Modeling method for identifying response relationship between multi-regional meteorological drought and hydrological drought

Abstract

The present application relates to a kind of multi-region meteorological drought and hydrological drought response relationship identification modeling method, comprising the following steps: drought index construction and time sequence acquisition, obtain the comparable drought index sequence;Drought event identification and feature extraction, extract the duration D of each drought and drought amplitude M;Regional response relationship modeling, parameter fitting is carried out to historical drought event sample by least square method;Space joint drought modeling and estimation, the joint probability distribution model of hydrological drought amplitude between two adjacent regions is established using Copula function.The present application can be used for drought risk early warning and cross-region hydrological drought estimation, especially in the basin with serious data missing or significant human intervention has strong applicability, can provide certain scientific basis and technical support for hydrological drought management and control strategy formulation.

Description

Technical Field

[0001] This invention relates to the field of hydrology and water resources technology, specifically to a modeling method for identifying the relationship between meteorological drought and hydrological drought response in multiple regions. Background Technology

[0002] Drought is a natural disaster with a wide impact, long duration, and severe damage, significantly affecting agricultural production, water resource allocation, the ecological environment, and socio-economic development. Drought can be classified into several types based on its causative factors and influencing processes, including meteorological drought, agricultural drought, hydrological drought, and socio-economic drought. Meteorological drought is typically caused by persistently low precipitation and is the initial stage of other types of drought. Hydrological drought manifests as reduced surface runoff, decreased reservoir inflow, or river flow interruption, reflecting the delayed response of meteorological drought within the hydrological system.

[0003] Understanding the propagation relationship between meteorological drought and hydrological drought is crucial in drought risk analysis and management, contributing to drought early warning, watershed management, and water resource allocation. Currently, commonly used drought identification methods include analysis based on indicators such as the Standardized Precipitation Index (SPI) and Standardized Runoff Index (SRI). These methods characterize the transformation mechanism from meteorological drought to hydrological drought by performing correlation analysis, function fitting, or time lag estimation on drought time series within a single region. However, most existing studies focus on drought response modeling in single regions, neglecting the coupling mechanisms of drought processes across multiple spatial regions, making it difficult to identify patterns of spatially simultaneous drought events (i.e., spatially synchronized droughts).

[0004] On the other hand, frequent human activities such as reservoir operation and water diversion projects have altered the drought development process, even rendering existing meteorological-hydrological drought models ineffective. Current technologies lack modeling methods that can simultaneously consider multi-regional collaborative relationships, the impact of human activities, and the ability to identify drought in areas with insufficient data. Therefore, a new drought modeling method is urgently needed to establish a correspondence between meteorological and hydrological drought across multiple regions, adapting to the new demands of drought analysis under complex backgrounds. Summary of the Invention

[0005] The purpose of this invention is to provide a modeling method for identifying the relationship between meteorological drought and hydrological drought response in multiple regions, so as to solve the problem in the prior art that it is difficult to simultaneously take into account the identification of drought relationship in multiple regions, the analysis of human activity interference, and the estimation of missing areas.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention provides a modeling method for identifying the relationship between meteorological drought and hydrological drought response in multiple regions, comprising the following steps:

[0008] Step 1: Construction and time series acquisition of drought indicators. The standardized precipitation index (SPI) and the standardized runoff index (SRI) are used to characterize meteorological drought and hydrological drought in each region, respectively. By standardizing the long-term precipitation and runoff series on the target time scale, a comparable drought indicator series is obtained.

[0009] Step 2, drought event identification and feature extraction: The SPI and SRI sequences are processed using run theory to identify the start and end positions of drought events and extract the duration D and amplitude M of each drought.

[0010] Step 3: Response relationship modeling within the region. Within each sub-region, based on the extracted meteorological drought amplitude and hydrological drought amplitude, a function response relationship model is constructed. The function can be linear, power function, or polynomial. The parameters of historical drought event samples are fitted using the least squares method.

[0011] Step 4: Spatial joint drought modeling and estimation. A joint probability distribution model of the hydrological drought amplitude between two adjacent regions is established using the Copula function. If hydrological observation data is lacking in one region, the probability of hydrological drought in the missing region is estimated by using the joint model and drought information from the other side. Furthermore, the changes in model structure under natural and disturbance periods are compared to assess the impact of human activities.

[0012] The standardization of long-term precipitation and runoff sequences in step 1 includes the following sub-steps:

[0013] The original monthly precipitation or runoff series are cumulatively processed according to the set target time scale to obtain the cumulative series;

[0014] Based on the statistical characteristics of different variables, probability distribution functions were selected to fit the cumulative precipitation series and runoff series respectively: precipitation data were fitted using the Gamma distribution, and runoff data were fitted using the Pearson Type-III distribution.

[0015] The cumulative probability value is calculated based on the selected distribution, and then mapped to the standard normal distribution value through equal probability transformation to obtain the standardized precipitation index SPI and the standardized runoff index SRI.

[0016] In step 2, when using run theory to identify drought events, if the interval between two drought segments does not exceed the set critical discontinuity time... If the drought index value does not exceed the set threshold during the intermittent period, then these events are merged into a single continuous drought event; the drought magnitude M is defined as the cumulative water shortage degree when the drought index is below the threshold during the drought period, i.e.:

[0017]

[0018] In the formula, D represents the duration of the drought. It is the first Monthly SPI or SRI value, This is the drought threshold, set to -0.5.

[0019] The function response relationship model constructed in step 3 includes one of the following forms:

[0020] Linear functions: ;

[0021] Power function: ;

[0022] Quadratic polynomial function: ,

[0023] In the formula, The extent of hydrological drought, The extent of meteorological drought, , , The model parameters are fitted to historical drought samples using the least squares method, and cross-validation is used to test generalization performance. The optimal ratio of training set to test set is 2:1. The goodness-of-fit evaluation index includes the coefficient of determination R. 2 Efficiency coefficient NSE and percentage deviation rate PBIAS.

[0024] In step 4, the Copula function is one of the Frank, Gumbel-Hougaard, or Clayton functions in the Archimedes family. The dependency parameters are determined by the maximum likelihood estimation method, and the optimal model is selected by the Akaike Information Criterion (AIC).

[0025] Compared with the prior art, the beneficial effects of the present invention are:

[0026] 1. The methodology is scientifically sound and allows for in-depth analysis of the meteorological, hydrological, and drought mechanisms within the watershed.

[0027] This invention proposes a multi-regional drought identification method that integrates fundamental functional equations and Copula joint analysis. This method can construct the functional response relationship between meteorological and hydrological drought within a single region, and also reveal the spatial synergistic characteristics of hydrological drought in adjacent regions through a joint distribution model. Furthermore, by comparing and analyzing the modeling results during natural and disturbed periods, the method can identify the impact of human activities on drought propagation paths and intensity, thereby improving the model's adaptability and explanatory power for complex drought processes.

[0028] 2. It can solve the problem of identifying hydrological drought in areas with insufficient data and improve cross-regional estimation capabilities:

[0029] The data index calculation method used in this invention is simple, and the model structure is clear. When the target area lacks runoff observation data and cannot be directly analyzed for hydrological drought, drought information from neighboring areas can be used in conjunction with a joint distribution model to estimate the drought amplitude distribution range. This method overcomes the limitation of traditional methods that rely heavily on local data, enhances the applicability of the model in data-scarce areas, and has good versatility and engineering application value. Attached Figure Description

[0030] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments of the present invention will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a flowchart of a modeling process for identifying the relationship between meteorological drought and hydrological drought in a watershed, as described in an embodiment of the present invention.

[0032] Figure 2 This is a schematic diagram illustrating the principle of identifying hydrological drought events based on runs theory in an embodiment of the present invention.

[0033] Figure 3 This is a graph showing the basic function fitting relationship between meteorological drought and hydrological drought characteristics in a certain watershed in an embodiment of the present invention;

[0034] Figure 4 The Archimedesian Copula joint probability distribution fitting map between hydrological drought intensity in adjacent areas in this embodiment of the invention includes a comparison of empirical distribution fitting of GH Copula, Frank Copula and Clayton Copula;

[0035] Figure 5 This is a distribution map of the conditional probability density function of hydrological drought intensity in a specific area during different periods (natural period and disturbance period) in an embodiment of the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will now be described with reference to the accompanying drawings. It should be noted that similar reference numerals and letters in the following drawings indicate similar items; therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0037] The terms “comprising,” “including,” or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase “comprising one…” does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0038] The terms “first,” “second,” etc., are used only to distinguish one entity or operation from another, and should not be construed as indicating or implying relative importance, nor as requiring or implying any such actual relationship or order between these entities or operations.

[0039] like Figures 1 to 5 As shown, this embodiment of the invention provides a modeling method for identifying the relationship between meteorological drought and hydrological drought response in multiple regions, including the following steps:

[0040] Step 1: Construction and time series acquisition of drought indicators. The standardized precipitation index (SPI) and the standardized runoff index (SRI) are used to characterize meteorological drought and hydrological drought in each region, respectively. By standardizing the long-term precipitation and runoff series on the target time scale, a comparable drought indicator series is obtained.

[0041] Step 2, drought event identification and feature extraction: The SPI and SRI sequences are processed using run theory to identify the start and end positions of drought events and extract the duration D and amplitude M of each drought.

[0042] Step 3: Response relationship modeling within the region. Within each sub-region, based on the extracted meteorological drought amplitude and hydrological drought amplitude, a function response relationship model is constructed. The function can be linear, power function, or polynomial. The parameters of historical drought event samples are fitted using the least squares method.

[0043] Step 4: Spatial joint drought modeling and estimation. A joint probability distribution model of the hydrological drought amplitude between two adjacent regions is established using the Copula function. If hydrological observation data is lacking in one region, the probability of hydrological drought in the missing region is estimated by using the joint model and drought information from the other side. Furthermore, the changes in model structure under natural and disturbance periods are compared to assess the impact of human activities.

[0044] This invention first quantifies meteorological and hydrological drought processes in various regions based on the Standardized Precipitation Index (SPI) and Standardized Runoff Index (SRI); then, it extracts characteristics such as the duration and magnitude of drought events using run theory to construct a functional response model between meteorological and hydrological drought within the region; next, it uses the Copula function to establish a joint probability model of hydrological drought between adjacent regions, using drought information from the other region to estimate the probability of spatially synchronized drought events when hydrological data is lacking in one region; finally, it assesses the impact of human activities on drought propagation by comparing the model results of the natural period and the disturbance period.

[0045] The specific implementation process of this invention is as follows: Figure 1 The steps are as follows:

[0046] Step 1: Construction and Time Series Acquisition of Drought Indicators. The Standardized Precipitation Index (SPI) and Standardized Runoff Index (SRI) are used to characterize meteorological drought and hydrological drought in each region, respectively. By standardizing long-term precipitation and runoff series on the target time scale, comparable drought indicator series are obtained.

[0047] Step 1 further includes the following sub-steps:

[0048] (1.1) Accumulate the original monthly precipitation or runoff sequence according to the set target time scale (such as 1 month, 3 months or 12 months) to obtain the cumulative sequence;

[0049] (1.2) Based on the statistical characteristics of different variables, select appropriate probability distribution functions to fit the cumulative precipitation series and runoff series respectively: precipitation data are fitted with Gamma distribution and runoff data are fitted with Pearson Type-III (P-III) distribution to establish the marginal distribution function required for the standardized index (SPI or SRI).

[0050] The Gamma distribution is a two-parameter probability distribution commonly used in precipitation modeling. It is suitable for right-skewed, non-negative cumulative precipitation series, and its cumulative distribution function is:

[0051] (1)

[0052] In the formula, It represents the cumulative precipitation over a given time scale (month, quarter, or year), and is a non-negative continuous random variable; The shape parameter describes the degree of skewness in the distribution; This is a scale parameter that reflects the flexibility of the distribution; This is the Gamma function.

[0053] The Pearson Type-III distribution is a three-parameter distribution that introduces a location parameter on top of the Gamma distribution. It is widely used in runoff sequence modeling and can better fit the skewed distribution characteristics in hydrological runoff data.

[0054] (2)

[0055] In the formula, Indicates the first The cumulative probability corresponding to the monthly traffic value. , and These are the shape, scale, and location parameters of the Pearson Type-III distribution, which can be estimated using the method of moments.

[0056] (1.3) Calculate the cumulative probability value based on the selected distribution, and map it to the standard normal distribution value through equal probability transformation to obtain the standardized precipitation index (SPI) and the standardized runoff index (SRI).

[0057] (3)

[0058] (4)

[0059] In the formula, This represents the inverse function of the standard normal distribution. The resulting SPI (SRI) value reflects the degree of deviation of rainfall (flow) j from the historical baseline at a given time scale, and can be used to determine the occurrence and severity of meteorological (hydrological) drought.

[0060] Step 2, Drought Event Identification and Feature Extraction. Run-length theory is used to process the SPI and SRI sequences to identify the start and end points of drought events, and to extract the duration (D) and magnitude (M) of each drought event. Consecutive drought segments with short intervals are merged to improve the stability of drought identification.

[0061] Taking the SRI (Self-Drought Index) as an example, such as Figure 2 As shown, this step identifies hydrological drought events based on the three-parameter run theory: drought identification threshold z1 (usually -0.5), mild drought discrimination threshold z0 (usually -1), and event interval merging threshold z2 (usually 0). When multiple consecutive periods in the SRI time series are lower than z1, it is identified as a complete drought event; if only one period has an SRI value lower than z0, and there are no other drought periods before or after it, it can also be regarded as an independent mild drought event; if there is a brief interruption between two drought processes, and its SRI value is lower than z2, it is regarded as a complete drought process and merged.

[0062] For each identified drought event, its duration D is defined as the total number of consecutive periods within that event that are below the drought criterion, calculated as follows:

[0063] (5)

[0064] in, and These represent the start and end times of the drought event, respectively.

[0065] The drought magnitude M represents the cumulative number of missing values ​​in the SRI that are below the drought identification threshold during the drought event, defined as follows:

[0066] (6)

[0067] The identification and index extraction process for meteorological drought events is the same as that for hydrological drought events, and the same run theory calculation steps are used for processing.

[0068] Step 3: Regional Response Relationship Modeling. Within each sub-region, a functional response relationship model is constructed based on the extracted meteorological drought amplitude and hydrological drought amplitude. The function form can be linear, power function, or polynomial, such as... Figure 3 As shown, the parameters of historical drought event samples are fitted using the least squares method. To improve the model's stability and generalization ability, cross-validation is used for model validation. A typical approach is to divide the samples into training and test sets to evaluate the model's goodness of fit.

[0069] The constructed function-response relationship model can include one of the following forms:

[0070] Linear functions: (7)

[0071] Power function: (8)

[0072] Quadratic polynomial function: (9)

[0073] The model parameters are fitted to historical drought samples using the least squares method, and cross-validation is employed to test generalization performance. The optimal ratio of training set to test set is 2:1. The goodness-of-fit evaluation metric includes the coefficient of determination R0. 2 Nash-Sutcliffe efficiency coefficient (NSE) and percentage deviation rate (PBIAS).

[0074] (10)

[0075] (11)

[0076] (12)

[0077] in, and They represent the first Actual and simulated M values ​​for a drought event; and Represents the mean of each sequence; n is the total number of drought events. Higher NSE and R... 2 A higher PBIAS value indicates better performance of the fitting function.

[0078] Step 4: Spatial Joint Drought Modeling and Estimation. A joint probability distribution model of hydrological drought intensity between two adjacent regions is established using the Copula function. If hydrological observation data is lacking in one region, the probability of hydrological drought in the missing region can be estimated using this joint model and drought information from the other region. Furthermore, the model structure changes under natural and disturbance periods are compared to assess the impact of human activities.

[0079] The Copula function is preferably one of the Frank, Gumbel-Hougaard, or Clayton functions from the Archimedes family, such as... Figure 4 As shown, the dependency parameters are determined by the maximum likelihood estimation method, and the optimal model is selected using the Akaike Information Criterion (AIC); its joint distribution function is:

[0080] (13)

[0081] in , These are the marginal distribution functions of hydrological drought characteristics (D or M) for Region 1 and Region 2, respectively.

[0082] Given the lack of hydrological drought data in region 2, the extent of hydrological drought in region 1 is known. When, through the Copula conditional probability density function Probability estimate of the extent of drought in Region 2:

[0083] (14)

[0084] like Figure 5 As shown, when the hydrological drought intensity of a region is known to be m, the hydrological drought probability distribution of another adjacent region can be estimated based on the constructed Copula conditional probability density function (Equation (14)). By comparing the estimation results under natural and disturbed periods, the impact of human activities on the spatial propagation path and intensity of drought can be quantified, thereby providing a basis for drought risk assessment and regulation strategy formulation.

[0085] In summary, this invention discloses a modeling method for identifying the response relationship between meteorological drought and hydrological drought in multiple regions. It aims to address the limitations of traditional methods in effectively identifying drought processes under conditions lacking monitoring stations or spanning multiple regions, and in failing to consider the impact of human activities. This method constructs a standardized precipitation index (SPI) and a standardized runoff index (SRI), combined with three-parameter run theory, to extract the duration and amplitude characteristics of drought events, thereby establishing a fundamental functional response relationship between meteorological drought and hydrological drought within the region. Subsequently, a joint hydrological drought probability model between adjacent regions is established using a Copula function. This allows for the estimation of the probability of spatially synchronized drought events using drought information from one region when hydrological data is lacking in the other. Furthermore, by comparing the natural period and the disturbance period, the interference effect of human activities on the propagation path and intensity of drought is identified. This invention possesses strong adaptability and versatility, and can be used for cross-regional hydrological drought estimation and drought risk early warning. It is particularly applicable to watersheds with severe data gaps or significant human intervention, providing a scientific basis and technical support for regional hydrological drought management and drought risk control.

[0086] The above description is merely an embodiment of the present invention and is not intended to limit the scope of protection of the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A modeling method for identifying the relationship between meteorological drought and hydrological drought response in multiple regions, characterized in that, Includes the following steps: Step 1: Construction and time series acquisition of drought indicators. The standardized precipitation index (SPI) and the standardized runoff index (SRI) are used to characterize meteorological drought and hydrological drought in each region, respectively. By standardizing the long-term precipitation and runoff series on the target time scale, a comparable drought indicator series is obtained. Step 2, drought event identification and feature extraction: The SPI and SRI sequences are processed using run theory to identify the start and end positions of drought events and extract the duration D and amplitude M of each drought. Step 3: Response relationship modeling within the region. Within each sub-region, based on the extracted meteorological drought amplitude and hydrological drought amplitude, a function response relationship model is constructed. The function can be linear, power function, or polynomial. The parameters of historical drought event samples are fitted using the least squares method. Step 4: Spatial joint drought modeling and estimation. A joint probability distribution model of the hydrological drought amplitude between two adjacent regions is established using the Copula function. If hydrological observation data is lacking in one region, the probability of hydrological drought in the missing region is estimated by using the joint probability distribution model and drought information from the other side. Furthermore, the model structure changes under natural and disturbance periods are compared to assess the impact of human activities. Its dependency parameters are determined by the maximum likelihood estimation method, and the optimal model is selected using the Akaike Information Criterion (AIC). Its joint distribution function is: ， in , These are the marginal distribution functions of the hydrological drought characteristics of Region 1 and Region 2, respectively. Given the lack of hydrological drought data in region 2, the extent of hydrological drought in region 1 is known. When, through the Copula conditional probability density function Probability estimate of the extent of drought in Region 2: ， When the hydrological drought intensity of a region is known to be m, the hydrological drought probability distribution of another adjacent region can be inferred based on the constructed Copula conditional probability density function.

2. The modeling method for identifying the relationship between multi-regional meteorological drought and hydrological drought response as described in claim 1, characterized in that, The standardization of long-term precipitation and runoff sequences in step 1 includes the following sub-steps: The original monthly precipitation or runoff series are cumulatively processed according to the set target time scale to obtain the cumulative series; Based on the statistical characteristics of different variables, probability distribution functions were selected to fit the cumulative precipitation series and runoff series respectively: precipitation data were fitted using the Gamma distribution, and runoff data were fitted using the Pearson Type-III distribution. The cumulative probability value is calculated based on the selected distribution, and then mapped to the standard normal distribution value through equal probability transformation to obtain the standardized precipitation index SPI and the standardized runoff index SRI.

3. The modeling method for identifying the relationship between meteorological drought and hydrological drought response in multiple regions according to claim 1, characterized in that, In step 2, when using run theory to identify drought events, if the interval between two drought segments does not exceed the set critical discontinuity time t... c If the drought index value does not exceed the set threshold during the intermittent period, then these events are merged into a single continuous drought event; the drought magnitude M is defined as the cumulative water shortage degree when the drought index is below the threshold during the drought period, i.e.: ， In the formula, D represents the duration of the drought. It is the first Monthly SPI or SRI value, This is the drought threshold, set to -0.

5.

4. The modeling method for identifying the relationship between meteorological drought and hydrological drought response in multiple regions according to claim 1, characterized in that, The function response relationship model constructed in step 3 includes one of the following forms: Linear functions: ; Power function: ; Quadratic polynomial function: , In the formula, The extent of hydrological drought, The extent of meteorological drought, , , The coefficients are used to represent the model parameters. The model parameters are fitted to historical drought samples using the least squares method, and cross-validation is employed to test generalization performance. The training set to test set ratio is 2:

1. The goodness-of-fit evaluation metrics include the coefficient of determination. Efficiency coefficient NSE and percentage deviation rate PBIAS.

5. The modeling method for identifying the relationship between multi-regional meteorological drought and hydrological drought response as described in claim 1, characterized in that, In step 4, the Copula function is one of the Frank, Gumbel-Hougaard, or Clayton functions in the Archimedes family. The dependency parameters are determined by the maximum likelihood estimation method, and the optimal model is selected by the Akaike Information Criterion (AIC).

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