Geography Reference
In-Depth Information
(
h
)
C
C
1
e
h
a
0
(15)
where,
C
0
+C
is the sill,
a
is the range, and
h
is the separation vector or lag
distance.
(D) Selection of the Best-Fit Model
Once the fitting of experimental and theoretical variograms is over, the
best-fit geostatistical model can be selected based on a set of goodness-of-fit
criteria viz., mean error (ME), root mean squared error (RMSE), correlation
coefficient (r), mean standard error (MSE), mean reduced error (MRE),
2
R
S
), and coefficient of determination (r
2
). The details
about these goodness-of-fit criteria can be found in Table 3.
5.2.2. Inverse Distance Weighting Technique
Inverse distance weighting (IDW) technique is one of the moving average
methods for spatial interpolation. Moving average method performs a
weighted averaging on point values and returns a spatial map as output
based on a specified weight function and a limiting distance (Webster and
Oliver, 2001). While applying the IDW technique for interpolating values of
any water quality variable for an output point, the distances of all points
(where the water quality parameter is known) towards the output point are
calculated to determine weight factors for the points. The weight factors for
the points are then calculated according to the specified weight function.
Two weight functions are available (Burrough and McDonnell, 1998):
inverse distance and linear decrease. Weight for the inverse distance function
is expressed below:
reduced variance (
Weight
(
/
d
n
)
1
(16)
where, d = D/D
0
= relative distance of a known water quality point to output
point, D = Euclidean distance of known water quality point to output point, D
0
= limiting distance, and n = weight exponent.
The weights vary according to the relative distance of any known water
quality point to output point and the weight exponent (Figure 5).
Thereafter, for each output pixel, value of particular water quality variable
is calculated as the sum of the products of calculated weight values and point
values divided by the sum of weights. That is,
