Precipitation trend identification with a modified innovative trend analysis technique over Lake Issyk-Kul, Kyrgyzstan

Precipitation is a key meteorological variable for water resource planning and management. It is also an important factor in the global water cycle, which can alter the redistribution of water energy and heat in the atmosphere, affecting weather and climate, and further influencing natural ecosystems and socio-economic development (Guptha et al. 2021, 2022; Swain et al. 2021b; Patel et al. 2022). Therefore, research on precipitation has always been the focus of experts and scholars worldwide (Hu et al. 2015; Croitoru et al. 2016; Li et al. 2019; Lu et al. 2021; Swain et al. 2022a). Central Asia has a particular geographical advantage in connecting the economic and cultural exchanges between Asia and Europe. As one of the ‘Belt and Road’ core areas, it has attracted great attention from international scholars (Chen et al. 2018). However, the region is deep inland, far from the ocean, and the ecological environment is fragile and susceptible to climate change. In addition, the economy is relatively underdeveloped. Therefore, the ability to resist natural disasters is insufficient and vulnerable to climate change (Li et al. 2015). In the context of global warming, the precipitation pattern in Central Asia has changed. Previous studies have shown that precipitation in this area has increased, winter precipitation has increased significantly, and spatial heterogeneity is apparent (Ligang et al. 2015; Taheri et al. 2020).

Alpine lakes in Central Asia are located in high mountains (plateaus) and low-lying basins. A steady meltwater supply from alpine glaciers is the main water resource in Alpine lake (Wang et al. 2006). It is less affected by human activities, can better reflect regional climate change, and is in its natural state (Xu et al. 2018). High evaporation, less precipitation, and limited water resources impact sustainable development in an arid region. Therefore, mountain lakes significantly impact the ecological environment of arid areas and are necessary water resources in dry areas. Lake Issyk-Kul is one of the largest alpine lakes in Central Asia. Against the background of global warming, the precipitation change pattern of the Issyk-Kul Lake basin has gradually attracted attention (Mathis et al. 2014; Salamat et al. 2015; Alifujiang et al. 2020). Studies have shown that changing from warm and dry to warm and humid signals a strong climate change on the northern slope of the Tian-Shan Mountains (Deng et al. 2015). During this transition, the Issyk-Kul Lake Basin is an essential part of the economic belt on the northern slope of the Tian-Shan Mountains, a critical development in Central Asia. Therefore, analyzing the precipitation trends in the past few years is an important issue for the sustainable development of the eco-environment in this region.

Trends of metro-hydrologic variables have been investigated by many researchers using different methodologies such as the linear regression (Haan 2002), Mann–Kendall (MK) trend test (Kendall 1938; Mann 1945), and Sen's slope (SS) (Sen 1968) for detecting the spatial variability of annual streamflow (Kale & Nagesh Kumar 2018), lake level variations (Sattari et al. 2020), groundwater quality (Sakizadeh et al. 2019), air temperature (Mohorji et al. 2017), pan evaporation (Djaman et al. 2017), and precipitation (Jones et al. 2015). Rahman et al. (2016) investigated the trends of monthly rainfall data in Bangladesh using MK, Spearman's rho (SR) tests, and SS estimators. Swain et al. (2021a) analyzed meteorological drought characteristics (frequency, severity, and persistence) using precipitation data from 1954 to 2013 for 24 districts in the Namada River basin using the Modified MK test, which showed an increasing trend in drought in 21 sections and a significant increase in 11 areas. Guo et al. (2018) detected global vegetation changes using the MK trend test for the 1982–2015 time period. Swain et al. (2022b) provide a comprehensive spatial and temporal assessment of drought trends and variability in the agriculture-dominated Marathon region by using the nonparametric tests, standardized precipitation index (SPI), modified Mann–Kendall (MMK), and SS tests. Tayfur & Yacoub (2019) analyzed the annual temperature and rainfall trends employing the Şen trend, SR, and the MK trend tests in Mauritania in Africa for 1970–2013, and they found that temperatures and rainfall time series had statistically significant increasing trends. Milentijevi et al. (2020) analyzed temperature and precipitation trends in the Mačva district (1949–2015) by using parametric methods. They concluded that expressed trends, especially in the case of air temperatures, lead to the possibility of drought. Swain et al. (2022c) analyzed the spatial averages of climate variables across the Narmada river basin using various nonparametric techniques, namely MMK, SS, and Spearman's rho (SR) tests. The results showed significant spatial and temporal differences in the trends of maximum temperature (T_MAX) and minimum temperature (T_MIN) within the basin. Guntu et al. (2020) introduced a novel measure, the wavelet entropy energy measure (WEEM), based on wavelet transformation and information entropy for quantification of intrinsic predictability of time series. Guo & Tang (2021) used the MK test and regression analysis to investigate the precipitation and temperature on the Qinghai-Tibetan Plateau. They indicated that long-term variability in daily precipitation and temperature is critical for assessing the impacts of climate change on ecosystems. Ay (2021) evaluated the annual maximum rainfall datasets to detect potential trends and assess their significance for the Aegean region by applying the parametric Student's t-test and the nonparametric MK trend test. Their results show that this new method provides some results that differ from other methods.

The MK, SR test, regression analysis, and wavelet analysis are classical nonparametric tests commonly used for analyzing hydro-meteorological time series. These methodologies can identify the overall trend and statistically quantify its intercept and slope. Still, the main shortcomings of these traditional methods are a set of basic assumptions, such as the sequence independence of a given time series, pre-whitening, normality of the data, and the absence of sequence comparisons between different parts of the same record. They cannot analyze the variability in different time series intensities well. On the other hand, these trend detection methods are purely statistical methods that do not allow detecting trends in ‘low,’ ‘medium,’ and ‘high’ values in one computational procedure. Without graphical and exploratory data analysis, most nonparametric tests may be worthless in some cases. Onyutha (2016) demonstrates that using a combination of graphical and statistical trend testing methods provides more useful and impactful information than using only statistical methods.

The innovative trend analysis (ITA) method was newly developed by Şen (2012, 2015) and can detect any time series in metro-hydrological and environmental variables without restrictive assumptions. For instance, Kisi (2015) used the ITA method and MK trend test to investigate the monthly pan evaporation at six locations. Water quality parameters from the Kizilirmak River of Turkey were detected by Kisi & Ay (2014) and similar methods used by Huang et al. (2018), which applied the ITA method to investigate the evolution rules with the time of the water parameters at six different aquifers. Chandole et al. (2019) considered the ITA method to determine the annual mean, annual minimum, and annual maximum temperature in India's Lower Tapi River Basin of Gujarat. Boudiaf et al. (2021) detected the trends in ‘High,’ ‘Medium,’ and ‘Low’ rainfall based on ITA methodology instead of using monotonic trend analysis methods. The results displayed that the ITA index has high consistency with other statistical methods, which proves that it is a feasible and effective method for trend analysis (Güçlü et al. 2018b). In addition, the ITA method supports the classical MK trend identification test, resulting in more reliable results (Alashan 2020).

Compared with other nonparametric approaches, the ITA method has general applicability regardless of distribution assumptions, seasonal period, serial correlation, and data series size (Swain et al. 2022d). Some unrecognized trends revealed using the classical MK test can be identified by applying the ITA methodology, and critical hidden sub-trends in the graph can be identified (Güçlü 2018a; Güçlü et al. 2019). Şen (2019) recently proposed a single trend identification method of change point, which provides general local trend analysis through the change point in a particular data series. In addition, the change points on the difference series were determined by the Pettitt test, and then the two sub-categories were defined objectively as ‘high’ and ‘low’ values. The number of data points in the ‘high’ and ‘low’ values was obtained (Güçlü 2020). Overall, trend detection through the above parametric and nonparametric methods is essential. Still, they do not reflect the trend characteristics of each cycle, which is very important for describing seasonal trend behavior. Significantly seasonal trend detection can help regulate or manage water resource systems, agriculture, and agricultural irrigation projects. Hence, trend characteristics are critical when illustrating seasonal trend behavior.

To our knowledge, a seasonal trend analysis is required, and no published work is related to applying new trend tests of the seasonal precipitation in the Lake Issyk-Kul basin, so a proposed novel approach is first applied to these datasets. To fill the knowledge gap and better understand the seasonal trend of precipitation, a new type of ITA method is needed to characterize further the turning point likelihood sequence of the seasonal, temporal difference of precipitation in the Lake Issyk-Kul basin. This study collected the 62-year precipitation time series of different locations around the Lake Issyk-Kul basin. The statistical MK trend test and the graphical new ITA methodology are employed to determine the annual and seasonal precipitation trends.

The main objectives of this paper were the following: (1) to use the ITA method, which is not dependent on any restrictive assumption as serial correlation, non-normality, and sample number to seasonal precipitation (2) to compare long-term annual and seasonal precipitation variability by applying the MK and ITA methods, (3) to determine the data series change point on the new graph through the Pettit test for sub-categories, and (4) to enhance the visual effect of the ITA methodology through the new type of ITA method that classifies the annual and seasonal time series in detail and better explains the trend detection.

The Lake Issyk-Kul basin has 118 large and small rivers with a surface runoff of about 36.7 × 10⁸m³, and a drainage basin occupies 22,080 km² (Romanovsky 2002). The main river flows are Cholpon-Ata, Chong-Koi-Suu, Chong-Ak-Suu, Chong-Uryukty, Ak-Suu, Pzhergalan, Tossor, Ak-sai, Ton, Tamga, Dzhuuku, Chong-Kyzyl-Su, and Karakol (Alifujiang et al. 2017). Lake Issyk-Kul is a closed inland lake with no outlet. Many rivers are used for irrigation before flowing into the lake, but rivers are not the only lake water source. The annual surface water supply is 13 × 10⁸m³, and the precipitation and groundwater are 330 mm. The evaporation of the lake is 820 mm (Romanovsky 2002).

This research attained the three weather stations' monthly and annual time series data (precipitation; covering the 1951–2012 period) selected from Balykchy, Cholpon-Ata, and Kyzyl-Suu (Figure 1 different locations in the Issyk-Kul basin). In this study, the four prominent seasons include spring (from March to May), summer (from June to August), autumn (from September to November), and winter (from December to February). Besides, the analysis of trends was carried out in seasonal and annual data series.

This study used the monotonic MK trend test (Kendall 1938; Mann 1945) and selected the Şen (2012, 2014, 2015, 2017, 2019) method to evaluate the temporal trends and features of the precipitation at the Issyk-Kul basin. These approaches are introduced in the following sections.

The Pettit change point test was proposed by Pettitt (1979). It detects change points in a sequence based on non-parameters, clarifies the time of the change, and can better identify the change points in the sequence distribution. It is widely used in change point detection methods and has a clear physical meaning. This method can determine the change points' number, location, and statistical significance.

In a given data series, the realization of Pettitt (1979) resulted in a single point of change. The statistical test T may follow several probability distribution functions with the same position parameters (no change) rather than substitution functions with change points.

Given the significance level α = 0.5, the detected mutation point is statistically significant when p is less than or equal to the value corresponding to the significance level.

Şen (2012) explained the basic procedure of ITA in detail by dividing the observation data from the first data values to the end data values into two equal parts and sorting the two sub-data series in ascending order, respectively. Based on two-dimensional Cartesian coordinates, the first half of the data value (x_i) is located on the horizontal axis (X-axis), and the second half of the data value (x_j) is located on the vertical axis (Y-axis). The range of both axes should be equal. The 1:1(45°) line divides the diagram into two similar triangles. If the data points accumulated on the 1:1 line, it is conducted that there is trendless time series. If all data points fall above (below) the 1:1 line in the upper (lower) triangle area, there is a monotonic increasing (decreasing) trend present in the time series data. Suppose the data points non-linear accumulated above (below) the 1:1 line in the upper (lower) triangular area. In that case, the time series data exhibits a non-monotonic increasing (decreasing) trend.

The ITA method cannot show the number of time series and sub-categories. But the new innovative trend test analysis as the new type of Şen's methodology indicates mentioned trends and describes the number of data and sub-categories. This further ITA step calculation includes the first two phases of a simple ITA, as shown below.

• (1)
  Any given data series, α₁, α₂, α₃, …, α_n is divided into two halve series {β_{1, n/2}} and {β_{2, n/2}} as,

  

  (9)

  and

  

  (10)

  and each semi-series is sorted according to the time series values ascending manner. Therefore, there are two ordered series, {γ₁} and {γ₂} have the same number of elements,

  

  (11)

  and

  

  (12)

This study collected the 62-year (1951–2012) precipitation time series of different locations around the Lake Issyk-Kul basin. Where {γ₁} is obtained by sorting the data in ascending manner from 1951 to 1981 (first half of the series); {γ2} is obtained by sorting the data in ascending manner from 1982 to 2012 (second half series).

• (2)

  The data of {γ₁} are on the horizontal axis, the data of {γ₂} are on the vertical axis, and the different values of {γ₂} and {γ₂} ({γ₂} − {γ₁}) are pointed on the vertical axis against the values of data series on the horizontal axis (differences = {γ₂} − {γ₁})

Objectively, the right side is called the ‘high’ value, and the left is called the ‘low’ value. In Figure 3(a) and 3(b), the brown and light blue parallel lines reflect the trends of increase and decrease according to the mean value of the sub-category difference. The average difference on the left refers to the mean of the data from 1951 to 1967, which is −0.5640. The average of the first half of data from 1951 to 1967 is 2.5307; the average difference on the right refers to the mean of the data from 1968 to 2012, which is 0.3383. The average of the second half of data from 1968 to 2012 is 3.4814, in which the percentage of each sub-group is calculated as follows:

• 100 × (the average of the left side difference)/ (the average of the first half of the left) as 22.3%;

• 100 × (the average of the right side difference)/ (the average of the second half of the right) as 9.8% (Figure 3(a) and 3(b)).

Figure 4(a), 4(c) and 4(e)) shows the annual precipitation data series derived through five steps of the new innovative trend test. With a 31-year duration, the first half runs from 1951 to 1981, and the second half is from 1982 to 2012. In each case, the given data groups are arranged in ascending order. Their comparisons were existing non-monotonically or monotonically different trends, demonstrating the importance of the recommended graphical method.

As shown in Figure 4(c), the Cholpon-Ata station has two significant increasing trend conditions. According to the Pettit test of the difference series, the ‘low’ and ‘high’ sub-categories have significant increasing trends (8 and 20%). The data series of Balykchy and Kyzyl-Suu stations have no change points according to the Pettit test analyzed by the proposed new innovation trend test. Still, they show obvious non-monotonic growth trends of 7 and 12%, respectively (Figure 4(a) and 4(e)).

The three weather stations (Balykchy, Cholpon-Ata, and Kyzyl-Suu station) trend conditions are also obtained from different series of Pettit tests, indicating that the trends and dimensions of ‘low’ and ‘high’ values appear to coincide with each other. As seen in Figure 5(a), the new type of ITA for the Balykchy station reveals a 14% significant increasing trend in the ‘low’ values category. In comparison the ‘high’ values category has a −29% significant decreasing trend. In comparison, the Kyzyl-Suu station on the ‘high’ sub-categories has a significant increasing trend (17%), and the ‘low’ sub-categories has an insignificant decreasing trend (−4%) (see Figure 5(e)). The trend on the Cholpon-Ata station appears a non-monotonic increasing type. The ‘high’ values indicate a significant increasing trend, which is 14%, and the ‘low’ values trend is 3% (<5%), an insignificantly increasing trend (Figure 5(c)).

Also, the Pettit test obtained two different significant increasing trend conditions on difference series because the new ITA method shows a 14% increasing trend in the ‘low’ values category. In contrast, as seen in Figure 7(e), the ‘high’ values category has a 25% increasing trend. Although all trend tests showed the same results recorded at the Cholpon-Ata (Z_MK = 1.707 > 1.645) station (Figure 7(d) and Table 1), the new type of ITA showed an increasing trend with 1 and 39% in the ‘low’ and ‘high’ sub-category, respectively (Figure 7(c)).

The trend on the Balykchy (Z_MK = 1.488 > 1.282) station appears to be a significantly increasing one (Table 1 and Figure 7(b)). The new type of ITA has two trend types; the ‘low’ data series revealed a significant decreasing trend with −21%, and the ‘high’ values trend has a 10% significant increasing trend (Figure 7(a)).

The MK test is implemented in the winter precipitation data (Table 1). It shows that the data records in Balykchy (Z_MK = 2.788 > 2.58), Cholpon-Ata (Z_MK = 1.283 > 1.282), and Kyzyl-Suu (Z_MK = 1.427 > 1.282) stations have a significant increasing trend. The Balykchy station appears at a 5% significance level (high confidence level), and the Cholpon-Ata and Kyzyl-Suu stations appear at a 20% significance level (low confidence level).

This study applied the new ITA method to annual and seasonal precipitation data from three weather stations (1951–2012), Balykchy, Cholpon-Ata, and Kyzyl-Suu (Figure 1), surrounding Lake Issyk-Kul. Several studies were conducted on precipitation, temperature, evapotranspiration, and groundwater level trend identification in other study areas (Kisi 2015; Mohorji et al. 2017; Sahoo et al. 2021; Swain et al. 2022d). However, no studies were conducted on Lake Issyk-Kul's seasonal trend and change point analysis. Therefore, the new ITA Lake Issyk-Kul was chosen to study trends in precipitation on annual and seasonal time scales. Future studies will attempt to apply the modified methods, such as MMK, and conduct in-depth investigations (Sahoo et al. 2021; Swain et al. 2021a; Guptha et al. 2022; Swain et al. 2022c). The MK trend detection method is often the most common. It requires the existing time series records to be series independent and can only detect monotonic increases, decreases, and no trends (Kisi & Ay 2014; Huang et al. 2018). The ITA method supports the classical MK trend identification test, resulting in more reliable results. It is not affected by sequence correlation, and this powerful feature was attempted to be added to MK. The combination of the MK and ITA methods produces more reliable results based on the annual temperature record of Oxford station (Alashan 2020). Thus, accurate trend detection enables authorities to properly plan future planning projects under the influence of climate change.

The ITA approach is monotonic and non-monotonic to identify and visualize five different trend types (Figure 2). A new illustrated graph is proposed to contribute to the classical ITA method to obtain more information about the trends (Jhajharia et al. 2021). Unlike classic ITA applications, the new ITA method visualization clearly shows the amount of data (Ahmadi et al. 2017). In addition, the point of change on the different sequences is determined by the general Pettit test. Then the two sub-categories are objectively defined as ‘high’ and ‘low’ values (Figure 3). Therefore, the new method runs counter to the previous ITA method. It describes the possibility of turning points in the different data series, the ‘high’ and ‘low’ categories, and the number of data points in each category (Mirabbasi et al. 2020). The application of the proposed method is introduced into a set of 62-year precipitation records from weather stations in different locations of the Issyk-Kul basin. The results show the importance of the new graph type through comparison (from Figures 4–8).

The classical MK trend tests and ITA for Balykchy stations show the monotonic increasing trend on the annual, spring, autumn, and winter precipitation data. According to the Pettit test, the new approach reveals that the annual precipitation data series has no change point, showing obvious monotonic increasing trends with 7% (Figure 4(a) and 4(b)).

On autumn and winter precipitation data, it offers two different increasing trends, with 10 and 160% on ‘high’ values and a significant decreasing (increasing) trend with −21% (293%) on ‘low’ values, respectively (Table 2). The precipitation data for spring and summer have been trendless by the classical MK trend test (Table 1). Still, the new type of ITA reveals a 14 and 61% significant increasing trend in the ‘low’ values category. The ‘high’ values category has −29 and −4%, respectively (Table 2). The classical MK trend test cannot identify any significant trend in the same season.

The spring, summer, and annual data series of the Cholpon-Ata station have no trend by MK trend test (Table 1). The proposed new ITA methodology showed no significant increasing trend of 3 and 0.8%, respectively. It also showed a significant increasing trend of 8.01% on the ‘low’ value, and a 14, 13.62, and 20% significant increasing trend on the ‘high’ values, respectively (Table 2). In addition, the MK trend test, the ITA method, and the novel graphics show a unified increasing trend in winter (30%) and autumn (1 and 39% of the ‘low’ and ‘high’ values, respectively) (Figure 8(c) and 8(d), and Table 2).

The ITA and MK trend tests of the autumn and winter precipitation data at Kyzyl-Suu station showed a monotonic increasing trend; the new method revealed two different increasing trends, on the ‘low’ value it was 14 and 27%, and the ‘high’ value it was 25 and 0.02%, respectively (Table 2).

According to Pettit's test, there is no change point in the annual data series. The ITA graphs show a non-monotonic increasing trend of 12% (Figure 4(e) and 4(f)). However, the MK trend test cannot reveal an increasing trend with a low or high confidence level. In addition, the suggested graph showing sub-categories is sometimes unnecessary. The ‘high’ values of the precipitation data in spring and summer have a significant increasing trend, at 17 and 20%, respectively. In comparison, the ‘low’ value is −4%, and −3% (<5%) shows a decreasing trend insignificantly (Table 2). The MK trend test also did not reveal any significant trends in the same season. Thus, the suggested illustration shows climate differences not made by the MK trend test.

Among the 15 annual and seasonal data series (3 weather stations annually, spring, summer, autumn, and winter) studied, the MK trend test found significant increasing trends of 3 data series (20%). However, using the new ITA method, 6 data series (40%) ‘high’ and ‘low’ simultaneously showed a significant increasing trend. The new ITA method can also detect all significant trends identified by the MK trend test. As for the new ITA method, the ‘high’ values of the 12 data series (80%) exhibited significant increasing patterns, and the 9 data series (60%) displayed significant increasing patterns for ‘low’ values. According to the ‘low’ and ‘high’ values, a gain one data series (6.7%) manifested significant decreasing trends. These results detailed annual and seasonal precipitation data series patterns by evaluating ‘low’ and ‘high’ values (Tables 1 and 2).

Based on the monthly precipitation data recorded for 1951–2012 from three stations in the Lake Issyk-Kul basin, this study investigated the performances of the MK trend test and the new ITA method for annual and seasonal precipitation. The following conclusions were drawn:

• (1)

  The autumn and winter precipitation data records of the three stations have a significant increasing trend, and the spring and summer of the same stations have no trend by classical MK trend test.

• (2)

  According to the Pettit test, the new ITA method reveals that the annual and winter precipitation data series has no change point on the Balykchy (Kyzyl-Suu) and Cholpon-Ata stations, showing obvious monotonic increasing trends with 7, 30, and 12%, respectively.

• (3)

  Significant increasing trends for the ‘high’ values of autumn precipitation in all the stations occur at 10, 39, and 25%, respectively.

• (4)

  The spring, summer, and winter precipitation time series for the ‘low’ values have a positive trend detected for Balykchy stations. In comparison, the Kyzyl-Suu stations have no trend for the ‘low’ values in the spring, summer, and winter precipitation.

• (5)

  Among the 15 annual and seasonal data series studied, the MK trend test found significant increasing trends of 3 data series (20%) but using the new ITA method, 6 data series (40%) ‘high’ and ‘low’ simultaneously showed a significant increasing trend.

• (6)

  For the new ITA method, the ‘high’ values of the 12 data series (80%) exhibited significant increasing patterns, and the 9 data series (60%) displayed significant increasing patterns for ‘low’ values. According to the ‘low’ and ‘high’ values, a gain one data series (6.7%) manifested significant decreasing trends.

This study was supported by the State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Open-ended fund (G2022-02-05), Doctoral Research Startup Foundation of Xinjiang University (BS180245), and 100 Young Doctors Introduction Program of Xinjiang (Tianchi Doctor Program) Foundation (tcbs201819), and the Department of Water Resources and Irrigation, Ministry of Agriculture and Land Reclamation of the Kyrgyz Republic for the provision of data, National Science & Technology Infrastructure Center-Data Sharing Infrastructure of Earth System Science.

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

The authors declare there is no conflict.