CN114840802B - Method for distinguishing natural evolution type of hydrologic climate process - Google Patents
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Abstract
The invention discloses a method for distinguishing the natural evolution type of a hydrologic climate process, which comprises the following steps: solving the time sequences of the five natural evolution types, performing differential processing, and estimating the corresponding first-order autocorrelation coefficients and second-order autocorrelation coefficients by a Monte Carlo test to obtain the corresponding 95% confidence intervals; identifying a mutation component in a time sequence to be analyzed, removing the mutation component and the seasonal component of the time sequence, and taking the rest component as a new time sequence; after the difference processing is carried out on the new time sequence, the first-order autocorrelation coefficient and the second-order autocorrelation coefficient of the new time sequence are solved, and compared with 95% confidence intervals corresponding to the various types, the specific natural evolution type of the time sequence to be analyzed is determined. The invention utilizes Monte Carlo test to determine the confidence interval of various natural evolution type statistical characteristics, and accurately distinguishes white noise, unit root process, AR (1) process and AR (2) process based on the confidence interval, thereby avoiding that the AR (1) process and the AR (2) process are misjudged as the error result of long-lasting process.
Description
Technical Field
The invention belongs to the technical field of hydrologic climate science, and particularly relates to a method for distinguishing the natural evolution type of a hydrologic climate process.
Background
The method accurately reveals the evolution characteristics of the hydrologic climate process, grasps the future evolution situation of the hydrologic climate process, and is a basic basis and a necessary premise for scientifically evaluating the climate change and reasonably coping with the influence of the climate change. The actual hydroclimate process is very complex, particularly in recent decades, being increasingly affected by global changes, due to the combined action and influence of various complex factors, including random factors.
The evolution characterization studies of current hydroclimate processes focus mainly on trends and natural evolution characteristics, which focus mainly on short-duration and long-duration characteristics. The sequence exhibits a short duration characteristic when the autocorrelation function C(s) decays rapidly to 0 with increasing time interval or decays as an exponential function; conversely, when the autocorrelation function C(s) decays very slowly or in a power function, the sequence exhibits a long-lasting characteristic. Earlier studies on short duration properties, researchers have sequentially proposed AR, MA, ARMA, etc. models to describe the short duration properties of time series. Hurst analyzes long-term observations of nile and finds that the autocorrelation function of the sequence exhibits a slowly decaying state, a phenomenon known as the "Hurst phenomenon" by the latter. Since the sequence value with the "Hurst phenomenon" is still related for a long time, it is also called a long-lasting property, a long-correlation property, or a long-distance dependence property, and the long-lasting property size of the sequence is represented by a parameter d. When d >0, the sequence exhibits long-lasting properties; when d <0, the sequence exhibits anti-persistence properties; when d=0, the sequence exhibits short duration properties or no correlation. In particular, when d=1, the time series is converted into a unity root process, which not only produces a significant randomness trend, but also a "pseudo regression" phenomenon between time series. Therefore, distinguishing and differentiating different natural evolution types of the hydrologic climate process is an important premise for accurately revealing the evolution characteristics of the hydrologic climate process, scientifically evaluating the climate change and reasonably coping with the influence of the climate change.
Currently, the research of natural evolution characteristics of hydrologic climate processes is mainly based on a long-lasting characteristic evaluation method. The long-lasting property evaluation methods are mainly classified into three types: a non-parameter estimation method, a parameter estimation method and a semi-parameter estimation method; the non-parameter estimation method mainly comprises an autocorrelation coefficient analysis method, an R/S method, a re-standard variance method, trend-removal fluctuation analysis (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 spectrum density method and a wavelet analysis method; semi-parametric methods mainly include GPH methods, local Whittle (LW) methods, and correction methods based on GPH estimators and LW estimators. However, the above-described long-duration property evaluation methods are based on the basic premise and assumption that the long-duration property exists in the hydroclimate process, and neglecting whether the assumption is truly true in practice. The existing research shows that the long-duration characteristic evaluation method is easy to misdetect the short-duration characteristic as the long-duration characteristic, and the d value of the AR (1) process gradually tends to 0 along with the increase of the data sample size, so that the AR (1) process can be accurately detected and does not belong to the long-duration characteristic. However, the method is limited by the length of the observed data, and the long-duration characteristic and the short-duration characteristic cannot be accurately evaluated and distinguished, so that the alternative data such as tree rounds and the like are used for the study of the long-duration characteristic. Studies have shown that surrogate data underestimates long-lasting characteristics, while low resolution surrogate data overestimates long-lasting characteristics, i.e., surrogate data cannot be used to distinguish between short-lasting characteristics and long-lasting characteristics of the hydroclimate process. In the actual time series, components such as noise and trend often exist, so that deviation or error occurs in the result of most long-duration characteristic estimation methods. Compared with the long-duration characteristic evaluation method, the DFA method can effectively filter out various orders of trend components in the time sequence, is suitable for long-duration characteristic analysis of non-stationary time sequences, and is widely applied to long-duration characteristic research of hydrologic climate processes because the principle is to eliminate trend components generated by external factors in the time sequence and then to evaluate the long-duration characteristic of the residual components.
In recent years, it has been proposed by the scholars to accurately distinguish between the AR (1) process and the long-lasting process using the DFA method. The AR (1) process has d >0 on the entire time scale, d=0 on the large time scale, and the long duration process has long duration characteristics d >0 on both the entire time scale and the large time scale. Based on this, the DFA method can avoid the AR (1) procedure from being misjudged as a result of the long duration procedure. However, this method is only suitable for the AR (1) procedure, and the actual observation time series is difficult to describe accurately by using the AR (1) procedure, and higher-order autocorrelation characteristics need to be considered. However, for higher order AR (p) (p > 1) processes, the DFA method still cannot accurately distinguish between short duration and long duration processes. Typically an autocorrelation function is used to determine the order of the AR process, but there is a large deviation in the autocorrelation coefficients due to the influence of the determined components.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method for distinguishing the natural evolution type of the hydrologic climate process, so as to solve the defect that the applicability of a long-duration characteristic evaluation method is ignored in the prior art, so that different natural evolution types of the hydrologic climate process cannot be distinguished and distinguished accurately.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the invention discloses a method for distinguishing the natural evolution type of a hydrologic climate process, which comprises the following steps:
1) Respectively generating five types of time sequences of white noise, AR (1) process, AR (2) process, unit root process and long-duration process which are the same as the length of the time sequence TS (t) to be analyzed, carrying out differential processing on each generated time sequence, and then solving the corresponding first-order autocorrelation coefficient and second-order autocorrelation coefficient;
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 obtaining 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) Identifying a mutation component B 0 in the time sequence TS (t), solving a season component S 0 which is averaged for a plurality of years, eliminating a mutation component B 0 and a season component S 0 of the time sequence TS (t), and taking the rest components as a new time sequence TS' (t) =TS (t) -B 0-S0;
4) After differential processing is carried out on the new time sequence TS '(t), a first-order autocorrelation coefficient AC_diff (1) and a second-order autocorrelation coefficient AC_diff (2) of the new time sequence TS' (t) are solved;
5) The first-order autocorrelation coefficients AC_diff (1) and the second-order autocorrelation coefficients AC_diff (2) are compared with 95% confidence intervals corresponding to the first-order autocorrelation coefficients and the second-order autocorrelation coefficients obtained in the step 2) after time series difference processing of white noise, AR (1) process, AR (2) process, unit root process and long-duration process to determine the specific natural evolution type of the time series TS (t).
Further, the step 1) specifically includes:
11 Generating a time sequence y 1 (t) of white noise using a monte carlo method;
12 A time series y 2 (t) of the AR (1) generation process using the first-order autoregressive model is as follows:
y2(t)＝ρ×y2(t-1)+u(t)
Wherein t represents a time sequence; ρ is a first-order autocorrelation coefficient, and |ρ| <1, u (t) is a white noise sequence with an average value of 0, which accords with independent same distribution;
13 A time series y 3 (t) of the AR (2) generation process using the second-order autoregressive model is as follows:
y3(t)＝ρ1×y3(t-1)+ρ2×y3(t-2)+u(t)
Wherein ρ 1 and ρ 2 are the first-order and second-order autocorrelation coefficients, respectively, ρ 1+ρ2<1,ρ2-ρ1<1,-1<ρ2 <1;
14 A time series y 4 (t) of the generation unit root process is as follows:
y4(t)＝y4(t-1)+u(t)
15 A time series y 5 (t) of long duration is generated using ARFIMA models.
Further, the step 5) specifically includes:
51 When ac_diff (1) and ac_diff (2) belong to the 95% confidence interval of white noise, then the natural evolution type of the time series TS (t) is determined as white noise process;
52 When ac_diff (1) and ac_diff (2) belong to 95% confidence intervals of the unit root process, then the natural evolution type of the time series TS (t) is determined as the unit root process;
53 When ac_diff (1) and ac_diff (2) belong to the AR (2) procedure within the 95% confidence interval, then the natural evolution type of the time series TS (t) is determined as AR (2) procedure;
54 If ac_diff (1) and ac_diff (2) belong to a 95% confidence interval of a long-duration process or an AR (1) process, solving a scale index α of a new time sequence TS' (t) by using a DFA method, and further judging a natural evolution type of the TS (t).
Further, the step 54) specifically includes:
541 Obtaining a fluctuation function F(s) of a new time sequence TS' (t) and a double-logarithmic scatter diagram (ln (F (s)), ln (s)) of a time scale s by using a DFA method;
542 Identifying a structural mutation point B 1 of the double pair number scatter plot;
543 Linear fitting of the intervals B 1 < s < L/4 ln (F (s)) and ln(s) by means of the least square method, the linear trend being the scale index α, L being the sequence length of the time sequence TS (t);
544 If α=0.5, then the natural evolution type of the time series TS (t) is determined as AR (1) procedure;
545 If α >0.5, the natural evolution type of the time series TS (t) is determined to be a long duration.
The invention has the beneficial effects that:
the invention utilizes Monte Carlo test to determine the confidence interval of various natural evolution type statistical characteristics, and accurately distinguishes white noise, unit root process and AR (2) process based on the confidence interval, thereby avoiding that the AR (2) process is misjudged as the error result of long-lasting process;
The invention further distinguishes the AR (1) process and the long-lasting process by using the DFA method, avoids misjudging the AR (1) process as the wrong operation of the long-lasting process by directly adopting the Local Whittle method, thereby accurately distinguishing and distinguishing five main types of natural evolution of the hydrologic climate process, has more reasonable and reliable distinguishing result compared with the conventional method, and can provide scientific basis for scientifically evaluating climate change and reasonably coping with the influence of the climate 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) procedure;
FIG. 3b is a schematic diagram of an artificially generated sequence S22 of the AR (1) procedure;
FIG. 3c is a schematic diagram of an artificially generated sequence S23 for a long duration process;
fig. 3d is a schematic diagram of an artificially generated sequence S24 of a long duration process.
Detailed Description
The invention will be further described with reference to examples and drawings, to which reference is made, but which are not intended to limit the scope of the invention.
Referring to fig. 1, the method for distinguishing the natural evolution type of the hydrologic climate process comprises the following steps:
1) Randomly setting the values of all parameters, respectively generating five types of time sequences of white noise, AR (1) process, AR (2) process, unit root process and long-duration process which are the same as the length of the time sequence TS (t) to be analyzed, performing differential processing on all the generated time sequences to eliminate the influence of the randomness trend, and then solving the first-order autocorrelation coefficient and the second-order autocorrelation coefficient of all the time sequences after the differential processing;
wherein, the step 1) specifically comprises:
11 Generating a time sequence y 1 (t) of white noise using a monte carlo method;
12 A time series y 2 (t) of the AR (1) generation process using the first-order autoregressive model is as follows:
y2(t)＝ρ×y2(t-1)+u(t)
Wherein t represents a time sequence; ρ is a first-order autocorrelation coefficient, and |ρ| <1, u (t) is a white noise sequence with an average value of 0, which accords with independent same distribution;
13 A time series y 3 (t) of the AR (2) generation process using the second-order autoregressive model is as follows:
y3(t)＝ρ1×y3(t-1)+ρ2×y3(t-2)+u(t)
Wherein ρ 1 and ρ 2 are the first-order and second-order autocorrelation coefficients, respectively, ρ 1+ρ2<1,ρ2-ρ1<1,-1<ρ2 <1;
14 A time series y 4 (t) of the generation unit root process is as follows:
y4(t)＝y4(t-1)+u(t)
15 A time series y 5 (t) of long duration is generated using ARFIMA models.
2) Setting different values of each parameter, repeating the step 1) to generate different time sequences of each type, and carrying out 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 time sequence difference treatment of each type tend to be stable;
3) Obtaining the interval of the mean value +/-2 times standard deviation of the first-order autocorrelation coefficient and the second-order autocorrelation coefficient after the time sequence difference processing of each type as the corresponding 95% confidence interval, and realizing the accurate quantification and differentiation of the difference between five natural evolution types (white noise, AR (1) process, AR (2) process, unit root process and long-duration process);
4) Identifying a mutation component B 0 in a time sequence TS (t) by adopting a Mann-Kendall test method, solving a seasonal component S 0 which is averaged for a plurality of years, eliminating a mutation component B 0 and a seasonal component S 0 of the time sequence TS (t) to eliminate the interference and influence of the mutation component B 0 and the seasonal component S 0 on the natural evolution type discrimination, and taking the rest component as a new time sequence TS' (t) =TS (t) -B 0-S0;
5) After differential processing is carried out on the new time sequence TS '(t), a first-order autocorrelation coefficient AC_diff (1) and a second-order autocorrelation coefficient AC_diff (2) of the new time sequence TS' (t) are solved;
6) Comparing the AC_diff (1) and the AC_diff (2) with 95% confidence intervals corresponding to the first-order autocorrelation coefficient and the second-order autocorrelation coefficient obtained in the step 3) after time sequence difference processing of white noise, an AR (1) process, an AR (2) process, a unit root process and a long-duration process to determine the specific natural evolution type of the time sequence TS (t); the method specifically comprises the following steps:
61 When ac_diff (1) and ac_diff (2) belong to the 95% confidence interval of white noise, then the natural evolution type of the time series TS (t) is determined as white noise process;
62 When ac_diff (1) and ac_diff (2) belong to 95% confidence intervals of the unit root process, then the natural evolution type of the time series TS (t) is determined as the unit root process;
63 When ac_diff (1) and ac_diff (2) belong to the AR (2) procedure within the 95% confidence interval, then the natural evolution type of the time series TS (t) is determined as AR (2) procedure;
64 If 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 a scale index alpha of a 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 fluctuation function F(s) of a new time sequence TS' (t) and a double-logarithmic scatter diagram (ln (F (s)), ln (s)) of a time scale s by using a DFA method;
642 Identifying a structural mutation point B 1 of the double pair number scatter plot;
643 Linear fitting of the intervals B 1 < s < L/4 ln (F (s)) and ln(s) by means of the least square method, the linear trend being the scale index α, L being the sequence length of the time sequence TS (t);
644 If α=0.5, then the natural evolution type of the time series TS (t) is determined as AR (1) procedure;
645 If α >0.5, the natural evolution type of the time series TS (t) is determined to be a long duration.
Examples:
Because the conditions such as the natural evolution type of the artificially generated sequence are known, the artificially generated sequence is beneficial to checking the effectiveness of the method, the natural evolution type of the actually measured hydrologic time sequence is often unknown, and the accuracy of the result of judging the natural evolution type of the hydrologic climate 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 design and are respectively used for verifying the effectiveness of the method for distinguishing the AR (2) process from the long-duration process and the effectiveness of the method for distinguishing the AR (1) process from the long-duration process. The natural evolution of the time series of the first type is characterized by the AR (2) process, the sequence length being the same, but the autoregressive coefficients of the time series being different, denoted S11, S12, S13 and S14 respectively (fig. 2a, 2b, 2c, 2 d). The second class of sequences has the same sequence length but a different nature of evolution, where S21, S22 are AR (1) processes (fig. 3a, 3 b) and S23 and S24 are long duration processes (fig. 3c, 3 d). The natural evolution types of the artificially generated time sequences are respectively judged by adopting different methods, and the judging results of the two types of time sequences are respectively shown in the table 1 and the table 2 (the judging results of the different methods on the natural evolution types of the artificially generated sequences):
TABLE 1
TABLE 2
And (3) displaying a natural evolution type discrimination result: the DFA method can not accurately identify the AR (2) process, which results in misjudgment of the natural evolution type of the time sequence, and the invention can accurately distinguish the AR (2) process from the long-lasting process. For the AR (1) procedure and the long duration procedure, the Local Whittle method cannot distinguish it accurately. Compared with a Local Whittle method for directly evaluating the long-lasting characteristic of the time sequence, the method of the invention firstly carries out differential processing on the time sequence, and utilizes the first-order and second-order autocorrelation coefficients of the differential time sequence to identify the AR (2) process, thereby overcoming the limitation of the DFA method and avoiding the AR (2) process from being misjudged as a 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.
By comparing the discrimination results of the natural evolution types of the time sequences, the following important conclusions can be obtained:
(1) The DFA method can identify the AR (1) process and the long-lasting process, but cannot accurately distinguish the AR (2) process and the long-lasting 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 misjudge the AR (1) process as a long-lasting process;
(3) The method provided by the invention has the advantages that the AR (2) process is firstly identified, the error that the AR (2) process is misjudged to be a long-lasting process is avoided, then the AR (1) process and the long-lasting process are further distinguished by using the DFA method, and the limitations of other conventional methods are overcome, so that the judgment result of the natural evolution type of the time sequence is more reasonable and reliable, and scientific basis can be provided for revealing the evolution characteristics of the hydrologic climate process, scientifically evaluating the climate change and the like.
The present invention has been described in terms of the preferred embodiments thereof, and it should be understood by those skilled in the art that various modifications can be made without departing from the principles of the invention, and such modifications should also be considered as being within the scope of the invention.
Claims (2)
1. A method for distinguishing the natural evolution type of a hydrologic climate process is characterized by comprising the following steps:
1) Respectively generating five types of time sequences of white noise, AR (1) process, AR (2) process, unit root process and long-duration process which are the same as the length of the time sequence TS (t) to be analyzed, carrying out differential processing on each generated time sequence, and then solving the corresponding first-order autocorrelation coefficient and second-order autocorrelation coefficient;
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 differential processing of each type tend to be stable, and further obtaining 95% confidence intervals corresponding to the first-order autocorrelation coefficients and the second-order autocorrelation coefficients after the time series differential processing of each type;
3) Identifying a mutation component B 0 in the time sequence TS (t), solving a season component S 0 which is averaged for a plurality of years, eliminating a mutation component B 0 and a season component S 0 of the time sequence TS (t), and taking the rest components as a new time sequence TS' (t) =TS (t) -B 0-S0;
4) After differential processing is carried out on the new time sequence TS '(t), a first-order autocorrelation coefficient AC_diff (1) and a second-order autocorrelation coefficient AC_diff (2) of the new time sequence TS' (t) are solved;
5) Comparing the first-order autocorrelation coefficients AC_diff (1) and the second-order autocorrelation coefficients AC_diff (2) with 95% confidence intervals corresponding to the first-order autocorrelation coefficients and the second-order autocorrelation coefficients obtained in the step 2) after the time series difference processing of the various types to determine the specific natural evolution type of the time series TS (t);
The step 5) specifically comprises the following steps:
51 When ac_diff (1) and ac_diff (2) belong to the 95% confidence interval of white noise, then the natural evolution type of the time series TS (t) is determined as white noise process;
52 When ac_diff (1) and ac_diff (2) belong to 95% confidence intervals of the unit root process, then the natural evolution type of the time series TS (t) is determined as the unit root process;
53 When ac_diff (1) and ac_diff (2) belong to the AR (2) procedure within the 95% confidence interval, then the natural evolution type of the time series TS (t) is determined as AR (2) procedure;
54 If 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 a scale index alpha of a new time sequence TS' (t) by using a DFA method, and further judging the natural evolution type of the TS (t);
The step 54) specifically includes:
541 Obtaining a fluctuation function F(s) of a new time sequence TS' (t) and a double-logarithmic scatter diagram (ln (F (s)), ln (s)) of a time scale s by using a DFA method;
542 Identifying a structural mutation point B 1 of the double pair number scatter plot;
543 Linear fitting of the intervals B 1 < s < L/4 ln (F (s)) and ln(s) by means of the least square method, the linear trend being the scale index α, L being the sequence length of the time sequence TS (t);
544 If α=0.5, then the natural evolution type of the time series TS (t) is determined as AR (1) procedure;
545 If α >0.5, the natural evolution type of the time series TS (t) is determined to be a long duration.
2. The method for distinguishing a natural evolution type of a hydrographic climate process according to claim 1, wherein the step 1) specifically comprises:
11 Generating a time sequence y 1 (t) of white noise using a monte carlo method;
12 A time series y 2 (t) of the AR (1) generation process using the first-order autoregressive model is as follows:
y2(t)＝ρ×y2(t-1)+u(t)
Wherein t represents a time sequence; ρ is a first-order autocorrelation coefficient, and |ρ| <1, u (t) is a white noise sequence with an average value of 0, which accords with independent same distribution;
13 A time series y 3 (t) of the AR (2) generation process using the second-order autoregressive model is as follows:
y3(t)＝ρ1×y3(t-1)+ρ2×y3(t-2)+u(t)
Wherein ρ 1 and ρ 2 are the first-order and second-order autocorrelation coefficients, respectively, ρ 1+ρ2<1,ρ2-ρ1<1,-1<ρ2 <1;
14 A time series y 4 (t) of the generation unit root process is as follows:
y4(t)＝y4(t-1)+u(t)
15 A time series y 5 (t) of long duration is generated using ARFIMA models.
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