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the mean areal values with the Thiessen method
10
(Fig. 1). Second, all
the data were standardized to the interval from 0.1 to 0.9.
11
Third, the
data were partitioned into calibrations set (160 records) and validation set
(120 records) according to the modified differential split-sample method
proposed by Tokar and Johnson.
12
Multilayer perceptron (MLP) with one-hidden-layer and sigmoid func-
tion as the transformation function was chosen as the network. Detailed
information about MLPs may be found in the literatures (e.g. Ref. 1).
Three groups of neural networks, each consisting of four networks, were
constructed. Each group had different types of causal variables and the
networks within the same group had different time lags (Table 1). The
performances of the networks were evaluated with root mean square error
(RMSE) and the coecient of multiple determination (
R
2
).
11
The best per-
forming network of each group was identified and their performances were
compared to the MLR models which had the same input combinations.
4. Results and Discussion
Twelve ANNs were calibrated, validated, and evaluated. The RMSE and
R
2
in the calibration and validation periods of these ANNs are listed in
Table 2. ANN 4, ANN 6, and ANN 9 were the best performing networks in
their corresponding groups, respectively. Three regression models, MLR A,
MLR B, and MLR C, which have the same inputs as ANN 4, ANN 6, and
Table 1.
Input combinations of the ANNs.
ANNs
Inputs
Group I
1
(
T,R
)
t
2
(
T,R
)
t
,(
T,R
)(
t
−
1)
3
(
T,R
)
t
,(
T,R
)(
t
−
1), (
T,R
)(
t
−
2)
4
(
T,R
)
t
,(
T,R
)(
t
−
1), (
T,R
)(
t
−
2), (
T,R
)(
t
−
3)
Group II
5 (
T,R,R
25
,N
25
,R
50
,N
50
)
t
6 (
T,R,R
25
,N
25
,R
50
,N
50
)
t
,(
T,R
)(
t
−
1)
7 (
T,R,R
25
,N
25
,R
50
,N
50
)
t
,(
T,R
)(
t
−
1), (
T,R
)(
t
−
2)
8
T,R,R
25
,N
25
,R
50
,N
50
)
t
,(
T,R
)(
t
−
1), (
T,R
)(
t
−
2), (
T,R
)(
t
−
3)
Group III
9
(
T,R,W
)
t
10
(
T,R,W
)
t
,(
T,R,W
)(
t
−
1)
11
(
T,R,W
)
t
,(
T,R,W
)(
t
−
1), (
T,R,W
)(
t
−
2)
12
(
T,R,W
)
t
,(
T,R,W
)(
t
−
1), (
T,R,W
)(
t
−
2), (
T,R,W
)(
t
−
3)
