Time series data and rainfall pattern subjected to climate change using non-parametric tests over a vulnerable region of Karnataka, India

Climate change threatens the basic components of survival, such as drinking water, clean air, food availability, and shelter, while at the same time it can destroy a decade worth of progress achieved by mankind. The precipitation pattern of the Indian sub-continent is subjected to the highly seasonal Indian monsoon which makes up almost 70–90% of the total annual rainfall received (Pal et al. 2019). The economy of the country stands on a balance mainly dependent on the rain-fed agricultural outcome which is subjected to extreme fluctuations due to the unreliable pattern of the rainfall causing a major disturbance in the socio-economic condition of the country. With the increase in the frequency of extreme weather events as a direct impact of climate change, there is a growing concern over the anthropogenic factors contributing to it. One of the major components of the Earth's climate system is the hydrological cycle and any fluctuation will result in a disturbance in the water resources and food security and induce events of drought and floods (Wu & Qian 2017). This further puts into focus the need to devise better prediction models for better monitoring of the rainfall pattern. It is important to have a complete grasp of the mechanism of the rainfall process as it forms a key factor in addressing the difficulties posed by the drastic modification in the spatiotemporal pattern of rainfall (Dankwa et al. 2021). The Sixth Assessment Report of IPCC strongly suggests that the temperature rise will increase the chances of drought conditions in Central, West, and South Asia and floods in monsoon regions of South Asia. There is a high probability of heat waves across Asia which could mean a 5–20% increment in the drought condition in the following decades as a result of global warming. Asia is prone to climate change-induced diseases from events such as heatwaves, floods, drought, and others which in turn will hurt food prices and availability (IPCC 2022). The temperature is projected to increase by 5.3 °C and rainfall will increase by 17% across the Upper Indus River Basin (Baig et al. 2022). The desiccation of the Aral Sea by 42,944.32 km² is mainly attributed to the impact of climate change and evapotranspiration (Huang et al. 2022). Spanning over South and South East Asia, and the western Amazon, a consistent increase in flooding was reported under the changing climatic conditions (Eccles et al. 2019). There has been a large increase in the rate of depletion of water storage as a compounding effect of climate change and human activities (Ashraf et al. 2019). The impact of climate change on water resources in the Pungwe river basin was assessed using climate change experiments (Andersson et al. 2011). Over the past decade, there is a greater focus on trend analysis in the field of climatology and hydrology (Güçlü 2020). Evolving technologies have allowed us to access both satellite data and ground-based data for the study of rainfall anomalies (Kumar et al. 2022). Various methods are available to analyze the trend and some of them include the Mann–Kendall (MK) test (Mann 1945), Sen's slope (Sen 1968), and innovative trend analysis (ITA) (Şen 2012).

There is an increasing amount of research analyzing the precipitation trend from various lengths of data and to forecast the future scenario where many of the studies mainly focus on the trend analysis methods. Hasan et al. (2022) utilized Sen's slope estimate and MK test to identify the groundwater influencing parameters in the Ganga basin. The study also included the determination of water budget, storage, and groundwater flow analysis. Saini et al. (2020) implemented multiple statistical techniques such as the modified Mann–Kendall (MMK) test, linear regression, ITA, Sen's slope, Pearson's coefficient of skewness, Weibull's recurrence interval, and others to analyze the monthly, seasonal, and decadal rainfall trend in Hill Agro-Climatic Region and West Coast Plain of India. Pal et al. (2019) investigated the fluctuation in the rainfall trend due in the semi-arid region of Chhattisgarh state in India. The MMK test along with discrete wavelet transformation was utilized to achieve the result of the study. Alemu & Bawoke (2019) examined the rainfall trend using the MMK test and determined other indices for multiple precipitation datasets to evaluate the variability of rainfall in Ethiopia. Singh et al. (2021) studied the rainfall variability using MK, MMK, Sen's slope, ITA, and other methods in Maharashtra. The study concluded that although various methods were successful in identifying the trend, ITA was able to observe trends given by all the other methods. Praveen et al. (2020) worked on forecasting rainfall and analyzing the trend in India. Methods of non-parametrical statistical techniques like MK test and Sen's ITA were used for trend analysis and machine learning using Artificial Neural Network (ANN)-multilayer perceptron in forecasting was mainly employed. Dankwa et al. (2021) addressed concerns regarding the implications of climate on rainfall patterns in northeastern Ghana. The trend and forecasting were achieved by utilizing ARIMA and simple seasonal exponential smoothing models. Yang et al. (2020) analyzed the daily rainfall data in Ningxia, China to arrive at the seasonal and annual precipitation trend using the ITA method. Ridwan et al. (2021) conducted a comparative evaluation of several machine learning models when applied to rainfall forecasting under different time horizons. Nisansala et al. (2020) employed MK and ITA methods to analyze the precipitation trend in Sri Lanka. The results obtained from both tests indicated a similar percentage of increasing and decreasing trends in the region. Further, the ITA was said to be better suited as it depicted trends at different values. Rydén (2022) worked on the trend of extreme flood events in northern Sweden through statistical analysis.

The current study aims to understand the rainfall pattern in the semi-arid region of Karnataka, India from 1952 to 2019 using the MMK, Sen's slope, and ITA methods. Tumakuru is a fast-growing area in terms of urbanization and industrialization which inherently adds stress to the available resources in the region. With worsening conditions, the governance is struggling to cater to the needs of all the sectors and hence a detailed study regarding the condition of the source of water is of prominence. The lack of any major river in the district and the lack of research in this region makes it even more crucial to correctly manage the rainfall resource. The trend is further scrutinized by calculating the point of sudden shift by the change point detection tests such as the Pettitt test, SNHT test, and Buishand test. The ARIMA (Autoregressive Integrated Moving Average) model is also applied for the prediction of rainfall from 2019 to 2029. Having a better understanding of the rainfall scenario makes a good basis to build a better monitoring system for extreme events and better water management systems.

Ground-based rainfall data collected from the meteorological rain gauge stations form the basis of all the methodologies presented in this study. For more than 125 years, the daily precipitation data covering most of the country are provided by the India Meteorological Department (IMD). The data from the rain gauge stations spread across the country are checked for typographic errors and the location information is verified. The interpolation technique is applied at fixed grid points with a spatial resolution of 0.25° × 0.25° (Pai et al. 2014). The National Data Centre (NDC) of IMD is responsible for the compilation, digitization, quality control, and data archiving (https://www.imdpune.gov.in/cmpg/Griddata/Rainfall_25_Bin.html). Rainfall data set from 11 grid points which mainly caters to hydro-climatic studies is used for the present research. The data in the .grd file format are available for download which are then converted using a C program into Excel readable format. The analysis of rainfall data was pursued from 1952 to 2019 for 68 years over the study area. The monthly average of the daily rainfall data was calculated from which the seasonal and annual rainfall data were derived.

The methodology of this research follows the non-parametrical tests to analyze the trend pattern and detect the change point in the region from 1952 to 2019. Along with this, the ARIMA model was also employed to attempt to predict the rainfall for the following 10 years.

A positive indicates an increasing trend while a negative indicates a decreasing trend. This study is performed for an α value of 0.05 giving a 5% significance level. With the standard normal variate given by Z_1−α/2, if |Z_S| > Z_1−α/2, the null hypothesis for no trend is rejected. If |Z_S| > 1.96, the null hypothesis is rejected.

For years a and b, the consecutive data values are defined as and ⁠, respectively. for the trend slope of the data denotes the magnitude.

The z values greater than 1.65 are considered an increasing trend while z > 1.96 are significantly increasing. Z > 2.58 are a very significantly increasing trend. Similar values are defined for the negative values for the decreasing trend.

The abrupt change in the precipitation time series data is detected using the Pettitt test, SNHT, test, and Buishand test.

represents the mean and the standard deviation is given by s.

The value of is then calculated using the Buishand critical value.

The rainfall data analysis was carried out for the Tumakuru district from 1952 to 2019. The result shows the analysis of the time series precipitation data and the trend for each of the 11 grid points present in the study area. The seasonal study is carried out for the trend analysis defined by pre-monsoon (January to May), southwest monsoon (June to September), northeast monsoon (October to December), and annual (January to December). The change point for all the stations was analyzed and furthermore, the ARIMA model was run to depict the temporal and spatial changes in the precipitation from 2019 to 2029.

The rainfall time series analysis discovered that the rainfall was nearly evenly distributed. The description of the rainfall in the area is detailed in Table 1. With the elevation varying between 406 and 1,193 m, the topography of the region is nearly plain with very little undulation; there is not much variation in rainfall with elevation changes.

The MMK test was performed on the rainfall dataset at a chosen significance level in this research of 0.05. This leaves us with positive z values indicating an increasing trend while values greater than 1.96 indicate a significant increase and at the same time, negative values indicate a decreasing trend with a z-value less than −1.96 showing a significant decrease in trend. The trend is defined at different time scales based on the z value for all the stations.

In the pre-monsoon season, stations such as Madhugiri, Tiptur, Tumakuru, and Tumakuru-1 showed a significant increase in the trend with values of 2.02, 3.3, 3.33, and 3.72, respectively, while the rest of the stations showed an increasing trend (Table 2). The only exception is Chikkanayakanahalli having a decreasing trend at −0.37. For the southwest monsoon, only an increasing trend is noted for all the stations with Gubbi, Sira, Tiptur, Tumakuru-1, and Turuvekere holding a significant increasing trend with z values of 2.37, 2.05, 3.17, 2.2, and 3.64, respectively. In the northeast monsoon, we observe that there is a lack of significant increase or significant decrease in the rainfall trend. Chikkanayakanahalli, Koratagere, Kunigal, Pavagada, and Tumakuru-1 displayed a negative trend and rest of the stations of Gubbi, Madhugiri, Sira, Tiptur, Tumakuru, and Turuvekere had a positive trend. At the annual timescale, Madhugiri shows an increasing trend while Gubbi, Sira, Tiptur, Tumakuru, Tuamkuru-1, and Turuvekere witness a significant increase with z values of 3.85, 2.12, 4.99, 2.62, 2.84, and 3.22, respectively. The rest of the stations recorded a negative trend on the annual scale.

ITA was conducted at a confidence level of 95% for the study region and the trend is shown as increasing or decreasing for positive and negative z values, respectively. The significance of the trend is defined for values beyond ±1.96. The trend is described on the ITA z value for the 11 grid points at the annual and seasonal timescale.

There is consistency in the spatial distribution of the trend throughout all the timescales where the central and southwestern parts have increasing trends while the rest of the region mostly experiences a decreasing trend. Chikkanayakanahalli and Sira have a monotonic decreasing and increasing trend, respectively, in all the timescales. Kunigal has a non-monotonic trend throughout with an increase in pre-monsoon while the rest of the seasons have a decrease in trend. Pavagada has a consistent decreasing trend where it is monotonic only in the northeast monsoon. Koratagere displayed a non-monotonic decrease.

The homogeneity test was conducted for the precipitation data for the 11 grid points at a confidence level of 95%. These tests are sensitive to shifts in the homogeneous series. The p-value for the tests varies for the stations with only Tiptur carrying a common value of 0.01. For the Turuvekere station, only Buishand shows a statistically significant value of 0.02 while Pettitt and SNHT showed 0.08 and 11, respectively (Table 3).

This test compares the observation from a certain station with the average of all the stations which are then standardized. SNHT revealed a change at Gubbi in 2007 from 16.97 to 23.65, at Madhugiri in 1971 from 15.16 to 21.32, and at Tiptur from 24.49 to 18.52 in the year 1971 (Figure 6(b)).

The Buishand test has the advantage of operating over any type of distribution. Here the test disclosed a change point in three of the stations. Madhugiri changed from 15.16 to 21.32 in the year 1971, Tiptur in 1973 shifted from 18.83 to 24.605, and in 2003 from 21.54 to 30.13 in Turuvekere (Figure 6(c)).

When comparing the three tests, it is apparent that most of the stations show a homogeneity result. Heterogeneity is observed mainly in the Madhugiri and Tiptur stations. This is confirmed by the change point detected in the early 1970s in all three tests. Gubbi although showing change in 1970 is seen only in the Pettitt test. Tururvekere displayed heterogeneity only in the Buishand test.

The MMK result showed a greater occurrence of a significantly increasing trend in comparison to the ITA result in both annual and seasonal timescales. Tiptur and Pavagada stations have the lowest and the highest values for variance, standard deviation, skewness, and kurtosis. The plot of the z score for MMK and ITA shows a greater correlation wherein the station-wise fluctuation is consistent. Pre-monsoon, southwest monsoon, and annual timescales have values exceeding the threshold of positive significance. Northeast monsoon has a significant decreasing value of the threshold and in this season, we see the best correlation of both the MMK and ITA values. The annual value of Z also agrees well for all the stations. Although pre-monsoon and southwest monsoon follow a similar fluctuation for each station, there is a difference in the z value which seems to be consistent to an extent (Figure 9 given in supplementary material). The plot of the slope shows a similar result with the exception of the southwest monsoon (Figure 10 given in supplementary material). There is a larger gap between the two slopes of Kunigal and Pavagada seen. The trend of rainfall is similar when we compare both the MMK and ITA result for all the stations. In both cases, for all the seasons, Tiptur, Turuvekere, and Gubbi tend to show higher z values while Chikkanayakanahalli, Koratagere, and Pavagada hold very low values for z in comparison to other stations. The MK test is a nonparametric test where the Kendall τ can be derived directly from the rainfall time series data and cuts back on the hassle of other data. Also, it works faster than the parametric tests. The main advantage of the ITA approach is its ability to produce results in the graphical form which benefits from detecting the pattern of the trend of precipitation time series data.

There is a greater similarity between the Pettitt and Buishand test wherein five of the stations show the same value of change point. Three stations have the same value for SNHT and Buishand test whereas only Kunigal and Madhugiri hold the same change year for all three tests. All three homogeneity tests detected change in the Madhugiri station in 1971. Although the tests showed a shift in Tiptur also, the year of change varied to 1973 for Pettitt and Buishand while SNHT showed a shift in 1971. Further, Pettitt and SNHT identified changes in Gubbi in the years 1972 and 2007, respectively. Turuvekere was noticed only in the Buishand test with change occurring in 2003. Despite the slight variation in the year of shift, Pettitt and SNHT showed a similar result with a change in Gubbi, Madhugiri, and Tiptur. Buishand slightly varies from the other tests by detecting change points in Madhugiri, Tiptur, Tumakuru-1, and Turuvekere. The p-value was in favor of the alternative hypothesis of a lack of homogeneity for Gubbi, Madhugiri, and Tiptur stations for all three tests. The above statement sits well with the change point graphs obtained for the same stations.

ARIMA is utilized to plot the rainfall values for 10 years. The result shows that there is a consistent decrease in the rainfall values with progression in time. At the same time, the northern region of the study has low values while the south and the southwestern regions have the highest values for rainfall. The central and eastern regions have intermediate values. The ARIMA model, although not the true representation of the rainfall forecast as it takes into consideration only the rainfall parameter, displays the rainfall from 2019 to 2029. The trend represented by MMK and ITA_R method does not fully agree with the ARIMA result.

The study of the Tumakuru District analyses the rainfall parameter from 1952 to 2019. The time series analysis, trend analysis, and homogeneity tests were employed and the ARIMA model was run to follow the prediction of rainfall from 2019 to 2029.

• The MMK method showed more occurrence of a significant increasing trend in comparison to the ITA. MMK and ITA showed consistency in stations with respect to depicting the increase or decrease although not the magnitude.

• Kunigal and Madhugiri are the only stations that show similar change points in all three tests. Pettitt and Buishand tests are found to carry higher similarities.

• The ARIMA model shows a declining trend of rainfall for all the stations with an average RMSE of 10.94. The average autoregressive value is 0.877.

The result hopes to contribute to the policymaking processes which can help the farmers who mainly depend on the monsoons. Conditions of drought can find better management practices by inculcating such results.

Sanjay Kumar worked on conceptualization, formal analysis, methodology, resources, software, visualization, writing – original draft, writing – review & editing. Syed Ashfaq Ahmed focused on conceptualization, resources, supervision, validation, writing – review & editing. Jyothika Karkala rendered support in data curation, formal analysis, investigation, methodology, software, validation, writing – review & editing.

The authors are thankful to the Indian Meteorological Department for providing the precipitation dataset with high resolution at 0.25° × 0.25°.

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

The authors declare there is no conflict.