Keywords

13.1 Introduction

The Himalaya, which is in the northern part of the Indian Peninsula, is the abode of eternal snows, from which the rivers of the Ganga, the Indus and the Brahmaputra originate. These river systems, besides supplying water for urban and rural household uses, generate millions of kilowatts of power and are also extensively used for irrigating millions of hectares of agricultural land. Therefore, monitoring the distribution of snow in mountainous basins is necessary for accurate streamflow simulation which is of great importance for optimal water resources planning and management, and climate change studies. Significant amount of runoff is generated from both melting of ice and snow but due to lack of detailed ground truth observations, their relative contribution to runoff is difficult to quantify (Wulf et al. 2016).

Many conceptual and physically based hydrological models are used to explore, quantify and understand the processes associated with the discharge. The runoff generated from ice and snow is commonly estimated using either surface energy balance (Anderson 1976) or temperature-index models (Rango and Martinec 1981; Lang and Braun 1990; Rulin et al. 2008). Temperature-index models are commonly used for snowmelt modelling studies owing to easy accessibility to air temperature data and good performance in spite of their simplicity (Hock 2003). Temperature-index models are developed based on empirical relationships between ablation and air temperature. Many studies have established that a high degree of correlation exists between snowmelt and air temperature. Surface air temperature is important to many fields of research as it is one of the main controlling factors of many environmental processes. Near-surface temperature typically decreases with increase in elevation. However, the opposite effect may occur under certain conditions. Temperature lapse rates vary regularly and seasonally (Blandford et al. 2008). The variation in lapse rates is found to be more during the warmer months as compared to colder months and during daytime than at nighttime. Frequent temperature inversions during colder months partly describe the seasonality of temperature lapse rate (Whiteman et al. 1999). Factors such as location and time of the year affect the atmospheric lapse rate. Quantity of water vapour present in the air also strongly affects the lapse rate (Bandyopadhyay et al. 2014).

Many researches in the Himalayan basins used an annual constant lapse rate of 0.65 °C/100 m (Singh and Jain 2003; Pandey et al. 2014; Romshoo et al. 2015). Blandford et al. (2008) found that taking the lapse rate as 0.65 °C/100 m, which is the average value of environmental lapse rate, incurred some errors which led to lower accuracy of the modelling results.

Based on the existing hydro-meteorological information and the basin hydrological characteristics, the Snow Runoff Model (WinSRM) was used to simulate the discharge for the study area. The main objective of this study is to evaluate the impact of employing seasonally varied and annual constant near-surface lapse rates on hydrological simulations for the Nuranang watershed in the Eastern Himalayas.

13.2 Methodology

13.2.1 Description of WinSRM

WinSRM developed by Martinec et al. (2008) was used for this study to evaluate the effect of variation of near-surface lapse rate on snowmelt modelling. WinSRM is a deterministic, degree-day hydrological model developed to simulate and forecast daily runoff in hilly catchments where snowmelt is one of the dominant runoff contributing components. The model can be used for mountainous basins of any size and of any elevation range with a maximum simulation period of 366 days. Computed daily runoff from rainfall and snowmelt when superimposed on the recession flow gives daily streamflow as follows:

$${Q}_{n+1}=\left[{c}_{Sn}{a}_{n}\left({T}_{n}+{\Delta T}_{n}\right){S}_{n}+{c}_{Rn}{P}_{n}\right]\frac{{A}_{Z}{\text{10,000}}}{\text{86,400}}\left(1-{k}_{n+1}\right)+{Q}_{n}{k}_{n+1}$$
(13.1)

where Q is mean daily runoff, m3   s−1; a represents degree-day factor, cm ℃−1 d−1; cS express snowmelt runoff coefficient; ΔT is temperature lapse rate adjustment, ℃ d; T means number of degree-days, ℃ d; S represents ratio of snow-covered area to basin area; cR is rainfall runoff coefficient; P is runoff contributing precipitation, cm; AZ is catchment area or zonal area, km2; n represents the number of days for runoff calculation; k represents recession coefficient. Figure 13.1 shows the flowchart of WinSRM.

Fig. 13.1
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(Source Singh and Bengtsson 2005)

Flowchart of WinSRM

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13.2.2 Study Area

The study area, Nuranang watershed which is dominated by seasonal snow, is situated at Tawang district of Arunachal Pradesh (Fig. 13.2). Nuranang River which is one of the tributaries of Tawang River originates from Sela Lake and meets Tawang River at Jang. The total area of the watershed is 53.45 km2 and extends from 27°30′ N to 27°35′ N latitude and from 92° E to 92°7′ E longitude. Elevation of the study area ranges from 3465 to 4835 m above mean sea level (MSL) with a mean slope of 51%. The study area receives an average annual precipitation of 1139 mm between the summer monsoon months of May and September. Snowfall begins from late October and lasts till March, and the ablation period begins from February and ends in early June.

Fig. 13.2
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Nuranang River basin

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13.2.3 Acquisition of Data

13.2.3.1 Hydro-meteorological Data

Hydro-meteorological data for the Nuranang watershed was acquired from Central Water Commission (CWC), Jang. The daily data for discharge, precipitation and temperature for three years, i.e. 2004, 2005, and 2008, was used for this study. The Nuranang watershed was delineated at Jang, which is the CWC discharge monitoring site. The watershed outlet is located at 27°33′01″ N latitude and 92°01′13″ E longitude with an elevation of 3465 m above MSL. The watershed was further subdivided into three zones with 456 m elevation difference between each one of them (Table 13.1).

Table 13.1 Zonal elevation area and mean hypsometric elevations
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13.2.3.2 Moderate Resolution Imaging Spectroradiometer (MODIS) Snow Cover

MODIS/Terra snow cover product (MOD10A1) for the years 2004, 2005 and 2008 was obtained from https://reverb.echo.nasa.gov/ and was converted from HDF-EOS format to GeoTIFF format with the help of MODIS Reprojection Tool (MRT). The images obtained after preprocessing were used to get the snow cover area (SCA) information about the study area.

13.2.4 Input Data and Model Parameters

Precipitation, temperature and SCA were supplied as the input data to WinSRM. Temperature data was preprocessed to get the maximum, minimum and mean temperatures on a daily time scale. Daily degree days were then calculated using the mean temperature. Altitude adjustment of degree days was applied for all the elevation zones as follows:

$${T}_{\mathrm{adj}}= T-\Delta T$$
(13.2)

where the altitude adjustment \(\Delta T\) was computed as:

$$\Delta T= \gamma \left({h}_{\mathrm{st}}- \stackrel{-}{h}\right) \frac{1}{100}$$
(13.3)

where Tadj is adjusted temperature; ΔT is change in temperature; γ is temperature lapse rate, ℃/100 m; hst is elevation at which temperature was measured, m; and h̅ is zonal hypsometric mean elevation, m.

The SRM model parameters include critical temperature, runoff coefficients, rainfall contribution area (RCA), recession coefficient, degree-day factor (DDF), time lag and temperature lapse rate (Martinec and Rango 1986). Using the observed streamflow of Nuranang River at the outlet, recession coefficients of Nuranang watershed were calculated as Senzeba et al. (2015). In this paper, time lag (L) of 2 h was adopted for all the calibration years (Senzeba et al. 2015). Values of DDF for each month were taken as per the recommendation given by WMO (1964). Table 13.2 shows the monthly variation of DDF value considered for this study. Yearly average temperature lapse rate of 0.5 °C/100 m (Table 13.3) was used for model calibration as per the finding of Bandyopadhyay et al. (2014) over the region. Detailed description about the model parameters can be found in Martinec and Rango (1986).

Table 13.2 Adopted degree-day factor (a) cm/°C (WMO 1964)
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Table 13.3 Monthly variation of lapse rate
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13.2.5 Calibration and Validation of WinSRM

The model was calibrated by matching the observed runoff with the simulated runoff for the depletion period of 2004 (13 April–21 August) and 2005 (17 April–4 September) and was validated for the depletion period of 2008 (17 April–20 September). Out of the seven model parameters, critical temperature TCRIT, runoff coefficient for rain, cR and runoff coefficient for snow, cS, were calibrated, while the others were taken from the previous research findings (Senzeba et al. 2015). Calibration of the model parameters was done by varying one parameter at a time while keeping the rest of the parameters at their initial values. Table 13.4 shows the initial sets of the calibration parameters used for the calibration period.

Table 13.4 Starting sets of parameters for calibration years
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The average values of calibration parameters obtained during the calibration years were used for validating the model.

13.2.6 Accuracy Assessment

The accuracy assessment of the simulation was done by comparing the simulated streamflow with the observed streamflow. Two dimensionless statistical performance criteria were used as follows:

$${\text{Modelling}}\,{\text{Efficiency}},\,{\text{ME}} = \frac{{\left[ {\mathop \sum \nolimits_{i = 1}^{{n_{d} }} \left( {O_{v,i} - \overline{O}_{v} } \right)^{2} - \mathop \sum \nolimits_{i = 1}^{{n_{d} }} \left( {P_{v,i} - O_{v,i} } \right)^{2} } \right]}}{{\mathop \sum \nolimits_{i = 1}^{{n_{d} }} \left( {O_{v,i} - \overline{O}_{v} } \right)^{2} }}$$
(13.4)
$$\mathrm{Coefficient\,of\,Residual\,Mass},\mathrm{ CRM}=\frac{\left[\sum_{i=1}^{{n}_{d}}{O}_{v,i}-\sum_{i=1}^{{n}_{d}}{P}_{v,i}\right]}{\sum_{i=1}^{{n}_{d}}{O}_{v,i}}$$
(13.5)

where Pv,i = simulated streamflow; Ov,i = observed streamflow; O̅v = mean observed streamflow and nd = number of days. Lower value of ME indicates poor model performance, while a value close to 1 or equal to 1 indicates a good model performance. CRM value of zero indicates a perfect model, whereas a positive value of CRM indicates underestimation and a negative value of CRM indicates an overestimation.

13.3 Results and Discussion

The model was calibrated for the years 2004 and 2005 by matching the model simulated runoff with the observed runoff at the basin outlet. Depending on the values of the model performance indicators, while comparing the simulated runoff with the observed runoff, the best possible values of TCRIT were obtained as 1 °C for 2004 and 3 °C for 2005 as shown in Table 13.5. Better matches were obtained for cR as 0.6 and cS as 1.0 for both the calibration years (Table 13.5). The average values of calibration parameters obtained during the calibration years were used for validating the model.

Table 13.5 Calibrated parameters for the years 2004 and 2005
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Figures 13.3, 13.5 and 13.7 show the time series plots of observed versus simulated daily runoff from WinSRM, precipitation and mean temperature for the calibration years 2004 and 2005, and validation year 2008. Figures 13.4, 13.6 and 13.8 show the scatter plots of observed and simulated runoff for the calibration years and validation year.

Fig. 13.3
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Time series plot of observed versus simulated daily runoff, precipitation and mean temperature for the year 2004

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Fig. 13.4
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Scatter plot of observed versus simulated runoff for the year 2004

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Fig. 13.5
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Time series plot of observed versus simulated daily runoff, precipitation and mean temperature for the year 2005

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Fig. 13.6
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Scatter plot of observed versus simulated runoff for the year 2005

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Fig. 13.7
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Time series plot of observed versus simulated daily runoff, precipitation and mean temperature for the year 2008

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Fig. 13.8
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Scatter plot of observed versus simulated runoff for the year 2008

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During the calibration years 2004 and 2005, ME values of 0.610 and 0.608 were obtained, respectively, while ME value of 0.611 was obtained during the validation period 2008. CRM values of −0.148 and 0.027 were obtained during the calibration period 2004 and 2005, respectively, while during the validation period 2008, CRM value of −0.0256 was obtained. The positive value of CRM in the year 2005 shows model underestimation in the simulated runoff and negative values of CRM show model overestimation in the simulated runoff during the years 2004 and 2008. Overall, the statistical performance indicators show acceptable modelling results during calibration and validation for the data scarce Himalayan watershed.

13.3.1 Effect of Monthly Variation of Near-Surface Lapse Rate (LR) on Runoff Simulation

While constant lapse rate of 0.5 °C/100 m was employed for calibration and validation, to observe the effect of employing different lapse rates on model simulation, the model was re-simulated for three years 2004, 2005 and 2008 with different lapse rates as follows: (i) constant lapse rate of 0.65 °C/100 m; (ii) constant lapse rate as determined for Eastern Himalayas (0.5 °C/100 m); and (iii) monthly varying lapse rate specific to Eastern Himalayas (Table 13.3) (Bandyopadhyay et al. 2014).

Figures 13.9, 13.10 and 13.11 show the hydrographs generated by the model for the years considered for this study. The hydrographs represent the observed runoff, runoff generated by using annually constant lapse rate of 0.65 °C/100 m, runoff generated by using a constant lapse rate of 0.5 °C/100 m and runoff generated by using the monthly varying lapse rates. From the given figures, we can observe that all the hydrographs generated with different lapse rates follow a similar trend with the observed hydrograph.

Fig. 13.9
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Daily time series plot of observed and simulated streamflow for the year 2004

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Fig. 13.10
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Daily time series plot of observed and simulated streamflow for the year 2005

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Fig. 13.11
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Daily time series plot of observed and simulated streamflow for the year 2008

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Table 13.6 shows the hydrograph characteristics of the observed and simulated stream flows. From the table, it was observed that in the year 2004, the average runoff generated by taking a constant lapse rate of 0.5 °C/100 m when compared with the observed runoff was found to be better than the average runoff from the other two conditions where the lapse rates were taken as an annual constant of 0.65 °C/100 m and a monthly varying lapse rate. For the year 2005, the average runoff generated by taking the monthly varying lapse rate was found to give better results than the other two conditions, while, for the year 2008, the average runoff generated by using a constant LR of 0.5 °C/100 m was found to give better results than the other two conditions.

Table 13.6 Hydrograph characteristic of observed and simulated runoffs
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For the year 2004, from Table 13.7, it can be seen that the monthly varying LR-based simulation gave an ME value of 0.621 which was found to be the best when compared with the ME values from the other two simulations. The ME value from the simulation based on constant LR of 0.5 °C/100 m gave the second best value of 0.610 which is close to 0.621. It is worth noting that although using a constant lapse rate of 0.5 °C/100 m resulted in better volumetric water balance for the year 2004 than using monthly varying lapse rate, trends in high and low flows are being captured better by the latter. For the other two years, i.e. 2005 and 2008, the simulation based on constant lapse rate of 0.5 °C/100 m gave the best ME value of 0.608 and 0.611, respectively. CRM value shows an overestimation for all the years when the lapse rate was taken as 0.65 °C/100 m and also when it was varied monthly. In the year 2005, when the lapse rate was taken as 0.5 °C/100 m, a positive CRM value was obtained which indicates an underestimation in the runoff by the model.

Table 13.7 Statistics of the hydrographs
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13.4 Conclusions

In this study, in order to understand the implication of near-surface lapse rate on snowmelt runoff simulation in Nuranang watershed in Arunachal Pradesh, snowmelt runoff modelling using WinSRM was carried out. The model was calibrated by matching the observed runoff with the simulated runoff at the outlet for the depletion period of 2004 and 2005. The average values of calibration parameters obtained during the calibration period were used for validating the model. Acceptable modelling results were obtained during calibration and validation for the data scarce Himalayan watershed. After obtaining satisfactory model performance for calibration and validation, runoff simulation was carried out for all the three years 2004, 2005 and 2008 using different lapse rates as follows: (i) constant lapse rate of 0.65 °C/100 m, (ii) constant lapse rate of 0.5 °C/100 m (specific to Eastern Himalayas) and (iii) monthly varying lapse rate specific to Eastern Himalayas.

For the years 2004 and 2008, the average runoff generated by taking a constant lapse rate of 0.5 °C/100 m when compared with the observed runoff was found to give better results than the average runoff from the other two conditions where the lapse rates were taken as an annual constant value of 0.65 °C/100 m and a monthly varying lapse rate, while, for the year 2005, the average runoff generated by taking the monthly varying lapse rate was found to give better results than the other two conditions. For the years 2005 and 2008, simulations based on constant lapse rate of 0.5 °C/100 m gave the best ME values of 0.608 and 0.611, respectively, while the best ME value of 0.621 was obtained using monthly varying lapse rate in the year 2004. In all the scenarios, simulations based on a constant lapse rate of 0.65 °C/100 m perform the worst. The model overestimates runoff for all the periods considered when monthly varying lapse rate and constant lapse rate value of 0.65 °C/100 m were used. Overall, using a constant lapse rate of 0.5 °C/100 m gave better simulations results. Instead of using average environmental lapse rate, specific lapse rate designed for a particular region must be used for better hydrological modelling. Based on the results obtained, a constant near-surface lapse rate of 0.5 °C/100 m is recommended for the temperature-index based snowmelt models in the Eastern Himalayas.