Statistical Downscaling of Precipitation for Mahanadi Basin in India - Prediction of Future Streamows

Climate change has long-term impacts on precipitation patterns, magnitude, and intensity, affecting 15 regional water resources availability. Besides, understanding the interannual to decadal variations of 16 streamflows in a river basin is paramount for watershed management, primarily extreme events such 17 as floods and droughts. This study investigates impact of climate change in streamflows estimation 18 for four sub-basins of the Mahanadi River, in India. The study includes three major components: (i) 19 Historical trend analysis of hydroclimatic variables, using Mann-Kendall test; (ii) Statistical 20 downscaling of GCM generated precipitation using change factor method and KnnCAD V4 stochastic 21 weather generator; (iii) Dependable flow analysis of future streamflows predicted using Soil Water 22 Assessment Tool (SWAT) model for various future GCM scenarios. It is observed that during the 23 historical period, there is a decrease in number of rainy days and total annual precipitation in all sub- 24 basins. However, the analysis also indicates an increase in flood intensity in two of the sub-basins. 25 The decadal future precipitation has a marginal decrease in precipitation (up to 10%) for future 26 scenarios; however, the precipitation events with high intensities increases. The results indicate that 27 the magnitudes of 5% and 10% dependable flows are higher than the historically observed 28 streamflows, for all future scenarios. This indicates a significant increase in extreme flood events in 29 the basin. Further, only one of the sub-basins has shown an increase in water availability for 30 agriculture and drinking water purposes (75% and 95% dependable flows) in the future. 31 Understanding future flood events in the Mahanadi basin can help decision-makers to implement 32 appropriate mitigation strategies.


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Several studies indicate that the increased global temperature is mainly due to the rising impacts on the regional water resources, extremes such as floods and droughts, forecasting, 49 hydro-climatological projections, water balance analysis, and water quality modelling (Singh et al. 50 2017, Sun et al. 2016, Apurv et al. 2015. Downscaling is one of the most widely used methods to 51 identify and evaluate the future extreme flood risks for efficient planning, mitigation, and 52 management. Because of the complexity in the coarse GCMs and the simplifications of the 53 hydrological cycle, the coarse resolution GCM variables cannot be directly employed in the 54 hydrological models. Climate models such as, the Generation Circulation Models (GCMs) 55 estimate the future climate projections at global scale representing the complex processes which 56 involves the coupling of land-atmosphere-ocean circulations. These are the only state-of-the-art 57 models available for deriving the long-term climate change studies especially for the 58 hydroclimatic variables such as temperature, wind, humidity, precipitation. These climate 59 projections are simulated based on the expected future carbon emission scenarios or radiative 60 forcings (IPCC 2014). There is a high degree of consent in the scientific community that GCMs 61 are able to model the varying field types of variables correctly (e.g., surface pressure) and capture 62 the large scale circulation patterns. However, the GCMs are unable to mimic complex processes 63 of variables such as precipitation especially at the regional scales (Hughes and Guttorp 1994). 64 According to IPCC 2014, the sources responsible for climate change includes natural internal 65 processes (such as modulations in solar irradiance, volcanic eruptions, etc.) and external forcings 66 (such as land-use changes, high GHG emissions, etc.). However, anthropogenic factors have 67 caused persistent changes in the compositions of the atmosphere, thus are more attributable to 68 climate change. 69 To capture the variations in spatial and temporal scale hydroclimatic variables, number of down-70 scaling methods are developed (Singh et al. 2017, Sun et al. 2016, Humphrey et al. 2016. 71 Trzaska and Schnarr (2014) described "Downscaling is a process that converts large-scale 72 information to finer scale information". In case of coarser spatial resolution (e.g., 500x500 km 2 ) 73 is converted to finer spatial resolution (e.g., 50 x 50 km 2 ), it is referred to as Spatial Downscaling. 74 On the other hand, if the downscaling is adopted to con-vert the GCM's coarser temporal scale 75 (e.g., monthly precipitation) to finer temporal scale (e.g., daily precipitation), which is referred to 76 as Temporal Downscaling (Xue et al. 2014). In climate research studies, the downscaling is 77 mainly distinguished into the following categories: (i) Dynamical downscaling (Xue et al. 2014, 78 Mishra et al. 2014, Shukla et al. 2013); (ii) Statistical/empirical downscaling (Wilby et al. 2014) 79 and (iii) Weather generators. Dynamical downscaling is numerically advantageous to statistical 80 downscaling; however, these models are computationally intensive, require large amounts of 81 datasets and a high level of manpower to generate results (Trzaska and Schnarr 2014). Statistical 82 downscaling methods are computationally inexpensive and efficient. These methods develop a 83 statistical relationship between the observed climate data and baseline GCM data to derive future 84 predictions. They can provide point-scale climate variables for GCM-scale outputs. Weather 85 generator based statistical downscaling generates sub-daily information at multiple sites and 86 variables simultaneously to represent the long-term uncertainty due to climate change and its 87 variations. Each downscaling method has its own limitations and uncertainties. There is no 88 official guideline available in selecting a downscaling method that best suits the users' demands.

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Therefore, the climate research community is still developing the downscaling methods.

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The feedback from various climatic and ecological variables regulates the hydrologic behavior of a catchment. Thereby it is difficult to formulate the relationships between these variables. Whitefield and Cannon (2000) has brought out the importance of the correlations between various hydroclimatic variables using an extensive study across Canada. The changes observed in temperature, precipitation, and streamflow (obtained from climate and hydrology stations) were clustered into different classes and investigated their spatial distribution. It was noted that there is a strong correspondence between the distribution of ecozones and hydroclimatic variables in Canada. Besides, the study highlighted that uncertainty in the variables due to climate have a major impact on the hydrologic systems.
During recent decades, India has experienced multiple destructive climate extremes.
According to the Planning Commission (2011), flood disasters have affected nearly 33 million people during year 1953 to 2000. Kumar et al. (2005) reported that on July 26, 2005, the financial capital of India, Mumbai has recorded about 950mm of rainfall, causing havoc and several casualties. Gosain et al. (2006 and2011) used HadRM2 weather simulations for 12 river basins in India to simulate the changes in future streamflows due to climate change using the SWAT model and GCM. They predicted severe flood conditions in at least three large river basins, namely, Godavari, Brahamani, and Mahanadi. Further, a report by the World Bank (2008)  Ganges, Brahmaputra, and Narmada. However, for river Mahi and Tapi basins it is observed that the streamflows are decreasing. In addition, it is observed that under high emission scenario (RCP8.5) it is reported that there will be a significant increase in streamflows for all the major river basins in India. Das and Simonovic (2012) found that the mean future streamflows in Wainganga River Basin are likely to decrease when compared to the historical period. Tamor River Basin and quantified uncertainty related to elevation bands, hydrologic response units, and number of sub-basins. Lee et al. (2018) evaluated the impacts of changing precipitation, temperature and Carbon-dioxide on the crop growth. Sharannya et al. (2018) evaluated climate change impacts on precipitation, temperature, and runoff, using SWAT model.
For baseline period analysis, the daily weather data generated by CORDEX was used, while the future period analysis was done using RCP4.5 scenario. Shiferaw et al. (2018) developed a SWAT model for Ilala watershed (Ethiopia) for surface runoff generation under changing climate scenarios. The Change Factor Methodology was adopted for statistical downscaling of RCP4.5 and RCP8.5 data. It was observed that there is a significant decrease in runoff in the near future under RCP4.5, while the decrease at the end of the century is minimal for RCP8.5. Shrestha et al. (2018) used SWAT model to identify the impacts of climate change on future streamflows and found a significant decrease in streamflows (19.5% and 24%) and nitrate loadings (11.25% and 15.25%) for RCP4.5 and RCP8.5, respectively. Khalilian and Shahvar (2019) studied the climate change impacts on streamflows and drought characteristics using SWAT and SPI, respectively in Salt Lake sub-basin, Iran. It is observed that under A2 climatic scenario (2027) there is a 2 o C and 20% decrease in temperature and precipitation, respectively, causing increase in drought severity.
The study area also reported 10% reduction in surface water resources, 16% reduction in aquifer recharge, and 20% reduction in renewable water under changing climate.
The study examines climate change impacts on floods in the Mahanadi basin, India. Climate scenarios developed from the GCMs are linked to hydrological models to extract the peak flow values. Trend analysis has been proposed in the study to examine the behavior of rainfall and runoff variables. The large-scale GCM precipitation is downscaled using the delta change method.
Further to assess the impacts of climate change, the future streamflows are predicted using SWAT model based on represented concentration pathways (RCPs) as future scenarios.

Case Study
The Mahanadi River Basin (Latitude 19°8'-23°32' N and Longitude 80°28'-86°43' E) is one of the largest watersheds among the major river systems in India. The majority of the basin Pune is used for climate change investigation.

Statistical Trend Analysis
The Mann-Kendall (M-K) is adopted in this study to identify the linear trends in time series of precipitation and discharge. Several studies have extensively used the M-K test to determine whether a time series of climatic variables, particularly the rainfall characteristics has a monotonic upward or downward trend in relation to climate change (Taylor and Loftis 1989, Burn 1994, Burn et al. 2004). Before applying M-K test it is necessary to recognize the serial correlation present in the data. For the Mahanadi River Basin data, various blocks are tested to identify serial correlation. For the detailed steps involved in the M-K test, readers are referred to (Salas 1993, Storch and Navarra 1995, Partal and Kahya 2006.

Statistical Downscaling
The Global Circulation Models (GCMs) provide the climate information at global or continental scale. Downscaling is adopted to build a relationship between GCM outputs and regional or local climate variable (coarser to finer spatial resolution). Downscaling is classified as dynamical and statistical downscaling approaches. The first approach deals with the regional scale derivation of GCM outputs, using the boundary conditions of GCMs and local physiographic information. The models obtained are called regional climate models (RCMs). The latter one is preferred to spatially downscale GCM outputs to local scale. The dynamic downscaling process demands ample amount of data and is computationally extensive. Also, the uncertainty in the GCMs significantly affects the outcomes of the dynamically downscaled results [42,43]. on the contrary, statistical downscaling is a less computationally demanding approach. It is based on the principle of interdependency among the climate data and regional data having physiographic characteristics (IPCC 2014).
Weather generators are generally used to replicate statistical characteristics of local climate data to generate long simulations of climatic variables. they have also adopted for temporal downscaling of monthly or annual average data to obtain multiple daily time series of weather variables. The method requires large amount of data and post-processing of the outputs. On the other hand, the Change Factor (CFM) or Delta change Method is being extensively used in statistical downscaling due to its easy and computationally straight forward application. changes projected by future climate models can be incorporated in the historically observed climate variables using Change Factors (CFs). Different change factor methodologies are comprehensively explained in Anandhi et al. (2011). There are two types of CFs, namely additive and multiplicative CFs as given in equations 1 and 2.
Where, and are average of modelled climate values over baseline and future period respectively. These CF add and CF mult are then added and multiplied respectively to the observed local climate variables to obtain the future modelled values.

KnnCAD Version 4 Algorithm
In this study KnnCAD V4 based stochastic weather generator (King et al 2015) is used to simulate multi-variable hydroclimatic data for future time-periods. The two major components of the KnnCAD V4 model are: (i) preservation of spatial characteristics using identification of 'k' nearest neighbors, covariance matrix of potential neighbors and PCA; and (ii) preservation of temporal characteristics using Mahalanobis distance and block bootstrapping. In addition, the method uses perturbation to generate the extremes. The nearest-neighbor models are easily applicable for several sites unlike the parametric weather generators which is restricted by the statistical assumptions. For the detailed steps involved in KnnCAD V4 algorithm, the readers are referred to (King et al. 2015). The SWAT model performance is evaluated using Nash-Sutcliffe efficiency N SE . The details about model performance measures is presented as follows:

SWAT Model Description
Where, 0 are observed and modelled discharges at time t, respectively. is average observed discharge. NSE value of 1 implies an exact fit between the model simulated and observed values.

Spatial Interpolation of Gridded Observed Data and GCM Data
The Inverse Distance weighting (IDW) method is adopted to determine the unknown value of any ungauged location. In this method, the nearest grid points to the ungauged station are weighted by an inverse distance function from the station to the grid points. Thus, the closest grid points are weighted more than the grid points further away from the station.
The mathematical expression for IDW method is given as: Where, d i is a distance from the ungauged station to the i th grid point. k is number of nearest grid points. Spatially interpolated precipitation for the ungauged station using the above weights can be calculated using formula given by:

Trend Analysis for Precipitation and Discharge Data
The precipitation and discharge trends are identified using the Mann-Kendall test. The discharge data series is tested for serial correlation, and it is observed that a significant correlation is obtained at 95% confidence level. Thus, the pre-whitened data series is used further for the M-K test.  Table 3, which shows that the precipitation series does not experience a significant statistical trend during monsoon months. Despite that the seasonal precipitation shows a decreasing trend at all gauging stations in both the seasons (Table 4) Further analysis is carried out to verify the precipitation pattern using total number of rainy days ( Figure 3). For all sub-basins, the plots indicate a decreasing number of rainy days over the years for all four sub-basins, with the highest decrease in precipitation events observed for Kesinga sub-basin. The precipitation events with 50 mm, 75 mm, and 100 mm intensities for four subbasins are plotted and presented in Figures 4 and 5. It is observed that the precipitation events are increasing for all sub-basins. However, the Sundergarh sub-basin has a marginal decrease in number of rainy days for all precipitation intensities. This has resulted in the increased dry spells within the catchment. It is also evident from the analysis that although the Tel river basin has experienced fewer precipitation events, their intensities have increased. It is also evident from the increasing discharge trends observed for Kantamal and Kesinga gauging sites.

Statistically Downscaled GCM Data for Mahanadi Basin
In this analysis, an integrated approach combining change factor methodology (CFM) and KnnCAD weather generator is used to predict future climate variables ( with the maximum increase observed in the Kesinga sub-basin (Figures 9 and 10). This indicates the Tel river basin can experience more precipitation events with higher intensities.

SWAT model Application to Mahanadi Basin
The  Figure 11, respectively. In this analysis, 5 years of warm-up period is considered. Based on the availability of the gauging sites data, different calibration periods are adopted for each site, such as Salebhata , Sundergarh (1983Sundergarh ( -2000, Kesinga (1983Kesinga ( -2000, and Kantamal (1978Kantamal ( -2000. The remaining data record of 9 years (2001 to 2009) is used for validation at all the sites.
The efficacy of the SWAT model performance is carried out using Nash-Sutcliffe Efficiency (NSE). It is observed that the models have been well calibrated and have shown reasonably good NSE values. The efficiencies for Kantamal, Kesinga, Sundergarh, and Salebhata sub-basins are reported as 78%, 82%, 76%, and 68% respectively. Table 5 represents the calibrated parameters and efficiency for different gauging sites during calibration. Figure

Future Water Resources Scenario in Mahanadi Basin
The future projected precipitation at four gauging sites is adopted in for calibration and validation of SWAT model. It is simulated for different combinations of GCMs, i.e., from low to high (RCP2.6 to RCP8.5) emission scenarios with different realisations and for the three selected time horizons (2006-40, 2041-70, and 2071-99). These alternate climate scenarios are further analysed for simulating outflows: (i) to identify changes in availability of water and (ii) the extreme events.
An empirical distribution is fitted to perform the dependable flow analysis (Weibull 1951).
Dependable flow represents a relationship between volume of water available for utilization and the period of time for which its available during a year. In this study, the dependable flow is estimated at five exceedance probability which includes: (i) extreme flood events (5% and 10% dependability), (ii) moderate flood events (20% dependability), (iii) median flows (50% dependability), (iv) water availability for agriculture (75% dependability), and (v) water availability for domestic drinking demand (95% dependability). The annual dependable flows at four gauging sites for different GCM emission scenarios are compared and represented in Figure   13-16. It is observed that for all future scenarios in Mahanadi River Basin there is a considerable increase in 5% and 10% dependability flows. This indicates an increase in extreme to moderate future flood events for few sub-basins. The depend-able flows in each sub-basin are compared with the historical observed flows and the results are as follows: 1. Salebhata sub-basin (a) The 5% dependability flows have decreased in the future, which indicates decrease in extreme future flood events.
(b) The 10% and 20% dependability flows have increased considerably, indicating increase in moderate flood events.
(c) Also, there is availability of median flow (50% dependability) during the future periods.
(d) The 75% and 95% dependability flows are not observed in the future periods. (c) The median flows have also increased for all scenarios in future period.

Sundergarh sub-basin
(d) The 75% and 95% dependability flows are not observed in the future periods.

Kesinga sub-basin
(a) There is a significant increase in 5% and 10% dependability flows indicating increase in extreme flood events in the future.
(b) The 20% dependability flows have increased in the future period, which indicates in-crease in moderate flood events.
(c) The median flows are also increased in the future period.
(d) There is no availability of 75% and 95% dependability flows.

Kantamal sub-basin
(a) There no change in 5% dependability flows. This indicates similar future extreme flood events as the historical period.
(b) The 10% and 20% dependability flows have moderately increased in the future period, which indicates increase in the moderate flood events.
(c) The median flows are significantly increased in future period.
(d) There is significant increase in 75% and 95% dependability flows, indicating availability of water in future period for agriculture and domestic drinking requirement.

Summary and Conclusions
In the present study, a Mann-Kendall trend analysis is carried out for historical rainfall and discharge series for the Mahanadi river basin of Odisha. After finding a significant correlation in discharge data, the pre-whitened discharge series is provided for M-K test. Daily discharge trends are analysed for various gauging sites, and it is observed that the Tel tributary is experiencing an increasing trend, whereas the Ong tributary is experiencing decreasing trend. Daily, monthly and seasonal precipitation trends are analysed for the period between 1961 and 2004. No trend is found for daily and monthly precipitation data. It is to be noted that during the monsoon period, rainfall decreases significantly for two sub-basins (Salebhata and Sundergarh) using the M-K test. During the non-monsoon season, a decreasing trend is observed for all stations, but these are not significant. The historical (1961 to 2004) precipitation variation points out a reduction in number of rainy days and total annual precipitation for all sub-basins. Kesinga sub-basin has observed the highest decrease in precipitation events in the Mahanadi basin. However, the precipitation events with high intensities (more than 100mm precipitation) have increased over the Kesinga and Kantamal sub-basins, indicating an increase in the Tel tributary discharge.
The precipitation data obtained from CanESM2 GCM has been downscaled using the change factor method in combination with KnnCAD to extract future climate projections . It is observed that the KnnCAD approach can capture the statistical relationship between the observed and GCM simulated data. The decadal analysis of projected precipitation shows a slight decrease in precipitation (1.5 to 10%) for all RCP scenarios. However, the number of precipitation events with high intensities are increasing in the Tel tributary. All the RCP scenarios indicate an increase in future precipitation intensities. It is observed that the RCP2.6 and RCP4.5 show a moderate increase in the precipitation intensities, whereas RCP8.5 shows a significant increase. The SWAT model has been developed for four sub-basins to generate future discharge scenarios using downscaled data. The SWAT model simulations show that an increase in the extreme rainfall events will get translated into floods in the Mahanadi basin. The dependable flow analysis using the future model simulations indicated that the magnitude of flood events is expected to increase substantially compared to observed historic floods.

Limitations and extensions
1. The study includes change factor methodology for statistical downscaling of precipitation; however various regression-based techniques can be adopted to improve the performance.
2. The study is restricted to only precipitation as a predictor for its downscaling; however other hydroclimatic variables such as temperature, humidity, pressure, geopotential height, etc. can be included in the analysis for better prediction of precipitation.
3. In this study, only CanESM2 model data has been adopted to obtain climate change projections; however various GCM ensembles with their realisations can be included in the analysis.

Declaration
Funding: This research did not receive any specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Conflicts of interest/Competing interests:
Authors declare that they have no conflict of interest.
Availability of data and material : Some data pertaining to the rainfall, river flow which is classified data used in the study were provided by a third party (