Analysing model disparity in diagnosing the climatic and human stresses on runoff variability over India

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S0022-1694(19)31142-4 https://doi.org/10.1016/j.jhydrol.2019.124407 HYDROL 124407

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31 August 2019 13 November 2019 25 November 2019

Please cite this article as: Sinha, J., Das, J., Jha, S., Goyal, M.K., Analysing Model Disparity in Diagnosing the Climatic and Human Stresses on Runoff Variability over India, Journal of Hydrology (2019), doi: https://doi.org/ 10.1016/j.jhydrol.2019.124407

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Analysing Model Disparity in Diagnosing the Climatic and Human Stresses on Runoff Variability over India Jhilam Sinha1, Jew Das2*, Srinidhi Jha3, Manish Kumar Goyal4 1

Junior Research Fellow, Discipline of Civil Engineering, Indian Institute of Technology Indore 2 Research Associate, Discipline of Civil Engineering, Indian Institute of Technology Indore 3 Research Scholar, Discipline of Civil Engineering, Indian Institute of Technology Indore 4 Associate Professor, Discipline of Civil Engineering, Indian Institute of Technology Indore *

Corresponding Author, email id: [email protected]

___________________________________________________________________

Abstract Water availability is crucial for sustaining the development and even existence of human civilization. Identifying major sources of its variability is of paramount importance. The climate elasticity method provides a suitable platform to quantify the relative influences of climatic variables and anthropogenic stresses using Budyko hypothesis to the changes in runoff but judicious selection of Budyko based equations with relevant runoff elasticities is vital. In this paper, comparative study is carried out using climate elasticity approach in 19 catchments across India, to evaluate the disparity among runoff elasticities and percentage contributions of climatic variables (precipitation, maximum and minimum temperature, wind speed, sunshine duration, and relative humidity) and anthropogenic stress in runoff alterations. Among climatic parameters, precipitation has shown the maximum influence in 16 catchments. In 15 catchments, maximum temperature has higher relative contribution than minimum temperature. In addition, anthropogenic influence is higher in 9 catchments for Two-parameter approach (precipitation and potential evapotranspiration) whereas it has higher impact in 10 catchments as per Multi-parameter (including evapotranspiration elasticities) approach. Decomposing evapotranspiration elasticity to five climatic variables has been proven to be unproductive as it has produced more disparity among the percentage contribution values. The standard deviation values in contributions are more in the case of the

Multi-parameter model. Thus, it is pragmatic to adopt Multi-parameter model that constitutes runoff elasticities to different climatic variables, when assignment demands the individual influences of these variables on hydrology. Adding more parameters into the framework introduces more error in the assessment of impacts of climatic variabilities.

Keywords: Anthropogenic stress, Budyko framework, Evapotranspiration, Climate variability, Runoff elasticity

1. Introduction With the increasing evidence from the past studies, it is well established that climate change has become a paramount factor influencing the hydrological behaviour (Arnell, 1999; Huntington, 2006; Simonovic, 2017). As per the Intergovernmental Panel on Climate Change (IPCC), the anthropogenic greenhouse gas emissions have increased since the pre-industrial era (IPCC, 2014), which has led to the warming of the Earth’s atmosphere (Karl & Trenberth, 2003). The rising temperature modify the climatic patterns around the globe, which in turn alter the spatiotemporal patterns of precipitation thereby affecting the hydrological systems and altering the quality and quantity of available water resources (Immerzeel et al., 2010). For instance, a study carried out by Schewe et al. (2014) reported that 2oC of global warming will confront an additional 15% of the global population under water scarcity condition. Similarly, anthropogenic activities viz., deforestation, urbanization, industrialization, construction of the dam, irrigation, etc. are likely to influence the hydrological processes directly or indirectly (Huntington, 2006), which consequently redistribute the spatio-temporal availability of water resources (Milly et al., 2005). Moreover, the anthropogenic activities heavily affect the regional hydrologic cycle globally (Wada et al., 2010; D. Wang & Hejazi, 2011), promoting anthropogenic droughts (AghaKouchak et al., 2015), which suggest unsustainable water resources management as a result of human-induced water stress. It is worth mentioning that the term “climate change” encompasses climate evolution due to naturally and anthropogenically induced variability and the quantification of the changeability in the hydrological processes reflects the combined feedback from both natural and anthropogenic forcing. India, being an agrarian country with more than 1.2 billion population, has a huge demand of water resources and due to the dual pressure of population growth and climate change, the gap between demand and supply has increased substantially. Subsequently,

urbanization and industrialization, due to India’s booming economic growth, have greatly altered the land use pattern in the most parts of the country (Unnikrishnan et al., 2016). In addition to the anthropogenic activities, the changing climate is one of the major threats to the water resources and food security as the country holds only 4% of total water resources and 9% of the arable land of the globe (Goyal & Surampalli, 2018). In this sense, understanding the water resources system and its exposure to the adverse natural and anthropogenic stressors are crucial to fulfill the demand of the growing population. Understating the individual effects of climatic variability and anthropogenic activities on water availability (Q) are beneficial to promote optimal water resources management (Chawla & Mujumdar, 2015), to develop water management strategies to sustain the functionality of the ecosystem (Gao et al., 2016), to devise adaptive measures against climate change (X. Wang, 2014) and to ensure the dependable water resources for domestic and agricultural uses (Liang et al., 2015). Hence, in the recent years numerous studies have been attempted to examine the variability in the streamflow as a result of natural (hereafter climatic variability) and human-induced changeability but are not limited to Creed et al. (2014), Helman et al. (2017), Liang et al. (2015), Sinha et al. (2018), Wang (2014), Wu et al. (2017). In order to examine the extent of influence due to climatic variability and human activities in the long-term average changes in the streamflow, the commonly used methodologies are categorized into empirically-based, hydrological modelling-based and elasticity-based approaches. The empirically-based approach needs long record of hydro-climatological datasets and establishes statistical relationships between the streamflow and other climatic variables of interest using regression analysis, time-trend analysis, double-mass curve method, etc (Zhao et al. , 2015; Kong et al., 2016; Zhang et al., 2011). Hydrological modelling serves as a powerful tool for conceptual/physical representation of the hydrological cycle and capable of

modelling the individual impact of climatic and anthropogenic activities on runoff variability (Chawla and Mujumdar, 2015; Zeng et al., 2015; Li et al., 2012). Elasticity based methods determine the sensitiveness of hydrological responses to variability in climatic parameters. This climate elasticity approach (explained in the methodology section in detail) has an advantage over the hydrological modelling as it uses fewer hydro-climatic datasets and provides a generalized relationship based on the annual mean and without incorporating the underlying surface of a basin (Li et al., 2012). The commonly used elasticity-based methods include statistically based non-parametric method and analytically derived Budyko framework (Arora, 2002; Budyko, 1974; Fu et al., 2007; Sankarasubramanian et al., 2001). In the initial stage, runoff elasticity to precipitation (P) was defined by Schaake, (1990) as:

 P ( P, Q ) 

dQ P dP Q

(1)

Sankarasubramanian et al. (2001) opted the methodology to prepare a contour map of precipitation elasticity across the United States. Arora (2002), with his comprehensive analytical elasticity method, introduced two runoff elasticity to precipitation and potential evaporation using four non-parametric and one parametric equations (L. Zhang et al., 2001). Fu et al. (2007) derived the runoff elasticity to precipitation and temperature (T) and the relative change in discharge is defined as:

Q P T  P  T Q P T

(2)

The idea of introducing the temperature parameter was to include the influence of global warming that intensifies the hydrological cycle and ultimately leads to precipitation extremes. It had been acknowledged that other climatic parameters along with temperature

impact the evaporation process and this along with precipitation could represent the impact of climate change as a whole on the runoff. Subsequently, Zheng et al. (2009) proposed a similar expression including the runoff elasticity to precipitation and potential evapotranspiration (Eo) as:

E0 Q P  P   E0 Q P E0

(3)

Yang and Yang (2011) extended this expression to observe the individual impacts of climatic parameters namely temperature, wind speed (U), net radiation (Rn), relative humidity (RH) on runoff change. The relative change in discharge was expressed as:

Rn Q P T U RH  P  T  U   Rn   RH Q P T U Rn RH

(4)

Wang et al. (2016) further discussed the importance of decomposing the temperature variable to maximum (TX) and minimum temperature (TN) and insisted on considering sunshine duration (N) in place of Rn to avert from the relative errors due to inter-dependency of Rn on N, RH, TX, and TN. For addressing the issue of variability of surface characteristics like topographical attributes, soil moisture, vegetation covers etc., predominantly influenced by human activities and its impact on hydrology, Wang et al. (2016) added elasticity to catchment characteristics using Budyko framework for quantifying the relative change in discharge. The equation thus stated as: Q P TX TN U N RH n  P   TX   TI  U  N   RH  n Q P TX TN U N RH n

(5)

The Budyko based equation given by Choudhury (1999) was used by Wang et al. (2016). Budyko framework works on the assumption that the hydrological system is in steady state while considering a temporal span of approximately 10 years (Wu, Miao, Wang, et al.,

2017). It is a simple framework that adheres to the constrictions of water and energy availability. Generally, Budyko equations are expressed as

where E is actual

evapotranspiration and Φ represents dryness index which is the ratio of potential evapotranspiration (Eo) to precipitation (P). In recent times, researchers have successfully incorporated basin surface attributes like soil properties, land covers, geographical properties etc. into the Budyko framework and produced mathematical expressions (Table 1) (Choudhury, 1999; Fu et al., 2007; D. Wang & Tang, 2014; D. Yang et al., 2007; H. Yang et al., 2008; L. Zhang et al., 2001). With all the available methods, selection of an appropriate approach remains a tough task pertaining to the complexity involved in hydrological processes and the methodologies discussed above. There is no clear affirmation of a technique on what climate elasticities to consider for impact assessment studies. In addition, elasticity magnitudes depend on the type of Budyko based equation selected for the study. Performances of these elasticity models with different Budyko based equations, in context to the intricacy involved within the models, have not been examined. Thus, comparing the models and observing the differences in the outcomes would assist in addressing the issues of consideration of appropriate climatic parameters for assessing climatic impacts on runoff generation process. In the present study, a comparative analysis is carried out to observe the disparities involved in the models discussed above. Two models are considered, involving precipitation and evapotranspiration elasticity (herein referred as Two-parameter model: TPM) in one case and in the other, the evapotranspiration elasticity is extended to five elasticity as was done by Wang et al. (2016) using the famous FAO-penman Monteith equation (herein referred as Multi-parameter model: MPM). The TPM is a simple model that incorporates the two key climatic variables as per the mean annual water balance principle to observe the assimilated impact of climate variability. The FAO-penman Monteith equation includes all the climatic

parameters that influences the evapotranspiration process and thus serve in quantifying separate impacts of these parameters in runoff change. In addition, to see the disparities involved within the models, eight Budyko based equations are engaged in the analysis. The investigation is carried out over 19 catchments from 11 river basins across India. They are selected based on long term continuous data availability. Note that the Budyko equations (Table 1) are equally appropriate and applicable on all catchments. [Table 1 to be here]

2. Study area and data used 2.1 Study area In the present study, 19 catchments from 11 major river basins of India are considered. The spatial distribution of the catchments along with the locations of their runoff gauging stations are shown in Figure 1. The hydro-meteorological and surface data of all the catchments are given in Table 2. The catchments cover a total area of 207388.7 km2, thus blanketing about 6.31 % of India. [Figure 1 to be here] [Table 2 to be here] 2.2 Hydro-meteorological dataset The precipitation and temperature (maximum and minimum) dataset are acquired from the India Meteorological Department (IMD) during 1970-2013. The wind velocity data is downloaded from the Terrestrial Hydrology Research Group of Princeton University (http://hydrology.princeton.edu/getdata.php?dataid=1, accessed on 15th October 2018). The relative humidity datasets for all the catchments are downloaded the National Center for Environmental Prediction/ National Center for Atmospheric Research (NCEP/ NCAR) reanalysis data (https://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.html, accessed

on 15th October 2018). The potential evapotranspiration (PET) is computed using the Penman method (Penman, 1948) as it is considered as a most optimal approach to incorporate climate change (Liu & Yang, 2010). Sunshine duration datasets are obtained from India Meteorological Department (IMD) and World Meteorological Organization (WMO) (http://worldweather.wmo.int/en/home.html, accessed on 15th October 2018). Daily observed discharge data of 19 catchments are obtained from India-WRIS (Water Resources Information System) WebGIS portal (http://www.india-wris.nrsc.gov.in/). It provides discharge datasets from Central Water Commission (CWC), Ministry of Water Resources, Govt. of India, New Delhi.

3. Methodology 3.1 Change point analysis Due to the significant contribution of climatic variability and anthropogenic activities in modifying the long-term streamflow pattern, it has become indispensable to examine the change point or inflection point in the hydro-meteorological time series for effective planning and management of the water resources (Raje, 2014). The change point analysis is a powerful technique for identifying the change in the statistical properties in the time series. The commonly used change point analysis techniques viz., standard normal homogeneity test and Wilcoxon’s nonparametric rank test provide a single change point over the entire time series. However, in the present analysis, we have used Bayesian approach proposed by Barry and Hartigan (1993) to examine the change point in the annual streamflow. Unlike the classical approach, Bayesian analysis provides the probability density function of the change at each point in the time series. Moreover, several other advantages of the Bayesian approach include: (i) Bayesian approach incorporates the uncertainty associated with the data series; (ii) Bayesian approach employs the prior distribution of the data and overcomes the shortcomings of the frequentist approach. The product partition model proposed by Hartigan

(1990) is opted to segregate the data into different blocks. The model assumes that within the block the observations are independent and identically distributed having a normal distribution with constant mean and variance. The prior distribution of the partition probability is updated using Markov Chain Monte Carlo (MCMC) process without affecting the likelihood function and the posterior distribution is obtained using the Bayes theorem. In the present study, the Bayesian change point analysis is carried out using the R package “bcp” and can be downloaded from (https://cran.r-project.org/package=bcp). 3.2 Runoff elasticity 3.2.1 Climate elasticity from two-parameter model Elasticity or sensitivity-based methods use coefficients that define the sensitivity of a dependent parameter to variability in the independent parameters (Sankarasubramanian et al., 2001; Schaake, 1990). An analytical elasticity-based method was proposed by Arora (2002) using the Budyko hypothesis to compute the relative influences of anthropogenic stresses and climatic variability to changes in runoff generation. Annual scale (long-term) water balance equation of a catchment is defined as:

P  E  Q  S

(6)

Here P is precipitation, E is actual evapotranspiration, Q is discharge and ∆S is the change in water storage. All parameters are in annual mean scale. Budyko hypothesis conceives the idea of long-term water balance (approximately 10 years or more) (Wu, Miao, Wang, et al., 2017) for a catchment and considers the change in water storage to be negligible (∆S = 0). Total differentiation of QC i.e. changes in discharge due to climatic variability is shown as:

dQC 

QC Q dP  C dE0 P E0

Relative change in runoff is expressed as:

(7)

QC  P QC  dP  E0 QC  dE0     Q  P  E P  P  P  E E0  E0

The

coefficients

of

the

relative

(8) changes

in

precipitation

and

Potential

evapotranspiration, as expressed in the above equation, are the elasticity of runoff to P and E0 (

respectively. From Eq. 6, 8 and Budyko hypothesis, the following expressions

can be derived for the elasticity of runoff:

 f ( )  E0 QC  P QC   P  E P   1  1  f ( ) ,  P  E E   0 

  f ( )   1  f ( )

(9)

The sum of elasticity to precipitation and E0 equals 1. Substituting Eq. 9 in Eq. 8, we get the equation for change in runoff due to variability in climatic parameters i.e. P and E 0, as per the two-parameter model.

dQC dE0 dP P  E0 Q P E0 (10) 3.2.2 Climatic elasticity from Multi-parameter model The widely used FAO Penman-Monteith equation is adopted to calculate daily potential evapotranspiration and described as:

 900  0.408( Rn  G )     UVPD T  273   E0     (1  0.34U )

(11)

where ∆ is the slope of vapour pressure curve (kPa 0C-1); Rn is net radiation at the surface (MJ m-2 d-1); G is ground heat flux (MJ m-2 d-1); γ is the psychrometric constant (kPa 0C-1); T is mean daily air temperature at 2 m height (0C); U is wind speed at 2 m height (ms-1); VPD is vapour pressure deficit (kPa) which is the difference between saturated and actual vapour pressures.

Yang and Yang (2011) used 4 climatic parameters i.e. Rn, Temperature (T), U, Relative humidity (RH) to quantify the impacts on the evapotranspiration process. Contrary to this, due to the dependence of relative humidity on maximum temperature (TX), minimum temperature (TN), net radiation (N) and RH and to see the individual contributions of TX and TN, subjected to data availability, Wang et al. (2016) conducted the contribution analysis with five climatic variables namely TX, TN, U, N, RH. By the use of first-order approximation, the differential equation of E0, considering all the parameters, is stated below as:

dE0 

E0 E E E E0 dTX  0 dTN  0 dU  0 dN  dRH TX TN U N RH

(12)

All the parameters in the above equation are in daily time scale. The equation needs to be in annual time scale for further analysis. Thus, variation in annual E0 can be expressed as: n

n

i 1

i 1

E0,Y   E0  

n n n n E0 E E E E dTX  0 dTN  0 dU  0 dN  0 dRH TX i 1 TN i 1 U i 1 N i 1 RH

(13)

The subscript Y denotes the yearly time scale. ‘n’ represents the number of days in a year. Relative change in E0,Y is given by: dE0,Y E0,Y



1 E0,Y

E0 1 dTX   E0,Y i 1 TX n

E0 1 dTN   E0,Y i 1 TN n

E0 1 dU   E0,Y i 1 U n

E0 1 dN   E0,Y i 1 N n

n

E0

 RH dRH

(14)

i 1

The Budyko framework implemented in the climate elasticity method functions in annual time scale. To be consistent with the assumption of steady-state (∆S = 0), it is necessary to consider multi-year time scale (annual mean). Therefore, Eq. 14 can be written as: d E0,Y E0,Y



1 E0,Y

E0 1 dTX   E0,Y i 1 TX n

E0 1 dTN   E0,Y i 1 TN n

E0 1 dU   E0,Y i 1 U n

E0 1 dN   E0,Y i 1 N n

n

E0

 RH d RH i 1

(15)

Here, E0,Y , TX , TN ,U , N and RH are the mean annual potential evapotranspiration, maximum temperature, minimum temperature, wind speed, sunshine duration, and relative humidity respectively. Following terms can be re-written as: n

E0,Y  n  E0 ,  i 1

E0  E   n 0  X  X 

(16) In the above equation, X represents the climatic variables. Therefore, Eq. 15 can be expressed as: d E0,Y E0,Y

 1  E   0  E0  TX

 1  E0      U  E0   dU  1  E0    RH  E0   d RH   d N     dTX    TN   dTN    U            U  E0  N    E0   E0   E0  RH   RH

(17)

To achieve similar expressions of relative change as in Eq. 10, the following equation can be written as:

dE0 dU dRH TX ,1 dTX  TN ,1 dTN  U ,1  N ,1 dN  RH ,1 E0 U RH and

(18)

represents the evapotranspiration elasticity to

maximum temperature, minimum temperature, wind speed, sunshine duration and relative humidity respectively. Incorporating Eq. 18 in Eq. 10, we obtain the expression to quantify the change in discharge due to climatic variability by using multi-parameter model. The equation is as stated below:

dQC dP P  E0 Q P

dU dRH    N ,1 dN  RH ,1 TX ,1 dTX  TN ,1 dTN  U ,1  U RH  

(19)

The final equation is obtained by combining elasticity of runoff and evapotranspiration as:

dQC dP dU dRH P  TX dTX  TN dTN  U  N dN  RH Q P U RH

(20)

where,

TX,

TN,

U,

N,

and

RH

are the runoff elasticity to maximum temperature,

minimum temperature, wind speed, sunshine duration, and relative humidity, respectively.

3.3 Attribution analysis From change point analysis, non-stationarity is defined for the discharge dataset of each catchment considered in the study. The time period is divided accordingly into portions and termed as pre-assessment and post-assessment period. It is assumed that the total change in discharge from pre to post assessment period includes both the changes in discharge due to climatic variability and anthropogenic stress as defined below.

Q  QC  QA

(21)

where, Q is the total change in discharge, QC is the change in discharge due to climatic variability and ∆QA is the change due to anthropogenic stress. The study captures the influence of anthropogenic activities as a whole (subtly capturing factors that chiefly depend on anthropogenic stress like catchment efficiency). Also, note that additional assessments have not been undertaken to explicitly demonstrate the influence of anthropogenic stress (quantifying land use land cover changes), since the major objective of the study is to determine the disparities in the models. Thus, from Eq. 21, QA is defined as:

QA  Q  QC  Q  (QP  QE0 )

(22)

where, QP and QE0 are defined as the changes in discharge due to variability in precipitation and PET respectively. This representation is consistent with the hypothesis of TPM. In the case of MPM, the Eq. 22 can further be derived as:

QA  Q  QC  Q  (QP  QTX  QTN  QU  QN  QRH )

(23)

where, QTX , QTN , QU , QN and QRH are defined as the changes in discharge due to variability in maximum temperature, minimum temperature, wind speed, sunshine duration, and relative humidity respectively.

4. Results 4.1 Trend analysis of hydro-meteorological variables The trend analysis of hydro-meteorological datasets is carried out to detect the slowly varying monotonic pattern of the hydro-meteorological dataset. The non-parametric MannKendall test is used to identify the trend at 95% confidence level. Hence, the Z values outside the bound of -1.96 and 1.96 denote significantly decreasing and increasing trends, respectively. The Z-statistics of the trend test for all the hydro-meteorological variables in different catchments is presented in Figure 2. It can be noted from the Figure that out of 19 catchments, catchment ID 14 and 19 have significantly increasing and decreasing trend for discharge, respectively. Catchment ID 12 and 4 have shown a significant rising and declining trend respectively for PET. In addition, about half of the total catchments show a significantly increasing trend in maximum temperature. In the case of minimum temperature, only catchment ID 8 has registered a significantly decreasing trend. Moreover, no noticeable trend is observed in precipitation and sunshine duration. [Figure 2 to be here] 4.2 Change point analysis of runoff data Generally, the change point analysis is performed using Pettitt’s test, Buishand’s test and Von Neumann’s test, which results in a single change point over the time series. However, it is to be noted that a minimum of 10 years should be taken as the pre-assessment period for the adoption of Budyko hypothesis. Hence to avoid the case of arrival of a change point in a year that is within the first ten years of the study period, a Bayesian approach is

adopted. In the case of Bayesian change point analysis, it is assumed that each point in the data set has likelihood of witnessing a change point. The point having higher posterior density value is considered as the change point for the time series. In this sense, if a change point lies within the initial ten years, a point having second highest posterior density is taken and so on. In the present study, the change point is computed only for the runoff data. Performing the analysis on other climatic variables and assessing the relationships would definitely shed more light on the results but to explicitly document the runoff changes and see the influences of other factors in it, the analysis is performed for streamflow datasets only. The changing years correspond to change points are displayed in Table 2 as pre- and postassessment period. It can be noticed from Table 2 that seven catchments (ID 1, 4, 10, 12, 13, 17, 19) have experienced a decrement in runoff generation from pre to post assessment period. As shown in Figure 2, downward trend is observed in all these catchments except ID 13. However, decreasing trends in rainfall have not been registered for these catchments except IDs 10 and 19. This is attributable to the intricacy of the catchment hydrology, heavily interlinked with the anthropogenic activities. 4.3 Dryness attributes of catchments The dryness index for all the catchments in both the temporal periods (pre and post assessment periods) are shown in Table S1 (supplementary information). It is seen that only 3 catchments (ID 10, 13, 19) have become drier in the post-assessment period. The spatial distributions of the aridity index for both the periods are shown in Figure S1 (supplementary information). Most of the catchments in the southern and central part of India have shown higher aridity index in both the periods. It ranged from 1.152 (ID 3; Anandapur) to 3.039 (ID 14; Singavaram) with a mean value of 1.915 in the pre-assessment period. The values decreased in the post-assessment period, having ranged between 1.078 (ID 3; Anandapur) and 3.004 (ID 14; Singavaram) with a mean value of 1.818. Highest negative changes from pre-

to post- assessment periods (more wet) have been observed in all the catchments of western and a few from the southern part of India. In addition, a significant relationship is observed between absolute change in aridity index from pre to post assessment period and aridity index during the pre-assessment period when we considered 17 catchments out of 19 (R = 0.663, p < 0.01; Figure 3(a)). The relationship appeared stronger when we considered only those catchments that became wetter in the post-assessment period (R= -0.765, p < 0.01; Figure 3(b)). This indicates that catchments with higher aridity index in pre-assessment period became wetter in the post-assessment period. [Figure 3 to be here] 4.4 Two-parameter model 4.4.1 Elasticities As stated above, the two parameters that determine the variability in runoff generation as per the two-parameter model are PET and Precipitation. The mean runoff elasticities to PET ( E0 ) and P (

P)

are calculated and their spatial distributions are shown in Figure4(a).

For all the catchments, E0 is negative and thus implying that the change in runoff is negatively correlated with the variability in PET. E0 ranged from -1.051 (ID 3) to -2.071 (ID 18) with an average value of -1.451. The catchments in the southern part of India have shown lesser values of E0 and higher values are observed in catchments in the central, eastern and western part of India. Furthermore,

P

is positive for all the catchments and varied between

3.071 (ID 18) to 2.051 (ID 3) with an average of 2.451. In addition, the absolute value of E0 is less than

P

for all catchments considered in the study, indicating that runoff change is

more sensitive to variability in Precipitation than PET. The spatial discrepancy of

P

is

oppositely similar to E0 due to the relationship between the two elasticities i.e. the sum of the elasticities equals 1, consistent with the two-parameter model. [Figure 4 to be here] 4.4.2 Quantitative characteristics of runoff change The contributions of climatic variability to runoff changes for all the catchments are quantified using the attribution analysis with the elasticities calculate as per TPM (Table S2). It is observed that 8 catchments (ID 3, 6, 7, 9, 10, 11, 15, 16) are having the highest contributions of climatic variability. A similar result is observed for anthropogenic contributions. Eight catchments (ID 1, 4, 8, 12, 13, 14, 17 and 18) have shown highest contributions from anthropogenic stress (Table not shown). Within climatic variability, it is observed that contributions from precipitation are more than that of PET for all catchments except Thammavaram (ID 17) (Table S3 and S4). Negative contributions in some of the catchments (ID 4, 12, 17) indicate that the direction of total change in runoff and that of change caused due to climatic variability is opposite to each other. If runoff has decreased then climatic variability has increased it from pre-assessment to post-assessment period and vice versa. It can be observed that in some catchments (ID 4, 7, 9, 12, 16), the percentage contribution values are more than 100% (Table S2). It means that the change in runoff caused due to climatic variability is more than the actual runoff change observed for the catchments during the study period. Furthermore, contributions from 2 Budyko equations, suggested by Zhang et al. (2001) and Wang and Tang (2014) were not quantified for one catchment (Pathagudem; ID 11) following the position of its evaporative index (AET/P) in the proximity of the suggested values by the lower limits of the Budyko curves (almost on the curve where catchment parameter w=0 in Budyko equation given by Zhang et al., (2001) and in equation given by Wang and Tang (2014)). This generally happens due to

underestimation of AET (calculated as P-Q). These underestimations of AET may have resulted from considering runoffs generated from sources other than precipitation (Sinha et al., 2018). One of the possible sources is the irrigation water that may percolate and join the base flow and comes into the considerations of total runoff. The percentage contributions obtained from all the eight Budyko equations are different from each other. This discrepancy has been discussed in Section 5. For further analysis, their averages are considered as there is no irregularity in the sign of contributions for each catchment. The Highest climatic contribution is seen for Jaraikela (ID 7) with a value of 283.028 % and the lowest is -282.277 % for Sarati (ID 12). The spatial disparity of climatic and anthropogenic contributions is shown in Figure 5(a). It is to be noted that the spatial variations for both the influencers are similar but opposite in nature as the sum of the changes become 100%. The climatic variability over catchments in the western part of India have contributed negatively. Moreover, catchments in the central, southern, and eastern part of India have shown low climatic contributions. In addition, the catchments in the western part of India have shown high negative contributions of precipitation. PET contributions are very low compared to precipitation (Table S3 and S4). It is maximum in catchment Jaraikela (ID 7) with a value of 59.890 %. Furthermore, it can be noted that there are considerable differences in the contribution values for the same river basins (Figure 5(a)). This is due to the significant variabilities in the precipitation and PET values within the same basins for different catchments as can be observed from Table 2. [Figure 5 to be here] 4.5 Multi-parameter model 4.5.1 Elasticities

MPM deals with parameters that influence the evapotranspiration process. Therefore, in this model, the evapotranspiration elasticities to five climatic parameters (TX, TN, U, N, and RH) are calculated and then combined with the runoff elasticity to evapotranspiration to obtain the sensitivity of runoff to the five climatic parameters. The mean values (Range) of TX, TN, U, N

and

RH

are 0.028 (0.015 (ID 13) to 0.061 (ID 16)), 0.017 (0.010 (ID13) to

0.035 (ID 16)), -0.297 (-0.469 (ID 19) to -0.071 (ID 12)), -0.051 (-0.083 (ID 18) to -0.038 (ID 11)) ,0.711 (0.321 (ID 13) to 1.591 (ID 16)), respectively. It is observed that wind speed and sunshine duration are negatively correlated with runoff change. Moreover, changes in runoff are more sensitive to variability in relative humidity for most of the catchments considered for the study. Compared to the elasticity of runoff to evapotranspiration from TPM, the elasticities of runoff to five parameters in MPM are less. This may be due to further decomposition of the evapotranspiration variable that resulted in lowering the sensitivity of runoff change to individual climatic variables. Figure 4(b-f) shows the spatial variation of the elasticities. The runoff elasticity to maximum temperature, minimum temperature, and relative humidity have shown similar spatial trait with higher values in the western and southern part of India. Catchments in the central part of India have shown lower elasticity values to wind speed compared to other catchments. Unlike other elasticities, in the case of runoff elasticities to sunshine duration, the values are found to be higher in the central and eastern part of India. 4.5.2 Quantitative characteristics of runoff change The contributions of climatic parameters to runoff change, considered following decomposition of the evapotranspiration, are quantified using the MPM in the climate elasticity method. It is seen that N is having the highest contributions to runoff changes among the five parameters in 14 catchments with U, having their highest influence in 4 catchments (ID 5, 6, 7, and 10). Sunshine duration and U ranged from 13.765 % (ID 9; Kotni)

to -33.238 % (ID 4; Cholachguda) and 60.716 % (ID 7; Jaraikela) to -8.037 % (ID 10; P.G.Bridge), respectively. Maximum temperature, having a range from 14.226 % (ID 7; Jaraikela) to -7.798 % (ID 12; Sarati), has shown the highest influence in catchment Sarati (ID 12). It has also been noticed that between TX and TN, TX has higher contributions to runoff changes in 15 catchments, leaving the rest 5 catchments (ID 3, 8, 9, 16 and 18) with higher influence from TN. This shows the importance of separating the temperature variable to TX and TN. Minimum temperature has the highest contribution of 4.008% in T.K.Halli (ID 16) and lowest of -1.497 % in Kashinagar (ID 8). Moreover, RH ranged between 9.941 % (ID 7; Jaraikela) to -11.094 % (ID 19; Zari). The above outcomes are documented in Table S5 to S9. As discussed before, in the study, 8 Budyko equations are incorporated to quantify contributions and therefore it yields discrepancies within the model outputs. These differences are discussed in Section 5. For analysis, average contributions are considered due to consistency in the sign of the contribution values. The spatial variations of the contribution values are shown in Figure 5(b-f). It is observed that TX in catchments in the western and a few in the central and eastern part of India have contributed negatively to runoff changes. A similar trend is observed in the case of TN with higher contributions in the southern part of India. U has contributed positively in most of the catchments of the southern and eastern part of India. Furthermore, most of the catchments in the central and eastern part of India are having positive influences of N to runoff variations. RH has contributed negatively in most of the catchments in the eastern part of India. Similar to the results from TPM, differences in the results for catchments of same basins are solely due to variabilities in the climatic variables within the river basins.

5. Discussions 5.1 Intra-model disparity

In the study, eight Budyko based equations are employed for the quantification of percentage contributions of climatic variables and anthropogenic stressors to runoff changes from pre-assessment to post-assessment period. The results obtained from the study shows disparity among themselves. Figure 6 depicts the discrepancy in the climatic contributions obtained from the Budyko Equations. PET contributions in the case of MPM mean the summation of all the five contributions (TX, TN, U, N, and RH). Table 1 shows the four nonparametric and parametric Budyko equations incorporated in the study. The disparity may have risen from the different approaches with which the equations were developed using the hydro-meteorological variables. Moreover, the contributions from parametric and nonparametric equations form clusters. This is due to the incorporation of catchment characteristics like soil properties, land cover etc. into the Budyko hypothesis for parametric equations that may upsurge the possibilities of these equations to replicate the hydrological processes at catchment scale. In this section, the disparity within the models due to incorporation of eight Budyko based equations is discussed. Since, contributions from climatic parameters that influences evapotranspiration process are quantified with the MPM, to maintain uniformity, disparities in percentage contributions from PET calculated using TPM is analysed. [Figure 6 to be here] In TPM, highest range of contribution values is seen in Jaraikela (ID 7). Standard deviations of contributions are obtained and shown in Figure 7(a). Three catchments (IDs 7, 11, 19) are having high standard deviation. Furthermore, difference in the average percentage contributions from parametric and non-parametric equations are calculated and is termed as ‘D’. It is observed that the slope of the trend-line has reduced near to aridity index 1.965, when plotted between summation of D and summation of pre-assessment aridity index (Figure 7 (b)). It signifies that the rate of change of D per unit change in pre-assessment

aridity index has reduced after the aridity index value 1.965. This may be the reason for higher inconsistency in the contributions for two catchments out of three (IDs 7 and 11) with pre-assessment aridity index 1.436 and 1.507, respectively (Figure 7(a)). Similar observations are seen in the case of MPM. Jaraikela (ID 7) has the highest standard deviation (Figure 7 (a)). In addition, the slope of the trend-line has decreased from pre-assessment aridity index 1.679, when plotted between summation of D and summation of pre-assessment aridity index as shown in Figure 7(c). It explains the higher discrepancy in the percentage contributions of two (IDs 1, 7) out of three catchments (IDs 1, 7, 19) that showed high value of standard deviation (Figure 7(a)). [Figure 7 to be here] 5.2 Inter-model disparity One of the key objectives of our study is to evaluate the differences between the TPM and MPM. The differences in contributions values emerged from the disintegration of the evapotranspiration elasticity into five climatic elasticities. To discuss this disparity, PET contributions are considered for both the cases and plotted as shown in the Figure 8(a). A significant and strong linear relationship is observed between PET contributions from both the models (R = 0.761, p < 0.01). Quadrant 2 and 4 denote the state where both the models produced contradictory results (One method showing positive and the other showing negative contributions). Six out of 19 catchments (IDs 3, 8, 10, 11, 12, and 15) have shown inconsistent results. A possible explanation is the propagation of errors due to incorporation of more climatic parameters into the framework. In addition, as discussed above, adding more variables may contribute to explaining the differences and improve the framework further. Although, the contribution values are near to the 1:1 line (green line), few catchments have shown significant deviation from the line (shown with red markers). These deviations are due to disproportionate performance of the MPM. As mentioned above about the parameter ‘D’,

it is detected that the change in the slope of the trend-lines (shown with blue and red colours) are more in the case of MPM (∆SMPM = -3.980 and ∆STPM = -3.533) with an early occurrence of the change point (φMPM = 1.679 and φTPM = 1.965). Therefore, the likelihood of occurrence of higher inconsistency within the Budyko based equations is more in MPM compared to TPM. Moreover, it can be seen from Figure 7(a) that in 13 catchments (IDs 1, 2, 3, 4, 5, 6, 8, 9, 14, 15, 17, 18, 19), standard deviation is more when multi-parameter model is conducted, which is also evident from Figure 6. These suggest the instability in the performance of multi-parameter model that eventually may lead to erroneous predictions of the impacts of climatic and anthropogenic influences on runoff changes. To acquire a wider interpretation of the present study, the differences in the influence of climatic variability and anthropogenic stress on runoff change, when performed using two different models are further observed. Note that the impact from climatic variability includes the influences of precipitation (same in both the model) and evapotranspiration (summation of five climatic parameters for MPM). The percentage climatic contributions from both the models are plotted and shown in Figure 8(b). A very strong and significant linear correlation is observed between the two models (R = 0.99, p < 0.01). It showcases confidence in the derivation of elasticities using the theoretical arrangement. However, separating the PET variable into five climatic components may increase the chances of error propagation into the derived framework. Contradictory results have been observed in catchment ID 1. It is seen that ‘D’ is higher in 12 catchments (IDs 1, 4-6, 8, 9, 12-17) for the case of MPM Figure 8(c). In addition, Figure 8(d-f) show the standard deviation of percentage contributions of climatic variability when four non-parametric, four parametric and all Budyko equations are considered respectively. It is higher in 12 catchments (Non-parametric: IDs 1, 4-6, 8, 9, 1217; Parametric: IDs 1, 4-6, 8, 9, 12-17; All: IDs 1, 4-6, 8, 9, 12-17) for multi-parameter model compared to Two-parameter model for all the three cases. These clearly implies that

there is a greater inconsistency in percentage contribution values from multi-parameter model. [Figure 8 to be here] 5.3 Applicability of the models The present study highlights the differences in the performance of two and multi parameter models. MPM includes more climatic elasticities, initiated from extending the evapotranspiration elasticity. Elasticities explain the sensitivity of a parameter to disturbances in its surroundings. The elasticity concept was first introduced by Schaake (1990). Till now, the elasticity theory is extended to precipitation and five evaporation related parameters (TX, TN, U, N, RH) that unfolds the correlation of solar radiation with temperature and relative humidity (W. Wang et al., 2016). Although the decomposition of the evapotranspiration elasticity seems to be judicious, the results project a dissimilar sight. Higher inconsistency is obtained, both within the model (among eight Budyko equations) and compared to TPM, while conducting contribution analysis using MPM. Moreover, Wang et al. (2016) has also documented the instability in the presentation of multi-parameter model while comparing the computed total runoff change with the observed runoff values. The present study utilised the six runoff elasticities (precipitation and evaporation related) to determine the influence of variation in climatic variables to changes in runoff generation. There is a possibility of occurrence of more runoff elasticity that could better explain the impact and minimise the variations between the two models. Thus, it is not invalid to say that the use of multiparameter model should be restricted to only when evaluation of the influence of individual climatic parameters is the main goal. Considering climatic influence as a whole seems promising to quantify the impact of climatic variability to hydrology at catchment scale using TPM. 5.4 Uncertainty in the analysis

In these kinds of studies of impact assessment, many sources of uncertainties are involved. During the quantification of contributions using two-parameter model, climatic variability and anthropogenic stress are considered to be independent of each other. In real world, both the elements hold a very intricate relationship between them (Wu, Miao, Wang, et al., 2017; Zeng et al., 2015). They work together collectively in a hydrological system and are complementary to each other. During the implementation of Budyko hypothesis in the climate elasticity method, the water storage was considered to be negligible in the mean annual water balance. It highly depends on the physiographical, land surface and soil properties of a catchment. There is no such firm evidence to ascertain this assumption (Wu, Miao, Wang, et al., 2017). Furthermore, change in runoff due to climatic variability is calculated by ignoring the higher orders in Taylor expansions. Therefore, considering first order expansion of runoff change may introduce error in the framework (H. Yang et al., 2014). Thirdly, during the quantification of runoff elasticity, the catchment parameters (4 parametric Budyko equations) are kept unchanged throughout the temporal range of analysis for each catchment. Catchment parameters define the surface and soil attributes that are subjected to alterations due to anthropogenic (Surface and sub-surface water withdrawals, construction of hydraulic structures) and climatic factors. Consideration of these issues ensures the natural flow conditions. The present study captured the prime characteristics of the precipitation partitioning process by taking the mean annual values of the catchment parameters (Budyko hypothesis). Incorporating catchment parameter as a variable and quantifying runoff elasticity to catchment parameter would further enhance the results of contribution analysis. As the framework works on mean annual water balance, it considers only the temporal changes of mean values. Sometimes, temporal variabilities may occur in variables with mean remaining almost similar, which may be addressed by considering anomalies in the variables. This calls for further research works on anomalies to see the

changes in the temporal variabilities. Moreover, human errors in collection of observed datasets add more sources of uncertainty in the study.

6. Conclusions It is vital to isolate and understand the relative contributions from the naturallyinduced and human-induced forcings to runoff variability. The elasticity-based method presents a simple framework and thus widely used to differentiate the impacts of changing environment on runoff. Climatic elasticity of runoff generation assists in examining the sensitivity of the streamflow to the change in different meteorological variables. The present study demonstrated a comparative assessment using Budyko based equations, on performance of two models that differs in the incorporation of number of climatic parameters into the climate elasticity framework. Higher inconsistency in relative contributions to changing runoff is observed in the multi-parameter model that designates a degrading effect of decomposition of evapotranspiration into five climatic parameters. In addition, possibility of occurrence of considerable inconsistency in multi-parameter model is more compared to two-parameter model. Thus, it can be inferred that two-parameter model works well for the case of calculating the influence of climatic variability all together. Decomposing the evapotranspiration elasticity totally depends on the nature and purpose of plans and policies. Similar conclusions on extending the climatic elasticities have been noticed in previous studies. Our results suggest that the selection of the method, based on Budyko hypothesis (Budyko based equations) should be done cautiously while quantifying the impacts of changing parameters which would ultimately help to formulate sustainable management and effective adaptation strategies.

References AghaKouchak, A., Feldman, D., Hoerling, M., Huxman, T., & Lund, J. (2015). Water and

climate: Recognize anthropogenic drought. Nature, 524(7566), 409–411. https://doi.org/10.1038/524409a Anandhi, A., Steiner, J. L., & Bailey, N. (2016). A system’s approach to assess the exposure of agricultural production to climate change and variability. Climatic Change, 136(3–4), 647–659. https://doi.org/10.1007/s10584-016-1636-y Arnell, N. W. (1999). Climate change and global water resources. Global Environmental Change, 9(SUPPL.), S31–S49. https://doi.org/10.1016/S0959-3780(99)00017-5 Arora, V. K. (2002). The use of the aridity index to assess climate change effect on annual runoff. Journal of Hydrology, 265(1–4), 164–177. https://doi.org/10.1016/S00221694(02)00101-4 Barry, D., & Hartigan, J. A. (1993). A Bayesian Analysis for Change Point Problems. Journal of the American Statistical Association, 88(421), 309. https://doi.org/10.2307/2290726 Budyko, M. I. (1974). Climate and life. New York, CA: Academic Press. Chawla, I., & Mujumdar, P. P. (2015). Isolating the impacts of land use and climate change on streamflow. Hydrology and Earth System Sciences, 19(8), 3633–3651. https://doi.org/10.5194/hess-19-3633-2015 Choudhury, B. J. (1999). Evaluation of an empirical equation for annual evaporation using field observations and results from a biophysical model. Journal of Hydrology, 216(1– 2), 99–110. https://doi.org/10.1016/S0022-1694(98)00293-5 Creed, I. F., Spargo, A. T., Jones, J. A., Buttle, J. M., Adams, M. B., Beall, F. D., et al. (2014). Changing forest water yields in response to climate warming: results from longterm experimental watershed sites across North America. Global Change Biology, 20(10), 3191–3208. https://doi.org/10.1111/gcb.12615 Fu, G., Charles, S. P., & Chiew, F. H. S. (2007). A two-parameter climate elasticity of streamflow index to assess climate change effects on annual streamflow. Water Resources Research, 43(11). https://doi.org/10.1029/2007WR005890 Gao, G., Fu, B., Wang, S., Liang, W., & Jiang, X. (2016). Determining the hydrological responses to climate variability and land use/cover change in the Loess Plateau with the Budyko framework. Science of the Total Environment, 557–558, 331–342.

https://doi.org/10.1016/j.scitotenv.2016.03.019 Goyal, M. K., & Surampalli, R. Y. (2018). Impact of Climate Change on Water Resources in India. Journal of Environmental Engineering, 144(7), 04018054. https://doi.org/10.1061/(ASCE)EE.1943-7870.0001394 Hartigan, J. A. (1990). Partition models. Communications in Statistics - Theory and Methods, 19(8), 2745–2756. https://doi.org/10.1080/03610929008830345 Helman, D., Lensky, I. M., Yakir, D., & Osem, Y. (2017). Forests growing under dry conditions have higher hydrological resilience to drought than do more humid forests. Global Change Biology, 23(7), 2801–2817. https://doi.org/10.1111/gcb.13551 Huntington, T. G. (2006a). Evidence for intensification of the global water cycle: Review and synthesis. Journal of Hydrology, 319(1–4), 83–95. https://doi.org/10.1016/j.jhydrol.2005.07.003 Huntington, T. G. (2006b). Evidence for intensification of the global water cycle: Review and synthesis. Journal of Hydrology, 319(1–4), 83–95. https://doi.org/10.1016/j.jhydrol.2005.07.003 Immerzeel, W. W., Van Beek, L. P. H., & Bierkens, M. F. P. (2010). Climate change will affect the asian water towers. Science, 328(5984), 1382–1385. https://doi.org/10.1126/science.1183188 IPCC. (2014). Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Core Writing Team, R.K. Pachauri and L.A. Meyer. https://doi.org/10.1017/CBO9781107415324.004 Karl, T. R., & Trenberth, K. E. (2003). Modern Global Climate Change. Science, 302(5651), 1719–1723. https://doi.org/10.1126/science.1090228 Kong, D., Miao, C., Wu, J., & Duan, Q. (2016). Impact assessment of climate change and human activities on net runoff in the Yellow River Basin from 1951 to 2012. Ecological Engineering, 91, 566–573. https://doi.org/10.1016/j.ecoleng.2016.02.023 Li, H., Zhang, Y., Vaze, J., & Wang, B. (2012). Separating effects of vegetation change and climate variability using hydrological modelling and sensitivity-based approaches. Journal of Hydrology, 420–421, 403–418. https://doi.org/10.1016/j.jhydrol.2011.12.033

Liang, W., Bai, D., Wang, F., Fu, B., Yan, J., Wang, S., et al. (2015). Quantifying the impacts of climate change and ecological restoration on streamflow changes based on a Budyko hydrological model in China’s Loess Plateau. Water Resources Research, 51(8), 6500– 6519. https://doi.org/10.1002/2014WR016589 Liu, Q., & Yang, Z. (2010). Quantitative estimation of the impact of climate change on actual evapotranspiration in the Yellow River Basin, China. Journal of Hydrology, 395(3–4), 226–234. https://doi.org/10.1016/j.jhydrol.2010.10.031 Milly, P. C. D., Dunne, K. A., & Vecchia, A. V. (2005). Global pattern of trends in streamflow and water availability in a changing climate. Nature, 438(7066), 347–350. https://doi.org/10.1038/nature04312 Penman, H. L. (1948). Natural evaporation from open water, hare soil and grass. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 193(1032), 120–45. https://doi.org/10.1098/rspa.1948.0037 Raje, D. (2014). Changepoint Detection in Hydrologic Series of the Mahanadi River Basin Using a Fuzzy Bayesian Approach. Journal of Hydrologic Engineering, 19(4), 687–698. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000844 Sankarasubramanian, A., Vogel, R. M., & Limbrunner, J. F. (2001). Climate elasticity of streamflow in the United States. Water Resources Research, 37(6), 1771–1781. https://doi.org/10.1029/2000WR900330 Schaake, J. C. (1990). From climate to flow. Climate Change and US Water Resources., 177– 206. Schewe, J., Heinke, J., Gerten, D., Haddeland, I., Arnell, N. W., Clark, D. B., et al. (2014). Multimodel assessment of water scarcity under climate change. Proceedings of the National Academy of Sciences, 111(9), 3245–3250. https://doi.org/10.1073/pnas.1222460110 Simonovic, S. P. (2017). Bringing Future Climatic Change into Water Resources Management Practice Today. Water Resources Management, 31(10), 2933–2950. https://doi.org/10.1007/s11269-017-1704-8 Sinha, J., Sharma, A., Khan, M., & Goyal, M. K. (2018). Assessment of the impacts of climatic variability and anthropogenic stress on hydrologic resilience to warming shifts

in Peninsular India. Scientific Reports, 8(1), 13833. https://doi.org/10.1038/s41598-01832091-0 Unnikrishnan, C. K., Gharai, B., Mohandas, S., Mamgain, A., Rajagopal, E. N., Iyengar, G. R., & Rao, P. V. N. (2016). Recent changes on land use/land cover over Indian region and its impact on the weather prediction using Unified model. Atmospheric Science Letters, 17(4), 294–300. https://doi.org/10.1002/asl.658 Wada, Y., Van Beek, L. P. H., Van Kempen, C. M., Reckman, J. W. T. M., Vasak, S., & Bierkens, M. F. P. (2010). Global depletion of groundwater resources. Geophysical Research Letters, 37(20), n/a-n/a. https://doi.org/10.1029/2010GL044571 Wang, D., & Hejazi, M. (2011). Quantifying the relative contribution of the climate and direct human impacts on mean annual streamflow in the contiguous United States. Water Resources Research, 47(9). https://doi.org/10.1029/2010WR010283 Wang, D., & Tang, Y. (2014). A one-parameter Budyko model for water balance captures emergent behavior in darwinian hydrologic models. Geophysical Research Letters, 41(13), 4569–4577. https://doi.org/10.1002/2014GL060509 Wang, W., Zou, S., Shao, Q., Xing, W., Chen, X., Jiao, X., et al. (2016). The analytical derivation of multiple elasticities of runoff to climate change and catchment characteristics alteration. Journal of Hydrology, 541, 1042–1056. https://doi.org/10.1016/j.jhydrol.2016.08.014 Wang, X. (2014). Advances in separating effects of climate variability and human activity on stream discharge: An overview. Advances in Water Resources, 71, 209–218. https://doi.org/10.1016/j.advwatres.2014.06.007 Wu, J., Miao, C., Wang, Y., Duan, Q., & Zhang, X. (2017). Contribution analysis of the longterm changes in seasonal runoff on the Loess Plateau, China, using eight Budyko-based methods. Journal of Hydrology, 545, 263–275. https://doi.org/10.1016/j.jhydrol.2016.12.050 Wu, J., Miao, C., Zhang, X., Yang, T., & Duan, Q. (2017). Detecting the quantitative hydrological response to changes in climate and human activities. Science of the Total Environment, 586, 328–337. https://doi.org/10.1016/j.scitotenv.2017.02.010 Yang, D., Sun, F., Liu, Z., Cong, Z., Ni, G., & Lei, Z. (2007). Analyzing spatial and temporal

variability of annual water‐ energy balance in nonhumid regions of China using the Budyko hypothesis. Water Resources Research, 43(4). Yang, H., & Yang, D. (2011). Derivation of climate elasticity of runoff to assess the effects of climate change on annual runoff. Water Resources Research, 47(7). https://doi.org/10.1029/2010WR009287 Yang, H., Yang, D., Lei, Z., & Sun, F. (2008). New analytical derivation of the mean annual water-energy balance equation. Water Resources Research, 44(3). https://doi.org/10.1029/2007WR006135 Yang, H., Yang, D., & Hu, Q. (2014). An error analysis of the Budyko hypothesis for assessing the contribution of climate change to runoff. Water Resources Research, 50(12), 9620–9629. https://doi.org/10.1002/2014WR015451 Zeng, S., Zhan, C., Sun, F., Du, H., & Wang, F. (2015). Effects of Climate Change and Human Activities on Surface Runoff in the Luan River Basin. Advances in Meteorology, 2015, 1–12. https://doi.org/10.1155/2015/740239 Zhang, L., Dawes, W. R., & Walker, G. R. (2001). Response of mean annual evapotranspiration to vegetation changes at catchment scale. Water Resources Research, 37(3), 701–708. https://doi.org/10.1029/2000WR900325 Zhang, Y., Guan, D., Jin, C., Wang, A., Wu, J., & Yuan, F. (2011). Analysis of impacts of climate variability and human activity on streamflow for a river basin in northeast China. Journal of Hydrology, 410(3–4), 239–247. https://doi.org/10.1016/j.jhydrol.2011.09.023 Zhao, Y., Zou, X., Gao, J., Xu, X., Wang, C., Tang, D., et al. (2015). Quantifying the anthropogenic and climatic contributions to changes in water discharge and sediment load into the sea: A case study of the Yangtze River, China. Science of the Total Environment, 536, 803–812. https://doi.org/10.1016/j.scitotenv.2015.07.119 Zheng, H., Zhang, L., Zhu, R., Liu, C., Sato, Y., & Fukushima, Y. (2009). Responses of streamflow to climate and land surface change in the headwaters of the Yellow River Basin. Water Resources Research, 45(7). https://doi.org/10.1029/2007WR006665

Figure Caption Figure 1: Location map of the catchments superimposed over River Basins of India. Figure 2: Trend analysis of different hydro-climatic variables. Figure 3: Dryness attributes of the catchments. (a) relationship between absolute change in the aridity index from pre- to post-assessment period and preassessment aridity index for 17 catchments; (b) relationship between change in aridity index from pre- to post-assessment period and pre-assessment aridity index for 14 catchments that experienced wetter conditions in post assessment period. Figure 4: Spatial distribution of runoff elasticities obtained from TPM. (a) runoff elasticity to precipitation and PET obtained from MPM; (b) runoff elasticity to TX obtained from MPM; (c) runoff elasticity to TN obtained from MPM; (d) runoff elasticity to U obtained from MPM; (e) runoff elasticity N obtained from MPM; (f) runoff elasticity to RH obtained from MPM. Figure 5: Spatial distribution of percentage contributions to runoff change. (a) percentage contributions of climatic variability and anthropogenic stress; (b) percentage contributions of TX; (c) percentage contributions of TN; (d) percentage contributions of U; (e) percentage contributions of N; (f) percentage contributions of RH. Figure 6: Boxplot of the discrepancy in climatic contributions obtained from the 8 Budyko Equations. (a) discrepancy in TPM; (b) discrepancy in MPM. Figure 7: Intra-model disparity. (a) standard deviations of percentage contributions from PET to runoff change for 19 catchments under both the models; (b) relationship between cumulative absolute D and cumulative preassessment aridity index for TPM; (c) relationship between cumulative absolute D and cumulative pre-assessment aridity index for MPM. Figure 8: Inter-model disparity. (a) relationship between PET percentage contributions from MPM and TPM; (b) relationship between percentage climatic contribution from MPM and TPM; (c) absolute D for all the catchments under MPM and TPM; (d) standard deviation of climatic contribution from nonparametric Budyko equations for all the catchments under MPM and TPM; (e) standard deviation of climatic contribution from parametric Budyko equations

for all the catchments under MPM and TPM; (f) standard deviation of climatic contribution from all Budyko equations for all the catchments under MPM and TPM.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Table 1: The eight Budyko equations implemented in the study Equation Name B1

B2

B3

B4

Non-parametric Equations  E0 P

E  1 e P  P  E E0  tanh   P P  E0  E  P E  P

(Ol’dekop 1911)

 E0   P  E0 tanh   1  e P  P  E0    1

E  1  0   P

References (Schreiber 1904)

(Budyko 1963)

(Pike 1964; Turc 1954)

2

Parametric Equations 1

B5

E P

 E0   E0     1  1   P   P   E 1 w 0 P  1 E0  E0  1 w  P  P 

B6

E P

B7

n E   E0   n  1   P   P  

B8

E E  E  1  0  1  0   4 (2   ) 0 P P P E   P 2 (2   )

1

(Fu et al. 2007; Yang et al. 2007)

(Zhang et al. 2001)

(Choudhury 1999; Yang et al. 2008)

2

(Wang and Tang 2014)

Table 2: Details of hydro-meteorological variables, surface and temporal characteristics of 19 catchments considered in the study (Provided as per the basin names) River Basins

ID

Gauging station

Latitude

Longitude

Area (km2)

Preassessment period

Postassessment period

P (mm)

PET (m

Baitarini

3

Anandapur

21.739

85.794

8890.133

1973-1982

1983-2012

1488.661

1630

5

Gomlai

22.667

84.804

22340.545

1979-1993

1994-2012

1315.699

1767.

7

Jaraikela

22.855

85.039

10708.862

1973-1993

1994-2012

1296.013

1831.

Cauvery

16

T.K.Halli

12.98

76.9

8101.977

1979-1995

1996-2013

729.735

2029.

East coast subzone

8

Kashinagar

19.42

83.848

8074.27

1972-1989

1990-2013

1297.171

1786.

15

Srikakulam

18.919

83.356

8633.538

1988-2005

2006-2013

1303.195

1778.

17*

Thammmavaram

15.864

79.363

7992.959

1988-2000

2001-2011

872.674

1672.

18

Vazhavachanur

12.559

78.207

11594.074

1979-1995

1996-2012

842.013

1849.

6

Hivra

21.057

78.123

10187.118

1988-2005

2006-2013

950.822

1983.

P.G.Bridge

20.03

78.275

14093.192

1970-1990

1991-2013

1068.764

1860

Brahmani

East flowing rivers (Between Krishna and Pennar) East flowing rivers (Between Pennar and Cauvery)

10 Godavari

Krishna Mahanadi Pennar Subernarekha *

*

11

Hydro-meteorological

Pathagudem

19.101

80.387

39148.235

1970-1990

1991-2013

1458.869

2156.

13

*

Satrapur

21.692

78.77

7398.06

1987-1999

2000-2013

1114.997

1905.

19

*

Zari

19.697

76.033

5524.573

1988-1997

1998-2011

821.235

2275.

Cholachguda

15.642

75.227

9897.489

1983-2000

2001-2011

1048.831

2009.

Sarati

18.108

74.302

6754.838

1970-1994

1995-2011

885.921

1578.

9

Kotni

20.865

80.953

7012.965

1979-1993

1994-2011

1191.302

1833.

2

Alladupalli

15.294

78.407

8697.704

1986-1995

1996-2013

757.153

1911.

14

Singavaram

14.152

77.848

5921.54

1988-2000

2001-2011

642.935

1943.

Adityapur

22.487

85.897

6416.672

1988-1997

1998-2011

1320.579

1849.

4

*

12

1

*

*

mark represents decrement in runoff from pre to post assessment period

Highlights 1. Disparity analysis of two and multi parametric models is performed with 8 Budyko based equations 2. The study is carried out over 19 catchments across India. 3. Higher discrepancy in percentage contributions values for the case of multi-parameter model.