ORIGINAL ARTICLE

Modeling of groundwater recharge using a multiple linear

regression (MLR) recharge model developed from geophysical

parameters: a case of groundwater resources management

Kehinde Anthony Mogaji Hwee San Lim

Khiruddin Abdullah

Received: 16 January 2014 / Accepted: 19 June 2014

Springer-Verlag Berlin Heidelberg 2014

Abstract In this paper we developed a simple multiple

linear regression (MLR) recharge model that relates the

recharge estimates obtained from rainfall to the geophysi-

cal parameters obtained from the interpretation of two-

dimensional (2D) resistivity imaging data for the purpose

of efficient groundwater resources management in the

southern part of Perak, Malaysia through recharge rate

estimation and prediction. Through application of linear

regression model, the estimated recharge from rainfall and

the corresponding estimated unsaturated layer resistivity

and its thickness (Depth to aquifer top) parameters

obtained from geophysical measurements were regressed in

R software written code environment for generating a MLR

recharge model. The sensitivity of analyzed results of the

MLR recharge model based on the parameter estimation of

the model predictors (resistivity and depth) evaluated at

Pr B 0.05 is 5.39 9 10-06 and 8.39 9 10-04, respectively.

The accuracy and predictive power test conducted on the

developed model using both t test and v2 distribution at

a = 5 % significance level established the model estima-

tion and prediction capability. The obtained results of v2

distribution test and parameters estimation test confirmed

the reliability and accuracy of the proposed model in

recharge rate estimation and prediction in the area. The

application of the MLR recharge model gives estimate of

242.30 mm/year for regional groundwater recharge rate in

the area. Through GIS tool, the MLR recharge model was

used to produce groundwater recharge rate prediction map.

A quick and independent estimate of recharge by simple

geophysical measurement has been established based on

these results. The information on the prediction map could

serve as a scientific basis for groundwater resources man-

agement and exploration in the area. The approach suggests

a new application of geoelectric parameters in determining

recharge rate due to infiltration. The technique provides a

good alternative to other methods used for this purpose.

Keywords Multivariate regression recharges model

Groundwater recharge prediction 2D resistivity imaging

Geophysical parameters 2D resistivity imaging Hydrogeological

Introduction

The management of groundwater resources requires a

method to accurately calculate groundwater recharge rates

either on local scale or regional scale. As emphasized in the

studies according to Jyrkama and Sykes (2007) and Kaliraj

et al. (2014), the understanding of groundwater recharge is

fundamental to the management of groundwater resources.

In addition, for an effective watershed management strat-

egy, the quantification of groundwater recharge is vital in

ensuring the protection of groundwater resources from an

unavoidable climate change impact and other stresses like

industrial revolution, urbanization, etc. (Robins 1998).

Moreover, it has also been reported in the study of Nolan

et al. (2007) that recharge is a major component of the

K. A. Mogaji

Department of Applied Geophysics, Federal University

of Technology, P.M.B. 704, Akure, Nigeria

K. A. Mogaji (&) H. S. Lim K. AbdullahSchool of Physics, Universiti Sains Malaysia,

11800 Georgetown, Penang, Malaysia

e-mail: mogakeh@yahoo.com

H. S. Lim

e-mail: hslim@usm.my

K. Abdullah

e-mail: khirudd@usm.my

123

Environ Earth Sci

DOI 10.1007/s12665-014-3476-2

groundwater system as well as its importance in shallow

groundwater quality evaluation. The situation and fluctua-

tion of groundwater quantity measurement required for an

exploitation of optimal groundwater resources are largely a

function of rate of groundwater recharge (Kumar 1977;

Omorinbola 2009). This was recently corroborated in the

study according to Gontia and Patil (2012), where it was

reported that locating groundwater potential zones for

groundwater resource development not only is enough to

salvage potable water resources supply demands for

domestic, agricultural, industrial, and other purposes, but

also requires quantifying the natural and artificial recharge

rates of an area of interest. Therefore, in lieu of sustaining

these precious natural resources, several studies have

emphasized on the estimation of groundwater recharge to

the aquifer system as very essential for the proper man-

agement of resources (Chandra et al. 2004; Leipnik and

Loaiciga 2006). However, according to Kumar and

Seethapathi (2002), in evaluation of groundwater resour-

ces, the rate of aquifer recharge is one of the most difficult

factors to measure and as such aquifer recharge rate esti-

mation by any other method is always characterized with

uncertainties and errors. This was due to the fact that

recharge variable is a complex function of multiple factors

such as meteorological conditions, soil, vegetation, phys-

iographic characteristics, and properties of the geologic

material within the paths of flow (Kumar and Ish 2012).

Besides, topography which is a factor that exerts more

influence on groundwater flow direction cannot be over-

emphasized in determining the rate of recharge of an area

(Akpan et al. 2013; Doumouya et al. 2012). Thus, an

approach that can reliably estimate and reduce uncertainty

in recharge rate estimation and prediction is needed.

Numerous studies have estimated groundwater recharge

rate via conventional methods such as water balance,

Darcian approach, lysimeter, water table fluctuation,

numerical simulation, etc. (Simmers 1998; Scanlon et al.

2002; Nimmo et al. 2005). The limitation of these prior

methods is their inadequacy in analyzing large volumes of

hydrological data including precipitation, surface runoff,

evapotranspiration, etc. over a considerable time span as

reported in the study of Chandra et al. (2004). On the other

hand, considering the different mode of recharge, the out-

put of these aforementioned methods are limited for

regional scale application. Though, according to the report

of Izuka et al. (2010), the potentials of geographic infor-

mation system (GIS) have been explored in enhancing the

capability of some analytical methods, including soil water

budget for estimating the rate of groundwater recharge at

any spatial scale. However, this latter approach still

requires the input of large and diverse spatial data sets that

may not be available for regions under investigation or

period of interest. Exploring an empirical model that uses

the available data that are applicable for both local and

regional scales recharge estimate is the quest of this study.

According to Kumar (2000), empirical method can be used

to conveniently estimate groundwater recharge rate from a

few input variables that are relatively easy to obtain for

most regions. As such, the usefulness of empirical methods

in estimating groundwater recharge rate using the basic

theory of regression model has been documented in the

studies of Gontia and Patil (2012), Nolan et al. (2007),

Shuy et al. (2007), Chandra et al. (2004), and Rangarajan

and Athavale (2000). In accordance with the previous

studies including Misstear et al. (2009), Xi et al. (2008),

Kumar and Seethapathi (2002) and Rangarajan and Atha-

vale (2000), the precipitation/rainfall variable was used as

the major input variable in the adopted rainfall recharge

model for the estimation of recharge rate in the investi-

gated area. Consequently, this study will explore the con-

cept of estimating recharge rate from precipitation/rainfall

data of the area using the rainfallrecharge relationship

model applicable for the area (Gontia and Patil 2012;

Yusoff et al. 2013). The determined recharge values will be

correlated with the interpreted geoelectric parameters

obtainable in the area. A multiple linear regression (MLR)

equation where the computed recharge rates (dependent

variable) and the interactive model regression between the

geoelectric parameters (layer resistivity and layer thick-

ness) (independent variables) will form the underlying

recharge model. However, to actualize this objective,

detailed geophysical survey for hydrogeological evaluation

must be carried out.

The determination of geoelectrical parameters for

hydrogeological evaluation can only be mapped by sub-

surface investigation. The usefulness of the non-invasive

geophysical prospecting methods in delineating subsurface

layers and determining their geoelectric parameters has

been documented in the studies of Aizebeokhai et al.

(2010), Mogaji et al. (2011), and Oladapo et al. (2009).

Establishing also from the Mohamed et al.s (2012) report,

the geophysical techniques together with geological tech-

niques have gained widespread acceptance in groundwater

exploration. As such, previous researchers have exploited

geoelectrical method among others to quantitatively esti-

mate the water-transmitting properties of aquifers,

groundwater recharge, and so on (Mufid al-hadithi et al.

2006; Louis et al. 2004; Chandra et al. 2004; Cook et al.

1992; Barker 1990). In addition to this, the direct-current

(DC) electrical resistivity method has been reported by

researchers as a very powerful and cost-effective technique

in groundwater studies (Rubin and Hubbard 2005; Koef-

oed 1979; Jupp and Vozoff 1975). The lithological prop-

erties including resistivity, depth to water table, soil types,

water content, etc. which influence groundwater flow and

percolation to subsurface were easily mapped with this

Environ Earth Sci

123

geoelectrical method as emphasized in the priors studies.

The 2D resistivity imaging technique of geoelectrical

method which has been applied in various domains of

groundwater studies including groundwater pollution (Is-

lami et al. 2012; Bahaa-eldin et al. 2011), salinity mapping

(Pujari and Soni 2009; Sathish et al. 2011), aquifer

potential mapping (Asry et al. 2012; Ewusi et al. 2009),

and aquifer parameter estimation (Niwas et al. 2011) was

efficiently explored for the used geophysical data in those

studies. However, little research has been conducted

exploring geophysical data in groundwater recharge rate

estimation such as the works according to Mufid al-hadithi

et al. (2006) and Chandra et al. (2004). The determined

geophysical parameters from the surface electrical method

acquired in those studies were correlated with the esti-

mated recharge rates in the investigated area via regression

analysis. The application of regression model analysis in

modeling recharge equations has also been documented in

studies according to Nolan et al. (2007), Izuka (2006) and

Shuy et al. (2007) with appeal results. The output of their

recharge models is feasibly useful to provide independent

estimates of recharge.

In this study, we proposed modeling groundwater

recharge on regional scales by correlating the estimated

recharge rate due to rainfall with multiple lithological

parameters (layer resistivity and layer thickness) derived

from geophysical data. The empirical method was exploited

to develop the proposed multiple linear regression (MLR)

recharge model that can allow interactive modeling of

multiple factors that are significant for modeling recharge

rate with reasonable certainty. The proposed MLR recharge

model is different from the previous empirical approaches,

such as those of Chaturvedi (1973) and Kumar and

Seethapathi (2002), where recharge estimation was done

from rainfall data but lithological control on recharge was

ignored. Although, Mufid al-hadithi et al. (2006) and

Chandra et al. (2004) considered lithological control mea-

sures, however, the interactive significance of multiple

factors is overlooked. In our proposed MLR recharge

model, the recharge model depends simultaneously on two

factors namely resistivity of the material composition of

vadose zone and its thickness which is accordance with the

reports of the studies of Wang et al. (2008) and Nolan et al.

(2007). The developed MLR recharge model can yield more

reliable groundwater recharge rate estimates than the con-

ventional methods. The proposed model may be applicable

in any other areas with similar geology.

Materials and methods

Geography, hydrology, and hydrogeology of the study

area

The study area is situated between the boundary of Perak

and Selango in Peninsular Malaysia. Figure 1 presents the

Fig. 1 Location of the study area in Peninsular Malaysia

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123

2,884 km2 study area showing other important features.

The site lies between longitudes 10100E and 101400E and

between latitudes 3370N and 4180N in the southern part

of Perak. The area has four major rock types, namely,

QUA: Quaternary (mainly recent alluvium), DEV: Devo-

nian (sedimentary rocks), SIL: Silurian (sedimentary rocks

with lava and tuff), and ING: acidic and undifferentiated

granitoids (Fig. 2). The region is characterized by an

equatorial maritime climate with nearly uniform air tem-

peratures throughout the year. The average daily temper-

ature is approximately 27 C, and relative humidity has a

monthly mean value of 62 and 78 % for the dry period and

peak of the rainy season, respectively. The regional topo-

graphic elevation variation in the area is in the range

792,131 m as extracted from the world topo map. The

general annual precipitation in Perak state ranges from 830

to 3,000 mm. However, the daily records of rainfall

amount for several locations within the study area for

periods of 10 years (20002010) were extracted from the

Tropical Rainfall Measuring Station (TRMM) database

acquired at 0.25 resolution (0.25) using MatLAB soft-

ware and analyzed for this study (see Table 1).

2D resistivity imaging data acquisition, processing,

and interpretation

The 2D resistivity imaging data acquisition was carried out

with the use of modern field equipment, ABEM SAS 4000

which is a multi-electrode resistivity meter system highly

suitable for high-resolution 2D resistivity surveys. The

established 30 survey lines cutting across the diverse

geological settings in the area (see Table 2; Fig. 2) were

combed using both WennerSchlumberger array and Sch-

lumberger array with the ABEM SAS 4000 system. Data

were recorded automatically along the profile at the elec-

trode stations. The obtained data on each profile were

processed and inverted using the RES2DINV software

developed by Loke and Barker (1996). The software uses a

least squares optimization technique to invert the 2D-

acquired apparent resistivity pseudosections to define true

resistivity distribution in the subsurface (Loke 2004; Sasaki

1992). Least squares optimization minimizes the square of

the differences between the observed and the calculated

apparent resistivity values. The program automatically

creates a 2D model by dividing the subsurface into rect-

angular blocks (Loke 2004), and the resistivity of the

blocks is iteratively adjusted to reduce the difference

between the measured and the calculated apparent resis-

tivity values. The program calculates the apparent resis-

tivity values and compares these to the measured data.

During the iteration, the modeled resistivity values are

adjusted until the calculated apparent resistivity values of

the model agree with the actual measurements. The itera-

tion is stopped when the inversion process converges (i.e.,Fig. 2 Geological map of the area showing the rock types and 2D

locations

Table 1 The estimated average annual rainfall amount and recharge

rate estimated in the area

Loc nos Latitude Longitude Estimated average

rainfall amount

(mm/year)

Estimated

recharge rate

(mm/year)

1 418242.6 735417.6 1,382 249.66

2 428841.4 735594.2 1,082 220.59

3 455868.3 742483.4 2,083 307.03

4 460107.8 745663.1 829 192.7

5 511511.9 735770.9 1,294 241.5

6 401637.8 762974.4 1,430 254

7 429018.4 763504.4 1,150 227.51

8 456574.9 763327.7 2,161 312.77

9 467173.7 763857.7 920 203.17

10 511865.2 763151.1 1,315 243.47

11 414179.7 783818.7 1,510 261.08

12 429371.3 786097.0 1,248 237.12

13 453218.6 781168.0 2,168 313.28

14 461344.3 775516.3 992 211.09

15 511688.6 790707.9 1,345 246.26

Environ Earth Sci

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either when the root mean square error falls to acceptable

limits or when the change between RMS errors for con-

secutive iterations becomes negligible). However, before

the geoelectric parameters were determined, the subsurface

layers were first delineated. It should be noted that the

boundary of lithology units in the subsurface is fuzzy in

nature where there is no clear demarcation boundary to

define the extent of each underlying lithologies as depicted

by the inverted 2D imaging sections (see Fig. 3). One of

the efficient technique of salvaging this challenge and

correctly interpreting these 2D imaging sections is by

constraining them with an in situ hydrogeological data

measurement obtainable from borehole logs. Hence, the

litho-logs of the available boreholes drilled within the

vicinity or on the 2D profiles were used as constraints that

guided the interpretation of the inverted 2D sections. We

achieved this by studying and interpreting the logs con-

sidering the borehole log description and Gamma log

lithology description for the various subsurface layers

mapping at varying depths. Thereafter, the subsurface

parameters such as resistivity of the overburden layer

(Unsaturated layer) and its thickness (Depth to aquifer top)

were determined. The delineated overburden layer is

regarded as the vadose zone (Unsaturated layer) in this

study. Since the geology of the study area is largely het-

erogeneous, the unsaturated (vadose zone) layers in most

cases are multilayered as depicted by the 2D sections

where resistivity section labeled (a) is located at 12; (b) is

located at 19; (c) is located at 9; (d) is located at 14; (e) is

located at 11 and (f) is located at 29. The resistivity of the

vadose zone (overburden layer) was estimated by first

saving the 2D section in XYZ format where the Z repre-

sents the resistivity parameters at varying depth Y.

Thereafter, the mean of the multilayered resistivity values

was estimated with reference to the depth Y of the

delineated aquifer top. Typical examples of the inverted 2D

resistivity sections showing various subsurface strata are

presented in Fig. 3af.

The interpretation shows that resistivity of the unsatu-

rated layer in the area varies from 7 to 2,301 Xm. The

depth to aquifer top is also in the range 273 m (see

Table 3). The large variation in resistivity of the unsatu-

rated layer generally indicates the varying nature of this

layer. These results suggest that there is existence of var-

ious heterogeneities which typifies the presence of linea-

ments, intrusive, differential weathering, fractured rocks,

and changes in the mineralogical composition of the rocks

constituting this soil formation column (Ewusi et al. 2009;

Chandra et al. 2008). The delineated unsaturated layer

which is a regolith column of soil formation lying just over

the aquifer has direct bearing on the moisture flux move-

ment or recharge to aquifer. Hence, its lithological prop-

erties namely resistivity and depth to aquifer top as

discussed above were determined to remodel the ground-

water recharge rate in the area.

Recharge estimation

The recharge rate estimation due to rainfall was carried out

using an existing model equation. This was done using one

of the empirical models of groundwater recharge namely the

UP Irrigation Research Institute, Roorkee (1954) [Cha-

turvedi formula] documented in Gontia and Patil (2012)

study. The ad hoc approach used by Yusoff et al. (2013) was

adopted to modify the renowned Chaturvedic formula to be

applicable in tropical zones area. The modification is in

agreement with the report of Kumar and Seethapathi (2002)

who said that this equation can be suitably altered for a

specific hydrogeological condition. The modified version of

the Chaturvedi formula is expressed as

R 6:75 P 14 0:5 1

where R is the recharge due to precipitation during the

year, and P is the annual precipitation. Based on Eq. (1),

which can be referred as a rainfallrecharge model, the

recharge rate within the area was estimated and presented

in Table 1. Thereafter, the results of the estimated recharge

rate at various locations in Table 1 were processed with

kriging interpolation technique in GIS environment to

produce the potential recharge map shown in Fig. 4.

Table 2 Summary of geophysical survey

Survey line Geology Array-type used

Loc 7, Loc 12, Loc 17, Loc 18 Loc 22, Loc24 and

Loc 23

QUA: Quaternary (mainly recent

Alluvium)

Wenner-Schlum and Schlumberger a = 5.0 m

e = 200 m, 400 m, d = 40 m, 80 m

Loc 19, Loc 20 Loc 21 Loc 25 and Loc 26 DEV: (sedimentary rocks) Wenner-Schlum and Schlumberger, a = 5.0 m,

e = 200 m, 400 m d = 40 m, 80 m

Loc 1, Loc 2, Loc 5 Loc 8, Loc 9, Loc 10, Loc 11,

Loc 13, Loc 15 and Loc 16,

SIL: (sedimentary rock with

associated lava and tuff)

Wenner-Schlum and Schlumberger a = 5.0 m,

e = 200 m, 400 m d = 40 m, 80 m

Loc 3, Loc 4, Loc 6, Loc 14, Loc 27, Loc 28 Loc 29

and Loc 30

ING: Igneous rock (granitoid) Wenner-Schlum and Sch lumberger, a = 5.0 m,

e = 200 m, 400 m d = 40 m, 80 m

a The electrode spacing, e the spread length, d the expected depth

Environ Earth Sci

123

Unsaturated layer

Vadose zone

Aquifer layer

Aquifer layer Vadose zone

Unsaturated layer

Aquifer layer

Vadose zone

Unsaturated layer

a

b

c

Fig. 3 Examples of 2D sections showing how geoelectrical layers were delineated

Environ Earth Sci

123

Geoelectric parametersrecharge relationship

To establish the influence of lithology control on the rate

of recharge due to rainfall, a relationship between the

recharge rate estimated and the determined geoelectric

parameters was established. Based on GIS analysis, the

actual estimated recharge rate and the corresponding

interpreted geoelectric parameters obtained for each 2D

Aquifer layer Unsaturated layer

Vadose zone

Aquifer layer

f

Aquifer layer

Unsaturated layer

Vadose zone

Unsaturated layer

Vadose zone

e

d

Fig. 3 continued

Environ Earth Sci

123

resistivity location within the study area were deter-

mined. The results of the estimated recharge rate and the

corresponding geoelectric parameters values are presented

in Table 3. The obtained results in Table 3 were used to

generate linear graphs showing relationship of the esti-

mated recharge values versus the unsaturated layer

resistivity values and thickness of the unsaturated layer

(depth to aquifer top) as shown in Fig. 5a, b. However, it

is important to note that we log the resistivity variable in

the regression equations, because the measured resistivity

values in the subsurface are often changes from low

magnitude to high magnitude. Besides, the complexity of

the subsurface is non-linear and requires the use of non-

linear equation to resolve the subsurface features cor-

rectly (Loke 2014). Therefore, computing the log values

of the measured resistivity data is to enhance the linear

scaling representation of the resistivity data.

Multiple linear regression (MLR) recharge model

Consider the following generalized multiple linear regres-

sion model:

Y b0 b1x1 b2x2 bnxn i 2

where b0 is the intercept; b1 and b2 are the slopes of the

regression line with x1 and x2, respectively; i is the error

terms; and Y is the dependent variable (response) as

reported in Koutsoyiannis (1977).

The estimated recharge (RE) values using the rainfall

recharge model (Eq. 1) were used as the dependent

Table 3 Results of the

estimated recharge rate and the

corresponding geoelectric

parameters

2D Loc. no Easting Northing Geoelectrical parameters Recharge estimate

Resistivity of

unsaturated

layer (Xm) q

Depth to aquifer

top (m) [D]

Recharge values

(mm/year) [RE]

Loc 1 4.1,878 101.2168 94 9 211.95

Loc 2 4.2064 101.2983 178 2 237.43

Loc 3 4.2270 101.3820 50 3 203.57

Loc 4 4.1920 101.4540 126 13 225.27

Loc 5 4.0869 101.2458 445 4 257.98

Loc 6 4.1180 101.4180 1,202 35 278.37

Loc 7 4.0280 101.1338 359 15 256.61

Loc 8 4.0490 101.2376 391 20 259.48

Loc 9 4.0690 101.2416 472 25.1 258.62

Loc 10 4.0390 101.2956 559 18 265.39

Loc 11 4.0323 101.3675 645 23 243.03

Loc 12 3.9549 101.2017 219 15.4 252.88

Loc 13 3.9519 101.3629 363 15.7 250.04

Loc 14 3.8920 101.5230 201 14 251.08

Loc 15 3.7401 101.4558 355 18 242.57

Loc 16 3.7160 101.4830 334 15 247.14

Loc 17 3.7176 101.3295 408 15 228.37

Loc 18 3.6840 101.3070 312 15 260.04

Loc 19 3.8720 101.2740 222 9 243.24

Loc 20 3.7230 101.2340 316 15 243.93

Loc 21 3.7720 101.3040 180 11 255.37

Loc 22 3.9200 101.1440 86 12 245.45

Loc 23 3.7652 101.1270 7 73 248.96

Loc 24 3.8857 101.1078 251 20 221.83

Loc 25 3.9841 101.2658 532 12 250.54

Loc 26 3.7730 101.5817 141 6.2 257.9

Loc 27 3.8661 101.3327 562 25 233.99

Loc 28 4.0462 101.4455 562 38 267.85

Loc 29 4.0747 101.5551 2,301 5 301.74

Loc 30 4.1921 101.4984 95 5.7 220.19

Environ Earth Sci

123

(response) variable for the development of multiple linear

regression model in this study. The combination of resis-

tivity of unsaturated layer (q) and thickness of the unsat-

urated layer (depth to aquifer top, D) was used as the

independent (predictors) variables.

Therefore, the multiple linear regression model in the

present phase is expressed as

RE b0 b1 log10 q b2 D i: 3

The coefficients b0, b1 and b2 were determined through

interactive model regression analysis of the records in

Table 3 using R software. From the interactive model

regression analysis, b1 = 25.83, b2 = 0.57 and b0 =

175.12 and R2 = 0.84 are obtained. By substituting the

obtained results in Eq. (3), the RE model becomes

RE 175:12 25:83 log10 q 0:57 D : 4

Equation (4) is a multiple linear regression (MLR)

equation having (RE) as the dependent variable and (q) and

(D) as the multiple independent variables. Based on the

submission of Mazac et al. (1985) reported in the study

according Mufid al-hadithi et al. (2006), Eq. (4) is referred

to as a model. Hence, Eq. (4) is established as the multiple

linear regression (MLR) recharge model developed for the

study area.

Results and discussion

Sensitivity analysis result of the developed MLR

recharge model

The sensitivity analysis carried out on the developed MLR

recharge model enabled parameters significance evalua-

tion. This analysis was carried out using the R software.

Table 4 presents the parameters evaluation results of the

developed MLR recharge models. This is in line with the

view of evaluating the essentiality of the independent

variables (predictors) in modeling the recharge estimate in

the area. The results in Table 4 show that the evaluated

resistivity and depth parameters have a significant rela-

tionship to the response variable (RE) at Pr B 0.05 (5 %)

in the area. This implies that the significance of both

predictors (resistivity of unsaturated layer q) and thickness

of the unsaturated layer (depth to aquifer top, D) at

probability Pr C 95 % can explain the RE in the MLR

recharge model (Eq. 4). Beside this, the computed statis-

tically t test at a = 0.05 for both q and D gives the results

of the calculated values to be 9.27 and 7.09 representing

the predictors, respectively, which are lesser compared to

the tabulated values of 18.49. The latter results also con-

firmed the significance of the considered predictors in the

recharge model (Eq. 4). Hence, the considered geoelec-

trical parameters of varying influences and their interac-

tive effect on recharge due to rainfall are significant for

estimating and predicting recharge rate in the study area.

This finding is in agreement with the reports of the studies

of Kumar and Ish (2012), Wang et al. (2008), and Nolan

et al. (2007). The RE model can reliably be used for

estimating and predicting recharge rate in the area if the

required geoelectric parameters in the study area are

known.

Appraisal of model prediction accuracy

The predictive power of the developed MLR recharge

model needs to be apprised to determine the feasibility of

using the RE model to predict and estimate groundwater

recharge in the area. Neil (1990) and Koutsoyiannis (1977)

suggested a systematic measure of accuracy for any fore-

cast obtained from a model. This measure is called the

Theil inequality coefficient, which is given by

K X

n

l1

yi y^

y^

0

@

1

A

2

5

where yi is the actual estimated recharge rate observed in

the area, y is the corresponding predicted recharge rate of yifrom the RE model (see Table 5), and K the Theil

inequality coefficient.

Fig. 4 Spatial distribution of recharge estimate using UPRI ground-

water recharge model

Environ Earth Sci

123

Equation (5) was used to measure the prediction accu-

racy of the RE model. The determined Theil inequality

coefficient K value was then gaged by the critical value of

v2p; a, where P = n - 1, n is the number of occupied 2D

locations, and a at 5 % significance level. The smaller the

value of K compared with the v2-tabulated value, the better

the prediction accuracy of the model under investigation

(Neil 2003). The accuracy appraisal result of the MLR

recharge model is shown in Table 6. The result obtained

confirmed the reliability and accuracy of using the RE

model to predict groundwater recharge in the non-investi-

gated part in the area. Therefore, the output of this recharge

rate predictive model can be harnessed for groundwater

resources evaluation and management in the study area.

Groundwater recharge rate estimation using the MLR

recharge model

The MLR recharge model in Table 6 was used to estimate

the mean groundwater recharge rate in the area. The

obtained result of the mean regional groundwater recharge

rate in the area was estimated to be 242.30 mm/year.

Thereafter comparisons of this result with the mean

groundwater recharge rate results obtained with the

y = 1.1725x + 227.5

R2 = 0.6477,R=0.8048

150

170

190

210

230

250

270

290

310

330

Depth to aquifer top (m)

Es

tim

ate

d r

ec

ha

rge r

ate

(m

m/y

r)

y = 37.556x + 156.59

R2 = 0.7541, R=0.8684

150

170

190

210

230

250

270

290

310

0 10 20 30 40 50 60 70 80

0 0.5 1 1.5 2 2.5 3 3.5 4

Log resistivity of unsaturated layer (Ohm-m)

Es

tim

ate

d r

ec

ha

rge r

ate

(m

m/y

r)

a

b

Fig. 5 Linear relationships

between recharge rate and

geophysical parameters

Table 4 Parameter estimation analysis of the developed multiple linear regression (MLR) recharge model developed in the area

Developed recharge model Parameters Standard error and parameters significance testing using

standard value of a at 5 % significance level

Remark: parameters

significance OK

at Pr\ 5 %t value Pr ([i tj j) value

RE 175:12 25:83 log10 q 0:57 D q 4.5746 5.39 9 10-06 OK

D 3.757 8.39 9 10-04 OK

q Resistivity of unsaturated layer (Xm), D depth to aquifer top (m)

Environ Earth Sci

123

rainfallrecharge relationship in Eq. (1) were analyzed.

The comparison result shows that an underestimation of

*5.78 mm/year was observed in the model (Table 1). This

difference may be due to the fact that the rainfallrecharge

model did not account for lithological factors in the model.

The use of recharge model that can simultaneously

integrate the influences of multiple factors that have direct

bearing on moisture flux movement or recharge to aquifer

is thus established in this study with intrinsic property of

evaluating recharge rate with reasonable certainty.

Modeling groundwater recharge prediction

with the MLR recharge model

Based on the records in Table 5, the predicted recharge rate

from the MLR recharge model was interpolated using

Kriging technique to produce the recharge rate prediction

map of the area (Fig. 6). It was observed from the model

map that the recharge rate for the study area varies between

199.81 and 303.55. The visual interpretation of Fig. 6 using

the legend zoning classes values shows that the eastern arm

of the area is mostly characterized with moderately high

recharge rate with few isolated patches of high, moderate

and moderate to low recharge rate. However, the areas with

moderate and few isolated patches of low to moderate and

moderately high recharge rate cover the southeastern parts

of the area. The western part and the central are mostly

covered with moderate and patches of moderately high

recharge rate. Whereas, the northern arm is found to be

overlain mostly with moderate to low and a noticeable low

Table 5 The records of the actual estimated recharge rate and the

predicted recharge rate

2D location

nos

Actual estimated

recharge rates observed

in the area yi

Predicted recharge

rates from the

RE model (y)

1 211.95 231.22

2 237.43 234.38

3 203.57 220.74

4 225.27 236.77

5 257.98 245.81

6 278.37 274.63

7 256.61 249.67

8 259.48 253.48

9 258.62 256.35

10 265.39 260.80

11 243.03 250.19

12 252.88 251.25

13 250.04 251.10

14 251.08 248.09

15 242.57 240.86

16 247.14 248.25

17 228.37 231.93

18 260.04 258.49

19 243.24 244.34

20 243.93 243.16

21 255.37 248.86

22 245.45 239.64

23 248.96 248.51

24 221.83 199.80

25 250.54 252.37

26 257.9 260.40

27 233.99 234.19

28 267.85 267.81

29 301.74 303.57

30 220.19 229.45

Table 6 MLR recharge model prediction accuracy analysis

S/n Proposed MLR

recharge models

Nos of 2D

locationsv2p; a 5% K value

1 RE 175:12 25:83 log10 q 0:57 D

30 17.70 0.000423

q Resistivity of unsaturated layer (Xm), D depth to aquifer top (m)

Fig. 6 Groundwater recharge prediction map of the area produced

from MLR recharge model

Environ Earth Sci

123

recharge rate. The moderately high to high recharge rate

zones in the area are observed to be characterized by the

presence of porous and permeable unsaturated columns as

indicated by the layer resistivity. On the other hand, the

low to moderately recharge rate areas could be attributed to

the presence of hardpan or high clay content in a highly

weathered/low-resistive unsaturated layer. By hydrogeo-

logical implication, any aquifer units found associated with

moderately high to high recharge rate zones will be greatly

recharged for high groundwater potential due to direct

rainfall infiltration. Conversely, the aquifer units associated

with very low to moderate recharge rate zones can only be

potentially accumulated through indirect recharge from the

sources like stream, topographic depression, and spring for

producing good groundwater potential in the area (De

Vries and Simmers 2002). However, the very low to

moderate recharge zones are area characterized with high

protective capacity against impending groundwater con-

tamination compared to the moderate high to high recharge

rate zones. Therefore, in terms of shallow groundwater

aquifers, the groundwater quality will be more protected in

the very low to moderate recharge zones area and vice

versa for other zones. Hence, the produced groundwater

recharge rate prediction map (Fig. 6) is a viable tool for

monitoring assessment of groundwater quality status which

can enhance groundwater resources management in the

area. In summary, the study area is underlain by both

unconfined and confined aquifers where water can mostly

be potentially accumulated through direct and indirect

modes of recharge (Scanlon et al. 2002; Nolan et al. 2007).

Although, the accuracy of the developed recharge model is

site specific; however, it can be reliably applied for

recharge rate assessment in other areas of similar geology

for the purpose of groundwater resources exploration and

management.

Conclusion and future works

In this study, groundwater recharge rate assessment was

adequately evaluated on regional scale using a developed

MLR recharge model. The newly proposed recharge model

was based on relating recharge estimated from a rainfall

recharge model to geoelectric parameters interpreted from

2D resistivity imaging acquired in the area. Sensitivity and

prediction accuracy analyses of the newly proposed models

using t test and v2 distribution at a = 0.05 significance

level were conducted using R software. The MLR recharge

model was used to estimate recharge rate and to produce

groundwater recharge rate prediction map using GIS

techniques for the area. The regional recharge rate in the

area was estimated to be 242.30 mm/year. The regional

groundwater recharge rate prediction map produced

provided an excellent insight into assessing the varying

susceptibility of the underlain aquifers to potentially

recharge as well as its vulnerability to pollution in the area.

The information on this prediction map can serve as a

scientific basis for groundwater resource exploration and

management in the area. Furthermore, the proposed MLR

recharge model which was developed with variables from

multifaceted geologic settings can be used in any area with

similar geology for groundwater resource potential evalu-

ation and groundwater quality status monitoring if the

required geoelectrical parameters are known.

Compared with other recharge estimation models, the

approach used in this study can provide a quick, indepen-

dent, and cost-effective estimation of recharge by simple

geophysical measurement. Despite the advantages of the

proposed model, its recharge estimates should still be

corroborated by estimates from other methods because

multiple techniques are highly recommended in the esti-

mation of any groundwater recharge. However, further

improvement on the accuracy of the MLR recharge model

can be achieved if the RE component of the model which

was obtained basically from climate data is re-evaluated

from a natural groundwater recharge in situ measurement

using an injected tracer technique in the area. In the same

hand, more predictor variable can be evaluated by carrying

out a survey to determine the water-level fluctuation

measurement from groundwater wells in the area at two

different seasons. Such water-level fluctuation parameter

which has a direct relationship with recharge rate of an area

can form an additional independent variable component of

the model to enhance the future accuracy output of this

recharge model.

Acknowledgments This project was carried out using the financial

support from RUI, Investigation Of The Impacts Of Summertime

Monsoon Circulation To The Aerosols Transportation And Distribu-

tion In Southeast Asia Which Can Lead To Global Climate Change,

1001/PFIZIK/811228.

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Modeling of groundwater recharge using a multiple linear regression (MLR) recharge model developed from geophysical parameters: a case of groundwater resources managementAbstractIntroductionMaterials and methodsGeography, hydrology, and hydrogeology of the study area2D resistivity imaging data acquisition, processing, and interpretationRecharge estimationGeoelectric parameters--recharge relationshipMultiple linear regression (MLR) recharge model

Results and discussionSensitivity analysis result of the developed MLR recharge modelAppraisal of model prediction accuracyGroundwater recharge rate estimation using the MLR recharge modelModeling groundwater recharge prediction with the MLR recharge model

Conclusion and future worksAcknowledgmentsReferences