Conformity of groundwater recharge rate by tritium method and mathematical modelling

Journal of Hydrology, 30(1976)167--178

167

© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

CONFORMITY OF GROUNDWATER RECHARGE RATE BY TRITIUM METHOD AND MATHEMATICAL MODELLING

B.S. S U K H I J A * and C.R. S H A H

National Geophysical Research Institute, Hyderabad (India) Engineering Research Institute, Baroda (India) (Accepted for publication October, 23, 1975)

ABSTRACT Sukhija, B.S. and Shah, C.R., 1976. Conformity of groundwater recharge rate by tritium method and mathematical modelling. J. Hydrol., 30: 167--178. Environmental tritium profiles studied over an interval of two years in a semi-arid region of western India (Gujarat) have been utilised to evaluate groundwater recharge to unconfined and confined aquifers. The recharge rate (11% of local rainfall) determined for confined aquifers for a part of the selected area using a diffusion-type unsteady groundwater flow model is in fair agreement with that determined using the tritium method. The tritium method wherever applicable has the advantages of being direct, fast, economical and does not require much hydrological data.

INTRODUCTION

For evaluation of groundwater recharge rate, several conventional methods such as storage, inventory, lysmetric, are generally employed. These in turn require the analysis of a large volume of hydrological data(precipitation, surface runoff, evapotranspiration, changes in groundwater storage etc.) accumulated over a considerable time span. However, such data is generally inadequate or lacking or unreliable in many areas where groundwater resources are yet to be fully exploited. In recent years there has been an increasing emphasis on the use of isotopic techniques since they obviate the above mentioned difficulties to some extent. Two direct methods using environmental and artificial tritium developed by Miinnich and his coworkers (Zimmermann et al., 1965, 1966, 1967; MUnnich et al., 1967; Mtinnich, 1968) are noteworthy contributions to recharge determination methods. Since the first demonstration of such an application by Miinnich and his colleagues, many researchers have explored the utility of the methods in diverse climatic and hydrological conditions. Smith et al. (1970) utilised the method for studying the soft-water movement and recharge in chalk and clay profiles. Sukhija (1972) and Sukhija *Present address: Bundesanstalt flir Bodenforschung, Hannover, Federal Republic of Germany.

168 and Rama (1973) have ascertained the validity of environmental tritium methods for semi-arid alluvial tracts of Gujarat. Recently quite a few investigations employing these techniques were reported in a symposium (IAEA, 1974). More recently Dincer et al. (1974) have utilised the tritium m e t h o d for the study of infiltration and recharge through the sand dunes in an arid zone. The present paper aims at a comparative study of recharge rates determined at six selected sites in Gujarat, western India using the environmental tritium m e t h o d and those c o m p u t e d using a diffusion-type unsLeady groundwater flow model for a part (Mehsana district) of the selected area. Such an approach combining the application of isotopic and simulation techniques is seldom a t t e m p t e d (Bredenkamp et al., 1974), though in principle, it ought to prove useful in obtaining correct recharge rates. The present study obtains a fair agreement between the recharge rates determined by the two altogether different techniques. INVESTIGATION AREA The present investigation has been carried o u t in the alluvial tracts of Gujarat which cover an area of a b o u t 45,000 km 2 and are situated in semiarid climate in western India (Fig. 1). The tracts are surrounded by the Aravalli hills in NNE and Saurshstra high lands in the southwest. The study area merges into the Indian Desert and the Rann of Kutch in the west. The rain fall is peaked during the m o n s o o n months of June to September with an annual average of 70 cm, ranging from 50 to 100 cm in different regions. The surface water resources are meagre and the main source of irrigation in the region is groundwater. Except the rivers Narbada and Tapti which are perennial the rest of streams run only during the m o n s o o n period. Thus an evaluation of recharge is extremely vital for proper groundwater management. Geohydrological studies carried o u t by different workers (Deshpande, 1954; Sharma, 1971) indicate a thick deposit of alluvium with water table, semiartesian, and artesian conditions. The productive aquifers are mainly sand which occurs in pockets and lenses. Main source of recharge to the unconfined aquifers is vertical percolation of local rainfall. In general, groundwater flows from northeast to southwest and the confined aquifers are recharged by rain occurring on the outcrop areas in the northeast b o u n d a r y near Taranga (Fig. 1). In order to have a broad coverage of different soil types and climatic conditions, six sites: Ahmedabad, Balol, Kosamba, Sankeshwar, Taranga and Varahi were selected for this investigation. The northeast part of the tracts is represented by the site Taranga, lying at the f o o t of northeastern hills. The top soil is largely coarse sand. Ahmedabad and Balol lie in the middle of tracts, relatively less arid than north Gujarat, with sandy loam soils. The northwest portion of tracts is represented b y the sites of Sankeshwar and Varahi. This zone is close to the Rann of Kutch and is almost arid. Kosamba lies in the southern part of the tracts where the t o p soil is clayey and the area is relatively humid. The

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tritium experiments were first undertaken in 1967 and repeated in 1969. The results of recharge rates using a mathematical model have been obtained only for a part of the selected area located in the Mehsana district (Figs. 1 and 4) because of the limited availability of hydrological data. PRINCIPLE OF THE TRITIUM METHOD USED

Tritium produced either by the interaction of cosmic rays and the atmosphere or resulted from the testing of thermonuclear weapons precipitates in the form of HTO in rain, snow. Since 1952, the onset of the thermonuclear era, the concentration of tritium in precipitation had increased several folds and had masked the natural levels, a few TU (TU is defined as the concentration of one tritium atom per 10 ~8 H atoms). Tritium concentration in precipitation is found to vary with latitude, altitude, meteorological factors, distance from the sea etc. Tritium concentration along with precipitation amounts is measured by a number of laboratories all over the world and the data are compiled by the IAEA, Vienna. Study of the past history of tritium in the northern hemisphere indicates that the release of tritium was in pulses with a peak concentration in 1 9 6 3 - - 1 9 6 4 and thereafter tritium levels have slowly dropped (e.g., Fig. 2). TRITIUM ioo

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171

There are two different m e t h o d s (Mi]nnich, 1968) in which tritium can be used for evaluation of recharge. The use of tritium is based on the fact that the fate of tritium in precipitation is the same as that of precipitated water. In case of a sufficiently homogenous aquifer, where it can be established that recharge predominantly to groundwater takes place in such a way that younger water pushes the older water beneath and the movement of water can be said to be piston-type flow, in such cases the tritium concentration variation with depth should be a replica of the tritium history of rain water. However, in practice there will always be some dispersion which will smear o u t the profile and the tritium peak will be damped. The position of 1963/1964 precipitation (having peak tritium concentration) in a soil profile could still be located (except for cases where soil-water movement is very fast and the peak has reached quite deep) and the recharge due to successive years of rainfall will be piled above the soil segment containing predominantly 1963/1964 rain water. The computation of recharge is made up by finding the amount of water present up to the tritium peak position from surface downwards and this amount is compared with total precipitation since 1963 to the time of investigation. The ratio determines the recharge rate since the model of such water movement prevents any percolation across the 1 9 6 3 / 1 9 6 4 precipitation layer:

r=s/p where r = recharge as fraction of precipitation; s = soil moisture (cm) in the column from surface downwards to the depth where the tritium peak occurs; p = precipitation during the period from 1963 to the time of investigation. This m e t h o d is called peak m e t h o d and in this m e t h o d uncertainty lies in locating the correct position of the peak, which will lead to some error in recharge estimation. In another m e t h o d called the total tritium m e t h o d (Munnich et al., 1967; Munnich, 1968; Atakan et al., 1974), a balance between tritium fallout and tritium accumulated in groundwater is found, the difference is attributed to evapotranspiration and runoff. The ratio of tritium deposited in groundwater to total tritium precipitated is the recharge rate as fraction of precipitation. Assuming some suitable model of recharge, the tritium input function at a site is calculated by summing up the products of m o n t h l y precipitation and its tritium concentration. The tritium concentrations are corrected for radioactive decay up to the time of investigation and the summation is carried o u t for the period since 1952 (onset of thermonuclear era) to the time of investigation. For a simple model of equal a m o u n t of recharge for all the rainfalls: T = Y, A i P i 1952

where T = total tritium input (TU cm); A i = tritium concentration (TU) (corrected for radioactive decay) in precipitation for m o n t h i; and Pi = precipitation (cm) in m o n t h i. Similarly the amount of tritium percolated in groundwater is computed by the following relation: d

t= Z ajmj

172

where t = total a m o u n t of tritium (TU cm) deposited in the aquifer; a] = tritium concentration (TU) in moisture of segment ] of aquifer; m ] = moisture (cm) in segment ] of aquifer; and d = depth of aquifer where tritium concentration of water is negligible. Since T represents the total input at a site and t represents the amount percolated (which escaped evapotranspiration and run off losses), t / T determine the fraction of rainfall that goes to recharge groundwater. This method is more accurate since it provides recharge rate averaged over the last 1 5 - 2 0 years, however, these results are biased to recharge during years having higher tritium rain-out. E V A L U A T I O N O F R E C H A R G E R A T E S BY T H E T R I T I U M M E T H O D

The above discussed peak and total tritium methods have been applied to obtain recharge at the six selected sites. The soil samples were obtained by means of a hand auger and moisture contents of soil samples were determined using conventional gravimetric method. The rainwater samples were routinely collected at the stations close to the sites selected for recharge evaluation. Tritium concentration of precipitation samples and soil-water samples were measured at the Tata Institute of Fundamental Research, Bombay, by converting water into methane gas and subsequently counting in a Oeschger proportional counter (Oeschger, 1963) having a low background of 0.7 cpm and sensitivity of 70 TU per cpm w i t h o u t any enrichment step. Fig. 2 shows the yearly distribution of tritium at Ahmedabad w i t h o u t decay correction. The tritium data prior to 1962 has been extrapolated from Ottawa data. Fig. 3 shows the depth variation of tritium at six selected sites. All the profiles show an increase in tritium concentration from surface downwards to a certain depth where the tritium peak occurs and further down the concentration falls to negligible value, thus incorporating total tritium deposited since 1952. This disposition of tritium in different profile allows use of both of the tritium methods. A detailed discussion on tritium profiles is given in Sukhija and Rama (1973). The mean of recharge rates as determined in 1967 and 1969 experiments are shown in Table I. CALCULATION OF RECHARGE RATES BY A MATHEMATICAL MODEL

Recharge rates have also been calculated b y a mathematical model in a part of the alluvial tracts, called Mehsana district (Fig. 1). The district has an area of 10,963 km 2 and lies between latitude 23°0 '' and 24°10 '' and longitude 71°18 ' and 72°55 ' and forms a b o u t 25% of the total area investigated. Fig. 4 shows a rectangular grid actually selected for the mathematical model. The five sites o u t of the six selected for recharge evaluation by the tritium method lie within or round a b o u t the area selected for mathematical modelling. The rectangular grid has 13 rows and 19 columns with a node spacing of 5 km. The diffusion-type unsteady state groundwater flow in confined aquifers defined

173

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TABLE I Evaluation of groundwater recharge by tritium methods Sites

Total tritium metho d

Peak tritium method

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175

by the following partial differential equation was used in the mathematical model. ~h

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= Sxy--~t + Wxyt where x, y = space coordinates t = time coordinate T x y = the transmissivity at node x , y S x y = the storage coefficient at node x , y Wxy t = the recharge/withdrawal at node x , y at time t h = head The partial differential equation was converted into a difference equation for every node. By using the alternate direction implicit procedure (Rushton, 1974), the simultaneous equations were solved with an initial time step of 0.5 day. The c o m p u t e r programme was prepared in F O R T R A N IV and was run on an IBM 360 PRL Ahmedabad. The node wise data of T , S and withdrawals by tube wells for 1958/1959 to 1970/1971 was collected from the field. The rate of recharge was first assumed at some node points on northeast b o u n d a r y (i.e., node points 2--10 to 2--13) and a computer run was made to predict static water levels (SWL) at the end of every year, i.e. for the years 1959/1960 to 1971/1972. The c o m p u t e d SWL's were compared with observed SWL's at the same node points for the same period. There was no agreement initially. Later the rates of recharge and the effective node points were adjusted till the observed SWL's and the c o m p u t e d ones agreed at all the node points for all the years. The final adjusted recharge rates for the selected grid is given in Table II. From Table II it can be seen that the highest rate of recharge is 6.4 cm/year on nodes 2--13 and 2--14 in the outcrop area. The surrounding nodes 2--11 to 2--16, 3--11 to 3--18 and 4--11 to 4--18 also lie in the outcrop areas and have recharge rates varying from 5.5 to 6.5 cm/year which agrees very well with that determined using tritium. For other sites the tritium study provides recharge rates for only local unconfined aquifers, which probably have little or no hydrological connections with confined aquifers. DISCUSSION

The errors in the determination of recharge rate by the tritium m e t h o d can be grouped into: (1) errors in the c o m p u t a t i o n of tritium input function; and (2) errors in the c o m p u t a t i o n of tritium deposition. Errors in the input function consist of: (1) error due to measurements of tritium contents which is _+10% and (2) error due to the usage of tritium data of Ahmedabad precipitation at other sites which is about +_5%, as has been found from the comparison of measured values at Hyderabad and those extrapolated from Ahmedabad.

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The tritium depositions as calculated in t w o different experiments in 1967 and 1969 are in agreement b e t w e e n themselves within + 15%. Therefore, the total error in the estimation of recharge would be ~/102 + 52 + 152 = + 20%, assuming that there are no further errors due to by passing of tritium to deeper depth through worm holes or cavities or due to the adoption of this particular model of recharge. Atakan et al. (1974) also show an error of + 25% in their experiment. It must be pointed o u t that the recharge rates obtained using the tritium m e t h o d are only point measurements. These measurementsmust be averaged for a number of points to get a representative recharge rate. On the other hand the recharge rate obtained by the mathematical model represents the groundwater system investigated, though the procedure involves many assumptions. There is no d o u b t that the tritium m e t h o d wherever applicable is simple, direct and accurate It essentially requires data on precipitation and its tritium concentration in different years. Even in the absence of tritium data at the investigation site, the data can be extrapolated from other stations for which the data is compiled by the IAEA, Vienna. Further one needs only moisture and tritium c o n t e n t at different depths. F e w representative tritium profiles which can be obtained quickly and economically will estimate the recharge fairly accurately.In contrast, mathematical modelling requires continuous water-level measurements and of parameters from pumping tests which are expensive propositions. CONCLUSIONS

Depending u p o n the climatic and hydrological condition in the alluvial tracts of Gujarat, the recharge rates as determined by environmental tritium m e t h o d are found to vary between 1.5 and 6 cm (3--11% of local rainfall). There exists a fair agreement between the recharge rate obtained by the tritium m e t h o d and that calculated by digital modelling for the outcrop area of Mehsana aquifers. ACKNOWLEDGEMENTS

The authors are grateful to Prof. M.A. Geyh of Niedersachsisches Landesamt fiir Bodenforschung, Hannover, Dr. C. Sonntag and Prof. K.O. Miinnich of the University of Heidelberg for various discussions and suggestions for the improvement of the paper.

REFERENCES Atakan, Y., Roether, W., Miinnich, K.O. and Mathess, G., 1974. The Sandhausen shallow groundwater tritium experiment. In: Isotopes Techniques in Groundwater Hydrology, Vol. 1, IAEA, Vienna, pp. 21--43. Bredenkamp, D.B., Schutte, G.J. and DuToit, G.J., 1974. Recharge of a dolomitic aquifer as determined from tritium profiles. In: Isotope Techniques in Groundwater Hydrology, Vol. 1, IAEA, Vienna, pp. 73--95.

178 Deshpande, B.G., 1954. Groundwater resources of the alluvial tracts of Gujarat. Bulletin of the Geological Survey of India, No. 4, pp. 1--93. Dincer, T., A1-Murgin, A. and Zimmermann, U., 1974. Study of infiltration and recharge through the sanddunes in arid zones with special reference to the stable isotopes and thermonuclear tritium. J. Hydrol., 23 (1/2): 79--109. IAEA, 1974. Isotope Techniques in Groundwater Hydrology, Vols. I and 2. Proc. Symp. IAEA, Vienna, 504 pp. and 499 pp. Miinnich, K.O., 1968. Infiltration and deep percolation. In: Nuclear Techniques in Hydrology, IAEA, Vienna, Ch. V-3a, pp. 191--197. Miinnich, K.O., Roether, W. and Thilo, L., 1967. Dating of groundwater with tritium and C-14. In: Isotopes in Hydrology, IAEA, Vienna, pp. 305--320. Oeschger, H., 19('3. Low level counting methods. In: Radioactive Dating. IAEA, Vienna, pp. 13--34. Rushton, K.R., 1974. Critical analysis of the alternating direction implicit method of aquifer analysis. J. Hydrol., 21(2): 153--172. Sharma, S.C., 1971. Hydrogeological investigation in parts of Sabarkantha district, Gujarat. Semin. on Water Resources of Rajasthan and Gujarat, Jaipur, Geological Survey of India (Sponsor). Smith, D.B., Wearn, P.L., Richards, H.J. and Rowe, P.C., 1970. Water movement in the unsaturated zone of high and low permeability strata by measuring natural tritium. In : Isotope Hydrology, IAEA, Vienna, pp. 73--87. Sukhija, B.S., 1972. Evaluation of groundwater recharge in semi-arid region of India using environmental tritium. Ph.D. Thesis, University of Bombay, Bombay, 139 pp. Sukhija, B.S. and Rama, 1973. Evaluation of groundwater recharge in semi-arid region of India using environmental tritium. Proc. Indian Acad. Sci., 77(6): 279--292. Zimmermann, U., Miinnich, K.O., Roether, W., Kretz, W., Schubuack and Siegel, O., 1965. Downward movement of soil moisture traced by means of hydrogen isotopes. Proc. 6th Int. Conf. on Radiocarbon and Tritium Dating. Pullman, Washington, D.C., 577 pp. Zimmermann, U., Miinnich, K.O. and Roether, W., 1966. Tracers determine movement of soil moisture and evapotranspiration. Science, 152: 346--347. Zimmermann, U., Ehhalt, D. and Munnich, K.O., 1967. Soil water movement and evapotranspiration, Changes in isotopic components of soil water. In: Isotopes in Hydrology, IAEA, Vienna, pp. 567--585.