Selection of target layers
The soil moisture contents in 5 to 300 cm soil layers were selected as the research target. The variation coefficient of soil moisture content in each soil layer were estimated. The variation coefficient of soil moisture content in 5 cm soil layer, CV5, is more than 30%, that is to say, CV5 > 30%, 20% < CV20−80 < 30%, 5% < CV100−180 < 20%, CV200−300 < 5%, respectively, so the 5 to 300 cm soil layers can be classified into four groups, 0 to 5 cm, 20 to 80 cm, 80 to 180 cm and 200 to 300 cm soil layer. Because soil moisture content in the 5 cm soil layer is surface soil and interfered by outside factors and the change trend of soil water in the soil layer was uncertainty in Caragana brushland, it was not be selected as the research target. Finally, the soil water contents in the rest three soil layers such as 40 cm, 100 cm and 200 cm soil layers were chosen respectively as the analysis object.
Wavelet Analysis Of Soil Moisture
First, the soil water content in the 100 cm layer were selected as the research objects, and the interpolated 113 sets of data in 100 cm layer were selected as the original wavelet sequence s1, then db2 was selected to do single scaling wavelet decomposition and reconstruction (Jiang and Liu, 2004; Zhang ,2012), as shown in figure 1.
In figure 1, s1 is time series trend diagram of soil moisture data measured in 100 cm soil layer, a1 is the general picture part of low frequency and its variation trend is consistent with the original signal. The high frequency detail part is d1 after soil water data were decomposed using single scale wavelet, which reflects the change of the original signal frequency. s1, s1= a1+d1, is the synthesized reconstruction signal of decomposed by single scaling wavelet.
The Selection Of Input Variable
This article selected the soil moisture content in the soil layers that highly correlated with s1 as the inputs, the correlation results at each soil layer are shown in Table1. Besides, a1 can be used as an model inputs because it has the similar dynamic change trend with s1, so input variables of model I were as follows: 60cm, 80cm, 120cm, 140cm, a1 and output variables was s1.
Table 1. The Correlation analysis among soil water contents in 40cm to 160cm soil lavers
Soil layer (cm)
|
40
|
60
|
80
|
100
|
120
|
140
|
160
|
40
|
1
|
0.893
|
0.717
|
0.423
|
0.375
|
0.32
|
0.177
|
60
|
0.893
|
1
|
0.889
|
0.616
|
0.525
|
0.416
|
0.228
|
80
|
0.717
|
0.889
|
1
|
0.683
|
0.62
|
0.51
|
0.323
|
100
|
0.423
|
0.616
|
0.683
|
1
|
0.892
|
0.711
|
0.229
|
120
|
0.375
|
0.525
|
0.62
|
0.892
|
1
|
0.923
|
0.431
|
140
|
0.32
|
0.416
|
0.51
|
0.711
|
0.923
|
1
|
0.598
|
160
|
0.177
|
0.228
|
0.323
|
0.229
|
0.431
|
0.598
|
1
|
The selection of input variables in model II: (1) when predicting a1, the soil water contents in 60cm, 80cm, 100cm, 120 cm and 140cm soil layers were inputs, a1 was outputs; (2) when predicting d1, s1 is only related to s1, d1 was output variable.
Comparison Between Model I And Model Ii
The range of soil moisture content was volatile due to much affecting factors, so this article was only used for short-term prediction. The input variables of week N and output variables of week N + 1 form a sample set, and there was a total of No.112 samples sets. Data sets was divided as follows: the data from 1 to 90 groups was taken as the training set, which used for fitting model; the data from No.91 to No.101 sets was taken as the validation set, which used for the prediction of error estimation in the selected model; the remaining data in II sets be used as a test set to ultimately evaluate the generalization error of selected model.
Figure 2 showed the simulation correlation analysis in training set s1 for model I and model II. of d1 is only related to s1, d1 was output variable. It can be seen from Figure 2 that model II was better than model I in the overlap of the simulated values predicting d1, s1 was input variable for the change and the measured values and in the correlation analysis, showing that the NARX recursive neural network has the better learning ability than BP neural network.
Table 2
Comparison of predicted error of validation set No. 92 to No.98 at 40 cm and 200 cm soil layers
Items
|
Relative error (%)
|
Items
|
Relative error %
|
92
|
6.99
|
99
|
-3.27
|
93
|
5.98
|
100
|
-4.75
|
94
|
6.27
|
101
|
2.68
|
95
|
10.90
|
102
|
4.77
|
96
|
5.56
|
Average relative error(%)
|
3.52
|
97
|
-0.08
|
98
|
3.66
|
Table 2 is the validation set of forecast error analysis for the model I and model II. It can be seen from the Table 2 that average relative error of model I was 3.5% and that of model II was 0.3%, showing that the prediction accuracy using the model II is higher than that using model I.
The Applicant Of Model Ii
In order to study the feasibility of actual operation of model II, in the paper soil water content from 103 to 113 weeks in the 100cm soil layer were forecasted, as shown in table 3.
Based on wavelet analysis, the model II was more suitable than model I for forecasting soil water content in the Caragana shrubland by comparing the results of correlation analysis of simulated and measured values and the prediction error analysis of validation set.
The average relative error of predicted soil water from 103 to 113 weeks is 0.8%, and absolute values of relative error of soil water in the 11 weeks’were lower than 10%, showing that modelⅡ is feasible in prediction of soil water content in the woodland.
The model after training (learning) right reflects the samples that did not occurred in training set. Learning is not simply to memorize the studied inputs, but to learn the inner regularity of environment itself embedded in the sample through the study of a finite number of training samples16. In order to further test the model generalization ability, moisture contents from 103 to 113 weeks in 40 cm and 200 cm soil layer were predicted. The correlation analysis of the predicted values and the measured values were shown in figure 3. The error analysis of prediction values was shown in table 4.
The figure 3 and table 4 showed that the curves of predicted values were consistent with the measured values in 40 cm and 200 cm soil layer. The correlation coefficients of the linear regression equation were 0.981, 0.984 respectively, and p< 0.05. The average relative errors were less than 5%, suggesting that the wavelet neural network model II has good generalization performance.