] S2. Outlier detection was performed on the drought data acquired within the study area. The criteria perform outlier detection on a pixel-by-pixel and variable-by-variable basis (including precipitation data, runoff data, and soil moisture data). If outliers are found, they are deleted, and missing values ​​are filled in using linear interpolation to ensure the continuity of the time series. If no outliers are found, step S3 is executed directly.

[0077] Outliers are defined as values ​​in a time series that deviate from the mean by more than three standard deviations.

[0078] S3. Calculate multiple types of drought indices, including: Standardized Precipitation Index (SPI), Standardized Runoff Index (SRI), and Standardized Soil Moisture Index (SMI), and apply these three drought indices to 1-12 months (i.e., Months Multi-scale calculations are performed on the cumulative time scale of ).

[0079] The specific calculation methods for the three types of drought indices are consistent: First, the historical series of each variable (including precipitation data, runoff data, and soil moisture data) are processed according to... A sliding cumulative processing method is applied over several months to construct a cumulative value series at the corresponding scale. Based on this cumulative value series, its long-term mean is calculated as a climate baseline, and a probability distribution model suitable for this variable is fitted. This is achieved by using observations within a specific time period... By placing the monthly cumulative value within this probability distribution, the cumulative probability of that value occurring under historical climate conditions can be obtained, thus quantitatively assessing the degree of deviation of current moisture conditions from the long-term average and its probability of occurrence. Secondly, to eliminate the influence of different variable dimensions and distribution characteristics, the inverse function of the cumulative distribution function of the standard normal distribution is used to convert the above cumulative probability values ​​into corresponding Z-scores. This conversion makes variables of different properties comparable on the same standardized scale, and the magnitude of the Z-score directly reflects the direction and magnitude of the deviation of the observed value from the historical mean. Finally, the final standardized index is calculated based on the standardized deviation. Specifically, by subtracting the series mean and dividing by the standard deviation, the Z-score is further unified into a standardized value under the standard normal distribution. After the above processing, all variables are mapped to the same reference frame, and their numerical magnitude characterizes the degree of standardized deviation of the observed value from historical climate.

[0080] S4. Identify drought events based on three-dimensional connectivity: Set a drought index threshold, aggregate continuous drought areas into discrete patches through 3×3 neighborhood connectivity analysis, and screen patches with an area greater than 1.5% of the study area and a duration of 2 months or more as valid drought events.

[0081] First, arid regions were identified based on a drought index threshold. In this study, the drought index threshold was set to -0.5, meaning that arid grid cells were marked when the drought index was less than -0.5. Second, different discrete patches were divided according to the spatial characteristics of the arid regions. Starting from the initial grid cells, adjacent drought-affected cells within a 3×3 neighborhood were recursively identified until no connected cells were detected. Third, arid patches were further screened based on their area. In this study, 1.5% of the study area was defined as the area threshold for arid patches. If a drought patch was smaller than the area threshold, it was eliminated. Finally, drought events were identified. Arid patches were divided and screened at different times. When the duration of a drought patch was 2 months or more, consecutive spatiotemporally arid patches were considered drought events.

[0082] S5. Based on the identified drought events, calculate four drought characteristic parameters—drought duration, drought area, drought intensity, and drought centroid—to quantify the identified drought events, and simultaneously quantify the migration trajectory of the drought events. This yields the spatiotemporal evolution characteristics of the drought events. The drought characteristics are defined as follows:

[0083] Drought duration refers to the interval from the onset to the end of a drought event.

[0084] The drought area is defined as the union of the projected areas of drought patches at different time periods:

[0085] (1);

[0086] in, For the drought area, This refers to the duration of the drought event (in months). Indicates the first Projected area of ​​drought patches in each time period .

[0087] Drought intensity is quantified as the absolute value of the product of the drought index (dimensionless) and the area of ​​the grid cell (square kilometers), resulting in an intensity unit of square kilometers.

[0088] The drought centroid is defined as the weighted center during a drought event.

[0089] The migration trajectory of a drought event includes both the migration distance and the migration direction, calculated as follows:

[0090] The migration distance of a drought event is defined as the distance between the initial and final centroids of the drought event, and is calculated using a half-sine equation:

[0091] (2);

[0092] in, The migration distance of the drought event. It is the Earth's radius (approximately 6,371 kilometers). and The geographic coordinates (in radians) of the centroids at the start and end points of the drought event are represented respectively.

[0093] The formula for calculating the migration direction of drought events is:

[0094] (3);

[0095] in, The initial azimuth angle from the start point to the end point of the drought event (0° is due north, 90° is due east, 180° is due south, and 270° is due west). .

[0096] S6. Analyze the causal relationships among drought types using Granger causality tests. Perform Granger causality tests on the time series of multiple drought indices to quantify the interdependencies among drought types.

[0097] Granger causality test is an analytical method for assessing causal relationships between time series data. Using Granger causality analysis within a vector autoregression framework, this study quantifies the bidirectional dependency between any two types of drought: meteorological drought, hydrological drought, and agricultural drought. Through predictive correlation analysis of time series data, the driving and response logic between two types of drought is clarified.

[0098] For drought type A (corresponding to drought index sequence) (and Class B drought (corresponding to the drought index sequence)) Any combination of ) is used to test the null hypothesis in two separate tests:

[0099] First test of the null hypothesis: "The lag value of drought type A has no predictive effect on drought type B," meaning it is included. The earlier sequence cannot improve the effect on The accuracy of predictions for subsequent changes;

[0100] Second test of the null hypothesis "The lag value of drought type B has no predictive effect on drought type A," meaning it is included. The earlier sequence cannot improve the effect on The accuracy of predicting subsequent changes.

[0101] Based on the Vector Autoregression (VAR) framework, construct "only containing "Restricted model of early sequence" and "containing" The prediction errors of the two types of models were compared using an "unrestricted model of the early sequence" and an F-test.

[0102] If you refuse ,illustrate The hysteresis value can be significantly reduced The prediction error indicates that drought type A has a one-way dependency on drought type B.

[0103] If you refuse ,illustrate The hysteresis value can be significantly reduced The prediction error indicates that drought type B has a one-way dependent driving force on drought type A.

[0104] If both are rejected and This indicates that the preceding sequences of the two types of drought can mutually improve the prediction accuracy of each other, that is, there is a two-way dependency between drought type A and drought type B.

[0105] If neither can be refused and If the condition is met, then it can be determined that there is no significant Granger dependency between the two types of drought.

[0106] When building the vector autoregressive model, all time series variables were seasonally adjusted to ensure time stationarity. The optimal lag order at the pixel scale was determined using the Akaike Information Criterion (AIC), with a maximum lag order constraint of 6 months.

[0107] S7. Calculate the drought propagation rate among meteorological, hydrological, and agricultural droughts.

[0108] Drought propagation rate is a quantitative indicator characterizing the temporal correlation between two drought types (source drought type and target drought type) during their propagation from one type to another. It can clearly quantify the propagation rate and spatial distribution of drought in different directions among multiple drought types, expanding the scope of propagation rate analysis to include agricultural and hydrological drought. The drought propagation rate is expressed as:

[0109] (4);

[0110] in, For the rate of drought spread, This represents the duration of overlap between the source drought event and the target drought event on the timeline. The duration of the drought event itself.

[0111] S8. Based on the maximum cross-correlation coefficient method, the correlations between meteorological, hydrological, and agricultural droughts at multiple scales were calculated to quantify drought propagation time. This method was used to analyze different propagation directions and spatial propagation characteristics among various types of drought. Simultaneously, the seasonal characteristics of drought propagation were analyzed, identifying key seasons and spatial distributions of propagation between meteorological, hydrological, and agricultural droughts, and expanding the spatial distribution of propagation time and seasons for agricultural and hydrological droughts.

[0112] The Spearman correlation coefficient is used to characterize the maximum cross-correlation number (MCC). Based on this method, multi-scale drought indices, including the standardized precipitation index (SPI), standardized runoff index (SRI), and standardized soil moisture index, are used to calculate the drought propagation time between any two drought systems of meteorology, hydrology, and agriculture.

[0113] The calculation method for the transmission between the two types of drought is as follows:

[0114] (5);

[0115] in, The correlation coefficient, and They represent the first The first time scale Drought-like index and the first The first time scale Drought-like index, Indicates the first Drought-like index types, These correspond to the Standardized Precipitation Index (SPI), Standardized Runoff Index (SRI), and Standardized Soil Moisture Index (SMI), respectively. Indicates the first Drought-like index types, These correspond to the Standardized Precipitation Index (SPI), Standardized Runoff Index (SRI), and Standardized Soil Moisture Index (SMI), respectively. and Different values; Indicates the first A time scale , Indicates the first A time scale . The covariance of the rank variable. For the first At the first time scale, the first The original sequence of the drought-like index, before being rank-transformed into a hierarchical variable. For the first At the first time scale, the first The original sequence of the drought-like index, before being rank-transformed into a hierarchical variable. Representing rank, Indicates the first Drought-like index in the 1st rank variable sequence at each time scale standard deviation Indicates the first Drought-like index in the 1st rank variable sequence at each time scale The standard deviation.

[0116] The timescale of the source drought index corresponding to the maximum cross-correlation number (MCC) represents the drought propagation time from the target drought to the source drought. The month in which the source drought index was used to calculate the maximum cross-correlation number is determined as the critical month for the propagation process at this grid point. Subsequently, based on the correspondence between months and seasons (March-May is spring, June-August is summer, September-November is autumn, and December-February is winter), the months are mapped to the critical seasons.

[0117] Example verification:

[0118] The data for this example comes from the Yellow River, China's second longest river, which is 5,464 kilometers long with an elevation difference of 4,480 meters. Its basin extends from 32°N to 42°N, and from 96°E to 119°E, covering an area of ​​approximately 795,000 square kilometers. The basin is approximately 1,900 kilometers long from east to west and 1,100 kilometers long from north to south. The Yellow River basin exhibits a three-tiered topographic structure, with the terrain gradually sloping down from west to east.

[0119] Figure 2Figures (a) to (i) illustrate the spatial distribution characteristics of the area, duration, and intensity of the three types of drought. Statistics show that between 1981 and 2022, a total of 119 meteorological drought events, 159 hydrological drought events, and 124 agricultural drought events were identified (all lasting more than two months). Meteorological drought has a wide spatial distribution, mainly concentrated in the middle and upper reaches of the Yangtze River, including the Ningxia Hui Autonomous Region, Inner Mongolia Autonomous Region, and central Gansu. For example... Figure 2 As shown in (a) to (c), although the extent of drought impact fluctuated over time, drought intensity peaked between 1990–1999 and 2000–2009. The longest meteorological drought event lasted 12 months. The duration of drought was particularly pronounced during the period of 1981–1999, especially with large-scale and exceptionally severe drought events occurring in the Tibetan Plateau and the Wei River basin. Downstream meteorological drought, however, remained concentrated in a single region. Compared to meteorological drought, hydrological drought has a wider spatial distribution and greater intensity. Figure 2 As shown in (d) to (f), these events are mainly concentrated in the upper reaches of the Yellow River, characterized by long duration (3-17 months) and high intensity. Hydrological drought events were frequent between 1990 and 1999, mostly concentrated in the central part of the basin; while between 2010 and 2022, the frequency of hydrological droughts in the upper mountainous areas increased. Overall, hydrological droughts show a spatial clustering trend. Since 2010, both the frequency and duration of agricultural droughts have increased. Figure 2 Figures (g) to (i) indicate that the most severe agricultural drought events in history occurred in the central part of the basin between 1990 and 1999 and between 2010 and 2022. The intensity of agricultural drought was significantly higher than normal, and it was more concentrated in the Yellow River Basin between 2010 and 2022, with both drought intensity and duration showing a clear worsening trend.

[0120] Figure 3Figures (a) to (l) show the spatial distribution and direction of migration distances of drought events in the Yellow River Basin during four different periods. Meteorological drought events mainly occurred in the upper and middle mountainous areas of the Yellow River Basin. Between 1981 and 2009, these droughts mainly migrated westward and southwestward, with generally short migration distances. A few drought events had longer migration distances, moving from the upper to the middle reaches of the basin. After 2010, drought events tended to migrate eastward and northward, with an increase in average migration distance. Compared to other types of drought, hydrological drought events had the longest average migration distance, mainly migrating eastward. Over time, hydrological drought gradually shifted from the upper to the middle and lower reaches of the basin. Agricultural drought events mostly migrated eastward; however, by 2010, the number of drought events migrating northwestward increased. Notably, agricultural drought events had the longest migration distances between 1990 and 1999, and almost all of them migrated eastward. Overall, prior to 2010, the migration directions of all drought types remained largely consistent: meteorological droughts mainly migrated westward and southwestward, hydrological droughts migrated eastward and northeastward, and agricultural droughts mainly migrated eastward. In contrast, after 2010, the migration paths of drought events became more uncertain, exhibiting multi-directional migration characteristics.

[0121] Figure 4 The images (a) to (c) show the spatial distribution of the three drought types in the Yellow River Basin, representing a two-way dependence. Figure 4 As shown in (a), the interaction between the Spiral Influence (SPI) and the Southern Influence (SRI) in the Hetao Plain and Ningxia Plain mainly exhibits a two-way dependence. In Shaanxi Province and the Fen River Basin, the SRI has a dominant unidirectional influence on the SPI, while the upper and lower mountainous areas of the Yellow River Basin are mainly affected by the unidirectional influence of the SPI on the SRI. It is noteworthy that there are significant regional differences in the interaction between the SPI and SRI. Figure 4 As shown in (b), the unidirectional dependence of SPI on SMI is concentrated in the mountainous areas of the upper reaches of the Yellow River and the eastern part of the Hetao Plain, while the western part of the Hetao Plain is dominated by the unidirectional influence of SMI on SPI. The regional differences exhibited in the Hetao Plain may be due to factors such as artificial irrigation. Other areas are dominated by the bidirectional dependence of SPI and SMI. The bidirectional dependence between SRI and SMI is widespread throughout the Yellow River Basin, indicating a close relationship between soil moisture and river runoff.

[0122] Figure 5 Figures (a) to (d) clearly demonstrate the spatial distribution characteristics of the rates of drought propagation in the four directions in the Yellow River Basin. The drought propagation rates in the Yellow River Basin exhibit significant regional heterogeneity. Regarding the propagation of meteorological drought to hydrological drought, the propagation rate is relatively low in the upper mountainous areas, while it is higher in other areas. The propagation rate of meteorological drought to agricultural drought is particularly prominent in the central region and the southern part of the Wei River Basin. Figure 5(c) clearly shows that in the process of hydrological drought spreading to agricultural drought, the central region, which lacks a river network, exhibits a lower spread rate compared to the surrounding areas. Meanwhile, the spread rate is relatively low in the upstream mountainous areas and the Fen River system. Similarly, the spread from agriculture to hydrological drought demonstrates considerable spatial heterogeneity. Figure 5 In the middle (d) region, only the Hetao Plain and Ningxia Plain showed relatively high propagation rates, while other areas had limited drought propagation capacity. Regarding the numerical range of drought propagation rates, the meteorological-hydrological drought propagation rate ranged from 0.11 to 0.67, while the meteorological-agricultural drought propagation rate ranged from 0.17 to 0.72. This indicates that the propagation effect of meteorological drought on agricultural drought in the Yellow River Basin is generally stronger than its propagation effect on hydrological drought. Furthermore, the hydrological-agricultural drought propagation rate (mainly ranging from 0.11 to 0.78) is higher than the agricultural-hydrological drought propagation rate (mainly ranging from 0.08 to 0.73), suggesting that the impact of hydrological drought on the agricultural system may be more significant than the reverse impact of agricultural drought on the hydrological system.

[0123] Figure 6 Figures (a) to (c) show the spatial distribution of the maximum correlation coefficient (MCC) among the three drought indices in the Yellow River Basin. As shown in the figure, the MCC of SPI and SRI is relatively high in the middle and lower reaches of the basin. In contrast, the MCC of SPI and SMI is relatively low in the upper mountainous areas and the Fen River Basin. The MCC of SRI and SMI remains low only in the upper mountainous areas, while it is generally high in other areas, with a maximum value of 0.99.

[0124] Figure 7 Tables (a) to (h) show the corresponding seasonal variations and response time scales of the maximum correlation coefficient (MCC). Regarding the propagation of meteorological to hydrological drought, regions with significant seasonal MCC characteristics accounted for 39.6% (spring), 15.5% (summer), 40.0% (autumn), and 4.2% (winter) of the basin area, respectively. This distribution characteristic indicates that the significant impact of meteorological drought on runoff generation mainly occurs in spring and autumn. The most significant impact in spring is located in the upstream mountainous areas and the Ordos inland drainage basin, while the autumn impact is concentrated in the Weihe and Fenhe river basins and extends to the middle and lower reaches of the Yellow River. The affected areas in winter and summer are relatively small: the winter impact is mainly confined to the southern region, while the summer impact is spatially dispersed, mainly appearing in the transition zone between the spring and autumn impact areas. Figure 7(d) As shown in the figure, areas with a hydrological drought response time of 1-2 months account for approximately 72.4% of the basin area, mainly distributed in the central part of the basin. This spatial pattern confirms that hydrological drought usually lags behind meteorological drought by 1-2 months. Regarding the propagation of meteorological drought to agricultural drought, areas exhibiting significant seasonal MCC characteristics account for 0.5%, 34.6%, 35.6%, and 8.5% of the basin area in spring, summer, autumn, and winter, respectively. These results indicate that the significant impact of meteorological drought on soil moisture conditions mainly occurs in summer and autumn. Summer impacts are mainly concentrated in the northern part of the Wei River, the central part of the Fen River, and the Dahei River basin, primarily appearing in the transition zone between the spring and autumn impact areas. Figure 7 (d) Conversely, the autumn impact is mainly distributed in the southern part of the basin. The affected areas in spring and winter are relatively small: the spring impact is mostly limited to the central part of the Wuding River basin, while the winter impact is locally distributed in the upstream mountainous areas, especially in the Tao River basin. The area with a response time of 1 month accounts for 36.05% of the basin area, mainly concentrated in the northern and downstream regions; the area with a response time of 2-5 months accounts for 49.9%, mainly located in the Weihe and Fenhe River basins. This spatiotemporal pattern indicates that the time range of agricultural drought response to meteorological drought is usually 1 to 5 months. The lag time between SPI and SMI is longer than that between SPI and SRI, which is due to the difference in their response mechanisms to meteorological signals. The seasonal transmission structure between hydrological and agricultural drought is relatively similar, with autumn being the dominant season and summer the next, and its impact is mainly concentrated in the central part of the basin. In the transmission from hydrological to agricultural drought, the Ningxia Plain is susceptible to the spring impact, while the winter impact area is extremely small; in the transmission from agricultural to hydrological drought, the winter impact is mainly limited to the western part of the Weihe River basin and the lower reaches of the Yellow River. In most regions, the response time of hydrological drought to agricultural drought is 1-3 months, which is usually faster than the response time of agricultural drought to hydrological drought (1-4 months).

[0125] In another embodiment, the system used in the method includes:

[0126] The data processing unit is used to select representative watersheds as study areas, acquire data on drought affecting the study areas, including precipitation data, runoff data, and soil moisture data, and organize the runoff data and soil moisture data.

[0127] The outlier detection unit is used to detect outliers in the drought data affecting the study area. If outliers are found, they are processed; if no outliers are found, the multi-scale drought index calculation unit is executed directly.

[0128] The multi-scale drought index calculation unit is used to calculate various types of drought indices, including standardized precipitation index, standardized runoff index and standardized soil moisture index, and to perform multi-scale calculations on drought indices.

[0129] The drought event identification unit is used to identify drought events based on three-dimensional connectivity, including: setting a drought index threshold, aggregating continuous drought areas into discrete patches through neighborhood connectivity analysis to obtain drought patches, and screening drought patches with an area greater than the area threshold and a duration exceeding the threshold time as valid drought events;

[0130] The spatiotemporal evolution feature acquisition unit is used to quantify the identified effective drought events by calculating four drought feature parameters: drought duration, drought area, drought intensity, and drought centroid, and at the same time quantify the migration trajectory of the drought events to obtain the spatiotemporal evolution features of the drought events.

[0131] The causality test unit is used to perform Granger causality tests based on the time series of multiple drought indices, quantifying the bidirectional dependency between any two of the three drought types: meteorological drought, hydrological drought, and agricultural drought.

[0132] The drought propagation rate calculation unit is used to calculate the drought propagation rate among meteorological, hydrological, and agricultural droughts.

[0133] The drought identification unit is used to calculate the correlation between meteorological, hydrological and agricultural droughts at multiple scales based on the maximum cross-correlation coefficient method, quantify the drought propagation time, and identify the key seasonal and spatial distribution characteristics of the propagation between meteorological-hydrological-agricultural droughts.

Claims

1. A method of assessing the dynamic propagation of drought processes within a catchment, characterized in that, Includes the following steps: S1. Select a representative watershed as the study area, obtain data on drought in the study area, including precipitation data, runoff data and soil moisture data, and organize the runoff data and soil moisture data. S2. Perform outlier detection on the drought data affecting the study area. If outliers are found, process them; otherwise, proceed directly to step S3. S3. Calculate multiple types of drought indices, including standardized precipitation index, standardized runoff index and standardized soil moisture index, and perform multi-scale calculations on the drought indices. S4. Identifying drought events based on three-dimensional connectivity, including: setting a drought index threshold, aggregating continuous drought areas into discrete patches through neighborhood connectivity analysis, obtaining drought patches, and screening drought patches with an area greater than the area threshold and a duration exceeding the threshold time as valid drought events; S5. Based on the identified effective drought events, calculate four drought characteristic parameters—drought duration, drought area, drought intensity, and drought centroid—to quantify the identified effective drought events. At the same time, quantify the migration trajectory of the drought events to obtain the spatiotemporal evolution characteristics of the drought events. S6. Based on the time series of multiple drought indices, perform Granger causality tests to quantify the bidirectional dependency between any two of the three drought types: meteorological drought, hydrological drought, and agricultural drought. S7. Calculate the drought propagation rate among meteorological, hydrological, and agricultural droughts; S8. Based on the maximum cross-correlation coefficient method, calculate the pairwise correlations between meteorological, hydrological and agricultural drought at multiple scales, quantify drought propagation time, and identify key seasonal and spatial distribution characteristics of the propagation between meteorological-hydrological-agricultural drought.

2. The method of assessing the progression of a drought dynamic process within a catchment according to claim 1, wherein, In step S1, the runoff data and soil moisture data are organized, including: calculating the total runoff data based on surface runoff, groundwater runoff and snowmelt, and converting the surface moisture content into volumetric soil moisture content.

3. The method for assessing the dynamic propagation process of drought within a watershed according to claim 1, characterized in that, In step S2, outliers are values ​​in a time series that deviate from the mean by more than three standard deviations. The criteria involve scanning the time series pixel by pixel and variable by variable to check for outliers. The specific method for handling outliers is to delete them and then fill in the missing values ​​using linear interpolation.

4. The method for assessing the dynamic propagation process of drought within a watershed according to claim 1, characterized in that, The calculation method for the multiple drought indices in step S3 is as follows: First, the historical sequence of each variable is sorted by A sliding cumulative processing method is applied over several months to construct a cumulative value series at the corresponding scale. Based on this cumulative value series, its long-term mean is calculated as a climate baseline value, and a probability distribution model suitable for this variable is fitted. This model is then used to calculate the cumulative values ​​observed within a specific time period. The monthly cumulative value is placed in this probability distribution to obtain the cumulative probability of the cumulative value occurring in the historical climate background, thereby quantitatively assessing the degree of deviation of the current water conditions from the long-term average state and its probability of occurrence. Secondly, the inverse function of the cumulative distribution function of the standard normal distribution is used to convert the cumulative probability value into the corresponding Z score; Finally, the final standardized index is calculated based on the standardized deviation.

5. The method for assessing the dynamic propagation process of drought within a watershed according to claim 1, characterized in that, The specific method in step S4 is as follows: First, drought areas are determined based on drought index thresholds; Secondly, different discrete patches are divided into arid patches based on the spatial characteristics of the arid region. The third step is to further screen drought patches based on their area. If a drought patch is smaller than the area threshold, it is eliminated. Finally, drought patches were divided and screened at different times. When the duration of a drought patch exceeded the time threshold, consecutive spatiotemporal drought patches were considered as valid drought events.

6. The method for assessing the dynamic propagation process of drought within a watershed according to claim 1, characterized in that, The definition and calculation method of drought characteristic parameters in step S5 are as follows: Drought duration refers to the interval from the occurrence of an event to its end; The drought area is defined as the union of the projected areas of drought patches at different time periods: ； in, For the drought area, It refers to the duration of the drought event. Indicates the first Projected area of ​​drought patches in each time period ; Drought intensity is quantified as the absolute value of the product of the drought index and the area of ​​the grid cell, resulting in an intensity unit of square kilometers. The drought centroid is defined as the weighted center during a drought event; The migration trajectory of a drought event includes both the migration distance and the migration direction, calculated as follows: The migration distance of a drought event is defined as the distance between the initial and final centroids of the drought event, and is calculated using a half-sine equation: ； The formula for calculating the direction of drought migration is: ； in, The migration distance of the drought event. For the Earth's radius, and These represent the geographic coordinates of the centroids at the start and end points of the drought event, respectively. Let be the initial azimuth angle from the start point to the end point of the drought event. .

7. The method for identifying and quantifying multiple types of drought events in a watershed according to claim 1, characterized in that, Step S6 is as follows: For any combination of drought type A and drought type B, the null hypothesis is tested in two separate tests: First test of the null hypothesis The lag value of drought type A has no predictive effect on drought type B, therefore it is included. The earlier sequence cannot improve the effect on The accuracy of predictions for subsequent changes, among which, This represents the corresponding drought index sequence. This represents the corresponding drought index sequence; Second test of the null hypothesis The lag value of drought type B has no predictive effect on drought type A, therefore it is included. The earlier sequence cannot improve the effect on The accuracy of predictions for subsequent changes; Based on the vector autoregression framework, construct separate structures containing only... Restricted models and containing early sequences For the unrestricted model of the early sequence, the prediction errors of the two types of models are compared using the F-test: If you refuse ,but The hysteresis value can be significantly reduced The prediction error indicates that drought type A has a one-way dependent driving force on drought type B. If you refuse ,but The hysteresis value can be significantly reduced The prediction error indicates that drought type B has a one-way dependent driving force on drought type A. If both are rejected and If the preceding sequences of the two types of drought mutually enhance each other's prediction accuracy, then there is a bidirectional dependency between type A drought and type B drought. If neither can be refused and If the condition is met, then it can be determined that there is no significant Granger dependency between the two types of drought.

8. The method for identifying and quantifying multiple types of drought events in a watershed according to claim 1, characterized in that, The formula for calculating the drought propagation rate in step S7 is: ； in, For the rate of drought spread, This represents the duration of overlap between the source drought event and the target drought event on the timeline. The duration of the drought event itself.

9. The method for identifying and quantifying multiple types of drought events in a watershed according to claim 1, characterized in that, The formula for calculating the pairwise correlation between meteorological, hydrological, and agricultural drought at multiple scales in step S8 is as follows: ； in, The correlation coefficient, and They represent the first The first time scale Drought-like index and the first The first time scale Drought-like index, Indicates the first Drought-like index types, These correspond to the standardized precipitation index, standardized runoff index, and standardized soil moisture index, respectively. Indicates the first Drought-like index types, These correspond to the standardized precipitation index, standardized runoff index, and standardized soil moisture index, respectively. and Different values; Indicates the first A time scale , Indicates the first A time scale ; The covariance of the rank variable. For the first At the first time scale, the first The original sequence of the drought-like index, before being rank-transformed into a hierarchical variable. For the first At the first time scale, the first The original sequence of the drought-like index, before being rank-transformed into a hierarchical variable. Representing rank, Indicates the first Drought-like index in the 1st rank variable sequence at each time scale standard deviation Indicates the first Drought-like index in the 1st rank variable sequence at each time scale The standard deviation.

10. A system for assessing the dynamic propagation of drought within a watershed, characterized in that, include: The data processing unit is used to select representative watersheds as study areas, acquire data on drought affecting the study areas, including precipitation data, runoff data, and soil moisture data, and organize the runoff data and soil moisture data. The outlier detection unit is used to detect outliers in the drought data affecting the study area. If outliers are found, they are processed; if no outliers are found, the multi-scale drought index calculation unit is executed directly. The multi-scale drought index calculation unit is used to calculate various types of drought indices, including standardized precipitation index, standardized runoff index and standardized soil moisture index, and to perform multi-scale calculations on drought indices. The drought event identification unit is used to identify drought events based on three-dimensional connectivity, including: setting a drought index threshold, aggregating continuous drought areas into discrete patches through neighborhood connectivity analysis to obtain drought patches, and screening drought patches with an area greater than the area threshold and a duration exceeding the threshold time as valid drought events; The spatiotemporal evolution feature acquisition unit is used to quantify the identified effective drought events by calculating four drought feature parameters: drought duration, drought area, drought intensity, and drought centroid, and at the same time quantify the migration trajectory of the drought events to obtain the spatiotemporal evolution features of the drought events. The causality test unit is used to perform Granger causality tests based on the time series of multiple drought indices, quantifying the bidirectional dependency between any two of the three drought types: meteorological drought, hydrological drought, and agricultural drought. The drought propagation rate calculation unit is used to calculate the drought propagation rate among meteorological, hydrological, and agricultural droughts. The drought identification unit is used to calculate the correlation between meteorological, hydrological and agricultural droughts at multiple scales based on the maximum cross-correlation coefficient method, quantify the drought propagation time, and identify the key seasonal and spatial distribution characteristics of the propagation between meteorological-hydrological-agricultural droughts.

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