An accurate assessment of key ecosystem services (ES) such as water yield has gained focus in recent years in ES modeling, as fresh-water availability in a region is essential for agriculture, industry, human consumption, hydropower, etc. (Redhead et al., 2016). Hydrological ecosystem services generally include drinking water supply, power production, industrial use, irrigation and many more. The accurate estimation of water yield further facilitates in the identification of hotspots for storm-water harvesting in order to fulfill fresh-water demand in the region (Pathak et al., 2017). The hydrological ES are dependent on different factors, such as watershed characteristics (e.g., topography, land use and land cover – LULC, soil type and climatic condition. To incorporate these parameters into assessment and decision-making, there has been a proliferation of ecosystem-modeling tools and methods. Models for ES evaluation often focus on using globally available data, accepting large number of spatially explicit inputs producing spatially explicit output, and limiting the model structure to key biophysical processes involved in land use change (Guswa et al., 2014). The precise estimation of ES using these models is a complicated task owing to spatial variability and dependence of ES on various topographical and climatic factors. Further, the validation and uncertainty assessments in model outputs have proven to be key obstacles to the application of ES models. In the literature, studies focusing on comparison of different ES models have projected some light over the model output validation issues; however, a lack of studies highlighting the validation of these models for Indian river basins still exists. The benefits that can be derived from ES should be analyzed and quantified in a spatially explicit manner (Sánchez-Canales et al., 2012). The uncertainties involved in the determination of spatial and temporal distribution of the climatic variables, especially precipitation, constitute a major obstacle to the understanding of hydrological behavior at the catchment scales (Milly and Dunne, 2002).

The Integrated Valuation of ES and Tradeoffs (InVEST) model, developed by Natural Capital Project (Tallis et al., 2010), is a tool that provides a framework for planners and decision makers to assess trade-offs among ES and enables their comparison in various climate and land use change scenarios. The model includes a biophysical component, which facilitates the provision of fresh water or water yield from different parts of the landscape, and a valuation component, representing the benefits of water provisioning to people. The model works on simplified Budyko theory, which has a long history and still continues to receive attention in the hydrological literature (Budyko and Ronov, 1979; Zhang et al., 2001; Zhang et al., 2004; Ojha et al., 2008; Zhou et al., 2012; Donohue et al., 2012; Xu et al., 2013; Wang and Tang, 2014). The InVEST model applies a one-parameter formulation of the Budyko theory in a semi-distributed manner (Zhang et al., 2004). The model is capable of quantifying the water yield of a catchment under the influence of change in different drivers, viz. climate variables and catchment characteristics (e.g., land use change). Various studies have been carried out in the past demonstrating the application of the InVEST model to different river basins around the world. Sánchez-Canales et al. (2012) carried out a sensitivity analysis of three parameters, i.e., z (seasonal precipitation coefficient), precipitation (annual) and ET0 (annual reference evapotranspiration), and using the InVEST model for a Mediterranean basin, they found precipitation to be the most sensitive parameter for the study region. Later, Terrado et al. (2014) applied the InVEST model for the heavily inhabited defined as Llobregat river basin. The model is applied for both extreme wet and dry conditions, and the role of climatic parameters is emphasized. Hoyer and Chang (2014) applied this model in the Tualatin and Yamhill basins of northwestern Oregon under a series of urbanization and climate-change scenarios. The results show that the climatic parameters have more sensitivity than other inputs for a water yield model. Hamel and Guswa (2015) applied the same water yield model for the Cape Fear catchment, North Carolina, and concluded that the precipitation is the most influencing parameter. Goyal and Khan (2017) employed the InVEST water yield model for the hilly catchment by considering two catchments, i.e., the Sutlej River catchment and Tungabhadra River catchment. The climate parameters, i.e., precipitation and ET0, are observed to be the most influencing parameters for water yield in both the river basins. With the aforementioned studies, certain factors exist that limit the application of InVEST model such as the absence or inadequate comparison with observed data, the calibration of the model without prior identification of sensitive parameters and a lack of validation of the predictive capabilities in the context of land use and land cover change (Bai et al., 2012; Nelson et al., 2010; Su and Fu, 2013; Terrado et al., 2014).

The InVEST model operates on the principle of the Budyko theory (Budyko, 1958, 1974). Based on works of Schreiber (1904) and Ol'Dekop (1911), Budyko proposed formulations explaining the relationship between precipitation and potential evapotranspiration (PET) in order to couple water and energy balances, defined as the Budyko hypothesis. Several attempts have later been made to obtain an analytical solution of the Budyko hypothesis (Schreiber, 1904; Ol'Dekop, 1911; Turc, 1954; Mezentsev, 1955; Pike, 1964; Fu, 1981; Choudhury, 1999; Zhang et al., 2001, 2004; Porporato et al., 2004; Yang et al., 2008; Donohue et al., 2012; Wang and Tang, 2014; G. Zhou et al., 2015; S. Zhou et al., 2015). Among these studies, solutions provided by Fu (1981) called Fu's equation, gained significant attention as the work represented the effect of catchment properties on water balance components by incorporating an addition parameter “w”. Fu's equation can provide a full picture of the evaporation mechanism at the annual timescale. Therefore, Fu's equation can be used through a top-down analysis for providing insight into the dynamic interactions among climate, soils, vegetation, and their controls on the annual water balance at the regional scale (Yang et al., 2007).

Considering the lack of studies on analysis and validation of ES on the Indian subcontinent, especially for Himalayan catchments, and to assess the applicability of various water-balance models to Himalayan catchments, the present work attempts to compute and analyze water yield in the upper Ganga Basin using a semi-distributed InVEST model and a Lumped Zhang model. The work primarily considers, in detail, the spatial variation of InVEST model parameters and uses different strategies to compute water yield. Accordingly, water yield is estimated for 4 years, i.e., 1980, 1990, 2001 and 2015 and the most appropriate strategy is identified. The parameters that are adopted as lumped at the basin scale in previous studies are estimated at the pixel scale in order to avoid the dependence of the model parameters on size of the catchment. In addition, pixel-level estimations of water yield are expected to be more accurate than output obtained using the conventional approach with basin-lumped output. The term “finer scale” in the paper represents the incorporation of spatial variations through the pixel-level estimation of parameters involved in InVEST model, which are otherwise taken as lumped. The work also compares the outcomes of spatially distributed water yield models and the conventionally used Lumped Zhang model.

In the present work, five different strategies are employed to compute water yield. For the ease of presentation, these strategies are referred to as A–E. In strategy A, an average value of precipitation, temperature, extraterrestrial radiation and parameter w is used for the entire basin. This strategy is essentially based on Lumped Zhang model. Strategies B–E are designated, corresponding to a particular variation of the InVEST model where water yield is computed using different approach for estimating parameter w. For computing parameter w, relationships for large basins and for the global model from Xu et al. (2013) are given by Eqs. (9) and (10), respectively.

For large basins, w=0.69387-0.01042×lat+2.81063×NDVI+0.146186×CTI. For the global model, w=3.50412-0.09311×slp-0.03288×lat+1.12312×NDVI-0.00205×long-0.00026×elev, where, “slp” is the slope gradient, “lat” is the absolute latitude of basin center, “CTI” is the compound topographic index, “NDVI” is the normalized difference vegetation index, “lat” is latitude, “long” is longitude and “elev” is elevation.

In strategy B, the entire basin is considered for computing the parameter w for large basins, using Eq. (9), which is given by Xu et al. (2013). In strategy C, the parameter w is computed for entire basin using Eq. (10), which is given by Xu et al. (2013). In strategy D, parameter w is computed at each pixel in order to incorporate the spatial distribution of the hydrologic variables involved in the computations. In Strategy E, parameter z is computed according to the number of rain events in a year; subsequently, Eq. (4) is used to compute the parameter w.

For all the strategies, the extraterrestrial radiation (RA) parameter is computed for each month using Eq. (8), and a raster layer is generated. Precipitation data are obtained from Indian Meteorological Department (IMD) at a grid size of 0.25∘ for the study area. It has been interpreted and converted to the raster format by using the inverse distance weighted (IDW) interpolation technique in the ArcGIS environment for obtaining the values for all pixels at a resolution equal to the resolution of the Landsat satellite images. The temperature dataset is obtained from the IMD at a grid size of 1∘ × 1∘ for the study area and has also been converted to a raster format by using the IDW interpolation technique for obtaining the values for all pixels. Subsequently, the mean monthly value of average temperature (Tavg) and the difference between the mean daily maximum and mean daily minimum (TD) are obtained. The climate datasets used in the present study are of the finest resolution available so far for the study region. Gridded datasets of temperature and precipitation used in the present study have been developed using quality-controlled stations and well-proven interpolation techniques. Further details about the datasets of precipitation and temperature are given in Srivastava et al. (2009) and Pai et al. (2014), respectively.

The modified Hargreaves method is applied for obtaining the value of reference evapotranspiration at each pixel for each month (Droogers et al., 2002). To compute potential evapotranspiration, the yearly values obtained for the reference evapotranspiration are multiplied by the vegetation evapotranspiration coefficient (Kc), which depends on the LULC characteristics, as expressed in Eq. (3). The value of Kc is taken from Allen et al. (1998), as shown in Table 1. In this study, Kc is taken in the same was for all 4 years, as shown in Table 1, and is used to obtain potential evapotranspiration, which is subsequently used to obtain annual water yield at each pixel of the study area.

The study aimed to apply the InVEST water yield model to compute the water yield for upper Ganga Basin having highly variable topography consisting of hilly, plain and snow-covered areas. The InVEST model is based on the Budyko theory, which requires low amounts of data and low levels of expertise, thus making it acceptable worldwide. The mean monthly precipitation, temperature, monthly value of difference of the mean daily maximum and mean daily minimum, and extraterrestrial radiation parameters for the upper Ganga Basin of all 4 years, i.e., 1980, 1990, 2001 and 2015, are converted into the raster format for various analyses. The monthly reference evapotranspiration is thus computed using input parameters in GIS environment by applying the modified Hargreaves equation for all the months, except for a few months in which the modified Hargreaves equation gives negative results for the reference evapotranspiration. For those months, the Hargreaves method is applied to obtain the positive value of reference evapotranspiration, as also suggested by Goyal and Khan (2017). Reference evapotranspiration when multiplied with Kc gives the potential evapotranspiration. All monthly values are added up to obtain the annual value of reference evapotranspiration. Kc is a function of land use and land cover; thus, supervised classification is done to prepare the raster map of land use and land cover for the upper Ganga Basin. Subsequently, the annual value of potential evapotranspiration is obtained for the study area for the years 1980, 1990, 2001 and 2015.

The paper employs various methodologies for water yield estimation, as discussed in the methodology section for the upper Ganga Basin. Thus, water yield is computed both from the InVEST model as well as the Lumped Zhang model. The value of the parameter w is computed using four different approaches, i.e., the mean single value obtained from Xu et al. (2013) for large basins, mean single value obtained from Xu et al. (2013) for the global model, pixel-level estimated value of parameter w from Xu et al. (2013) and pixel-wise value of parameter w from Donohue et al. (2012). Although the upper Ganga Basin lies in large basin category as per the definition from Xu et al. (2013), the yield computed using global model is in good agreement with the observed data for the region. In the study, the pixel-level estimation of parameter w is made in order to incorporate the spatial variability of the parameter involved in water yield estimation. Thus, two pixel-wise values of parameter w are computed for the upper Ganga Basin for years 1980, 1990, 2001 and 2015 by considering two approaches given by Xu et al. (2013) and the approach given by Donohue et al. (2012). Also, the basin-lumped water yield is computed using Lumped Zhang model, which considers the single mean values for entire basin of all the parameters involved in the computation of water yield. The water yield is computed in five different ways for the upper Ganga Basin for the years 1980, 1990, 2001 and 2015.

At the Rishikesh gauging site, surface runoff data are obtained by extracting the snowmelt from the discharge data, as the melting snow contributes about 32 % of total runoff in the Himalayan basins (Maurya et al., 2011). For validating the water yield obtained from different strategies, the observed yield is compared with the computed water yield based on different proposed strategies for the years 1980, 1990, 2001 and 2015, as represented in Table 3. The results obtained from Donohue et al. (2012) and Xu et al. (2013) are computed at pixel level (Strategy C–E); thus, they exhibit better performance than other approaches and are in good agreement with the observed data. These results exhibit the superiority of pixel-level computation to hydrological analyses for a watershed. The parameters involved in the Budyko model are dependent on various factors, such as basin characteristics (size, topography, stream length, slope, etc.), climate seasonality, etc. (Li et al., 2013). Again, the factors affecting model parameters vary both spatially and temporally. Moreover, the relationship between these factors and model parameters are not yet well defined (Ahn and Merwade, 2017). In such scenarios, adopting a hypothesis by assuming either of these controlling factors (such as “w”) to be spatially or temporally constant is inappropriate. Considering these facts, the present study attempts to incorporate the spatial variability of model parameter for estimation of water yield at the pixel level. As the computations are made at pixel level (on a grid of size 30 m × 30 m), the assumption of dependence of model parameters on the size of the catchment may also be disregarded. The computations made in the present work are based on empirical equations; however, the application of these equations has been well documented worldwide for estimations of various water balance components at various basin scales (Zhang et al., 2008; Ma et al., 2008; Ning et al., 2017; Rouholahnejad Freund and Kirchner, 2017; Wang and Zhou, 2016). Hence, it is recommended that for such a large basin, it is required to compute all the parameters involved in the computations of water yield at the pixel scale rather than adopting mean values for entire watershed.

The present study aimed to apply the InVEST annual water yield model, a tool that is gaining interest in the ecosystem services community, in the upper Ganga Basin. While such simple models have low requirements for data and level of expertise, practical applications of such a model with single representative values of the model parameter for the entire basin do not provide accurate estimates of water yield. Performing pixel scale computation of water yield in the study indicates a better performance, and the results obtained show better agreement with the observed water yield. As far as parameter w is concerned, the global model works better than other representations of parameter w available in literature, especially in the upper Ganga Basin. In the study, the water yield is computed using five different strategies, and results are validated with the observed data at the outlet of the upper Ganga Basin. The present study attempts to quantify annual water yield at the pixel level, making the computations independent of the size of catchment. Therefore, the proposed methodology is expected to perform well for a catchment of any given size. Changes in catchment water storage over time are required to be quantified in order to validate the applicability of Budyko's model to long-term data for the studied catchment. Earlier, some of the important parameters defining water yield used to be computed at a basin-level scale, which caused errors in the results.

The study attempts to incorporate the spatial variability of parameters involved in the model through the pixel-level estimation of parameters that are otherwise taken as lumped in the previous studies. Study results show that the estimated water yield, considering spatial variability in model parameters, is in better agreement with the observed water yield compared to the water yield estimated when considering the parameters to be lumped over the study region. Further, the computations of various parameters are made at the pixel level; therefore, the estimates of water balance components using this approach are expected to be independent of the assumption of dependence of parameters on catchment size. As the relationship between Budyko's model parameters and their controlling factors has not been well defined (Ahn and Merwade, 2017), the study emphasizes water yield estimation using pixel-based computations. The study outcomes can be summarized as follows: (i) between two approaches used in the study, i.e., considering the entire basin and pixel-level approach, the pixel-level approach is found to provide better results; and (ii) in pixel-based computations, results are further improved with the use of a parameter w based on a global model rather than regional models of parameter w, especially for large basins in the Himalayan region.