Assessment of spatially explicit annual water-balance model for Sutlej River Basin in eastern Himalayas and Tungabhadra River Basin in peninsular India

Hydrological ecosystem services (ES) often include drinking water supply, power production, industrial use, irrigation, and many more. These hydrological ES are dependent on different watershed characteristics such as land use and land cover (LULC), soil type, topography, and climatic conditions. LULC has a dominant influence in producing spatial variability of ES and tradeoffs. With the change in different ES due to climate change, proper analysis and quantification of ES are playing a major role in policy-making of a country. Proper analysis of ES is not easy but rather complicated due to its spatial variability and dependency on so many topographical and climatic factors. The benefits which are derived from ES, should be analyzed and quantified in a spatially explicit manner. Sound quantification techniques also play a crucial role in ES assessment (Burkhard et al. 2012). Over the years, efforts have been made to develop different ecosystem assessment tools. In this regard, Integrated Valuation of Ecosystem Services and Tradeoffs (InVEST), developed by Natural Capital Project (www.naturalcapitalproject.org) (Tallis et al. 2014) can be used. Although it is a simplified model, it can provide us with satisfactory conclusions regarding different ES.

Sánchez-Canales et al. (2012) used the InVEST model in a Mediterranean region basin (the Llobregat basin, Catalonia, Spain) and carried out sensitivity analysis of three main coefficients: Z (seasonal precipitation distribution), prec (annual precipitation), reference evapotranspiration (ET₀) (annual evapotranspiration) using Morris index method and found Z as the least sensitive parameter and precipitation as the most sensitive parameter in humid areas of the study area, but in some watersheds, ET₀ had greater influence than precipitation. Terrado et al. (2014) used the InVEST model in the heavily humanized Llobregat River Basin (Catalonia, Spain) to assess three ES (i.e., water provisioning, water purification, erosion control) in extreme dry and wet years and found that climatic parameters are very sensitive in semi-arid basins under continuing population pressure. Hoyer & Chang (2014) used this model in Tualatin and Yamhill basins of northwestern Oregon under a series of urbanization and climate change scenarios and found that sensitivity of climatic parameters is higher as compared to other inputs in the water yield model. Most recently, Hamel & Guswa (2014) analyzed the uncertainty of the water yield model in Cape Fear catchment, North Carolina and found precipitation as the most influencing parameter and Z parameter as comparatively more sensitive than K_C within the specified range.

To the authors’ best knowledge, no significant work has been done using InVEST in a hilly catchment. In this paper we have used the water yield model of InVEST. We have applied this model in a hilly catchment, Sutlej River Basin (up to Kasol gauge station), with aridity index ranging from 0.139 to 2.39 with a mean of 0.764, situated in the eastern Himalayas and in one peninsular region, Tungabhadra River Basin (up to Haralahalli gauge station), with aridity index ranging from 0.22 to 1.98 with a mean of 0.949, in Karnataka, India and determined the performance of this model in these regions. Some parts of the two regions have a humid (0.75 > PET/P ≥ 0.375) and sub-humid climate (2 > PET/P ≥ 0.75) and also semi-arid (5 > PET/P ≥ 2) (Sutlej River Basin (up to Kasol gauge station)), depending upon aridity index (PET/P) as described by Ponce et al. (2000). Different equations (modified Hargreaves, normal Hargreaves, Hamon's equation) for calculating ET₀ have been used and potential applicability of these methods discussed for the basins. We have also compared the model outputs with the observed field data and with estimated values of the lumped Zhang model. The sensitivity of different parameters, which are responsible for determining the amount and nature of water yield from the study area, has also been discussed.

The whole study includes two sub-areas which are discussed below.

The InVEST model (Tallis et al. 2014) is designed to provide information about how changes in ecosystems are likely to change the flows of benefits to people. This model runs on a gridded format where input parameters are given in raster format which, in turn, help us to understand heterogeneity of key driving factors in water yield, such as soil type, precipitation, vegetation type, etc. In this study we have used the water yield model.

Root restricting layer depth is generally defined as soil depth up to which soil can allow the penetration of roots and root depth is defined as the depth where 95% of the root biomass occurs. PAWC is generally taken as the difference between field capacity and wilting point.

The ‘seasonality factor’ Z varies depending upon the local precipitation patterns, such as rainfall intensity and topographical and hydrological characteristics of an area. Three methods have been discussed in the user's guide of InVEST (Tallis et al. 2014). The work of Donohue et al. (2012) suggested that Z can be linked to the number of rain events per year, N, and can be computed by (N/5). The work of Xu et al. (2013) gave values of ω globally in their study. So if we know the average values of AWC, P, then we can calculate the value of Z using Equation (4), mentioned above. A third method of determining Z value is by calibrating the model through comparing model outputs with the observed values.

In our study, we have analyzed the sensitivity of Z and K_C parameter for the two regions. The work of Tallis et al. (2014) has shown the uncertainties in choosing Z parameter. As Z is also dependent on AWC, so it also depicts the sensitivity of AWC as well. In this study, the baseline value of Z has been calculated by means of Equation (4). The mean value of ω (ω = 2.06 for Sutlej River Basin and ω = 2.02 for Tungabhadra River Basin) has been estimated as suggested by Xu et al. (2013). The mean values of available water content (AWC), calculated by means of Equation (5) and precipitation (P) for the whole basin, have been used in Equation (4) to find out the baseline value for each study area. A baseline value of 13 has been used for Sutlej River Basin (up to Kasol gauge station) and a value of 10 has been used for the Tungabhadra River Basin (up to Haralahalli gauge station). All the Z values are taken at whole watershed level. We have varied the values of Z in between 1 and 30 and observed changes in water yield at watershed level. We have also calculated the value of Z via calibration. Due to lack of exact rain events data we could not use the method specified by Donohue et al. (2012).

From the work of McMahon et al. (2013), it has been observed that it is quite difficult to estimate the values of K_C for forest exactly, due to variation of K_C depending upon different characteristics of trees in a forest. We have chosen the baseline value of K_C of forest as 1 from the FAO 56 guidelines (Allen et al. 1998) and varied the value between 0.7 and 1.1 as it is expected to remain to be so for both the catchments. But the Tungabhadra River Basin (up to Haralahalli gauge station) is mainly crop dominated. Thus we have taken the baseline value of K_C as 0.75 for crop and then varied the value between 0.7 and 0.9 as it is expected to be so in that watershed and determined the changes in water yield with respect to baseline run, which is shown in Table 4. We have also varied the values of precipitation and ET₀ and compared the results with the baseline run for each of the basins. The ranges of sensitivity analysis of different parameters are given in Table 5.

Performance of the model has been assessed by comparing the model outputs with the observed data for both the catchments. We have run the model with the baseline values of Z and also tried to calibrate the model by varying the Z parameter. Uncalibrated model run is necessary to find out the sensitivity of different parameters of the model.

We tried to find out the appropriateness of the method of determining Z using the value of ω given by Xu et al. (2013). We have taken Z value as 13 for the Sutlej River Basin (up to Kasol gauge station) and 10 for the Tungabhadra River Basin (up to Haralahalli gauge station) for the baseline run. The changes in water yield with the changes of K_C, P, ET₀ in both of the catchments and the dependency of the model on these parameters are found from these analyses.

The model has been calibrated by eliminating the error that is the difference between observed and calculated water yield by varying the value of Z between 1 and 30 for the catchments. We have observed that the sensitivity of Z parameter to the model is much smaller in the hilly catchment and we could not calibrate the model varying Z values in the case of the Sutlej River Basin (up to Kasol gauge station). In the case of the Tungabhadra River Basin (up to Haralahalli gauge station), we calibrated the model with a Z value of 4.

In the case of the Sutlej River Basin (up to Kasol gauge station), precipitation is the most sensitive parameter, 10% increment of which results in 16.52% increase in water yield with respect to baseline run. A 10% increment in ET₀ decreases the baseline water yield by 5.51%. The baseline value of Z is taken as 13 and a change of Z value from 13 to 1 results in 22.8% increase in water yield, and a change of Z value from 13 to 30 results in a 2.4% decrease in water yield. A 30% change in K_C results in 1.28% change in water yield within the specified range of K_C values (0.7 to 1.1 for forest), which shows that Z parameter has more effect on the water yield within its range (1–30) than K_C if we restrict the value of K_C within its probable specified range. Otherwise, K_C is more sensitive than Z parameter if no specified range is given.

In the case of Tungabhadra River Basin (up to Haralahalli gauge station), a 10% increase in precipitation results in 19.6% increase in water yield with respect to the baseline. Whereas a 10% increase in ET₀ results in 5.8% decrease in water yield. Thus precipitation and ET₀ are more sensitive in Tungabhadra River Basin than Sutlej River Basin. A change of Z value from baseline value of 10 to 1 results in 50% increase in water yield. We have run the model for different combinations of K_C for both crop and forest and have observed the variation in water yield to remain within 1–8% within the specified range of K_C. Hence Z parameter is comparatively a more sensitive parameter than K_C within the specified range of Kc.

In the case of Sutlej River Basin (up to Kasol gauge station), the value of water yield from the lumped Zhang model underpredicts by 29.066% with respect to the result from the distributed InVEST model. In the case of Tungabhadra River Basin (up to Haralahalli gauge station), the lumped Zhang model underpredicts by 15.4% as compared to the distributed InVEST model.

Here the baseline values of Z parameter are determined by Equation (4) using values of ω obtained from the study of Xu et al. (2013). In the case of Sutlej River Basin (up to Kasol gauge station), the model overpredicts by 6.7% as compared to observed water yield when the model is run for Z = 13 as baseline value.

In the case of Tungabhadra River Basin (up to Haralahalli gauge station), the model underestimates by 28.14% as compared to the observed water yield at Haralahalli gauge station (observed gauge discharge values have been taken from India-WRIS (Water Resources Information System of India)) when the model is run for Z = 10 as baseline value.

The model is calibrated by varying the Z parameter for each of the two catchments. We observed that for the Sutlej River Basin (up to Kasol gauge station) we could not calibrate the model, i.e., the simulated model output value could not be matched with the observed water yield value by varying the value of Z parameter within its range of 1–30, due to low sensitivity of Z parameter. The baseline and calibrated values of Z of each catchment are given in Table 6.

From our study, it has been observed that the climate parameters precipitation and ET₀ are the most influential parameters as compared to Z and K_C, in both of the basins. The sensitivity of both P and ET₀ are comparatively higher in the case of Tungabhadra River Basin (up to Haralhalli gauge station). Moreover, our watersheds are gauged catchments and so any error in precipitation or ET₀ input will impart significant error in the water yield output. Thus we have to process and prepare the climatic inputs cautiously (i.e., choosing the proper method of calculation of ET₀, and proper method of interpolation of point data).

First, this gives an insight into the difference using the InVEST model which runs the Budyko theory at pixel to pixel level using Equation (2) in a spatially explicit manner and the Zhang lumped model which calculates the water yield at watershed level using the average values of P, PET, AWC, and Z. Our first study sub-area, Sutlej River Basin (up to Kasol gauge station), is a hilly catchment with almost 24% snow and glacier. The lumped Zhang model is underpredicting compared to the InVEST model with underprediction of 29.1% for Sutlej River Basin (up to Kasol gauge station) and 15.4% for Tungabhadra River Basin. The difference between the results of the spatially explicit InVEST model output and manually calculated lumped Zhang model output on which the InVEST model is based, suggests that the InVEST model could not fully capture the lumped Zhang model characteristics applied at watershed level with mean values of parameters, averaged over the whole watershed, otherwise the two model outputs would have produced the same output results. The reason behind the significant underestimation by the Zhang model may be due to overestimation from the non-vegetated LULC, which is consistent with the findings of Hamel & Guswa (2014) in the Cape Fear catchment, North Carolina. This is also due to non-linearity of Equation (2) and differences between values of ω used in the lumped model and explicit model, as mean value of ω has been considered for the lumped model whereas the value of ω varies from pixel to pixel in the InVEST model according to Equation (4).

The model does not consider the contribution of snowmelt separately but we have tried to capture the contribution of the snow and glacial portion by using a high value of K_C (= 2) for the snow and glacial part of the watershed. The global PET data have been downloaded from the website of CGIAR CSI (Consultative Group on International Agricultural Research Consortium on Spatial Information) (Trabucco & Zomer 2009) and the PET data for the snow and glacial portion of Sutlej River Basin has been extracted. The ET₀ has been calculated using the modified Hargreaves method for the basin and the ET₀ data for the snow and glacier portion of the basin has been extracted from these calculated data. The value of K_C has been found by taking the mean value of the raster obtained by dividing the PET raster by ET₀ raster [PET(x) =K_C(x) ×ETo(x)] in ArcGIS which gave us a value of K_C around 2 for the snow and glacier portion. The error due to ground water withdrawals is also not considered due to lack of reliable data. However, the results obtained from our analysis are satisfactory as far as the simplicity of the InVEST model is concerned.

In this study, an attempt has been made to determine the compatibility of the model and sensitivity of the parameters involved in it for hilly terrain as well as a peninsular region. From this study, the following may be inferred:

1. Precipitation is the most sensitive climatic input parameter in this model and has comparatively greater impact in the Tungabhadra River Basin. As a result, errors in precipitation inputs may impart major discrepancy in water yield in regions with high rainfall.

2. Modified Hargreaves method has been proved to be the most reliable method in calculating ET₀ under limited data conditions especially in the hilly catchment although it has been observed that in certain months this method is not applicable in Tungabhadra River Basin where the modified Hargreaves method along with normal Hargreaves method can be used as replacement for those months. We can also conclude that the method given by Thornthwaite & Mather (1955) is also not applicable in this hilly catchment where temperature in certain months remains well under 0 °C.

3. The sensitivity of Z parameter is much smaller in all the regions, especially in the hilly catchment and it is quite difficult to calibrate the model when sensitivity of Z parameter is less, as happened in the case of Sutlej River Basin (up to Kasol gauge station). It suggests that application of this model depends upon the sensitivity of Z parameter especially in hilly catchments.

4. From the results, we may conclude that the model is generating satisfactory results at watershed level which is a good aspect for any model.

5. Lumped Zhang model could not consistently match the distributed model especially in the hilly catchment.

Although this study is catchment specific, we believe that these results may be utilized in the study of water-balance equations in hilly catchments as well as in peninsular catchments using InVEST.