Geology Reference
In-Depth Information
where
h
(
t
) is water level,
d
is the initially chosen time interval between two
measurement periods;
t
and (
t
+
d
) with
d
as tolerance on time interval.
d
is actual time for the corresponding calculated variogram.
N
d
is the number
of pairs for a particular time interval. The additional equation 3 avoids the
rounding-off error of pre-decided time intervals (only multiples of the initial
time is taken in conventional cases). It is very important to account for every
term carefully while calculating variograms.
WATER LEVEL ESTIMATION IN TIME
Method of ordinary kriging was used for geostatistical estimation by Kitanidis
(1997). Given the monsoon climate in the area and if there is no heavy
pumping, the water level time series could be assumed stationary. The
estimation were made at the month(s) for each well where the water level
was not monitored due to some unavoidable cause e.g., due to the pumping
in the nearby well. Thus the water level was estimated using the existing
observed data and the corresponding best fitted variogram's model parameters.
The estimation was made by ordinary kriging using equations 4-7 which
gives the estimated water level along with the variance of the estimation
error.
METHODOLOGY APPLIED
The theory of regionalized variable (Matheron, 1971) was used to analyze
the water level data. The Ordinary Kriging equation used are as follows:
n
/0
)
ht
h
* (
t
o
)=
(4)
i
i
i
1
n
/ 0
)
tt
,
+
=
(
t
i
,
t
o
),
i
= 1,………
n
(5)
j
i
j
j
1
n
)
= 1
(6)
i
i
1
n
/
0
)
2
t
=
tt
,
+
(7)
/0
i
i
o
o
i
1
where
h
* (
t
o
) is the estimated value of water level at the point
t
o
and
t
o
is
the particular time. The ,','
2
o
and are the kriging weight, variogram,
kriging variance and Lagrange multiplier respectively.
RESULTS AND DISCUSSIONS
The estimated water level was combined with the existing (observed) water
level data and the plot was made to view the trend of the water level
fluctuations. The observed and the estimated water level were plotted along
