Investigation of the trend and cycles using the long-term records of annual precipitation in Shandong, China

Precipitation is one of the most important hydrologic elements for the climate and hydro-meteorology analysis, which form the basis of hydrologic modeling and watershed planning. The trend and cycle characteristics of regional precipitation affect the regional water availability and future prediction. It is found that the observed precipitation trends are largely influenced by the study period (Hannaford et al. 2013) and some periodic events may affect the trend of precipitation series (Li et al. 2013). Therefore, proper statistical analysis of the impact of the study period and periodic events on precipitation trends and the selection of representative precipitation record length for its further characteristic analysis remain a crucial but unclear issue.

In the past decades, precipitation trend and cycle analysis has attracted more attention globally as the changing climate has caused increasing extreme floods and droughts. Taking Africa as an example, an insignificantly decreasing trend of mean annual precipitation from 1930 to 2014 was observed in the Horn of Africa (Ghebrezgabher et al. 2016). Most of the stations exhibit statistically insignificant negative trends in the annual analysis from 1940 to 2015 in Benin of West Africa (Ahokpossi 2018). In North America, the precipitation in California, USA shows a notable and statewide downward trend in fall and an upward trend in winter based on the precipitation data of 249 stations from 1950 to 2009 (Sayemuzzaman & Jha 2014). Observed precipitation trends over South America are less spatially coherent with both negative and positive values across the continent during 1975–2004 (de Barros Soares et al. 2017). In Oceania, the records showed a notable downward trend of rainfall in southeast Australia and an upward trend in northwest Australia since 1950 (Dey et al. 2019). In Europe, an increase in precipitation has been identified in many places, such as Slovakia (1981–2013) (Zeleňáková et al. 2017) and western Scotland (1961–2000) (Afzal et al. 2015), whereas a decrease in precipitation has been identified in southern Italy (1918–1999) (Longobardi & Villani 2010). No global trend was found, except for March, with high spatial and temporal variability of the eastern Mediterranean fringe of the Iberian Peninsula (Gonzalez-Hidalgo et al. 2009).

Numerous studies on the precipitation trend and cycle analysis were also found in Asia. For example, the precipitation concentration index (CI) and the precipitation concentration period were used to research the characteristic of precipitation in Xinjiang, China, based on 50 weather stations from 1961 to 2008, and the significant cycles of precipitation CI were concentrated on a 2- to 5-year band (Li et al. 2011). Spatial and temporal patterns of rainfall time series from 14 evenly distributed stations in Ho Chi Minh City, Vietnam, were analyzed for the period 1980–2016, and the outcomes showed high domination of positive trends in the annual and seasonal precipitation (Phuong et al. 2019). A predominant downward trend in the annual precipitation of Xi'an, northwest China, during 1951–2018 was detected and the precipitation had a significant periodic change, with the time scale of cycles of 6, 13, 19, and 27 years (Han et al. 2021). Overall, most of these previous studies around the world focus on only precipitation trends or only cycles in the study area and perform the analyses separately.

This study focuses on Shandong Province, China, which is in the first place in northern China in terms of the population and gross domestic product (GDP). The regional development is largely dependent on precipitation-induced water resource availability. Much research has been conducted to analyze the precipitation trend and cycle in Shandong Province (Zhai et al. 2005; Liu et al. 2017; Chen et al. 2020; Niu et al. 2020), but their results on the trend of precipitation are not consistent, with both an upward trend and a downward trend. Xu et al. (2007) adopted the Mann–Kendall (M–K) method and concluded that the average annual precipitation in Shandong during 1958–1998 showed a declining trend, and the largest decrease was observed on the southeast coast. Zuo et al. (2018) calculated the standardized precipitation evapotranspiration index (SPEI) of Shandong Province during 1960–2012 and detected an insignificant downward trend in annual precipitation at most stations. Li et al. (2021) analyzed the trend of precipitation data in Jinan of Shandong Province from 1972 to 2016 and found that the annual precipitation increased at a rate of 8.23 mm/10 years. It is found that the precipitation record lengths around 60 years or shorter were generally used in the previous literature on Shandong Province, China; however, their concluding precipitation trends may be different. This might be due to the sensitivity of linear, monotonic trends to periodical oscillations or other patterns; it is thus worth noting that the proper selection of the representative period of records affects trends obtained from the statistical precipitation analysis.

The main analysis methods of precipitation trends include parametric and non-parametric test methods. Linear trend analysis is one of the commonly used parametric test methods (Hu et al. 2017); the commonly used non-parametric test methods include the M–K trend test (Sayemuzzaman & Jha 2014), Sen's slope estimator test (Gajbhiye et al. 2016), innovative trend analysis (ITA) (Alifujiang et al. 2020), and ensemble empirical mode decomposition (EEMD) (Gao & Shi 2016). The analysis methods of the precipitation cycle mainly consist of Fourier analysis (Barmet et al. 2009) and wavelet analysis (Liu et al. 2016). Multi-temporal trend analysis is widely used to test moving window standard trends in time series that are often sensitive to such quasi-periodic oscillations or other modes by linear monotonic trends (Wilby 2006; Petrow & Merz 2009; Hannaford et al. 2013). But such multi-temporal trend testing is mostly focused on runoff time series, such as flood, annual, or seasonal runoff, and has yet to be adopted at a large scale in north China.

This study aims to (i) compare the differences in the trends and cycles of precipitation between long-term records and relatively short-term records of four rain gauge stations in Shandong Province, China and (ii) explore the impact of cycles on trends by proposing the concept of representative cycle and quantifying the length. In the first step, the M–K test and Sen's slope are used to detect the trends, and the Morlet wavelet analysis is applied to find the periodicity oscillation strength of series to detect the different timescale of cycles for both the long-term records and short-term records. Secondly, the ‘Multi-temporal’ Sliding Window with Fixed-Length (MSWFL) and wavelet analysis are used to find the representative cycle.

It is worth noting that the trends obtained from the statistical analysis depend crucially on the selection of the period of records used (Peña-Angulo et al. 2020). An important consideration is that a trend in any fixed period (even over a very long timescale) may not be representative of historical variability, let alone trends identified from short-term records. Specifically, in the short-term future planning or design such as in the next 10 and 20 years, it may not predict more ‘accurate’ results of the trend as expected when using long series that is larger than 20 years as the study period. For example, when the current year is at the lowest point of a cycle period, the trend seems to be descending with a specific selected study period. However, the actual situation may be that the precipitation of the current year is at the turning point of a cycle intermediately followed by an upward trend occurring in the near future. Therefore, the traditional approach often causes a ‘one-sided’ trend analysis result. To avoid such biased estimation in the trend analysis, much attention should be paid to the impacts of cycles as well as the study period on the trends (Pekárová et al. 2003).

We aim to explore the impact of cycles on trends as well as the impact of the study period on the trend of precipitation series. The basic idea is to use the sliding window to test the multi-temporal trend according to a specific length combined with the moving average method to quantify the representative cycle. The specific steps are (i) Morlet wavelet analysis is applied to find the periodicity oscillation strength of series to detect the different timescale of cycles; (ii) the MSWFL is used to test the multiple trends varying the beginning and ending year analyzed; (iii) combined with the moving average method to find which periodicities, i.e., the representative cycle, are mainly responsible for the trend of measurement series, based on the time scales of cycles detected by the wavelet analysis.

The rank-based non-parametric M–K statistical test (Mann 1945; Kendall 1948) is commonly used to assess the significance of monotonic trends in hydrometeorological time series (Yue & Pilon 2004).

In Equation (3), m is the number of tied groups and denotes the number of ties of extent k. A tied group is a set of sample data with the same value.

Positive values of Z indicate upward trends, while negative Z values show downward trends. Trends are tested at a specific α significance level. When ⁠, the null hypothesis is rejected, and a significant trend exists in the time series. is obtained from the standard normal distribution table. In this study, α = 0.05, ⁠.

Wavelet analysis includes two approaches: one is the continuous wavelet transform (CWT) and the other is the discrete wavelet transform (DWT). The equations of CWT and DWT were referred to (Li et al. 2013).

Real part-time frequency distribution from Morlet wavelet transform coefficients can reflect the periodic oscillation of precipitation at different time scales. The positive real part of the wavelet coefficient means more precipitation, whereas the negative real part indicates less rainfall.

The process of wavelet variance with the scale can get a map of wavelet variance. It reflects the distribution of fluctuation energy with time scales; thus, it could determine the main time scale in time series.

The annual precipitation trend of the four stations with exceptional large lengths ranging from 91 to 135 years is analyzed by the M–K test and Sen's slope. The statistic Z of the M–K test and of Sen's slope, as well as and for the significance test, is shown in Table 2. In this paper, ⁠. The results show an insignificant upward trend of four stations.

Table 2

The results of the M–K test and Sen's slope for the long-term record of precipitation at four stations

Stations .	Z .	.	.	.
Yantai	1.567 (+)	0.559 (+)	1.357	− 0.171
Qingdao	0.638 (+)	0.326 (+)	1.244	− 0.624
Linqing	1.250 (+)	0.675 (+)	1.699	− 0.411
Huangtaiqiao	1.049 (+)	0.634 (+)	2.133	− 0.775

Stations .	Z .	.	.	.
Yantai	1.567 (+)	0.559 (+)	1.357	− 0.171
Qingdao	0.638 (+)	0.326 (+)	1.244	− 0.624
Linqing	1.250 (+)	0.675 (+)	1.699	− 0.411
Huangtaiqiao	1.049 (+)	0.634 (+)	2.133	− 0.775

Note: ‘ + ’ indicates an insignificant upward trend, and ‘ − ’ indicates an insignificant downward trend.

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Specifically, the blue part of the color bar of Figure 3 indicates more precipitation, and the red part indicates less precipitation. It shows the fluctuation characteristics of the real part of the wavelet coefficients, which reflect the alternative variation of precipitation (more than normal or less than normal). The precipitation series of the four stations have several more (less) precipitation centers at different time scales. Figures 3 and 4 clearly show the time scale fluctuations of 6, 10, 17, 32, and 60 years at the Yantai station, 7 , 11, 19, 36, and 64 years at the Qingdao station, 4 , 14, 36 and 58 years at the Linqing station, and 5, 23 and 56 years at the Huangtaiqiao station. The oscillation signal of 60 years is insignificant for the Yantai station, while 32 years is more significant, but not global, which shows up after 1960. The oscillation signals of 36 years of Qingdao, 36 years of Linqing, and 56 years of Huangtaiqiao are relatively more significant.

The results of precipitation trends and cycles based on long-term records are shown in Table 3. Table 3 shows that the longest is 135 years in Yantai and the shortest is 91 years in Huangtaiqiao. For the trend analysis of four stations, the results of statistic Z of the M–K test and of Sen's slope test are consistent, showing an insignificant upward trend. This is consistent with the increase of precipitation in the Northern Hemisphere mid- to high-latitude lands by the Global Precipitation Climatology Centre (GPCC) data set and model simulations (Gu & Adler 2015). For the cycle analysis of four stations, the maximum length cycle of the four stations is about 60 years. The representative cycle of the Huangtaiqiao station is the maximum length cycle, and that of the other three stations is about 30 years.

Table 3

The results of trend and cycle analysis for the long-term record of precipitation at four stations

Series (years) .	Stations .	Trend .		Cycles .
		Z .	.	Wavelet (years) .
1887–2021	Yantai	1.567 (+)	0.559 (+)	6, 10, 17, 32, 60
1899–2021	Qingdao	0.638 (+)	0.326 (+)	7, 11, 19, 36, 64
1918–2021	Linqing	1.250 (+)	0.675 (+)	4, 14, 36, 58
1931–2021	Huangtaiqiao	1.049 (+)	0.634 (+)	5, 23, 56

Series (years) .	Stations .	Trend .		Cycles .
		Z .	.	Wavelet (years) .
1887–2021	Yantai	1.567 (+)	0.559 (+)	6, 10, 17, 32, 60
1899–2021	Qingdao	0.638 (+)	0.326 (+)	7, 11, 19, 36, 64
1918–2021	Linqing	1.250 (+)	0.675 (+)	4, 14, 36, 58
1931–2021	Huangtaiqiao	1.049 (+)	0.634 (+)	5, 23, 56

Note: ‘ + ’ indicates an insignificant upward trend, and ‘ − ’ indicates an insignificant downward trend.

The bold values are the representative cycles of four stations.

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Comparing the results of FL = representative cycle of the four stations, it is evident that the precipitation trend performance of Yantai and Qingdao stations is similar for both coastal stations. Furthermore, if the focus is on the MAV, both precipitation series have shown a ‘down-up-down’ trend since the 19th century. As an inland station, the precipitation at the Linqing station shows an opposite ‘up-down-stable’ trend. The Huangtaiqiao station has an ‘up-fluctuant-down’ trend, which may be due to its high topography.

Based on this, we determined that the representative cycles of the long-term precipitation series at Yantai, Qingdao, Linqing, and Huangtaiqiao stations are 32, 36, 36, and 56 years, respectively.

Compared with the results of long-term records, the precipitation trends and cycles of short-term records have significant changes. The cycles of small time scales are basically the same tested by the Morlet wavelet analysis for long-term and short-term records, but the long-term record can test longer lengths of cycles. The reasons are mainly that small-scale alternating variations are nested into large-scale ones with macro-structure. In addition, the MSWFL shows that the detection results of the cycle are affected by many factors, including the start and end years of the series and the selection of the analysis methods. Thus, the trend depends crucially on the period of record. Without sufficient record length, false attribution statements could be obtained (Hannaford et al. 2013; Hu et al. 2017; Peña-Angulo et al. 2020; Slater et al. 2021).

For the analysis of trends, a long series is not always ideal, but a short series lacks representativeness. Thus, cycle analysis should be the foundation of trend analysis. The above results also indicate the sequence used in China's third water resource investigation on the lack of representativeness from 1960 to 2016. Without considering cycles, the result's credibility is under question, which may arise with potentially significant management implications.

Figure 7 shows that the trend-tested results of the time subsets with the same length, but different initial and terminal years also have significant differences. This indicates that the selection of precipitation series (length and start year) is crucial for analyzing the trend of the series.

Taking the Huangtaiqiao station as an example, for the precipitation records from 1960 to 2016, the decreasing trend is tested by the M–K test and Sen's slope (the test results are shown in Section 4.2). This will make people hold a negative attitude towards the future precipitate in this region (the trend is downward). But is it true? According to the new records (2018–2021), the precipitation of Huangtaiqiao station has shown an upward trend after 2017. Moreover, based on the representative cycle (a 56-year cycle) obtained in Section 4.3, it shows that the precipitation of 2014 and 2015 is just around the bottom of a 56-year cycle (like a turning point of a cycle), followed by an upward trend occurring in the near future.

In addition, selecting study periods of different lengths will result in different representative cycles. However, the longer length of the study period, the more cycles of different time scales can be obtained and the more ‘representative cycles’ are available for analysis, which will lead to the more complete characteristics of the precipitation series.

Long-term records are rare and inhomogeneous, making them unsuitable for analysis. Generally, the solution is to use the data as long as possible with high spatial density. However, this is just a fixed study period. Selecting a fixed study period to analyze the precipitation trends may not justify, and extrapolation (into past or future) of such a selective viewpoint could easily be misleading (Svensson et al. 2005; Chen & Grasby 2009).

This paper demonstrates that the MSWFL is a powerful method to provide a foundation for indexing the sensitivity of precipitation trends to study periods for a range of existing studies.

Short-term trends in fixed periods may be influenced by decadal-scale variability. Some short-term trends that are revealed in previous studies, such as the study period from 1960 to 2016, are shown to be unrepresentative of long-term change. Long-term records may enhance the stability and representativeness of trend detection, but they may be challenging to obtain widely due to their heterogeneity. The MSWFL can balance this contradiction between short-term and long-term records.

We, therefore, advocate the added value of balancing the findings from short-term periods with a separate multi-temporal analysis. More specially, using long available records for multi-temporal analysis to find representative study periods can improve the reliability of the result of using a short-term, fixed period (to capture regional trend patterns).

Financial support for this work is provided by the National Natural Science Foundation of Shandong Province (No. ZR2021QE009).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.