Contribution of climate and catchment characteristics to runoff variations in Indian river basins: a climate elasticity approach

ABSTRACT The relative influence of climate and catchment characteristics to the variations in runoff in five Indian river basins is assessed using the climate elasticity approach based on the Budyko hypothesis. From 1980 to 1999, catchment characteristics are found to be the main contributor to runoff variation for all of the basins except Upper Mahanadi sub-basin, where climatic factors are the major contributor. Among the climatic factors, runoff is more responsive to changes in precipitation than to changes in potential evapotranspiration. The mean contribution of climate (catchment) to runoff variation is largest at the Cauvery (Krishna) basin. The findings may be useful in planning sustainable water resources infrastructure. Investigation of the relationship between runoff changes in the basins and their land use and land cover changes, as well as the vegetation index, adds to the novelty and usefulness of the study.


Introduction
The regional hydrological cycle is a complicated process that is affected by the physical characteristics of the catchment, changing climate, and anthropogenic activities (Joseph et al. 2018, Wu et al. 2020. The components of the hydrological cycle such as streamflow, evapotranspiration, and soil moisture content are extremely sensitive to even minor temperature and precipitation changes (Chattopadhyay and Hulme 1997, Milly et al. 2005, Seneviratne et al. 2010, Joseph et al. 2018. With rising global mean temperature under a changing climate the duration, intensity, and frequency of regional precipitation events are likely to be altered (Kumar et al. 1992, Trenberth et al. 2003, Wild and Liepert 2010. Such climatic changes along with the catchment characteristics influence the runoff from rivers at various time scales (Jiang et al. 2015. In the regional hydrological cycle, the yearly runoff variation is critical for assessing the water-energy balance between the land surface and the atmosphere (Yang et al. 2008). Hence, efforts have been made to partition the precipitation into runoff and evapotranspiration to evaluate water availability (Zhou et al. 2016, Zheng et al. 2018. Annual runoff in a river basin is influenced by both direct and indirect factors. Direct factors includes changes in precipitation and evapotranspiration, while changes in catchment characteristics (e.g. change in vegetation cover and anthropogenic activity) are classified as indirect factors (Zheng et al. 2018). Partitioning the effects of climate change and watershed change on runoff variation is particularly important for policymaking and optimal management of regional water resources in areas with water scarcity.
The Budyko (1974) framework captures a complex relationship between mean annual evaporation ratio (E/P) and aridity index (PE/P) that complies with the theory of energy limit and water limit (Donohue et al. 2007, Gerrits et al. 2009, Padrón et al. 2017, Sinha et al. 2018, 2019. Climatic variables such as precipitation (P), evapotranspiration (E), and potential evapotranspiration (PE) along with catchment characteristics (c) of a region play an intricate role in this hypothesis. This model proposes a concept to partition the precipitation into actual evapotranspiration and runoff (Sinha et al. 2018). Budyko's framework indicated that with an increase in the dryness index (ϕ = PE/P), the part of precipitation contributing to runoff decreases. In recent years, in addition to climate change, anthropogenic activities have also affected the regional water cycle by changing the land cover and extensive use of surface water and groundwater to meet the demands of the growing population. The Budyko curve is generally expressed using eight commonly available equations (Table 1). Among those, four are non-parametric and the rest are parametric equations, which incorporate the effect of catchment characteristics.
To quantify the impact of watershed characteristics and climate on runoff using the Budyko hypothesis, two methods are available. The first method is based on the concept of runoff sensitivity or elasticity (Schaake 1990, Sankarasubramanian et al. 2001, Sinha et al. 2018. Using partial derivatives, the coefficient of sensitivity of runoff with respect to precipitation and potential evapotranspiration can be computed independently (Koster and Suarez 1999, Ma et al. 2008, Zhou et al. 2016, Shen et al. 2017. Runoff change due to climate variation can be obtained by adding the impacts of precipitation as well as potential evapotranspiration on runoff. The difference between the observed change in runoff and the estimated change in runoff due to climate change is considered the runoff change due to change in catchment characteristics. Some Budyko-type equations introduce a parameter to incorporate catchment characteristics, such as Turc-Pike (Turc 1954, Pike 1964, Milly and Dunne 2002, Yang et al. 2008, Fu (1981, Zhang et al. 2004, Zhang et al. (2001) and Wang and Tang (2014).
The decomposition approach is the second method to apply a Budyko-type equation to separate the contributions of climate variables and catchment characteristics to runoff change (Wang and Hejazi 2011). The decomposition method assumes that, for a catchment without direct impact of catchment characteristics, if the climate moves to a drier or wetter state (indicated by the ratio PE/P), the evaporation ratio (E/P) will also change to a new state but will still follow the same Budyko-type curve. Therefore, with the change of climate (i.e. PE/P), the catchment will acquire a new state (i.e. change of evaporation ratio) but will remain on the same Budyko curve. Moreover, a watershed can move along the Budykotype curve because of climate change only, and direct human interference can push the watershed to move along the vertical direction ( Fig. 1), i.e. a change of E/P due to change of evapotranspiration (Wang and Hejazi 2011). Hence, in Fig. 1, the initial state M of the watershed may move to N due to the combined effect of climate and catchment change.
A number of studies have assessed the effects of anthropogenic activities and climate change on streamflow in various basins around the world (Choudhury 1999, Zhou et al. 2015, Zheng et al. 2018. India is the world's second most populous country, with a tremendous demand for freshwater and a widening gap between the demand for and supply of freshwater (Bobba et al. 1997). For instance, in the Mahanadi River basin, the freshwater demand is projected to increase until 2050, generating stress on the per capita water availability (Asokan and Dutta 2008). In recent years, India's booming economy has accelerated industrialization and urbanization, resulting in changes in land use/land cover (LULC) across the country (Schlosser et al. 2014). Paul et al. (2016) found that the leaf area index (LAI) decreased by approximately 20% during the period 1987-2005 in the core monsoon zone of India. Cropland (from 57.86% to 58.33% of basin area), built-up area (from 0.51 to 1.15%) and water bodies (from 3.08 to 3.24%) in Godavari River basin have increased, while forest cover (from 29.52 to 29.33%) has decreased between 1985 and 2014 (Koneti et al. 2018). Similarly, for Mahanadi River basin, direct conversion of forest region to agricultural land decreased the LAI, subsequently reducing the evapotranspiration and enhancing runoff and frequent flood events (Naha et al. 2021). Sinha et al. (2020) conducted a comparative study using a climate elasticity approach to evaluate the inconsistency within runoff elasticity and the percentage contribution of climatic variables and anthropogenic stress to runoff variation. The climate elasticity approach using a two-parameter model (precipitation and evapotranspiration) has been shown to perform better than the multi-parameter model (precipitation and five parameters related to evapotranspiration) considering climate influence as a whole. This study suggests that Budykobased equations should be selected with caution when quantifying the impacts of climate and catchment changes for sustainable water management (Sinha et al. 2020 Schreiber, Ol'dekop, Budyko, Turc-Pike, Fu, Zhang, Mezentsev-Choudhury-Yang and Wang-Tang are denoted as BD-Sc, BD-Ol, BD, BD-TP, BD-Fu, BD-Zh, BD-MCY and BD-WT  q Non-parametric Turc (1954) and Pike (1964) BD-Fu Fu (1981) and Zhang et al. (2004) BD-Zh Mezentsev (1955), Choudhury (1999) and Yang et al. (2008) BD-WT ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi assessment of human impact on long-term surface water partitioning was carried out for 520 regional divisions of India using the satellite-based Budyko frame work. Random forest and classification and regression tree algorithms were used to shortlist potential Tixeront-Fu parameter (ω) governing factors among 33 physico-climatic and socio-economic attributes. Climatic, soil-and vegetation-based factors were found to be the dominant factors influencing precipitation partition, while human influence was found to be a minor but important factor (Vora and Singh 2021). Some previous studies observed that climate change is the major contributor to the runoff change over a watershed, such as in the headwater region of the Yellow River, China (Li et al. 2008, Zheng et al. 2018, in the upper catchment of the Yellow River Basin (Zhao et al. 2009), and in 30 watersheds of China with various climatic types (Wang et al. 2016). Trends in runoff and climate were investigated in seven catchments across China (Zhai and Tao 2017). Long-term runoff observations from 1961 to 2014 and the Variable Infiltration Capacity (VIC) Model were used to assess the contributions of climate change and human activities to runoff change. The contribution of climate change was dominant during the initial period of study in the seven climatic zones of China, whereas during the latter period of the study, human activities contributed more to the runoff variation. However, in other parts of the world, such as plantation-affected catchments in Australia, catchment characteristics were found to be a more significant contributor to runoff variation (Zhou et al. 2016). Different analytical approaches along with the use of different spatial and temporal datasets results in considerably different conclusions in various studies.
In the context of Indian river basins, investigative studies on runoff partitioning are rather scarce. Because this is a rapidly developing region under a changing climate, understanding the altered hydrological response and partitioning of precipitation, incorporating the role of catchment characteristics and climate, is essential in Indian river basins (Sinha et al. 2018). In this study the sensitivity approach has been used to assess the runoff change/variation over five peninsular river basins in India using the two most extensively used parametric equations within the Budyko framework, i.e. the Budyko type equation given by Mezentsev-Choudhury-Yang (BD-MCY) and Fu (BD-Fu). The complementary relationship of partial elasticity of runoff with respect to P and that with respect to PE are combined to enumerate variation in runoff during the study period. Finally, the effects of climate and catchment change on runoff are compared with changes in LULC and vegetation index of each basin for the years 1985 (Normalized Difference Vegetation Index (NDVI) for 1990), 2009 and 2014. The changes in the percentage of the different land use types are examined across the study period. This adds novelty to this study. Additionally, this investigative study can be used to regenerate the results obtained by numerous Budyko-based runoff partitioning studies over India (Sinha et al. 2018, Bharat and Mishra 2021, Vora and Singh 2021 and across the globe (Zheng et al. 2018, Sharma andMondal 2022). The findings of this study can also be used to compare the water balance evaluation from different physical models (VIC, Soil & Water Assessment Tool (SWAT), etc.) (Bharat and Mishra 2021) and highresolution regional climate model (RCM) simulations (Rasmussen et al. 2014).

Study area and data
The study comprises three major river basins -Godavari (GRB), Krishna (KRB), Cauvery (CRB), and two sub-basins -Upper Mahanadi (UMS) and Upper Narmada (UNS) of peninsular India. Four of these rivers flow eastward into the Bay of Bengal while the Narmada flows westward into the Arabian Sea. The GRB is the second largest river basin in India, after the Ganga-Brahmaputra-Meghna system. A total area of 7-13,857 km 2 is covered by the five catchments, thus blanketing about 21.7% of the Indian landmass. In this study, the gauging stations at the basin outlets are selected considering two criteria: (i) a long record of reliable daily discharge data and (ii) the absence of major diversion structures in the upstream. The locations of the river basins are depicted in Fig. 2 and the basin information is summarized in Table 2. The annual average precipitation for UNS, UMS and GRB is 1210.9, 1158.0 and 1107.6 mm, respectively, during the period of analysis. The annual average precipitation of KRB and CRB is much less: 755.9 and 884.9 mm, respectively.

Data sources
The daily station-observed discharge datasets for the river basins are obtained from the India Water Resources Information System (WRIS) portal (https://indiawris.gov.in) for the longest available period (Pai et al. 2014). The daily precipitation (P) data is obtained from the India Meteorological Department (IMD) with 0.25° latitude × 0.25° longitude spatial resolution. The daily precipitation series at each grid intersection point is aggregated into the annual series and the mean annual precipitation in each river basin is calculated as the spatial average of the annual precipitation at all grids falling inside that particular basin (Fig. 3). The annual potential evapotranspiration (PE) data is obtained from the Global Land Evaporation Amsterdam Model (GLEAM) at a spatial resolution of 0.25° latitude × 0.25° longitude. The GLEAM dataset employs the Priestley and Taylor equation to compute potential evaporation based on observations of surface net radiation and near-surface air temperature (Martens et al. 2017). Several previous studies have extensively evaluated the GLEAM data and confirmed its relatively high quality (Bai and Liu 2018, Khan et al. 2018, Pan et al. 2020, Liu et al. 2021. Similar to P, the average annual PE series in the basin is also obtained as the mean PE value of all grids falling within the basin. Although P (from IMD) and PE (from GLEAM) have a similar spatial resolution, the grids are staggered as shown in Fig. 3. Hence, the inverse distance weighting (IDW) interpolation method has been used to prepare the raster of mean PE and P in QGIS to bring them into the same grids. Table 3 summarizes the source and resolution of the datasets.

Land cover/class dataset
Decadal LULC classification products at 100 m resolution across India for 1985 (Roy et al. 2016) and a global annual land-cover map produced by the European Space Agency Climate Change Initiative (ESA-CCI) for 2009 and 2014 have been used in this study (Kansara and Lakshmi 2021). The land-cover distribution obtained from these data products is reclassified into the major land-cover type for each river basin. Land-cover maps between 1985 and 2009 for the KRB and CRB basins and between 1985 and 2014 for UNS, UMS and GRB are compared to get the variation across each land-cover type. However, some uncertainty remains in the estimation of LULC changes, especially because (a) the LULC of the two periods was obtained from two sources with different spatial resolutions, and (b) differences exist between classification schemes and methods of data extraction for the two periods.

Landsat archive data from Google Earth Engine
The calibrated top-of-atmosphere (TOA) Landsat archived data from Google Earth Engine (GEE) have been used in this study to calculate the normalized difference vegetation index (NDVI) (Huang et al. 2017). Landsat 5 Thematic Mapper (TM), Landsat 7 Enhanced Thematic Mapper Plus (ETM+),   (Gorelick et al. 2017). As the Landsat dataset did not spatially cover the entire study area prior to 1990, this was used as the first year for calculating the NDVI.

Budyko framework
The water balance model over a watershed may be expressed as: where R is runoff, P denotes the precipitation, E denotes the actual evapotranspiration, ΔS is water storage change in the watershed,  and Δt is the time step. On an annual scale, the change in storage within the catchment can be considered negligible (ΔS = 0) (Gerrits et al. 2009, Jiang et al. 2015, Sinha et al. 2018, Zheng et al. 2018. Hence, the annual actual evapotranspiration for a particular river basin is obtained by computing the difference between precipitation and runoff (Equation 2).
The evaporation ratio (ε) is the ratio of actual evapotranspiration and precipitation: ε ¼ E P . The evaporation ratio of a region is limited by two factors: water supply and energy supply. For a given watershed, P is used to represent available water, while potential PE is used to represent available energy (Fig. 4). A relationship between the evaporation ratio (ε) and dryness index (ϕ) was demonstrated by Budyko (1974), which may be expressed as Equation (3). where c represents different catchment characteristics. The dryness index (ϕ) is the ratio of potential evapotranspiration (PE) and precipitation (P), i.e. ϕ ¼ PE P . If ϕ > 1, the evapotranspiration is restricted by water supply, and if ϕ < 1, the evapotranspiration is limited by total available energy (see Fig. 4).
In this study two extensively used functions within the Budyko framework have been considered. The first is the BD-MCY function (Mezentsev 1955, Choudhury 1999, Yang et al. 2008 which is as follows (Equation 4): The other is the BD-Fu function (Fu 1981, Zhang et al. 2004) (Equation 5): where n and ω represent catchment parameters such as agricultural activity, relative infiltration capacity, vegetation covering, soil characteristics, average slope, and anthropogenic activities.
In this study, these catchment parameters were obtained by calibrating the Budyko models (Equations 4 and 5) with satellite-derived datasets (GLEAM PE) and station observations (IMD rainfall, station discharge) for each of the river basins. According to Zhou et al. (2015), the BD-MCY function is superior for describing the water energy balance of a hydrological system, among the available Budyko functions. Figure 4 depicts the relationship between the dryness index (PE/P) and evaporation ratio (E/P) with varying catchment coefficients for the BD-MCY and BD-Fu equations, respectively.

Climate elasticity approach
The climate elasticity of runoff suggested by Schaake (1990), defined as the proportional change in runoff (R) divided by the proportional change in climatic variables, is considered a valuable hypothesis for identifying the temporal variability of runoff due to climate change (Sankarasubramanian et al. 2001). Based on the Budyko function, a total differential method was introduced to measure the runoff change by assuming that P, PE, and c are independent of each other Farquhar 2011, Zheng et al. 2018). The partial derivatives represent the sensitivity coefficients of runoff (R). Thus, @R @P is the runoff sensitivity with respect to P, @R @PE is the runoff sensitivity with respect to PE, and @R @c is the runoff sensitivity with respect to c. Equation (6) is a generalized form of the total differential method.
The first two terms on the right side of Equation (6) (i.e. @R @P dP þ @R @PE dPE) are used to calculate the runoff change due to climate change. The runoff change due to the variation of catchment characteristics is computed using the last term on the right-hand side, @R @c dc, of Equation (6). To separate climate and catchment influences on mean annual runoff, Zhou et al. (2016) suggested a complementary relationship for runoff that relies on the Budyko hypothesis. Although the Budyko framework does not allow for a specific division, the complementary method provides for an assessment of the lowest and highest contributions for both climatic and catchment effects. Equation (7) shows the complementary relationship between the partial elasticity of runoff with respect to P and with respect to PE, assuming that they are independent from each other. where runoff (R) is the difference between P and E in the water balance (Equation 3). Equation (7) can easily be reformulated as where @R @P and @R @PE are the runoff sensitivity which can be determined using Equations (1) and (4) for the BD-MCY model.
Similarly, using Equations (1) and (5) for the BD-Fu model: To calculate the change in runoff based on the complementary relation of runoff in Equation (8): Similar to the total differential method of runoff (R) in Equation (6), the combination of the first two terms on the right-hand side of Equation (13), i.e. @R @P dP þ @R @PE dPE À � , represents the contribution of climate changes to the variation of runoff. Zhou et al. (2016) demonstrated that the combination of the last two terms on the right-hand side of Equation (13), d @R @P À � P þ d @R @PE À � PE, is assumed to represent a contribution of catchment change and is equivalent to @R @c dc in Equation (6).

Separating the effects of climate change and catchment characteristics on runoff
To express the mean annual water-energy balance for a specific watershed, we incorporate the state space (P, PE, E). Let the initial state be M (P 1 , PE 1 , E 1 ) and the final state be N (P 2 , PE 2 , E 2 ). Runoff (R) and catchment characteristics c, change from R 1 and c 1 to R 2 and c 2 , respectively, from initial state to final state. Similarly, the sensitivity coefficients change from the initial state of @R @P À � 1 and @R @PE À � 1 to the final state of @R @P À � 2 and @R @PE À � 2 , respectively (Yang et al. 2008, Zhou et al. 2016. The details of space change from initial to final state are shown in Fig. 1. Unlike the total differential method, ΔR can be accurately broken down into two components -a forward approximation for the contribution of climate variation and a backward approximation for the contribution of catchment variation, and, in a similar way, a backward approximation for the contribution of climate variation and a forward approximation for the contribution of catchment variation, The difference operator (Δ) denotes the changes between the ending and starting states of a variable, for example ΔP = P 2 − P 1 . According to Equations (14) and (15) Within these upper and lower boundaries, the contributions of climate change and catchment change vary with different linear combinations of Equations (14) and (15), but the sum of the two always equals the overall change in the runoff. We incorporate a weighting factor (α) to generate ranges of possible values of contribution to ΔR from climate change ΔR climate ð Þ and catchment change ΔR catchment ð Þ. Linear combinations of Equations (14) and (15) have been used to estimate ΔR climate and ΔR catchment because the contributions of climate change and catchment change cannot be separated independently (Equation 16).
The value of the weighting factor (α) varies from 0 to 1. As ΔR is a combined effect of climate change and catchment change, ΔR can be written as where the contribution of climate changes to the change of runoff is represented by ΔR climate , Similarly, the contribution of catchment change is represented by ΔR catchment , ΔR climate and ΔR catchment vary linearly with the value of α. When the weighting factor α takes extreme values of 0 or 1, the upper and lower boundaries, respectively, of ΔR climate are achieved. When the ΔR climate reaches its upper bound, ΔR catchment reaches its lower bond. Similarly, when ΔR catchment reaches its maximum value, ΔR climate reaches its minimum value. While Equations (14) and (15), as well as any linear combination of them, are mathematically similar, the sum of ΔR climate and ΔR catchment for the complementary technique will always equal ΔR, regardless of the value of α.
In the present study, for each river basin, the study period has been divided into sub-periods of five years, and the effects of climate change and catchment characteristics on runoff changes in each are determined using the theory presented so far.

Climatic characteristics and basin runoff
The variation of P, PE, and R of all river basins for the respective study periods is shown in Fig. 5. Table 4 presents the calculated catchment characteristics i.e. n (for BD-MCY) and ω (for BD-Fu) as well as other climatic parameters of GRB for the different sub-periods. The corresponding results for the other four river basins are shown in Tables S1 to S4 in the Supplementary material. It may be noted that each sub-period spans five years for all the river basins. As stated in the methodology section, soil moisture content and change in water storage may be considered negligible over a five-year long sub-period. Therefore, actual evapotranspiration can be calculated as the difference between precipitation and runoff (Equation 3).
Mean annual precipitation and potential evapotranspiration vary in the range of 1107.67 ± 176.9 mm (mean ± standard deviation [SD]) and 1584.32 ± 57.29 mm, respectively, over the GRB. The runoff at the outlet of GRB fluctuates around 276.45 ± 114.18. Among all five basins, the KRB (Table S3) has the least fluctuation in mean annual P, with 755.9 ± 104.6 mm. On the other hand, the maximum annual P is observed at UNS, which is in the range of 1210.9 ± 238.47 mm. Among all the variables, PE fluctuated the least across all the river basins over the study period. UNS has the lowest PE, in the range of 1482.11 ± 65.93 mm, while the CRB has a higher PE, in the range of 1776.84 ± 66.97 mm.
The UNS has very high runoff coefficient (R c ) values, in the range of 0.74 ± 0.19. The causes of the significantly higher values of R c may be the decrease in infiltration and increase in surface runoff due to land use changes. In fact, between the years 1990 and 2009, intense deforestation in the catchment area increased the number of fallow fields, which account for 12% of the total area of this basin (Khare et al. 2014). The KRB and CRB are also among the most rapidly developing regions of peninsular India (CSO 2018, Garg and Azad 2019). As a consequence of the fast economic growth of this region, the demand for water in households and for industrial and agricultural uses is increasing day by day in the KRB (Chanapathi and Thatikonda 2020). Water demand exceeds supply in half of the Krishna River's sub-basins (Middle Krishna, Musi, Lower Krishna, Munneru, Vedavathi, and Paleru), resulting in water shortage and inter-state conflict (Yee et al. 2009).
However, to accommodate the extensive freshwater demand, a significant number of water retention structures have also been built and the R c values of the KRB and CRB are found to be lower compared to the other river basins (see Tables S3 and S4 in the Supplementary material). The runoff coefficient of KRB is unusually low (~0.02); this is supported by earlier studies (Bharat andMishra 2021, Gupta et al. 2022). Due to the huge consumption of water during the highly drought-affected years 2002 and 2003, the runoff was reduced at the basin outlet of this region (Mahajan andDodamani 2016, Shaik et al. 2020).
The distribution of the mean annual aridity index (PE/P) for each river basin is shown in Fig. S1 (Supplementary material). Comparing Fig. S1 with Fig. 3 (which shows the distribution of mean annual precipitation for each river basin), it is clear that regions with larger values of precipitation correspond to a lower PE/P ratio. This is because regions with high mean annual precipitation will typically have more vegetation cover, which enhances the soil moisture content of a region. Hence, a region with a lower vegetation cover will have less soil moisture content and drier catchments. For such basins with a high aridity or dryness index, R c values tend to be lower, which is in accordance with previous studies in other parts of the world (Merz et al. 2006, Merz andBlöschl 2009). Fig. S2 in the Supplementary material depicts the correlation between aridity index and runoff coefficients for each river basin.

Sensitivity coefficients of runoff for the BD-MCY and BD-Fu models
For each basin, using the BD-MCY model, the sensitivity coefficients of runoff have been determined with respect to P and PE (i.e. @R @P and @R @PE ) ( Table 5). The value of @R @P is highest, with an average of 0.87 (ranging from 0.82 to 0.96) for UNS, indicating that runoff is highly sensitive to precipitation. However, the coefficients are significantly lower for KRB and CRB, with an average value of 0.25 (ranging from 0.07 to 0.33) and 0.26 (ranging from 0.19 to 0.31), respectively. On the other  hand, the coefficient of sensitivity of runoff with respect to PE is always negative, indicating an inverse relationship between the two. The values of @R @PE are higher for KRB, with an average of −0.08 (ranging from −0.11 to −0.02). The average value of @R @PE is lowest for UMS at −0.22 (ranging from −0.26 to −0.19) for the BD-MCY model. The runoff sensitivity coefficients are also determined using BD-Fu and shown in Table S5 (Supplementary material). The sensitivity coefficients obtained using BD-Fu are on the same order as -indeed, almost identical to -those of the BD-MCY function. Hence, we conducted further analysis using the BD-MCY results only. Figure 6 shows the distribution of sensitivity coefficients of runoff with the aridity index (ϕ). For all the river basins, runoff is more responsive to precipitation than to potential evapotranspiration, which accords with the study conducted by Bharat and Mishra (2021). Sensitivity coefficients of runoff with respect to precipitation @R @P À � decrease significantly with ϕ for UMS (R 2 = 0.77, p value < .05) and GRB (R 2 = 0.86, p value < .05) (Fig. 6(a)); while @R @PE À � increases slightly with ϕ for UMS (R 2 = 0.98, p value < .05), GRB (R 2 = 1, p value < .05), KRB (R 2 = 0.83, p value < .05) and CRB (R 2 = 0.75, p value < .05) ( Fig. 6(b)). Additionally, with an increase in the aridity index the sensitivity of runoff decreases, as both sensitivity coefficients increase and approach zero with an increase of ϕ -except for @R @PE of UNS, which decreases with an increase of ϕ. However, the coefficient of determination is very low for UNS (R 2 = 0.12). Figure 6 shows that the change in the sensitivity coefficient is less with the increase of ϕ for UNS and CRB as compared to the other three basins. In fact, the figure depicts three clusters of river basins. First is the UNS with a high runoff coefficient (R c ); second are UMS and GRB with moderate R c values; and third are the KRB and CRB with low R c values. An assessment conducted in peninsular river basins also found exceptionally low runoff coefficients for KRB and CRB (Gupta et al. 2022).
It can be observed from Fig. 7 that there is a significant positive correlation between E/P and n, which confirms that with an increase in the vegetation cover of a basin, actual evapotranspiration also increases. Figure 8(a), (b), and (c) depicts the NDVI distribution for 1990 shows the distribution of the mean annual E/P ratio for 2009 for each river basin. The variation of E/P ratio is in accordance with that of NDVI for the year 2009 as shown in Fig. 8. The northern part of the CRB and the areas near the KRB and GRB estuaries have high NDVI values (0.2 to 0.8) where high E/P ratios are also observed. Additionally, the basin with the relatively high evaporation ratio (E/P) has lower runoff coefficients, as the sum of the evaporation ratio and runoff coefficients is unity. As vegetation cover increases, more precipitation infiltrates the soil and returns to the atmosphere through evapotranspiration, leading to reduced runoff. We observed an increasing trend of NDVI values for each of the river basins over the period 1990 to 2014. However, the rate of increase is found to vary from basin to basin (Fig. 8(a), (b), and (c)).

Sub-period variation of runoff due to climate and catchment changes
For each basin, the change in runoff (ΔR) between two adjacent sub-periods is obtained by the difference in runoff between the latter state and the former state, for example, ΔR 1 = R 2 − R 1 . At the same time, the sum of ΔR climate and ΔR catchment also provides ΔR for a specific value of the weighting factor α. Here, ΔR climate and ΔR catchment are obtained from the runoff sensitivity coefficient (i.e. @R @P and @R @PE ) discussed in the preceding subsection. ΔR climate and ΔR catchment fluctuate with variation in the weighting factor α; however, the sum of ΔR climate and ΔR catchment always equals ΔR for a given period  irrespective of the weighting factor α. Table 6 shows the ΔR climate and ΔR catchment with varying values of the weighting factor (α = 1, 0.5, 0) for GRB using the BD-MCY function. The results for the other basins are shown in the Supplementary material, in Tables S6-S9. The fluctuation of ΔR is reasonably high for UNS (see Supplementary material, Table S6), in the range of (−218.47 to 477.21), while it is relatively low for CRB (Table S9) It is interesting to note that the contribution to runoff may show opposite characteristics in response to climate versus catchment change, and hence the individual effects may not be prominent unless a formal attempt at partitioning is undertaken. For example, at GRB, the change in runoff due to climate variation for the first sub-period, with α = 0.5, is ΔR climate,1 = 2.32 mm, indicating a positive contribution to runoff fluctuation, whereas ΔR catchment , 1 = −38.09 mm, indicating a negative contribution to runoff fluctuation. At the same time, for UMS (Table S7) at α = 0.5, ΔR climate,1 = −51.19 mm, indicating a negative contribution to runoff fluctuation; and ΔR catchment , 1 = 11.48 mm, indicating a positive contribution to runoff fluctuation. In some sub-periods, there is unidirectional  behaviour of climate and catchment contribution to change in runoff, while in other sub-periods it is bidirectional. The latter is in contrast to many prior studies in other basins where the effects were found to be unidirectional, making the detection of such changes quicker (Wang et al. 2006, Bao et al. 2012). However, unidirectional and bidirectional contributions of climate and catchment to the change in runoff are not uncommon, as this was also noticed earlier in some studies (Zheng et al. 2018). Among the climatic factors, the change in precipitation is proportional to the variation in runoff of a basin, as evidenced by Table 4 and Tables S1-S4 of the Supplementary material. The aridity index (PE/P) also influences the runoff. As discussed in sub-section 4.1, a high aridity index for a given basin corresponds to low runoff. Among the catchment factors, the vegetation cover of a basin influences its runoff generation. As the vegetation cover increases, the amount of evapotranspiration and infiltration also increases, leading to reduced runoff. This phenomenon is discussed in detail in sub-section 4.2. As a five-year sub-period is considered in this study, the direction of variation of the above-mentioned climate and catchment characteristics across different sub-periods may differ, which may lead to unidirectional and bidirectional contributions to the change in runoff in different sub-periods.
A visible increase in the variation of runoff for different values of α can be observed in KRB and CRB from the fourth sub-period (2000-2009) onwards. As mentioned in subsection 4.1, runoff for these basins is reduced due to heavy consumption in drought-affected years (2002)(2003) (Mahajan andDodamani 2016, Shaik et al. 2020). In addition, these drought conditions have possibly affected other water balance components of the basin (soil moisture, groundwater storage, etc.), which increases the uncertainty in runoff partitioning in this period.
The dominant factor influencing the runoff of each river basin varies across sub-periods. However, it can be observed that catchment change in the initial stage (1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999) and climate change in the later stage (2000 onwards) dominate the runoff variation for UNS, GRB and CRB. The main reason for this is the extensive LULC change during the initial sub-period of this investigation in each river basin. As observed in Figs 8-10 and Table 7, the distribution of LULC classes and NDVI reflects a significant change in catchment characteristics between 1985 and 2009, while the change between 2009 and 2014 is less prominent, although the interval between the two periods is smaller for the later period. The runoff variation of the CRB in the three initial sub-periods is influenced by catchment characteristics, which is evident as a large portion of fallow land and a portion of forest land are converted to agricultural areas (Figs 9, 10 and Table 7). In the later subperiods, climate change dominates the runoff variation in all three river basins. However, during the initial stage (1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999) of the UMS, runoff variation is dominated by climate change. In contrast, for the entire study period, runoff variation in the KRB is dominated by the catchment characteristics of the basin. In the case of KRB, this is mainly due to the increased agricultural land and increased number of dams in this basin.  9. Land use/land cover change of the river basins during the study period.

Overall impacts of climate and catchment changes on runoff variation
In order to determine the overall impacts of climate and catchment changes on runoff, the first sub-period (T 1 ~ 1980-1984)  with time periods are shown in Figs 11 and 12, respectively. The runoff variation due to climate change (ΔR 0 climate; i ) shows a positive correlation with P, whereas the ΔR 0 catchment; i has a clear negative correlation with catchment parameter n. As we move from the initial sub-period to the final sub-period, the runoff differences between various values of α increase. This is because we assumed that changes in soil moisture content and water storage between two neighbouring periods are negligible. This results in a slight inaccuracy for the neighbouring sub-periods, and the error accumulates over time.

Partitioning the impacts of climate and catchment change on runoff variation
The distribution of land-cover classes in each river basin over time (years 1985, 2009, 2014) is presented in Fig. 9. Basin wise land-cover distribution change from the initial to the final period is shown in Fig. 10 and Table 7. The results show that the area of water bodies increased for GRB (from 3.5 to 3.7% of the basin area) between 1985 and 2014, KRB (2.0 to 2.1%) and CRB (1.5 to 2.3%) between 1985 and 2009. There has been a significant decrease in the area of dense vegetation and forest cover in every river basin except the CRB, where forest cover increased from 22.2% to 25% between 1985 and 2009. Similarly, agricultural fields or area with light vegetation increased between 1985 and the end of the study period in each river basin, mainly due to deforestation and conversion of forest land to agriculture and other purposes. The amount of fallow land in CRB was significantly high in 1985 (23.1%) and it decreased to 0.4% in 2009, mainly due to the conversion of fallow land to agriculture which increased from 52.9 to 71.6% between 1985 and 2009. An increase in the builtup area is obvious between 1985 and the end of the investigation period. Additionally, the cumulative number of dams on KRB in 1980 was around 200, and this increased to approximately 450 at the end of 2009. In the GRB the cumulative number of dams was around 250 in 1980; it reached more than 600 in 2014. Similarly for the CRB, the cumulative number of dams in 1980 was around 15, and it increased to approximately 40 in 2009 (Das 2021). These above-mentioned catchment changes have greatly affected the runoff variation of each river basin.
The runoff difference between a particular sub-period and the initial sub-period (T 1 ) for all five river basins is depicted in Fig. 13 and summarized in Table 8. As in case of individual sub-periods, the overall runoff variations with respect to the initial sub-periods i.e. ΔR 0 climate; i and ΔR 0 catchment; i have been calculated corresponding to α = 1, 0.5 and 0. In Fig. 13, for a specific basin, the bars between sub-period 1 and 2 represent ΔR 0 1 ; similarly, the bars between sub-period 2 and 3 represent ΔR 0 2 , and so on. Within each sub-period interval, six bars are shown, three each for R 0 climate; i and ΔR 0 catchment; i for the different values of α. From Table 8, it is observed that the overall reduction of runoff (−38.95 mm) for UNS over the complete study period is dominated by catchment change for this basin. The mean contribution to runoff change (corresponding to α = 0.5) is 4.52% and −8.50% corresponding to climate and catchment change respectively. Similarly, the mean contribution to runoff variation (corresponding to α = 0.5) at UMS is 18.90% and 29.78% for climate and catchment change, respectively. The contributions of both climate and catchment change to runoff difference (138.07 mm) are positive between the initial (T 1 , i.e. 1980-1984) and final (T 7 , i.e. 2010-2014) sub-periods. The difference of runoff for GRB with respect to the initial sub-period is primarily negative except for ΔR 0 2 ( Fig. 13(c)). The runoff difference between T 3 (1990)(1991)(1992)(1993)(1994) and T 1 (1980)(1981)(1982)(1983)(1984) is positive and substantially contributed by climatic parameters. Figure 13(d) depicts the impacts on runoff change corresponding to various α values for the KRB. The negative contribution of catchment characteristics dominates the runoff changes in this basin. The impact of climate and catchment characteristics to runoff variation is of the opposite order for ΔR 0 2 and ΔR 0 5 ; however, the overall effective runoff change is negative for the KRB. The variation of α at KRB causes fluctuation in the direction of contribution; for instance, for α = 1, the contribution of climate is negative and the contribution of catchment characteristics is positive; whereas at α = 0.5 and 0, the situation is the reverse. The reduction of runoff is maximum at KRB (-13.10%) which is a largely caused by the contribution of changes in catchment characteristics. In Fig. 13(e), for CRB, ΔR 0 1 , ΔR 0 2 , and ΔR 0 3 are greatly influenced by catchment changes in the basin, while at ΔR 0 4 , the impact on runoff variation is contributed mainly by climate change. Similarly, the runoff difference between sub-period T 1 and sub-period T 6 (over the complete study period) is almost nil (7.27 mm); however, this is because the climate and catchment contributions are equal in magnitude and opposite in sign.
Overall, the mean runoff at the final sub-period has increased with respect to the initial sub-period in UMS (138.07 mm) and CRB (7.27 mm), whereas for the other river basins, the runoff variation is negative, i.e. the runoff in the final sub-period has decreased with respect to the initial sub-period. However, the runoff variation is negligible over the study period (−3.19 mm) at GRB. Thus, the relative contribution of changes in climate and in catchment characteristics to runoff change varies spatially (across basins) and temporally (across subperiods for a particular basin). The temporal variations may, of course, change if the sub-period intervals are changed.
According to the results obtained in this investigation, it is clear that the catchment characteristics of each basin make a dominant contribution to the runoff change at the end of most sub-periods, whereas climate change is a significant contributor to the runoff change in the UMS. Each sub-period of the KRB is influenced by the catchment characteristics of the basin, which is also evident from the LULC and NDVI distribution of the basin. Runoff variation of the CRB in the three initial sub-periods is Figure 11. Variation of ΔR' climate and P across the sub-periods. dominated by catchment characteristics which are evident in the form of the conversion of a large portion of fallow land and a portion of forest cover to agricultural area (Figs 9-10 and Table 7). Every sub-period except ΔR 2 ' in GRB is influenced by catchment characteristics, which is likely because there has been a significant increase in agricultural land and water bodies in the area during the study period.
In this study, three different values of α were considered to exhibit the extent of runoff variation that may be attributed to climate and catchment. However, the most suitable one may be chosen after examining the evolution of LULC conditions and the climatology of the basin over time. For example, if the catchment conditions are found to have altered substantially, then the value of α which reflects this may be more suitable. Although it is difficult to select a precise value of the weighting factor, a weighting factor (α) of 0.5 can be safely used when catchment conditions and climate change both have considerable impact on a basin.

Conclusions
This study focusses on partitioning the effects of climate change and watershed change on runoff variation in Indian river basins using a complementary relationship based on the Budyko hypothesis. Using only three types of observed data -precipitation, potential evapotranspiration, and runoff -the effect of climate and catchment on mean annual runoff variation is estimated using runoff sensitivity coefficients. Using five-year sub-periods, the temporal variations of the climate and catchment characteristics of the river basins are investigated. The findings indicate that among the basins studied, there are three distinct clustersthat with a high runoff coefficient (R c ) (UNS), those with moderate values of R c (UMS and GRB), and those with low R c (KRB and CRB). Typically, if a region has a high dryness index (PE/P) value, it has a correspondingly low runoff coefficient. The runoff change due to climatic change is proportional and strongly sensitive to precipitation (rather than potential evapotranspiration) while that due to catchment change is inversely proportional to catchment characteristics (n or ω) -i.e. with an increase (decrease) of n or ω, ΔR' catchment decreases (increases).
The results of this study show that catchment parameters are the major contributors to the change in runoff during the initial sub-periods of all basins, except for UMS, where climate change is the major contributor to the change in runoff. In most of the basins, rapid development during the initial sub-periods led to significant land use changes, as is evident from the LULC maps. In later sub-periods (from 2000 onwards), the contributions from climate change dominate the runoff variation, although it shows considerable temporal variation. Although the precise contributions of climate and catchment change to runoff variation are difficult to estimate, this study presents upper and lower bounds on the magnitude of the climate and catchment change on runoff variation for the peninsular river basins, which is essential for sustainable infrastructure development. This comprehensive assessment of basin-scale runoff partitioning can be replicated for other river basins.

Disclosure statement
No potential conflict of interest was reported by the authors.