An analytical method for identifying scale-dependent relationships between groundwater level and influencing factors

Abstract

The present invention discloses an analytical method for identifying the scale dependence relationship between groundwater level and influencing factors. After removing the interference of interfering factors by partial wavelet coherence analysis, the coherence and relative phase characteristics of the influencing factors and groundwater level are revealed; Monte Carlo simulation is used to perform a significance test on the coherence relationship, and the percentage of the area of ​​the significance test region and the average wavelet coherence coefficient are compared to identify the dominant factor of the scale dependence that controls the groundwater level fluctuation; and the hysteresis characteristics of the groundwater level response to the influencing factors are explored through the relative phase characteristics. Aiming at complex groundwater flow systems, the present invention provides a method with the characteristics of accurately characterizing the scale dependence relationship between a single influencing factor and the groundwater level in the time-frequency domain, which is suitable for the study of identifying and quantifying the scale dependence control of the influencing factors on the groundwater flow process.

Description

Technical Field

[0001] The present invention belongs to the research field of dynamic processes of complex groundwater flow systems, and specifically relates to an analysis method for identifying the scale dependence relationship between groundwater level and influencing factors. Background Art

[0002] Groundwater is an important source of water for industrial production, agricultural irrigation, and daily life. In recent decades, the increase in water demand has caused over-exploitation of groundwater, leading to a series of environmental problems such as land subsidence, wetland disappearance, river drying, and seawater intrusion in coastal areas. The simulation and prediction of groundwater level changes are the prerequisites for optimizing the design of groundwater exploitation plans, rationally developing groundwater resources, and preventing and controlling groundwater pollution. Among them, determining the spatiotemporal response patterns of groundwater levels and influencing factors is crucial to improving the accuracy of groundwater prediction and simulation. Due to the many influencing factors and complex processes of the groundwater system, it is a huge challenge to identify and quantify the scale-dependent relationship characteristics of groundwater levels and influencing factors.

[0003] The study of groundwater level fluctuation process has obvious uncertainty and complexity, and it is difficult to clearly describe its changing laws and characteristics by conventional methods. Therefore, hydrological time series are generally studied from two aspects: time domain and frequency domain. Among them, time domain analysis can mainly characterize the positioning ability of time, and cannot obtain more information on water level series fluctuations. In order to more accurately extract the characteristics of the signal, it is usually necessary to convert the time series into the frequency domain for research and analysis. Among them, wavelet transform can simultaneously characterize information in the time and frequency domains. Research on the basis and application of wavelet analysis covers almost all research directions in hydrology. Therefore, binary wavelet coherence analysis based on wavelet transform has been used in many scientific disciplines to explore the local and scale-dependent coherence characteristics of time series signals (see reference 1: Guo Lin, Gong Huili, Zhu Feng, Guo Xiaomeng, Zhou Chaofan, Qiu Lin, 2014. Study on the periodic characteristics of groundwater level and precipitation based on wavelet analysis [J]. Geography and Geographic Information Science, 30(2), 35-38; reference 2: Holman, IP, Rivas-Casado, M., Bloomfield, JP, Gurdak, JJ, 2011. Identifying non-stationary groundwater level response to North Atlantic ocean-atmosphere teleconnection patterns using wavelet coherence [J]. Hydrogeology Journal, 19(6), 1269-1278). Because the groundwater flow system involves complex recharge and discharge modes, the coherence characteristics of the influencing factors and groundwater level fluctuations are disturbed by other influencing factors, thereby misleading the response pattern of groundwater level and influencing factors. Therefore, the binary wavelet coherence analysis cannot accurately reveal the scale-dependent relationship characteristics between groundwater level and influencing factors. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide an analytical method for identifying the scale dependence of groundwater level and influencing factors. This method can accurately reveal the coherence characteristics of local and scale dependence of groundwater level and influencing factors in the time-frequency domain, and effectively demonstrate the lag relationship of the dynamic process of groundwater level to the response of influencing factors.

[0005] Technical solution: An analytical method for identifying the scale dependence relationship between groundwater level and influencing factors of the present invention comprises the following steps:

[0006] S1. Select the groundwater system area to be studied, obtain the groundwater level time series and influencing factor time series at equal time intervals in the area, and standardize the time series;

[0007] S2, performing outlier detection on the groundwater level time series and the influencing factor time series after the standardization processing in step S1 to determine whether there are outliers. If there are outliers, process the outliers; if there are no outliers, directly execute step S3;

[0008] S3, performing continuous wavelet transform on the groundwater level time series and the influencing factor time series after the outlier detection in step S2;

[0009] S4, according to the continuous wavelet transform of the groundwater level time series and the influencing factor time series obtained in step S3, respectively calculating the self-coherent wavelet transform of the groundwater level time series and the influencing factor time series;

[0010] S5, according to the continuous wavelet transform of the groundwater level time series and the influencing factor time series obtained in step S3, calculating the cross wavelet transform between the groundwater level time series and the influencing factor time series and the relative phase between the groundwater level and the influencing factor;

[0011] S6. According to the self-coherent wavelet transform and cross wavelet transform obtained in steps S4 and S5, the scale-dependent partial wavelet coherence of the groundwater level time series and the influencing factor time series is calculated, and the relative phase of the groundwater level and the influencing factor time series after eliminating the interference of the interference factor is calculated. The partial wavelet coherence is tested at a significance level of 5% using Monte Carlo simulation, and the percentage of the area passing the significance test at different scales to the total area of ​​the corresponding scale is calculated to obtain the percentage of the scale-dependent significance test area area;

[0012] S7. The scale-dependent average wavelet coherence coefficient is obtained by calculating the average value of partial wavelet coherence at different scales, and the dominant control factor of groundwater level scale dependence is identified according to the percentage of the significance test area and the average wavelet coherence coefficient;

[0013] S8. Analyze the lag relationship characteristics of the groundwater level response to the influencing factors based on the relative phase of the groundwater level and the influencing factor time series calculated in step S6 after eliminating the interference of the interference factors.

[0014] Furthermore, the time series is standardized in step S1 as follows: the time series value point is subtracted from the mean of the time series and the ratio is calculated with the standard deviation.

[0015] Furthermore, the outlier in step S2 refers to a value whose deviation from the mean value exceeds two standard deviations. A box plot is used to scan the standardized groundwater level time series and the influencing factor time series to see if there are outliers. For outliers, the mean values ​​before and after the outliers are used as replacements.

[0016] Furthermore, step S3 is specifically as follows:

[0017] The time series of influencing factors X = {x 1 ,x 2 ,…,x N} and groundwater level time series Y = {y 1 ,y 2 ,…,y N}, at the i-th moment, i.e., t i =iδt and the continuous wavelet transform on scale s are expressed as:

[0018]

[0019]

[0020] in, and They represent the continuous wavelet transform of the influencing factor time series X and the groundwater level time series Y, respectively. N represents the length of the influencing factor time series X and the groundwater level time series Y. j is the jth observation data point of the impact factor time series X, y j is the jth observation data point of the groundwater level time series Y, t j represents the jth moment, j=0,1,…,N-1, “*” represents the complex conjugate, Ψ is the wavelet function, is the normalization factor that converts Ψ to a value with unit energy.

[0021] Furthermore, the wavelet function Ψ adopts Morlet wavelet, and the expression is:

[0022]

[0023] Among them, ω 0 represents dimensionless frequency, η represents dimensionless time;

[0024] The scale s is chosen as the exponential form of 2, and the expression is:

[0025] s j =s 0 2 jδj ,j=0,1,…,J

[0026] J=δj -1 log 2 (Nδt / s 0 )

[0027] Among them, s 0 represents the minimum scale, J is used to define the maximum scale, δt is the equal time interval for data sampling, and N represents the length of the time series.

[0028] Further, in step S4 at time t i =iδt and scale s, the self-coherent wavelet transform of the influencing factor time series X and the groundwater level time series Y are:

[0029]

[0030]

[0031] Where, “*” indicates complex conjugation, W i X (s) and W i Y (s) represent the continuous wavelet transform of the influencing factor time series X and the groundwater level time series Y respectively.

[0032] Furthermore, in step S5, at time t i = iδt and the cross wavelet transform W between the time series of groundwater level and influencing factors calculated on scale s i YX , expressed as:

[0033]

[0034] Where, “*” indicates complex conjugation, W i X (s) and W i Y (s) represents the continuous wavelet transform of the influencing factor time series X and the groundwater level time series Y respectively;

[0035] At time t i = iδt and the relative phase characteristics between the time series of groundwater level and influencing factors calculated on scale s Φ i :

[0036] Φ i =tan -1 (ImW i YX (s) / ReW i YX (s))

[0037] Among them, Im and Re represent W i YX The imaginary and real parts of (s).

[0038] Further, in step S6 at time t i =iδt and scale s, after excluding the influence of interference factor Z, the partial wavelet coherence of the influencing factor time series X and the groundwater level time series Y is expressed as:

[0039]

[0040] in, is the wavelet coherence coefficient between the time series of influencing factors, groundwater level and interference factors, is the wavelet coherence coefficient of the time series of the influencing factors and the time series of the groundwater level, is the wavelet coherence coefficient of the groundwater level time series and the interference factor time series, is the wavelet coherence coefficient of the influencing factor time series and the interference factor time series; the calculation formulas are:

[0041]

[0042]

[0043]

[0044]

[0045] Among them, “·” means excluding variable symbols, represents the smooth operator, W i YZ (s) is the cross wavelet transform of groundwater level time series Y and interference factor time series Z, W i XZ (s) is the cross wavelet transform of the influencing factor time series X and the interference factor time series Z, W i YX (s) is the cross wavelet transform of groundwater level time series Y and influencing factor time series X, W i XX (s), W i YY (s), W i ZZ (s) represents the self-coherent wavelet transform of groundwater level time series, influencing factor time series and interference factor time series, respectively, and “*” represents complex conjugate;

[0046] At time t i =iδt and scale s, after excluding the influence of interference factor Z, the relative phase characteristics of the influencing factor time series X and the groundwater level time series Y are expressed as:

[0047]

[0048] in,

[0049]

[0050] Φ iRepresents the relative phase of the cross wavelet transform of the influencing factor time series X and the groundwater level time series Y.

[0051] An analysis system for identifying the scale dependency relationship between groundwater level and influencing factors of the present invention comprises:

[0052] The data acquisition module is used to select the groundwater system area to be studied and obtain the time series of groundwater level and influencing factors at equal time intervals in the area;

[0053] The data processing module standardizes the time series and performs outlier detection. For outliers, the average value before and after the outlier is used to replace them.

[0054] The wavelet transform module of a single time series is used to perform continuous wavelet transform on the groundwater level and influencing factor time series after data processing;

[0055] The wavelet transform calculation module of the two time series is used to calculate the self-coherence wavelet transform, cross wavelet transform and its relative phase characteristics, partial wavelet coherence and its relative phase characteristics of the groundwater level and its influencing factor time series respectively;

[0056] The identification and analysis module is used to identify the dominant controlling factors that control the scale dependence of groundwater level through the percentage of significance test area and the average wavelet coherence coefficient at different scales; and to analyze the lag relationship characteristics of the groundwater level response to the influencing factors based on the relative phase characteristics of the groundwater level and the influencing factor time series.

[0057] A device of the present invention includes a memory and a processor, wherein:

[0058] A memory for storing computer programs that can be run on the processor;

[0059] The processor is used to execute the steps of the above-mentioned analysis method for identifying the scale dependency relationship between groundwater level and influencing factors when running the computer program.

[0060] Principle of the invention: Partial wavelet coherence analysis can eliminate the influence of interference factors and effectively reveal the response pattern characteristics of single influencing factors and groundwater level scale dependence. The present invention gives full play to the advantages of partial wavelet coherence multi-resolution analysis and develops a technology for identifying the scale dependence relationship between groundwater level and influencing factors.

[0061] Beneficial effects: Compared with the prior art, the present invention uses partial wavelet coherence analysis to identify the scale-dependent coherence characteristics of groundwater level and influencing factors, and reveals the lagging response characteristics of groundwater level to influencing factors by studying the relative phase of influencing factors and groundwater level. The use of partial wavelet coherence analysis can effectively reveal the spatiotemporal response pattern between groundwater level and influencing factors. In addition, it provides a convenient and reliable method for studying complex groundwater flow processes, which has important theoretical and engineering significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is a flow chart of the method of the present invention;

[0063] Figure 2 is the continuous wavelet power spectrum, where (a) is the annual and monthly precipitation fluctuation characteristics and the daily precipitation continuous wavelet power spectrum, (b) is the annual and monthly average precipitation intensity fluctuation characteristics and the daily precipitation intensity continuous wavelet power spectrum, (c) is the annual and monthly precipitation duration fluctuation characteristics and the daily precipitation duration continuous wavelet power spectrum;

[0064] Figure 3 is the continuous wavelet transform power spectrum of groundwater level fluctuation;

[0065] Figure 4 (a) is the average wavelet coherence coefficient between precipitation characteristics at different scales and groundwater level, (b) is the percentage value of the significance test area between precipitation characteristics at different scales and groundwater level;

[0066] Figure 5 is the partial wavelet coherence power spectrum, where (a) is the partial wavelet coherence power spectrum between groundwater level and precipitation after excluding the influence of surface water; (b) is the partial wavelet coherence power spectrum between groundwater level and surface water after excluding the influence of precipitation. DETAILED DESCRIPTION

[0067] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0068] The present invention uses partial wavelet coherence analysis to remove the interference of other influencing factors, and then reveals the coherence and relative phase characteristics of the influencing factors and the groundwater level. Monte Carlo simulation is used to perform a significance test on the coherence relationship, and the percentage of the area that passes the significance test and the average wavelet coherence coefficient at different scales are compared to identify the scale-dependent dominant factor that controls the groundwater level fluctuation. And the hysteresis characteristics of the groundwater level response to the influencing factors are explored through the relative phase characteristics. Aiming at complex groundwater flow systems, the present invention has developed a method that can accurately characterize the scale-dependent relationship characteristics of a single influencing factor and the groundwater level in the time-frequency domain, which is suitable for the study of identifying and quantifying the scale-dependent control of the influencing factors on the groundwater flow process.

[0069] like Figure 1 As shown, the analytical method for identifying the scale dependence relationship between groundwater level and influencing factors proposed by the present invention includes the following steps:

[0070] S1. Select the groundwater system area to be studied, obtain the time series of groundwater level and influencing factors at equal time intervals in the area, and standardize the obtained time series;

[0071] The groundwater system selected in this example is the Tuscaloosa Lake Basin in the United States. The main factors affecting the groundwater flow process are surface water and precipitation. Different precipitation characteristics have different effects on the groundwater system. Therefore, the relationship characteristics between the total precipitation, precipitation intensity, and precipitation persistence and the groundwater level are studied; data standardization refers to subtracting the mean and dividing by the standard deviation, that is, subtracting the mean of the time series from the time series value point and making a ratio with the standard deviation.

[0072] S2, performing outlier detection on the groundwater level time series and the influencing factor time series after the standardization processing in step S1 to determine whether there are outliers. If there are outliers, process the outliers; if there are no outliers, directly execute step S3;

[0073] The method for outlier detection is: use a box plot to scan the standardized groundwater level time series and influencing factor time series data, and replace the outliers with the mean values ​​before and after the outliers.

[0074] The outliers are values ​​that deviate from the mean by more than two standard deviations.

[0075] S3, performing continuous wavelet transform on the groundwater level time series and the influencing factor time series after the outlier detection in step S2;

[0076] Continuous wavelet transform can effectively extract characteristic information of data series and is a common tool for analyzing local intermittent oscillations in time series. 1 ,x 2 ,…,x N} and groundwater level time series Y = {y 1 ,y 2 ,…,y N}, at the i-th moment, i.e., t i =iδt and the continuous wavelet transform on scale s are expressed as:

[0077]

[0078]

[0079] Among them, Wi X (s) and W i Y (s) represents the continuous wavelet transform of the influencing factor sequence X and the groundwater level sequence Y, respectively, N represents the length of the influencing factor time series X and the groundwater level time series Y, x j and j are the jth observation data point of the influencing factor sequence X and the groundwater level time series Y, respectively. j represents the jth moment, j=0,1,…,N-1, “*” represents the complex conjugate, Ψ is the wavelet function, is a normalization factor that converts Ψ into unit energy. The wavelet function Ψ can be stretched or compressed by changing the wavelet scale s, and the wavelet function can be translated by changing the local time index t. The wavelet power spectrum is defined as |W i (s)| 2 .

[0080] Morlet wavelet is often chosen as the wavelet function in geophysical time series analysis and is 0 =6, Morlet wavelet can achieve a better balance between time and frequency. Therefore, this example selects Morlet wavelet as the wavelet function of continuous wavelet transform, and Morlet wavelet is expressed as:

[0081]

[0082] Among them, ω 0 represents dimensionless frequency, and η represents dimensionless time.

[0083] In this embodiment, the exponential form with a scale of 2 is selected:

[0084] s j =s 0 2 jδj ,j=0,1,…,J (4)

[0085] J=δj -1 log 2 (Nδt / s 0 ) (5)

[0086] Among them, s 0 represents the smallest scale, J can define the largest scale, δt is the equal time interval of data sampling, and N is the length of the time series. In this embodiment, the data is sampled at equal time intervals with daily resolution, and N=2547.

[0087] S4. Calculate the self-coherent wavelet transform of the time series of groundwater level and its influencing factors respectively.

[0088] The influencing factor time series X and groundwater level time series Y at time t i =iδt and the self-coherent wavelet transform on scale s are expressed as:

[0089]

[0090]

[0091] Where, “*” indicates complex conjugation, W i X (s) and W i Y (s) represent the continuous wavelet transform of the influencing factor sequence X and the groundwater level sequence Y respectively.

[0092] S5, calculate the cross wavelet transform and relative phase between the groundwater level and the influencing factor time series;

[0093] The groundwater level time series Y and the influencing factor time series X at time t i =iδt and the cross wavelet transform on scale s is:

[0094]

[0095] Where, “*” indicates complex conjugation, W i X (s) and W i Y (s) represent the continuous wavelet transform of the influencing factor time series X and the groundwater level time series Y respectively.

[0096] The relative phase between the groundwater level and the influencing factor time series is expressed as:

[0097] Φ i =tan -1 (ImW i YX (s) / ReW i YX (s)) (9)

[0098] Among them, Im and Re represent the cross wavelet transform W between the groundwater level and the influencing factor time series, respectively. i YX The imaginary and real parts of (s).

[0099] S6. Calculate the scale-dependent partial wavelet coherence of the time series of groundwater level and influencing factors, as well as the relative phase characteristics of groundwater level and influencing factors after eliminating the interference of interfering factors. Use Monte Carlo simulation to test the partial wavelet coherence at a significance level of 5%, calculate the percentage of the area passing the significance test at different scales to the total area of ​​the corresponding scale, and obtain the percentage of the scale-dependent significance test area area;

[0100] At time t i =iδt and scale s, after excluding the influence of interference factor precipitation (or surface water) Z, the partial wavelet coherence of groundwater level time series Y and influencing factor surface water (or precipitation) time series X is:

[0101]

[0102] Among them, the wavelet coherence coefficient between the time series of influencing factors, groundwater level and interference factors is It is expressed as:

[0103]

[0104] Wavelet coherence coefficients of time series of influencing factors and groundwater level It is expressed as:

[0105]

[0106] Wavelet coherence coefficients of groundwater level time series and disturbance factor time series It is expressed as:

[0107]

[0108] Wavelet coherence coefficients of time series of influencing factors and interference factors It is expressed as:

[0109]

[0110] Among them, “·” means excluding variable symbols, represents the smooth operator, W i YZ (s) is the cross wavelet transform of groundwater level time series Y and interference factor time series Z, W i XZ (s) is the cross wavelet transform of the influencing time factor series X and the interference factor time series Z, W i YX (s) is the cross wavelet transform of groundwater level time series Y and influencing time factor series X, W i XX (s), Wi YY (s), W i ZZ (s) represents the self-coherent wavelet transform of the groundwater level time series, the influencing factor time series and the interference factor time series, respectively, and “*” represents the complex conjugate.

[0111] After excluding the influence of the interference factor time series Z, the relative phase characteristics of the groundwater level time series Y and the influencing factor time series X are expressed as follows:

[0112]

[0113]

[0114] Among them, Φ i Represents the relative phase of the cross wavelet transform of the influencing factor time series X and the groundwater level time series Y.

[0115] S7. The scale-dependent average wavelet coherence coefficient is obtained by calculating the average value of partial wavelet coherence at different scales. The dominant factor controlling the scale dependence of groundwater level is identified according to the percentage of the significance test area and the average wavelet coherence coefficient.

[0116] The larger the values ​​of the average wavelet coherence coefficient and the percentage of the significance test area, the more groundwater level changes can be explained by the relevant influencing factors.

[0117] S8. Analyze the lag relationship between the response of the groundwater level to the influencing factors based on the relative phase of the groundwater level and the influencing factor time series calculated in step S6 after eliminating the interference of the interference factors.

[0118] In the partial wavelet coherence power spectrum, the arrows ( Figure 5 The arrows pointing to the right indicate that the influencing factor and the groundwater level have the same phase characteristics; the arrows pointing to the left indicate that the influencing factor and the groundwater level have the opposite phase characteristics; the arrows pointing upwards indicate that the groundwater level fluctuation lags the influencing factor by 90°.

[0119] An analysis system for identifying the scale dependency relationship between groundwater level and influencing factors of the present invention comprises:

[0120] The data acquisition module is used to select the groundwater system area to be studied and obtain the time series of groundwater level and influencing factors at equal time intervals in the area;

[0121] The data processing module standardizes the time series and performs outlier detection. For outliers, the average value before and after the outlier is used to replace them.

[0122] The wavelet transform module of a single time series is used to perform continuous wavelet transform on the groundwater level and influencing factor time series after data processing;

[0123] The wavelet transform calculation module of the two time series is used to calculate the self-coherence wavelet transform, cross wavelet transform and its relative phase characteristics, partial wavelet coherence and its relative phase characteristics of the groundwater level and its influencing factor time series respectively;

[0124] The identification and analysis module is used to identify the dominant controlling factors that control the scale dependence of groundwater level through the percentage of significance test area and the average wavelet coherence coefficient at different scales; and to analyze the lag relationship characteristics of the groundwater level response to the influencing factors based on the relative phase characteristics of the groundwater level and the influencing factor time series.

[0125] A device of the present invention includes a memory and a processor, wherein:

[0126] A memory for storing computer programs that can be run on the processor;

[0127] The processor is used to execute the steps of the above-mentioned analysis method for identifying the scale dependence relationship between groundwater level and influencing factors when running the computer program, and can achieve the technical effect consistent with the above-mentioned method.

[0128] Example

[0129] The data of this embodiment are from the Tuscaloosa Lake Basin, and Tuscaloosa is a city in the central and western part of Alabama, USA. The local climate is significantly affected by the Gulf of Mexico climate, bringing relatively warm and humid air, and sufficient rainfall. Precipitation and surface water are the main sources of groundwater resource recharge, so the impact of surface water and precipitation on the groundwater flow system is explored. On the other hand, precipitation characteristics include total precipitation, precipitation persistence and precipitation intensity, which show the difference in controlling groundwater level fluctuations. Therefore, the response mode of surface water, total precipitation, precipitation intensity and precipitation persistence and groundwater level scale dependence is analyzed in this embodiment. In the selection of research sites, the distance of three monitoring stations and the integrity of the data in the same period are mainly considered. In the Tuscaloosa Lake Basin, groundwater, surface water and precipitation monitoring stations are located at (33.528°, -87.548°), (33.472°, -87.599°), and (33.210°, -87.594°).

[0130] The average annual and monthly total precipitation in the Tuscaloosa Lake Basin is as follows: Figure 2 As shown in (a), the average annual precipitation during the study period was 1159 mm / year. The precipitation in 2003 and 2001 was relatively high and recorded as wet years, while the precipitation in 2000 was the least and recorded as a dry year. Figure 2(a) shows that the monthly average precipitation has significant differences, with the largest and smallest fluctuations occurring in March and November, respectively. The continuous wavelet power spectrum of daily precipitation shows a periodic feature of 563-730 days. Figure 2 (b) shows the fluctuation characteristics of the annual and monthly average precipitation intensity and the continuous wavelet power spectrum of the daily precipitation intensity. The precipitation intensity in 2001 and 2003 was relatively large, and the intensity of heavy precipitation was concentrated in June-September. In summer, the precipitation intensity showed a periodicity of 2-60 days. In the wet years (2001 and 2004), the precipitation periodicity of 180-365 days was more obvious. The annual and monthly precipitation duration has similar characteristics or trends as the precipitation intensity, and the wavelet power spectrum period is similar to the daily precipitation characteristics. Figure 3 The wavelet power spectrum of groundwater level fluctuations in Tuscaloosa, Alabama, was plotted, and the results show that groundwater level fluctuations exhibit a continuous periodicity over a year. On a small scale, the periodicity is more pronounced in the wet years of 2001 and 2003.

[0131] Figure 4 The fluctuation characteristics of precipitation characteristics including average wavelet coherence (AWC) and percentage of significant coherence area (PASC) between precipitation amount (TP), precipitation duration (DU), precipitation intensity (IN) and groundwater level fluctuations at different time scales in the Tuscaloosa Lake Basin are shown. "All" represents the global scale, 1week represents the scale of less than 1 week, 1Month represents the scale of 1 week to 1 month, 6Months represents the scale of 1 to 6 months, 12Months represents the scale of 6 to 12 months, and >12Months represents the scale of more than 12 months. On the scale of less than 6 months, precipitation has the strongest coherence with groundwater level fluctuations. On the scale of 6-12 months, the duration of precipitation is the key factor controlling the groundwater flow system. However, on the scale of more than 12 months, precipitation intensity is the best factor to explain groundwater level fluctuations. Different precipitation characteristics show large differences in the explanation of groundwater level fluctuations on the scale of more than 12 months, and the differences are not significant on the scale of less than 1 week. On a global scale, total precipitation has obvious advantages in explaining groundwater flow systems.

[0132] Figure 5 The partial wavelet coherence power spectrum between the groundwater level (GL) and precipitation and surface water in the Tuscaloosa Lake Basin is shown. After removing the influence of surface water, the periodic characteristics of significant coherence between precipitation and groundwater level are mainly reflected on the scale of 16-256 days. After removing the influence of precipitation, the periodic characteristics of significant coherence between surface water and groundwater level show obvious seasonal characteristics on the scale of less than 120 days. In addition, the groundwater level fluctuation shows anti-phase characteristics with both precipitation and surface water.

[0133] Table 1. Wavelet coherence and partial wavelet coherence results of groundwater level fluctuations with precipitation and surface water

[0134]

[0135]

[0136] Table 1 shows the partial wavelet coherence results of precipitation, surface water and groundwater level, and “-” indicates the elimination of influence. The results show that precipitation has a clear advantage in controlling the groundwater flow system on a scale greater than 120 days; however, surface water has a more obvious advantage in controlling the groundwater flow system on a scale less than 120 days. By comparing the AWC and PASC of precipitation, surface water and groundwater level, it can be seen that surface water is the best control factor for controlling the groundwater flow system at different scales.

Claims

1. An analytical method for identifying the scale dependence relationship between groundwater level and influencing factors, characterized by: The following steps are involved: S1. Select the groundwater system area to be studied, obtain the groundwater level time series and influencing factor time series at equal time intervals in the area, and standardize the time series; S2, performing outlier detection on the groundwater level time series and the influencing factor time series after the standardization processing in step S1 to determine whether there are outliers. If there are outliers, process the outliers; if there are no outliers, directly execute step S3; S3, performing continuous wavelet transform on the groundwater level time series and the influencing factor time series after the outlier detection in step S2; S4, according to the continuous wavelet transform of the groundwater level time series and the influencing factor time series obtained in step S3, respectively calculating the self-coherent wavelet transform of the groundwater level time series and the influencing factor time series; S5, according to the continuous wavelet transform of the groundwater level time series and the influencing factor time series obtained in step S3, calculate the cross wavelet transform between the groundwater level time series and the influencing factor time series, and calculate the relative phase of the groundwater level and the influencing factor time series; S6. According to the self-coherent wavelet transform and cross wavelet transform obtained in steps S4 and S5, the scale-dependent partial wavelet coherence of the groundwater level time series and the influencing factor time series is calculated, and the relative phase of the groundwater level and the influencing factor time series after eliminating the interference of the interference factor is calculated. The partial wavelet coherence is tested at a significance level of 5% using Monte Carlo simulation, and the percentage of the area passing the significance test at different scales to the total area of ​​the corresponding scale is calculated to obtain the percentage of the scale-dependent significance test area area; S7. The scale-dependent average wavelet coherence coefficient is obtained by calculating the average value of partial wavelet coherence at different scales, and the dominant control factor of groundwater level scale dependence is identified according to the percentage of the significance test area and the average wavelet coherence coefficient; S8. Analyze the lag relationship characteristics of the groundwater level response to the influencing factors based on the relative phase of the groundwater level and the influencing factor time series calculated in step S6 after eliminating the interference of the interference factors.

2. The analysis method for identifying the scale dependence relationship between groundwater level and influencing factors according to claim 1 is characterized in that: The time series is standardized in step S1 as follows: the time series value point is subtracted from the mean of the time series and the ratio is calculated with the standard deviation.

3. The analysis method for identifying the scale dependence relationship between groundwater level and influencing factors according to claim 1 is characterized in that: The outlier in step S2 refers to a value whose deviation from the mean value exceeds two standard deviations. A box plot is used to scan the standardized groundwater level time series and the influencing factor time series to see if there are outliers. For outliers, the mean values ​​before and after the outliers are used as replacements.

4. The analysis method for identifying the scale dependence relationship between groundwater level and influencing factors according to claim 1 is characterized in that: Step S3 is specifically as follows: The time series of influencing factors X = {x1, x2, ..., x N } and groundwater level time series Y = {y1,y2,…,y N }, at the i-th moment, i.e., t i =iδt and the continuous wavelet transform on scale s are: Among them, W i X (s) is the continuous wavelet transform of the time series of influencing factors, W i Y (s) is the continuous wavelet transform of the groundwater level time series, N represents the influencing factor and the length of the groundwater level time series, x j is the jth observation data point of the impact factor time series X, y j is the jth observation data point of the groundwater level time series Y, t j represents the jth moment, j=0,1,…,N-1, "*" represents the complex conjugate, Ψ is the wavelet function, is the normalization factor that converts Ψ to a value with unit energy.

5. The analytical method for identifying the scale dependence relationship between groundwater level and influencing factors according to claim 4, characterized in that: The wavelet function Ψ adopts Morlet wavelet, and its expression is: Among them, ω0 represents dimensionless frequency, η represents dimensionless time; The scale s is chosen as the exponential form of 2, and the expression is: and j =s02 jδj ,j=0,1,…,J J=δj -1 log2(Nδt / s0) Among them, s0 represents the minimum scale, J is used to define the maximum scale, and δt is the equal time interval for data sampling.

6. The analytical method for identifying the scale dependence relationship between groundwater level and influencing factors according to claim 1, characterized in that: In step S4, at time t i =iδt and scale s, the self-coherent wavelet transform of the influencing factor time series X and the groundwater level time series Y are: W i XX (s)=W i X (s)·W i X* (s) W i YY (s)=W i Y (s)·W i Y* (s) Where "*" indicates complex conjugation, W i X (s) and W i Y (s) represent the continuous wavelet transform of the influencing factor time series X and the groundwater level time series Y respectively.

7. The analysis method for identifying the scale dependence relationship between groundwater level and influencing factors according to claim 1 is characterized in that: In step S5, at time t i = iδt and the cross wavelet transform W between the time series of groundwater level and influencing factors calculated on scale s i YX (s), expressed as: W i YX (s)=W i Y (s)·W i X* (s) Where "*" indicates complex conjugation, W i X (s) and W i Y (s) represents the continuous wavelet transform of the influencing factor time series X and the groundwater level time series Y respectively; At time t i = iδt and the relative phase characteristics between the time series of groundwater level and influencing factors calculated on scale s Φ i : Φ i s tan -1 (ImW i YX (s) / ReW i YX (s)) Among them, Im and Re represent W i YX The imaginary and real parts of (s).

8. The analytical method for identifying the scale dependence relationship between groundwater level and influencing factors according to claim 1, characterized in that: In step S6, at time t i =iδt and scale s, after eliminating the interference of the interference factor Z, the partial wavelet coherence of the influencing factor time series X and the groundwater level time series Y is expressed as: in, is the wavelet coherence coefficient between the time series of influencing factors, groundwater level and interference factors, is the wavelet coherence coefficient of the time series of the influencing factors and the time series of the groundwater level, is the wavelet coherence coefficient of the groundwater level time series and the interference factor time series, is the wavelet coherence coefficient of the influencing factor time series and the interference factor time series; the calculation formulas are: Among them, "·" means excluding variable symbols, represents the smooth operator, W i YZ (s) is the cross wavelet transform of groundwater level time series Y and interference factor time series Z, W i XZ (s) is the cross wavelet transform of the influencing factor time series X and the interference factor time series Z, W i YX (s) is the cross wavelet transform of groundwater level time series Y and influencing factor time series X, W i XX (s), W i YY (s), W i ZZ (s) represents the self-coherent wavelet transform of groundwater level time series, influencing factor time series and interference factor time series, respectively, and "*" represents complex conjugate; At time t i =iδt and scale s, after excluding the influence of interference factor Z, the relative phase characteristics of the influencing factor time series X and the groundwater level time series Y are expressed as: in, Φ i Represents the relative phase of the cross wavelet transform of the influencing factor time series X and the groundwater level time series Y.

9. An analysis system for identifying the scale dependence of groundwater level and influencing factors, characterized in that: include: The data acquisition module is used to select the groundwater system area to be studied, obtain the groundwater level time series and the influencing factor time series at equal time intervals in the area, and standardize the time series; The data processing module performs outlier detection on the groundwater level time series and the influencing factor time series after the standardization processing in the data acquisition module to determine whether there are outliers. If there are outliers, the outliers are processed; if there are no outliers, the wavelet transformation module of the single time series is directly executed; The wavelet transform module of a single time series is used to perform continuous wavelet transform on the groundwater level time series and the influencing factor time series after the outlier detection in the data processing module; The wavelet transform calculation module of two time series is used to calculate the self-coherence wavelet transform of the groundwater level time series and the influencing factor time series respectively according to the continuous wavelet transform of the groundwater level time series and the influencing factor time series obtained in the wavelet transform module of a single time series; calculate the cross wavelet transform between the groundwater level time series and the influencing factor time series, and calculate the relative phase of the groundwater level and the influencing factor time series; calculate the scale-dependent partial wavelet coherence of the groundwater level time series and the influencing factor time series according to the self-coherence wavelet transform and the cross wavelet transform, and calculate the relative phase of the groundwater level and the influencing factor time series after eliminating the interference of the interference factor, use Monte Carlo simulation to perform a 5% significance level test on the partial wavelet coherence, calculate the percentage of the area passing the significance test at different scales to the total area of ​​the corresponding scale, and obtain the percentage of the scale-dependent significance test area area; The identification and analysis module is used to obtain the scale-dependent average wavelet coherence coefficient by calculating the average value of partial wavelet coherence at different scales, and to identify the dominant control factor of groundwater level scale dependence according to the percentage of the significance test area and the average wavelet coherence coefficient; According to the relative phase of the groundwater level and the influencing factor time series calculated in the wavelet transform calculation module of the two time series after excluding the interference of the interference factors, the lag relationship characteristics of the groundwater level response to the influencing factors are analyzed.

10. A device, characterized in that: comprising a memory and a processor, wherein: A memory for storing computer programs that can be run on the processor; A processor is used to execute the steps of an analysis method for identifying the scale dependence relationship between groundwater level and influencing factors as described in any one of claims 1 to 8 when running the computer program.

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