Variations of precipitation and runoff in the Bagmati river basin, Bihar, India

Precipitation is a key climatic variable in regulating hydrology, vegetation, and water quality. The variability and occurrence of precipitation and temperature both determine the variety of crops in the agricultural field. Understanding the characteristics of rainfall is beneficial to improve agricultural output (Gajbhiye et al. 2016a, 2016b; Meshram et al. 2017).

Climate change has become a serious environmental problem in the last 20 years. The changing pattern of rainfall requires constant attention since it will influence access to water and, as a result, food. Global temperature has increased by 0.65–1.65°C over the period of 1880–2012 (IPCC 2014). Temperatures are comparatively high in the summer and too frigid in the winter due to the effects of climate change (Manton et al. 2001; Tangang et al. 2007; Caesar et al. 2011). With temperature variations, sea surface temperature rises, resulting in significant fluctuations in rainfall and rainfall extremes (Trenberth 2011).

The influence of climate change on water resources may be studied using rainfall trend analysis. Climate change has a number of key consequences, including changes in temperature and rainfall intensity (Dinpashoh et al. 2013). As per the IPCC 2007 report (Parry et al. 2007) , water availability and annual average runoff may fall by 10–30% in dry regions while increasing by 10–40% in moist tropical areas. High agricultural water demands are caused by rising temperatures, and a lack of rainfall will increase crop water problems.

Various research works have been conducted to determine the rainfall trend and variability in various locations (Goswami et al. 2006; Guhathakurta & Rajeevan 2006; Joshi & Rajeevan 2006; Fu et al. 2008; Kampata et al. 2008; Murphy & Timbal 2008; Taschetto & England 2009; Chowdhury & Beecham 2010; Kiem & Verdon-Kidd 2010). Archer & Fowler (2004) investigated rainfall trends in the Himalayan region. Annual and seasonal data analysis showed no significant trend in the region from 1893 to 1990 (Pant et al. 1999). Increasing and decreasing rainfall trend is observed at some stations in the Kosi basin, Bihar, India (Chadha & Sharma 2000). Xu et al. (2010) investigated rainfall and runoff trends in major Chinese rivers to determine human impacts on them during the period 1951–2000.

Mann–Kendall (MK) statistics have been used for finding precipitation trends. Many studies have been carried out in South Asia. Jiang et al. (2007) studied the annual and seasonal trend of precipitation using MK and linear regression methods. Rana et al. (2012) used linear regression and MK statistics to explore the long-term trend in rainfall in Mumbai and Delhi. Chandniha et al. (2017) studied the trend of precipitation using autocorrelation and modified MK in the Jharkhand state. However, no detailed study on rainfall trends for the Bagmati river basin is found in the literature.

Correlation analysis is used to check the dependence of one parameter on others. The correlation coefficient was better explained by Pearson (1920), Weida (1927) and Walker (1928). Many authors used correlation analysis to determine the predictors for the different models (Hessami et al. 2008; Liu et al. 2008; Hassan et al. 2014). Estimating runoff from a catchment is necessary for a variety of reasons, including determining flood peaks, determining the amount of water available for municipal use, designing storage facilities, planning irrigation operations for agricultural or industrial purposes, protecting wildlife, and estimating future dependable water supplies for power generation.

The modified MK test and Sen's slope approach have been widely used to determine precipitation trends (monthly, seasonal and annual). The purpose of this study was to examine the homogeneity and stationarity of precipitation data using data analysis. The research of the variation in the trend of precipitation at four rain gauge stations (Benibad, Dhenge, Kamtaul, and Hayaghat) in the Bagmati river basin was carried out on a monthly, seasonal, and yearly basis and also compared the trend of primary (observed) data with the secondary (NCEP/NCAR reanalysis) data. Finally, a monthly and seasonal correlation between the observed rainfall and runoff is calculated for selected stations. This study shows the long-term trends of precipitation and the contribution of precipitation to a runoff.

Monthly rainfall data from 1981 to 2013 at four rain gauge stations – Dhenge, Benibad, Kamtaul, and Hayaghat – in the Bagmati Basin were obtained from the Indian Meteorological Department (IMD), Pune, and monthly runoff data from 1981 to 2009 at Hayaghat from the Central Water Commission (CWC), Patna. Secondary (reanalysis) precipitation data were downloaded from the National Center for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) for the same period.

The modified MK test is a non-parametric tool for detecting trends in climate variables. Many researchers have used the MK test to find the trend in climatic variables (Rana et al. 2012; Zhang et al. 2015; Gajbhiye et al. 2016a). The MK test is used to determine precipitation trends at gauge sites in the Bagmati basin. Monthly and seasonal correlation analysis between observed rainfall and runoff data is also carried out.

The MK test determines a monotonic trend in the time series. Monotonic trends represent constantly decreasing and increasing change over time.

If the Z-statistic value is within the range of ±1.96, the null hypothesis of having no trend in the series cannot be rejected at a 95% level of confidence.

Monthly observed and NCEP/NCAR reanalysis rainfall data from 1981 to 2013 have been used to analyze the behaviour of observed rainfall data. Homogeneity test, stationary test, Box plot, and correlation analysis have been done to analyze the rainfall data.

Monthly rainfall time series in the basin were homogeneous and stationary according to the results of Dickey–Fuller and Pettitt's tests. The Pettitt test results showed that all four rainfall station data were homogeneous. The null hypothesis is accepted between 54 and 91% of the time, indicating that the observed and NCEP data are homogenous.

The Dickey–Fuller test is used to determine whether observed and NCEP rainfall data are stationary or not. Two hypotheses were selected, null hypothesis H0 – the series has a unit root – and an alternate hypothesis – the series has no unit root, indicating that it is stationary. All four stations were observed and NCEP rainfall data were confirmed to be stationary. The null hypothesis is rejected since all of the observed stations’ p-values and NCEP rainfall data are less than 0.0001. Table 1 displays the results of both tests.

Tables 2,³⁴–5 show the MK trend results and estimated Sen's slope for monthly actual and NCEP reanalysis data. Whether the Sen slope is increasing or decreasing, if the computed probability (p) exceeds 0.05, the significance is below 95%, and if p is below 0.05, the significance exceeds 95%.

The modified MK trend results for monthly rainfall data and the estimated Sen's slope at the Dhenge station are shown in Table 2. The computed Sen's slope shows that the trend is decreasing in March, July, September, October, November, and December and increasing in April, May, June, and August, with no trend in the other months. In all months, p exceeds 0.05, indicating that the significance is below 95%. As a result, the computed trends are not statistically significant. Table 3 shows the trend decreasing in the months of April, July, and September and is increasing in the months of January, May, June, August, and October and there is no trend in the remaining months at the Benibad station. The computed trends are not statistically significant except for January. The monthly trends at Dhenge, Benibad, Kamtaul, and Hayaghat are presented in Tables 4 and 5.

After comparison of trends of the observed monthly and NCEP reanalysis data, it is found that the months of April, May, June, July, August, and September show the same trend at all four stations, but not in January, February, March, October, November, and December.

In Figure 8, the annual rainfall shows the increasing trend for the selected station. The results are in accordance with the results of Sunil & Sujeet (2015).

Tables 6 and 7 present the MK trend results and estimated Sen's slope for actual monthly and seasonal runoff at the Hayaghat station.

Table 6 shows the modified MK results for monthly runoff data and estimated Sen's slope at Hayaghat. Sen's slope shows that the trend is increasing in January, February, March, April, May, June, October, November, and December and is decreasing in July, August, and September. In all months, p exceeds 0.05 so the significance is below 95% – i.e. the computed trends are not statistically significant.

Table 7 shows the modified MK trend results for seasonal and annual runoff data and estimated Sen's slope at the Hayaghat station. The computed Sen's slope shows that the trend is increasing in the winter, pre-monsoon, and post-monsoon seasons and it shows a decreasing trend in the monsoon season. However, in all months, the computed probability (p) is greater than 0.05, i.e. the level of significance is not at 95%. So, the computed trends are not statistically significant. The pre-monsoon seasonal trend of runoff shows an increasing trend while the pre-monsoon seasonal trend of rainfall shows a decreasing trend which indicates that the increasing trend may be due to the contribution of runoff due to the melting of snow from Himalayan regions.

NCEP data are the model output data based on carbon emission. Many authors have used reanalysis data for the climate change study. Hence, for the betterment of model development, variation of actual data and NCEP reanalysis data is needed. Trend analysis of precipitation and runoff is carried out in the Bagmati river basin using the modified MK test and Sen's slope method. Monthly, seasonal, and annual trends of precipitation are computed at four rain gauge stations (Dhenge, Benibad, Kamtaul, and Hayaghat) using observed and NCEP/NCAR reanalysis rainfall data for the period 1981–2013. Furthermore, the trend of observed runoff at the Hayaghat gauging site is also computed for the period 1981–2009. The homogeneity and stationarity of the actual and secondary rainfall data were analyzed by Pettitt and augmented Dickey–Fuller tests. It is found that the observed and NCEP data of precipitations are homogeneous and stationary. Correlation between observed and NCEP precipitation data is also computed for monthly and seasonal data and found that the correlation coefficient varies from 0.6111 to 0.7435. Trend analysis of precipitation is carried out using the modified MK test and the Sen slope method. The study reveals that the same trend is found from April to September at all four stations in the basin, but they differed from one another from January to March and October to December. The seasonal trend analysis of precipitation shows an increasing trend in pre and post-monsoon seasons except in monsoon, where it is decreasing. The annual trend analysis of runoff shows a decreasing trend for the selected time period. The correlation value between the monthly observed rainfall at all stations and monthly runoff at the Hayaghat station ranges from 0.3724 to 0.4721. The correlation value is less due to non-uniformity in rainfall. Based on the above study, proper management measures have to be taken to cope up with the water scarcity problems.

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

The authors declare there is no conflict.