1 Introduction

The Sutlej and Beas rivers originate from the western Himalayan mountains. Both rivers get water from rainfall and the melting of Himalayan glaciers and flow towards the northwestern state of Punjab and meet at Harike. Bist interfluve is between the Sutlej and Beas rivers in northeast Punjab. There are single to multiple aquifers in the Bist interfluve used for the drinking and irrigation of crops. The hydrogeology of this basin or interfluve is highly dynamic. The river water (Sutlej and Beas) can interact with groundwater due to infiltration and seepage. The loss of river water to groundwater, seepage of groundwater to a river water body, or a combination of both can occur [1]. Apart from these two rivers, there are too many small tributaries of the Sutlej and Beas rivers that empty water into them. Stable isotopes are non-radioactive forms of atoms that are used in hydrological studies widely nowadays [2, 3]. Stable isotopes of water, heavy oxygen (18O), and deuterium (2H) can be used as tracers in the hydrological studies of river catchments [2,3,4]. The isotopic signatures of the tributaries may be different from the main rivers (Sutlej and Beas). The mixing of two different sources of water represented by different isotopic values can result in totally different isotopic signature of the entire river or at certain sections.

The isotopic fractionation of the water molecule makes these stable isotopes the ideal choice for studying the hydrogeology and hydrometeorology of the study area. The spatial and temporal variation of the stable isotopes is affected due to many features of topography and climate which affect the rate of isotope fractionation. Natural processes like evaporation and condensation can alter the relative proportion of the stable isotopes in water. The evaporation of 18O is more at higher elevations or altitudes [5,6,7,8]. This phenomenon is called as altitude or relief effect. The depletion of 18O increases with increasing latitude [9,10,11,12]. The enrichment of water by 18O increases with increasing longitude and can be seen in both rivers and groundwater [12,13,14,15,16,17]. The deuterium excess (d-excess) is a second-order stable isotope parameter measured in meteoric water to understand both the source of precipitation and the evolution of moisture during transport [18]. Meteoric water is derived from precipitation (snow and rain) and the Global Meteoric Water Line (GMWL) describes the global annual average relationship between the stable isotopes (18O and 2H) ratios in natural meteoric waters. Local meteoric water lines (LMWLs) represent the site-specific long-term covariation of hydrogen and oxygen stable isotope ratios. LMWLs have practical utility to identify the evaporation and source of precipitation [2,3,4,5].

In Punjab, agricultural production is adequate due to easily available water from the surface as well as groundwater for irrigation. In recent years, the groundwater extraction in the Bist interfluve has increased which might result in over-exploitation and may cause complete drying of aquifers. The decrease in water level in both shallow and deep aquifers were confirmed using the isotope techniques [2]. In Bist interfluve, due to the continuous groundwater extraction (at the rate of 8600 m3/ha/year), 23 blocks out of 30 are in the “over-exploited” zone [2].

Globally, isotope hydrology tools are used to study the groundwater, surface water and meteorology of different basins around the entire world and is imperative to use to understand hydrology of major river basins of developing countries like India in detail. The Bist interfluve is home to millions of people dependent mainly upon the agriculture for livelihood. The state of Punjab (where Bist interfluve is located) is one of the largest producer of grains, rice and fruits. Also, Bist interfluve is one of the most agriculturally productive region of Punjab state. Because of the immense importance of this interfluve, a detailed study of the water resources in this region is needed for the isotope characterization. Stable isotopes of water have already been used in previous studies around the world for hydrogeological and meteorological purposes. However, considering the surface area of the Bist interfluve, its population and economic importance, such studies are not commonly done around the world.

The Sutlej and Beas rivers are particularly important for the northern plains of Punjab. These rivers pass through diverse kinds of topographies from Himalayas to the plains of Punjab. The stable isotopes of water i.e., 18O and 2H can provide a good understanding of hydrogeology and hydrometeorology of the Bist interfluve. This will help in recharging the aquifers thereby storing sufficient water for the irrigation of crops. This study has the potential to help prepare a water resources management plan for the Bist interfluve. The objectives of this study are to investigate the stable isotopic composition of Sutlej and Beas rivers, their spatial and temporal variations, and various controls.

2 Study area

2.1 Topography

The Bist interfluve is located in the northeastern part of the state of Punjab in India. Two rivers; Sutlej and Beas form this interfluve. The river Beas originates from Rohtang La pass at a height of 3978 m. The total length of the river Beas till Harike, Punjab is 470 km. It passes through Maharana Pratap Sagar lake, in Himachal Pradesh, before entering Punjab through Talwara. From several kilometers high Himalayan mountains, the river reaches a low-lying plain area in the Bist interfluve as shown in Fig. 1b. River Sutlej originates from Mount Kailash located at a height of 6638 m. The total length of the river Sutlej is 1450 km. The river Sutlej also enters low-lying plain areas of the Bist interfluve. The river Beas flows south and the river Sutlej flows west. This interfluve is characterized by Shiwalik hills in the northeast and plains in the rest of the interfluve. Figure 1c shows the elevation of the study area.

Fig. 1
figure 1

The state of Punjab is shown in pink in the map of India in a, Bist Doab (interfluve) between the River Beas and the River Sutlej is shown in b, the elevation map from the mean sea level (msl) in meters is shown in c, the slope (degree) map of the study area is shown in d, and the slope direction and the contour map of the study area is shown in e

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Most of the interfluve is covered with an alluvial plain formed due to the two soil deposited by the Sutlej and Beas rivers. The rivers have flood plain on both banks. Many smaller waterbodies are located in the plains of the interfluve. The northeast of the interfluve is covered with highly dissected hills the of outer Himalayas, i.e., Shiwalik hills. The Aeolian dune complex structures are located the in southwest of the interfluve.

2.2 Climate

The climate of the Bist interfluve is tropical along with semi-arid weather and subtropical monsoon. Tropical marine air masses from the Arabian Sea and the Bay of Bengal bring rains during the monsoon period. Most of the rainfall (80% of the annual rainfall) occurs during the monsoon period from June to September. The Sutlej and Beas rivers pass through areas with rainfall of 514 mm to 933 mm. The rainfall in the interfluve decreases from northeast to southwest parallel to the Shiwalik hills, as shown in Fig. 2a. The spatial distribution of the annual average temperature is shown in Fig. 2b. The spatial distribution of relative humidity (%) is shown in Fig. 2c. The relative humidity is higher in lower-temperature areas.

Fig. 2
figure 2

The rainfall (mm) map of Bist interfluve is shown in a, the relative humidity (%) of the Bist interfluve is shown in b, and the temperature (°C) is shown in c

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In the winter season from November to February, a sufficient quantity of rainfall (more than 100 mm in January and February) is observed. The coldest, warmest, wettest, and driest months are January, June, July, and November, respectively. The annual average maximum temperature is 32.37 °C and the annual average minimum temperature is 19.19 °C. The temperature keeps changing throughout the year as shown in Fig. 3b. The summer temperature can reach a value of more than 40 °C. The winter temperature can reach 0 °C sometimes at a few locations. This is the reason for the very high relative humidity in winter. The relative humidity is highest in the month of August while the lowest is in the month of April. The temporal variation of relative humidity is shown in Fig. 3c. The phenomena of ground frost can be visible in the majority of the area during winters.

Fig. 3
figure 3

The monthly rainfall time series is shown in a, the monthly temperature series is shown in b, and the monthly relative humidity is shown in c

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3 Materials and methods

3.1 Sampling and analytical procedures

The flow chart of the study is shown in Fig. 4. The water samples of the river Sutlej (2009–2013) from 7 stations, the river Beas (2010–2015) from 7 stations, the rainfall (2010–2015) from 12 stations and the groundwater (2010–2014) from 14 stations were collected (Fig. 5), respectively. The samples were collected at the end of each month in the case of both rivers. The samples for the rainfall and the groundwater were collected weekly. The geographical coordinates along with the elevation of the sampling stations are shown in Table 1. The collected samples were brought to the Nuclear Hydrology Laboratory at the National Institute of Hydrology, Roorkee and were analyzed using a Dual–Inlet Isotope Ratio Mass Spectrometer (DI–IRMS). The DI–IRMS is a precise mass spectrometer that uses gas samples to determine the stable isotope ratio. The isotope ratio is given by

$${\text{R }} =\, ^{18}{\text{O}}/^{{{16}}} {\text{O and}}\,^{{2}} {\text{H}}/^{{1}} {\text{H}}$$
(1)
Fig. 4
figure 4

Flow chart of the methodology

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Fig. 5
figure 5

The water sampling stations of the Bist interfluve shown with numbers

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Table 1 Latitude, longitude, elevation of the water sample stations of the river Beas, the river Sutlej, rainfall and groundwater
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The isotope ratio can be used to calculate δ. It can be defined as follows.

$$\updelta =\left( \frac{\mathrm{R }\left(\mathrm{sample}\right)}{\mathrm{R }\left(\mathrm{V}-\mathrm{SMOW }2\right)}-1\right)*1000$$
(2)

The values of δ18O, and δ2H is reported in per mill or per mil (‰). Per mill is an expression that means parts per thousand. The measurement precision for δ18O and δ2H were ± 0.1% and ± 1% respectively. The VSMOW-2 in Eq. (2) stands for Vienna Standard Mean Ocean Water which was made at IAEA Isotope Hydrology Laboratory in 2006 [19,20,21].

3.2 Data analysis

The values of δ18O, and δ2H for the rivers Beas and Sutlej were arranged month wise for each station. Average of δ18O, and δ2H of all the stations of the same month was calculated for the river Beas (2010 to 2015) and the river Sutlej (2009–2013) to get the monthly data of all the years. The monthly data for the river Beas and the river Sutlej of the respective time period was averaged to obtain the average monthly data of 12 months. The same method was applied to the rainfall and groundwater samples.

3.3 Stable isotope modelling

When working on the global annual average isotopic composition of heavy oxygen (18O) and deuterium (2H) in meteoric water a geochemist, Harmon Craig, observed a correlation between these two stable isotopes. The equation for GMWL was then developed and defined by Harmon Craig [2,3,4,5,6]:

$$\delta^{{2}} {\text{H}} = {8}*\updelta^{{{18}}} {\text{O}} + {1}0$$
(3)

The meteoric water lines were calculated by linear regression between yearly average values of δ18O and δ2H. The average of all monthly values of δ18O and δ2H gives the average yearly values of δ18O and δ2H the river Beas, the river Sutlej, rainfall, and groundwater for the respective sampling years. The time series analysis of δ18O for the stations of the river Beas and the river Sutlej was performed using average monthly values of δ18O. Kendall’s rank correlation coefficient (τ) is used to correlate the isotope composition of two different water bodies [22].

Kendall rank correlation coefficient

$$\left(\uptau \right)= \frac{0.5\mathrm{N}(\mathrm{N}-1) -\mathrm{d }(\mathrm{P},\mathrm{ P^{\prime}})}{0.5\mathrm{N}(\mathrm{N}-1)}$$
(4)

where P, P′ = sets of observations; d (P, P′) = distance between sets; N = number of elements in sets.

Linear regression is a linear model, e.g. a model that assumes a linear relationship between the input variables (x) and the single output variable (y). Linear regression equations are of the following form

$${\text{y }} = {\text{ b}}_{0} + {\text{ b}}_{{1}} {\text{x}}$$
(5)

with the regression coefficients b0, and b1 which are the intercept and the slope respectively [23]. The linear regression can be used effectively to know the factors affecting the variation of the stable isotopes. The coefficient of determination (R2) is a statistical measurement that examines how differences in one variable can be explained by the difference in a second variable, when predicting the outcome of a given event. The coefficient of determination can be calculated by

$${\text{R}}^{{2}} = { 1 }{-}\frac{{{\text{SSDres}}}}{{{\text{SSDtot}}}}$$
(6)

where, SSDres = the residual square sum; SSDtot = the total square sum.

The coefficient of determination is a statistical measure of how well the regression predictions match the real data points in regression. The regression predictions exactly fit the data if the R2 is 1. The spatial maps of climatic factors were prepared using Inverse Distance Weighted (IDW) techniques. The IDW is a type of deterministic method for multivariate interpolations with a known scattered set of points. The benefits of using IDW are that it is simple, easy to understand, and efficient. Deuterium excess (d-excess) is a function of the isotopic composition of oxygen (δ18O) and hydrogen (δ2H) in water

$${\text{d-excess }} = \, \updelta^{{2}} {\text{H-8 }} \times \,\updelta ^{{{18}}} {\text{O}}$$
(7)

4 Results

Spatial and temporal analysis of the isotopic data of both the rivers in the Bist interfluve has been performed. Apart from spatial variations, isotope values vary due to temperature, rainfall, relative humidity, and other climatic factors. The depletion and enrichment in isotope values of rivers are affected by relationships between geographical factors and environmental factors and to show these linear regressions and several statistical techniques are used.

4.1 Spatial variations

The average of the stable isotopes for the sampling stations, shown in Table 1, gives an idea of the variations in isotopic composition. The average of all the stations has been calculated by using the monthly values (January to December) of all years (2008 to 2015). In the case of the river Sutlej, the δ18O varies from − 11.27‰ to − 7.54‰ as shown in Fig. 6a. While going from east to west δ18O first decreases and then increases. The value of δ2H varies from − 44.47‰ to − 76.80‰ as shown in Fig. 6b. This also first decreases from east to west and then increases. However, deuterium excess (d-excess) shows an opposite trend.

Fig. 6
figure 6

Spatial distribution of δ18O (‰) of the river Sutlej, the river Beas, rainfall and groundwater. Spatial distribution of δ2H (‰) of the river Sutlej, the river Beas, the rainfall, and the groundwater. Spatial distribution of d-excess (‰) of the river Sutlej, the river Beas, the rainfall and the groundwater

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The standard deviations have been calculated using the average isotopic values (δ18O, δ2H, and d-excess) of the 7 stations each of Sutlej river, and Beas river to see the variations. These values of standard deviation are more than the standard errors of the instrument (IRMS). The standard deviation (σ) of δ18O, δ2H, and d-excess are 1.35‰, 11.25‰, and 10.59‰ respectively for the Sutlej river show significant spatial variation in the Sutlej river. The elevation of the ground level on the course of the Sutlej river varies from 219 to 419 m showing topographical variations. The possible evaporation or condensation at the different stations of the Sutlej river shows the removal or addition of water from different sources. The easternmost point of the river Sutlej, i.e., Aur has δ18O value of − 10.92‰ while the westernmost point Harike has δ18O value of − 7.54‰. The minimum and maximum values of δ18O for Aur (− 12.43‰ and − 8.43‰,), Harike (− 9.73‰ and − 6.04‰), Kanaun (− 13.31‰ and − 4.12‰), Ropar (− 13‰ and − 8.57‰), Sidhwan (− 12.49‰ and − 8.49‰), Yusufpur (− 17.44‰ and − 5.83‰), and Phillaur (− 12.76‰ and − 9.27‰) are shown in Fig. 7. Harike is the confluence point of both the rivers Sutlej and Beas. On the Sutlej river, Kanaun and Yusufpur are odd stations. It can be observed (from Fig. 7) that the extremities and interquartile range of these two stations are much larger than the rest of the five stations. The topography of Kanaun and Yusufpur reveals the presence of an oxbow lake. As the isotopic fractionation of the oxbow lakes is different from the parent river and shows enriched values and can help in a study of the fluvial morphology of the entire course. The variation of 2H in the Sutlej river is unlike of 18O (Fig. 7). The minimum and maximum values of δ2H for Aur (− 80.24‰ and − 44.72‰), Harike (− 44.41‰ and − 55.08‰), Kanaun (− 84.14‰ and − 50.45‰), Ropar (− 91‰ and − 55.66‰), Sidhwan (− 85.86‰ and − 69.91‰), Yusufpur (− 80.81‰ and − 39.34‰), and Phillaur (− 85.63‰ and − 67.69‰) are shown in Fig. 7. The negative d-excess values at stations can be due to many reasons. The negative d-excess was observed on days when it’s cold, foggy, and generally high pressure (1016 mbar to 1019 mbar), or high rainfall. At Kanaun, the minimum value of d-excess was recorded. It has been found that the negative d-excess is a result of higher 18O and lower 2H than the stable isotope’s (18O and 2H) usual concentration. However, higher d-excess (more than 30‰) has been observed in heavy rainfall season. Therefore, in this study, a large variability in the d-excess values was found.

Fig. 7
figure 7

The box and whisker plot diagram of δ18O (a), δ2H (b), and d-excess (c) for Sutlej river

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The standard deviation (σ) of δ18O, δ2H, and d-excess are 1.13‰, 6.63‰, and 2.63‰, respectively for the Beas river. Again, the values of the σ are much higher than 0.1‰ for δ18O, and 1‰ for δ2H. The δ2H changes from − 30.98‰ to − 48.83‰. The d-excess varies from 6.45‰ to 14.95‰. The northernmost point of the river Beas, i.e., Mirthal has δ18O value of − 4.68‰ while the southernmost point Goindwal has δ18O value of − 8.16‰. The minimum and maximum values of δ18O for Beas (− 9.97‰ and − 5.11‰), Goindwal (− 9.45‰ and − 6.90‰), Hargobindpur (− 7.31‰ and − 5.62‰), Mirthal (− 5.83‰ and − 3.07‰), Naushera (− 8.91‰ and − 3.11‰), Rarra Bridge (− 9.60‰ and − 4.0‰), and Talwara (− 9.77‰ and − 4.29‰) are shown in Fig. 8. On the Beas river, Naushera is an odd station. It can be observed (from Fig. 8) that the extremities and interquartile range of Naushera is much larger than the rest of the six stations. The topography of Naushera reveals the presence of an oxbow lake. The variation of 2H in the Beas river is unlike of 18O (Fig. 8). The minimum and maximum values of δ2H for Beas (− 61.34‰ and − 37.20‰), Goindwal (− 57.75‰ and − 39.68‰), Hargobindpur (− 47.03‰ and − 40.08‰), Mirthal (− 37.54‰ and − 22.28‰), Naushera (− 57.63‰ and − 21.48‰), Rarra Bridge (− 62.59‰ and − 40.40‰), and Talwara (− 61.92‰ and − 35.38‰) are shown in Fig. 8.

Fig. 8
figure 8

The box and whisker plot diagram of a δ18O, b δ2H, and c d-excess for Beas river

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The isotopic signatures of the groundwater at different stations are different. The value of δ18O for stations Burj Tahaldas, Dholwaha dam, Harsha Kalota, Mandi Kalu, and Takia Yusufpur are − 4.97‰, − 6.93‰, − 6.19‰, − 9.31‰ and − 6.31‰ respectively. At Yusufpur, the value of δ18O in the Sutlej river is − 10.09‰ and the nearby groundwater at Mandi Kalu is − 9.31‰. This shows that the isotopic signatures of the groundwater and the Sutlej river are similar at Yusufpur. This can be due to a possible groundwater and surface water interaction at Yusufpur. The aquifer at Yusufpur is shallow. It is normal for the river water to seep into the groundwater.

The isotopic water lines (IWL) of both rivers again confirm the evaporation in the Bist interfluve. The intercept of the equations shown in Fig. 9 are 47.9‰ and 16.4‰ for the river Sutlej and the river Beas showing considerable deviation from the normal 10‰ (GMWL) and shows higher evaporation in the river Sutlej than the river Beas [2]. There is a deviation in the slope of rainfall, and groundwater equations are shown in Fig. 9. The slope and intercept of the usual Global Meteoric Water Line (GMWL) are 8 and 10 respectively. The values of intercepts are equal to the deuterium excess (d-excess).

Fig. 9
figure 9

The isotopic water lines of the river Sutlej, the river Beas, the rainfall, the deep aquifer, and the shallow aquifer compared with the global meteoric water line defined by Craig (1964)

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All of the stations of the Sutlej river and the Meteoric Water Line (MWL) of the Sutlej itself lie above the GMWL. This means that there is evaporation in the water of the Sutlej river. The case is similar for Beas river, shallow groundwater, and deep groundwater. It means that the waters of Beas river and aquifers have experienced evaporation. However, the MWL for rainfall lies below the GMWL proving that there is evaporation during the rainfall. The values of slopes for the isotopic water lines are 10.65, 8.85, 11.69, − 9.88, and 7.34 for Sutlej river, Beas river, shallow groundwater, deep groundwater, and rainfall respectively. The values of the intercepts (or d-excesses) for the isotopic water lines are 47.52‰, 16.35‰, 37.63‰, − 107.38‰, and 1.38‰ for Sutlej river, Beas river, shallow groundwater, deep groundwater, and rainfall respectively. All the isotopic water lines are deviating much higher than the GMWL with slope and intercept values of 8 and 10. This is due to the isotopic fractionation taking place in the waters of the rivers, groundwater and rainfall.

4.2 Temporal variation

The δ18O values change month-wise. In September and October at Aur, the value of heavy stable isotopes is low (Fig. 10a). At Kannaun, the value of δ2H drops from March through July while increasing from November through February as shown in Fig. 10b. At Ropar, the value of d-excess is lowest in winter and highest in summer as shown in Fig. 10c. This temporal analysis reveals that the evaporation rate is higher in the summer and lower in the winter may be due to isotopic fractionation with the change in the season or month. In summer, the value drops to a low of − 12.5‰ from − 10‰ in the winters. The temporal trend of the d-excess proves that the rate of evaporation is higher during the summer months (Fig. 10c).

Fig. 10
figure 10

The time series graphs of the δ18O (‰), the δ2H (‰), and the d-excess (‰) of Aur, Kannaun and Ropar as shown in a–c respectively

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4.3 Factors causing spatial and temporal variation of stable isotopes

The spatial and temporal variation of isotope tracers (i.e. stable isotopes of water) in the rivers show specific trends and are affected by the climate and geography of the region. The contribution from each factor cannot be equal and it can be negligible in some places.

4.4 Longitude v/s isotopes

The linear relationship between δ18O and δ2H with longitude shows a negative correlation with a coefficient of determination (R2 = 0.23 approximately for both) for River Sutlej (Fig. 11). However, the accuracy of these relationships is very low. In Fig. 11a and b, only one point is located on the trend line. In Fig. 11a, the linear equation has been obtained using only 7 points. The percentage error in the value of δ18O calculated using the equation in Fig. 11a for the stations of Sutlej are 5% (Aur), 17.27% (Harike), 13.7% (Kanaun), 12.35% (Ropar), 13.48% (Sidhwan), 10.64% (Yusufpur), and 12.90% (Phillaur). The calculated values of δ18O are − 10.59‰ (Aur), − 7.54‰ (Harike), − 9‰ (Kanaun), − 10.92‰ (Ropar), − 11.01‰ (Sidhwan), − 10.09‰ (Yusufpur), and − 11.27‰ (Phillaur). In the terms of the values of δ18O, the error varies from − 1.3‰ to 1.48‰. The percentage error in the value of δ2H calculated using the equation in Fig. 11b for the stations of Sutlej are: 15.62% (Aur), 32.27% (Harike), 6.42% (Kanaun), 1.24% (Ropar), 16.07% (Sidhwan), 10.35% (Yusufpur), and 11.34% (Phillaur). The calculated values of δ2H are − 68.85‰ (Aur), − 58.82‰ (Harike), − 70.28‰ (Kanaun), − 73.82‰ (Ropar), − 64.46‰ (Sidhwan), − 60.25‰ (Yusufpur), and − 66.84‰ (Phillaur). In the terms of the values of δ2H, the error varies from − 14.35‰ to − 12.34‰.

Fig. 11
figure 11

The linear regression relationships are shown in a δ18O and longitude for River Sutlej, b δ2H and longitude for River Sutlej, c δ18O and latitude for River Sutlej, and d δ2H and latitude for River Sutlej. The linear regression relationships are shown in e δ18O and longitude for River Beas, f δ18O and latitude for River Beas, and g δ2H and latitude for River Beas

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4.5 Latitude v/s isotopes

The linear relationship between δ18O and δ2H with latitude shows a positive correlation with a coefficient of determination (R2 = 0.42 and 0.47 respectively) for River Sutlej. These results show that the two equations in Fig. 11c and d are almost 50% accurate. But still it cannot be considered a really good relationship. A really good relationship must have the value of coefficient of determination near to 1 or at least more than 0.9. The percentage error in the value of δ18O calculated using the equation in Fig. 11c for the stations of Sutlej are: 28.75% (Aur), 59.38% (Harike), 54.06% (Kanaun), 26.97% (Ropar), 28.03% (Sidhwan), 20.25% (Yusufpur), and 23.03% (Phillaur). The calculated values of δ18O are − 13.63‰, − 12.02‰, − 13.86‰, − 13.86‰, − 14.09‰, − 12.13‰, and − 13.86‰ for Aur, Harike, Kanaun, Ropar, Sidhwan, Yusufpur, and Phillaur respectively. In the values of δ18O, the error varies from − 4.86‰ to − 2.03‰. The percentage error in the value of δ2H calculated using the equation in Fig. 11d for the stations of Sutlej are 14.85%, 21.23%, 6.70%, 3.35%, 5.55%, 18.25%, and 6.53% for Aur, Harike, Kanaun, Ropar, Sidhwan, Yusufpur, and Phillaur respectively. The calculated values of δ2H are − 68.39‰, − 53.91‰, − 70.46‰, − 70.46‰, − 72.53‰, − 54.94‰, and − 70.46‰ for Aur, Harike, Kanaun, Ropar, Sidhwan, Yusufpur, and Phillaur respectively. In values of δ2H, the error varies from − 9.43‰ to 12.27‰.

The linear relationship between δ18O and δ2H with latitude shows a positive correlation with a coefficient of determination (R2 = 0.71 and 0.47 respectively) for River Beas. The percentage error in the value of δ18O calculated using the equation in Fig. 11e for the stations of Beas are 14.90%, 20.78%, 11.62%, 18.38%, 5.44%, 22.45%, and 30.25% for Beas, Goindwal, Hargobindpur, Mirthal, Naushera, Rarra Bridge, and Talwara respectively. The calculated values of δ18O are − 6.17‰, − 6.46‰, − 5.77‰, − 5.54‰, − 5.64‰, − 5.71‰, and − 4.93‰ for Beas, Goindwal, Hargobindpur, Mirthal, Naushera, Rarra Bridge, and Talwara respectively. In values of δ2H, the error varies from − 14.35‰ to 12.34‰. The percentage error in the value of δ18O calculated using the equation in Fig. 11f for the stations of Beas are 5.31%, 0.43%, 7.81%, 17.52%, 0.25%, and 4.82% for Beas, Goindwal, Hargobindpur, Mirthal, Naushera, Rarra Bridge, and Talwara respectively. The calculated values of δ18O are − 7.63‰, − 8.12‰, − 7.04‰, − 5.5‰, − 5.95‰, − 7.0‰, and − 6.09‰ for Beas, Goindwal, Hargobindpur, Mirthal, Naushera, Rarra Bridge, and Talwara respectively. The percentage error in the value of δ2H calculated using the equation in Fig. 11g for the stations of Beas is − 32.79%, − 24.32%, − 45.95%, − 101.64%, − 61.90%, − 23.99%, and − 27.93% for Beas, Goindwal, Hargobindpur, Mirthal, Naushera, Rarra Bridge, and Talwara, respectively. The calculated values of δ2H are − 62.13‰, − 59.79‰, − 62.47‰, − 62.47‰, − 62.80‰, − 59.96‰, and − 62.47‰ for Beas, Goindwal, Hargobindpur, Mirthal, Naushera, Rarra Bridge, and Talwara respectively. In values of δ2H, the error varies from − 31.49‰ to − 11.60‰.

4.6 Meteorological variables v/s isotopes

The correlation of the stable isotopes of water with climatic factors has not been found considerable. The values of δ18O and δ2H are negatively correlated with rainfall showing the value of R2 as 0.17 and 0.14 respectively. The d-excess is negatively correlated with relative humidity (Fig. 12). The d-excess is positively correlated with the temperature. δ2H and temperature are positively correlated with each other. δ18O and temperature are negatively correlated with each other. However, these equations in Fig. 12 are almost inaccurate as the value of R2 is lesser than 0.20.

Fig. 12
figure 12

The linear regression relationships are shown in a δ2H and temperature for River Sutlej, b δ18O and temperature for River Beas, c d-excess and temperature for River Sutlej, d d-excess and temperature for River Beas, e δ18O and rainfall for the River Sutlej, f d-excess and relative humidity for River Beas, g δ2H and rainfall for River Sutlej

Full size image

4.6.1 Temperature (°C)

The percentage error in the value of d-excess calculated using the equation in Fig. 12c for the stations of Sutlej are 31.65%, 18.24%, − 898.70%, 33.73%, 26.92%, − 65.48% and − 6.76% for Aur, Harike, Kanaun, Ropar, Sidhwan, Yusufpur, and Phillaur respectively. The calculated values of d-excess are 24.64, 14.49, 17.08, 12.21, 8.25, 20.15, and 12.06 for Aur, Harike, Kanaun, Ropar, Sidhwan, Yusufpur, and Phillaur respectively. In values of d-excess, the error varies from − 3‰ to 15.37‰. The percentage error in the value of d-excess calculated using the equation in Fig. 12d for the stations of Beas are 17.45%, 18.75%, 14.79%, − 36.28%, 4.14%, 36.88%, and 10.03% for Beas, Goindwal, Hargobindpur, Mirthal, Naushera, Rarra Bridge, and Talwara respectively. The calculated values of d-excess are 9.65‰, 12.13‰, 8.01‰, 8.79‰, 8.79‰, 7.29‰, and 9.32‰ for Beas, Goindwal, Hargobindpur, Mirthal, Naushera, Rarra Bridge, and Talwara respectively. In values of d-excess, the error varies from − 4.26‰ to − 0.38‰. The percentage error in the value of δ2H calculated using the equation in Fig. 12a for the stations of Sutlej is 2.73%, − 50.71%, 2.03%, 5.28%, 5.45%, 7.82%, and 8.20% for Aur, Harike, Kanaun, Ropar, Sidhwan, Yusufpur, and Phillaur respectively. The calculated values of δ2H are − 57.92‰, 67.02‰, − 64.70‰, − 69.06‰, − 72.62‰, − 61.95‰, and − 69.20‰ for Aur, Harike, Kanaun, Ropar, Sidhwan, Yusufpur, and Phillaur respectively. In values of δ2H, the error varies from − 22.55‰ to 6.19‰.

4.6.2 Rainfall (mm)

The percentage error in the value of δ18O and rainfall (mm) calculated using the equation in Fig. 12e for the stations of Sutlej is 4.09%, 4.75%, 1.80%, − 42.52%, − 11.73%, 16.10%, and 3.18% for Aur, Harike, Kanaun, Ropar, Sidhwan, Yusufpur, and Phillaur respectively. The calculated values of δ18O are − 6.95‰, − 7.77‰, − 6.41‰, − 6.67‰, − 6.67‰, − 6.17‰, and − 6.85‰ for Aur, Harike, Kanaun, Ropar, Sidhwan, Yusufpur, and Phillaur respectively.

4.6.3 Relative humidity (%)

The percentage error in the value of d-excess and relative humidity (%) calculated using the equation in Fig. 12f for the stations of Beas are 32.79%, 24.32%, 45.95%, 101.64%, 61.90%, 23.99%, and 27.93% for Beas, Goindwal, Hargobindpur, Mirthal, Naushera, Rarra Bridge, and Talwara respectively. The calculated values of d-excess are 10.39‰, 11.37‰, 8.65‰, 10.63‰, 10.45‰, 11.88‰, and 9.54‰ for Beas, Goindwal, Hargobindpur, Mirthal, Naushera, Rarra Bridge, and Talwara respectively. In values of d-excess, the error varies from − 4‰ to 4‰. The percentage error in the value of δ2H calculated using the equation in Fig. 12g for the stations of river Sutlej are − 8.55%, − 45.13%, 4.69%, 14.36%, 13.44%, − 1.53%, and 0.78% for Beas, Goindwal, Hargobindpur, Mirthal, Naushera, Rarra Bridge, and Talwara respectively. In values of δ18O, the error varies from − 20.1‰ to 10.47‰.

4.7 Kendall’s correlation coefficient (τ)

A positive Kendall’s correlation coefficient (τ) shows a positive relationship between two variables while a negative τ shows a negative relationship. If the value of τ is zero, then it means that there is no relationship between the two variables. The isotope signatures of the water source are visible in the receiving water bodies. The correlation coefficient (τ) calculated tells magnitude of similarity among the d-excess of water of the river Sutlej, the river Beas, rainfall, deep aquifer, and shallow aquifer in the Bist interfluve [17]. From Table 2, there is a negligible correlation between the d-excess of waters of rivers Sutlej and Beas. The correlation of the river Beas with rainfall is also insignificant. This is due to the change in the stable isotopic composition during condensation and evaporation. Therefore, the concentration of δ18O and δ2H is very different from each in Sutlej, Beas, rainfall and various groundwater samples (Fig. 13).

Table 2 The Kendall’s correlation coefficient (τ) value by comparing d-excess of the river Sutlej, the river Beas, the rainfall, the deep aquifer, and the shallow aquifer
Full size table
Fig. 13
figure 13

The linear regression relationships are shown in a δ18O and elevation for River Sutlej, b δ2H and elevation for River Sutlej, c δ18O and elevation for River Beas, and d δ2H and elevation for the River Beas

Full size image

Because of failure of linear regression to show any correlation of the values of the δ18O, δ2H and d-excess with geographical and climatic factors, multiple linear regression analysis was performed on the data. The linear regression also did not show good value of R2 when more than 10 points were used for regression (including Sutlej and Beas river stations). The multiple linear regression gave the following results:

$$\updelta^{{{18}}} {\text{O}} = {4}.{11} + 0.000{\text{8 Rainfall}} - 0.{\text{32 Temperature}} - 0.0{\text{93 Relative Humidity}}$$
(8)
$${\text{d-excess}} = - {35}.{1}{-}0.00{\text{56 Rainfall}} + {1}.{\text{82 Temperature}} + 0.{\text{15 Relative Humidity}}$$
(9)
$$\updelta^{{{18}}} {\text{O}} = - {86}.{65 } + { 4}.{\text{28 Latitude}} - 0.{\text{73 Longitude }} - 0.00{\text{4 Elevation}}$$
(10)
$$\updelta^{{2}} {\text{H }} = - {329}.{5} + { 27}.{\text{2 Latitude}} - {7}.{\text{53 Longitude}} - 0.0{\text{37 Elevation}}$$
(11)

As per multiple linear regression (MLR) Eq. (8), the value of δ18O increases with rainfall, decreases with temperature and relative humidity both in the case of Sutlej and Beas rivers. As per MLW Eq. (9), the value of d-excess decreases with rainfall, increases with temperature and relative humidity both in the case of Sutlej and Beas rivers. As per MLR shown in Eq. (10), the value of δ18O increases with latitude, decreases with temperature and elevation both in the case of Sutlej and Beas rivers. As per MLR shown in Eq. (10), the value of δ2H increases with latitude, decreases with longitude and elevation both in the case of Sutlej and Beas rivers. The value of R2 is 0.51, 0.65, 0.86, and 0.80 for Eqs. (8), (9), (10) and (11) respectively. The coefficient of determination obtained for all the four multiple linear regression equations is much more significant than the simple linear regression equations obtained earlier.

5 Discussion

The spatial and temporal variation of the values of δ18O and δ2H is very useful to understand the process of isotopic fractionation in the studies area. If during the fractionation more 18O or 2H is evaporated, then it corresponds to enriched values of δ18O or 2H. In hydrological terms, the enriched δ18O or 2H value means higher rates of evaporation. This is due to the fact that the mass of 18O is higher than the mass of 16O. If higher weight molecule is lifted more easily from the water surface, then the rate of evaporation must be much higher. In the case of Sutlej river, the rate of evaporation of water at Yusufpur (δ18O = − 5.14‰) is much higher than at Sidhwan (δ18O = − 11.01‰). The formula to calculate the value of deuterium excess (d-excess) is d-excess = δ2H-8* δ18O. For the value of d-excess to become negative the value of δ2H must be much lower than δ18O on a comparison basis. As on 12 Oct 2012, the δ18O = − 3.0‰ and the δ2H = − 56.6‰ at Yusufpur. However, the average value of δ18O = − 10‰ at the same station. This shows that there is enrichment of 18O in the water at Yusufpur that day. This phenomenon of 18O enrichment in the water implies that highly enriched water is added to the river. The highly enriched water in 18O could be due to evaporation.

The variation of stable isotopes in rivers is affected by many factors. The linear regression relationships with elevation, geographical co-ordinates, rainfall, temperature and relative humidity might provide some possible explanation of the variation in the heavy stable isotopes [2,3,4,5]. The linear regression analysis with geographical coordinates like latitude, longitude and elevation with δ18O and δ2H is highly insignificant except the case of elevation where the coefficient of determination is near to 0.64. This is because the rate of isotopic fractionation is not dependent upon just one factor only.

The geographical factors like latitude, longitude and elevation affects the isotope fractionation of the stable isotopes. The variation in the δ18O can be 1‰ per 100 m elevation change in the case of River Sutlej as shown in Fig. 11a. The variation in the δ2H can be 7.7 ‰ per 100 m elevation change in the case of River Sutlej as shown in Fig. 11b. The variation in the δ18O can be 3.1‰ per 100 m elevation change in the case of River Beas as shown in Fig. 11c. The variation in the δ2H can be 17‰ per 100 m elevation change in the case of River Beas as shown in Fig. 11d.

The origin of rivers Sutlej and Beas are located at different heights. As discussed earlier, the river Sutlej is derived from much higher elevation than the river Beas. Generally, the river water depletes in 18O as the elevation increases. The overall depletion of isotope values of the river Sutlej is found higher than the river Beas due to the altitude effect [8]. The source of the river water also affects their stable isotope composition. Each source has got different isotope signatures. The river Beas and the river Sutlej get water from many sources.

The source of rain water is Arabian Sea or Bay of Bengal in the monsoon season from June to September. The source of rain water is changed to Mediterranean Sea i.e. western disturbance, in the winter season from December to February. The source of river water is changed to glaciers of Himalayas in the summer season staring March. Changes in isotope values in air moisture are already shown in Indo-Gangetic basin [24].

The variation in the stable isotopes of water must be due to different signatures of isotopes of rainwater or other sources of water. The rainfall in Bist Doab occurs during the southwest monsoon (June to September) from Bay of Bengal and Arabian Sea. For example, at Bhaddi the value of δ18O in the months of June and August was found to be − 0.44‰ and − 16.3‰ respectively. The monsoon rainfall in the months of June and August corresponds to two different branches of monsoon from Arabian Sea and Bay of Bengal. The isotopic composition of rainfall from Arabian sea is higher than that from Bay of Bengal because of proximity of Arabian Sea to the study area. However, the value of δ18O in the month of February was found − 14‰. The rainfall in February is due to a western disturbance originating in the Mediterranean Sea.

The temporal variation of δ18O and δ2H is dependent upon variations in temperature, rainfall, and relative humidity. The different sources of water discussed earlier do not have the same d-excess value. The seasonal variation of the stable isotopes in both rivers is the affected by melting of snow, monsoon, temperature, and the western disturbance. Winter precipitation originating from the Mediterranean Sea is characterized by distinctly higher d-excess values, reflecting the specific source conditions during water vapor formation [6]. As per the regression lines, the value of δ18O depletes as the temperature rises. This is due to more evaporation taking place at increased temperatures.

An improvement in the value of R2 of the relationship when multiple factors are input proves this assumption. However, Eqs. (8), (9), (10) and (11) do not have R2 anywhere near to 1. This shows that the value of δ18O and δ2H depends upon other factors. In this study, only latitude, longitude, and elevation were considered. More geographical or topographical factors may also affect the variation of the stable isotope. When the slope of the channel of the rivers or streams is steeper than the rate of evaporation is more. This can cause even more depletion of the 18O and the 2H. In the case of Bist interfluve, the slope changes drastically from Shiwalik hills towards the plains. This study includes the elevation impact assessment however slope is more related to the velocity of water. Some fluvial properties of the river channel like rugosity coefficient, hydrochemical reactions with the material of the river course, the length of catchment and travel time of water to reach the river stations. A comprehensive study that includes the evaluation of the aforementioned parameters might improve the value of R2.

The soil in the interfluve is mostly alluvial deposited by the running waters of the Sutlej and Beas rivers. These kinds of soils show good rechargeability of the area. Despite good aquifer recharge potential, the groundwater levels are falling [25,26,27,28] due to high pumping. There is a need to recharge the aquifers using the canals [25] taken off from the rivers Beas and Sutlej. The Kendall’s correlation coefficient proves that the isotopic fraction is highly significant in the Bist interfluve. The more the enrichment of the stable isotopes in the river water the higher is the rate of evaporation. At certain places it is observed that the value of δ18O and δ2H is lesser in the river water than the nearby aquifers. The d-excess of the river stations is higher than the adjacent aquifers. This means that the water from the river enters the aquifers after undergoing evaporation. The local factors like new water addition from the catchment near the stations of the Sutlej and Beas rivers, and local channel characteristics can also affect the isotopic composition. The more is the travel time of water to the river stations the more is the depletion of the stable isotopes in it. The higher travel time corresponds to higher infiltration of water to the aquifers in the area near the river station. It can be concluded that the lower δ18O and δ2H corresponds to more groundwater recharge in the specific area.

6 Conclusion

The phenomenon of the isotopic fractionation is useful to understand a river basin hydrology. The observations of the spatial variation of the stable isotopes of water (δ18O and δ2H) reveal some insightful information.

  1. (1)

    At Harike, a station on the confluence of Sutlej and Beas rivers, the difference between minimum and maximum values of δ18O and δ2H is the least on river Sutlej while Kanaun (− 13.31‰ and − 84.14‰) and Yusufpur (− 4.12‰ and − 50.45‰) have a large range between minimum and maximum values of δ18O and δ2H.

  2. (2)

    At Naushera, a station on the river Beas, a large ranges between the minimum and maximum of δ18O (− 8.91‰ to − 3.21‰) and δ2H (− 57.63‰ to − 21.48‰) have been observed. The topography reveals the presence of oxbow lakes at the sampling site of Naushera. Beas river stations. These values of δ18O and δ2H are enriched than that of the Sutlej river.

  3. (3)

    The isotopic water lines reveal that evaporation in Sutlej river is less (d-excess = 47.52‰) than in Beas river (d-excess = 16.35‰). The Kendall’s correlation between d-excess of Sutlej, Beas, shallow groundwater, deep groundwater, and rainfall does not show any similarity in their isotopic compositions.

  4. (4)

    Spatial modelling of the climate variables and the stable isotopes of water was carried out with 7 stations of each river (Sutlej and Beas). The error analysis of all the regression equations have been carried out in the current study and the coefficient of determination is found to be a good indicator of the accuracy of the equations. Most of the linear regression equations do not show any dependence of the stable isotopes of water upon the geographical and climatic factors.

  5. (5)

    The linear regression of δ18O with the temperature of Beas river and rainfall of Sutlej river has yielded a coefficient of determination of 0.20 and 0.17. The linear regression of δ2H with rainfall and temperature of Sutlej river has yielded a coefficient of determination of 0.14 and 0.20. The linear regression of d-excess with the relative humidity of Beas river, and temperature of Sutlej river and Beas river separately has yielded a coefficient of determination of 0.16, 0.27, and 0.38 respectively. All of the regression equations obtained for the climatic factors do not possess any significant coefficient of determination (R2 is less than 0.40).

  6. (6)

    The linear regression between the δ-values of the stable isotopes of water (18O and 2H) and geographical parameters like longitude, latitude, and elevation is almost negligible (the value of R2 varies from 0.18 to 0.71). This proves that there are other factors affecting the values of δ18O and δ2H.

  7. (7)

    The multiple linear regression has shown tremendous improvement in the value of R2.

This study is useful in the identification of areas with poor groundwater recharge and higher groundwater recharge with the help of stable isotopes. Further, this study suggests that a detailed study may be carried out for the measurement of length of the catchment and the slope, slope of the river channel, and daily climate variables in order create better models for the spatial and temporal variation of the stable isotopes.