Analysis of Temporal Evolution Characteristics of Annual Precipitation in the Yellow River Delta

Precipitation is an important component in the climate system and plays a key role in water resources protection, drought and flood prevention. Innovation Trend Analysis (ITA) method, R/S method, maximum entropy spectrum analysis and wavelet analysis were used to study the evolution characteristics of the Yellow River Delta annual precipitation from 1954 to 2014. The results suggest that the precipitation series changed significantly and showed an overall downward trend, and may show an upward trend in the future, which is relatively strong. There are three-time scales of annual precipitation variation: 20-32a, 8-18a, and 3-6a. The quasi-27 year was the main oscillation period of the average annual precipitation in the Yellow River Delta, the secondary major period was 13 years, and the small-scale oscillation period was 5 years. Precipitation changed suddenly in 1980 and 2003. In contrast, there was no significant mutation point in 2002-2014.


INTRODUCTION
Precipitation is the main climate change factor that affects the distribution and function of a wetland and is one of the leading factors for the rational development of water resources and regional freshwater supply. Freshwater has become the key factor restricting the development of the Yellow River Delta. Therefore, it is necessary to study the characteristics and law of precipitation evolution, which can provide a theoretical and scientific basis for the sustainable development of the Yellow River Delta. At present, the study of precipitation evolution has become a public topic for many scholars at home and abroad. Common trend analysis methods include moving average method (Pei & Guo 2001), Mann Kendall rank correlation method (Mann 1945), cumulative horizon method (Ran et al. 2010), quadratic smoothing method (Li et al. 2018), R/S analysis method (Liu et al. 2019). Liebimnn & Marengo (2001) studied the relationship between seasonal rainfall characteristics and temperature changes in the Amazon. Galy-Lacaux et al. (2009) studied the long-term trend of precipitation chemical characteristics in rural areas of Banizoumbou. Sohoulande Djebou et al. (2014) and other scholars applied the entropy theory to study the relationship and its evolution characteristics between precipitation time and precipitation in the southwestern United States. Zhang et al. (2020) studied the historical trend of temperature, precipitation and runoff in the North China plateau basin by Mann Kendall. Zuo et al. (2019) analysed the precipitation characteristics in Tongzhou district of Beijing from 1966 to 2016 with Morlet wavelet transform. Ding et al. (2014) studied the temporal and spatial evolution of precipitation in a typical small watershed in the humid region of South China. Yang & Sun (2013) used the R/S method to analyze the runoff time series period. The above traditional methods only analysed the variation of sequence from one side of trend or mutation, but not from the whole (including cycle, trend and mutation, etc.) to judge whether the sequence has a mutation. According to the previous research results, this study adopts a new trend research method-ITA (Wu & Qian 2017, Huang et al. 2018. The ITA method has no limitations and is suitable for series-related, non-normal distribution, or short record lengths. It can identify the trend of low, medium and high value simply and clearly. Hurst coefficient can represent the variation of hydrological series as a whole from the perspective of time. R/S analysis method is usually used to analyze the time-series features and long-term memory :1 line, it indicates that the time series presents an increasing trend. On the ere is a downward trend in the time series. At the same time, precipitation nto low, medium and high parts with 40% and 60% as the boundary o the ascending sequence. ITA index D is used to characterize the trend, as ormula (1). When the range of value variation is small, but the influence of end on production and life is too large to be ignored, the index value is not clearly show the variation trend, then formula (2) can be referred to.
is method: R/S analysis method was first proposed by Hurst (Hurst et al. is & Matalas 1970, Rao & Bhattacharya 1999, a British hydrologist, and as the standard range analysis method. It was first used in hydrological recent years, with the progress of science and technology, it has been d and developed in data analysis (Hjelmfelt et al. 1988, Tarboton et al. g et al. 2005. Set time seriesError! Reference source not found.
1,2, ⋯ , . Where ≥ 1 and is an integer, when any value is taken: ruct a mean number column: lative dispersion: …(1) hod to identify and test the variation and degree of variation of hydrological s a whole, which provides basic data support for agricultural production, ce management and social and economic development of the Yellow River

LS AND METHODS recipitation Trend Analysis
: ITA method (Wu et al. 2017, Huang & Qian 2018) is an innovative is method based on the linear comparison of the scattered points 1:1 (45°) ian coordinate system. It is divided into two equal parts according to the and the sub-series are arranged in ascending order. The first sub-series is nd the second sub-series is the Y-axis. If two subsequences are equal, o trend, the points in the scatter plot fall on the 1:1 line. If these points fall 1 line, it indicates that the time series presents an increasing trend. On the re is a downward trend in the time series. At the same time, precipitation to low, medium and high parts with 40% and 60% as the boundary the ascending sequence. ITA index D is used to characterize the trend, as rmula (1). When the range of value variation is small, but the influence of nd on production and life is too large to be ignored, the index value is not early show the variation trend, then formula (2) can be referred to.
…(2) s method: R/S analysis method was first proposed by Hurst (Hurst et al. & Matalas 1970, Rao & Bhattacharya 1999, a British hydrologist, and as the standard range analysis method. It was first used in hydrological recent years, with the progress of science and technology, it has been and developed in data analysis (Hjelmfelt et al. 1988, Tarboton et al. et al. 2005. Set time seriesError! Reference source not found.
,2, ⋯ , . Where ≥ 1 and is an integer, when any value is taken: ct a mean number column: ative dispersion: R/S analysis method: R/S analysis method was first proposed by Hurst (Hurst et al. 1965, Wallis & Matalas 1970, Rao & Bhattacharya 1999, a British hydrologist, and also known as the standard range analysis method. It was first used in hydrological research. In recent years, with the progress of science and technology, it has been widely used and developed in data analysis (Hjelmfelt et al. 1988, Tarboton et al. 1988, Zhang et al. 2005. Set time series analysis method to identify and test the variation and degree of variation of hydrological time series as a whole, which provides basic data support for agricultural production, water resource management and social and economic development of the Yellow River Delta.

Method of Precipitation Trend Analysis
ITA method: ITA method (Wu et al. 2017, Huang & Qian 2018 is an innovative trend analysis method based on the linear comparison of the scattered points 1:1 (45°) on the cartesian coordinate system. It is divided into two equal parts according to the time series, and the sub-series are arranged in ascending order. The first sub-series is the X-axis, and the second sub-series is the Y-axis. If two subsequences are equal, indicating no trend, the points in the scatter plot fall on the 1:1 line. If these points fall above the 1:1 line, it indicates that the time series presents an increasing trend. On the contrary, there is a downward trend in the time series. At the same time, precipitation is divided into low, medium and high parts with 40% and 60% as the boundary according to the ascending sequence. ITA index D is used to characterize the trend, as shown in formula (1). When the range of value variation is small, but the influence of variation trend on production and life is too large to be ignored, the index value is not enough to clearly show the variation trend, then formula (2) can be referred to.
R/S analysis method: R/S analysis method was first proposed by Hurst (Hurst et al. 1965, Wallis & Matalas 1970, Rao & Bhattacharya 1999, a British hydrologist, and also known as the standard range analysis method. It was first used in hydrological research. In recent years, with the progress of science and technology, it has been widely used and developed in data analysis (Hjelmfelt et al. 1988, Tarboton et al. 1988, Zhang et al. 2005. Set time seriesError! Reference source not found. { ( )}, = 1,2, ⋯ , . Where ≥ 1 and is an integer, when any value is taken: Construct a mean number column: Cumulative dispersion: and is an integer, when any value is taken: Construct a mean number column: od to identify and test the variation and degree of variation of hydrological a whole, which provides basic data support for agricultural production, e management and social and economic development of the Yellow River

S AND METHODS recipitation Trend Analysis
ITA method (Wu et al. 2017, Huang & Qian 2018 is an innovative method based on the linear comparison of the scattered points 1:1 (45°) an coordinate system. It is divided into two equal parts according to the nd the sub-series are arranged in ascending order. The first sub-series is d the second sub-series is the Y-axis. If two subsequences are equal, trend, the points in the scatter plot fall on the 1:1 line. If these points fall line, it indicates that the time series presents an increasing trend. On the e is a downward trend in the time series. At the same time, precipitation o low, medium and high parts with 40% and 60% as the boundary the ascending sequence. ITA index D is used to characterize the trend, as ula (1). When the range of value variation is small, but the influence of d on production and life is too large to be ignored, the index value is not arly show the variation trend, then formula (2) can be referred to.
…(2) method: R/S analysis method was first proposed by Hurst (Hurst et al. & Matalas 1970, Rao & Bhattacharya 1999, a British hydrologist, and s the standard range analysis method. It was first used in hydrological ecent years, with the progress of science and technology, it has been nd developed in data analysis (Hjelmfelt et al. 1988, Tarboton et al. et al. 2005. Set time seriesError! Reference source not found.
,2, ⋯ , . Where ≥ 1 and is an integer, when any value is taken: ct a mean number column: tive dispersion: Cumulative dispersion: Construct a mean number column: Cumulative dispersion: Range sequence: Range sequence: Standard deviation: For the ratio: ( )/ ( ) = / , if / ∝ , it can be said that seque has Hurst phenomenon. H is the Hurst function. Judging the persistence sustainability of time series trends (Teverovsky et al. 1999, Huang et al. 200 Reference source not found. according to definitions. If 0 ≤ ≤ 0.5, it m the time series is an anti-persistent or ergodic time series with a stronger m variability than the random sequence, and the general trend of precipitation contrary to the past in terms of precipitation index. If = 0.5, it means tha series is a random swimming series, the observations are completely indepe the precipitation indicators change randomly in terms of precipitation index. If indicating that the time series is persistent or trend-enhancing, the overall tre change in precipitation in the future is the same as in the past

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive (Bassingthwaighte et al. 1994) is a commonly used maximum entropy analysis method. The algorithm is simple and the spectral resolution is relati The specific steps are as follows: Calculate the initial value Find 1 ( ), 1 ( ) from 1 and the following formuls Standard deviation: Range sequence: Standard deviation: For the ratio: ( )/ ( ) = / , if / ∝ , it can be said that seque has Hurst phenomenon. H is the Hurst function. Judging the persistence sustainability of time series trends (Teverovsky et al. 1999, Huang et al. 20 Reference source not found. according to definitions. If 0 ≤ ≤ 0.5, it m the time series is an anti-persistent or ergodic time series with a stronger m variability than the random sequence, and the general trend of precipitation contrary to the past in terms of precipitation index. If = 0.5, it means tha series is a random swimming series, the observations are completely indepe the precipitation indicators change randomly in terms of precipitation index. I indicating that the time series is persistent or trend-enhancing, the overall tr change in precipitation in the future is the same as in the past

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive (Bassingthwaighte et al. 1994) is a commonly used maximum entropy analysis method. The algorithm is simple and the spectral resolution is relati The specific steps are as follows: Calculate the initial value Find 1 ( ), 1 ( ) from 1 and the following formuls For the ratio: Range sequence: Standard deviation:

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursi (Bassingthwaighte et al. 1994) is a commonly used maximum ent analysis method. The algorithm is simple and the spectral resolution is The specific steps are as follows: Calculate the initial value Find 1 ( ), 1 ( ) from 1 and the following formuls , if , it can be said that sequence has Hurst phenomenon. H is the Hurst function. Judging the persistence and anti-sustainability of time series trends (Teverovsky et al. 1999, Huang et al. 2002 according to definitions. If Range sequence: Standard deviation: For the ratio: ( )/ ( ) = / , if / ∝ , it can be said that sequence{ ( )} has Hurst phenomenon. H is the Hurst function. Judging the persistence and antisustainability of time series trends (Teverovsky et al. 1999, Huang et al. 2002Error! Reference source not found. according to definitions. If 0 ≤ ≤ 0.5, it means that the time series is an anti-persistent or ergodic time series with a stronger mutation or variability than the random sequence, and the general trend of precipitation change is contrary to the past in terms of precipitation index. If = 0.5, it means that the time series is a random swimming series, the observations are completely independent and the precipitation indicators change randomly in terms of precipitation index. If 0.5<H<1, indicating that the time series is persistent or trend-enhancing, the overall trend of the change in precipitation in the future is the same as in the past

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive algorithm (Bassingthwaighte et al. 1994) is a commonly used maximum entropy spectrum analysis method. The algorithm is simple and the spectral resolution is relatively high.
The specific steps are as follows: Calculate the initial value Find 1 ( ), 1 ( ) from 1 and the following formuls , it means that the time series is an anti-persistent or ergodic time series with a stronger mutation or variability than the random sequence, and the general trend of precipitation change is contrary to the past in terms of precipitation index. If H = 0.5, it means that the time series is a random swimming series, the observations are completely independent and the precipitation indicators change randomly in terms of precipitation index. If 0.5 < H < 1, indicating that the time series is persistent or trend-enhancing, the overall trend of the change in precipitation in the future is the same as in the past

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive algorithm (Bassingthwaighte et al. 1994) is a commonly used maximum entropy spectrum analysis method. The algorithm is simple and the spectral resolution is relatively high. The specific steps are as follows: Calculate the initial value Range sequence: Standard deviation: For the ratio: ( )/ ( ) = / , if / ∝ , it can be said that seque has Hurst phenomenon. H is the Hurst function. Judging the persistence sustainability of time series trends (Teverovsky et al. 1999, Huang et al. 20 Reference source not found. according to definitions. If 0 ≤ ≤ 0.5, it m the time series is an anti-persistent or ergodic time series with a stronger m variability than the random sequence, and the general trend of precipitation contrary to the past in terms of precipitation index. If = 0.5, it means tha series is a random swimming series, the observations are completely indepe the precipitation indicators change randomly in terms of precipitation index. I indicating that the time series is persistent or trend-enhancing, the overall tr change in precipitation in the future is the same as in the past

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive (Bassingthwaighte et al. 1994) is a commonly used maximum entropy analysis method. The algorithm is simple and the spectral resolution is relati The specific steps are as follows: Calculate the initial value Find 1 ( ), 1 ( ) from 1 and the following formuls Following the recursive relationship of Levinson of = −1, + and = , when = 2, 11 , 22 , 2 2 are obtained.

…(7)
Range sequence: Standard deviation: For the ratio: ( )/ ( ) = / , if / ∝ , it can be said that sequ has Hurst phenomenon. H is the Hurst function. Judging the persistence sustainability of time series trends (Teverovsky et al. 1999, Huang et al. 20 Reference source not found. according to definitions. If 0 ≤ ≤ 0.5, it the time series is an anti-persistent or ergodic time series with a stronger m variability than the random sequence, and the general trend of precipitation contrary to the past in terms of precipitation index. If = 0.5, it means th series is a random swimming series, the observations are completely indep the precipitation indicators change randomly in terms of precipitation index.
indicating that the time series is persistent or trend-enhancing, the overall t change in precipitation in the future is the same as in the past

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive (Bassingthwaighte et al. 1994) is a commonly used maximum entropy analysis method. The algorithm is simple and the spectral resolution is relat The specific steps are as follows: Calculate the initial value Find 1 ( ), 1 ( ) from 1 and the following formuls Following the recursive relationship of Levinson of = −1, + and = , when = 2, 11 , 22 , 2 2 are obtained.

…(8)
Let p = 1, find the reflection coefficient Range sequence: Standard deviation: For the ratio: ( )/ ( ) = / , if / ∝ , it can be said that sequenc has Hurst phenomenon. H is the Hurst function. Judging the persistence an sustainability of time series trends (Teverovsky et al. 1999, Huang et al. 2002 Reference source not found. according to definitions. If 0 ≤ ≤ 0.5, it mea the time series is an anti-persistent or ergodic time series with a stronger muta variability than the random sequence, and the general trend of precipitation ch contrary to the past in terms of precipitation index. If = 0.5, it means that t series is a random swimming series, the observations are completely independ the precipitation indicators change randomly in terms of precipitation index. If 0.
indicating that the time series is persistent or trend-enhancing, the overall trend change in precipitation in the future is the same as in the past

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive alg (Bassingthwaighte et al. 1994) is a commonly used maximum entropy sp analysis method. The algorithm is simple and the spectral resolution is relativel The specific steps are as follows: Calculate the initial value Find 1 ( ), 1 ( ) from 1 and the following formuls Following the recursive relationship of Levinson of = −1, + and = , when = 2, 11 , 22 , 2 2 are obtained.

…(9)
Range sequence: Standard deviation: indicating that the time series is persistent or trend-enhancing, the overall trend of th change in precipitation in the future is the same as in the past

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive algorithm (Bassingthwaighte et al. 1994) is a commonly used maximum entropy spectrum analysis method. The algorithm is simple and the spectral resolution is relatively high The specific steps are as follows: Calculate the initial value Find 1 ( ), 1 ( ) from 1 and the following formuls Following the recursive relationship of Levinson of = −1, + −1, − and = , when = 2, 11 , 22 , 2 2 are obtained.
Find e 1 (n), b 1 (n) from K 1 and the following formuls Standard deviation:

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive (Bassingthwaighte et al. 1994) is a commonly used maximum entrop analysis method. The algorithm is simple and the spectral resolution is rel The specific steps are as follows: Calculate the initial value Find 1 ( ), 1 ( ) from 1 and the following formuls

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive (Bassingthwaighte et al. 1994) is a commonly used maximum entrop analysis method. The algorithm is simple and the spectral resolution is rela The specific steps are as follows: Calculate the initial value Find 1 ( ), 1 ( ) from 1 and the following formuls Following the recursive relationship of Levinson of = −1, + and = , when = 2, 11 , 22 , 2 2 are obtained.
… (11) Following the recursive relationship of Levinson of Range sequence: Standard deviation: For the ratio: ( )/ ( ) = / , if / ∝ , it can be said that sequence{ ( )} has Hurst phenomenon. H is the Hurst function. Judging the persistence and antisustainability of time series trends (Teverovsky et al. 1999, Huang et al. 2002Error! Reference source not found. according to definitions. If 0 ≤ ≤ 0.5, it means that the time series is an anti-persistent or ergodic time series with a stronger mutation or variability than the random sequence, and the general trend of precipitation change is contrary to the past in terms of precipitation index. If = 0.5, it means that the time series is a random swimming series, the observations are completely independent and the precipitation indicators change randomly in terms of precipitation index. If 0.5<H<1, indicating that the time series is persistent or trend-enhancing, the overall trend of the change in precipitation in the future is the same as in the past

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive algorithm (Bassingthwaighte et al. 1994) is a commonly used maximum entropy spectrum analysis method. The algorithm is simple and the spectral resolution is relatively high.
The specific steps are as follows: Calculate the initial value Find 1 ( ), 1 ( ) from 1 and the following formuls Standard deviation: For the ratio: ( )/ ( ) = / , if / ∝ , it can be said that sequence has Hurst phenomenon. H is the Hurst function. Judging the persistence an sustainability of time series trends (Teverovsky et al. 1999, Huang et al. 2002 Reference source not found. according to definitions. If 0 ≤ ≤ 0.5, it mea the time series is an anti-persistent or ergodic time series with a stronger muta variability than the random sequence, and the general trend of precipitation ch contrary to the past in terms of precipitation index. If = 0.5, it means that th series is a random swimming series, the observations are completely independe the precipitation indicators change randomly in terms of precipitation index. If 0.
indicating that the time series is persistent or trend-enhancing, the overall trend change in precipitation in the future is the same as in the past

Precipitation Cycle Test Method
Maximum entropy spectrum analysis: The Burg recursive alg (Bassingthwaighte et al. 1994) is a commonly used maximum entropy sp analysis method. The algorithm is simple and the spectral resolution is relativel The specific steps are as follows: Calculate the initial value are obtained.
Repeat the above process untilequals the required AR model order. Find all the AR model parameters a pk , and then use the following formula to find the power spectral density. t the above process until equals the required AR model order. Find all the parameters , and then use the following formula to find the power nsity. The form of wavelet generating function is: del parameters , and then use the following formula to find the power density. Where, the parameter a represents the scale of expansion and the parameter b represents the translation distance. In the Fourier analysis, T has the following relationship with parameter a: nsity. The trend of time series and the information of time and position can be obtained by wavelet analysis. To obtain valuable information, the essence of the wavelet transform is to analyze one-dimensional signals in terms of time and frequency, to analyze the time-frequency structure of the climate system in detail. The wavelet coefficients obtained from the analysis are related to time and frequency, so the transformation results can be presented in a two-dimensional image.
When analysing the precipitation, the wavelet real part contour map can reflect the periodic changes of the precipitation series at different time scales and its distribution in the time domain, to judge the future trend of precipitation at different time scales. The contour curve is the real part value of the wavelet coefficient, and the real part value of the wavelet coefficient is positive, which represents abundant precipitation. Instead, it means less precipitation.
Precipitation mutation research method: Precipitation abrupt change refers to the sharp change of precipitation from one stable state to another stable state. The test and analysis of precipitation abrupt change is an important part of studying the long-term change characteristics of precipitation. When the statistical law of the data sample changes obviously at a certain moment, the moment point is called the change point. The discrimination of the variable point is generally considered from two different aspects: one is whether the numerical characteristics of the distribution change under the premise that the observed value distribution before and after the change point remains unchanged; The other is whether the distribution function of the observed value changes before and after the change point. The observed value originally obeys a certain distribution, but changes to another distribution after the change point. The contour curve is the real part value of the wavelet coefficient, and the real part value of the wavelet coefficient is positive, which represents abundant precipitation.
Instead, it means less precipitation.

Precipitation mutation research method: Precipitation abrupt change refers to the
sharp change of precipitation from one stable state to another stable state. The test and analysis of precipitation abrupt change is an important part of studying the long-term change characteristics of precipitation. When the statistical law of the data sample changes obviously at a certain moment, the moment point is called the change point. Where, ( ), ( ) is the mean and variance of , is the normalization of . By reversed sequence data ( , −1 , ⋯ , 1 ) repeat the above process, make | | = − , = , − 1, ⋯ , 1 = 0. If the UF and UB curves intersect within the confidence interval, they are the possible abrupt transition points.

Data Sources
Taking the annual precipitation data of the Yellow River Delta from 1954 to 2018 as an example, this paper studies and analyzes the evolution characteristics of annual precipitation in the Yellow River Delta. The location of the study area is shown in Fig.   1. The data were obtained from the China meteorological data website

Data Sources
Taking the annual precipitation data of the Yellow River Delta from 1 as an example, this paper studies and analyzes the evolution characteristi precipitation in the Yellow River Delta. The location of the study area is sh 1. The data were obtained from the China meteorological da

Data Sources
Taking the annual precipitation data of the Yellow River Delta from as an example, this paper studies and analyzes the evolution characteris precipitation in the Yellow River Delta. The location of the study area is

Data Sources
Taking the annual precipitation data of the Yellow River Delta fro as an example, this paper studies and analyzes the evolution characte precipitation in the Yellow River Delta. The location of the study area 1. The data were obtained from the China meteorological (http://data.cma.gov.cn/) and the Statistical Yearbook of Shandong

is the mean and variance of
The contour curve is the real part value of the wavelet coefficient, and the real part value of the wavelet coefficient is positive, which represents abundant precipitation.

Data Sources
Taking the annual precipitation data of the Yellow River Delta from 1954 to 2018 as an example, this paper studies and analyzes the evolution characteristics of annual precipitation in the Yellow River Delta. The location of the study area is shown in Fig.   1. The data were obtained from the China meteorological data website (http://data.cma.gov.cn/) and the Statistical Yearbook of Shandong province. The is the normalization of C k . By reversed sequence data value of the wavelet coefficient is positive, which represents abundant precipitation.
Instead, it means less precipitation.
Precipitation mutation research method: Precipitation abrupt change refers to the sharp change of precipitation from one stable state to another stable state. The test and analysis of precipitation abrupt change is an important part of studying the long-term change characteristics of precipitation. When the statistical law of the data sample changes obviously at a certain moment, the moment point is called the change point.
The discrimination of the variable point is generally considered from two different aspects: one is whether the numerical characteristics of the distribution change under the premise that the observed value distribution before and after the change point Where, ( ), ( ) is the mean and variance of , is the normalization of . By reversed sequence data ( , −1 , ⋯ , 1 ) repeat the above process, make | | = − , = , − 1, ⋯ , 1 = 0. If the UF and UB curves intersect within the confidence interval, they are the possible abrupt transition points.

Data Sources
Taking the annual precipitation data of the Yellow River Delta from 1954 to 2018 as an example, this paper studies and analyzes the evolution characteristics of annual precipitation in the Yellow River Delta. The location of the study area is shown in Fig.   1. The data were obtained from the China meteorological data website (http://data.cma.gov.cn/) and the Statistical Yearbook of Shandong province. The repeat the above process, make The contour curve is the real part value of the wavelet coefficient, an value of the wavelet coefficient is positive, which represents abundan Instead, it means less precipitation.

Data Sources
Taking the annual precipitation data of the Yellow River Delta from as an example, this paper studies and analyzes the evolution characteri precipitation in the Yellow River Delta. The location of the study area is 1. The data were obtained from the China meteorological (http://data.cma.gov.cn/) and the Statistical Yearbook of Shandong . If the UF and UB curves intersect within the confidence interval, they are the possible abrupt transition points.

Data Sources
Taking the annual precipitation data of the Yellow River Delta from 1954 to 2018 as an example, this paper studies and analyzes the evolution characteristics of annual precipitation in the Yellow River Delta. The location of the study area is shown in Fig. 1. The data were obtained from the China meteorological data website (http://data.cma.gov.cn/) and the Statistical Yearbook of Shandong province. The sequence independence test was conducted by Von Neuman's Q statistics. The test results showed that under the confidence level a = 0.05, the test statistics -Q was 1.724 and was not in the critical value. Therefore, the null hypothesis was accepted and the precipitation data from 1954 to 2014 were considered as independent samples.

Evolution Characteristic Analysis
Trend analysis: (1) ITA method was used to analyze the average annual precipitation for 61 consecutive years from 1954 to 2014, and the data of the first year was omitted. The first subsequence is 1955-1984, is the X-axis; The second subsequence is 1985-2014, which is the Y-axis. Draw the precipitation trend analysis diagram, and the analysis results are shown in Fig. 2. ITA index D is calculated according to formula (2), as shown in Table 1.
As can be seen from Fig. 2, each point fell below the 1:1 line, showing a downward trend as a whole. When the precipitation is between 400mm-600mm, each point was close to the 1:1 line, with no obvious trend change. When the results showed that under the confidence level = 0.05, the test statistics -Q was 1.724 and was not in the critical value. Therefore, the null hypothesis was accepted and the precipitation data from 1954 to 2014 were considered as independent samples.  ITA index D is calculated according to formula (2), as shown in Table 1.

Evolution Characteristic Analysis
Trend analysis: (1) ITA method was used to analyze the average annual precipitation for 61 consecutive years from 1954 to 2014, and the data of the first year was omitted.
The first subsequence is 1955-1984, is the X-axis; The second subsequence is 1985-2014, which is the Y-axis. Draw the precipitation trend analysis diagram, and the analysis results are shown in Fig. 2. ITA index D is calculated according to formula (2), as shown in Table 1.   precipitation is between 650mm-800mm, the precipitation decreased significantly and gradually increased. However, at 800mm-850mm, the downward trend suddenly rebounded. When the precipitation reaches above 900mm, the downward trend became more obvious. At the same time, according to ITA index D in Table 1, the overall precipitation showed a downward trend, which gradually increased with the increase of precipitation.
(2) R/S analysis was performed on the annual average precipitation for 61 consecutive years from 1954 to 2014, and the R/S annual precipitation diagram was drawn. The results are shown in Fig. 3.

Periodic analysis:
(1) In order to clarify the implied period of the precipitation time series, different time series lengths were selected to determine the consistency and stability of the implied period of different time series lengths. Therefore the three-time series of 40, 50 and 60 years were selected. The maximum entropy power spectrum was shown in Fig. 4. (2) The Morlet continuous complex wavelet transform commonly used in the analysis of complex hydrological time series is selected to calculate the annual average precipitation of in the Yellow River, Shandong Province from 1954-2014. The wavelet coefficient transform diagram of precipitation and precipitation wavelet variance diagram are shown in Fig.  5 and Fig. 6 respectively.
Morlet continuous complex wavelet transform indicates that there were obvious interannual and chronological changes in precipitation, from top to bottom there were three-time scales of 20-32a, 8-18a, and 3-6a. The wavelet variance graph of precipitation suggests that there were three peaks of precipitation, corresponding to the time scale of 27, 13 and 5 years. Among them, the 27 year scale corresponds to the peak of wavelet variance and the period of oscillation are the strongest, which was the first main period of precipitation change, and plays a major role in the evolution of precipitation series. The second to third main periods of precipitation change were 13 and 5 years in turn. The three periods play a decisive role in the change characteristics of precipitation in the whole time domain of the Yellow River Delta, but the 27 year period is the main one Precipitation mutation test: The M-k method is used to analyze the annual average precipitation of the meteorological station in the Yellow River Delta from 1954 to 2014. The calculation results are shown in Fig. 7.
According to the M-K mutation test, UF is a standard normal distribution with a significance level of 0.05. From 1954 to 1980, the curve of UF and UB showed an upward trend. In the 1960s, the curve of UF exceeded the critical line of confidence level. It intersected in 1980 and 2003. Since 1987, the curve of UF was less than 0. From 2002 to 2014, there were many intersections between the curve of UF and UB. R/S analysis was performed on the annual average precipitation for 61 ive years from 1954 to 2014, and the R/S annual precipitation diagram was he results are shown in Fig. 3.

DISCUSSION
The precipitation trend analysis chart of 60 years is obtained by the ITA method. It indicates that the precipitation in the Yellow River Delta had a significant downward trend, and the downward trend increased gradually with the increase of precipitation. The results of R/S analysis suggest that the annual precipitation in this area showed a significant decreasing trend, which is consistent with the results of ITA analysis. In the future, the precipitation may show an increasing trend, and the trend is relatively strong.
The maximum entropy spectral analysis indicates that the optimal frequency value of the three sequence lengths was 0.24, the reciprocal was 4.167, and 5 years was chosen as the quasi period of the 61-year annual average precipitation sequence of the Yellow River Delta.
Morlet continuous complex wavelet transform indicates that there were three-time scales of precipitation: 20-32a, 8-18a, and 3-6a. From the scale of 20-32 years of analysis, the precipitation changes had a period of abundance -dryabundance -dry -abundance -dry -abundance, with strong turbulence and globality. For this large-scale alternation of abundance and dry, the precipitation in Yellow River Delta showed a significant abrupt change characteristic. Specifically, before 1963Specifically, before , 1971Specifically, before -1980Specifically, before , 1988Specifically, before -1997Specifically, before , after 2007Specifically, before , the precipitation was abundant. 1963Specifically, before -1970Specifically, before , 1981Specifically, before -1987Specifically, before , 1998Specifically, before -2007, the precipitation was poor. By 2014, the contours have not been closed, indicating that the period after 2014 is in an abundant period. At this time, the periodic variation of precipitation was localized on the large time scale and the vibration was the strongest. From the 8-18 year scale analysis, the precipitation had 13 periods of abundance and  Morlet continuous complex wavelet transform indicates that there were obvious interannual and chronological changes in precipitation, from top to bottom there were three-time scales of 20-32a, 8-18a, and 3-6a. The wavelet variance graph of precipitation suggests that there were three peaks of precipitation, corresponding to the time scale of 27, 13 and 5 years. Among them, the 27 year scale corresponds to the peak of wavelet variance and the period of oscillation are the strongest, which was the first main period of precipitation change, and plays a major role in the evolution of precipitation series. The second to third main periods of precipitation change were 13 and 5 years in turn. The three periods play a decisive role in the change characteristics of precipitation in the whole time domain of the Yellow River Delta, but the 27 year period is the main one Precipitation mutation test: The M-k method is used to analyze the annual average precipitation of the meteorological station in the Yellow River Delta from 1954 to 2014.
The calculation results are shown in Fig. 7. According to the M-K mutation test, UF is a standard normal distribution with a dry alternating. Specifically, before 1957Specifically, before , 1963Specifically, before -1965Specifically, before , 1971Specifically, before -1974Specifically, before , 1978Specifically, before -1985Specifically, before , 1995Specifically, before -1998Specifically, before , 2003Specifically, before -2006Specifically, before , after 2012Specifically, before , the precipitation was abundant. 1958Specifically, before -1962Specifically, before , 1966Specifically, before -1970Specifically, before , 1975Specifically, before -1977Specifically, before , 1986Specifically, before -1994Specifically, before , 1999Specifically, before -2002Specifically, before , 2007Specifically, before -2011, the precipitation was poor. For the change of precipitation on a smaller scale below 8 years, the shock centre in 1954-1990 is 4a. At this time, the change of the runoff period was the weakest on the small time scale. The results of Morlet continuous complex wavelet transform and R-S analysis are consistent with each other.
According to the M-K mutation test, UF is a standard normal distribution with a significance level of 0.05. Observing the UF and UB curves, the precipitation was larger during 1954-1980, showing an upward trend. During the 1960s, the UF curve exceeded the confidence level critical line and precipitation increased significantly. UF and UB curves intersected in 1980 and 2003. Influenced by the sudden change of sunspot and earth rotation period, the precipitation changed abruptly in 1980 and 2003. Since 1987, the UF curve has been less than 0, indicating a downward trend in precipitation. UF and UB curves have multiple intersections. Combined with trend analysis results, there was no significant mutation time in the annual precipitation in this region from 2002 to 2014. The reason may be that the annual natural precipitation is small. The annual natural precipitation change is more sensitive to the impact of heavy rainfall, and the relative variation of precipitation is large, resulting in poor precipitation variation and complex mutations. In addition, the impact of human activities is also an important reason for the complexity of precipitation mutations.

CONCLUSIONS
1. The analysis of ITA indicates that the precipitation in the Yellow River Delta had a significant downward trend in the past 61 years, and the downward trend gradually increased with the increase of precipitation. The R/S analysis suggests that the annual precipitation in the region had a significant downward trend in the past 61 years, which is consistent with the results of ITA analysis. However, the precipitation may show an upward trend in the future, and the trend is relatively strong.
2. The quasi-period of 61 annual precipitation in the Yellow River delta was about 5 years, which is consistent with the small scale oscillation period obtained by wavelet analysis based on maximum entropy spectral analysis and Burg recurrence theory.
3. According to the M-K mutation test, during 1954-1980, the precipitation showed an upward trend. In the 1960s, the trend is obvious. In contrast, it showed a downward trend after 1987. In 1980 and 2003, the precipitation had a mutation. In 2002-2014, there was no significant mutation time point.
4. Although this paper comprehensively evaluates the evolution characteristics of precipitation, it doesn't consider the physical mechanism of precipitation change. There are some shortcomings, which need to be further optimized.