CN111177211A - Runoff sequence change characteristic analysis method based on pole symmetric modal decomposition - Google Patents

Runoff sequence change characteristic analysis method based on pole symmetric modal decomposition Download PDF

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CN111177211A
CN111177211A CN201911263813.9A CN201911263813A CN111177211A CN 111177211 A CN111177211 A CN 111177211A CN 201911263813 A CN201911263813 A CN 201911263813A CN 111177211 A CN111177211 A CN 111177211A
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李继清
王爽
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Abstract

The invention relates to a runoff sequence change characteristic analysis method based on pole symmetric modal decomposition. In view of the fact that the runoff sequence is a nonstationary sequence with multiple time scales and nonlinear trend aliasing, the method utilizes a pole symmetric modal decomposition method which has the advantages of self-adaption, no base, large-scale circulation and nonlinear trend discrimination of the runoff sequence and does not need integral transformation advantage in time frequency analysis, researches hydrological characteristics and change rules contained in the runoff sequence, and takes the upper reaches of Yangtze river as an example to carry out application description. Firstly, the runoff sequence at the upper reaches of the Yangtze river is gradually decomposed into stable modal components and trend remainders with different time scales. Then, a fast Fourier transform periodic chart, trend remainder under the optimal self-adaptive global mean line and a frequency and amplitude time variation chart of time frequency analysis are respectively utilized to obtain periodic variation, nonlinear trend variation and mutation rules of the runoff sequence in multiple time scales, and meanwhile, the variation characteristics of the runoff sequence are comprehensively mastered from the three aspects of the period, the trend and the mutation.

Description

Runoff sequence change characteristic analysis method based on pole symmetric modal decomposition
Technical Field
The invention relates to the field of analysis of change characteristics of runoff time sequences, in particular to an analysis method of runoff sequence period, trend and mutation rules based on pole symmetric modal decomposition.
Background
The climate change superposes the continuously enhanced human activities, so that the river basin hydrologic cycle system and the underlying surface are changed to different degrees, the physical causes of the river basin hydrologic cycle and water resources are obviously changed, the runoff sequence is changed to different degrees, extreme hydrologic events such as drought, flood and the like are frequently caused, and the sustainable utilization of the water resources is influenced. Therefore, scientific knowledge of the water circulation process and the change thereof which take the runoff as a main indication is the premise of reasonably utilizing water resources, and has important value for mastering the change characteristics of the runoff in the drainage basin. In recent years, characteristics of runoff sequence variation in watersheds have been a great concern for climatologists and hydrographers. The research on the runoff sequence change characteristics can help people to know the spatial and temporal evolution rule of the watershed water resource under the change environment more deeply, and has important significance on the comprehensive development and utilization, scientific management and optimized scheduling of the water resource.
Technical scheme of prior art
The variation characteristics of runoff sequences can be analyzed from three aspects of periods, trends and mutations, and at present, around the variation characteristics of hydrological sequences, various methods such as power spectrum analysis, Morlet wavelet transform, Mann-Kendall (M-K) trend test, sliding average method, Mann-Kendall (M-K) mutation test, sliding T test, Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD) and the like have been proposed and applied by domestic and foreign hydrological researchers. The power spectrum analysis method can reveal the periodicity of the discrete data sequence and is commonly used for analyzing the periodic rule of the runoff time sequence; the Morlet wavelet transform has a multi-resolution function, and can clearly reveal the periodic variation rules of different time scales hidden in a runoff sequence; the M-K trend testing method is a nonparametric testing method, samples of which do not need to follow a certain specific distribution and are often applied to trend testing of hydrological time series; the moving average method has the advantages of simplicity and intuition, and is widely applied to hydrology; the M-K mutation detection is simple and convenient to calculate, has a wide detection range, and is often applied to mutation point detection of a hydrological time sequence; sliding T test is to measureTwo subsequences in the flow sequence are regarded as two overall samples, and the mean value of the samples is checked to have significant difference; the EMD method is a novel nonlinear and non-stable time-frequency analysis method and has the characteristics of self-adaption, no basis and signal local change based; the EEMD method is an improvement of the EMD method, not only retains all the advantages of the EMD method, but also carries out EMD decomposition by adding different white noises to the original signal for multiple times, and averages the results of the multiple decomposition to obtain the final modal component, thereby solving the problem of modal aliasing in the EMD decomposition process. The method of continuous power spectrum and the like is utilized by Zyonghua et al to analyze the periodic law of runoff in the watershed above the dense cloud reservoir. Xu et al and gulizir anival et al respectively utilize wavelet transformation to study the periodic variation law of runoff sequence on multiple time scales.
Figure BDA0002312313160000021
Et al and
Figure BDA0002312313160000022
the man-Kendall (M-K) trend test method and the comprehensive Addition Wavelet Transform (AWT), M-K trend test and sequential M-K (SMK) trend test are respectively utilized by the people to research the runoff trend change rule. Nourani et al analyzed the time scale characteristics and trend change rules of runoff sequences using discrete wavelet transform and M-K trend testing. Xie et al studied the trend law of annual runoff in the black river basin by M-K trend test. Wangfeng et al, by integrating M-K trend test, wavelet transform and other methods, studies the change rule of Changjiang river Anhui section runoff. Chenlihua and other people comprehensively study the trend change and mutation rule of rainfall runoff by methods such as sliding average, M-K inspection and the like. Yanminda et al studied the sudden change of precipitation in river basin of river inkstone by using M-K sudden change test and sliding T test. Ye et al studied the periodic variation law of the jing zhang mountain station using the EMD method. Wang et al used the EEMD method to analyze the change law of runoff.
Disadvantages of the prior art
The above methods can analyze and master the change characteristics of the runoff sequence from different sides, but have certain disadvantages: the power spectrum analysis focuses on directly carrying out single-time-scale periodic rule analysis on the runoff sequence, and the periodic change characteristics of multiple time scales in the runoff sequence evolution process are difficult to accurately reveal; the result of wavelet transform is affected by the preselected basis function, and the intrinsic law of runoff cannot be really explored; the linear trend obtained by M-K trend inspection cannot reflect the change condition of each stage of the runoff sequence, and the ascending or descending trend of the runoff sequence is partially exaggerated or reduced in the change degree; the application effect of the moving average method depends on the selection of parameters to a great extent, and certain subjectivity and arbitrariness exist; the runoff mutation rule obtained by the M-K mutation test method may have false mutation years; the sliding T test is mainly used for identifying and testing mean value variation, and possibly causes incomplete mutation results; the EMD method has the problem that different modal components may not be effectively separated according to time scale characteristics; the EEMD method has the problems that decomposed trend residuals are rough and the screening times are difficult to determine. The runoff time sequence contains various frequency components, is a typical non-linear trend and non-stationary sequence with multi-time scale aliasing, and needs to adopt a time-frequency analysis method suitable for analyzing the non-linear and non-stationary sequences.
Disclosure of Invention
Aiming at the defects in the prior art, the invention utilizes an Extreme-point Symmetric Mode Decomposition (ESMD) method which is developed in recent years and is good at searching for the change trend from a years observation sequence to research the change characteristics of the runoff sequence. The method is a data self-adaptive analysis method, does not need prior basis functions, has variable frequency and amplitude in a decomposition mode, and is suitable for analyzing nonlinear and non-stationary time sequences. The ESMD method comprises two parts of modal decomposition and time-frequency analysis. The modal decomposition utilizes internal pole symmetric interpolation to decompose according to the self-scale characteristics of data, and gradually decomposes the runoff sequence into steady modal components and trend remainders with different time scales, thereby effectively discriminating large-scale circulation and nonlinear trend of the runoff sequence. The trend remainder obtained by the decomposition is an optimal Adaptive Global Mean square (AGM) in the meaning of least square, and the Mean square accurately reflects the optimal variation trend of each stage of the time sequence. The time-frequency analysis directly generates instantaneous frequency from the discrete data by using a straight line interpolation method without integral transformation of the data, and gets rid of the constraint of mathematical theory on the process of converting the discrete signals into analytic functions.
The ESMD method is a novel nonlinear and non-stable time sequence analysis method, and can simultaneously analyze the period, the trend and the mutation rule through a modal decomposition internal pole symmetric interpolation and a time-frequency analysis linear interpolation method, so as to comprehensively research the change characteristics of the runoff sequence. Firstly, internal pole symmetric interpolation of ESMD modal decomposition is utilized, the runoff sequence is decomposed into stable modal components and trend residuals of different time scales step by step according to the time scale characteristics of data, and secondly, the periodic variation rule of multiple internal time scales in the runoff sequence and the trend variation characteristics of the runoff sequence are identified by utilizing a Fast Fourier Transform (FFT) periodogram method. And finally, intuitively reflecting the mutation rule of the runoff sequence by using a frequency and amplitude time-varying graph of ESMD time-frequency analysis.
In order to achieve the above purposes, the invention adopts the specific technical scheme that:
a runoff sequence change characteristic analysis method based on pole symmetric modal decomposition utilizes an ESMD method to research the change characteristics of a runoff sequence from three aspects of period, trend and mutation simultaneously, and comprises the following steps:
step 1: the method comprises the following steps of modal decomposition, namely, the runoff sequence is decomposed into stable modal components with different frequencies and trend remainders step by step;
step 2: grasping the general trend change of the runoff sequence by using an optimal adaptive global Average (AGM);
and step 3: mastering a multi-time scale periodic variation rule of the runoff sequence by using a Fast Fourier Transform (FFT) periodogram method;
and 4, step 4: and (3) mastering the mutation rule of the runoff sequence by using time-frequency analysis.
Step 1: the method comprises the following steps of modal decomposition, namely, the runoff sequence is decomposed into stable modal components with different frequencies and trend remainders step by step; the method specifically comprises the following calculation steps:
step 1-1: inputting a runoff sequence X (t), setting the maximum screening times K and the number l of residual poles, finding out all poles in the runoff sequence X (t), and recording as Ei(1≤i≤n)，Ei＝(zi，yi) (ii) a Connecting adjacent poles by line segments, and recording the middle point of the line segment as Fi(i is more than or equal to 1 and less than or equal to (n-1)); supplementing the left and right boundary midpoint F0，Fn；
Figure BDA0002312313160000051
Using the 1 st and 2 nd maximum points as linear interpolation, and using the 1 st and 2 nd minimum points as linear interpolation to obtain two interpolation lines respectively marked as y1(z) ═ p1z + b1And y2(z)＝p2z+b2(ii) a Then 1 st point of the data is marked as Y1。
1) If b is2≤Y1≤b1Then b is1And b2Respectively defining the boundary maximum value point and the boundary minimum value point;
2) if b is1＜Y1≤(3b1-b2) 2, then Y is1And b2Respectively defining the boundary maximum value point and the boundary minimum value point; if (3 b)1-b2)/2≤Y1＜b2Then b is1And Y1Respectively defining the boundary maximum value point and the boundary minimum value point;
3) if Y is1＞(3b1-b2) 2, then Y is1Defining as a boundary maximum point and defining a boundary minimum point by using a line drawn from the first minimum point, where the magnitude of the slope is determined by crossing the left boundary point (0, Y)1) And the first maximum point; if Y is1＜(3b1-b2) 2, then Y is1Defining as a boundary minimum point and defining the boundary or maximum point by the line drawn from the first minimum point, where the magnitude of the slope is determined by the left boundary point (0, Y)1) And the first maximum point;
step 1-2: two interpolation curves are made through the acquired (n +1) middle points, and are respectively marked as L1And L2；
L1Generated by cubic spline interpolation for the midpoint of odd ordinal number, L2The mean value curve L is calculated for the midpoint of even ordinal number generated by cubic spline interpolation*:
L*＝(L1+L2)/2 (12)
Step 1-3: construction of the sequence (X (t) -L)*) For the sequence (X (t) -L)*) Repeating steps 1-1 to 1-2 until | L*| ≦ ε or a set maximum number of screenings K is reached, where ε is a predetermined tolerance, the decomposition then yields the first empirical mode M1(t)；
Step 1-4: construction of the sequence (X (t) -M1(t)), for the sequence (X (t) -M1(t)) repeating the steps 1-1 to 1-3 to obtain M in sequence2(t)，M3(t)，…，Mq(t) until the trend remainder R (t) meets the residual pole number l preset in the step 1-1, wherein the trend remainder R (t) is generally called as 'AGM';
step 1-5: the value range of the given maximum screening times K is in an integer interval [ Kmin，Kmax]Calculating variance ratio G, recording flow sequence
Figure BDA0002312313160000061
Trend remainder
Figure BDA0002312313160000062
And σ0Relative standard deviations of X (t) -R (t) and standard deviations of runoff sequence X (t), respectively;
Figure BDA0002312313160000063
Figure BDA0002312313160000064
Figure BDA0002312313160000065
G＝σ/σ0(16)
in the formula
Figure BDA0002312313160000066
The average value of the runoff sequence X (t) is shown. Wherein, when G is minimum, the result means that the sequence of the trend-removing remainder R (t) is closest to the runoff sequence X (t), namely the decomposition result is the best.
Step 1-6: drawing a variation graph of the variance ratio along with K, and selecting the maximum screening times K corresponding to the minimum variance ratio0When K is equal to K0When R (t) is the best fit curve of the runoff sequence, at K0And (3) repeating the steps 1-5 to obtain an optimal decomposition result, wherein the optimal decomposition result is modal components with different frequencies and a trend remainder R (t).
Reconstructing modal components of different frequencies obtained by decomposition and the trend remainder R (t) to obtain a runoff sequence X (t), which can be expressed as:
Figure BDA0002312313160000071
step 2: and acquiring the general trend change of the runoff sequence by using an optimal adaptive global average linear sum (AGM): the optimal adaptive global average linear (AGM) curve is influenced by the number l of the remaining poles, and the greater l is, the greater the fluctuation of the optimal adaptive global average linear (AGM) curve is, and the higher the fitting degree with the runoff sequence is. However, excessive increase of l may reduce the number of modal components obtained by decomposition, and the obtained runoff cycle rule may not be comprehensive. Considering that the modal components obtained by the pole symmetric modal decomposition (ESMD) method reflect the variation trend under different modes, the optimal adaptive global Average (AGM) reflects the general trend of the runoff sequence, and both reflect the variation trend of the runoff sequence, so that the fitting degree between the optimal adaptive global Average (AGM) and the original runoff sequence is not required to be high. Therefore, under the condition of ensuring that the obtained periodic rule is comprehensive, the optimal adaptive global average linear sum (AGM) can accurately reflect the general trend change of the runoff sequence, the number of the residual poles is continuously adjusted, and the optimal decomposition result is found. Then, the trend change rule of different stages of the runoff sequence is mastered based on the optimal adaptive global average linear sum (AGM).
And step 3: mastering a multi-time scale periodic variation rule of the runoff sequence by using a Fast Fourier Transform (FFT) periodogram method;
and calculating power spectrums of modal components with different frequencies obtained by decomposition by a pole symmetric modal decomposition (ESMD) method by using a Fast Fourier Transform (FFT) periodogram method, and obtaining the frequency of the runoff signal according to the magnitude of the amplitude, thereby calculating the average period of each modal component.
Available power spectrum
Figure BDA0002312313160000081
Expressed as:
Figure BDA0002312313160000082
Figure BDA0002312313160000083
in the formula: h is the total number of run-off samples, oH(v) For energy-limited signals, OH(omega) is oH(v) The frequency domain value of the fourier transform, v is a random analog signal, and ω is the signal frequency of the fourier transform.
The modal components described in the above schemes are classified as internal odd-dipole point symmetry, outer envelope symmetry, or other symmetries.
And 4, step 4: the method comprises the following steps of (1) mastering the mutation rule of the runoff sequence by utilizing time-frequency analysis:
step 4-1: obtaining a time-amplitude variation curve: taking an envelope curve of an internal odd-dipole point symmetry mode component or an external envelope symmetry mode component decomposed by a pole symmetry mode decomposition (ESMD) method to obtain a time-amplitude change curve; taking an absolute value of a numerical value corresponding to the mode component, and generating an upper envelope line and a lower envelope line by interpolation from a maximum value point to obtain a time-amplitude change curve, wherein an amplitude function is marked as A (t);
step 4-2: generating a phase angle: according to the pole E obtained in the step 1-1i(i is more than or equal to 1 and less than or equal to n), and function value corresponding to the first point of the modal component
Figure BDA0002312313160000084
And instantaneous amplitude
Figure BDA0002312313160000085
Taking an inverse sine to generate a phase angle:
Figure BDA0002312313160000086
sequentially calculating t is more than or equal to 2 and less than or equal to E according to a formula (20)1The phase angle of the point of (a);
Figure BDA0002312313160000091
Figure BDA0002312313160000092
by analogy, every time two poles are added, the phase is increased by 2 pi.
Step 4-3: obtaining a time-frequency change curve: calculating instantaneous frequency in hertz (Hz) by taking the center difference quotient relative to 2 time steps Δ C according to the phase angle obtained in step 4-2:
Figure BDA0002312313160000093
and the left and right boundary values are supplemented by a linear interpolation method:
f1＝2f2-f3， (24)
fH＝2fH-1-fH-2(25)
and obtaining a time-frequency change curve according to the instantaneous frequency.
Step 4-4: obtaining a time-varying graph of frequency and amplitude: and (4) obtaining a time-varying graph of the frequency and the amplitude of each modal component according to the time-amplitude and time-frequency variation curves, and researching the mutation rule of the runoff sequence.
And 4, carrying out runoff change characteristic analysis in an all-around manner according to the general trend change of the runoff sequence obtained in the step 2, the periodic change rule obtained in the step 3 and the mutation rule obtained in the step 4.
The technical scheme of the invention has the following beneficial effects:
(1) the large-scale circulation and nonlinear trend of the runoff sequence are screened by using the internal pole symmetric interpolation of the ESMD method. Furthermore, by using an FFT periodogram method, the multi-time scale periodic variation rule of the runoff sequence can be mastered;
(2) based on the trend remainder under the optimal AGM, the trend changes of different stages of the runoff sequence can be mastered;
(3) the time-varying graph of each modal frequency and amplitude obtained by ESMD time-frequency analysis can be used for intuitively mastering the mutation rule of the runoff sequence;
(4) the ESMD method can simultaneously analyze the period, the trend and the mutation rule, obtains good effect in the runoff change rule analysis of 8 hydrological stations of the main and branch streams at the upstream of the Yangtze river, and provides basic support and decision basis for hydrological prediction and reasonable allocation of water resources. Similarly, the method can be applied to runoff analysis and water resource development and utilization of hydrological stations of other drainage basins.
The technical key points and points to be protected of the application are as follows:
the ESMD method is applied to the change characteristic analysis of the runoff sequence, the FFT periodogram method, the optimal AGM and the time-varying graph of frequency and amplitude are respectively utilized to obtain the periodic change, the nonlinear trend change and the mutation rule of the runoff sequence in multiple time scales, and the change characteristic of the runoff sequence is mastered in an all-round way.
Drawings
The invention has the following drawings:
FIG. 1 is a research framework diagram of the present invention.
Fig. 2 is a schematic diagram of the geographical location of a main tributary 8 station upstream of the Yangtze river.
FIG. 3 is a periodic variation rule of runoff sequences of 8 stations of main branches and branch streams in the upper reaches of the Yangtze river at different time scales;
(a) comparing ESMD with Morlet wavelet transform annual runoff period;
(b) the period of the runoff of the month and the day is regular.
FIG. 4 is a trend remainder of 8 station runoff sequences of a main tributary upstream of the Yangtze river obtained by ESMD decomposition;
(a) annual runoff;
(b) annual runoff;
(c) annual runoff.
FIG. 5 is a time-varying graph of modal frequency (F) and amplitude (A) of a Qingxi, Wulong standing year runoff series;
(a) a hydrological station of a Qingxi farm;
(b) wulong hydrology station.
FIG. 6 shows the mutation time of 8-year-old monthly runoff sequence of the main tributary upstream of the Yangtze river;
(a) yanshan, Gao Fang, Zhu Tuo, Bei hydrographic station;
(b) cun Ting, Wulong, Qingxi, Yichang hydrology station.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings 1 to 6.
By utilizing the advantages that the ESMD method has self-adaption and no basis, can discriminate large-scale circulation and nonlinear trend of the runoff sequence, does not need integral transformation for time-frequency analysis, comprehensively researches the change characteristics of the runoff sequence from three aspects of period, trend and mutation, and takes 8 hydrological stations of main and branch streams at the upstream of Yangtze river as an example for application description.
The Yangtze river basin (24-35 degrees in north latitude and 90-122 degrees in east longitude) is the third world basin, and spans three economic areas of east, middle and west of China, and the total area of the basin is 180 km2Accounting for 18.8 percent of the area of the Chinese territory. The main stream of Yangtze river is above Yichang city, and has a length of 4504km, and accounts for 70.4% of the total length of Yangtze river, and the area of the controlled drainage basin is 100 km2The main tributes include Yazhenjiang, Minjiang, Tuojiang, Jialin and Wujiang. Rich natural resources exist in the runoff region, and the runoff law is masteredOn the basis, the reasonable development and utilization of the water resources of the Yangtze river basin have important significance for the development of social economy. Selecting 8 hydrological stations of the main and branch streams at the upstream of the Yangtze river as research objects, wherein the hydrological stations comprise the following components from top to bottom: yangshan hydrology station, Gaoshi hydrology station, Zhutuo hydrology station, Bei hydrology station, cun Tin hydrology station, Wulong hydrology station, Qingxi hydrology station, Yichang hydrology station. The flow direction of the upstream runoff of the Yangtze river is as follows: the Jinshajiang Yangshan station and the Minjiang high-rise station converge into the Yangtze river dry flow Zhutuo station; continuing to move downstream, the Yanglingjiang Beibei beacon station converges into the Yangtze river main stream cun beach station; thereafter, the Wujiang Wulong station merges into the Changjiang LianLianXi station and finally merges into the Changjiang LianLianXichang station. The geographical position of the upstream main branch 8 station of the Yangtze river is shown in figure 2, and the basic data is shown in table 1.
TABLE 1 basic data of 8 Changjiang river upstream main and branch flows
Figure BDA0002312313160000121
Law of periodic variation
The runoff sequence is affected by linear and nonlinear factors, the change is very complex, and the fluctuation period is difficult to determine. The method can effectively separate the period and trend components of the runoff sequence based on an ESMD (electronic data mining) method, the ESMD method is utilized to carry out multi-time scale decomposition on the runoff sequence of years, months and days of 8 stations of the main tributaries at the upstream of the Yangtze river, the unstable runoff sequence is converted into stable modal components, the FFT (fast Fourier transform algorithm) periodogram method is utilized to calculate the average period of the modal components obtained by decomposing the runoff sequence of years, months and days, and the periodic variation rule of the runoff at the upstream of the Yangtze river is obtained. The periodic variation rule of the runoff sequence of 8 stations of the main tributaries at the upstream of the Yangtze river is shown in figure 3, and can be seen from figure 3: the 8-station annual runoff sequence mainly has short-period changes of 2-3 years, 5-7 years and 10-13 years and long-period changes of 15-22 years, the monthly runoff sequence mainly has short-period changes of 4-6 months, 1 year, 2-4 years, 6-9 years and 11-14 years and long-period changes of 15-23 years, and the daily runoff sequence mainly has short-period changes of 0.5-2 months, 6 months, 1 year, 2-4 years and 10-13 years, which respectively dominate the periodic characteristics of long-term changes of the upstream annual runoff sequence, monthly runoff sequence and daily runoff sequence of Yangtze river. Comparing 8 months and daily runoff sequences of the dry branches, finding that the periodic variation of 6 months and 1 year respectively exists in the dry flow Zhutuo station, the Qitan station, the Qingxi station, the Yichang station, and the daily runoff sequence, and the periodic variation of 6 months and 1 year also exists in the month and daily runoff sequence of the branch Beibei station. The high-field station and the Wulong station are slightly changed, and the Wulong station monthly runoff sequence has 4-month periodic change. The periodic variation rules of the moon and day runoff sequences of Jialing Jiangbei Bei beacon station and Yangtze river stem river hydrology stations are the same, and Minjiang Gastringji station and Wujiang Wulong station have respective periodic variation rules, which shows that the runoff relationship of Jialing Jiangbei and Yangtze river stem flow is more close. Short-period changes of 2-3 years and medium-period changes of 10-13 years exist in hydrological station year, month and day runoff sequences, and period changes of 6 months and 1 year exist in month and day runoff sequences. Meanwhile, runoff sequences of different time scales of each hydrological station have respective periodic laws. The ESMD method does not need a basis function, but decomposes the runoff sequence in a self-adaptive mode according to the data characteristics of the runoff sequence, so that the time scale and the cycle rule obtained by decomposition are not completely the same, and the characteristics and the cycle change rule of different runoff sequences of hydrological stations at the upstream of Yangtze river can be fully reflected.
In order to verify the feasibility and the effectiveness of the analysis period rule by the ESMD method, the Morlet wavelet transform is adopted to perform comparative analysis on the annual runoff sequence of the Yangtze river upstream main tributary 8 stations, which is shown in figure 3 (a). It can be seen from the figure that the ESMD method is similar to the periodic variation law obtained by Morlet wavelet transform, but has a certain difference, the wavelet transform is based on fourier transform and is bound by the aspects of wavelet basis function selection, constant multi-resolution and the like, while the ESMD method is free from the constraint of fourier transform, can be decomposed according to the time scale characteristics of the data, has strong flexibility and adaptability, and is more conducive to exploring the inherent periodic law characteristics of the runoff sequence. Meanwhile, the ESMD method has higher period resolution, and can obtain a smaller period rule of the runoff sequence.
Law of trend change
The ESMD method decomposes the runoff sequence into modal components and trend remainders of different time scales, and discriminates large-scale circulation and nonlinear trends. Furthermore, by utilizing the principle of least square, the trend remainder is automatically optimized to be the optimal AGM, and the change trend of each stage of the runoff sequence is accurately reflected. The ESMD method is utilized to decompose the annual, monthly and daily runoff sequence of 8 stations of the main branch flow in the upper reaches of the Yangtze river, and the obtained trend remainder is shown in figure 4. As can be seen in fig. 4: the runoff of the main current hydrological station from top to bottom increases gradually, and the runoff of the screen mountain station, the zhuo station is the trend of rising, and the runoff of all the other hydrological stations is the trend of descending. The runoff sequence trend of each hydrological station appears a plurality of fluctuations in year, month and day, the runoff rate of the Yichang station and the mini-beach station of the Changjiang river dry flow is in synchronous cycle change of reduction-increase, only one tributary of the Wujiang river is merged into the mini-beach station and the Yichang station, the runoff sequence fluctuation trend of the Wujiang Wulong station is small, and the influence on the runoff change of the Yichang station is small. Therefore, the runoff change of the Yichang station is mainly influenced by the runoff change of the beach station. Generally speaking, the radial flow rate at the upstream of the Yangtze river has a decreasing trend. The runoff quantity changes under the common influence of climate and human activities, the Jinsha river is located in the west of Sichuan and is slightly influenced by human activities, but the annual precipitation quantity of a watershed above the Yanshan station is increased, and the annual runoff quantity of the Yanshan station is slightly increased due to the decrease of the reference evaporation quantity. Jialing Jiang and Minjiang are located in east and middle of Sichuan, and at present, the influence of human activities in the areas is very obvious and can be an important factor for reducing runoff in high-field stations and Bei workstations. Meanwhile, the rainfall of the Jinshajiang mountain-holding station in the next year is obviously reduced, and the runoff of the hydrological station below the mountain-holding station is basically reduced. In order to compare trend change conditions of different hydrological stations, research areas are divided into 3 groups according to geographic positions, the first group is composed of a Jinsha Jiangshan station, a downstream Yangtze river Zhutuo station and two inter-area Minjiang river high-field stations, the second group is composed of the Yangtze river Zhutuo station, a downstream inch beach station and two inter-area Jialing Jianbei beaconing stations, and the third group is composed of the Yangtze river inch beach station, the downstream Qingxi field station, Yichang station and two inter-area Wujiang river Wulong-river Longjiang stations. In the first group, the runoff rate of the Yanshan station is slightly increased, the runoff of a downstream Zhutuo station is also slightly increased, and the runoff of a high station between two hydrological stations is decreased, which indicates that the runoff of the Minjiang high station is smaller than that of a main flow, and the change of the runoff of the Zhutuo station is more influenced by the Yanshan station. In the second group, the runoff of the downstream inch station is in a trend of obvious decline, and the radial flow of the north medium between the Zhuo station and the inch station is in a trend of reduction, which indicates that the change of the runoff of the Bei medium of Jialing has larger influence on the inch station than the change of the radial flow of the Zhuo station. In the third group, runoff of the Wulong station between the beach station and the Qingxi station is in a slightly descending trend, and runoff of the downstream Qingxi station and the Yichang station is in a descending trend.
In order to verify the feasibility and the effectiveness of the ESMD method for analyzing the trend change rule, the M-K trend inspection method is used for comparing and analyzing the trend change rule of the annual runoff of 8 stations of the main branch and the branch at the upstream of the Yangtze river. Meanwhile, the change trend of the runoff in the future period of the 8 stations of the main branch flow upstream of the Yangtze river is predicted by using the Hurst index. The trend of the change of the annual runoff of the 8 stations of the main tributary is compared in table 2, and the change can be seen from table 2: the M-K trend test shows that the annual runoff of the Yangshan station and the Zhutuo station is slightly increased, the annual runoff of the Wulong station is not remarkably reduced, the annual runoff of other hydrological stations is remarkably reduced, and the result is basically consistent with the result of the ESMD method analysis. However, the M-K trend test cannot discriminate large-scale circulation and trend changes, the obtained linear trend cannot reflect the change condition of each stage of the runoff sequence, and the ascending or descending trend of the runoff sequence is partially exaggerated or reduced in the change degree. The nonlinear trend obtained by the ESMD method can finely depict a specific change process, and better reflects the change trend of the runoff of each hydrological station at the upstream of the Yangtze river. Hurst index analysis shows that: except for the Zhutuo station and the Qingxi station, the Hurst indexes of the year runoff sequences of the other hydrological stations are larger than 0.5, which shows that the year runoff of the Zhutuo station and the Qingxi station has reverse persistence, and the runoff sequences of the other hydrological stations have persistence. In combination with the trend change of the annual runoff of 8 stations of the main tributaries obtained by the analysis above, the annual runoff of the Yangshan station and the Qingxi station tends to increase in a future period of time, and the annual runoff of the other hydrological stations tends to decrease.
TABLE 2 comparison of the trend of the annual runoff in 8 stations of the main tributaries upstream of the Yangtze river
Figure BDA0002312313160000161
note that a positive value of the statistic Z indicates an upward trend in the sequence, a negative value of the statistic Z indicates a downward trend in the sequence, a statistic critical value of ± 1.96 is set for the given significance level α of 0.05, a statistic 0 ≦ H <0.5 indicates that the future trend is opposite to the past, a statistic 0.5 indicates that the future trend is independent of the past, and a statistic 0.5< H ≦ 1 indicates that the future trend is consistent with the past.
Law of sudden change
Time-frequency analysis of ESMD utilizes a linear interpolation method to obtain a time-varying graph of each modal frequency and amplitude, and radial flow mutation rules of 8 stations of the main and branch streams at the upper reaches of Yangtze river are analyzed and mastered by observing low-frequency and large-amplitude or high-frequency and small-amplitude oscillation moments in the time-varying graph. Only the time-varying plot of modal frequency (F) versus amplitude (a) for the annual runoff series of the mountain-holding and tributary qing-creet stations is given, limited to space, as shown in fig. 5. As can be seen from fig. 5, the qing creel station: a Qingxi station: compared with F1 and A1, the vibration of low frequency and large amplitude occurs in 2002; in contrast to F2 and A2, high frequency, small amplitude oscillations occurred in 1991. Comparing F3 with A3, there was no obvious moment of low frequency, large amplitude or high frequency, small amplitude oscillation. The mutation of the terminal year runoff sequence of Qingxi province in 1991 and 2002 is shown. Wulong station: comparing F1 with a1, high frequency, small amplitude oscillations occurred in 1972. Comparing F2 with a2, F3 with A3, there was no obvious moment of low frequency, large amplitude or high frequency, small amplitude oscillation. The Wulong standing runoff sequence is mutated in 1972. The other hydrological stations are obtained by adopting the same judging method, and runoff sequences of the Yangshan station are mutated in 1955, 1980 and 2007; runoff sequences of high plants in 1956 and 2004 mutated; the runoff sequence of the Zhutuo station has no mutation. Mutations occurred in runoff sequences in the intertidal station in 1960, 1996 and 2001. The runoff sequence in 1972 of Wulong station was mutated. Mutations occurred in the runoff sequence in Yichang stand 1995 and 2002.
the runoff sequence is relatively complex, a certain error may exist in identification methods of different variation points, in order to avoid identification errors caused by a single method, a M-K mutation test method and a sliding T test are combined, meanwhile, the significance water α is 0.05, the significance of year and month runoff sequence mutation years is tested by using a run test, the significance mutation years obtained after the test are shown in figure 6, as can be seen from figure 6, year runoff sequences are compared, a Yangshan station and an Yichang station have mutation in 1994, a Gaoshi station and a Yochang station have mutation in 1993, a Titan station and a Yichang station have mutation in 1958, 1961 and 1963, month runoff sequences are compared, the high field station and a Zhutuo station have more same mutation moments, the other hydrological stations have the same mutation laws, if the Jutuo station and the Yongchang station have the same mutation laws in 1975, the high frequency stations and Qingchang stations have the same mutation laws, the high frequency and the high frequency mutation laws of the Changtian stations have the same mutation laws, the same change of the season, the high frequency and the change of the river rungs, the high frequency change of the river rungs, the year, the high frequency change of the river rungs of the high frequency change of the river, the high frequency change of the river station, the high frequency change of the river station, the high frequency change.
The method does not need a basis function, self-adaptively decomposes according to the self-scale characteristics of data, corresponding time-frequency analysis does not need to convert discrete signals into an analytic function, the constraint of mathematical derivation is eliminated, and compared with M-K mutation detection to obtain more false mutation years (such as mutation in the years of runoff in Yangshan stations, 1954, and 1969 in the Titan station) and sliding T detection which possibly causes incomplete mutation results (such as the years of runoff in Yangshan stations and Wulong stations without mutation) the mutation rule obtained by the ESMD method is relatively accurate and reliable.
Runoff sequence change characteristics
The ESMD method is adopted to research the runoff sequence change characteristics of 8 stations of the main tributaries in the upstream of the Yangtze river from three aspects of period, trend and mutation. In summary, it is possible to obtain: the short-period change rule of 8 stations of the main branch in the upper reaches of the Yangtze river mainly exists for 1 year, 2-3 years, 6-7 years, 9-10 years, 11 years and 14 years, and the long-period change rule of 15-17 years and 22-23 years. Except that runoff of the Yanshan station and the Zhutuo station is changed in an increasing trend, runoff of other hydrological stations is changed in a decreasing trend. The climate change is superimposed with violent human activities, so that the mutation time of 8 stations of the main tributary upstream of the Yangtze river is different, but the same mutation time also exists in each hydrological station.
Those not described in detail in this specification are within the skill of the art.

Claims (6)

1. A runoff sequence change characteristic analysis method based on pole symmetric modal decomposition is characterized in that a pole symmetric modal decomposition method is used for researching change characteristics of a runoff sequence from three aspects of period, trend and mutation, and comprises the following steps:
step 1: performing modal decomposition, namely decomposing the runoff sequence into modal components with different frequencies and trend remainders step by step;
step 2: the optimal adaptive global average line is utilized to master the general trend change of the runoff sequence;
and step 3: grasping the multi-time scale periodic variation rule of the runoff sequence by using a fast Fourier transform periodogram method;
and 4, step 4: and (3) mastering the mutation rule of the runoff sequence by using time-frequency analysis.
2. The runoff sequence variation feature analysis method based on pole symmetry modal decomposition of claim 1, wherein the step 1: performing modal decomposition, namely decomposing the runoff sequence into modal components with different frequencies and trend remainders step by step; the method specifically comprises the following calculation steps:
step 1-1: inputting a runoff sequence X (t), setting the maximum screening times K and the number l of residual poles, and finding out the runoff sequence XAll poles in (t), denoted Ei(1≤i≤n)，Ei＝(zi，yi) (ii) a Connecting adjacent poles by line segments, and recording the middle point of the line segment as Fi(i is more than or equal to 1 and less than or equal to (n-1)); supplementing the left and right boundary midpoint F0，Fn；
Figure FDA0002312313150000011
Using the 1 st and 2 nd maximum value points as linear interpolation, and using the 1 st and 2 nd minimum value points as linear interpolation to obtain two interpolation lines respectively marked as y1(z)＝p1z+b1And y2(z) ═ p2z+b2(ii) a Then 1 st point of the data is marked as Y1；
1) If b is2≤Y1≤b1Then b is1And b2Respectively defining the boundary maximum value point and the boundary minimum value point;
2) if b is1＜Y1≤(3b1-b2) 2, then Y is1And b2Respectively defining the boundary maximum value point and the boundary minimum value point; if (3 b)1-b2)/2≤Y1＜b2Then b is1And Y1Respectively defining the boundary maximum value point and the boundary minimum value point;
3) if Y is1＞(3b1-b2) 2, then Y is1Defining as a boundary maximum point and defining a boundary minimum point by using a line drawn from the first minimum point, where the magnitude of the slope is determined by crossing the left boundary point (0, Y)1) And the first maximum point; if Y is1＜(3b1-b2) 2, then Y is1Defining as a boundary minimum point, and defining a boundary maximum point by using a straight line drawn from the first minimum point, where the slope is determined by crossing the left boundary point (0, Y)1) And the first maximum point;
step 1-2: two interpolation curves are made through the acquired (n +1) middle points, and are respectively marked as L1And L2；
L1Generated by cubic spline interpolation for the midpoint of odd ordinal number, L2The mean value curve L is calculated for the midpoint of even ordinal number generated by cubic spline interpolation*:
L*＝(L1+L2)/2 (12)
Step 1-3: construction of the sequence (X (t) -L)*) For the sequence (X (t) -L)*) Repeating steps 1-1 to 1-2 until | L*| ≦ ε or a set maximum number of screening times K, where ε is a predetermined tolerance, and the decomposition yields a first empirical mode M1(t)；
Step 1-4: construction of the sequence (X (t) -M1(t)), for the sequence (X (t) -M1(t)) repeating the steps 1-1 to 1-3 to obtain M in sequence2(t)，M3(t)，…，Mq(t) until the trend remainder R (t) meets the number l of the residual poles preset in the step 1-1, wherein the trend remainder R (t) is called as an optimal adaptive global average line;
step 1-5: the value range of the given maximum screening times K is in an integer interval [ Kmin，Kmax]Calculating variance ratio G, recording flow sequence
Figure FDA0002312313150000031
Trend remainder
Figure FDA0002312313150000032
Sigma and sigma0Relative standard deviations of X (t) -R (t) and standard deviations of runoff sequence X (t), respectively;
Figure FDA0002312313150000033
Figure FDA0002312313150000034
Figure FDA0002312313150000035
G＝σ/σ0(16)
in the formula:
Figure FDA0002312313150000037
is the average value of the runoff sequence X (t); when G is minimum, the sequence of the trend residue removing R (t) is closest to the runoff sequence X (t), and the decomposition result is the best;
step 1-6: drawing a variation graph of the variance ratio along with K, and selecting the maximum screening times K corresponding to the minimum variance ratio0When K is equal to K0When R (t) is the best fit curve of the runoff sequence, at K0Repeating the steps 1-1 to 1-5 to obtain an optimal decomposition result, wherein the optimal decomposition result is modal components with different frequencies and a trend remainder R (t);
reconstructing modal components of different frequencies obtained by decomposition and a trend remainder R (t) to obtain a runoff sequence X (t), wherein the runoff sequence X (t) is represented as:
Figure FDA0002312313150000036
3. the runoff sequence variation feature analysis method based on pole symmetry modal decomposition of claim 2, wherein the step 2: the method comprises the following steps of obtaining the general trend change of a runoff sequence by using an optimal self-adaptive global average line, and specifically comprising the following steps:
the optimal adaptive global mean line curve is influenced by the number l of the remaining poles, and the greater l is, the greater the fluctuation of the optimal adaptive global mean line curve is, and the higher the fitting degree with the runoff sequence is; under the condition of ensuring that the obtained periodic rule is comprehensive, the optimal adaptive global average line can accurately reflect the general trend change of the runoff sequence, the number of the residual poles is continuously adjusted, and the optimal decomposition result is found; and then, mastering the trend change rule of different stages of the runoff sequence based on the optimal self-adaptive global average line.
4. The runoff sequence variation feature analysis method based on pole symmetry modal decomposition of claim 1, wherein step 3: grasping a multi-time scale periodic variation rule of a runoff sequence by using a fast Fourier transform periodogram method, and specifically comprising the following steps;
calculating power spectrums of modal components with different frequencies obtained by pole symmetric modal decomposition by using a fast Fourier transform periodogram method, and obtaining the frequency of a runoff signal according to the magnitude of the amplitude, thereby calculating the average period of each modal component;
available power spectrum
Figure FDA0002312313150000041
Expressed as:
Figure FDA0002312313150000042
Figure FDA0002312313150000043
in the formula: h is the total number of run-off samples, oH(v) For energy-limited signals, OH(omega) is oH(v) The frequency domain value of the fourier transform, v is a random analog signal, and ω is the signal frequency of the fourier transform.
5. The method for radial flow sequence variation characterization according to claim 4 and based on pole symmetric modal decomposition, wherein the modal components are classified as internal odd-dipole point symmetry, outer envelope symmetry or other symmetry.
6. The runoff sequence variation feature analysis method based on pole symmetry modal decomposition of claim 5, wherein step 4: the method comprises the following steps of (1) mastering the mutation rule of the runoff sequence by utilizing time-frequency analysis:
step 4-1: obtaining a time-amplitude variation curve: taking an envelope curve of an internal odd-dipole point symmetric mode component or an external envelope symmetric mode component decomposed by a pole symmetric mode decomposition method to obtain a time-amplitude change curve; taking an absolute value of a numerical value corresponding to the mode component, and generating an upper envelope line and a lower envelope line by interpolation from a maximum value point to obtain a time-amplitude change curve, wherein an amplitude function is marked as A (t);
step 4-2: generating a phase angle: according to the pole E obtained in the step 1-1i(i is more than or equal to 1 and less than or equal to n), and function value corresponding to the first point of the modal component
Figure FDA0002312313150000051
And instantaneous amplitude
Figure FDA0002312313150000052
Taking an inverse sine to generate a phase angle:
Figure FDA0002312313150000053
sequentially calculating t is more than or equal to 2 and less than or equal to E according to a formula (20)1The phase angle of the point of (a);
Figure FDA0002312313150000054
Figure FDA0002312313150000055
by analogy, every time two poles are added, the phase is increased by 2 pi;
step 4-3: obtaining a time-frequency change curve: calculating instantaneous frequency in hertz from the phase angle obtained in step 4-2 by taking the central difference quotient with respect to 2 time steps ac:
Figure FDA0002312313150000056
and the left and right boundary values are supplemented by a linear interpolation method:
f1＝2f2-f3， (24)
fH＝2fH-1-fH-2(25)
obtaining a time-frequency change curve according to the instantaneous frequency;
step 4-4: obtaining a time-varying graph of frequency and amplitude: and (4) obtaining a time-varying graph of the frequency and the amplitude of each modal component according to the time-amplitude and time-frequency variation curves, and researching the mutation rule of the runoff sequence.
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