1 Introduction

Clausius coined the word ‘Entropy’ from the Greek meaning transformation. Thus, entropy originated in physics and occupies an exceptional position among physical quantities. Its nature is, rather, a statistical or probabilistic one, for it can be interpreted as a measure of the amount of chaos within a quantum mechanical mixed state. It is an extensive property like mass, energy, volume, momentum, charge, number of atoms of chemical species, but, unlike these quantities, it does not obey a conservation law.

In physical sciences entropy relates macroscopic and microscopic aspects of nature and determines the behavior of macroscopic systems in equilibrium (or close to equilibrium). Entropy is not an observable; that means there does not exist an operator with the property that its expectation value in some state would be its entropy (Wehri 1978). It is, rather, a function of a state. Entropy is viewed in three different but related contexts and is hence typified by three forms such as (1) thermodynamic entropy given by Clausius in 1850 (Gull 1991), (2) statistical-mechanical entropy given by Boltzmann in 1866 (Lebowitz 1993), and (3) information–theoretical entropy (Shannon 1948).

This entropy is a measure of the degree of uncertainty of a probability distribution and in turn the random variable. Since the reduction in uncertainty by more observations is equal to the amount of information gained, entropy indirectly measures the information content of a given series of data. Once the statistical distribution of a random variable is known, its entropy can be computed and expressed in specific units. The concept of entropy was first developed by Shannon (1948) and recently has been applied in many different fields, such as ecology (Nicolae et al. 2009), biology (Rojdestvenski and Cottam 2000), mining industry (Siradeghyan et al. 2008), economic (Zhou et al. 2010), financial time-series analysis (Darbellay and Wuertz 2000), etc.

Amorocho and Espildora (1973) found that entropy yielded satisfactory results in comparing mathematical models and selecting the most appropriate model. Fiorentino et al. (1993) analyzed the basin morphological characteristics under the assumption that the only information available on a drainage basin is its mean elevation and the assumed connection between entropy and potential energy. Of on network assessment Yang and Burn (1994) have shown that entropy measures are more advantageous than other measures as they reflect a directional association among sampling sites. Singh (1997) discussed the entropy concept and its application to estimation of parameters of probability distributions, stream flow forecasting, characterization of landscapes, evaluation rainfall networks, reliability of water distribution systems, aquifer parameter estimation, distribution of velocity in open channel and assessment of water quality and design of its networks. Mogheir et al. (2006), Masoumi and Kerachian (2008), Karamouz et al. (2009) and Mogheir et al. (2009) applied entropy to assess and optimize data collection networks. This entropy theory is also formulated for modeling the potential rate of infiltration in unsaturated soils (Singh 2010).

In Indian context Jha and Singh (2008) assessed the water quality of the six river systems using entropy. It is an effective indicator of the pollution level at any section of any of the six river systems which indicates the Yamuna and Gomti River systems are highly polluted; Baitarani is moderately polluted; and Brahmani, Malprabha and Pachin river systems are marginally polluted. The entropy is also used to prove the early Permian Barakar Formation of the Bellampalli coalfield developed distinct cyclicities during deposition (Tewari et al. 2009). But the first attempt is to discriminate between various seismological phases, such as the primary converted waves arising from several depth boundaries in Earth’s interior, and the multiply reflected wave types using the concept of cluster entropy and related information dimension (Ramesh et al. 2010). The usability of entropy calculation demonstrated to identify measure and monitor urban sprawl in Hyderabad-Secundrabad city and its environs (Rahman et al. 2011). Recently Mondal and Singh (2011a) used entropy-based approach to assess the groundwater monitoring network that exists in Kodaganar River basin from Southern India. The use of information-based measures of groundwater table shows that the existing state government monitoring network contains a sufficient number of wells but is not well designed for the measurement of regional groundwater level. So far the entropy concept has not been applied to estimate natural groundwater recharge.

For management of groundwater resources in semi-arid regions, especially in hard rock areas, it is essential to determine natural recharge. There are several methods for determining groundwater recharge, such as groundwater balance (Scanlon et al. 2002), lysimeters (Nonner 2006), piston-flow model (Zimmermann et al. 1967; Rangarajan and Athavale 2000; Chand et al. 2005; Rangarajan et al. 2009); RS and GIS techniques (Saraf et al. 2004; Chowdary et al. 2009); photogeological (Salama et al. 1994), hydrogeological (Raj 2001), geophysical methods (Muralidharan and Shanker 2000), 14C-age dating (Bredenkamp and Vogel 1970); chloride mass balance method (Nonner 2006), and regional groundwater models (Sibanda et al. 2009). Among these methods, the tracer technique is the well-known method for estimation of groundwater recharge (Zimmermann et al. 1967). This technique estimates recharge on the basis of piston flow model, and has been found useful (Rangarajan and Athavale 2000; Chand et al. 2005; Rangarajan et al. 2009). The methods are time consuming, not easily accessible for many researchers and sometimes even uneconomical in developing countries, particularly when one has to deal with a large basin. Therefore, it is desirable to develop a simple and rapid method which can provide qualitative estimates of recharge/suitable recharge zones in data lacking areas where further investigations can be undertaken. This study explores the use of entropy to develop such a technique.

Thus the objective of this study is to employ the concept of entropy for assessing natural recharge of unconfined aquifers from Southern India, and compare the recharge zones so assessed with that obtained from remote sensing and geographical information system techniques.

2 Development Entropy-Based Approach for Estimation of Natural Recharge

The entropy of a random variable is a measure of the information or uncertainly associated with it. Measures of information include marginal entropy, joint entropy, conditional entropy and transinformation. For a random variable x, the marginal entropy, H(x), can be defined as the potential information of the variable. For two random variables x and y, the conditional entropy H(x|y) is a measure of the information content of x that is not contained in the random variable y. The joint entropy H(x, y) is the total information content contained in both x and y. The mutual entropy (information) between x and y, also called transinformation, T(x, y), is interpreted as the reduction in uncertainly in x, due to the knowledge of the random variable y. It can also be defined as the information content of x that is contained in y. Entropy measures can be expressed using both discrete and analytical approaches (Lubbe 1996; Singh 1998). Discrete forms of these entropies can be expressed as

$$ H(x) = - \sum\limits_{{i = 1}}^n {p({x_i})\ln p({x_i})} $$
(1)
$$ H(y) = - \sum\limits_{{j = 1}}^m {p({y_j})\ln p({y_j})} $$
(2)
$$ H(x,y) = - \sum\limits_{{i = 1}}^n {\sum\limits_{{j = 1}}^m {p({x_i},{y_j})} \ln p({x_i},{y_j})} $$
(3)
$$ H(x|y) = - \sum\limits_{{i = 1}}^n {\sum\limits_{{j = 1}}^m {p({x_i},{y_j})} \ln p({x_i}|{y_j})} $$
(4)
$$ H(y|x) = - \sum\limits_{{i = 1}}^n {\sum\limits_{{j = 1}}^m {p({x_i},{y_j})} \ln p({y_j}|{x_i})} $$
(5)
$$ T(x,y) = \sum\limits_{{i = 1}}^n {\sum\limits_{{j = 1}}^m {p({x_i},{y_j})\ln \left[ {\frac{{p({x_i},{y_j})}}{{p({x_i})p({y_j})}}} \right]} } $$
(6)

where x and y are two discrete variables with values xi, i = 1, 2, …, n; yj, j = 1, 2, …, m, defined in the same probability space, each of which has a discrete probability of occurrence p(xi) and/or p(yj); p(xi, yj) is the joint probability of xi, yj; and \( p({x_i}|{y_j}) \)is the probability of xi conditional on yj. Note that H(x, y) = H(y, x).

To calculate the information measures for more than one variable, the joint or conditional probability is needed, and this can be obtained using a contingency table. An example of a two-dimensional contingency table is given in Table 1. To construct a contingency table, let the random variable x have a range of values consisting of u categories (class intervals), whereas the random variable y is assumed to have v categories (class intervals). The cell density or the joint frequency of (x, y) represented by (i, j) is denoted by fij, i = 1, 2, …, u; j = 1, 2, …, v, where the first subscript refers to the column and the second subscript to the row. The marginal frequencies are denoted by fi. and fj. for the column and row values of the variables, respectively.

Table 1 Two dimensional contingency table (frequency)
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Further, transinformation T(x, y) also can be expressed by Jessop (1995) as

$$ T(x,y) = H(x) - H(x|y) $$
(7)
$$ T(x,y) = H(x) + H(y) - H(x,y) $$
(8)
$$ T(y,x) = H(y) - H(y|x) $$
(9)
$$ T(y,x) = H(y) + H(x) - H(y,x) $$
(10)

Rainfall is considered as first independent random variable (x) and the depth to water table for individual wells the second dependent variable (y). Then transinformation, T(x, y), is interpreted as the reduction in the original uncertainty of depth to water table, due to the knowledge of rainfall. It can also be defined as the information content of water table which is contained in rainfall. In other words, it is the difference between the total entropy and the sum of marginal entropies of these two variables. This is the information repeated in both water table and rainfall, and defines the amount of uncertainty that can be reduced in one of the variables when the other variable is known. On the other hand, marginal entropy, H(x), is defined as the potential information of rainfall. Then, the ratio of T(x, y) to H(x) is simply a fraction amount of recharge due to rainfall. Therefore, the percentage of rainfall, Re (%), contributing to the natural recharge of an unconfined aquifer is given as

$$ {R_e}(\% ) = \frac{{T(x,y)}}{{H(x)}} \times 100 $$
(11)

3 Application in a Hard Rock Area from Sothern India

3.1 The Study Area

The study area is a drought prone hard rock terrain with an area of about 209 km2 and located in between 10°13′44″–10°26′47″ N latitudes and 77°53′08″–78° 01′ 24″ E longitudes (see Fig. 1). The area is characterized by undulating topography with hills (Sirumalai) located in southern parts, sloping towards north and northeast. The elevation (altitude) in plains ranges from 360 m (amsl) in the southern part to 240 m in the northern part (Mondal et al. 2005). No perennial streams exist in the area, except for short distance streams encompassing 2nd and 3rd order drainage (Mondal and Singh 2011b). Runoff from rainfall within the area ends in small streams flowing towards the main Kodaganar River. From a period of 1971–2007, the average annual rainfall is of the order of 905.3 mm.

Fig. 1
figure 1

Location map showing rain gauge station and monitoring PWD wells

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3.2 Geological and Hydrogeological Setup

The study area is covered with Achaean granites and gneisses, intruded by dykes (Balasubrahmanian 1980). These rocks are crossed by sets of joints and fractures, which have also caused weathering of coarser rocks. The shallow hard and massive rocks are exposed mostly in the southern part. Red sandy soil is obtained in northern and southern parts of the area where black cotton soil occurs in the middle part. The weathered thickness varies from 3.1 to 26.6 m (Mondal and Singh 2011c). Such shallow weathered zones may not be stable sources of groundwater for meeting large demands of groundwater (Singh et al. 2003). There are many lineaments which are oriented mainly in the NNE-SSW, NEE-SWW, and NW-SE directions, but the major lineament is running in the NNE-SSW direction for several kilometers situated northwest of Dindigul along Kodaganar River (see Fig. 1). The weathered zone facilitates the movement and storage of groundwater through a network of joints, faults and lineaments, which form conspicuous structural features. Apart from the structural controls on the groundwater movement, the area is covered with pediment and buried pediment on southern and western sides of the area. The other most dominant formation is the charnokite, which is found in southern and southeastern parts of the Sirumalai hills. This formation is less weathered, jointed or fractured compared to the previous one and can therefore be considered as impermeable (Mondal and Singh 2005).

Groundwater occurs mostly in weathered and fractured zones, which are unconfined, semi-confined or confined (Mondal and Singh 2011b). These aquifer confining conditions may change rapidly and vary over a wide range from place to place. The thickness of weathered/fractured zone varies over even a small region. Shallow aquifers are usually phreatic, which may not be a stable source for meeting large demands on groundwater, but deeper aquifers are partly confined, i.e., they are recharged from shallow unconfined aquifers through dug-cum-bore wells/bore wells as water accumulates in dug wells, percolates into confined aquifers through bore wells which are provided in dug wells.

3.3 Data Collection and Analysis

Monthly rainfall data from the Dindigul rain gauge station (see Fig. 1) was collected for the period of January 1971 to December 2007. During January 1973 to December 2007, the monthly water level data was also collected at 6 Public Works Department (PWD) monitoring wells, which are not used for domestic and gardening uses. The missed water level data at the PWD wells varied from 0.48 % to 3.81 % with an average 2.24 % of total 2100 events, which were calculated using a moving average method (Medhi 2005). Although rainfall distribution in the study area may be non-uniform due to the presence of surrounding hills, undulating topography and other meteorological conditions, it was presumed that rainfall was uniformly distributed throughout the area, because there was only one rain gauge station. The monthly water level data, recorded at 6 monitoring wells for 35 years were considered along with rainfall recorded from Dindigul rain gauge station for analysis. The transformation values for rainfall and depth to water table for these PWD wells were determined. Then, the ratios between transformation of individual wells and marginal entropy of rainfall were calculated for assessing the natural recharge in different hydrological conditions.

Using Remote Sensing (RS) and Geographical Information System (GIS) techniques the Institute of Remote Sensing, Anna University, Chennai, India has also divided the study area into four recharge zones (person. Comm. 2000). These zones are (I) high, (2) moderate, (III) less, and (IV) poor zones for groundwater recharge. The categorization of zones are based on the integration of the different themes viz., geomorphology, geology, hydrological soil group, slope, depth to weathered zone, depth to basement, run-off, water level, land use, drainage density, lineament density, water quality and rainfall. The well areas of PWD 83520 and 83514 (see Fig. 1) are fallen in high and less groundwater recharge zones, respectively. The wells 83029A and 83503 are in moderate whereas poor groundwater recharge zones are found at the wells 83029 and 83515A.

3.3.1 Climate and Rainfall Patterns

Normally, sub-tropical climate prevails over the study area without sharp variations. The temperature increases slowly to a maximum in summer months upto May and after which it drops slowly. The mean of maximum temperature ranges from 36.5°C to 41.8°C and the mean of minimum temperature varies from 17.4°C to 24°C. The season wise normal rainfall values for the period from January 1971 to December 2007 are presented in Table 2. 4.11 % of the annual rainfall precipitated in winter (January and February), 15.77 % in summer (March–May), 31.39 % in Southwest monsoon period (June–September), and 48.73 % in Northeast monsoon period (October–December). As there was only one rain gauge station, the whole study area was considered to be affected by the same rainfall, which was monitored at the Dindigul rain gauge station (see Fig. 1). The average monthly rainfall was showing in four different stretches. More rainfall, however, occurred in the last stretch each year. The average annual rainfall was also estimated to be about 905.3 mm from January 1971 to December 2007 and a linear trend showed that the average annual rainfall was uniform.

Table 2 Season wise normal rainfall at Dindigul rain gauge station (Sothern India)
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3.3.2 Hydrological Provinces

The entire country (India) has been grouped into four main hydrogeological provinces based on the natural recharge values (Rangarajan and Athavale 2000). They are granitic, basaltic, sedimentary and alluvial. The best fit lines, obtained by the least square method, show a linear correlation between seasonal rainfall and natural recharge in each case. This linear relation between rainfall and natural recharge exists for all four major hydrogeological units. The regression equation derived for each of the hydrogeological provinces indicates a certain minimum rainfall requirement to initiate groundwater recharge. The minimum values were 255 mm//year for granite, 355 mm/year for basalt, 220 mm/year for sediments and 40 mm/year for alluvial areas. The average natural recharge value in 15 granitic areas (in India) is 10.11 % of rainfall during rainy season which is estimated by tritium injection technique. The seasonal normal rainfall in the proposed study area was 284.2 mm and 441.1 mm in SW- and NE-monsoons, respectively. Therefore these two seasonal and monthly rainfall values of the entire period were considered for estimation of recharge using entropy and for studying the rainfall influence in the measurement of groundwater recharge, its values > 200 mm and 255 mm were individually considered.

3.3.3 Water Level Fluctuation

The details of PWD well inventory are given in Table 3. All the open wells were rectangular shaped, except for two circular structures with depth ranging from 14.05 to 28.50 m (bgl). The depth to water bearing zone varied from 2.5 m to 3.8 m (bgl) and the thickness ranged from 4.0 to 14.6 m under phreatic conditions. The transmissivity (T) varied from 10 to 140 m2/day, whereas the specific yield (Sy) ranged from 0.002 to 0.004. The well reduced levels varied from 259.499 to 301.045 m above mean sea level (amsl), but the groundwater was measured from the measuring points, which varied from 0.45 to 1.05 m. When water level hydrographs with rainfall data were plotted, there was approximately one month time lag in the response of water table to rainfall events. One typical well hydrograph (at PWD well 83503) and monthly rainfall variation is shown in Fig. 2

Table 3 Well inventory of PWD wells, Southern India in details
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Fig. 2
figure 2

Comparison of water level fluctuation with rainfall at PWD well 83503 (Ambathurai village) from January 1973 to December 2007

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Measured groundwater levels at the 6 PWD wells of the study area in the months of September, October, November, December and January for the years 1974, 1994, 2000 and 2004 corresponding to monthly rainfall are shown in Figs. 3a–d. Depths to groundwater ranged from 6.50 to 18.10 m below the ground surface for the period of September 1974 to January 1975 (Fig. 3a). Median values decreased, which meant water level rose by 0.83 m from 12.23 m in September to 11.46 m in January. For the period of September 1994 to January 1995 depths to groundwater ranged between 1.55 and 13.05 m below the ground surface (Fig. 3b). Median values decreased, which meant the water level rose by 4.25 m from 9.53 m in September to 5.28 m in January. Below the ground surface, depths to groundwater ranged between 5.35 and 18.55 m for the period of September 2000 to January 2001 (Fig. 3c). Medians values also decreased, which meant the water level rose by 4.31 m from 13.98 m in September to 9.67 m in January. Further, the depth to groundwater ranged between 2.65 and 22.05 m (bgl) for the period of September 2004 to January 2005 (Fig. 3d). The median values decreased, which meant the water level rose by 8.00 m in the study area from 15.12 m in September to 7.12 m in January. This rise in the water level coincided with amount of monthly precipitation with 1-month lag in all the above cases (see Fig. 3). It indicates that the water table is responding to rainfall, for natural recharge takes place in the study area.

Fig. 3
figure 3

Ranges of depth to water (DTW) from September to January with monthly rainfall for year (a) 1974, (b) 1994, (c) 2000, and (d) 2004 in the study area

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3.3.4 Cross-Correlation Analysis

For confirming the response of water level at PWD wells, cross-correlation coefficients were determined between the depth to water table and corresponding rainfall for 35 years of data (Grewal 1993). The coefficient values with one-month lag between depth to water level and rainfall at PWD well 83520, 83029A, 83503, 83514, 83029 and 83515A were comparatively higher, which were 0.293, 0.285, 0.232, 0.224, 0.198 and 0.201, respectively. The correlation coefficient values were plotted against the corresponding lags in the water table rise, as shown in Fig. 4. It is seen that all PWD wells responded with one-month lag after the rainfall in this area. Applying cross-correlation analysis to the water table variation in response to rainfall, the following observations were made: (1) The time lag of one-month for the maximum response of unconfined aquifer after rainfall is observed; (2) the amplitude of correlation decreases when lag increases/decreases in a systematic manner; and (3) the depth to the aquifer (see Table 3, column 7) also plays an important role in the delay because of subsurface losses as well as travel time for vertical percolation (Todd 1980). The travel time may vary from a few minutes for shallow water tables in permeable formations to several months or years for deep water tables underlying sediments or weathered zones with low vertical permeabilities.

Fig. 4
figure 4

Plot of cross correlation coefficient in different lags

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Qualitative Recharge Estimates

On the basis of correlation coefficient values from September to February (including wet period) with corresponding response lag for the period of January 1973 to December 2007, a qualitative estimation of groundwater recharge zones of this hard rock area was made. The seasonal normal rainfall was 441.1 mm in the months of October to December. In this period unconfined aquifers are in more suitable condition for natural recharge (Rangarajan and Athavale 2000). High coefficient values indicated good recharge and low value indicated poor recharge. Due to rainfall in the month of October, PWD wells 83520 and 83503 responded in November where the values of correlation coefficients were −0.370 and −0.224, respectively. Well 83029 gave a good response to rainfall in December; the value being −0.147 (in Table 4). The PWD wells 83029A and 83515A responded in January due to rainfall in the month of December, where the values of correlation coefficients were −0.304 and −0.140, respectively. The correlation values indicated the behavior of the recharge response of unconfined aquifers in this area.

Table 4 Correlation matrix corresponding 1-month lag in PWD wells during January 1973 to December 2007
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3.4 Entropy-Based Analysis

In hard rock areas in many countries, such as India, where groundwater occurs in shallow weathered zones, the rise in groundwater table is a direct consequence of rainfall, particularly in the monsoon season, when the groundwater withdrawal is minimum. The rise in water table at a particular place is a characteristic feature of the unsaturated zone (Todd 1980). Therefore, for a particular region, there exists a definite relationship between the depth to water table and rainfall. From an entropy perspective these two variables possess individual information, and some information is transmitted from rainfall to the depth to water table; this transmission of information is referred to as transinformation and can be hypothesized as proportional to recharge. This concept is employed to measure groundwater recharge characteristic or favorable recharge zones and their locations in hard rock terrains.

For computation of information, joint or conditional probabilities were computed using a contingency table for monthly data as well as SW and NE monsoons data. The total 420, 140 and 105 events were used for constructing contingency tables of monthly, SW and NE monsoons data sets, respectively. An illustration of a two-dimensional contingency table for monthly data set of PWD well 83520 is given in Table 5. It was considered that rainfall had a range of values (0–200, 200–400, 400–600 and 600–800 mm) consisting of 4 categories (class intervals), whereas the depth to water table was assumed to have 6 categories (class intervals) with the range of 5.00 m (bgl). The cell density or the joint frequency for (i, j) is denoted by fij, i = 1, 2, …, 4; j = 1, 2, …, 6, where the first subscript refers to the column (rainfall) and the second subscript to the row (water table). The marginal frequencies are denoted by fi. and fj. for the column and the row values of these two variables, respectively. Then the marginal entropies of rainfall and water table, and total entropy were calculated with the aid of the equations (1), (2) and (3). Transinformation, T(x, y), given by the equation (8), was also calculated for each PWD well. For better understanding of marginal, conditional and joint entropies, and transinformation of rainfall and water table are presented graphically at the 83520 well for the period of 1973–2007 as shown in Fig. 5. Then, fractional amount of natural recharge due to rainfall was estimated with the aid of equation (11). The results are presented in Table 6 for the entire months, SW and NE monsoon data. Traninformation entropies vary from 0.007 to 0.025 bits for the monthly data set. In the SW monsoon 0.001 to 0.028 bits of uncertainty reduced in rainfall when depth to water level known in all the wells, whereas comparatively more of 0.034 to 0.112 bits of dependence between rainfall and water table in NE monsoon were observed. It implies that the calculated natural recharge is more dominant during the NE monsoon when the maximum rain occurs. In this period the natural recharge varies from 3.37 % to 11.10 % of rainfall with mean of 6.44 %, but the recharge influence due to the rainfall was a sequential order at all PWD wells for the other periods in the study area. When the rainfall was measured >200 mm (39 events observed from January 1973 to December 2007), the estimated recharge values vary from 3.93 % to 23.93 % of the rainfall, whereas it varies from 4.19 % to 31.68 % for the rainfall of > 255 mm (events: 25 for 35 years) corresponding to the PWD well areas. The estimated recharge proves that the fractional recharge due to rainfall depends on the magnitude, duration and intensity of rainfall. It is noticed that the joint entropies of all wells (see Table 6, column 5) are not systematic in the different periods. It may be due to non-uniformity of precipitation and different well hydrogeological characteristics. If the precipitation is measured at each nearby well corresponding to water table, measurements of natural recharge using this entropy will be more accurate.

Table 5 Absolute frequency contingency table for rainfall (mm) and depth to water table (m, bgl) at PWD well 83520 during January 1973 to December 2007
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Fig. 5
figure 5

T(R, WT): Information common to rainfall (R) and water table (WT); H (R|WT): information only in rainfall; H (WT|R): information only in water table; and H(R, WT): total information only in rainfall and water table together

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Table 6 Estimated natural recharge using entropy for monthly data, SW and NE monsoon data during January 1973 to December 2007
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3.5 Comparison with Recharge Zones Characterized by Remote Sensing and GIS

The study area has divided into four groundwater recharge zones (i.e., high, moderate, less and poor) using RS and GIS techniques. On the basis of estimated cross-correlation coefficients (r) of precipitation to depth to water table with considerable time lag, the well areas were also yielded a good agreement for these recharge zones (see Table 4). They are (I) zones of high recharge for value (r = −0.370), (II) moderate zone for recharge (r: −0.304 to −0.224), (III) zones of less recharge (r = −0.166), and (IV) zones of poor recharge (r: −0.147 to −0.140).

It was difficult to identify the response behavior of unconfined aquifers with coefficient values, because it depends on the combined effect of hydrogeological variables, such as precipitation-related variables (amount, duration, and intensity), stream levels, the thickness and materials of the vadose zone, geometry and properties of aquifer, crops and topography patterns, and bed-rock geology (Moon et al. 2004). The recharge rates of any unconfined aquifer are very site specific (Viswanathan 1983). This means that results obtained at one location may not be applicable to another. The highly favorable recharge zone was found around well 83520 in the Seelapadi village. This area is characterized by bajada, shallow pediment with high weathered (thickness >10 m), hydrological soil group ‘A’ with moderate infiltration characteristics as well as runoff (50–130 mm) with a slope of 3–10 %. Moderate recharge zones were around the A. Vellodu (at well 83029A) and Ambathurai (at well 83503) villages. These zones are characterized by pediment, moderated weathered zone (thickness 12–20 m), hydrological soil group ‘B’ with moderate infiltration rate and runoff (65–80 mm) with a slope of 5–10 %. The area around the Sinthalakundu village (well 83514) is less favorable for groundwater recharge. This is characterized by hydrological soil group ‘C’ with less runoff (75–95 mm) and a slope of <3 %. The poor condition for recharge zone existed only for hills and PI complex having less thickness (<20 m) of weathered chances zones within hydrological soil group ‘D’ having poor infiltration rate and runoff (>130 mm) with a slope of >15 % in A. Vellodu (at well 83029) and Dindigul town (at well 83515A).

Using tritium injection method the estimated average natural recharge ratio is about 10.11 % of seasonal rainfall for 15 granitic and gneiss areas in varying climatic and hydrogeological provinces in India (Rangarajan and Athavale 2000). Out of them, the average recharge ratio is about 9.90 % for four different granitic and gneiss areas in Tamil Nadu state of Southern India. The estimated natural recharge using entropy with the existing data varies from 1.41 % to 8.03 %, 0.35 % to 9.79 %, and 3.37 % to 11.10 % in the entire period, SW and NE monsoons, respectively, in the study area. But the mean of these six recharge values estimated was 6.44 % of rainfall in NE monsoon (see Table 6). This table shows that the estimated natural recharge at all PWD wells yields a good agreement with the results obtained from RS and GIS methods in each period, which are in sequential order corresponding to the demarcated groundwater recharge zones, classified from the transinformation values between precipitation and water table. The estimated recharges prove that the fractional recharge due to rainfall depends on the duration and intensity of rainfall. It is noticeable that the joint entropies of all wells are not systematic manner in the different periods. It may be due to non-uniformity of precipitation and different hydrogeological setup in well areas. If the precipitation is measured at each nearby well corresponding to water table, measurements of natural recharge using entropy will be more accurate at smaller and larger scales.

4 Conclusions

An entropy-based approach is developed for assessing natural groundwater recharge and it has applied in unconfined aquifers from Southern India. From this study it is concluded that the natural recharge (a fractional amount of rainfall) is a ratio of transinformation between rainfall and depth to the water table, and marginal entropy of rainfall. The estimated natural recharge using this entropy varies from 3.37 % to 11.10 % during NE monsoon with an average of 6.44 %. The estimated recharge at the PWD open wells yields a good agreement with the results obtained from RS & GIS techniques in each period, which are in sequential order corresponding to the demarcated groundwater recharge zones.

Thus entropy is a potential tool for assessing natural groundwater recharge and recharge potential zones using measured water table and rainfall in any geological formations under any meteorological conditions at a glance.