A Hydrological Drought Prediction Method Considering the Influence of Human Activities

Abstract

The present invention discloses a method for predicting hydrological drought considering the influence of human activities. First, the non-consistency test is performed on the cumulative runoff sequence, then the human activity index HI is constructed and calculated. The probability distribution function of the runoff sequence is fitted by the GAMLSS model, and then the non-consistent hydrological drought index NSRI sequence is calculated. The NSRI sequence is applied to the conditional probability model to derive the probability of converting the current NSRI value to the NSRI drought levels in different future prediction periods. This application can be applied to the prediction of hydrological drought under environmental changes, and can analyze the influence of human activities on hydrological drought, and can further improve the calculation accuracy and credibility of the drought conversion probability.

Description

Technical Field

[0001] The present invention relates to the field of drought prediction, and particularly to a method for predicting hydrological drought considering the influence of human activities. Background Art

[0002] As one of the major natural disasters, drought poses a serious threat to the ecological environment and social economy. Hydrological drought most intuitively reflects the drought situation of a basin. In order to reduce the impact of drought on human life, the prediction of drought is particularly important. Usually, the occurrence of hydrological drought can be predicted based on a hydrological detection or forecasting system. However, with the increasing impact of human activities, the hydrological sequence of a basin may exhibit non-uniform characteristics, resulting in the inapplicability of traditional drought prediction methods.

[0003] In recent years, many scholars have predicted drought by constructing mathematical statistics models, such as support vector machines, Markov chains, time series prediction models of grey system theory, etc. Although these research methods are simple and easy to implement, they rarely consider the impact of environmental changes and are no longer applicable under the background of changing environments. The prediction method of hydrological drought needs to be further improved to be applicable to changing environments. Summary of the Invention

[0004] Object of the Invention: The object of the present invention is to provide a method for predicting hydrological drought considering the influence of human activities, which can be applicable to the prediction of hydrological drought under environmental changes, analyze the influence of human activities on hydrological drought, and further improve the calculation accuracy and reliability of the drought conversion probability.

[0005] Technical Solution: A method for predicting hydrological drought considering the influence of human activities according to the present invention specifically includes the following steps:

[0006] S1: Use the Mann-Kendall test method and the moving t-test method to conduct a non-uniformity test on the cumulative runoff sequence x=(x1, x2,... x3) of the basin;

[0007] S2: Use the double cumulative curve of precipitation-runoff to identify the influence of human activities on the hydrological drought of the basin, thereby constructing a human activity index HI, and constructing and calculating the human activity index HI by the method of restoration and recurrence;

[0008] S3: Use the GAMLSS model to fit the distribution of the cumulative runoff sequence, and then calculate the non-uniform hydrological drought index NSRI sequence Z(x i ) with the human activity factor as the explanatory variable;

[0009] S4: Use the Kolmogorov-Smirnov test method to conduct a normality test on the NSRI sequence Z(x i );

[0010] S5: Construct a conditional probability model. Based on the NSRI sequence Z(x i ), calculate the probability that the NSRI value under the background of environmental change is converted into the NSRI level in the prediction period;

[0011] S6: Calculate the drought conversion probability without considering environmental change: Based on the runoff sequence of the basin, calculate the standardized hydrological drought index SRI sequence, and then calculate the probability that the SRI value is converted into the SRI level in the prediction period without considering environmental change;

[0012] S7: Conduct a comparative analysis on the probability that the NSRI value under the background of environmental change is converted into the NSRI level in the prediction period and the probability that the SRI value is converted into the SRI level in the prediction period without considering environmental change, so as to obtain the impact of environmental change on the drought conversion probability.

[0013] Preferably, in S1, non - consistency test is carried out. The moving t - test method is used for non - consistency test to obtain the mutation point x of the cumulative runoff sequence x=(x1, x2, …x3 t , and the specific formula is as follows:

[0014]

[0015] where n1 and n2 are the sample sizes before and after respectively, and are the variances of the samples before and after the mutation point x t . Given the significance level α, among all possible points satisfying t≥|t α |, the point that makes the t - statistic reach the maximum value is the most likely mutation point. Combining with the Mann - Kendall test method, the trend change of the sample sequence can be obtained.

[0016] Preferably, in S2, the double - cumulative curve of precipitation - runoff is used to identify the impact of human activities on the hydrological drought of the basin, so as to construct a human activity factor. The human index HI is constructed and calculated by the method of restoration and reappearance, specifically: taking the cumulative precipitation and cumulative runoff in the same period as the horizontal and vertical axes of the coordinate system respectively. If the curve mutates, it means that the sequence is affected by other factors such as human activities. The slopes of the curve before and after the mutation point will change significantly. Determine the mutation time point according to the position of the change in the curve slope, and the degree of deviation reflects the intensity of the impact of human activities. Approximately consider the period before the curve mutation point as the reference period, and the period after the mutation point as the human activity period:

[0017] ∑x = k∑y + b

[0018] where x is the runoff sequence, y is the rainfall sequence, k is the correlation coefficient of the regression equation, and b is the intercept of the regression equation;

[0019] Subsequently, through the method of restoration and reproduction, the theoretical SRI′ (the linear regression relationship established based on the cumulative precipitation and cumulative runoff before the mutation point, and the theoretical runoff sequence during the human activity period can be calculated from the measured precipitation sequence) is used to represent the standardized runoff index value without human activity interference. Then, the actual SRI value represents the standardized runoff index value under human activity interference. The difference between the theoretical SRI′ and the actual SRI is used as the human activity factor to quantify the impact of human activities on hydrological drought. The formula is as follows:

[0020] HI = SRI′ - SRI

[0021] If HI > 0, it indicates that human activities have aggravated hydrological drought; if HI < 0, the impact is opposite; if HI = 0, it means there is no impact.

[0022] Preferably, the theoretical SRI′ can be calculated from the measured precipitation sequence based on the linear regression relationship established between the cumulative precipitation and cumulative runoff before the mutation point.

[0023] Preferably, in S3, the non - consistent hydrological drought index NSRI is calculated as follows:

[0024] When the runoff sequence x satisfies the Gamma distribution at a certain time scale, the cumulative probability of the runoff sequence x at this time scale is:

[0025]

[0026] Assume that the scale parameter α of the Gamma distribution t and the location parameter β t are linear functions for calculating the human activity index HI. When constructing a time - varying moment model based on the GAMLSS framework, the probability density function G x (x|α t ,β t ) can be fitted:

[0027] g1(α t ) = α 10 +α 11 *HI

[0028] g2(β t ) = α 20 +α 21 *HI

[0029] Where g1(α t ) is the link function, which is determined by the domain of the scale parameter α t , that is, if the domain of the scale parameter α t is α t∈R, then the link function is g1(α t ) = α t ; if α t > 0, g1(α t ) = lnα t ; α i,j (i = 1, 2 j = 0, 1) are parameter coefficients. Similarly, g2(β t ) is the link function, determined by the domain of the location parameter β t , that is, if the domain of the location parameter β t is β t ∈R, then the link function is g2(β t ) = β t ; if β t > 0, g2(β t ) = lnβ t ; β i,j (i = 1, 2 j = 0, 1) are parameter coefficients;

[0030] Use the RS algorithm to estimate the parameter coefficients and model residuals, analyze whether the model residuals approximately follow a normal distribution, and screen the optimal fitting distribution through the AIC criterion:

[0031]

[0032] AIC = ln(MSE)+2m

[0033] where n is the number of samples, Pe i is the empirical frequency of the samples, P i is the theoretical frequency of the samples, m is the number of model parameters, and the smaller the AIC value, the better the function fitting. Then the NSRI can be calculated:

[0034] When 0 < F t (x) ≤ 0.5:

[0035]

[0036] When 0.5 < F t (x) ≤ 1:

[0037]

[0038] where c0 = 2.515517; c1 = 0.802853; c2 = 0.010328; d1 = 1.4132788; d2 = 0.189269; d3 = 0.001308; k represents the time scale of the drought index.

[0039] Preferably, in step S4, the Kolmogorov-Smirnov test method is used to perform a normality test on the NSRI sequence. The definition of the test statistic D of the Kolmogorov-Smirnov test method is as follows:

[0040] D n = max|N(x i ) - Z n (x i )|

[0041] where n is the number of samples, the empirical distribution curve function of the samples is Z n (x i ), N(x i ) represents the normal distribution curve function. If the critical value D a of the test statistic corresponding to the significance level a is greater than the test statistic D n , then the sample data satisfies the normal distribution; otherwise, the sample data does not satisfy the normal distribution.

[0042] Preferably, in step S5, when the NSRI sequence Z(x i ) follows the normal distribution, then:

[0043] E(Z v,λ+M |Z v,λ ) = ρz0

[0044] Var(Z v,λ+M |Z v,λ ) = 1 - ρ0

[0045] where Z v,λ represents the NSRI value of the current λ month, Z v,λ+M represents the NSRI value of the λ + M month. Here, E represents the expected value under the conditional distribution, Var is the conditional variance, and ρ is the correlation coefficient of the NSRI of the current month λ and the λ + M month. Thus, the probability of the NSRI drought level transmitted to the future under the current NSRI can be deduced as follows:

[0046]

[0047] where σ Z represents the variance of the NSRI sequence Z(x i ).

[0048] Preferably, in step S6, when calculating the drought conversion probability without considering climate change, it is also necessary to perform a normality test on the SRI sequence and then construct a conditional probability model for calculation.

[0049] Beneficial effects: In this application, a Nonstationary Standard Runoff Index (NSRI) with human activity factors as explanatory variables is constructed. Based on the conditional probability model, the probability of converting different NSRI values in the current period to different NSRI drought levels in the prediction period can be calculated. This application can be applied to hydrological drought prediction under environmental changes and can analyze the impact of human activities on hydrological drought, further improving the calculation accuracy and credibility of drought conversion probability. Brief Description of the Drawings

[0050] Figure 1 It is a flow chart of this application. Detailed Implementation Modes

[0051] The following further elaborates on this application in combination with specific embodiments.

[0052] As Figure 1 shown, it is a flow chart of this application, which specifically includes the following steps in this embodiment:

[0053] S1: Use the Mann-Kendall test method and the moving t-test method to conduct a nonstationarity test on the cumulative runoff sequence x = (x1, x2,... x3) of the basin. First, use the moving t-test method to conduct a nonstationarity test to obtain the mutation point x t of the cumulative runoff sequence x = (x1, x2,... x3). The specific formula is as follows:

[0054]

[0055] where n1 and n2 are the sample sizes before and after respectively, and are the variances of the samples before and after the mutation point x t . Given the significance level α, among all possible points satisfying t ≥ |t α |, the point that maximizes the t-statistic is the most likely mutation point. Combining with the Mann-Kendall test method, the trend change of the sample sequence can be obtained;

[0056] S2: Use the double mass curve of precipitation-runoff to identify the impact of human activities on hydrological drought in the basin, thereby constructing a human activity index HI. The human activity index HI is constructed and calculated by the method of restoration and reproduction. Specifically:

[0057] Taking the cumulative precipitation and cumulative runoff during the same period as the horizontal and vertical axes of the coordinate system respectively, a sudden change in the curve indicates that the sequence is affected by other factors such as human activities. The slope of the curve will change significantly before and after the mutation point. The time point of the mutation is determined according to the position of the change in the curve slope, and the degree of deviation reflects the intensity of the impact of human activities. The period before the curve mutation point is approximately regarded as the reference period, and the period after the mutation point is the human activity period:

[0058] ∑x = k∑y + b

[0059] where x is the runoff sequence, y is the rainfall sequence, k is the correlation coefficient of the regression equation, and b is the intercept of the regression equation;

[0060] Subsequently, through the method of restoration and reproduction, the theoretical SRI′ is used to represent the standardized runoff index value without human activity interference, while the actual SRI value represents the standardized runoff index value under human activity interference. The difference between the theoretical SRI′ and the actual SRI is used as the human activity factor to quantify the impact of human activities on hydrological drought. The formula is as follows:

[0061] HI = SRI′ - SRI

[0062] where the theoretical SRI′ can be calculated from the measured precipitation sequence based on the linear regression relationship established between the cumulative precipitation and cumulative runoff before the mutation point;

[0063] If HI > 0, it indicates that human activities have exacerbated hydrological drought; if HI < 0, the impact is opposite; if HI = 0, it means there is no impact.

[0064] S3: Use the GAMLSS model to fit the distribution of the cumulative runoff sequence, and then calculate the non - consistent hydrological drought index NSRI sequence Z(x i ) with the human activity factor as the explanatory variable. Specifically:

[0065] When the runoff sequence x satisfies the Gamma distribution at a certain time scale, the cumulative probability of the runoff sequence x at this time scale is:

[0066]

[0067] Assume that the scale parameter α t and the location parameter β t of the Gamma distribution are linear functions of the calculated human activity index HI. Based on the GAMLSS framework, a time - varying moment model can be constructed to fit the distribution of the two - parameter probability density function G x (x|α t ,β t ):

[0068] g1(αt ) = α 10 +α 11 *HI

[0069] g2(β t ) = α 20 +α 21 *HI

[0070] where g1(α t ) is a link function, determined by the domain of the scale parameter α t , that is, if the domain of the scale parameter α t is α t ∈ R, then the link function is g1(α t ) = α t ; if α t > 0, g1(α t ) = lnα t ; α i,j (i = 1, 2 j = 0, 1) are parameter coefficients. Similarly, g2(β t ) is a link function, determined by the domain of the location parameter β t , that is, if the domain of the location parameter β t is β t ∈ R, then the link function is g2(β t ) = β t ; if β t > 0, g2(β t ) = lnβ t ; β i,j (i = 1, 2 j = 0, 1) are parameter coefficients;

[0071] Estimate the parameter coefficients and model residuals using the RS algorithm, analyze whether the model residuals approximately follow a normal distribution, and screen the optimal fitting distribution through the AIC criterion:

[0072]

[0073] AIC = ln(MSE) + 2m

[0074] where n is the number of samples, Pe i is the empirical frequency of the samples, P i is the theoretical frequency of the samples, m is the number of model parameters, and the smaller the AIC value, the better the function fitting. Then the NSRI can be calculated:

[0075] When 0 < F t (x) ≤ 0.5:

[0076]

[0077] When 0.5 < F tWhen (x) ≤ 1:

[0078]

[0079] where c0 = 2.515517; c1 = 0.802853; c2 = 0.010328; d1 = 1.4132788; d2 = 0.189269; d3 = 0.001308; k represents the time scale of the drought index.

[0080] S4: Use the Kolmogorov - Smirnov test method to conduct a normality test on the NSRI sequence Z(x i ). The definition of the test statistic D of the Kolmogorov - Smirnov test method is given as follows:

[0081] D n = max|N(x i ) - Z n (x i )|

[0082] where n is the number of samples, the empirical distribution curve function of the samples is Z n (x i ), N(x i ) represents the normal distribution curve function. If the critical value D a of the test statistic corresponding to the significance level a is greater than the test statistic D n , then the sample data satisfies the normal distribution; otherwise, the sample data does not satisfy the normal distribution.

[0083] S5: Construct a conditional probability model. Based on the NSRI sequence Z(x i ), calculate the probability that the NSRI value under the background of environmental change is converted into the NSRI level in the prediction period. When the NSRI sequence Z(x i ) follows a normal distribution, then there is:

[0084] E(Z v,λ+M |Z v,λ ) = ρz0

[0085] Var(Z v,λ+M |Z v,λ ) = 1 - ρ0

[0086] where Z v,λ represents the NSRI value of the current λ - th month, Z v,λ+M represents the NSRI value of the (λ + M) - th month. Here, E represents the expected value under the conditional distribution, Var is the conditional variance, and ρ is the correlation coefficient of the NSRI of the current month λ and the (λ + M) - th month. Thus, the probability that the NSRI drought level is transmitted to the future under the current NSRI condition can be deduced as follows:

[0087]

[0088] where σ Z represents the variance of the NSRI sequence Z(x i ).;

[0089] S6: Calculate the drought conversion probability without considering environmental changes: Based on the runoff sequence of the basin, calculate the standardized hydrological drought index SRI sequence. After performing a normality test on the standardized hydrological drought index SRI sequence, calculate the probability of converting the SRI value without considering environmental changes to the SRI level in the prediction period;

[0090] S7: Conduct a comparative analysis of the probability of converting the NSRI value under the background of environmental changes to the NSRI level in the prediction period and the probability of converting the SRI value without considering environmental changes to the SRI level in the prediction period to obtain the impact of environmental changes on the drought conversion probability.

[0091] Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

Claims

1. A method for predicting hydrological drought considering the impact of human activities, characterized in that: Specifically, it includes the following steps: S1: Use the Mann-Kendall test method and the moving t-test method to conduct a non-consistency test on the cumulative runoff sequence x = (x1, x2, … x3) of the basin; S2: Use the double mass curve of precipitation-runoff to identify the impact of human activities on hydrological drought in the basin, thereby constructing a human activity index HI, and construct and calculate the human activity index HI by the method of restoration and reproduction; S3: Use the GAMLSS model to fit the distribution of the cumulative runoff series, and then calculate the non-stationary hydrological drought index NSRI series Z(x i ) with the human activity factor as the explanatory variable; S4: Use the Kolmogorov-Smirnov test method to perform a normality test on the NSRI sequence Z(x i ); S5: Construct a conditional probability model. Based on the NSRI sequence Z(x i ), calculate the probability that the NSRI value under the background of environmental change is converted into the NSRI level in the prediction period; S6: Calculate the drought conversion probability without considering environmental changes: Based on the runoff sequence of the basin, calculate the standardized hydrological drought index SRI sequence, and then calculate the probability that the SRI value without considering environmental changes is converted into the SRI level in the prediction period; S7: Conduct a comparative analysis on the probability that the NSRI value under the background of environmental changes is converted into the NSRI level in the prediction period and the probability that the SRI value without considering environmental changes is converted into the SRI level in the prediction period to obtain the impact of environmental changes on the drought conversion probability.

2. The method for predicting hydrological drought considering the influence of human activities according to claim 1, characterized in that: In S1, non - consistency test is carried out. The sliding t - test method is used to conduct the non - consistency test to obtain the mutation point \(x\) of the cumulative runoff sequence \(x=(x_1,x_2,\cdots,x_n)\). t , and the specific formula is as follows: where n1 and n2 are the sample sizes before and after respectively, and are the variances of the samples before and after the mutation point x t respectively. Given the significance level α, among all possible points satisfying t≥|t α |, the point that maximizes the t-statistic is the most likely mutation point. Combining with the Mann-Kendall test method, the trend change of the sample sequence can be obtained.

3. The method for predicting hydrological drought considering the influence of human activities according to claim 1, characterized in that: In S2, the double mass curve of precipitation-runoff is used to identify the impact of human activities on hydrological drought in the basin, thereby constructing a human activity factor, and construct and calculate the human index HI by the method of restoration and reproduction. Specifically: Take the cumulative precipitation and cumulative runoff in the same period as the horizontal and vertical axes of the coordinate system respectively. If the curve has a sudden change, it means that the sequence is affected by other factors including human activities, and the slope of the curve before and after the mutation point will change significantly. Determine the mutation time point according to the position of the change in the curve slope, and the degree of deviation reflects the intensity of the impact of human activities. Take the period before the curve mutation point as the reference period and the period after the mutation point as the human activity period: ∑x = k∑y + b Where x is the runoff sequence, y is the rainfall sequence, k is the correlation coefficient of the regression equation, and b is the intercept of the regression equation; Subsequently, by the method of restoration and reproduction, use the theoretical SRI' to represent the standardized runoff index value without human activity interference, then the actual SRI value represents the standardized runoff index value under human activity interference, and use the difference between the theoretical SRI' and the actual SRI as the human activity factor to quantify the impact of human activities on hydrological drought. The formula is as follows: HI = SRI' - SRI If HI > 0, it means that human activities have aggravated hydrological drought; if HI < 0, the impact is opposite; if HI = 0, it means there is no impact.

4. A method for predicting hydrological drought considering the impact of human activities according to claim 3, characterized in that: The theoretical SRI' can be calculated from the measured precipitation sequence based on the linear regression relationship established between the cumulative precipitation and cumulative runoff before the mutation point.

5. A method for predicting hydrological drought considering the influence of human activities according to claim 1, characterized in that: In S3, calculate the non-consistent hydrological drought index NSRI, specifically: When the runoff sequence x satisfies the Gamma distribution at a certain time scale, the cumulative probability of the runoff sequence x at this time scale is: Suppose the scale parameter α of the Gamma distribution t and the location parameter β t are linear functions for calculating the human activity index HI. When constructing a time-varying moment model based on the GAMLSS framework, the probability density function G x (x|α t ,β t ) of the two parameters can be fitted: g1(α t ) = α 10 + α 11 * HI g2(β t ) = α 20 + α 21 * HI where \(g_1(\alpha\) t ) is a link function determined by the domain of the scale parameter \(\alpha\) t , that is, if the domain of the scale parameter \(\alpha\) t is \(\alpha\) t \(\in R\), then the link function is \(g_1(\alpha\) t ) = \(\alpha\) t ; if \(\alpha\) t > 0, \(g_1(\alpha\) t ) = \(\ln\alpha\) t ; \(\alpha\) i,j (\(i = 1, 2\); \(j = 0, 1\)) are parameter coefficients. Similarly, \(g_2(\beta\) t ) is a link function determined by the domain of the location parameter \(\beta\) t , that is, if the domain of the location parameter \(\beta\) t is \(\beta\) t \(\in R\), then the link function is \(g_2(\beta\) t ) = \(\beta\) t ; if \(\beta\) t > 0, \(g_2(\beta\) t ) = \(\ln\beta\) t ; \(\beta\) i,j (\(i = 1, 2\); \(j = 0, 1\)) are parameter coefficients; Use the RS algorithm to estimate the parameter coefficients and model residuals, analyze whether the model residuals approximately follow a normal distribution, and screen the optimal fitting distribution through the AIC criterion: AIC = ln(MSE) + 2m where n is the number of samples, and Pe i is the empirical frequency of the samples, P i is the theoretical frequency of the samples, m is the number of model parameters, the smaller the AIC value, the better the function fitting, and then the NSRI can be calculated as follows: When 0 < F t (x) ≤ 0.5: When 0.5 < F t (x) ≤ 1: where c0 = 2.515517; c1 = 0.802853; c2 = 0.010328; d1 = 1.4132788; d2 = 0.189269; d3 = 0.001308; k represents the time scale of the drought index.

6. A method for predicting hydrological drought considering the influence of human activities according to claim 1, characterized in that: In S4, the Kolmogorov-Smirnov test method is used to perform a normality test on the NSRI sequence. The definition of the test statistic D of the Kolmogorov-Smirnov test method is given as follows: D n = max|N(x i ) - Z n (x i )| where n is the number of samples, and the empirical distribution curve function of the samples is Z n (x i ), N(x i ) represents the normal distribution curve function. If the critical value D a of the test statistic corresponding to the significance level a is greater than the test statistic D n , then the sample data satisfies the normal distribution; otherwise, the sample data does not satisfy the normal distribution.

7. A method for predicting hydrological drought considering the influence of human activities according to claim 1, characterized in that: In the above S5, when the NSRI sequence Z(x i ) follows a normal distribution, there is: E(Z v,λ+M |Z v,λ ) = ρz0 Var(Z v,λ+M |Z v,λ ) = 1 - ρ0 Among which Z v,λ represents the NSRI value of the current λ month, and Z v,λ+M represents the NSRI value of the λ + M month. Here, E represents the expected value under the conditional distribution, Var is the conditional variance, and ρ is the correlation coefficient between the NSRIs of the current month λ and the λ + M month. Thus, the probability of the NSRI drought level transmitted to the future under the current NSRI can be deduced as follows: where σ Z represents the variance of the NSRI sequence Z(x i ).

8. A method for predicting hydrological drought considering the influence of human activities according to claim 1, characterized in that: When calculating the drought transition probability without considering climate change in S6, it is also necessary to perform a normality test on the SRI sequence and then construct a conditional probability model for calculation.

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