Climate Variability and Rainfall Patterns in Hyderabad: A 42-Year Statistical Analysis

Hyderabad is located at a north latitude of 17.4065° and an east longitude of 78.4772° (Figure 1). The climate in this region is extreme, with monsoon-like weather on average. Summers are intensely hot, while winters are severely cold. The year consists of four distinct seasons. The South-West monsoon lasts from June to September, while the hot season extends from March to May. The months of October and November are considered post-monsoon. The cold season runs from December to February. The yearly average precipitation is 736.5 millimeters. The southwest monsoon is the primary cause of precipitation in Hyderabad. The JJAS season, which takes place from June through September, accounts for around 80% of the total rainfall. The annual temperature and rainfall seldom change from one year to the next. 

Fig.1. Study area map of Hyderabad 

 Weather data 

Rainfall, maximum and lowest temperature monthly s from 1981 to 2022 (43 years) were obtained from NASA's Power website, which was used in this study (https://power.larc.nasa.gov/data-access-viewer/). 

Trend analysis 

According to Webber and Hawkins (1980), a trend is the general movement of a series over time.  It also refers to the long-term evolution of the dependent variable over time. Trend is determined by the relationship between the two variables, rainfall and temperature, as well as by their temporal resolution. Regression analysis and the coefficient of determination R2 are two statistical techniques used to assess the significance of temperature and rainfall patterns. The trend was generated and evaluated using the Mann-Kendall (M-K) trend test, and the slope of the regression line was ascertained using the least squares approach. The mean, standard deviation (SD), and coefficient of variation (CV) of temperatures and rainfall were calculated to examine the relationship. 

Mann–Kendall's Test 

The MK test is a prominent nonparametric statistical test used to examine trends in hydrological and climatological time series data. Developed by Mann in 1945, it has been extensively used in environmental time series analysis. Using this exam has two advantages. Firstly, normally distributed data is not required since it's a nonparametric test. Secondly, the test shows low sensitivity to abrupt stops brought on by non-uniform time series. This test's null hypothesis (H0) suggests that there is no trend. This is contrasted with the alternative theory H1, which maintains that a trend exists. This is how the MK statistic is computed. 

A time series Xk rated from k = 1,2,3,…,n-1 and ranked from j = i + 1, i + 2, i + 3…..n is subjected to the trend test. Every single data point xj acts as a point of reference. 

 Sen's Slope Estimator Test 

Sen’s estimate (Sen, 1968) is a nonparametric method for determining the amplitude of a trend in a time series. Sen’s nonparametric method, tested using R software, is used to find the proper slope of an existing trend, such as the annual change in quantity. When Sen's slope is positive, the time series shows an upward or increasing tendency; when it is negative, the trend is downward or declining.  
 

Innovative Trend Analysis 

The data should be divided into two subsets before performing the ITA on any specific time series. The data for each subset is then sorted in ascending (or descending) order. Furthermore, the diagram is split into two separate triangles by the 1:1 (45°) axis of no trend, which indicates the increasing (area above the 1:1 line) and decreasing (area below the 1:1 line) time-series data trends (Aher & Yadav, 2021). The scattering of the data rises above (or falls below) the 1:1 line whenever the monotonic trend is increasing (or decreasing) (Aksu et al., 2021). Similarly, if the data points fall in the upper triangular portion of the 1:1 line, a positive trend is indicated. In contrast, a negative trend is shown by data points falling in the bottom triangular area of the 1:1 line (Aher & Yadav, 2021). For simpler understanding, the scatter points on 1:1-line graphs were divided into three groups: low, medium, and high. ITA may also detect and investigate the trends of any hydrometeorological variable’s low, middle, and high time-series values. 

Potential evapotranspiration 

The Penman-Monteith equation, recommended by the FAO in 1998, is widely used for computing ETo. Many studies have found that the Penman-Monteith equation is more appropriate for various regions (Alexandris et al., 2008). The total potential evapotranspiration (ET0) was estimated through built-in FAO Penman–Monteith equation as shown below using the ETo calculator version 3.2 developed by the FAO (Jabloun and Sahli, 2008) was used in this study to estimate ETo with these available inputs. 

Nonparametric approaches were widely employed, according to trend analysis of several studies (Hollander and Wolfe, 1973). Many researchers recommended the MK test (Mann, 1945; Kendall, 1975) as one of the finest methods. (Jain and Kumar, 2012). Table 1 displays the rainfall data's mean, standard deviation, coefficient of variation, kurtosis, and skewness. The computed data reveal that average monthly rainfall's coefficient of variation (CV) ranges between 43.5 and 269.4%. November had the most skewness (3.41) and kurtosis coefficient (14.30). The research area receives the most rain during the monsoon season, from June to September, as shown in Figure 2, indicating the monthly rainfall trend. The linear regression equation reveals that the seasonal rainfall in the studied region has a negative slope value (a = 0.08), as illustrated in Figure 3. 
 

Table 1. Statistical data about Hyderabad's rainfall 

Fig. 2. Boxplot of monthly rainfall (mm) for Hyderabad districts from 1981 to 2022 

 Fig.3 Trend of Seasonal Rainfall from 1981 to 2022 

Tables 2 and 3 show the highest and lowest temperatures and the descriptive statistics used (mean, SD, coefficient of variation, skewness, and kurtosis). The skewness and kurtosis data demonstrate higher variability than rainfall, even though the CV for the highest and lowest temperatures is shown to be lower than for rainfall. The findings of examining the observed data from 1981 to 2022 are displayed in Figures 5 and 7. In contrast to the lowest temperatures, which are low during post-monsoon seasons and relatively high during monsoon months, maximum temperatures are low during monsoon seasons and relatively high during pre-monsoon months, according to these figures. Seasonally-based temperature changes for both maximum temperature data from 1981 to 2022 are quite significant. Table 4 displays the result of the Penman-Monteith equation (ETo) and the descriptive statistics. Figures 6 and 8, respectively, examine the temperature trends at the highest and lowest values. Table 5 illustrates how often the MK test is used in trend testing. The findings (Table 5) demonstrate that the seasonal rainfall pattern in the area under study is trending. The MK method, a nonparametric test, was used to determine if the variable has a monotonic upward or decreasing trend over time. Rainfall patterns between 1981 and 2022 are statistically significant, with a 99% confidence level. The "z" score calculated a 99% confidence level. Rainfall has decreased during the JJAS season (Sen's slope = -0.0002). The trend analysis of rainfall, minimum temperature, and maximum temperature yields statistically significant results at the 95% confidence level, even though the minimum temperature trend (Sen's slope = 0.02) and maximum temperature trend (Sen's slope = 0.012) for the observed period showed a slight increasing trend. However, the trend analysis's conclusions are not statistically significant. A minor declining tendency is indicated by the findings of the innovative trend analysis for rainfall throughout the monsoon season (Fig. 4). 

Fig. 4. Innovative Trend Analysis of Seasonal Rainfall from 1981 to 2022 

Table 2. Statistical data about Hyderabad's maximum temperature 

Fig. 5. Boxplot of monthly Maximum temperature (°C) for Hyderabad districts from 1981 to 2022 

 Fig. 6. Trend of Seasonal Maximum temperature (°C) from 1981 to 2022 

 Table 3. Statistical data about Hyderabad's minimum temperature 

Fig. 7. Boxplot of monthly Minimum temperature (°C) for Hyderabad districts from 1981 to 2022 

Fig. 8. Trend of Seasonal Minimum temperature (°C) from 1981 to 2022 

Table 4. Statistical data about Hyderabad's ETo  

 Fig. 9. Boxplot of monthly ETo (mm) for Hyderabad districts from 1981 to 2022 

Fig. 10. Trend of Seasonal ETo (mm) from 1981 to 2022 

 Table 5.  Mann–Kendall trend analysis 

Because rainfall is crucial in influencing how water is used in a specific place, researchers and policymakers should consider the variation of meteorological data when making decisions. First, box plots were employed to show monthly rainfall fluctuations. The small size of box plots (Tukey, 1977) makes it simple to compare assessments of multiple datasets side by side, which is challenging when using more comprehensive representations such as histograms (Banacos, 2011). These charts provide a clear visual depiction of the statistical distribution for an extensive array of audiences. The horizontal line in the middle of the box plot, which is positioned between the interquartile range's top and bottom horizontal lines, represents the median. The 25th and 75th percentiles are indicated by the horizontal lines at the top and bottom of the boxes, respectively. Vertical lines denote the outer ranges.  

As evidenced by the lower kurtosis and skewness values, the kurtosis values suggest that the dataset is light-tailed and has a symmetric pattern throughout the monsoon months (June, July, August, and September). The other thing is that the examined area experiences symmetrical rainfall throughout the monsoon season. In comparison, rainfall during the post- and pre-monsoon months has a significant tail in the dataset, indicating the likelihood of outliers or extreme values. Precipitation in the research region is unpredictable before and throughout the monsoon season in its most basic form. Understanding surface air temperature behavior is critical for understanding climatic variability, which can occur on a local, regional, or global scale. Weather and climate forecasting are greatly influenced by surface air temperature (Ghasemi, 2015). Despite overwhelming evidence that global temperatures are rising, accurately tracking temporal trends remains difficult (Gil-Alana, 2018). The air temperature at the study site carries a substantial impact on the water cycle; therefore, more research is required to properly understand this phenomenon. The research region experiences the most rainfall in July, August, and September, resulting in lower seasonal maximum temperatures than in other months.  

Throughout the research period, Figure 5 displays the seasonal average maximum temperature and its trend. A linear regression model's slope, which in the present scenario is approximately 0.0132°C for 42 years from 1981 to 2022, indicates the pace of change. This result deviates from the previous ten-year projection of 0.9 °C global warming. This conclusion shows that the approach utilized in global warming studies significantly impacted the local climate throughout the previous 20 years in the study area. Furthermore, the coefficient of variation (CV) of the average monthly maximum temperature for the examined period ranges from 2.5 to 6.5%, showing that the maximum temperature remains relatively consistent over time. October has the most excellent kurtosis coefficient (2.26), and its maximum temperature readings are positively skewed. The linear regression's best-fit lines are commonly used to produce trends in seasonal mean minimum temperatures across several years. Figure 7 depicts linear regression trends and the matching linear regression equations and coefficients of determination. According to Hayelom et al. (2017), the monthly mean minimum temperature has a coefficient of variation ranging from 3.0 to 13.7%. Despite the modest difference, the study found that the lowest temperature swings were greater than the highest temperature swings. The maximum temperature and data exhibit a positive skew, coefficient of kurtosis reaching its peak in August at 1.72. The ITA's time series computations revealed that the higher and lower temperatures exceeded the 1:1 line, indicating that Hyderabad is trending higher (Figs. 11 and 12). As shown in Table 4, the computed data indicatedthat the statistical analysis of Hyderabad’s monthly evapotranspiration (ETo) data shows significant variations. January's mean ETo is 161.3 mm with a standard deviation (SD) of 18.9 mm and a coefficient of variation (CV) of 11.7%, indicating slight positive skewness. February has a mean ETo of 190.8 mm, an SD of 13.5 mm, and a CV of 7.1%, suggesting a nearly symmetrical distribution. March’s mean ETo is 251.9 mm with an SD of 18.5 mm and a CV of 7.3%, showing slight negative skewness. April’s mean ETo is 260.6 mm with an SD of 24.4 mm and a CV of 9.4%, indicating symmetry. May has a higher mean ETo of 289.4 mm, an SD of 40.6 mm, and a CV of 14.0%, with slight negative skewness. June’s mean ETo is 194.7 mm with an SD of 28.1 mm and a CV of 14.5%, indicating near symmetry. July has a mean ETo of 153.8 mm, an SD of 25.7 mm, and a CV of 16.7%, showing positive skewness. August’s mean ETo is 129.5 mm with an SD of 17.2 mm and a CV of 13.3%, indicating positive skewness. September’s mean ETo is 109.8 mm with an SD of 13.5 mm and a CV of 12.3%, showing near normal distribution. October has a mean ETo of 113.6 mm, an SD of 18.8 mm, and a CV of 16.5%, indicating strong positive skewness. November’s mean ETo is 119.3 mm with an SD of 24.5 mm and a CV of 20.5%, showing slight positive skewness. December’s mean ETo is 135.1 mm with an SD of 22.7 mm and a CV of 16.8%, indicating near symmetry. Overall, the data indicates considerable monthly variability in ETo, reflecting Hyderabad's diverse climatic conditions throughout the year. The overall decreasing trend of seasonal ETo in the studied region is shown in Figure 10, which illustrates the general declining trend of seasonal ETo in the examined region, and the linear regression equation reveals a negative slope value (a = -0.16). The ETo values that ITA computed using the time data exceeded the 1:1 line, suggesting general upward tendencies for Hyderabad (Figure 13). 

Fig. 11. Innovative Trend Analysis of Maximum temperature from 1981 to 2022 

Fig. 12. Innovative Trend Analysis of Minimum temperature from 1981 to 2022 

Fig.13. Innovative Trend Analysis of ETo from 1981 to 2022 

Meteorological data is a key source of data for assessing these patterns and comprehending the alterations in the climate system. In climate research, non-parametric tests are frequently employed because of their ability to identify trends in time series information instead of requiring assumptions about the underlying distribution (Ampofo et al., 2023). These tests assess various meteorological parameters, such as wind speed, humidity, temperature, precipitation, on various scales. Spatial distribution analysis is critical in climate research since it helps to understand regional differences in climatic variables and how they change over time. This research attempted to do so with statistical tools and rainfall data. The pre-monsoon, post-monsoon, and winter variables have large CV values, indicating that there tend to be significant annual variations in the amount of rainfall experienced throughout these seasons.  

The low coefficient of variation (CV) for the monsoon and yearly variables suggested that there may be some variation in the total amount of rainfall during these times, but not a substantial one. The outcomes of other researchers, including Chandniha et al. (2017), Shree and Kumar (2018), and Warwade et al. (2018), are consistent with the results of a recent study on rainfall variability. In particular, the study discovered significant variability in winter, post-monsoon, and pre-monsoon rainfall. Additionally, according to Yadav and Singh (2023), there has been a decline in intense rainfall during the past few decades. Sengupta and Thangavel (2023) examined variations in temperature and rainfall distribution patterns using meteorological data; they found that Maharashtra's altered precipitation patterns are causing a severe drought that seriously threatens the state's cotton production level. 

The main findings of this study highlight the necessity of ongoing monitoring and analysis of the local climate and rainfall patterns to develop effective strategies and policies for managing and adapting to the changing climate and its effects on the environment and human activity in the area. These results draw attention to the region's difficulties in controlling its water supplies and responding to severe weather. To address water-intensive patterns and promote climate resilience, researchers and policymakers need to consider these changes. To confirm that resources are owed and decisions are made with the best interests of the region's sustainability and climate resilience in mind, the study offers insightful information.