A Hydrological Drought Prediction Method under Changing Environments

Abstract

The present invention discloses a method for predicting hydrological drought under changing environments. First, non - consistency test and normality test are carried out on the cumulative rainfall sequence and the cumulative runoff sequence. Secondly, rainfall data and runoff data are normalized normally to obtain the meteorological drought index SPI value and the hydrological drought index SRI value. Then, a conditional probability model without considering environmental changes is constructed. Based on the SPI sequence and the SRI sequence, the probability of converting the SPI value without considering environmental changes into the SRI level is calculated. Finally, climate factors and human activity factors are selected and constructed, and a conditional probability model with climate factors and human activity factors as explanatory variables is constructed. Based on the SPI sequence and the SRI sequence, the probability of converting the SPI value under environmental changes into the SRI level is calculated. The present invention comprehensively considers the impacts of climate change and human activities on the conversion probability of hydrological drought, and can be adapted to the prediction of hydrological drought under changing environments.

Description

Technical Field

[0001] The present invention belongs to the field of hydrological drought, and particularly relates to a method for predicting hydrological drought under changing environments. Background Art

[0002] The occurrence of drought will have a serious impact on social economy and ecological environment. Generally, when meteorological drought develops to a certain extent, it can evolve into hydrological drought. Hydrological drought lags behind meteorological drought. We can predict the occurrence of hydrological drought based on the meteorological drought detection or forecasting system, and utilize its lag effect to take countermeasures, so as to reduce the impact of drought on social economy. However, under the influence of climate change and human activities, the environment of the basin is changing, and the hydrological sequence may be inconsistent, which may also affect the transmission process from meteorological drought to hydrological drought.

[0003] In recent years, some scholars have predicted hydrological drought by evaluating the grade conversion probability in the transmission process from meteorological drought to hydrological drought. However, such methods calculate the conversion probability between drought grades, with low accuracy. In addition, under the condition of environmental change, the traditional probability prediction method will no longer be applicable. The drought prediction method needs to be further improved to be applicable to hydrological prediction under changing environments. Summary of the Invention

[0004] Object of the Invention: The present invention provides a method for predicting hydrological drought under changing environments, which comprehensively considers the influence of climate change and human activities on the conversion probability of hydrological drought, and can be adapted to the prediction of hydrological drought under changing environments.

[0005] Technical Solution: The present invention proposes a method for predicting hydrological drought under changing environments, including the following steps:

[0006] (1) From the rainfall data and runoff data of the basin, calculate the cumulative precipitation sequence and runoff sequence at different time scales, and conduct non-consistency tests on the cumulative rainfall sequence and cumulative runoff sequence;

[0007] (2) Use the normal test method to conduct normality tests on the cumulative rainfall sequence and cumulative runoff sequence;

[0008] (3) Normalize and standardize the rainfall data and runoff data to obtain the meteorological drought index SPI value and the hydrological drought index SRI value;

[0009] (4) Construct a conditional probability model without considering environmental changes. Based on the SPI sequence and SRI sequence, calculate the probability that the SPI value without considering environmental changes is converted into the SRI grade;

[0010] (5) Select and construct climate factors and human activity factors;

[0011] (6) Construct a conditional probability model with climate factors and human activity factors as explanatory variables. Based on the SPI sequence and SRI sequence, calculate the probability of converting the SPI value to the SRI level under environmental changes.

[0012] Further, the step (1) includes the following steps:

[0013] (11) Use the Pettitt test method to identify whether there is a mutation point in the sample sequence, and use the Mann-Kendall test method to judge the trend of the sequence. Assume that the sample runoff sequence is x = (x 1 , x 2 , … x n ), then the formula is as follows:

[0014]

[0015]

[0016] Among them, U t,n is the test statistic, representing the cumulative number of times the value at the t-th moment is greater than or less than the value at the i-th moment. When t 0 satisfies the moment:

[0017] K t0,n = max|U t,n |(t = 1, 2, …, n) (3)

[0018] Then it is considered that there is a mutation point at t 0 . Combining with the Mann-Kendall test method, the trend characteristics of the sample sequence are obtained;

[0019] (12) The double cumulative curve method can test the non-consistency of the bivariate correlation relationship between the cumulative rainfall sequence and the cumulative runoff sequence. Plotting the cumulative values in a rectangular coordinate system respectively can obtain the double cumulative curve graph, and the change point of the rainfall-runoff relationship can be observed. The formula is as follows:

[0020] ∑x = k∑y + b (4)

[0021] Among them, x is the runoff sequence; y is the rainfall sequence, k is the correlation coefficient of the regression equation; b is the intercept of the regression equation.

[0022] Further, the implementation process of the step (2) is as follows:

[0023] Give the definition of the KS test statistic D as follows:

[0024] D n = max|N(X i ) - F n (X i )| (5)

[0025] where n is the number of samples, F n (X i ) is the empirical distribution curve function of the sample, and N(X i ) is the normal distribution curve function; if the critical value D α of the test statistic corresponding to the significance level α 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.

[0026] Furthermore, the implementation process of step (4) is as follows:

[0027] When a set of runoff data X follows the normal distribution and satisfies X ~ N(μ 1 , Σ 1 ), and another set of rainfall data Y also follows the normal distribution, that is, Y ~ N(μ 2 , Σ 2 ), then for the overall sequence B ~ N P (μ, Σ), p ≥ 2, it can be written in the following form:

[0028]

[0029] When the sequence Y follows the normal distribution, the distribution of the sequence X under the condition of Y is still the normal distribution, that is:

[0030] (X|Y) ~ N(μ 3 , Σ 3 ) (12)

[0031] μ 3 represents the expected value under the conditional distribution, and Σ 3 is the conditional covariance matrix:

[0032]

[0033]

[0034] If the SPI value of meteorological drought before

[0035]

[0036] and the future hydrological drought SRI drought level transmitted by meteorological drought satisfy a bivariate normal distribution, then the probability of the future SRI drought level transmitted under the current SPI condition is expressed as follows: v,λ where Z v,λ+M represents the SPI value of the current λ month, W Ms represents the SRI value of the λ + M month, C Mi , C MThe upper and lower limits, and the correlation coefficient between the current SPI value and the future SRI value is ρ; the current SPI and the future SRI are expressed by the standard normal cumulative distribution function Φ as follows:

[0037]

[0038] Among them, the calculation of the correlation coefficient ρ is as follows:

[0039]

[0040] Among them, k represents the time scale of the drought index, and both the cumulative rainfall Y and the runoff X satisfy the normal distribution. Then, after the standardization process, the SPI value corresponding to the cumulative rainfall Y and the SRI value W corresponding to the runoff X v,λ+M both follow the standard normal distribution, that is:

[0041]

[0042] represents the covariance between the current SPI and the SRI M months after the lag period, and its calculation is as follows:

[0043]

[0044] Furthermore, the implementation process of the step (5) is as follows:

[0045] Use Pearson correlation test to screen out the climate factor z i with the highest correlation with the runoff sequence x i as the covariate, and analyze the teleconnection relationship between the large-scale atmospheric circulation index CI and the runoff sequence; use the Pearson correlation index ρ xz to characterize the correlation between the runoff sequence x i and the climate factor c 0 The formula is as follows:

[0046]

[0047] In order to quantify the impact of human activities on hydrological drought, the difference between the theoretical SRI′ and the actual SRI is used as the human activity factor, and the formula is as follows:

[0048] HI = SRI′ - SRI (21)

[0049] When HI > 0, it means that human activities have aggravated hydrological drought. When HI < 0, the impact is opposite. When HI = 0, it means there is no impact.

[0050] Furthermore, the conditional probability model with climate factors and human activity factors as explanatory variables in step (6) is:

[0051]

[0052]

[0053] (σ′ z ) 2 = 1 - Σ′ 12 (Σ′ 22 ) -1 Σ′ 21 (24)

[0054] Σ′ 12 = [cov(W ν,λ+M , Z ν,λ ) cov(W ν,λ+M , C ν,λ ) cov(W ν,λ+M , H ν,λ )] (25)

[0055]

[0056] Σ′ 21 = (Σ′ 12 ) T (27)

[0057] Substitute the current SPI value z 0 , the climate factor value c 0 , and the human activity factor value h 0 into the model, and the probability of converting the SPI values of different droughts under changing environments to different future prediction periods M and different SRI drought levels can be calculated. By comparing the conversion probabilities without considering environmental changes, the impact of environmental changes on drought transmission can be quantitatively analyzed.

[0058] Advantageous effects: Compared with the prior art, the advantageous effects of the present invention are as follows: The present invention comprehensively considers the impacts of climate change and human activities on the conversion probability of hydrological droughts and can be adapted to hydrological drought forecasting under changing environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a flowchart of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0060] The present invention will be further described in detail below with reference to the accompanying drawings.

[0061] The present invention provides a method for predicting hydrological drought under changing environments. First, the non-consistency test is performed on the multi-year cumulative rainfall data and cumulative runoff data. Then, the rainfall data and runoff data are normalized to obtain the SPI sequence and SRI sequence. Next, climate factors and human activity factors are selected and constructed as explanatory variables to build a conditional probability model with climate factors and human activity factors as explanatory variables. Based on the SPI sequence and SRI sequence, the probability of converting the SPI value to the SRI level under environmental changes is calculated. As Figure 1 shown, the specific steps are as follows:

[0062] Step 1: Calculate the cumulative precipitation sequence and runoff sequence at different time scales from the rainfall data and runoff data of the basin, and perform a non-consistency test on the cumulative rainfall sequence and cumulative runoff sequence.

[0063] The Pettitt test method can identify whether there are mutation points in the sample sequence, and the Mann-Kendall test method (MK) is used to judge the trend of the sequence. Assume that the sample runoff sequence is x = (x 1 , x 2 , … x n ), then the formula is as follows:

[0064]

[0065]

[0066] where U t,n is the test statistic, representing the cumulative number of times the value at the t-th moment is greater than or less than the value at the i-th moment. When the t 0 moment satisfies:

[0067] K t0,n = max|U t,n | (t = 1, 2, …, n) (3)

[0068] Then it is considered that there is a mutation point at t 0 . Combining with the Mann-Kendall test method, the trend characteristics of the sample sequence can be obtained.

[0069] The double cumulative curve method can test the non-consistency of the bivariate correlation relationship between the cumulative rainfall sequence and the cumulative runoff sequence. Plotting the cumulative values in a rectangular coordinate system respectively can obtain the double cumulative curve graph, and the change point of the rainfall-runoff relationship can be observed. The relevant formula is as follows:

[0070] ∑x = k∑y + b (4)

[0071] Here, x is the runoff sequence; y is the rainfall sequence, k is the correlation coefficient of the regression equation; b is the intercept of the regression equation.

[0072] Step 2: Use the normal test method (Kolmogorov-Smirnov, KS) to conduct a normality test on the cumulative rainfall sequence and the cumulative runoff sequence.

[0073] As a test method that can examine whether the distribution of a sequence conforms to the normal distribution, the KS test method is particularly applicable when the sample size is small. Here, the KS test is used to check whether the rainfall sequence and the runoff sequence satisfy the normal distribution, and the definition of the test statistic D of KS is given as follows:

[0074] D n = max|N(X i ) - F n (X i )| (5)

[0075] where n is the number of samples, F n (X i ) is the empirical distribution curve function of the sample, and N(X i ) is the normal distribution curve function. If the critical value D α of the test statistic corresponding to the significance level α (usually taken as 0.05) 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.

[0076] Step 3: Normalize the rainfall data and runoff data to obtain the meteorological drought index SPI value and the hydrological drought index SRI value; assume that both the cumulative rainfall Y and the runoff X satisfy the normal distribution. Then, after the standardization process, the SPI value corresponding to the cumulative rainfall Y and the SRI value corresponding to the runoff X both follow the standard normal distribution.

[0077] Assume that x is the runoff at a certain time scale, and it satisfies the Gamma distribution. The cumulative probability of the runoff x at this time scale is:

[0078]

[0079] In the formula, λ and β are the scale and shape parameters respectively, x > 0, λ > 0, β > 0. The maximum likelihood method is used to estimate the parameters, and the corresponding SRI is obtained by normalizing the cumulative frequency F(X) of each item:

[0080] When 0 < F(X) ≤ 0.5:

[0081]

[0082]

[0083] When 0.5 < F(X) ≤ 1:

[0084]

[0085]

[0086] In the formula, the values of the parameters c and d with respect to k are as follows: c 0 = 2.515517; c 1 = 0.802853; c 2 = 0.010328; d 1 = 1.4132788; d 2 = 0.189269; d 3 = 0.001308. By replacing the runoff data with precipitation data, the SPI can be calculated in the same way.

[0087] Step 4: Construct a conditional probability model without considering environmental changes. Based on the SPI sequence and the SRI sequence, calculate the probability of converting the SPI value without considering environmental changes into the SRI level.

[0088] When a set of runoff data X follows a normal distribution and satisfies X ~ N(μ 1 , Σ 1 ), and another set of rainfall data Y also follows a normal distribution, that is, Y ~ N(μ 2 , Σ 2 ), then for the overall sequence B ~ N P (μ, Σ), p ≥ 2, it can be written in the following form:

[0089]

[0090] When the sequence Y follows a normal distribution, the distribution of the sequence X under the condition of Y is still a normal distribution, that is:

[0091] (X|Y) ~ N(μ 3 , Σ 3 ) (12)

[0092] μ 3 represents the expected value under the conditional distribution, and Σ 3 is the conditional covariance matrix:

[0093]

[0094]

[0095] Assume that the current meteorological drought SPI value and the future hydrological drought SRI drought level transmitted by the meteorological drought satisfy a bivariate normal distribution. Then, from formula (1), the probability of the SRI drought level transmitted to the future under the condition of the current SPI can be deduced as follows:

[0096]

[0097] Among them, Z v,λ represents the SPI value of the current λ month, and W v,λ+M represents the SRI value of the (λ + M)th month, and C Ms , C Mi is the upper and lower limits of the drought level C M . The correlation coefficient between the current SPI value and the future SRI value is ρ. Further, the current SPI and the future SRI can be expressed by the standard normal cumulative distribution function Φ as follows:

[0098]

[0099] Among them, the calculation of the correlation coefficient ρ is as follows:

[0100]

[0101] Among them, k represents the time scale of the drought index. From formula (1), assuming that the cumulative rainfall Y and the runoff X both satisfy the normal distribution, then after the standardization process, the SPI value corresponding to the cumulative rainfall Y and the SRI value W corresponding to the runoff X v,λ+M both follow the standard normal distribution, that is:

[0102]

[0103] represents the covariance between the current SPI and the SRI M months after the lag period. Its calculation is as follows:

[0104]

[0105] Step 5: Select and construct climate factors and human activity factors.

[0106] Screen climate factors: Use Pearson correlation test to screen out the climate factor z i with the highest correlation with the runoff sequence x i as the covariate, and analyze the teleconnection relationship between the large-scale atmospheric circulation indices CI (such as sea surface temperature anomaly (Nino3.4SST), Pacific Decadal Oscillation index (PDO), North Atlantic Oscillation index (NAO), and Arctic Oscillation index (AO), etc.) and the runoff sequence. Use the Pearson correlation index ρ xz to characterize the correlation between the runoff sequence x i and the climate factor c 0 . Its formula is as follows:

[0107]

[0108] Construct the human activity factor HI (Human Index): Through the method of restoration and reproduction, use 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) 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. 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:

[0109] HI = SRI′ - SRI (21)

[0110] When HI > 0, it means that human activities have aggravated hydrological drought. When HI < 0, the impact is opposite. When HI = 0, it means there is no impact.

[0111] Step 6: Construct a conditional probability model with climate factors and human activity factors as explanatory variables. Based on the SPI sequence and SRI sequence, calculate the probability of converting the SPI value to the SRI level under environmental changes.

[0112] The conditional probability model with climate factors and human activity factors as explanatory variables is expressed as follows:

[0113]

[0114]

[0115] (σ′ z ) 2 = 1 - Σ′ 12 (Σ′ 22 ) -1 Σ′ 21 (24)

[0116] Σ′ 12 = [cov(W ν,λ+M , Z ν,λ ) cov(W ν,λ+M , C ν,λ ) cov(W ν,λ+M , H ν,λ )] (25)

[0117]

[0118] Σ′ 21 = (Σ′ 12 ) T (27)

[0119] Substitute the current SPI value z 0 , the climate factor value c 0 , and the human activity factor value h0 Substituting into the model, the probabilities of SPI values of different droughts under changing environments being converted to different future prediction periods M and different SRI drought levels can be calculated. By comparing the conversion probabilities without considering environmental changes, the impact of environmental changes on drought transmission can be quantitatively analyzed.

Claims

1. A method for predicting hydrological drought under changing environments, characterized in that, it includes the following steps: (1) From the rainfall data and runoff data of the basin, calculate the cumulative precipitation sequence and runoff sequence at different time scales, and conduct non - consistency tests on the cumulative rainfall sequence and cumulative runoff sequence; (2) Use the normal test method to conduct normality tests on the cumulative rainfall sequence and cumulative runoff sequence; (3) Normalize the rainfall data and runoff data to obtain the meteorological drought index SPI value and hydrological drought index SRI value; (4) Construct a conditional probability model without considering environmental changes. Based on the SPI sequence and SRI sequence, calculate the probability of converting the SPI value without considering environmental changes into the SRI level; (5) Select and construct climate factors and human activity factors; (6) Construct a conditional probability model with climate factors and human activity factors as explanatory variables. Based on the SPI sequence and SRI sequence, calculate the probability of converting the SPI value under environmental changes into the SRI level; The conditional probability model is: (σ′ z ) 2 = 1 - ∑′ 12 (∑′ 22 ) -1 ∑′ 21 (24) ∑′ 12 = [cov(W ν,λ+M , Z v,λ ) cov(W ν,λ+M , C ν,λ ) cov(W v,λ+M , H ν,λ )] (25) ∑′ 21 ＝(∑′ 12 ) T (27) Substitute the current SPI value z 0 , the climate factor value c 0 , and the human activity factor value h 0 into the model, and the probability of converting the SPI values of different droughts under changing environments to different future prediction periods M and different SRI drought levels can be calculated. By comparing the conversion probabilities without considering environmental changes, the impact of environmental changes on drought transmission can be quantitatively analyzed.

2. The method for predicting hydrological drought under changing environments according to claim 1, characterized in that, the step (1) includes the following steps: (11) The Pettitt test method is used to identify whether there are mutation points in the sample sequence, and the Mann-Kendall test method is used to judge the trend of the sequence. Assuming that the sample runoff sequence is x = (x 1 , x 2 , … x n ), the formula is as follows: Among them, U t,n is the test statistic, representing the cumulative number of times the value at the t-th moment is greater than or less than the value at the i-th moment. When t 0 moment satisfies: K t0,n = max|U t,n |(t = 1, 2, …, n)(3) Then it is considered that t 0 is the mutation point. Combining with the Mann-Kendall test method, the trend characteristics of the sample sequence are obtained; (12) The double - cumulative curve method can test the non - consistency of the bivariate correlation relationship between the cumulative rainfall sequence and the cumulative runoff sequence. Plotting the cumulative values in a rectangular coordinate system respectively can obtain the double - cumulative curve graph, and the change point of the rainfall - runoff relationship can be observed. The formula is as follows: ∑x = k∑y + b (4) where x is the runoff sequence; y is the rainfall sequence, k is the correlation coefficient of the regression equation; b is the intercept of the regression equation.

3. The method for predicting hydrological drought under changing environments according to claim 1, characterized in that, the implementation process of the step (2) is as follows: The definition of the KS test statistic D is given as follows: D n = max|N(X i ) - F n (X i )| (5) where n is the number of samples, F n (X i ) is the empirical distribution curve function of the samples, N(X i ) is the normal distribution curve function; if the critical value D α of the test statistic corresponding to the significance level α 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.

4. The method for predicting hydrological drought under changing environments according to claim 1, characterized in that, the implementation process of the step (4) is as follows: When a set of runoff data X follows a normal distribution and satisfies X ~ N(μ 1 , ∑ 1 ), and another set of rainfall data Y also follows a normal distribution, that is, Y ~ N(μ 2 , ∑ 2 ), then for the overall sequence B ~ N P (μ, ∑), p ≥ 2, it can be written in the following form: When the sequence Y follows a normal distribution, the distribution of the sequence X under the condition of Y is still a normal distribution, that is: (X|Y)~N(μ 3 ,∑ 3 )(12)μ 3 represents the expected value under the conditional distribution, ∑ 3 is the conditional covariance matrix: The meteorological drought SPI value before and the hydrological drought SRI drought level transferred from the meteorological drought to the future satisfy a bivariate normal distribution. Then, the probability of the SRI drought level transferred to the future under the current SPI condition is expressed as follows: Among them, Z v,λ represents the SPI value of the current λ-th month, and W v,λ+M represents the SRI value of the (λ + M)-th month. C Ms , C Mi is the upper and lower limits of the drought level C M , and the correlation coefficient between the current SPI value and the future SRI value is ρ; the current SPI and the future SRI are expressed by the standard normal cumulative distribution function Φ as follows: where the calculation of the correlation coefficient ρ is as follows: Among them, k represents the time scale of the drought index. The cumulative rainfall Y and the runoff X both satisfy the normal distribution. After the standardization process, the SPI value corresponding to the cumulative rainfall Y and the SRI value W corresponding to the runoff X v,λ+M both follow the standard normal distribution, that is: Expressed as the covariance between the current SPI and the SRI M months in the lag period, it is calculated as follows:

5. The method for predicting hydrological drought under changing environments according to claim 1, characterized in that, the implementation process of the step (5) is as follows: Pearson correlation test was used to screen out the climate factor z i with the highest correlation with the runoff series x i as a covariate to analyze the teleconnection relationship between the large-scale atmospheric circulation index CI and the runoff series; the Pearson correlation index ρ xz was used to characterize the correlation between the runoff series x i and the climate factor c 0 and its formula is as follows: To quantify the impact of human activities on hydrological drought, the difference between the theoretical SRI′ and the actual SRI is used as the human activity factor. The formula is as follows: HI = SRI′ - SRI (21) When HI > 0, it indicates that human activities have aggravated hydrological drought. When HI < 0, the impact is opposite. When HI = 0, it indicates no impact.

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