Statistical Analysis of Thirty-Year Rainfall Variability in Udaipur District, Rajasthan, India

The rainfall variability for the Udaipur district for thirty years (1991–2020) was statistically analysed in this study. The linear regression (parametric) and Mann–Kendall (non-parametric) trend test along with precipitation indices performed using rainfall data collected from 9 rain gauge stations situated in different parts of the Udaipur district, Rajasthan, India. An increasing trend was found between the months March to November in the Udaipur district, indicating that total annual rainfall has increased in these months during the study period. About 85.20% of the total annual rainfall is occurred due to the southwest monsoon during the rainy season. The PCI (21.74 to 57.92) and CV (11.04 to 21.23) values show the high-nonuniformity and less rainfall variability, respectively. The SRA values for each year have been greater than -0.84 (no drought category) during the study period. The rainfall deficiency took place only four out of 30 years of the study period, 1995, 1999, 2000, and 2002, which fall under the category of large deficiency. The values of the wetness index indicate that during the study period,2006 was the wettest year due to the maximum rainfall (Wi = 179.07) while 2000 was the driest year due to the minimum rainfall (Wi = 54.26). Total annual rainfall has increased in the last three decades, which shows the need for implementation of all necessary plans by the government for proper rainwater utilization and management to prevent future natural disasters like floods.


Introduction
Climate variability refers to long-term variations in meteorological factors such as rainfall, humidity, temperature, wind speed, evaporation, and others. 1,2lobal warming is the most critical environmental concern as it is responsible for global climate change and leads to variations in long-term rainfall patterns that affect water availability worldwide. 3,4here are four principal greenhouse gases (GHGs) in the environment, namely, carbon dioxide, water vapour, methane, and nitrous oxide, that contribute to the problem of climate change. 5Rainfall's spatial and seasonal distribution changes affect overflow frequency, soil moisture and groundwater reserves, and droughts and floods. 6obal warming increases the earth's surface temperature, increasing the intensity and duration of drought. 7An increase in the moisture holding capacity of the air also causes heavy rainfall. 8Heavy rainfall results include devastating calamities, like landslides and floods, which lead to loss of life, property, and livestock. 9,10Global climate change increases the risks of famine and water scarcity, affecting the agricultural sector and causing the rapid melting of glaciers. 11,12anges in the amount, intensity, and frequency of rainfall occur yearly and over decades, affecting the environment and society. 13Even a change in the phase of precipitation in one year can ruin the agricultural conditions of the country and its associated economy.It is also a significant threat to the country's food security. 14Variation in rainfall patterns directly or indirectly affects regional water sources that are rainfed or recharged. 3The yield of crops, especially in rainfed areas, depends on the rainfall patterns. 4dia is an agriculture-based economy that is mainly dependent on monsoon rainfall.About 60 percent of India's total population depends on agriculture for livelihood, which contributes 14 percent to the country's GDP.The Indian Summer Monsoon (ISM) variability affects agricultural food production, industry, and hydropower generation, causing severe pressure on the national economy.In many parts of India, the lack of monsoon rainfall leads to drought conditions, for which the Government of India spends large sums of money on the affected areas to provide relief.The present study focuses on the rainfall variability of Udaipur district, Rajasthan (India).The annual average rainfall of the Udaipur district is always less than the annual average rainfall of India, so it is crucial to analyse the rainfall trends to get information on agricultural activity, drought conditions, and agricultural productivity in the region.The rainfall pattern for 30 years (1991-2020) has been used to characterise for Udaipur district, Rajasthan, India.

Study Area and Research Methodology
Udaipur district is a part of the Mewar region, situated in southern Rajasthan, and Udaipur city is world famous as the "City of Lakes". 15Udaipur district is located on the southern slopes of the Aravalli range, on the border with Gujarat state, at a distance of 403 km from the state capital Jaipur.Udaipur comes under a semi-arid climate, which occurs in most months of the year. 16The total number of population of the Udaipur district is 3,445,342. 17The longitudinal and latitudinal extent of the district is 73° 42' and 24° 45', respectively, and the district's total area is 13430 sq.km. 18,19The rainfall data is collected for 30 years from 9 raingauge stations situated in the Udaipur district, and these monitoring stations are shown in Figure 1 along with the study area.The geographical coordinates of all rain gauge stations are shown in Table 1.

Trend Analysis of Rainfall
The trend of rainfall is mainly analysed by linear regression and Mann-Kendall trend test.

Linear Regression Trend Test
This test defines the linear relationship between rainfall and time as well as predicts the increase or decrease in rainfall values with time.The equation for regression is shown below. 22,23ax+b … Where, a = slope and b = intercept.

Mann-Kendall Trend Test
The test is conducted between the null hypothesis and alternative hypothesis.There is no trend for the null hypothesis in the rainfall-time data series, on the contrary, there is a trend for the alternative hypothesis.The Mann-Kendall test is calculated by the following equations. 24,25. (2)   ...(3) The variance (σ 2 ) is calculated by the following formula. 26 The standard test is represented by this equation. 26

Precipitation Indices
The various precipitation indices such as CV, NAR, SRA, WI, PCI, and rainfall dependability have been calculated using the following equations.

Normal Annual Rainfall (NAR)
It is defined as the average annual rainfall for 30 consecutive years.In this study, the rainfall series are classified as monthly, seasonal, and annual rainfall.The NAR is calculated every 10 years to get an idea of its trend.The NAR is obtained by using the following equation. 27

…(6)
Where, P i = Rainfall value in the i th year.

Precipitation Concentration Index (PCI)
PCI defined as the non-uniformity, and uniformity of rainfall over a region for a period of time.Increasing values of PCI indicate increasing non-uniformity of rainfall and decreasing values indicate increasing uniformity of rainfall.PCI is calculated by the following equation. 28…( 7) Where, P i = Rainfall in the i th month.

Standardised Rainfall Anomaly (SRA)
Standardised rainfall anomalies are used to express the probability of drought in any region.The lowest and highest SRA values indicate the maximum and minimum probability of drought respectively.The value of SRA is determined through this formula. 29,30A= (P i - Where S represents the standard deviation and P i represents the rainfall value in the ith year.The different categories of SRA and PCI, according to their range, are tabulated in Table 2.

Wetness Index (W i )
The wetness index is calculated as the percentage ratio of rainfall at a place in a year to the normal annual rainfall.
W i (%)= (Rainfall in a specific year at a place)/ (Normal Annual Rainfall)*100 …(9) The wetting index can determine the rainfall deficiency.

Coefficient of Variation (CV)
The CV values measure the distribution of rainfall over a particular area.It determines an average's reliability and provides a foundation for controlling rainfall variability.It is determined by the formula given below. 31 (%)= (Standard deviation of Rainfall )/(Average Rainfall)*100 … (10)   Here, CV less than 20 shows less variability, 20-30 denotes moderate variability, and greater than 30 exhibits high variability.

Dependable Rainfall
It can be calculated by arranging rainfall-time series data in descending order and determining the rank.

Data Observation
The rainfall data were collected for nine (9) rain gauge stations from the WRD, Rajasthan.The data were further processed on M.S. Excel software to perform trends and other statistical tests for the Udaipur district.The monthly average rainfall for the Udaipur district from 1991 to 2020 is mentioned in Table 3.The standard deviation is also calculated to show the variation in the mean values of precipitation.The analysis of these parameters indicates a significant variation in rainfall concentration.
The rainfall variability for the Udaipur district through average annual rainfall for the months of January to December has been calculated by linear regression trend analysis using three decades of data from 1991 to 2020.
The linear regression trend analysis for thirty-year data of average rainfall in January, February, November, and December exhibit slopes of -0.096, -0.0827, -0.1068, and -0.0021, respectively, as shown in Figure 2. All four months (January, February, November, and December) are the months of the winter season, where no rainfall takes place, with some exceptional cases of Mawath (winter rain occurred in the Northwest of India due to cyclones arising from the Mediterranean Sea).Observations show that there was almost negligible rainfall occurred in January, February, November, and December.The linear regression trend analysis of rainfall variability for thirty-year data for seasonal and annual average rainfall for the Udaipur district is shown in Table 5 and Figure 5.The precipitation trend for winter shows a negative slope (-0.0187), which indicates no rainfall except in some exceptional cases of mawath (winter rainfall).The observations suggest that almost negligible rainfall took place in   The precipitation indices such as NAR, PCI, SRA, W i , CV, and Dependable rainfall are calculated and described in this section.
The variation in the values of SRA, CV, PCI, and W i is shown in Figure 6.The linear regression, and Mann-Kendall trend test for rainfall variability over the Udaipur district follow the same trend from January to December for thirty-year (1991-2020).The values of linear slope and sen's slope (determined from Mann Kendall trend test) are nearly the same from January to December, which verified that the rainfall trend is correct.Dependence on rainfall is essential for the sustainable use, and conservation of water.Therefore, dependable rainfall (50%, 75%, and 90%) for all months of the year was calculated and shown in Table 6 and Figure 7.
The maximum precipitation occurs in the region due to the southwest monsoon (July, August, September, and October), which is necessary to fulfil the water demand required for the rest months.

Conclusion
Rainfall variability in Udaipur district, Rajasthan (India), has been analysed from 1991 to 2020 by linear regression, Mann-Kendall trend, and various rainfall indices.This analysis shows a wide disparity in rainfall distribution.Udaipur district receives about 85.20% of the total annual rainfall through the southwest monsoon during the rainy season.
The trend tests shows a positive trend for most months (May to November) for the period of investigation over the past three decades.As a result, it shows an incre-asing total annual rainfall during the study period.for each year during the study period; hence, the study area can not fall under the category of droughtprone area.The highest value of the wetness index was found in the year 2006 (W i = 179.07),while the lowest value occurred in 2000 (W i = 54.26).Hence, 2006 was the wettest year and 2000 was the driest year during the study period the Udaipur district falls under the category of low rainfall deficiency with some exceptions.The maximum precipitation occurs in the region due to the southwest monsoon (July to October), which is necessary to fulfil the water demand required for the rest of the months.The current study helps ensure the availability of rainwater for the Udaipur district in the future for various demands like agricultural, industrial, and domestic water supply and hydropower generation.A significant trend has been observed in the annual rainfall of Udaipur from June to September during the study period, from which it can be predicted that it may increase in the future.Therefore, the main requirement to reduce the risk of flooding is the proper building and administration of water reservoirs, as well as the use of contemporary rainwater harvesting systems and drainage management.
Table 7: Regression slope and sen's slope for each month along with monthly rainfall dependability.

Fig. 2 :
Fig. 2: Linear Regression trend analysis of the rainfall recorded during the months from January to December for the years 1991 to 2020.The trend shows the positive slope in the months of March (0.2541), April (0.036), May (0.0162), and June (0.7411),representing the steadily increasing average rainfall in these months, as shown in Figure 3.All four months fall under the summer season category, where low rainfall occurs, but sometimes light rain (premonsoon rainfall) occurs along with dust storms.The observations show high variation in rainfall amount, and the amount of rainfall continuously increases over time.The linear regression trend shows a positive slope in the months of July, August, September, and October which are 0.6199, 6.4065, 1.1195, and 0.3847 respectively.The highest average rainfall observed in the months of July, August, September, and October are 516.28mm (2017), and 739.44 mm (2006), 242.56 mm (2012), and 88.89 mm (1998), respectively, while the minimum rainfall is 37.78 mm (2002) and 38.78 mm (1999), 10.78 mm (2001) and 0.00 respectively, as shown in Figure 4.The high variation in rainfall occurs from July to October due to the southwest monsoon (Winds blowing from the southwest direction (from the Arabian Sea) bring moisture with them, which it rains).The observations suggest that high rainfall occurred in these months of the rainy season.

Fig. 3 :
Fig. 3: Linear Regression trend analysis of the rainfall recorded during the months from March to June for the years 1991 to 2020.

Fig. 4 :
Fig. 4: Linear Regression trend analysis of the rainfall recorded during the months from July to October for the years 1991 to 2020.

Fig. 5 :
Fig. 5: Linear Regression trend analysis of the rainfall for seasonal and annual basis for the years 1991 to 2020.

Fig. 6 :
Fig. 6: Variation in SRA, PCI, CV, and Wi from 1991 to 2020.The trend of average annual rainfall exhibits a positive slope (0.7919), indicating that average rainfall continuously increases with time during the study period.The observations from 30 years of annual data show that the highest mean annual rainfall amount was found to be 104.47mm in 2006, and the lowest mean annual rainfall in 2002 was 33.90 mm.

Fig. 7 :
Fig. 7: (a) variation of linear regression slope and, sen's slope (b) Monthlty rainfall dependability for the study period from 1991 to 2020.

The
PCI values indicate a very high non-uniformity of rainfall, and CV values indicate less rainfall variability over the Udaipur district from 1991 to 2020.The overall CV and PCI values show a high non-uniformity and less rainfall variability.The SRA values are greater than -0.84 (No drought category) 21

Table 6 : Rainfall Index and Average Rainfall Values Precipitation indices Average Max Min
The overall CV and PCI values show a high nonuniformity and less rainfall variability.The average, maximum, and minimum values of precipitation indices and rainfall, are shown in Table6.