Streamflow represents the integrated response of a watershed to climatic variables, particularly precipitation and air temperature. In this study, relationships between discharge and hydro meteorological parameters near the snout of Gangotri Glacier were investigated. The auto correlations and multi day influence of temperature and rainfall on discharge can provide valuable information about the Glacier response which can be helpful for estimating discharge in data scarce regions. The data for eight continuous ablation seasons (2000-2007) were used investigating correlations, lag cross correlations and multivariate regression analysis between daily mean discharge, daily mean temperature and daily rainfall, whereas last four years data (2008-2011) was used to simulate the daily discharge from the established relations. Snowmelt discharge varies during the rise in the annual temperature cycle in response to the combination of temperature variation and the amount of water held in the evolving snowpack. The discharge and temperature is highly auto correlated. It was found that discharge of a particular day (Q_{i}) is well represented by the regression equation having Q_{i-1}, T_{i}, and R_{i}. Such developed regression equation can be used for computing discharge once its input variables are available. The regression equation developed using the eight year data i.e. Q_{i} = 2.962 + 1.011Q_{i-1} - 0.422T_{i} + 0.203R_{i} is used for forecasting of discharge. For all the years discharge was computed with high accuracy (R^{2} - 0.93).
Identification of the relationships between hydrologic and climatic variables is very important for many hydrologic applications such as prediction of missing records, analysis of climate change impacts, and estimation of hydrologic responses of ungauged basins. Statistical approaches have long been used in analyzing the relationships between hydrologic and climatic systems. A standard approach for finding the relationships between hydrologic and climatic variables is to compute pair-wise correlations between time series of hydrologic and climatic variables. Depending on the value of the correlation coefficients, this approach can help identify the strengths of the relationships between variables.
Precipitation-stream flow and precipitation-air temperature relationships are probably the most commonly investigated relationships. Cayan et al. [
Previous studies showed that although precipitation and air temperature are the two most important parameters affecting stream flow, some other climatic variables can also have major impacts. In glacierized basins the streamflow is dependent on the lag due to travel time and melt water storage characteristics. In this study, we included precipitation and temperature lags relationships between stream flow and climatic conditions. The data were collected by establishing a discharge site and meteorological observatory.
The present study was carried out for the Gangotri Glacier, which is one of the largest glaciers of Himalayas. This glacier is located in the Uttarkashi District of Uttarakhand State (UA) falling in the Garhwal Himalayan region. The location of Gangotri Glacier is shown in
out from the snout of the Gangotri Glacier at an elevation of 4000 m. The approach to the snout of the Glacier includes a trekking of about 18 km distance starting from the Gangotri town. The major part of the trekking is along the Bhagirathi River. A meteorological observatory and discharge site were established and data were collected for the entire ablation period.
The climate variability affects the streamflow of a glacierized basin. We calculated the correlation coefficients between stream flow and climatic variables. Basically regression analysis was performed and 1) Discharge auto-correlation; 2) discharge-temperature correlation and 3) discharge rainfall correlation were determined for different lag periods (0 - 3 days). Multivariate regression between discharge, temperature and rainfall was also performed.
As data collection was one of the major tasks for this study. We had continuous monitoring of hydro meteorological variables for about 12 years. In the present analysis, as such hydro-meteorological data of 12 years (2000-2011) have been used. The first 8 years data (2000-2007) were used for determining correlations, lag- cross-correlations and multivariate regression analyses between daily mean years discharge, daily mean temperature and daily rainfall. The last 4 years data (2008-2011) were used to estimate the discharge using established relationship. The time series for different variables (discharge, temperature and rainfall) were prepared as a function of time-lag of 0 - 3 days for each ablation seasons of 8 years (2000-2007). A combined series of these 8 ablation seasons was prepared by considering all ablation seasons together in chronological order and used in the analysis for developing generalized relationship.
The Discharge auto-correlations is determined to examine if there exist a cross correlation between past and future values of discharge.
Discharge auto-correlation | |||
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Year | Lag 1 | Lag 2 | Lag 3 |
2000 | 0.94 | 0.86 | 0.81 |
2001 | 0.97 | 0.93 | 0.89 |
2002 | 0.98 | 0.95 | 0.91 |
2003 | 0.98 | 0.95 | 0.93 |
2004 | 0.97 | 0.93 | 0.88 |
2005 | 0.98 | 0.94 | 0.90 |
2006 | 0.98 | 0.94 | 0.91 |
2007 | 0.95 | 0.91 | 0.86 |
2000-2007 | 0.97 | 0.93 | 0.88 |
for all considered time-lags, the maximum auto-correlation is found with the previous day’s discharge (0.98 - 0.94). This high discharge autocorrelation indicates the dominance of strong storage characteristics in the response of runoff from the glacierized basin. The results show that discharge for a particular day is very much dependent on the previous day’s discharge. It means that if previous days discharge is known then the forecasting of next day discharge can be easier. It is likely that the dominance of delaying characteristics of the glacier and little contribution from rainfall to the streamflow. In the present study basin has provided higher discharge auto-correlations.
The simple correlation coefficients for temperature, given for lags of up t o 3 d and taken as a function of time, indicate about the “mean” delay in melt-water runoff. The lag of the correlation maximum should represent a “mean” transit time of all melt water being recorded at the gauging station. Correlations established between discharge and air temperatures with a time-lag of temperature from 0 - 3 days (T_{i}, T_{i-1}, T_{i-2} and T_{i-3}) are shown in
The correlations between discharge and rainfall with time-lags between 0 and 3 days (R_{i}, R_{i-1}, R_{i-2}, R_{i-3}) for different ablation seasons were developed. The values of discharge and rain correlations for each ablation season and combined data series are given in
Discharge-temperature correlation | ||||
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Year | Lag 0 | Lag 1 | Lag 2 | Lag 3 |
2000 | 0.62 | 0.56 | 0.48 | 0.44 |
2001 | 0.63 | 0.56 | 0.52 | 0.50 |
2002 | 0.76 | 0.72 | 0.67 | 0.64 |
2003 | 0.82 | 0.76 | 0.70 | 0.67 |
2004 | 0.61 | 0.54 | 0.47 | 0.42 |
2005 | 0.76 | 0.73 | 0.71 | 0.67 |
2006 | 0.71 | 0.66 | 0.60 | 0.58 |
2007 | 0.65 | 0.59 | 0.52 | 0.46 |
2000-2007 | 0.66 | 0.60 | 0.55 | 0.51 |
Discharge-rain auto-correlation | ||||
---|---|---|---|---|
Year | Lag 0 | Lag 1 | Lag 2 | Lag 3 |
2000 | 0.21 | 0.16 | 0.03 | 0.02 |
2001 | 0.21 | 0.17 | 0.11 | 0.09 |
2002 | −0.11 | −0.10 | −0.09 | −0.07 |
2003 | 0.28 | 0.31 | 0.31 | 0.31 |
2004 | 0.04 | 0.05 | 0.06 | 0.07 |
2005 | 0.01 | 0.02 | 0.03 | 0.06 |
2006 | −0.05 | −0.04 | −0.03 | −0.02 |
2007 | −0.03 | −0.01 | 0.03 | 0.02 |
2000-2007 | 0.003 | 0.004 | −0.002 | 0.007 |
typically produced runoff immediately after a large storm. In general, discharge was positively correlated with rainfall, except years 2002, 2006 and 2007. A negative correlation is possible when rainfall occurs near the snout and low temperature conditions prevail. Such weather conditions allow for snowfall over the major part of glacier, which ceases the melting of glacier and in turn reduces discharge.
It is well established that energy input exerts a strong direct influence on discharge. Both form and timing of precipitation will have considerable influence on runoff. To establish the relations between discharge and meteorological elements, for instance, as a basic study for the purpose of forecasting discharge of a glacier river, regressive schemes for the time series were employed. Multiple regression equations relating total annual discharge to mean summer air temperature and precipitation variables provide a high degree of explanation in basins with higher proportions of ice cover. To estimate daily streamflow from the Gangotri Glacier basin, multiple regression equations were developed separately for each melting season (2000-2007) and the combined series of 8 melt seasons. Stepwise regression technique has been used to identify important variables for estimating the discharge of Gangotri Glacier basin. The regression equations were developed considering the possible climatic factors, which may significantly influence the runoff. Discharge from the basin was used as the dependent variable and 11 independent variables namely Q_{i-1}, Q_{i-2}, Q_{i-3}, T_{i}, T_{i-1}, T_{i-2}, T_{i-3} and R_{i}, R_{i-1}, R_{i-2}, R_{i-3} respectively, were used as independent variables.
The resulting multiple regression equations obtained through stepwise regression and corresponding values of correlation for each year and for the combined series of all 8 seasons is given in
The regression equations developed were used to estimate daily streamflow for four independent years (2008 to 2011). The estimation of discharge was made using generalized regression equation developed from combined data series of 8 ablation seasons. A comparison of computed and observed daily streamflow for 2008 to 2011 is given in
It is important to understand the sensitivity of streamflow to climatic variation because people and aquatic ecosystems are dependent upon a water supply that is adequate, particularly in summer low-flow seasons. The
Year | Mult_{i}ple regress_{i}on equat_{i}ons | R2 |
---|---|---|
2000 | Q_{i} = −5.975 + 0.869Q_{i-1} + 1.489T_{i} + 0.565R_{i} | 0.90 |
2001 | Q_{i} = 6.491+ 0.992Q_{i-1} − 0.679T_{i} + 0.962R_{i} | 0.94 |
2002 | Q_{i} = −2.382 + 0.951Q_{i-1} + 0.606T_{i} + 0.128R_{i} | 0.96 |
2003 | Q_{i} = 0.228 + 0.966Q_{i-1} + 0.124T_{i} + 0.977R_{i} | 0.97 |
2004 | Q_{i} = 3.498 + 0.987Q_{i-1} − 0.312T_{i} + 0.375R_{i} | 0.94 |
2005 | Q_{i} = −4.808 + 0.941Q_{i-1} + 0.942T_{i} + 0.289R_{i} | 0.96 |
2006 | Q_{i} = 0.709 + 0.965Q_{i-1} + 0.103T_{i} + 0.452R_{i} | 0.96 |
2007 | Q_{i} = −2.214+ 0.926Q_{i-1} + 0.583T_{i} + 0.241R_{i} | 0.91 |
2000-2007 | Q_{i} = 2.962 + 1.011Q_{i-1} − 0.422T_{i} + 0.203R_{iI} | 0.99 |
linkages between hydrologic and climatic data are based on complex physical processes that are difficult to conceptualize. In this study, an attempt was made to elucidate some of the characteristics of multi day influence between discharge and meteorological elements which occur in the course of an ablation season. We investigated the relationships between stream flow of Gangotri Glacier and lags in rainfall and temperatures in the basin. The discharge auto correlation provides valuable information about the storage characteristics and Glacier response. The seasonal distribution of discharge auto-correlation suggests that, although a good auto-correlation
exists for all the considered time lags, maximum auto-correlation (0.94 - 0.98) is observed with the previous day’s discharge (Q_{i-1}) and for the combined series as well (0.97). It suggests that discharge for a particular day is highly dependent on the previous day’s discharge. Therefore, for estimation/forecasting of discharge from the glacierised basin for a particular day, the previous day’s discharge becomes a significant predictor. The high discharge auto-correlation indicates the dominance of storage characteristics on the response of runoff from the glacierized basin. Discharge auto-correlation decreases with an increase in the lag period of discharge.
As such the discharge and temperature with time lag from 0 - 3 days were found to be reasonably well correlated. The highest correlation was found with same day temperature, which varied from 0.61 to 0.82 for different years. For the combined series the highest correlation between discharge and same day temperature was 0.66. Like discharge auto correlation, correlation between discharge and temperature also decreased with increase in lag in temperature. Poor and inconsistent correlation was found between discharge and rainfall for all the years.
Multiple linear regression equations developed for the Gangotri Glacier basin separately for each year and for the combined series of 8 years. Stepwise regression approach was used to identify the statistically significant parameters for computing discharge from the basin. It was found that discharge of a particular day (Q_{i}) is well represented by the regression equation having Q_{i-1}, T_{i}, T_{i-1}, T_{i-2} and R_{i}. The aim was not exactly to find a model, but to observe the simple correlations between the discharges and the meteorological variables (precipitation P, temperature T, with a 0 to 3 days lag). The established equation using combined series was used to compute discharge for 4 independent years (2008 to 2011). For all the years discharge was computed with high accuracy (R^{2} − 0.93). The results show that the developed regression equation can be used for computing discharge once its input variables are available.
The author is thankful to Director, National Institute of Hydrology, Roorkee for the support to carry out hydro meteorological investigation at Gangotri Glacier.