A comprehensive framework model for the trend, period and evaluation of the precipitation enhancement effect: TPEM Open Access

Short-term heavy precipitation is one of the most important severe convective disasters during summer in the world (Jauregui & Romales 1996; Schröter et al. 2018; Wu et al. 2021). Since large precipitation occurs in a short period of time, it often leads to disasters such as floods, mudslides, and urban waterlogging (Su et al. 2019; Xing et al. 2019; Zhang et al. 2019). The flood disaster event caused by ‘7.20 heavy rain’ in Zhengzhou City shocked the world. The extreme rainstorm caused 292 deaths in the city and economic loss was as high as 53.2 billion yuan. The precipitation distribution with the ‘rain island effect’ is an important segment of urban waterlogging prevention and control capacity (Yan 2015). High-rise buildings in cities are likened to ‘reinforced concrete forests’. With the increasing density of ‘forests’, especially in midsummer, buildings, air conditioners and automobile exhaust increase the excess heat emissions, making the urban heat island effect significant (Apreda et al. 2019). Due to the convergence and rise of airflow caused by urban heat island circulation, and the fact that there are more condensation nuclei over the city than in the suburbs, the precipitation over the city and downwind direction is more than in the suburbs. This effect is called ‘rain island effect’ (Zhang et al. 2019). To cope with challenges brought about by changes in precipitation, it is necessary to study the temporal and spatial variation law of rain island effect and formulate better strategies to deal with storm disasters (Andreae et al. 2004; Lu et al. 2019).

The spatial–temporal variation of precipitation is an important topic in global change research and hydrological science research. The variation characteristics of precipitation are different in different climatic regions (Song et al. 2017; Dai et al. 2020; Reder et al. 2022). In terms of the law of spatial change, drastic changes in conditions of the underlying surface of the city and frequent human activities have caused changes in the characteristics of the atmospheric boundary layer, which intensified the rain island effect and caused an increase in urban precipitation (Zhao et al. 2021a). In terms of spatial variation precipitation, analysis is mainly based on comparing precipitation between cities and suburbs to explain the spatial variation of precipitation (Yu et al. 2017).

Zhao et al. (2021b) comprehensively analyzed the impact of urbanization on temperature and precipitation in Shenzhen from 1979 to 2017; Peng et al. (2020) explored the relationship between urbanization and precipitation by combining the daily precipitation time series of 24 precipitation stations in Jinan from 1972 to 2016; Zhang et al. (2018) and others found that urbanization exacerbated the total precipitation brought by storms in Houston. This comparison method between urban and suburban areas is direct, simple, and reliable (Yu et al. 2017; Song et al. 2019). However, this method is generally based on a shorter time series of precipitation, results are limited in persuasiveness, and it cannot directly quantify the changing trend of rain island effect over time.

The study of precipitation time change rules is mainly divided into two types: trend and period (Song et al. 2019; Borys et al. 2000). Changnon (1968) used the mathematical statistics to study the changes in the number of rainy days in Indiana from 1925 to 1964. Jauregui & Romales (1996) used the linear trend method to study the changing trend of annual precipitation in Mexico from 1941 to 1985. Song et al. (2019) used the M-K test method to study the time variation of different extreme percentile thresholds of Beijing's precipitation extreme value index from 1960 to 2012. The use of these methods is based on long-term precipitation series data and it has been found that ‘indices such as precipitation in urban areas and the number of rainy days have an increasing trend over time’ (Drobinski et al. 2018). These studies have reached a consistent conclusion that precipitation has an increasing trend with the year, and will be significant during the period of rapid urban development. But these research methods are relatively simple and there is no quantification in forecast of future trends.

In the study of the regularity of the precipitation cycle, wavelet analysis methods, Fourier transform analysis, empirical mode decomposition (EMD), and other methods are often used (Miao et al. 2020). Among them, the basic functions of wavelet analysis and Fourier transform are difficult to choose, and the EMD method does not need a fixed basis function (Huang et al. 1998), which has a certain convenience. But when strong signals are mixed with intermittent small-amplitude noise, the decomposition of the data series by the EMD method shows modal mixing. The ensemble empirical mode decomposition (EEMD) method overcomes this phenomenon by artificially adding white noise processing, and takes the ensemble average based on EMD (Wu & Huang 2009; Amarnath & Krishna 2013), which makes the decomposition result more reliable. However, these methods are only explorations of precipitation change cycles. If there is no research on the temporal variation of precipitation, it is impossible to determine the increase or decrease of precipitation in the period.

In the study of spatio-temporal variation of urban precipitation, each method has its limitations, and one method may not be able to obtain effective results. Using these methods to comprehensively evaluate and compare the ‘urban rain island effect’ from three aspects, such as development trend, cycle change, and quantitative evaluation, is of a certain value in understanding the ‘urban rain island effect’. In most studies, there are many kinds of extreme climate indexes selected, there is no unified standard, and they are mostly carried out for the main urban area, lacking the relative reliability of suburban space comparison and urban development stage comparison. In terms of research methods, the use of a single method is not enough to systematically explain the rain island effect, and there is a lack of unified quantification. Therefore, it is urgent to build a rain island effect evaluation method system based on the combination of the urbanization development stage and multiple methods to comprehensively and quantitatively evaluate the urban rain island effect. Based on the analysis of the development level of urbanization, this paper compares the rainfall of cities and suburbs by using the rainfall enhancement coefficient method, and obtains the value of the long-time-series rainfall enhancement coefficient to explain its spatial variation. The rain island effect of Zhengzhou City is quantitatively analyzed by integrating the six-year rainfall cycle and the six-year rain island effect. The purpose of the study is to provide a scientific basis for cities to deal with the rain island effect in the future.

Based on the Matlab programming language, this research developed a model framework (Trend–Period–Evaluation Model, TPEM) for the trend, period, and degree of change of time series data. This model framework implements three parts of application functions in two-scale scenarios of 61-year annual precipitation increase coefficient and flood season precipitation increase coefficient in Zhengzhou City: (1) use the linear trend analysis method, M-K test method, MWP stage conversion test, and R/S analysis for trend analysis; (2) use the wavelet analysis method and EEMD empirical mode decomposition method for period analysis; (3) introduce the distance method to quantify the manifestation degree of the rain island effect.

This research aims to construct a framework model to quantitatively evaluate the effects of urban precipitation enhancement, namely TPEM. This model can perform a quantitative assessment of trend, period, and evaluation of urban precipitation enhancement effects. A case study was carried out in the downtown area and suburbs of Zhengzhou City. The technical framework is shown in Figure 1.

The Mann–Kendall test method (M-K test method) is a non-parametric statistical test method (Ning et al. 2021). Because the sample does not need to follow a certain distribution, the most prominent advantage is that the sample is not interfered with by a small number of outliers, and calculation is simple. It is currently a more commonly used trend diagnosis method.

The closer the P value is to 1, the more significant is the variability. Let be the confidence level; if then t is considered to pass the hypothesis test and is a significant variation point in the time series.

According to the H value, it is judged whether there is continuity in the time series. When ⁠, it indicates that the time series has a state of continuity, which means the original change trend will be maintained in the future. The larger the H value, the stronger the time series continuity. When ⁠, it indicates that the time sequence is random and is a random sequence. When ⁠, the time series is an anti-persistent sequence and the future trend of change will be reversed. The smaller the H value, the stronger the anti-persistence.

forms a cluster of functions through expansion and translation: ⁠, ⁠, and is called the sub-wavelet; a is the scale factor or frequency factor, which reflects the period length of the wavelet; b is the time factor, which reflects translation in time.

From Equation (15) or Equation (16), the wavelet transform reflects both the time domain and frequency domain characteristics ⁠. When a is small, the resolution in the frequency domain is low and the resolution in the time domain is high. If a increases, the resolution in the frequency domain is high and the resolution in the time domain is low. Therefore, the wavelet transform can achieve localization in the time domain with fixed window size and a variable shape.

The empirical mode decomposition (EMD) method is different from traditional Fourier analysis and wavelet analysis. It avoids the fixed basis function of wavelet analysis (Wu & Huang 2009). The EMD algorithm can get better decomposition results under normal circumstances but when a strong signal is mixed with intermittent small-amplitude noise, the decomposition result will show modal mixing. EEMD (Amarnath & Krishna 2013) artificially adds white noise and takes the ensemble average based on EMD, which overcomes the mixing phenomenon. Therefore, this study uses the EEMD method to analyze the time-series data of the flow extreme value and reveal the change in flow extreme value characteristics at different time-scales. The mathematical principles of the process of EEMD are detailed in Amarnath & Krishna (2013).

is the standard manifest value. The larger its value is, the more serious the rain island effect is; ⁠, represent the value of precipitation enhancement coefficient in the i-th year of rapid development and slow development respectively; and N represents the year of calculation.

This research selected Zhengzhou City as the study area. Zhengzhou City (112 °42′E–114 °14′E, 36 °16′N–34 °58′N), the capital of Henan Province, has six districts and six counties under its jurisdiction. At 7,446.2 km² it is one of China's 15 national-level central cities. It is located in the transition zone from Huanghuai Plain in the east of Henan Province to a mountainous hilly area in the west. It borders Mount Song in the west and the Yellow River in the north. The specific location is shown in Figure 3.

Zhengzhou City has a continental monsoon climate in the northern temperate zone, which is affected by the monsoon and has these characteristics during the four seasons: less precipitation in spring, more windy weather, more precipitation, and high temperature in summer, less precipitation in autumn, clear weather, less precipitation in winter with low temperature, and the annual average precipitation is 642.3 mm. Under the influence of the monsoon, precipitation in Zhengzhou City is unevenly distributed throughout the year. January is the month with the least precipitation of only 5–9 mm, and July is the wettest month, reaching 140–160 mm precipitation. The precipitation from June to September accounts for 60%–70% of annual precipitation, which is mostly in the form of short-duration heavy precipitation.

As shown in Figure 4, the total population of Zhengzhou City increased from 4.379 million in 1978 to 10.136 million in 2018 and the urban population increased from 1.256 million in 1978 to 5.225 million in 2018. The built-up area increased from 65 km² in 1981 to 543.9 km² in 2018. The GDP increased from 2.03 billion yuan in 1978 to 1,014.33 billion yuan in 2018, primary industry increased from 410 million yuan in 1978 to 14.71 billion yuan in 2018, secondary industry increased from 1.29 billion yuan in 1978 to 445.07 billion yuan in 2018, and tertiary industry increased from 330 million yuan in 1978 to 554.55 billion yuan in 2018. Social and economic development overall has shown a trend of steady growth, and society has developed rapidly and steadily (Wang et al. 2020). The GDP increasing trend of Zhengzhou City is the same as that of Beijing, Shanghai, Guangzhou, and other international cities, which shows Zhengzhou City's economically strategic position in China is very important. But since 2006, the average annual economic loss caused by heavy rains and waterlogging disasters has reached 200 million RMB, which is a huge loss (Lv et al. 2021). Therefore, it is necessary to explore the temporal and spatial changes in precipitation in Zhengzhou City for its future flood control and disaster mitigation policies.

We use the daily precipitation data of eight weather stations in Zhengzhou City from 1960 to 2020 to evaluate the temporal and spatial variation of precipitation in Zhengzhou City. The data were obtained from Henan Meteorological Bureau. Weather stations are those of Zhengzhou City, Dengfeng, Gongyi, Songshan, Xinmi, Xinzheng, Xingyang, and Zhongmu.

We propose using the method to count the years with characteristics of rain islands at different development stages and scales in Zhengzhou City. In Figure 5, blue dots represent the slow development stage of the city, red dots represent the rapid development stage of the city, and different color areas represent whether different development stages affect increasing precipitation (⁠>1). It can be seen from Figure 5(a) and 5(b) that under conditions of the annual precipitation statistical scale, the years with the characteristics of precipitation enhancement effect in the slow development stage of Zhengzhou City accounted for 45.86%; the years with the characteristics of precipitation enhancement effect in the rapid development stage of Zhengzhou City accounted for 61.49%, an increase of 15.63%. Under conditions of statistical precipitation scale at flood season scale, the years with characteristics of precipitation enhancement effect in the slow development stage of Zhengzhou City accounted for 40.6%; and the years with characteristics of precipitation enhancement effect in the rapid development stage of Zhengzhou City accounted for 66.46%, an increase of 25.86%. It proves with the rapid development of urbanization, the increasing trend of precipitation in urban centers is more significant than in suburbs; and the trend of increasing precipitation is more significant on a scale of the flood season than on an annual scale.

Figure 5(c) shows that the scatter values of follow a normal distribution. The box plot shows that the expected value during the rapid urban development stage is the largest, and the precipitation enhancement effect during the urbanization flood season is significant. Figure 5(d) is the cumulative distribution function of scattered points in the four cases. In the slow development stage of the city, the consistency of the distribution function of the value and value is small. There is a big difference between the value and ⁠. A value greater than 1 is the most in the rapid urban development period and the flood-season-scale precipitation effect is most significant in the rapid urban development period. It can be seen from Figure 5(d) that the probability distribution of value in the four cases is different, which also indicates that the stationarity of the rainfall enhancement effect has changed. This change is caused by a combination of climate change and human activity (Zhang et al. 2020).

Figure 6 is the M-K test result of and at the 99% confidence level. If the two curves of and have an intersection, and the intersection is between the critical straight lines (blue dotted lines, ±1.96), the year corresponding to the intersection is the significant year of change. In Figure 6(a), UF_k is greater than 0, indicating that the rain island effect on the annual rainfall scale is increasing year by year. UF_k and UB_k intersected in 1997 and 2004, respectively, and the intersection was between the critical lines of ±1.96, indicating that in 1997, 2004 was a year of significant growth; in Figure 6(b), since 1965, UF_k has been greater than 0, and the rain island effect on the annual flood season rainfall scale also showed an increasing trend year by year, exceeding the range of ±1.96 after 2007. It shows that the rain island effect on the scale of rainfall during the flood season is more obvious year by year. UF_k and UB_k intersected in 2004, and the intersection was between the ±1.96 critical lines, indicating that 2004 was a year of significant growth.

After the MWP test, the statistical values ⁠, confidence P of ⁠, and are shown in Figure 7. The 5% significance level is adopted for verification and the maximum statistical value is obtained. It is found that the P-value is greater than the 0.95 confidence level, which means the change in trend is significant. The closer the P-value is to one mutation point, the more significant the phenomenon. The values of and are largest in 1997 and 2004, and the corresponding P-value is greater than the 0.95 confidence level. It can be seen that 1997 and 2004 are years of variation of and ⁠. The first sudden change year is almost the same as the starting year of the rapid urban development stage, which shows that precipitation changes are closely related to the development of urbanization. It can be seen from Figure 7 that the value of is greater than that of ⁠, which shows that with the development of urbanization, precipitation changes are mainly manifested in the increase of precipitation during the flood season.

According to the Hurst index (H), and in Zhengzhou City from 1960 to 2020 are analyzed (Figure 8). It can be seen from Figure 8(a) that the H index values of and are 0.53 and 0.62, respectively, which are greater than 0.5, indicating that and have the same trend persistence in the future. Combined with the M-K test and analysis results, both and have increasing trends. It can be seen from Figure 8(b) that the V statistics of and fluctuate at and ⁠, respectively. N=4 and N=10 are deduced, which means that will in the next four years maintain the increasing trend, and will maintain the increasing trend in the next ten years and the rain island effect will be significant. This shows that there will still be an increasing trend of different durations in the future, increasing the pressure on flood control during the flood season and giving the water resources management department an early warning.

Figure 9 summarizes the brief conclusion of the trend rule of the TPEM model. The interannual variation change in trend and in Zhengzhou City increased year by year; mutated in 1997 and 2004 and increased faster; for the mutation occurred in 1997 and 2004, and the frequency of mutation increased faster. This is because the precipitation enhancement effect will become more pronounced as the city develops, and it is mainly concentrated on precipitation during the flood season. The TPEM model predicts that the effect of increasing rainfall in Zhengzhou City will continue to increase in the next ten years. In this way, the precipitation trend persistence obtained by multiple methods is more reliable than a single method.

In the wavelet analysis, we produced a two-dimensional contour map with the year as the abscissa and period as the ordinate (Figure 10), which shows the period of and relative to the annual time series.

In Figure 10 and Table 1, the dark purple line represents the positive phase meaning the real part is greater than or equal to 0; the light green line represents the negative phase meaning the the real-part is less than 0, which clearly shows the fluctuation characteristics of the real-part wavelet transform coefficient. Figure 10(a) and 10(b) specifically reflect the large and small alternating characteristics of and in Zhengzhou City. Figure 10(c) shows the wavelet variances of the study area and have the largest values of 0.040 and 0.016 at 9.5 and 17.5 years, respectively. Therefore, the main periods of change in and are 9.5 and 17.5 years respectively. There is significant fluctuation of on scales of 18a with positive and negative phases alternated. Fluctuations of more and less precipitation in the calculation time domain can be observed. There is very significant fluctuation of on the scale of 19a, and positive and negative phases alternately appear. Fluctuations of more and less precipitation in the calculation time domain can be observed. Also, formed a situation where positive and negative phases alternately appeared at 30a, but the figure was not closed and it was not significant, and a long sequence of data verification was required. The difference between the period of and further illustrates that precipitation in the flood season changes more rapidly and the effect of increasing precipitation is more significant. The urban flood control department should pay attention to flood control during the flood season (Nigussie & Altunkaynak 2019).

It can be seen from Figure 11 that changes of and ⁠, the IMF1, IMF2 and IMF3 components of ⁠, have the largest amplitudes in the late 1990s and early 21st century. This period is exactly the stage of rapid urban development, which shows that the rain island effect is closely related to the development of urbanization. The amplitude and duration of IMF4 components run through the entire research period. The R trend item shows the change characteristic continuously increasing with the increase of inter-annual time. It can be seen from Table 2 that the contribution rate under the IMF1 component of is the largest (67.06%), and its maximum period is 15.10 years followed by periods of 2.23, 3.34, and 4.60 years. The IMF1, IMF2, and IMF3 components of also had the largest amplitudes in the late 1990s and early 21st century, and the amplitudes were larger than that of ⁠. It shows that the impact of urbanization on the rain island effect is mainly the impact of precipitation during the flood season. The increasing trend of the R trend item of is significant, which shows that the rain-enhancing effect of precipitation during the flood season will be significant in the future. It can be seen from Table 2 that the contribution rate under the IMF1 component of is the largest (70.64%) and the maximum period is 19.72 years, followed by periods of 2.23, 3.12, and 5.37 years.

Figure 12 shows the standard manifest value of the rain island effect in Zhengzhou City after standardization using the distance method. In the rapid urban development stage, the standard manifest value of annual precipitation calculated by the distance method is 0, and of precipitation during the flood season is 0.643, which shows that total annual precipitation in Zhengzhou City has no significant rain island effect characteristics, but the flood season has a serious rain island effect. However, in the slow development stage, of annual precipitation is 0.33, and of precipitation during the flood season is 0.261. It shows that the total amount of annual precipitation and of the flood seasons in Zhengzhou City increases with inter-annual time, and characteristics of the rain island effect are not significant. Therefore, future urban flood control planning should focus on flood control during the flood season.

Based on the Matlab programming language, this research developed a model named TPEM for the trend, period, and degree of change of time series data. This model was applied in the case of Zhengzhou City, and the following conclusions were obtained. The precipitation in Zhengzhou City shows an increasing trend with the inter-annual time, and the increasing trend of precipitation in the flood season is significant. The added mutation year is around 1997, which is consistent with the beginning year of the city's rapid development. The trend of increasing precipitation in the year and flood season will continue into the next four and ten years, respectively. Zhengzhou City's precipitation enhancement effect has significant cyclical characteristics, and both the annual precipitation and precipitation enhancement effect during the flood season show a large-cycle trend of ‘enhance–weaken’ from 9.5 to 17.5 years. At the same time, there is also a trend of small cycles of 18 and 59 years. The wavelet variance of period assessment of the precipitation enhancement effect during the flood season is greater than the annual precipitation enhancement effect, indicating that the precipitation's temporal and spatial variability during the flood season is stronger. In the rapid urban development stage, of annual precipitation calculated by the distance method is 0, and of precipitation during the flood season is 0.643. It shows that total annual precipitation in Zheng-zhou City has no significant rain island effect characteristics, but the flood season has a serious rain island effect. In the slow development stage, of annual precipitation is 0.33 and of precipitation during the flood season is 0.261. It shows that total annual precipitation and flood seasons in Zhengzhou City increase with the inter-annual time, and the rain island effect is not significant.

The above conclusions confirm the validity of the TPEM model, which can comprehensively evaluate the temporal and spatial changes in precipitation in urban development. At the same time, research results show that the increase in precipitation in plain urban areas is mainly concentrated in the flood season and will continue to increase in the future. Therefore, the city's future flood control planning should focus on flood control during the flood season.

For this research paper with several authors, a short paragraph specifying their contributions is provided. Caihong Hu and Chengshuai Liu developed the original idea and contributed to the research design for the study. Sun Yue was responsible for data collecting. Qiying Yu provided guidance and contributed to the research design. Chaojie Niu and Shan-e-hyder Soomro provided some guidance for the writing of the article. All authors have read and approved the final manuscript.

This work was funded by Key Projects of the National Natural Science Foundation of China, grant number 51739009, National Natural Science Foundation of China, grant number 51979250.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.