Journal of Hydrology 402 (2011) 250–260

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Journal of Hydrology

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Lithologically constrained rainfall (LCR) method for estimating spatio-temporalrecharge distribution in crystalline rocks

Subash Chandra ⇑, Shakeel Ahmed, R. RangarajanNational Geophysical Research Institute, Council of Scientific and Industrial Research, Uppal Road, Hyderabad 500 606, India

a r t i c l e i n f o

Article history:Received 7 December 2010Received in revised form 5 March 2011Accepted 15 March 2011Available online 21 March 2011This manuscript was handled by G. Syme,Editor-in-Chief

Keywords:Natural rechargeLithologically constrained rainfall (LCR)Soil resistivityDepth-to-basementWater levelTemporal and spatial variability

0022-1694/$ - see front matter � 2011 Elsevier B.V. Adoi:10.1016/j.jhydrol.2011.03.018

⇑ Corresponding author. Tel.: +91 40 23434711x26E-mail addresses: schandra75@gmail.com, chandra

s u m m a r y

A lithologically constrained rainfall (LCR) method has been developed to estimate the spatial and tem-poral natural recharge distribution, a complex and high variable hydrological parameter in hard rocks.The lithological constraints are coupled to the rainfall in terms of soil resistivity (qs) and vadose zonethickness (H). In the absence of a bore-well in an over-exploited area with deep water table, it is dif-ficult to get the water table precisely from any surface exploration methods such as remote sensingand geophysics. However, water table variation being close to the basement in this situation, depth-to-basement was used as an alternative to the vadose zone thickness, which yielded equally reliableestimate.

The method facilitates to estimate temporal due to time varying rainfall and spatial due to litholog-ical variability, distribution of natural recharge for many numbers of years (say ±50) by inputtingthe precipitation of corresponding years, provided once hydrogeophysical (qs and H) parameters areknown. The method has been successfully validated and applied to study the watershed scale in agranitic terrain and found that the variability is much higher than otherwise expected or estimatedby a single method.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Recharge is a nonlinear hydrogeological parameter due to itsdependence on multiple factors, and is one of the most complexprocesses to quantify. However, it is very important to have a pre-cise and minimum error estimate of groundwater recharge per-taining to hard rock for resource management. There are severalconventional methods for recharge estimation such as groundwa-ter balance, water table fluctuation, soil water balance and chloridemass balance (Sophocleous, 1991; Moon et al., 2004; Maréchalet al., 2006; Batelaan and Smedt, 2007; Sibanda et al., 2009). Thesemethods require analysis of huge volume of hydrological data suchas precipitation, surface runoff, evapotranspiration, and change ingroundwater storage accumulated over a considerable time span,which is generally, inadequate or lacking or unreliable in manyareas (Sukhija and Rama, 1973). The water level fluctuation islinked with several factors such as base flow, precipitation, irriga-tion return flow, seepage from surface water bodies’ viz., lakes andponds. In addition, measuring the water level in the area withdense network of pumping wells is a difficult task, mostly influ-

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44; fax: +91 40 23434651._s75@ngri.res.in (S. Chandra).

enced by pumping wells and thus the measurement may not re-flect the actual peizometer.

Inverse groundwater modeling dealing with two-dimensionalfinite element or finite difference is another indirect approach ofrecharge estimation (Prasad and Rastogi, 2001; Bridget et al.,2002). However, it again requires huge amount of data to simulatethe real field conditions as well as the problem of inherent non-uniqueness of solution. Isotope tracer technique, a direct methodfor estimation of groundwater recharge, obviates the above men-tioned difficulties to some extent and therefore, it has been exten-sively used in various geological terrain throughout the world bymany researchers (Munnich et al., 1967; Munich, 1968; Zimmer-man et al., 1967; Sukhija and Rama, 1973; Dincer et al., 1974;Athavale et al., 1980, 1992, 1998; Rangarajan and Athavale,2000; Sukhija et al., 2003; Chand et al., 2004). However, it alsohas its own demerits due to its costly and time consuming factsas well as sometimes misleads the estimate due to heterogeneitypresent in the hard rocks. For an example, water bypasses throughin situ inclined cracks and fractures preserved in the soil, but insuch case, the tracer concentration distributions in vertical soilcore profile reflect relatively low displacement and hence rechargeunderestimation. Even questions were raised by several research-ers on the application of piston flow model of water movement jus-tifying with the some evidences of soil moisture flow not following

S. Chandra et al. / Journal of Hydrology 402 (2011) 250–260 251

piston flow model (Datta et al., 1990; Mookerjee, 1990; Singh andKumar, 1993).

Gupta and Paudyal (1988) have come out with an approxima-tion to the recharge estimation from rainfall combining hydrome-teorological parameters. As precipitation is the source of naturalrecharge, several studies have been carried out to correlate re-charge with annual precipitation directly (Chaturvedi, 1973;Sehgal, 1973; Datta et al., 1980; Bhandari et al., 1986). To the someextent, it can be applied in the alluvium, which consists of, in gen-eral, homogeneous stratified layers. But, due to differential weath-ering and fracturing in hard rocks, lithological changes areobserved very close by distances (Chandra et al., 2004, 2010;Dewandel et al., 2006; Chandra, 2006). Therefore, lithological con-tribution on natural recharge cannot be ignored. Some initiativeswere taken by few researchers (Chand et al., 2004; Israil et al.,2004) to study the lithological characteristics and its dependencyon natural recharge. However, they have analyzed contribution ofthe single lithological parameters on natural recharge at a time.Those were uncoupled relations and applicable to the specific con-ditions only.

Dripps and Bradbury (2010) developed a daily soil–water bal-ance model dealing with soil, land cover, topographic, and climaticdata to estimate the spatial and temporal distribution of ground-water recharge. However, the thickness of the unsaturated zonewas ignored. In hard rocks, despite the soil cover and land use pat-tern favourable to the infiltration, if basement is shallow, the infil-trated water will soon flow laterally towards the nearby deepwater table zone and hence recharging the distant aquifer.

Work has been carried out here to analyze the combined contri-bution of rainfall and lithological parameters on natural rechargeand evolved a coupled method to determine the spatial and tempo-ral recharge distribution that has been validated and applied ingranitic hard rock terrains of Bairasagara and Maheshwaramwatersheds in India (Fig. 1).

2. Study areas

Bairasagara watershed is the main study place that covers anarea of 111 km2 lying between latitudes 13�3202000 and13�4102400N, and longitudes 77�3902500 and 77�4501500E. Whereas,Maheshwaram watershed, bounded within Latitudes 17�060 and17�110N, and Longitudes 78�240 and 78�290E with an area of about55 km2, is located �400 km in the north (Fig. 1). Both the water-sheds do not have any perennial river and hence rainwater is theonly source to recharge the groundwater reservoir. The drainageis of dendritic and sub-dendritic pattern that roughly starts fromsouth i.e. upstream and flow towards north (Krishnamurthyet al., 2003; Kumar and Ahmed, 2003; Jain et al., 2003; Chandet al., 2004).

The geological setting is comprised of crystalline rocks i.e. leuc-ocratic and orthogeneissic granites. The rocks have undergone var-iable degree of weathering, and its thickness ranges from 3 to15 m, followed by fractured zones at up to maximum depth of�50 m (Dewandel et al., 2006). The major part of the watershedsis covered by red soils derived from the weathering of granitesand are classified as alfisols. Recent alluvia occur along streamcourses. The soil thickness varies from 0.5 to 3 m. They are pinkand grey coloured and medium to coarse grained in texture.

Groundwater occurs in the weathered, joints, fissures and frac-ture zone of the basement rocks under water table and semi con-fined conditions. The groundwater resources in the area havebeen over-exploited due to large scale pumping to meet the grow-ing demands of agriculture besides the essential requirements ofdrinking water. The area has a sub-humid climate, and receivesan average annual rainfall of �750 mm (Chand et al., 2004; Zaidi

et al., 2007). The main source of ground water is precipitationand to a lesser extent infiltration of water from the tanks and sur-face water applications.

3. Development of methodology

3.1. Theoretical development

Depending on the temperature and vegetation, a fraction of therainwater is lost to the atmosphere prior it reaches to the groundthrough the canopy as throughfall, where again the division takesplace into runoff, evapotranspiration, infiltration, etc. The interestlies here to quantify the part of the rainwater reached on theground, which under goes a long process of infiltration into thesoil, percolation through the vadose zone under the gravity till itreaches eventually to the water table recharging the aquifer. Therate of infiltration depends on the soil characteristics, which varieswith space. However, as the infiltrated water reaches to the zone ofsaturation passing the entire unsaturated zone, the thickness of va-dose zone also plays a role to the natural recharge and hence it canbe defined as:

R ¼ aðh;H;U; E; T; . . .Þ � P ð1Þ

where a, constitutive property of the formation, is the function ofsoil water content h, vertical thickness of pores space (i.e. zone ofaeration) H, topography U, evapotranspiration E, and temperatureT, etc. In order to simplify the above relation, we consider a flat re-gion, where temperature, evapotranspiration and cropping patternremains annually almost the same. In such conditions, the constitu-tive property a is mainly influenced by soil characteristics and ver-tical thickness of zone of aeration. It is well known fact that thesandy soil has relatively higher permeability than the clay andhence higher degree of infiltration. Being high porous and low per-meable the clay has high retention capacity to hold the water con-tent than the sand. Thus, the volume of water content in soil can betaken as a parameter to define its characteristics.

Due to wide range of variation in resistivity parameter, electri-cal methods are the most applicable tool applied to various geo-technical, hydrological problems such as delineation of aquifergeometry, characterizing lineament, contaminant migration, seep-age and hydraulic parameter estimation (Kelley, 1977; Niwas andSinghal, 1981; Ahmed et al., 1988; Frohlich et al., 1996; Buselliand Lu, 2001; Panthulu et al., 2001; Giao et al., 2003; Sjödahlet al., 2005; Chandra et al., 2006a–c, 2010). Since current flow inthe granite is mostly controlled by electrolytic conduction, electri-cal resistivity can be taken as a function of water saturation(Chandra et al., 2008). Thus, these two parameters i.e. h and Hcan easily be determined by electrical method.The density of pores(developed due to weathering, fissuring and fracturing) decreaseswith depth and ideally disappears to the basement in the hardrocks. Thus, H can be taken as depth-to-basement in hard rock. Itwould have been more ideal to include the water level, but inthe absence of borehole, determining deep water table from sur-face investigation methods is difficult. In an over-exploited aquifer,the water table is normally found close to the basement and henceit was decided to consider depth-to-basement as an alternative tothe thickness of zone of aeration. The depth-to-basement, is moreor less a time invariant property of the formation and easily detect-able by various geophysical methods such as electrical, seismic,gravity and magnetic. Magnitude of the recharge is of the orderof few millimeters, whereas depth-to-basement is found in orderof few tens of meters in the granite rock. Thus, H as depth-to-base-ment, in the situation, should not be a problem. Now the aboverelation can be written as:

R ¼ kqas HbPc ð2Þ

Fig. 1. Observation points and geomorphological map of study areas: Bairasagara and Maheshwaram watersheds.

Table 1Natural recharge Rt and Rg estimated respectively by tritium injection and LCR methods at Bairasagara watershed in 2001.

S.No.

Longitude Latitude Soil resistivity, ‘qs’(X m)

Depth-to-basement (m)

Water level(m)

Natural recharge, ‘Rt’(mm)

Natural recharge, ‘Rg’(mm)

Natural recharge, ‘Rgw’(mm)

1 77.71947 13.57433 40.00 4.32 3.62 6 22 192 77.70028 13.57183 32.26 6.62 7.00 21 25 263 77.69897 13.66431 51.00 10.77 9.80 32 49 464 77.69297 13.64622 50.69 6.87 6.98 34 36 365 77.71262 13.61746 64.42 5.98 – 39 38 –6 77.70844 13.59558 62.64 17.74 – 48 80 –7 77.74056 13.60289 56.30 7.62 7.45 54 41 418 77.70986 13.64550 125.72 6.00 7.17 69 61 709 77.70644 13.62547 110.82 9.39 12.80 82 76 96

10 77.68444 13.65411 52.23 10.70 11.89 91 49 5411 77.74347 13.55381 113.66 9.28 9.05 102 77 7712 77.72650 13.59911 48.23 39.57 20.50 129 117 7413 77.73814 13.59306 80.00 43.97 40.00 140 179 16914 77.67608 13.62577 111.05 27.16 16.37 158 161 11415 77.73622 13.60847 150.00 25.16 19.37 199 188 158

252 S. Chandra et al. / Journal of Hydrology 402 (2011) 250–260

where k is the constant that brings the effect of the other noncon-sidered parameters into the relationship. Weighting factors a, band c is assigned to respectively qs, H and P with the considerationthat the recharge is a nonlinear complex parameters. To apply theabove relation, the values of a, b, and c need to be defined.

Number of studies has been carried out by various researchers(Sehgal, 1973; Chaturvedi, 1973; Datta et al., 1980; Bhandari

et al., 1986) to relate the recharge with precipitation, whereweighting factor to precipitation is mostly found close to 0.5. Foran example, Chaturvedi (1973) established R = 1.35(P � 14)0.5 torecharge from rainfall over the flat terrain. Thus, a freedom canbe taken to chose value of c = 0.5 from previous studies, but thevalues of a and b need to be defined in the specific formation,where it has to be applied.

S. Chandra et al. / Journal of Hydrology 402 (2011) 250–260 253

3.2. Determination of a, b, and k for hard rocks

Since there are multiple unknowns and one equation, it is notpossible to get these values analytically at the moment. Therefore,it was decided to determine these values by statistical analysis ofthe field data, which will also bring the effect of complexity ofthe formation into the conceptualized relationship to make theestimate realistic. With this consideration, a joint study of naturalrecharge estimation from Tritium injection technique and delinea-tion of aquifer geometry by vertical electrical sounding (VES) havebeen carried out at Bairasagara watershed in 2001–2002. The Tri-tium was tagged at 36 locations in the un-irrigated land belowthe shallow root zone in the pre-monsoon and collected afterone hydrological cycle. The displaced position of tracer has indi-cated by the peak in its concentration distribution that corre-sponds to spot natural recharge to groundwater over the timeinterval between the injection of Tritium and the collection ofthe soil core profiles.

Total 47 VES were carried using Schlumberger configuration onthe log space that measured the apparent resistivity of the soilzone very well for short spacing and measured the signal fromthe deep basement for large current electrode spacing. This is awell known classical technique initiated by the work of Schlum-berger brothers in 1920s, which was used for quantitative interpre-tation in terms of layer resistivity and thickness (Keller andFrischknecht, 1966; Koefoed, 1979; Loke, 2000). Soil resistivityand depth-to-basement was determined from the inversion ofthe measured apparent resistivity.

Out of total 36 Tritium injections and 47 VES, 15 locations(Table 1) were close to each other representing the same subsur-face conditions and hence were utilized to derive the values of aand b by statistically analysis.

Least square estimate was applied over the logarithmic of Eq.(2) because that brings linear dependency. Log values of soilresistivity were correlated linearly with the log values of theknown recharge from tritium injection. Similar exercise was donefor depth-to-basement, which determined the values of a and brespectively as 0.4 and 0.6. Substituting the values of a = 0.4,b = 0.6 and c = 0.5, average value of k was calibrated to 3.50E–3corresponding to the field data. Finally using the values of a, b, cand k in the established relation (Eq. (2)) recharge was estimatedfrom the soil resistivity, depth-to-basement and rainfall. The esti-mated recharge has shown correlation coefficient 0.81 with theknown recharge.

Although by taking logarithms of the proposed relation (Eq. (2))was transformed into linear equation, but a single parameter wascorrelated at a time with known recharge. Thus, the power coeffi-cients determined by this process may not be very well coupledand the resultant estimate might be biased to some extent.

To overcome this problem a new approach is adopted that maybe called as physical relation based method. Computation wasdone using a formula Y = mXn with X as hydrogeological parameter(i.e. qs and H respectively in two parts, one by one) obtained fromthe field at 15 common points as mentioned above. The Y was com-puted with n varied over a range (0.1–0.9) with the considerationthat the values of a lies within this range and compared (root meansquare error, RMS) with the field recharge (Rt) values at corre-sponding points obtained from the tracer injection technique. Forexample taking n = 0.1, Y was computed at all the 15 points fol-lowed by its comparison with Rt and then switch to n = 0.2, andso on. However, it is also an important to have a right value ofm. Since, recharge is also dependent on H, which varies with space,therefore m was taken as square root of H in the above computa-tion (i.e. Y = m(qs)n). Similar exercise was also performed withthe depth-to-basement taking m as square root of qs and X = H.Fig. 2a and b presents comparative plots of Rt with Y (with X = qs

for soil resistivity and X = H for depth-to-basement respectively).The trend of the Y starts improving with n in the beginning, whereRMS error was found 91 (at n = 0.1) and attained the least RMS er-ror 24 (at n = 0.7). However, error starts rising afterwards and final-ly attained a value of 159 at n = 0.9. Similar result was obtained incase of depth-to-basement with least RMS error at n = 0.7 (Fig. 2c).Therefore, the n = 0.7, which gives the minimum RMS error, bringsthe computation Y closest possible to the real field data (Rt) andthus, it gives the value of a and b as 0.7. Now, substituting the val-ues of a, b, and c into Eq. (2), we have:

R ¼ kðqsHÞ0:7P0:5 ð3Þ

In the above computation of Y, precipitation was not taken into ac-count as it is a constant value for one hydrological cycle. Whiledetermining the values of a, b, and c the multiplication coefficientwere ignored with the consideration that the entire multiplicationfactor can be the part of k. Therefore, now to derive the value ofk, Eq. (3) has been applied on the known values of the R, qs, Hand P at Bairasagara watershed and the average value of k calibratedto 6 � 10�4 X�0.7 m�0.9. Thus, we can write the final equation as:

R ¼ 0:0006ðqsHÞ0:7P0:5 ð4Þ

The units of soil resistivity is X m, whereas, depth-to-basement,and precipitation in meter. It is important to note that recharge ob-tained in above equation is in meter as other parameters are in met-ric, but while discussing and presenting in the text, it will be done inmm, the internationally accepted unit. Since, the above equationcontains the soil resistivity and vertical thickness of zone of aera-tion or depth-to-basement, which introduces the lithological con-straints into the recharge estimate from rainfall, it is called aslithologically constrained rainfall (LCR) method. The recharge esti-mates at the 15 points by LCR method with power coefficient ob-tained by physical based relation gave high correlation coefficient(i.e. 0.86).

Sensitivity analysis of the qs, H and P was carried by introducingsmall changes to the respective parameters (Fig. 2d). Introducingpercentage change successively in increasing order from 0% to200% to the average soil resistivity (i.e. qs = 70 X m), rechargewas computed over constant average H = 15 m and P = 700 mm.Similar exercise was performed for H and P successively keepingother two remaining parameters constant. Soil resistivity anddepth-to-basement have same sensitivity i.e. for 100% change inthe respective parameter, recharge changed positively by 62%.However, rainfall got relatively lower sensitivity i.e. for 100%change in rainfall, recharge increased by 41%. Higher the sensitivityof lithological parameters than the rainfall looks to be quite logicalin the sense that even though there are heavy rainfall, but if litho-logical conditions are not favourable to recharge, the rainfall maygo as run off or surface water ponding may takes place.

3.3. Validation and generalization

Using the LCR method (Eq. (4)), natural recharge has been calcu-lated from soil resistivity, depth-to-basement and precipitation inBairasagara watershed and compared with the known values ofnatural recharge from Tritium injection at the 15 common loca-tions (Table 1, Fig. 3). To identify the method of recharge estima-tion, notations are used as Rt for recharge from Tritium injectionand Rg for LCR method. The correlation coefficient between Rt

and Rg is found 0.86. Thus, there is fairly good agreement betweenthem.

As it was mentioned previously that it would be more ideal toconsider the water level instead of depth-to-basement in theestablished relation, an exercise has been carried out to computethe natural recharge with H as water table depth. Since, the water

254 S. Chandra et al. / Journal of Hydrology 402 (2011) 250–260

table, Tritium injection and VES have their own requirement forthe measurement in the field; it was not always possible to havethese measurements exactly at the same locations. Therefore,nearby observation points representing the same lithology weretaken together for correlation, where out of the 15 common pointsof VES and tracer studies, 13 points have water level records (Ta-ble 1). Natural recharge (Rgw) were computed taking soil resistivity(qs), water level (H) below ground level and rainfall (P) using Eq.(4). Once again a strong correlation coefficient (0.79) found be-tween Rgw and Rt and validates the relationship.

0

100

200

300

400

500

600

0 50 100

Y a

nd R

t (m

m)

Natural recharge Rt

0

50

100

150

200

250

300

350

400

0 50 100

Y a

nd R

t (m

m)

Natural recharge Rt (m

020406080

100120140160180

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

RM

S E

rror

bet

wee

n R

t & Y

Power coefficient (n)

RMS error plot

RMS_soil res

RMS_H

(a)

(b)

(c)Fig. 2. Comparative plots: (a) between Y (X = qs) and Rt; (b) between Y(X = H) and Rt; (analysis of recharge parameters.

Surprisingly at some places, water level is found slightly deeperthan the depth-to-basement obtained from the VES. The differ-ences are probably due to the following reasons:

(1) The agriculture wells were monitored for water levelrecords. Although, all the possible precautions were takenand sufficient time gap were given for the well recoverybefore the measurements, but still due to unequal distribu-tion of current supply in the area, surroundings pumpingwells might have influenced the measurements.

150 200

(mm)

Rt

Y(n=0.1)

Y(n=0.2)

Y(n=0.3)

Y(n=0.4)

Y(n=0.5)

Y(n=0.6)

Y(n=0.7)

Y(n=0.8)

Y(n=0.9)

Linear (Rt)

Linear (Y(n=0.1))

Linear (Y(n=0.2))

Linear (Y(n=0.3))

Linear (Y(n=0.4))

Linear (Y(n=0.5))

Linear (Y(n=0.6))

Linear (Y(n=0.7))

Linear (Y(n=0.7))

Linear (Y(n=0.8))

Linear (Y(n=0.9))

150 200

m)

Rt

Y(n=0.1)

Y(n=0.2)

Y(n=0.3)

Y(n=0.4)

Y(n=0.5)

Y(n=0.6)

Y(n=0.7)

Y(n=0.8)

Y(n=0.9)

Linear (Rt )

Linear (Y(n=0.1))

Linear (Y(n=0.2))

Linear (Y(n=0.3))

Linear (Y(n=0.4))

Linear (Y(n=0.5))

Linear (Y(n=0.6))

Linear (Y(n=0.7))

Linear (Y(n=0.8))

Linear (Y(n=0.9))

020406080

100120140160180200

0 50 100 150 200

Per

cent

age

chan

ge in

rec

harg

e

Percentage change in ρs, H and P

Senstivity plot

Rt_% change in H

Rt_% change in ρs

Rt_% change in P

(d)c) RMS error (between Rt and Y) plot and power coefficient (n), and (d) sensitivity

Table 2Natural recharge Rt and Rg at Maheshwaram watershed in 1999.

S.No.

Longitude Latitude Depth-to-basement,‘H’ (m)

Soilresistivity,‘qs’ (X m)

Naturalrecharge,‘Rt’ (mm)

Naturalrecharge,‘Rg’ (mm)

1 78.4700 17.1317 9.8 59.1 10 142 78.4639 17.1186 20.4 25.5 13 133 78.4117 17.1472 11.7 57.6 15 164 78.4317 17.1375 20.0 51.1 18 215 78.4106 17.1306 22.9 49.8 20 236 78.4278 17.1317 19.6 35.4 20 167 78.4689 17.1539 16.3 64.6 20 228 78.4386 17.1519 13.7 80.0 22 229 78.4519 17.1269 18.7 65.9 24 24

10 78.4494 17.1572 23.6 50.6 27 2411 78.4416 17.1308 15.7 81.2 27 2512 78.4783 17.1530 18.0 72.0 31 2513 78.4294 17.1597 20.0 80.9 34 29

Table 3Comparative statistical data of recharge results Rt estimate at 36 points and Rg at 47points in Bairasagara watershed.

Parameters Rt estimated at 36points

Rg estimated at 47points

Recharge min. (mm) 0 8.5Recharge max. (mm) 199 308Average recharge (mm) 66 86Average recharge 6.8 8.9

S. Chandra et al. / Journal of Hydrology 402 (2011) 250–260 255

(2) The over-exploitation of groundwater resources due toexcessive pumping led the water table fall at deeper levelconfined to the micro fracture/fissured zone, where volu-metric amount of water is not sufficient enough to contrib-ute the significant contrast signal to the resistivitymeasurement at the ground level. This is another problemlinked with the resolution of the technique and can be dealtseparately.

However, the established method is valid to estimate the re-charge for the entire Bairasagara watershed, but it would be goodidea to further test in another area of the same geology and cli-matic condition to generalize the relationship.

The LCR method was tested in Maheshwaram watershed, whereTritium injections techniques were carried out in 1999 revealingnatural recharge in the range of 10–34 mm for the correspondingrainfall of 350 mm. Soil resistivity and depth-to-basement weretaken from VES results at the corresponding locations. As theMaheshwaram watershed is at �400 km far distance fromBairasagara, and has less topographic variation, the LCR method(Eq. (4)) was calibrated with the known results, where k was foundto 3 � 10�4 and used in the computation of recharge. The Rg isfound very well corroborating with the natural recharge Rt withthe correlation coefficient 0.83 and RMS error 3.0 (Table 2,Fig. 3). Thus, the LCR method is valid and generalized to estimaterecharge reliably and hence, it can be applied on a flat granitic hardrock terrain in semi-arid climate.

percentage (%)

4. Application at watershed scale: spatial and temporaldistribution

The LCR method has been applied at 47 VES points to estimatethe Rg in the Bairasagara watershed. A comparative summary of therecharge results estimated from tracer injection and LCR methodsare given in Table 3. The minimum, maximum and average values

Nat

ural

rec

hage

Rg

& R

gw (

mm

)

Natural Recharge Rt (mm)

Natural Recharge Rt (mm)

Bairasagara watershed

R² = 0.83

10

15

20

25

30

35

5 10 15 20 25 30 35 40

Nat

ural

rec

harg

e R

l(m

m)

Maheshwaram watershed

Fig. 3. Correlation plots of natural recharge Rg(H = depth-to-basement) andRgw(H = water table depth below ground level) estimated by LCR method with Rt

by tritium injection at: (a) Bairasagara watershed and (b) Maheshwaramwatershed.

of Rg at watershed scale are respectively 8.5, 306 and 86 mm forthe rainfall 968 mm in 2001, which is very close to the minimum,maximum and average values of Rt (i.e. 0, 199 and 66 mm). Ofcourse, the maximum recharge value at watershed scale has con-siderable difference. This is due to difference in the site distribu-tion of VES and Tritium injection points. The average rechargepercentage determined for the entire watershed by Tritium injec-tion technique is found 6.8, which is considered to be an underestimation as per the report of Groundwater Resource Estimationcommittee (Ministry of Water Resources, 1997). The report saysthat the natural recharge occurs in the range of 8–10% of total an-nual rainfall depending on the clay contents in weathered graniteand gneiss in India. The average recharge determined by LCR meth-od is 8.9%, which is relatively closer to the standard recharge rangein granite accepted by the expert committee. Thus, the LCR methodis valid at watershed scale too.

Recharge contour maps are prepared from the spot rechargevalues estimated from tracer technique as well as LCR and havebeen plotted along with the soil resistivity and depth-to-basementmaps (Fig. 4). These maps revealed that the soil resistivity has rel-atively high variability than the depth-to-basement. In general,resistivity, depth-to-basement and natural recharge Rt and Rg arefound very well corroborating with each other. For example, re-charge Rt and Rg maps have shown high (with its peak value�200 mm or more) in the central region of the watershed corrob-orating with the soil resistivity as well as depth-to-basement.

The natural recharge maps Rt and Rg have also shown dissimi-larity between them at few places, for an example in the northernpart of the watershed. The dissimilarity is due to difference of Rt

and Rg measurement points and its distribution. As hard rocksare heterogeneous, lithological characteristics vary sharply withinthe close distances and hence the reliability of the map will in-crease with the number of observation points.

As lithological alterations take place very slowly in the geolog-ical time scale, it can be considered almost constant (say for±50 years). Thus, the rainfall is the only parameter varying with

Depth-to-basement (H) map

Recharge (Rt) map

Top soil resistivity map

Recharge (Rg) map

10 ohm.m30 ohm.m50 ohm.m70 ohm.m90 ohm.m110 ohm.m130 ohm.m150 ohm.m170 ohm.m190 ohm.m210 ohm.m230 ohm.m250 ohm.m270 ohm.m

(a)

(b)

(c)

(d)

45 m42 m39 m36 m33 m30 m27 m24 m21 m18 m15 m12 m9 m6 m3 m0 m

320 mm

300 mm

280 mm

260 mm

240 mm

220 mm

200 mm

180 mm

160 mm

140 mm

120 mm

100 mm

80 mm

60 mm

40 mm

20 mm

0 mm

Fig. 4. (a) Soil resistivity, (b) depth-to-basement, (c) natural recharge ‘Rt’ and (d) Rg maps of Bairasagara watershed for the hydrological cycle of year 2001.

256 S. Chandra et al. / Journal of Hydrology 402 (2011) 250–260

time for such period. Therefore, once soil resistivity and depth-to-basement of an area are known, LCR method can be applied to esti-mate the temporal natural recharge distribution with the annualprecipitation. This is the great advantage over other available

techniques, where the entire processes are required to be com-pleted every year.

The spatial and temporal recharge pattern at Bairasagara wa-tershed has been studied by LCR method from 1990 to 2002.

S. Chandra et al. / Journal of Hydrology 402 (2011) 250–260 257

Fig. 5 presents spatial recharge distribution map of Bairasagarawatershed for high, medium and low rainfall years. High (i.e.P = 1353 mm), moderate (i.e. P = 717 mm) and low (i.e.P = 399 mm) rainfall occurred in 1991, 2000 and 2002 respectively.Very high recharge (P200 mm) zone can be seen in central portionof the watershed of the recharge map in 1991 that has shrunkdown during the moderate rainfall year in 2000 and finally disap-

Year: 1991

P=1353 mm

Year: 2000

P=717 mm

Year: 2002

P=399 mm

Fig. 5. Recharge estimated at watershed scale showing its spatial distribution for thr

peared during low rainfall year in 2002. Even though, the entirewatershed has received less than 500 mm rainfall in 2002, but cen-tral portion has received �100 mm rainfall. Thus, a bore hole fall-ing in this zone qualifies to be a sustainable that may probablyfunction during the low rainfall years too. Fig. 6 presents the aver-age recharge Rg and percentage recharge of the total annual rainfallfor the entire watershed from 1990 to 2002. The average recharge

0 mm

20 mm

40 mm

60 mm

80 mm

100 mm

120 mm

140 mm

160 mm

180 mm

200 mm

220 mm

240 mm

260 mm

280 mm

300 mm

320 mm

340 mm

360 mm

380 mm

Recharge (Rg)

ee typical years of high, moderate and low rainfall during 1991, 2000 and 2002.

10030050070090011001300150017001900

1

21

41

61

81

101

121

1990

1991

1992

1993

1994

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1996

1997

1998

1999

2000

2001

2002

Rai

nfal

l (m

m)

Rec

harg

e

Year

Bairasagara watershed

Rg (mm) Rg (%) Rainfall (P)

Fig. 6. Temporal distribution of average natural recharge ‘Rg’ with rainfall at Bairasagara watershed from 1990 to 2002.

258 S. Chandra et al. / Journal of Hydrology 402 (2011) 250–260

rises with the rainfall, but in contrary, the recharge percentage rel-atively decreases, which is quite logical due to its nonlinearproperty.

5. Discussion

Main aim of this study was to develop a generalized method toyield reasonably good estimate with the input parameters, whichcan be obtained easily in the field with good accuracy, less timeconsumption and cost-effective manner. The established LCRmethod of natural recharge estimation from precipitation in hardrock terrain is coupled with lithological constraints in terms of soilresistivity and vertical thickness of vadose zone. The LCR methodneeds three input parameters i.e. soil resistivity, vadose zone thick-ness and precipitation. However, in absence of bore-well it is diffi-cult to get the precise water table with the existing explorationmethods. To overcome of this problem, depth-to-basement as analternative to vadose zone thickness was used in the LCR method.Since over-exploitation resulted the lowering of the water tablequite close to the basement in granitic hard rock aquifer at Bairas-agara watershed, the method has worked well.

The coefficient k is empirically calibrated in the granitic hardrock terrain with respect to the recharge values estimated fromthe well known Tritium injection techniques and hence the meth-od further brings the effects of the other influencing factors such astemperature, evapotranspiration and vegetation.

The deep basement zone in hard rocks, normally, has high de-gree of weathering and fracturing, which favours the percolationin order to increase the rate of recharge. In other words, deeperthe basement, higher the degree of weathering and fracturing,and hence greater the natural recharge than the shallow basementzone. Thus, the LCR method, where H is taken as depth-to-base-ment, brings the inherent property of degree of weathering andfracturing of the zone above the basement. Since, recharge occur-rence is in the order of few mm, the LCR is expected to bring real-istic estimate. This is the probable reason why Rg got highercorrelation coefficient (0.86) than the Rgw (i.e. 0.79). The LCR meth-od was further validated at Maheshwaram watershed with correla-tion coefficient 0.83 between Rt and Rg and hence emerged as ageneralized tool to apply for natural recharge estimation in thegranitic hard rock terrain of semi-arid climate.

Almost similar recharge distribution obtained from Tritiuminjection and LCR methods at regional scale applied at Bairasagarawatershed. The LCR estimated average natural recharge 8.9% in2001 at watershed scale. The average recharge percentage foundvarying from 7.5 to 13.8 with mean 10.5 during 1990–2002. Thus,the average recharge obtained by LCR method at point andwatershed scale, lies within the recommended range of natural re-

charge in the weathered granite and gneiss by expert committeeand hence the method was further validated for the reliable esti-mate in crystalline rock.

VES and Tritium injection were performed over a flat terrain;hence both the methodologies gave the recharge values in the wa-tershed considering the flat topography. However, due to topo-graphic variation in an area, varying surface run off can influencethe recharge values. But, in the absence of any perennial riverstream, surface run on and surface run off take place one or otherplaces resulting to over all recharge in the watershed to be more orless of same magnitude. Of course, the ponding of excessive runoffwater causes additional evaporation loss to the atmosphere, whichmay further differ the recharge.

Being lithologically coupled, LCR method has an advantage overother conventional methods that it facilitates to compute rechargeon spatial and temporal dimension in an area, provided oncehydrogeophysical parameters are known. This was demonstratedat Bairasagara watershed, where the deterministic property of spa-tial and temporal recharge distribution by LCR method helped inidentifying as a sustainable well site in the form of high rechargezone.

The depth-to-basement can be well determined by resistivitymethod without any influence of climate variability. However, soilbeing exposed to the environment directly, variation in resistivityas a function of water saturation is quite obvious, and hence intro-duces an error to the recharge estimate. Engerrand (2002) studiedthe soil samples collected from the granite at Andhra Pradesh insemi arid India for resistivity measurement against the soil watersaturation. No change in the resistivity was observed for the sam-ple saturated with water P8%. However, it starts rising exponen-tially soon after the saturation falls below 8% (Fig. 7). The soilsample with P8% water saturation reveals the actual characteris-tics of the soil. For example, clayey sand is relatively less perme-able and has more capacity to absorb the organic and inorganiccompounds and thus reflected as relatively low resistive than thesandy soil. Along with the soil moisture, nutrients and compoundsalso contribute to the resistivity. This is the reason why sandy soilis less fertile than the loam or clayey sand.

The resistivity values of soil as a function of water saturation gi-ven by Engerrand (2002) were digitized and further used to com-pute recharge and the resultant relative error. The computationwas done with H = 1 m and 700 mm rainfall. Water saturation fall-ing below 8% introduces an error in recharge estimate due to in-crease of soil resistivity exponentially. Fig. 7 shows the rechargeestimate corresponding to the soil resistivity as a function of watersaturation. Approximately 12% error is found for the soil withwater saturation falling from 23% to 6.5% with the effective changefrom 8%. In the extreme case of 2.5% water saturation in soil raised

Δ

Δ

Fig. 7. Resistivity variation due to change of the water saturation in soil sample (after Engerrand, 2002). Its impact on recharge estimate (computed with H = 1 m andP = 700 mm).

S. Chandra et al. / Journal of Hydrology 402 (2011) 250–260 259

the recharge almost 20 times higher. Therefore, the precautionarymeasure must be taken for carrying out the resistivity measure-ment particularly for soil. Monsoon and post monsoon period willbe appropriate time for carrying out the resistivity measurementwhen soil is having at least 8% soil water content and thus errorin the recharge estimation could be avoided.

The soil thickness varies from 0.5 to 3 m, therefore, it is advisedto consider the average resistivity of the soil in order to minimisethe effect of the resistivity variation into recharge estimate. Inaddition to this, if we calibrate the established relation for the va-lue of k with respect to the known values of recharge in an area,error may be further reduced.

The backward calculation of natural recharge is being per-formed in Bairasagara watershed, but the forward calculationcould not be performed due to lack of precise rainfall prediction.

As these watersheds under experiment were over-exploitedresulting to the very deep water table close to the basement, ithardly matter, whether we take actual zone of aeration or depth-to-basement, results are not much affected, which is quite obvious.But, in case of un-exploited aquifer, there may be considerable dif-ference between water table and basement that will differ the Rg

with Rgw. But calibrating the LCR method with H as water tabledepth for the k value, will avoid the problem.

As the water level and rainfall are monitored regularly by theauthorized Groundwater agencies, the data can be used to com-pute the annual recharge at regional scale covering large area, pro-vided once soil resistivity measurement to the correspondinglocations are measured. This qualifies the LCR as a generalizedmethod to be used whether over-exploited or unexploited aquifers.

Since, electrical surveying is fast and cheaper than the otherexisting classical techniques and need to be done at one time only,the LCR method qualifies to be cost-effective and fast to estimatenatural recharge reliably with space and time.

6. Conclusion

The hydrogeophysical method has emerged as an efficient toolfor most groundwater applications and new approach of LCR isdeveloped to estimate the natural recharge in hard rocks. Litholog-ical contribution on small scale spatial variability is coupled to therainfall recharge using hydrogeophysical parameters such as qs (i.e.soil resistivity) and H (i.e. thickness of vadose zone or depth-to-basement). The hydrogeophysical parameters define the spatiallithological change in crystalline rock. Since, water table is quiteclose to the basement in the over-exploited aquifer, the depth-to-basement was used as an alternative to the vadose zone thickness.

Study also reveals that the degree of weathering and fracturing,which was not coupled initially in the LCR method, is an inherent

property in the form of depth-to-basement e.g. the deeper base-ment zone has high degree of weathering and fracturing favouringthe percolation rate and hence higher the recharge rate. However,further studies in this track will bring more generalized relation.

One of the important advantages of this technique is that thehydrogeophysical parameters, once known in an area, can be usedto estimate the temporal recharge for number of years with annualrainfall. The LCR method has been successfully applied to study therecharge at a point as well as on regional scale with time. The averagerecharge at Bairasagara watershed found varying from 7.5% to 13.8%with mean 10.5% during 1990–2002. Since, climate model is not wellestablished for rainfall pattern, at the moment, only backward esti-mation could be done. The measurement capability of LCR method inestimating the spatial and temporal variability in recharge distribu-tion helped in selecting a sustainable well site in an area.

Change in the soil resistivity with time will cause the variationin recharge estimate, which can be avoided by carrying out mea-surement during monsoon and post monsoon periods. The spatialand temporal natural recharge estimate will be useful input togroundwater flow and contaminant modeling and forecasting thefuture groundwater scenario.

Finally, the study concludes that the LCR is a generalized, cost-effective and fast method developed to estimate natural rechargespatially and temporally from rainfall in hard rock terrain and con-struct a useful time series of natural recharge in the studied wa-tershed for predictive studies.

Acknowledgements

We are thankful to Director, NGRI, Hyderabad for according per-mission to publish this paper. We thank to Dr. R.L. Dhar, Prof.Avadh Ram, Dr. Ananda Rao, Mr. S.C. Jain and Mr. Ramesh Chandfor useful discussion and support during the study. Departmentof Science and Technology, New Delhi, India has financed thestudy. This work is part of the unpublished thesis of the firstauthor. The first author would like to thank to Prof. Niels B.Christensen, Prof. Esben Auken and group members at Departmentof Earth Science, Aarhus University, Denmark for support and thefacility provided while writing the paper. Finally, we would liketo express our special thank the Dr. Geoff Syme Editor, anonymousreviewer (Dr. Emad Akawwi and others) for their critical reviewand the most importantly the valuable suggestions, which hastremendously improved the paper.

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