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TRANSCRIPT
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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: [email protected]
H. S. Lim
e-mail: [email protected]
K. Abdullah
e-mail: [email protected]
123
Environ Earth Sci
DOI 10.1007/s12665-014-3476-2
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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
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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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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
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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
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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
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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
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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
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(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
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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
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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
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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