INTRODUCTION
Many researches have worked on development of water table (Dingman,
2002; Maurer et al., 2002; Wolock,
2003: Fan et al., 2007). Management of this
concept is very important to meet the increasing demand of water for domestic,
agricultural and industrial use. Various management measures as discharge and
industrial implementation zones, require the spatial behaviour of watertable.
According to Isaaks and Srivastava (1989) and Kumar
and Ramadevi (2006), Kriging is an optimal and unbiased spatial method used
to evaluate regionalized variables at unsampled locations using an initial data
set values and various variogram models such as: pentaspherical, spherical,
exponential, gaussian, power, linear, etc. As the selected model influences
the prediction of the unknown values, this study is an attempt to determine
which theoretical variogram, can give acceptable results to predict the watertable
values based on the watertable observations for the last three years in Sangmelima
(SouthCameroon) region.
MATERIALS AND METHODS
Description of the study area: The Sangmelima city area is located from
longitudes 11°57’ to 12°01’ and latitudes 2°54’ to
2°58’ in the southern region of Cameroon, on the northern part of the
Congo craton (Fig. 13).
The study area has equatorial humid climate characteristics. Annual average
minimum and maximum temperatures are 28 and 40°C, respectively while annual
average temperature is 34°C. Annual average relative humidity is 81.6%.
Rainfall is observed in all seasons. Maximum rainfall is often observed in the
timeperiod from June to October, while minimum rainfall is from December to
March. Average annual rainfall is about 150.2 cm. Drainages are intermittent
and structurally controlled by foliation and faulting. The main water source
of the region is the Afamba River belonging to the Nyong basin system (Fig.
1). The electrical conductivity of the river water ranges from 0.56 to 0.73
dS m^{1} and the corresponding range in sodium absorption ratio is
from 0.65 to 2.00. There are more than 60 observation wells in this region,
geologically covered by various rocks types such as gneiss, shales, dolerite,
gabbro and peridotites (Klitgord and Schouten, 1986;
Fairhead, 1988; Guiraud and Maurin,
1992; ManguelleDicoum et al., 1992; Meli’i
et al., 2011, 2012). According to the same
authors, lateritic, gravel, granite, clay and fractured granite structures are
also observed in this region.

Fig. 1: 
Watersheds map of Sangmelima region 

Fig. 2: 
The simplified topographical map of Sangmelima region 

Fig. 3: 
Stations location map of of the studied area 

Fig. 4: 
Well sample obtained in the Leproserie area 
According to the population encountered in this area, rainfall behaviour, rivers
regime, wells and boreholes recharge process have been considerably modified
during this recent years and are probably due to the climate change and human
activities.
Origin of the data: The mean data used in this study (70 samples) were
collected between 2009, 2010, 2011 and 2012, with drilled piezometers from rivers,
swamps and water wells, generally constructed by the municipality city council
(Fig. 35).
Geostatistical method: The variogram measures the squared difference
between values as a function of distance. It’s defined according to Isaaks
and Srivastava (1989) and Kumar and Ramadevi (2006)
by the following equation:
where, γ(h)* represents the estimated value of the semivariance for lag
h; N(h) is the number of experimental pairs separated by vector h; Z(x_{i})
and Z(x_{i+h}) are values of variable z at x_{i }and x_{i+h},
respectively. x_{i} and x_{i+h} represent the position in two
dimensions.
In the linear kriging method, the interpolated value of z at any point x_{i}
is given as the weighted sum of the measured values:
where, λ_{i} is the weight for the observation z at location x_{i},
calculated by Eq. 3 so that Z^{*}(x_{0}) is
unbiased and optimal (minimum squared error of estimation):
where, μ is the Lagrange multiplier and γ(x_{j}, x_{i})
the semivariogram between two points x_{i} and x_{j}:
where, N is the number of samples, Z(x_{i}) and Z^{*}(x_{i})
are, respectively the estimated value and observed value at the point (x_{i}).

Fig. 5: 
Drilling sample obtained in the Afamba area 
RESULTS AND DISCUSSION
Experimental and fitted variograms models: The experimental variogram
and the fitted variograms (Fig. 6) are calculated using Eq.
1 and values of Table 1 with the data collected from 70
samples. The analytical variograms results obtain are follow (Eq.
58):
Table 1: 
Values obtained with various variogram models 

Table 2: 
RMSE values obtained with various variogram models 


Fig. 6: 
Experimental and fitted variogram models 
Exponential model:
and linear:
The analysis of experimental values and those obtained with various analytical
variograms (Fig. 6, Table 1) shows that,
results of linear model present the best approximation with those of experimental
model. But in the last line, the value of the linear model increases when the
experimental model value remains constant. Comparison with other models shows
that, the linear model is followed by the gaussian, spherical and exponential
models. This Table 1 also shows that, the pentaspherical model
values present very bad correlation with those of the experimental model.
Validation of the variogram models: The RMSE values obtained with various
variograms models (Table 2) shows that, the linear model presents
the lowest RMSE 1.67. This result is similar to those obtained previously. According
to Marcotte (1995), (Eq. 8) must
be used to map the water table level in the studied region).
Predicting the water table map: The variograms (Eq. 58)
are then used to construct the water table map by kriging with Golden
Software, 2002, at the nodes of the 1 km x 1km square grid from the collected
depth of some wells and depth of topsoil at some stations where shallow aquifer
was detected. These estimated level values are used to draw the isodepth maps.
In Fig. 711, the water table appears to
be continuous in all the study area with some contrasted observations. The depletion
varies with space from 0 to 20 m according to the maps generated by linear,
spherical and exponential variograms and from 0 to 160 m according to the map
obtained with the logarithmic variogram. If the predicted water table is generally
close, the maps are different from one variogram model to another. The figures
confirm that, the selected model influences the prediction of the unknown values.
In Fig. 7, the isocontours present features of the hills and
valleys in relative good correlation with the topography (Fig.
3). The water level is low where the surface of the ground is low and higher
where the surface is high. The minimum corresponds to the rivers or swamps whereas
the maximum corresponds to the region where soils and weathered rocks are thick.
But, the results of the Fig. 811 are
not the same. In fact, according to these figures, the isocontours are close
but they do not present good correlation with the topography.
Cross validation criteria: The comparison between the measured in field
and predicted values of water table by kriging using several analytical model
is presented in Table 3 and 4.

Fig. 7: 
Water table level (m) map above mean sea level obtained by
kriging using linear variogram model 

Fig. 8: 
Water table level (m) map above mean sea level obtained by
kriging using spherical variogram model 

Fig. 9: 
Water table level (m) map above mean sea level obtained by
kriging using gaussian variogram model 

Fig. 10: 
Water table level (m) map above mean sea level obtained by
kriging using exponential variogram model 

Fig. 11: 
Water table level (m) map above mean sea level obtained by
kriging using logarithmic variogram model 
Table 3: 
RMS values obtained from various variogram models according
to the cross validation criteria 

Table 4: 
Comparison between observed data and those obtained by kriging 

These results also confirm that, the linear variogram has the low RMSE 0.001
values and appears to be best one. In addition, the map obtained with the linear
model Fig. 7, enables to highlight swamps in the area and
tests made on wells and boreholes data present a good correlation with kriging
results. However, rivers don’t clearly appear, probably due to the narrowing
of their courses according to the scale of data.
CONCLUSION
The water table influences soil moisture climatology, continental climate dynamics
and is very important for peoples in the rural areas, particularly when they
need to know at what depth below the surface they can tap far enough into the
ground to get a functioning wells or which way pollutants may or may not flow
to come to wells or boreholes. The results obtained confirm the usefulness of
applying the geostatistic method to investigate water table. This study also
shows that, the best fitted variogram in the Sangmelima rural region is the
linear model. The map obtained by kriging allows to control the spatial behaviour
of watertable in the context of climate dynamics and can guide the urbanization
process while preserving the water quality in this region.