Spatio-temporal trends in observed and downscaled precipitation over Ganga Basin

This paper focuses on the spatio-temporal trends of precipitation over the Ganga Basin in India for over 2 10 centuries. Trends in precipitation amounts are detected using observed data for historical period in 20th century and using downscaled precipitation data from 37 GCMs for 21st century. The ranking of 37 GCMs (from CMIP5 archive) is done employing a statistics based skill score. The best ranked GCM output is then bias corrected with observed precipitation prior to further analysis. The direction and magnitude of trend in annual and seasonal precipitation series is determined using Mann Kendall’s test statistic (ZMK) and Thiel Sen’s Slope estimator (β). The plots depicting the spatial variation of ZMK 15 and β are prepared which provides a comprehensive inter-scenario comparison of spatio-temporal trends in precipitation series. Highly non-uniform spatio-temporal trends are detected for observed precipitation series. It is observed that the precipitation for annual and southwest monsoon season is indicating a rising trend for all future emission scenarios in the region adjacent to Himalayas (northeast side of study area) but shows falling trends in the plains away from the Himalayas. Insignificant trends are observed in pre-monsoon and winter season precipitation. An inter-emission-scenario comparison 20 shows that for higher emission scenarios the annual and southwest monsoon precipitation is showing rising trends with increasing spatial dominance i.e. the area under rising trends increases as we observe it from low to high emission scenarios.


Introduction
The Ganga basin is of great social, economic and religious importance to India.The basin which is a part of northern plains of India is predominantly covered by fertile alluvial soils brought down by various tributaries of Ganga.Agriculture being the dominant economy sector in this basin is therefore dependent on rainfall.The monsoon season for the region is mainly in the months of June to September.Similar is the season for cultivation of Kharif season crops in India.Main Kharif crops are rice and millet, which are highly dependent on quantity and timing of availability of rain water.More than 85% of the total rainfall occurs in monsoon season in this region.Rabi crops are sown in winter and harvested in spring season.In India, the Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-388Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 17 July 2017 c Author(s) 2017.CC BY 4.0 License.main Rabi crop is wheat, for which the main source of water is groundwater and irrigation.Excess rainfall in this season may spoil the Rabi crops but on the contrary is beneficial to Kharif crops.
Interpreting the importance of rainfall in the region, this study is targeted for determining the possible future trends in precipitation for the area.Ganga basin is already of great interest to many researchers, hydrologists and water resource planners.Few of them have already reported the trends in observed precipitation series in some regions which are subsets of Ganga basin (Kothyari et al. 1997;Duhan and Pandey 2013;Suryavanshi et al. 2013).They have utilized monthly time series of observed precipitation and aggregated them to annual and seasonal amount to capture the trends embedded in them.
A number of studies related to trends analysis of rainfall/precipitation are reported in literature.Diversities are found in various studies from around the world which include not only temporal trends but also spatial trends in precipitation patterns, out of which some of them are enlisted in Table 1.The studies are based on rainfall/precipitation on various time scales such: annual extreme of 5-30 min and 1-12 h rainfall (Adamowski et al. 2003), annual total rainfall, seasonal total rainfall (as per most of the authors enlisted in Table 1); whereas as in few studies, researchers have focused on rainfall amounts of a particular season only such as monsoon season rainfall (Bashistha et al. 2009).Some authors have also utilized certain indices for trend detection such as frequency indices in daily rainfall for total, light, moderate, intense and very intense rainfall (Gallego et al. 2011), seasonality index (Celleri et al. 2007).Most of the researchers have used rain-gauge station data, whereas few of them have considered data for meteorological subdivisions of a region for trend analysis (Guhathakurta and Rajeevan, 2008).
Popular methods used by researchers for trend analysis of rainfall/precipitation time series are parametric linear regression analysis (Guhathakurta and Rajeevan 2008;Caloiero et al. 2011;Kumar et al. 2013), robust locally weighted regression (Kothyari et al. 1997), non-parametric Mann-Kendall's test (used by most of the authors enlisted in Table 1), modified Mann-Kendall's Test (Bashistha et al. 2009), Sen's slope estimator (Gallego et al. 2011;Barua et al. 2013;Duhan et al. 2013;Suryavanshi et al. 2013).Jain and Kumar (2012) have shown insignificant Sen's slope estimates for annual as well as seasonal observed rainfall series in Ganga Basin as a whole.Duhan and Pandey (2013) have also observed a dominating negative trend at most of the rain gauge stations except for a few in the study area which lies in western part of Ganga Basin.Arora et al. (2016) have provided a scenario-wise comparison of downscaled rainfall over a upper Yamuna sub-basin.
A number of agencies have developed their own GCMs following the norms provided by Intergovernmental Panel on Climate Change, yet every GCM cannot be stated as ideal for a particular location.Ranking for best fitting GCMs is done on the basis of skill scores which are subsequently based on certain statistical parameters in order to determine the GCMs with best precipitation capturing capability (Perkins et al., 2007;Ojha et al., 2013) In this study, along with the spatial and temporal trends in annual and seasonal precipitation, future-emission-scenario-wise trends are also presented.For this, the observed and downscaled precipitation data is used which is made available by various sources in gridded form.Ranking is done on the basis of skill score which is further based on various statistical parameters and other statistics.Bias correction is performed on downscaled precipitation to reduce the systematic biases present in them.After that the trend analysis is performed on observed and bias-corrected downscaled precipitation series

Ranking of GCMs
Various researchers have practiced the ranking of GCMs for the purpose of getting better estimates of downscaled precipitation.In Fig. 3, just by visual inspection, it can be inferred that there is a large variability in predicted values of target variable, when an ensemble of GCMs is considered.Therefore ranking of GCMs is necessary to determine the GCMs in best agreement with observed data.Raju et al. (2016) have practiced a compromise programming based methodology for ranking of CMIP5 based GCMs for evaluating the performance of maximum and minimum temperature (Tmax and Tmin) simulations over India.For determining the performance of GCM for prediction of different hydro-meteorological variables, skill scores based ranking methods are also exercised by respective authors.(Anandhi and Nanjundiah, 2015;Fu et al., 2013).In this study, for evaluating the performance of GCM in simulating the precipitation series, ranking of GCMs is done based on an skill score (SS).This skill score is developed based on combined magnitude of several statistical measures.These are: coefficient of correlation (CC), absolute relative error in: means (REMN), standard deviation (RESD), coefficient of skewness (RECS), coefficient of kurtosis (RECK), Mann-Kendall statistic (REMK) (Kendall 1975), Thiel-Sen's slope (RETS) (Thiel 1950;Sen 1968), shape and scale parameters of gamma distribution (REG1 and REG2).The lower the value of SS the better will be the performance of GCM in predicting the precipitation for an area.
( ) Spatially averaged skill score (SASS) is obtained by averaging the SS values over study area.The formula is as shown below. 1 Where, SSp = skill score at a particular grid point, P = number of grid points covering the study area.
Where, p j and p i = data points of precipitation time series, Z MK =test statistic for Mann Kendall test, E(*)=Expected value, 5 Var(*)=variance, n=length of precipitation time series (in years), T=number of ties in precipitation time series, t i =number of data point for i th tie.

Thiel Sen's slope estimator
Although the Mann Kendall test shows its proficiency in detecting trends in a time series but does not provide slope estimates.Therefore Hirsch (1982) proposed a method for this using Thiel-Sen's slope estimator.The Thiel-Sen's slope (β) 10 is used to determine the magnitude of trend in terms of its slope (Thiel 1950a(Thiel , 1950b(Thiel , 1950c;;Sen 1968).Assumption of linear slope is applied to this method.Unlikely linear regression method, the Thiel-Sen's slope is insensitive to the presence of extreme values in the data series (Lettermaier et al. 1994), as it requires calculation of median.In this study, it is employed on seasonal and annual total precipitation time series.The slopes are determined between all data points of precipitation time series and the median of all slopes results in β.For a data series of size n, the total number of slopes will 15 be n C 2 (i.e., n(n-1)/2).The β is formulated as shown in Eq. 7.
Where, p j and p i = data points of precipitation time series, i and j = indices of data points.As per Z MK (Fig. 5), for all AR5 future scenarios the precipitation time series is showing a dominant rising trend in annual and SWM season near Himalayas.For lower emission scenario (RCP2.6),insignificant trend is observed in most part of study area.As per β (Fig. 6), the magnitudes of slopes for downscaled precipitation are smaller (0<β<1.645)for lower emission scenarios (RCP2.6)throughout the basin.The area classified under higher magnitudes of slopes (β>1.960) increases as we observe it from lower emission scenarios to higher emission scenarios.

Detection of trend in precipitation: North-East monsoon season (Post-monsoon)
In case of observed precipitation for NEM season (Fig. 5), a mixture of significant negative and insignificant trends are detected in upper and middle reaches of River Ganga respectively , with insignificant trends being spatially pre-dominant throughout the study area.. Similar pattern can be seen in β (Fig. 6) for observed precipitation, with β being negative (-1.645<β<0) in upper and middle reaches, and β being positive (0<β<1.645) in lower reaches of Ganga basin.
For downscaled precipitation, area under significant positive trends (Z MK ) has a greater spatial coverage for all emission scenarios.The trend remains significant in western region for all emission scenarios except RCP 4.5.As per β (Fig. 6), the downscaled precipitation has a mild positive slope (0<β<1.645)which is spatially dominant throughout the study area for all the AR5 emission scenarios.

Detection of trend in precipitation: Pre-monsoon season and winter season
A spatially dominant insignificant trend can be observed all over the study area for observed as well as all RCPs.Small clusters of significant positive trend can be seen at the downstream side of Ganga (eastern portion of Ganga basin) for observed, RCP 2.6 and RCP 8.
Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-388Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 17 July 2017 c Author(s) 2017.CC BY 4.0 License.2Study Area and Data Used2.1 Ganga BasinIndia lies in a tropical monsoon climate zone with spatially diversified rainfall pattern(Guhathakurta et al. 2011).The study area considered is the portion of Ganga basin which lies in India only.It lies between latitudes from 21.25º N to 31.5ºN and longitudes from 73.25º E to 89.25º E. As per the Köppen-Geiger climate type map of Asia(Peel et al. 2007), the study area predominantly lies in humid-subtropical climatic zone of India.A smaller region of it in the western most part lies in semiarid zone, whereas the downstream-most part of it lies in tropical wet and dry zone of India.The length of main stream of Ganga is more than 2500 kms and the catchment area is about 20% of the total geographical area of India.The River Ganga originates in the laps of Himalayas (at Gaumukh), flows eastwards through the northern plains of India and finally drains into the Bay of Bengal, forming the biggest delta in the world along with the River Brahmaputra.Along its complete stretch, many tributaries unite themselves with the Ganga at various locations.Tributaries like Gomati, Ghaghra and Gandak conjoins with main stream of Ganga from the northern side.These tributaries are glacier fed and are perennial.Whereas tributaries like Chambal, Sind, Betwa, Ken and Son conjoins it from the southern side.

Figure 1 :
Figure 1: Study Area -Ganga Basin 2.2 Precipitation Data Used The precipitation dataset used for the study in this paper consists of gridded observed and downscaled precipitation.Observed Precipitation data (Pobs): The observed daily precipitation is made available by the Indian Meteorological Department (IMD) in gridded form for the time period ranging between January 1901 and December 2015.The horizontal

Figure 2 :
Figure 2: Long term means of annual and seasonal (SWM, NEM, PM and WS) aggregates of precipitation amount.

Figure 3 :
Figure 3: Annual precipitation time series plots for observed and CMIP5 data for historical period (1950-2005) Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-388Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 17 July 2017 c Author(s) 2017.CC BY 4.0 License.calculated and ranking is done on its basis.The minimum score is obtained for the GCM named CESM1-CAM5 (GCM no. 9 in Table 2) developed by National Center for Atmospheric Research, USA.HadCM3 (Met Office Hadley Centre, UK) and IPSL-CM5A-MR (Institut Pierre Simon Laplace, France) holds second and third rank in skill for prediction of precipitation over Ganga basin.Fig 4 shows the SASS of all the 37 GCM in order of their ability to predict the precipitation in the study area.

Figure 5 :Figure 6 :
Figure 5: Spatio-temporal variation of Mann Kendall statistic (Z MK ) for annual and seasonal amounts of precipitation (observed and downscaled) over Ganga Basin in Indian administrative boundary

Table 1 : Summary of studies related to trend analysis of rainfall/precipitation No. References and study area Duration and data length Methods employed Studies around the World
Mann-Kendall Test, Thiel-Sen's slope estimator, Cumulative deviations test and Mann-Whitney-Pettitt method 4 Suryavanshi et al. (2013) Betwa Basin, India annual and seasonal precipitation (monsoon, winter and summer) Mann-Kendall Test, Thiel-Sen's slope estimator 5 Arora et al. (2016) Yamuna-Hindon Interbasin, India monthly precipitation series scenario-wise comparison

Table 2 List CMIP5 GCMs and developer agencies
Institute of Atmospheric Physics, Chinese Academy of Sciences (LASG-CESS), China.