A method for constructing a non-stationary drought index based on climate index and improved reservoir index

Abstract

The invention discloses a method for constructing a non-stationary hydrological drought index based on a climate index and an improved reservoir index, comprising the following steps: S1, obtaining a w-month cumulative runoff sequence of corresponding months through a monthly measured runoff sequence; S2, performing a sliding average of the climate index on a w-month scale, and performing a lagged correlation analysis, and taking the climate index significantly correlated with the cumulative runoff sequence as a climate change factor CI; S3, calculating an improved reservoir index MRI, and selecting CI and MRI as candidate explanatory variables of a GAMLSS model at the same time; S4, performing distribution function optimization through a stationary model, and then establishing an optimal non-stationary model through parameter estimation and model optimization; S5, performing a standard normalization process on the runoff cumulative probability obtained by fitting the optimal non-stationary model to obtain NSRI; the invention overcomes the defect that the traditional SRI cannot reflect the characteristics of non-stationary drought under a changing environment.

Description

Technical Field

[0001] The invention relates to the field of non-stationary drought evaluation, and in particular to a method for constructing a non-stationary drought index based on a climate index and an improved reservoir index. Background Art

[0002] Drought is a natural disaster that lasts for a long time, affects a wide range and occurs frequently. According to statistics, 70% of natural disasters are meteorological disasters, and drought disasters account for about 50% of meteorological disasters. In recent years, with the obvious increase in the frequency, intensity and scope of drought in my country, the risk of drought is also increasing.

[0003] Hydrological drought is one of the important types of natural drought, which is closely related to the hydrological cycle and water balance in nature. In order to quantitatively evaluate the characteristics of hydrological drought, domestic and foreign scholars have proposed a variety of hydrological drought indices, such as the surface water supply index (SWSI), Palmer drought index (PHDI), runoff Z index, standardized runoff index (SRI), runoff drought index (SDI), runoff anomaly percentage, standard water resource index, etc., which have been widely used.

[0004] However, due to the strong interference of climate change and human activities in recent years, the hydrological and meteorological extreme value process has shown non-stationary characteristics, that is, the statistical parameters (mean, variance, etc.) of the hydrological and meteorological extreme value series are time-varying, the stationary assumption of the hydrological time series has been severely challenged, and the traditional drought evaluation method has been questioned. Therefore, it is urgent to construct non-stationary drought detection indicators that take into account the dual influence of climate change and human activities, and to explore the evolution characteristics of non-stationary hydrological drought under a changing environment, which has important practical significance for regional drought relief and water resources management.

[0005] In recent years, some scholars at home and abroad have begun to pay attention to the non-stationary characteristics of hydrological and meteorological extreme value sequences, and have made some progress. Rigby and Stasinotoulos proposed a generalized additive model considering location, scale and shape (GAMLSS), which can flexibly describe the linear or nonlinear relationship between the statistical parameters of random variable sequences and explanatory variables, and has been preliminarily applied in the field of non-stationary drought assessment. Russo et al. proposed a non-stationary standardized precipitation index (SnsPI), considering that the precipitation sequence in a changing environment obeys the Gamma distribution with a distribution parameter μ that changes with time, and estimated the probability of an extreme dry / wet year in Europe. The results show that SnsPI is more stable than the ordinary SPI in precipitation forecasting of multi-model ensembles. Li et al. proposed a non-stationary standardized precipitation index (NSPI) with climate factors as covariates. The results show that NSPI can better reflect the drought characteristics of the basin than the traditional SPI. Bazrafshan et al. constructed a non-stationary observational drought index (NRDI). The results show that NRDI better reflects the temporal variation trend of drought than the traditional RDI. Wen Qingzhi et al. established a non-stationary standardized precipitation evapotranspiration index (NSPEI) that is applicable to both stationary and non-stationary states. The results showed that the NSPEI has a better fitting effect than the SPEI and can well predict future drought changes. The above studies have promoted the rapid development of non-stationary drought detection indicators, but they are mainly aimed at meteorological droughts, and use time or climate factors as explanatory variables to construct non-stationary models, and do not include human activity factors as explanatory variables. To this end, Li Min et al. constructed a time-varying standardized runoff index (SRIt) based on the time-varying moment model on the basis of the traditional standardized runoff index SRI to reflect the non-stationary characteristics of the hydrological drought index under a changing environment. Wang et al. proposed a non-stationary standardized runoff index (NSSI) using climate change factors and human influence factors as covariates. The results showed that compared with the traditional SSI, the NSSI index has a better effect on drought evaluation in the Luanhe River Basin.

[0006] Although some progress has been made in the study of non-stationary hydrological drought index based on the GAMLSS model, it is still worth further study on how to comprehensively consider the impact of climate change and human activities to screen appropriate explanatory variables. Summary of the invention

[0007] The purpose of the present invention is to overcome the shortcomings of traditional hydrological drought index, and to construct a non-stationary standardized runoff index based on the standardized runoff index and the GAMLSS model with climate index and improved reservoir index as explanatory variables, and to provide a method for constructing a non-stationary drought index based on climate index and improved reservoir index.

[0008] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for constructing a non-stationary drought index based on a climate index and an improved reservoir index, comprising the following specific steps:

[0009] S1, specify the time scale as w months, and obtain the w-month cumulative runoff series of the corresponding months through the monthly measured runoff series;

[0010] S2. Perform a sliding average of the climate index on a w-month scale, and conduct a 0-12-month lagged correlation analysis between the cumulative runoff series of each station and the selected climate index, and use the climate index that is significantly correlated with the cumulative runoff series as the climate change factor CI;

[0011] S3, calculate the improved reservoir index MRI, and select CI and MRI as candidate explanatory variables of the GAMLSS model at the same time;

[0012] S4, optimizing the distribution function through the stationary model, and then establishing the optimal non-stationary model through parameter estimation and model optimization;

[0013] S5. The runoff cumulative probability obtained by fitting the optimal non-stationary model is subjected to standard normalization to obtain the non-stationary standardized runoff index (NSRI);

[0014] Preferably, in step S1, a 12-month time scale is used to calculate the 12-month cumulative runoff series, and the unit root test method is used to analyze its stationary characteristics.

[0015] Preferably, in step S2, six low-frequency climate indices SOI, PDO, AO, NAO, AMO and NPO that have physical causes with the runoff sequence in the study area are selected, and a 12-month sliding average is performed on the climate index to reduce the randomness of the climate index. The lagged correlation analysis uses the Kendall rank correlation test method to screen the climate index that is significantly correlated with the cumulative runoff sequence (significance level α=5%) as a climate change factor.

[0016] Preferably, the improved reservoir index MRI in step S3 is defined as:

[0017]

[0018] Where N is the number of reservoirs upstream of the hydrological station; A i is the controlled catchment area above the dam site of the i-th reservoir (km 2 );A T is the controlled catchment area of ​​the hydrological station (km 2 );C i ′ is the beneficial storage capacity of the i-th reservoir (billion m 3 );C tis the annual runoff of the hydrological station (billion m 3 ).

[0019] Preferably, the definition of the GAMLSS model in step S3 is:

[0020]

[0021] Where, k = 1, 2, ..., p; η k and θ k is a vector of length n, β k The length is J k The regression parameter vector, X k is n×J k The explanatory variable matrix, Z jk For a known n×q jk Fixed design matrix, γ jk It is a q jk dimensional normally distributed random variable vector, Z jk γ jk represents the jth random effect, q jk represents the dimension of the random influence factor in the jth random effect;

[0022] If it is assumed that the random variable follows a two-parameter probability distribution and the influence of random effects on the distribution parameters is not considered, the general expression of the GAMLSS model is:

[0023]

[0024] Preferably, in step S4, five commonly used two-parameter probability distribution functions (Gamma, Lognormal, Weibull, Gumbel, Logistic) are used to fit a stable model (distribution parameters are fixed values), and the best distribution function is selected according to the principle of minimizing the AIC value.

[0025] Preferably, the parameters of the GAMLSS model in step S4 are estimated using the maximum likelihood method, and then two non-stationary models based on the optimal distribution function are constructed, one of which is a non-stationary model with time as the explanatory variable, and the other is a non-stationary model with CI and MRI as the explanatory variables. The cubic spline function is used as the connection function between the distribution parameters and the explanatory variables, and the model with the smallest AIC value is selected as the optimal non-stationary model.

[0026] Preferably, in step S5, the runoff sequence fitting value is obtained according to the optimal non-stationary model, the cumulative probability of the fitting sequence is calculated, and a standard normalization process is performed on it to obtain the NSRI index value.

[0027] Beneficial effects of the present invention: The present invention is based on the GAMLSS model, and the non-stationary model established by using the climate index and the improved reservoir index simultaneously considers the impact of climate change and human activities on hydrological drought. The constructed non-stationary standardized runoff index NSRI effectively reflects the non-stationary characteristics of the hydrological drought index under a changing environment, overcoming the defect that the traditional SRI cannot reflect the non-stationary drought characteristics under a changing environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 A roadmap of steps for constructing a non-stationary drought index based on a climate index and an improved reservoir index according to the present invention;

[0029] Figure 2 MRI time variation diagram of four hydrological stations of the present invention;

[0030] Figure 3 The normal QQ plot and residual worm plot of the optimal model of the runoff sequence of Huangzhuang Station in December of the present invention;

[0031] Figure 4 This is the quantile diagram of runoff series of different models at Huangzhuang Station in December of the present invention;

[0032] Figure 5 This is the time variation diagram of SRI and NSRI on a 12-month time scale at Huangzhuang Station from 1956 to 2020 in the present invention. DETAILED DESCRIPTION

[0033] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0034] like Figure 1 As shown in FIG, the method for constructing a non-stationary drought index based on the climate index and the improved reservoir index includes the following specific steps:

[0035] S1, specify the time scale as w months, and obtain the w-month cumulative runoff series of the corresponding months through the monthly measured runoff series;

[0036] S2. Perform a sliding average of the climate index on a w-month scale, and conduct a 0-12-month lagged correlation analysis between the cumulative runoff series of each station and the selected climate index, and use the climate index that is significantly correlated with the cumulative runoff series as the climate change factor CI;

[0037] S3, calculate the improved reservoir index MRI, and select CI and MRI as candidate explanatory variables of the GAMLSS model at the same time;

[0038] S4, optimizing the distribution function through the stationary model, and then establishing the optimal non-stationary model through parameter estimation and model optimization;

[0039] S5. The runoff cumulative probability obtained by fitting the optimal non-stationary model is subjected to standard normalization to obtain the non-stationary standardized runoff index (NSRI);

[0040] In the step S1, a 12-month time scale is used to calculate the 12-month cumulative runoff series, and the unit root test method is used to analyze its stationary characteristics.

[0041] In step S2, six low-frequency climate indices SOI, PDO, AO, NAO, AMO and NPO with physical causes in the study area runoff sequence are selected, and a 12-month sliding average is performed on the climate index to reduce the randomness of the climate index. The lagged correlation analysis uses the Kendall rank correlation test method to select climate indices that are significantly correlated with the cumulative runoff sequence (significance level α=5%) as climate change factors.

[0042] The improved reservoir index MRI in step S3 is defined as:

[0043]

[0044] Where N is the number of reservoirs upstream of the hydrological station; A i is the controlled catchment area above the dam site of the i-th reservoir (km 2 );A T is the controlled catchment area of ​​the hydrological station (km 2 );C i ′ is the beneficial storage capacity of the i-th reservoir (billion m 3 );C t is the annual runoff of the hydrological station (billion m 3 ).

[0045] The definition of the GAMLSS model in step S3 is:

[0046]

[0047] Where, k = 1, 2, ..., p; η k and θ k is a vector of length n, β k The length is J k The regression parameter vector, X k is n×J k The explanatory variable matrix, Z jk For a known n×q jk Fixed design matrix, γ jk It is a q jk dimensional normally distributed random variable vector, Z jk γ jk represents the j-th random effect, q jkrepresents the dimension of the random influence factor in the jth random effect;

[0048] If it is assumed that the random variable follows a two-parameter probability distribution and the influence of random effects on the distribution parameters is not considered, the general expression of the GAMLSS model is:

[0049]

[0050] In step S4, five commonly used two-parameter probability distribution functions (Gamma, Lognormal, Weibull, Gumbel, Logistic) are used to fit a stable model (distribution parameters are fixed values), and the best distribution function is selected according to the principle of minimizing the AIC value.

[0051] The parameters of the GAMLSS model in step S4 are estimated using the maximum likelihood method, and then two non-stationary models based on the optimal distribution function are constructed, one of which is a non-stationary model with time as the explanatory variable, and the other is a non-stationary model with CI and MRI as the explanatory variables. The cubic spline function is used as the connection function between the distribution parameters and the explanatory variables, and the model with the smallest AIC value is selected as the optimal non-stationary model.

[0052] In step S5, the runoff sequence fitting value is obtained according to the optimal non-stationary model, the cumulative probability of the fitting sequence is calculated, and the standard normalization process is performed on it to obtain the NSRI index value.

[0053] Taking the Hanjiang River Basin as an example, the unit root test method was used to analyze the stationary characteristics of the 12-month time scale runoff series of four hydrological stations in the Hanjiang River Basin from 1956 to 2020. As shown in Table 1, the P values ​​of the runoff series of the four hydrological stations in the Hanjiang River Basin are all greater than 0.05, indicating that the runoff series are non-stationary.

[0054] Table 1 Unit root test results of runoff series at four hydrological stations in the Hanjiang River Basin

[0055]

[0056] The key climate indices affecting the monthly runoff series at Huangzhuang Station were analyzed using the Kendall rank correlation test at a 5% significance level. As shown in Table 2, the climate indices significantly correlated with the runoff series varied in different months and with different lag times. Specifically, NPO was significantly correlated with the monthly runoff series at Huangzhuang Station from 1956 to 2020. For SOI, there was a strong correlation between SOI and monthly runoff series in all months except September to November. However, no significant correlation was observed between PDO, AO, NAO and monthly runoff series at Huangzhuang Station. Similar results were obtained at other hydrological stations. The results show that NPO is the main climate change factor affecting runoff changes in the Hanjiang River Basin, followed by SOI and AMO.

[0057] Table 2 CI screening results of Huangzhuang Station in each month from 1956 to 2020

[0058]

[0059] Note: The lag time of the correlation between climate indices and runoff series is indicated by a subscript in months.

[0060] Reservoir index MRI is established for each of the large reservoirs in the basins controlled by the four hydrological stations, such as Figure 2 As shown. Figure 2 It can be seen that MRI began to fluctuate irregularly after the reservoir was filled with water. López and Francés believed that the threshold of reservoir regulation on runoff change was 0.25. Figure 2 Let's take a look at Ankang Station ( Figure 2 a) The runoff process is affected by the Ankang Reservoir. The MRI value has generally fluctuated and increased since 1989, reaching 0.338 in 2002, indicating that it is significantly affected by the Ankang Reservoir. Figure 2 b) is also greatly affected by the Ankang Reservoir, but it has not reached a significant level. The MRI value reached a maximum of 0.118 in 1999. Huangjiagang Station ( Figure 2 c) The most significant influence is from the reservoir, mainly due to the water storage operation of Danjiangkou Reservoir. The MRI value jumped twice in 1967 and 2013, and reached a maximum of 1.275 in 2016. Figure 2 d) It is also greatly affected by the Danjiangkou Reservoir, with the maximum MRI value reaching 0.636 in 2014. This shows that large reservoirs in the Hanjiang River Basin, especially the controlling reservoirs such as Ankang and Danjiangkou, have a significant impact on runoff.

[0061] Five probability distribution functions were used to fit the stationary model, and the best fitting distribution was selected according to the principle of minimum AIC value. Table 3 summarizes the runoff fitting results of Huangzhuang Station. As can be seen from Table 3, the Lognormal distribution has the best overall fitting performance, followed by the Gamma distribution, while the Weibull, Gumbel and Logistic distributions have poor fitting effects.

[0062] Table 3 AIC values ​​of different probability distributions of runoff series at Huangzhuang Station

[0063]

[0064] Table 4 shows the AIC values ​​of the stationary model (Model 0) fitted by the monthly runoff data of Huangzhuang Station, the non-stationary model with time as the explanatory variable (Model 1), and the non-stationary model with CI and MRI as explanatory variables (Model 2). Compared with other models, Model 2 has the smallest AIC value, indicating that Model 2 has the best fitting effect on the runoff series in the study area. It is worth noting that due to the inclusion of climate and human factors as covariates, the non-stationary model presents a more robust fitting effect than the stationary model. In addition, Table 4 shows the explanatory variables of the optimal non-stationary model. The results show that NPO is the climate index that has the most significant impact on the runoff series at Huangzhuang Station. In addition, MRI is the best choice for fitting the monthly runoff series, indicating that reservoir regulation has a significant impact on the non-stationarity of runoff.

[0065] Table 4 AIC values ​​of different models at Huangzhuang Station in each month and explanatory variables of distribution parameters in the best model

[0066]

[0067] Table 5 summarizes the statistical parameters of the residual sequence of Model 2. For 64 samples, the Filliben coefficient at the 95% confidence level is approximately 0.981. As shown in Table 5, the Filliben coefficients are all greater than 0.981, indicating that the deviation between the residuals of Model 2 and normality is not significant. In addition, the mean and variance of the model residuals are close to 0.00 and 1.0, respectively, indicating that the residuals of Model 2 approximately follow the standard normal distribution. In other words, the fitting performance of the optimal non-stationary model is generally reliable.

[0068] Table 5 Statistical parameters of residual sequence of model 2

[0069]

[0070] like Figure 3 As shown in Figure 2, in order to further verify the reliability of the optimal non-stationary model, the normal QQ plot and residual worm plot of the runoff series of Huangzhuang Station in December were analyzed. Figure 3It can be seen that the results of the normal QQ plot and worm plot do not deviate significantly from normality, indicating that the optimized model fits the runoff series effectively.

[0071] like Figure 4 As shown in the figure, the quantile curves of the runoff series in December of Huangzhuang Station from 1956 to 2020 under three model conditions are shown (the curves in the figure are 95%, 75%, 50%, 25% and 5% quantiles from top to bottom). Figure 4 It can be seen that the quantile range of 5% to 95% covers almost all the observations of model 2, indicating that the distribution of observations of non-stationary model 2 ( Figure 4 c) The observed values ​​of the model are more reasonably distributed than those of other models. Specifically, compared with Model 0 ( Figure 4 a) Compared with the non-stationary model ( Figure 4 The quantile plot of (bc)) shows irregular fluctuations, which better describes the nonlinear changes of the measured runoff data in the study. Compared with model 1, the fluctuation amplitude of the results of model 2 is larger, which can more effectively characterize the extreme runoff behavior and significantly improve the model fitting ability.

[0072] like Figure 5 As shown in Figure 2, the SRI and NSRI of the Huangzhuang station on a 12-month time scale from 1956 to 2020 were calculated. Figure 5 It can be seen that the temporal changes of SRI and NSRI from 1956 to 2020 are similar, indicating that NSRI effectively identifies drought processes. Historical records and previous studies have shown that the Hanjiang River Basin suffered severe drought events in 1966, 2000, 2014, and 2016. It is obvious that the drought conditions identified by NSRI are more consistent with historical drought records. In addition, the severity of drought identified by NSRI is generally higher than that identified by SRI, indicating that drought conditions are more severe than SRI. In this study, typical drought events in 2014 and 2016 were selected to further evaluate the performance of NSRI and SRI. It is worth noting that NSRI and SRI can also identify these two severe drought events, which brought great damage to agricultural production, life and ecosystems in the Hanjiang River Basin. In 2014, about 5 million people in Hubei Province suffered from severe drought, with direct economic losses of nearly 2 billion yuan. In 2016, due to low precipitation, a rare drought occurred in northwestern Hubei, and more than 230,000 people had difficulty in drinking water. Nevertheless, for two typical drought events, the NSRI has lower values, showing more severe drought conditions than the SRI. It is obvious that the results of the NSRI reflect the actual drought conditions better than those of the SRI, which means that the NSRI is more reliable for drought assessment under changing environments.

[0073] The above-mentioned embodiments are only preferred technical solutions of the present invention and should not be regarded as limitations of the present invention. The embodiments and features in the embodiments of the present application can be arbitrarily combined with each other without conflict. The protection scope of the present invention shall be the technical solutions recorded in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A method for constructing a non-stationary drought index based on a climate index and an improved reservoir index, characterized in that: It includes the following specific steps: S1, specify the time scale as w months, and obtain the w-month cumulative runoff series of the corresponding months through the monthly measured runoff series; S2. Perform a sliding average of the climate index on a w-month scale, and conduct a 0-12-month lagged correlation analysis between the cumulative runoff series of each station and the selected climate index, and use the climate index that is significantly correlated with the cumulative runoff series as the climate change factor CI; S3, calculate the improved reservoir index MRI, and select CI and MRI as candidate explanatory variables of the GAMLSS model at the same time; S4, optimizing the distribution function through the stationary model, and then establishing the optimal non-stationary model through parameter estimation and model optimization; S5. The runoff cumulative probability obtained by fitting the optimal non-stationary model is subjected to standard normalization processing to obtain the non-stationary standardized runoff index NSRI; In step S2, six low-frequency climate indices SOI, PDO, AO, NAO, AMO and NPO with physical causes in the study area runoff series are selected, and the climate indices are moved averaged on a 12-month scale to reduce the randomness of the climate indices. The lagged correlation analysis uses the Kendall rank correlation test method to select the climate indices that are significantly correlated with the cumulative runoff series as climate change factors, wherein the significance level used for selecting the climate indices that are significantly correlated with the cumulative runoff series is α=5%; The improved reservoir index MRI in step S3 is defined as: ； Where N is the number of reservoirs upstream of the hydrological station; A i is the controlled catchment area above the dam site of the i-th reservoir, in km 2 ; A T is the controlled watershed area of ​​the hydrological station, in km 2 ; is the beneficial storage capacity of the ith reservoir, in billion m 3 ; C t is the annual runoff of the hydrological station, in billion m 3 .

2. The method for constructing a non-stationary drought index based on a climate index and an improved reservoir index according to claim 1, characterized in that: In the step S1, a 12-month time scale is used to calculate the 12-month cumulative runoff series, and the unit root test method is used to analyze its stationary characteristics.

3. The method for constructing a non-stationary drought index based on a climate index and an improved reservoir index according to claim 1, characterized in that: The definition of the GAMLSS model in step S3 is: ； Where k = 1, 2, …, p; η k and θ k is a vector of length n, β k The length is J k The regression parameter vector, X k is n×J k The explanatory variable matrix, Z jk For a known n×q jk Fixed design matrix, γ jk It is a q jk dimensional normally distributed random variable vector, Z jk γ jk represents the j-th random effect, q jk represents the dimension of the random influence factor in the jth random effect; If it is assumed that the random variable follows a two-parameter probability distribution and the influence of random effects on the distribution parameters is not considered, the general expression of the GAMLSS model is: 。 4. The method for constructing a non-stationary drought index based on a climate index and an improved reservoir index according to claim 1, characterized in that: In step S4, five two-parameter probability distribution functions are used to fit the stationary model, and the two-parameter probability distribution functions are Gamma distribution, Lognormal distribution, Weibull distribution, Gumbel distribution and Logistic distribution. When fitting the stationary model, the distribution parameters of the distribution function are fixed values, and the best distribution function is selected according to the principle of minimizing the AIC value.

5. The method for constructing a non-stationary drought index based on a climate index and an improved reservoir index according to claim 1, characterized in that: The parameters of the GAMLSS model in step S4 are estimated using the maximum likelihood method, and then two non-stationary models based on the optimal distribution function are constructed, one of which is a non-stationary model with time as the explanatory variable, and the other is a non-stationary model with CI and MRI as the explanatory variables. The cubic spline function is used as the connection function between the distribution parameters and the explanatory variables, and the model with the smallest AIC value is selected as the optimal non-stationary model.

6. The method for constructing a non-stationary drought index based on a climate index and an improved reservoir index according to claim 1, characterized in that: In step S5, the runoff sequence fitting value is obtained according to the optimal non-stationary model, the cumulative probability of the fitting sequence is calculated, and the standard normalization process is performed on it to obtain the NSRI index value.

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