CN114840802A - Method for distinguishing natural evolution type of hydrological and climatic process - Google Patents
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Abstract
The invention discloses a method for judging the natural evolution type of a hydrological and climatic process, which comprises the following steps: solving the time sequences of the five natural evolution types, carrying out differential processing on the time sequences, and then estimating the corresponding first-order autocorrelation coefficients and second-order autocorrelation coefficients respectively, and estimating the corresponding 95% confidence intervals respectively through a Monte Carlo test; identifying a mutant component in a time sequence to be analyzed, removing the mutant component and a seasonal component of the time sequence, and taking the residual component as a new time sequence; and after differential processing is carried out on the new time sequence, solving a first-order autocorrelation coefficient and a second-order autocorrelation coefficient of the new time sequence, comparing the first-order autocorrelation coefficient and the second-order autocorrelation coefficient with 95% confidence intervals corresponding to the various types, and determining the specific natural evolution type of the time sequence to be analyzed. The invention utilizes Monte Carlo test to determine confidence intervals of statistical characteristics of various natural evolution types, accurately distinguishes white noise, unit root process, AR (1) process and AR (2) process according to the confidence intervals, and can avoid misjudgment of AR (1) process and AR (2) process as error results of long-lasting process.
Description
Technical Field
The invention belongs to the technical field of hydrological climate science, and particularly relates to a method for judging a natural evolution type of a hydrological climate process.
Background
The method accurately reveals the evolution characteristics of the hydrological climate process and masters the future evolution situation thereof, and is a basic basis and a necessary premise for scientifically evaluating the climate change and reasonably dealing with the influence of the climate change. Under the combined action and influence of various complex factors (including random factors), the actual hydrologic climate process is very complex, and particularly under the increasing influence of global change in recent decades, the hydrologic climate process is more complex and variable.
The current study of evolution characteristics of hydroclimate processes is mainly concerned with trends and natural evolution characteristics, wherein the natural evolution characteristics are mainly concerned with short-duration and long-duration characteristics. The sequence exhibits a short-lasting property when the autocorrelation function c(s) rapidly decays to 0 or decays exponentially with increasing time interval; conversely, when the autocorrelation function c(s) decays slowly or in the form of a power function, the sequence exhibits a long persistence. Earlier, researchers proposed an AR model, a MA model, an ARMA model, and the like in succession to describe the short persistence characteristics of the time series. Hurst analyzes long-term observation data of Nile river, and finds that the autocorrelation function of the sequence presents a slow decay state, which is called Hurst phenomenon later. Since the value of the sequence having the "Hurst phenomenon" is still related for a long time, it is also called a long-persistence characteristic, a long-correlation characteristic, or a long-distance dependency characteristic, and the size of the long-persistence characteristic of the sequence is represented by a parameter d. When d >0, the sequence exhibits long-lasting properties; when d <0, the sequence exhibits an anti-persistence property; when d is 0, the sequence exhibits short persistence or no correlation. In particular, when d is 1, the time series is converted into a unit root process, which not only produces a clear randomness trend, but also a "pseudo regression" phenomenon occurs between the time series. Therefore, the judgment and the differentiation of different natural evolution types of the hydrological and climatic process are important prerequisites for accurately revealing the evolution characteristics of the hydrological and climatic process, scientifically evaluating the climatic change and reasonably dealing with the influence of the climatic change.
At present, the research on the natural evolution characteristics of the hydrological and climatic processes is mainly based on a long-lasting characteristic evaluation method. The long-lasting characteristic evaluation method is mainly divided into three categories: non-parametric, and semi-parametric estimation methods; the nonparametric estimation method mainly comprises an autocorrelation coefficient Analysis method, an R/S method, a re-standardization variance method, a Detrended Fluctuation Analysis (DFA) and the like; the parameter estimation method mainly comprises a mean value model, a fluctuation rate model, a periodogram method, a power spectral density method and a wavelet analysis method; the semi-parametric method mainly includes a GPH method, a Local Whitlle (LW) method, and a correction method based on the GPH estimator and the LW estimator. However, the above-mentioned long-lasting characteristic evaluation methods are all based on the basic premise and assumption that the hydrologic climate process has a long-lasting characteristic, and neglect whether the assumption really holds in practice. The existing research shows that the long-lasting characteristic evaluation method is easy to misdetect the short-lasting characteristic as the long-lasting characteristic, and the d value of the AR (1) process gradually tends to 0 along with the increase of the data sample size, and at the moment, the AR (1) process can be accurately detected and does not belong to the long-lasting characteristic. However, due to the limited length of the observed data, the long persistence characteristics and the short persistence characteristics cannot be accurately evaluated and distinguished, and therefore, substitute data such as tree rounds and the like are used for long persistence characteristic research. Studies have shown that substitute data underestimates the long-lasting property, whereas low-resolution substitute data overestimates the long-lasting property, i.e. substitute data cannot be used to distinguish between short-lasting and long-lasting properties of the hydroclimate process. Noise, trend and other components often exist in the actual time sequence, and the result of most long-lasting characteristic estimation methods is deviated or wrong. Compared with the long-lasting characteristic evaluation method, the DFA method can effectively filter trend components of each order in the time series, is suitable for long-lasting characteristic analysis of non-stationary time series, and is widely applied to research on long-lasting characteristics of the hydrological and climatic process because the principle is to eliminate the trend components generated by external factors in the time series and then estimate the long-lasting characteristics of the remaining components.
In recent years, researchers have proposed that the DFA method can accurately distinguish between the AR (1) process and the long-lasting process. The AR (1) process has d >0 over the entire time scale, d 0 over the large time scale, and the long-duration property of the long-duration process over both the entire time scale and the large time scale is d >0. Based on this, the DFA method can avoid that the AR (1) process is misinterpreted as a result of a long duration process. However, the method is only suitable for the AR (1) process, and the actual observation time series is difficult to be accurately described by using the AR (1) process, and higher-order autocorrelation characteristics need to be considered. However, for higher order ar (p) (p >1) processes, the DFA approach still does not accurately distinguish between short and long persistence processes. Usually the autocorrelation function is used to determine the order of the AR process, but there is a large deviation of the autocorrelation coefficients due to the influence of the determined components.
Disclosure of Invention
In view of the above disadvantages of the prior art, the present invention provides a method for determining a natural evolution type of a hydrographic climate process, so as to solve the problem that different natural evolution types of the hydrographic climate process cannot be accurately determined and distinguished due to the applicability of the long-lasting characteristic evaluation method in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention discloses a method for judging a natural evolution type of a hydrological climate process, which comprises the following steps of:
1) respectively generating white noise with the same length as a time sequence TS (t) to be analyzed, an AR (1) process, an AR (2) process, a unit root process and a long duration process, and carrying out differential processing on each generated time sequence to solve a first-order autocorrelation coefficient and a second-order autocorrelation coefficient which respectively correspond to each time sequence;
2) repeating the step 1) until the statistical characteristics of the first-order autocorrelation coefficients and the second-order autocorrelation coefficients after the time series difference processing of each type tend to be stable, and further acquiring 95% confidence intervals corresponding to the first-order autocorrelation coefficients and the second-order autocorrelation coefficients after the time series difference processing of each type;
3) identification of the mutant B in the time series TS (t) 0 Solving for the seasonal component S averaged over the years 0 Eliminating the mutant B of the time series TS (t) 0 And seasonal ingredient S 0 The remaining components are set as a new time series TS' (t) ═ TS (t) — B 0 -S 0 ；
4) After the new time sequence TS' (t) is subjected to differential processing, a first-order autocorrelation coefficient AC _ diff (1) and a second-order autocorrelation coefficient AC _ diff (2) are solved;
5) and comparing the first-order autocorrelation coefficient AC _ diff (1) and the second-order autocorrelation coefficient AC _ diff (2) with 95% confidence intervals corresponding to the first-order autocorrelation coefficient and the second-order autocorrelation coefficient obtained in the step 2) after time series difference processing of the white noise, the AR (1) process, the AR (2) process, the unit root process and the long-duration process to determine the specific natural evolution type of the time series TS (t).
Further, the step 1) specifically comprises:
11) generation of a time sequence y of white noise using the monte carlo method 1 (t)；
12) Generation of time series y of AR (1) process using first order autoregressive model 2 (t) the following:
y 2 (t)＝ρ×y 2 (t-1)+u(t)
wherein t represents a time sequence; rho is a first-order autocorrelation coefficient, and | rho | is less than 1, u (t) is a white noise sequence which is in accordance with independent and same distribution and has a mean value of 0;
13) generation of time series y of AR (2) process using second order autoregressive model 3 (t) the following:
y 3 (t)＝ρ 1 ×y 3 (t-1)+ρ 2 ×y 3 (t-2)+u(t)
in the formula, ρ 1 And ρ 2 First and second order autocorrelation coefficients, respectively, p 1 +ρ 2 <1，ρ 2 -ρ 1 <1，-1<ρ 2 <1；
14) Generating a time series y of Unit root Processes 4 (t) the following:
y 4 (t)＝y 4 (t-1)+u(t)
15) generation of long duration time series y using ARFIMA model 5 (t)。
Further, the step 5) specifically includes:
51) when AC _ diff (1) and AC _ diff (2) belong to a 95% confidence interval of white noise, the natural evolution type of the time sequence TS (t) is judged as the white noise process;
52) when AC _ diff (1) and AC _ diff (2) belong to 95% confidence intervals of the unit root process, judging the natural evolution type of the time series TS (t) as the unit root process;
53) when AC _ diff (1) and AC _ diff (2) belong to the 95% confidence interval of the AR (2) process, judging the natural evolution type of the time series TS (t) as the AR (2) process;
54) if the AC _ diff (1) and the AC _ diff (2) belong to the 95% confidence interval of the long-duration process or the AR (1) process, solving the scale index alpha of the new time series TS' (t) by using a DFA method, and further judging the natural evolution type of the TS (t).
Further, the step 54) specifically includes:
541) obtaining a double logarithmic scatter diagram (ln (F (s)) and ln (s)) of a fluctuation function F(s) and a time scale s of a new time sequence TS' (t) by using a DFA method;
542) identifying structural discontinuities B of a dual-log scatter plot 1 ；
543) Using least square method to segment B 1 <s<L/4, wherein ln (F (s)) and ln(s) are subjected to linear fitting, the linear trend is a scale index alpha, and L is the sequence length of the time sequence TS (t);
544) if α is 0.5, determining the natural evolution type of the time series ts (t) as an AR (1) process;
545) if α >0.5, the type of natural evolution of the time series ts (t) is determined to be a long-lasting process.
The invention has the beneficial effects that:
the invention utilizes Monte Carlo test to determine confidence intervals of statistical characteristics of various natural evolution types, accurately distinguishes white noise, unit root process and AR (2) process based on the confidence intervals, and can avoid the false judgment of the AR (2) process as the error result of the long continuous process;
the invention further distinguishes the AR (1) process and the long-lasting process by utilizing the DFA method, avoids the error operation of misjudging the AR (1) process into the long-lasting process by directly adopting the Local Whittle method, thereby accurately distinguishing and distinguishing five main types of natural evolution of the hydrological and climatic processes, has more reasonable and reliable distinguishing result compared with the conventional method, and can provide scientific basis for scientifically evaluating climatic change and reasonably dealing with the influence of the climatic change.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2a is a schematic diagram of an artificially generated sequence S11 of the AR (2) process;
FIG. 2b is a schematic diagram of an artificially generated sequence S12 of the AR (2) process;
FIG. 2c is a schematic diagram of an artificially generated sequence S13 of the AR (2) process;
FIG. 2d is a schematic diagram of an artificially generated sequence S14 of the AR (2) process;
FIG. 3a is a schematic diagram of an artificially generated sequence S21 of the AR (1) process;
FIG. 3b is a schematic diagram of an artificially generated sequence S22 of the AR (1) process;
FIG. 3c is a schematic diagram of a long-duration artificially generated sequence S23;
fig. 3d is a schematic diagram of a long-duration artificially generated sequence S24.
Detailed Description
In order to facilitate understanding of those skilled in the art, the present invention will be further described with reference to the following examples and drawings, which are not intended to limit the present invention.
Referring to fig. 1, the method for distinguishing the natural evolution type of the hydrological and climatic process of the invention comprises the following steps:
1) randomly setting values of all parameters, respectively generating five types of time sequences of white noise, an AR (1) process, an AR (2) process, a unit root process and a long duration process which have the same length as a TS (t) of a time sequence to be analyzed, carrying out differential processing on all generated time sequences to eliminate the influence of a randomness trend, and then solving a first-order autocorrelation coefficient and a second-order autocorrelation coefficient of all time sequences after differential processing;
wherein, the step 1) specifically comprises the following steps:
11) generation of a time sequence y of white noise using the monte carlo method 1 (t)；
12) Generation of time series y of AR (1) process using first order autoregressive model 2 (t) is as follows:
y 2 (t)＝ρ×y 2 (t-1)+u(t)
wherein t represents a time sequence; rho is a first-order autocorrelation coefficient, and | rho | is less than 1, u (t) is a white noise sequence which is in accordance with independent and same distribution and has a mean value of 0;
13) generation of time series y of AR (2) process using second order autoregressive model 3 (t) is as follows:
y 3 (t)＝ρ 1 ×y 3 (t-1)+ρ 2 ×y 3 (t-2)+u(t)
in the formula, ρ 1 And ρ 2 First and second order autocorrelation coefficients, respectively, p 1 +ρ 2 <1，ρ 2 -ρ 1 <1，-1<ρ 2 <1；
14) Generating a time series y of Unit root Processes 4 (t) the following:
y 4 (t)＝y 4 (t-1)+u(t)
15) generation of long duration time series y using ARFIMA model 5 (t)。
2) Setting different values of each parameter, repeating the step 1) to generate different time sequences of each type, and performing a Monte Carlo test (Monte-Carlo test) until the statistical characteristics (mean value and standard deviation) of the first-order autocorrelation coefficient and the second-order autocorrelation coefficient after the differential processing of the time sequences of each type tend to be stable;
3) obtaining an interval of the mean value of the first-order autocorrelation coefficients and the second-order autocorrelation coefficients after the differential processing of each type of time series +/-2 times of the standard deviation, and taking the interval as a corresponding 95% confidence interval to accurately quantify and distinguish the difference between five natural evolution types (white noise, an AR (1) process, an AR (2) process, a unit root process and a long continuous process);
4) identifying a mutation component B in a time sequence TS (t) by adopting a Mann-Kendall test method 0 Solving for the seasonal component S averaged over the years 0 Eliminating the mutant B of the time series TS (t) 0 And seasonal ingredient S 0 And the residual components are used as a new time sequence TS' (t) ═ TS (t) -B for eliminating the interference and the influence of the interference and the influence on the natural evolution type judgment 0 -S 0 ；
5) After the new time sequence TS' (t) is subjected to differential processing, a first-order autocorrelation coefficient AC _ diff (1) and a second-order autocorrelation coefficient AC _ diff (2) are solved;
6) comparing the AC _ diff (1) and the AC _ diff (2) with the white noise obtained in the step 3), the 95% confidence intervals corresponding to the first-order autocorrelation coefficient and the second-order autocorrelation coefficient after the time series difference processing of the AR (1) process, the AR (2) process, the unit root process and the long-duration process to determine the specific natural evolution type of the time series TS (t); the method specifically comprises the following steps:
61) when AC _ diff (1) and AC _ diff (2) belong to a 95% confidence interval of white noise, the natural evolution type of the time sequence TS (t) is judged as the white noise process;
62) when the AC _ diff (1) and the AC _ diff (2) belong to a 95% confidence interval of the unit root process, judging the natural evolution type of the time sequence TS (t) as the unit root process;
63) when AC _ diff (1) and AC _ diff (2) belong to the 95% confidence interval of the AR (2) process, judging the natural evolution type of the time series TS (t) as the AR (2) process;
64) and when the AC _ diff (1) and the AC _ diff (2) belong to a 95% confidence interval of a long-duration process or an AR (1) process, solving the scale index alpha of the new time sequence TS' (t) by using a DFA method, and further judging the natural evolution type of the TS (t).
Preferably, the step 64) specifically includes:
641) obtaining a double logarithmic scatter diagram (ln (F (s)) and ln (s)) of a fluctuation function F(s) and a time scale s of a new time sequence TS' (t) by using a DFA method;
642) identifying structural discontinuities B of a dual-log scatter plot 1 ；
643) Using least square method to segment B 1 <s<L/4, wherein ln (F (s)) and ln(s) are subjected to linear fitting, the linear trend is a scale index alpha, and L is the sequence length of the time sequence TS (t);
644) if α is 0.5, determining the natural evolution type of the time series ts (t) as an AR (1) process;
645) if α >0.5, the type of natural evolution of the time series ts (t) is determined to be a long-lasting process.
Example (c):
because the natural evolution type and other conditions of the artificially generated sequence are known, the artificially generated sequence is beneficial to checking the effectiveness of the method, and the natural evolution type of the actually-measured hydrological time sequence is often unknown, so that the accuracy of the result of judging the natural evolution type in the hydrological and climatic process by the method cannot be accurately judged. In order to prove the accuracy of the method for judging the natural evolution type result of the time sequence, two types of artificial sequences are generated during designing a scheme and are respectively used for verifying the effectiveness of the method for distinguishing the AR (2) process and the long-lasting process and the effectiveness of distinguishing the AR (1) process and the long-lasting process. The natural evolution of the first time series is characterized by the AR (2) process, the series length is the same, but the autoregressive coefficients of the time series are different, and are respectively denoted as S11, S12, S13 and S14 (fig. 2a, 2b, 2c, 2 d). The second class of sequences has the same sequence length but different types of natural evolution, where S21, S22 are AR (1) processes (fig. 3a, fig. 3b), and S23 and S24 are long-lasting processes (fig. 3c, fig. 3 d). And (3) respectively judging the natural evolution types of the artificially generated time sequences by using different methods, wherein the judgment results of the two types of time sequences are shown in tables 1 and 2 respectively (the judgment results of the natural evolution types of the artificially generated sequences by using different methods):
TABLE 1
TABLE 2
And (3) displaying a natural evolution type judgment result: the DFA method cannot accurately identify the AR (2) process, so that misjudgment on the time sequence natural evolution type is caused, and the AR (2) process and the long-lasting process can be accurately distinguished by the method. The Local Whittle method does not distinguish between the AR (1) process and the long duration process accurately. Compared with a Local Whittle method for directly evaluating the long-lasting characteristic of a time sequence, the method disclosed by the invention firstly carries out differential processing on the time sequence, and utilizes first-order and second-order autocorrelation coefficients of the differential time sequence to identify the AR (2) process, so that the limitation of a DFA method can be overcome, and the AR (2) process is prevented from being misjudged as the long-lasting process; secondly, distinguishing an AR (1) process from a long-lasting process by using a DFA method, further overcoming the misjudgment of a time sequence natural evolution type result caused by neglecting the limitation of a Local Whittle method, and finally obtaining an accurate time sequence natural evolution type result.
Comparing the above time series natural evolution type discrimination results, the following important conclusions can be obtained:
(1) the DFA method can identify the AR (1) process and the long duration process, but cannot accurately distinguish the AR (2) process from the long duration process;
(2) compared with the DFA method, the Local Whittle method is based on the basic assumption that the time sequence has long-lasting characteristics, and can falsely judge the AR (1) process as a long-lasting process;
(3) the method firstly identifies the AR (2) process, avoids the error that the AR (2) process is judged as the long continuous process by mistake, then further distinguishes the AR (1) process and the long continuous process by utilizing the DFA method, overcomes the limitation of other conventional methods, is more reasonable and reliable in the judgment result of the time series natural evolution type, and can provide scientific basis for revealing the evolution characteristics of the hydrological and climatic processes, scientifically evaluating the climatic changes and the like.
While the invention has been described in terms of its preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.
Claims (4)
1. A method for distinguishing the natural evolution type of a hydrological climate process is characterized by comprising the following steps:
1) respectively generating white noise with the same length as the TS (t) of the time sequence to be analyzed, an AR (1) process, an AR (2) process, a unit root process and a long continuous process, and carrying out differential processing on each generated time sequence to solve a first-order autocorrelation coefficient and a second-order autocorrelation coefficient which respectively correspond to each generated time sequence;
2) repeating the step 1) until the statistical characteristics of the first-order autocorrelation coefficients and the second-order autocorrelation coefficients after the time series difference processing of each type tend to be stable, and further acquiring 95% confidence intervals corresponding to the first-order autocorrelation coefficients and the second-order autocorrelation coefficients after the time series difference processing of each type;
3) identification of the mutant B in the time series TS (t) 0 Solving for the seasonal component S averaged over the years 0 Eliminating the mutant B of the time series TS (t) 0 And seasonal ingredient S 0 The remaining components are set as a new time series TS' (t) ═ TS (t) — B 0 -S 0 ；
4) After the new time sequence TS' (t) is subjected to differential processing, a first-order autocorrelation coefficient AC _ diff (1) and a second-order autocorrelation coefficient AC _ diff (2) are solved;
5) and comparing the first-order autocorrelation coefficient AC _ diff (1) and the second-order autocorrelation coefficient AC _ diff (2) with 95% confidence intervals corresponding to the first-order autocorrelation coefficient and the second-order autocorrelation coefficient obtained in the step 2) after the time series difference processing of each type, so as to determine the specific natural evolution type of the time series TS (t).
2. The method for distinguishing the natural evolution type of the hydroclimate process according to claim 1, wherein the step 1) specifically comprises:
11) generation of a time sequence y of white noise using the monte carlo method 1 (t)；
12) Generation of time series y of AR (1) process using first order autoregressive model 2 (t) the following:
y 2 (t)＝ρ×y 2 (t-1)+u(t)
wherein t represents a time sequence; rho is a first-order autocorrelation coefficient, and | rho | is less than 1, u (t) is a white noise sequence which is in accordance with independent and same distribution and has a mean value of 0;
13) generation of time series y of AR (2) process using second order autoregressive model 3 (t) the following:
y 3 (t)＝ρ 1 ×y 3 (t-1)+ρ 2 ×y 3 (t-2)+u(t)
in the formula, ρ 1 And ρ 2 First and second order autocorrelation coefficients, respectively, p 1 +ρ 2 <1，ρ 2 -ρ 1 <1，-1<ρ 2 <1；
14) Generating a time series y of Unit root Processes 4 (t) the following:
y 4 (t)＝y 4 (t-1)+u(t)
15) generation of long duration time series y using ARFIMA model 5 (t)。
3. The method for discriminating the type of natural evolution of a hydrographic climate process according to claim 1, wherein the step 5) comprises in particular:
51) when AC _ diff (1) and AC _ diff (2) belong to a 95% confidence interval of white noise, the natural evolution type of the time sequence TS (t) is judged as the white noise process;
52) when the AC _ diff (1) and the AC _ diff (2) belong to a 95% confidence interval of the unit root process, judging the natural evolution type of the time sequence TS (t) as the unit root process;
53) when AC _ diff (1) and AC _ diff (2) belong to the 95% confidence interval of the AR (2) process, judging the natural evolution type of the time series TS (t) as the AR (2) process;
54) if the AC _ diff (1) and the AC _ diff (2) belong to the 95% confidence interval of the long-duration process or the AR (1) process, solving the scale index alpha of the new time series TS' (t) by using a DFA method, and further judging the natural evolution type of the TS (t).
4. The method for discriminating the type of natural evolution of a hydrographic climate process according to claim 3, wherein said step 54) comprises in particular:
541) obtaining a double logarithmic scatter diagram (ln (F (s)) and ln (s)) of a fluctuation function F(s) and a time scale s of a new time sequence TS' (t) by using a DFA method;
542) identifying structural discontinuities B of a dual-log scatter plot 1 ；
543) Using least square method to segment B 1 <s<L/4, wherein ln (F (s)) and ln(s) are subjected to linear fitting, the linear trend is a scale index alpha, and L is the sequence length of the time sequence TS (t);
544) if α is 0.5, determining the natural evolution type of the time series ts (t) as an AR (1) process;
545) if α >0.5, the type of natural evolution of the time series ts (t) is determined to be a long-lasting process.
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