Radar Experiments and Results of Inversion
5.4 Wind inversion from radar first-order peaks using neural networksneural networks
5.4.1 Wind inversion during the Fedje experiment
After the training, validation and testing, the scatter plots of the wind direction and speed during the Fedje experiment are shown in Figure 5.21. Compared to the pattern fitting method and LSM method given in Figure 5.10, the neural network gives a better result.
Besides the wind direction, the wind speed could also be inverted from the radar first-order backscatter, the result is presented in Figure 5.21b. In WAM model data analysis, the inte-grated wave energy increases with the wind speed at certain wave frequencies, which gives one-dimensional description of wave growth. In Section 4.4.2, not only the integrated wave energy, but also the wave directional spreading pattern is considered, the two-dimensional information of the Bragg waves are used to invert wind speed, which contains more infor-mation and makes the wind speed inversion more accurate. Besides that, the threshold for Bragg wave saturation is higher if both amplitude and direction information are used for the wind speed inversion. For example, the wind speed inverted from the two-dimensional WAM data (Figure 4.11a) and radar first-order peaks (Figure 5.21b) shows a higher sat-uration value than if only the integrated Bragg wave energy is used (Figure 2.7c), which means, it will give a wider range for wind speed inversion if both Bragg wave amplitude
and directional spreading information are used. In Figure 5.21b, at a higher wind speed, more results of wind speed are located below the line y=x. That means if the wind speed is increasing beyond the saturation limit, the Bragg waves will come to a state of saturation (including integrated wave energy and the wave directional spreading pattern). In this case, the wind speed could no longer be inverted from radar first-order backscatter.
0 50 100 150 200 250 300 350
0 50 100 150 200 250 300 350
Wind direction (anemometer,Fedje 2000/02/14-04/13) [o] Radar Measurement (NN using first-order) [o]
Scatter plot of wind direction (RMSE = 21.4o,U>3m/s)
(a) Wind direction
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 20
Wind Speed (anemometer, Fedje 2000/02/14-04/13) [m/s]
Wind Speed (neural network output) [m/s]
Scatter plot of wind speed; CC = 0.8677
(b) Wind speed
Figure 5.21: Wind direction and speed derived from radar first-order backscatter using neural network and the anemometer wind measurement during the Fedje experiment
0 100 200 300 400 500 600 700 800 900
0 2 4 6 8 10 12 14 16 18 20
Valid data record (Fedje 2000)
Wind Speed [m/s]
Comparison of wind speed; CC = 0.8677
Neural network output from first-order peaks anemometer measurement
Figure 5.22: Comparison of wind speed derived from the first-order backscatter using neural network and the anemometer measurement during the Fedje experiment
The comparison of wind speed is demonstrated in Figure 5.22. The wind speed derived from radar first-order peaks using neural network can cover the low wind speed measure-ment. For example, from the data record 800 to 900, the radar measurements agree with the anemometer measurements very well, which is an advantage of the method using first-order peak power, because the Bragg resonant waves are sensitive to the change of the
wind speed. But for wind speed inversion from radar second-order sidebands, there is a disadvantage, because the sea surface could not calm down immediately when the wind becomes weak, the residual waves still remain. As a result, the wind inverted from the waves (significant wave height and peak wave frequency) is overestimated.
The network randomly divides the input and target vectors into three sets: 60% are used for training; 20% are used to validate that the network is generalizing and to stop training before over-fitting; The last 20% are used as a completely independent test of network generalization. The correlation coefficients of the training, validation and testing are given in Figure 5.23 as well as the correlation coefficient of the total data set. The illustrated example in Section 4.3.2 is the result of the network used in this application (Figure 4.6). The network output tracks the targets very well for training, validation and testing, the CC-value (Correlation Coefficient) is higher than 0.85 for the total data set.
0 5 10 15 20
0 5 10 15 20
Target
Output~=0.8*Target+1.4
(a)Training: CC=0.89677
Data Fit Y = T
0 5 10 15 20
0 5 10 15 20
Target
Output~=0.7*Target+2.3
(b)Validation: CC=0.77861
Data Fit Y = T
0 5 10 15 20
0 5 10 15 20
Target
Output~=0.79*Target+1.2
(c)Test: CC=0.86913
Data Fit Y = T
0 5 10 15 20
0 5 10 15 20
Target
Output~=0.78*Target+1.5
(d) All: CC=0.86772
Data Fit Y = T
Figure 5.23: Correlation coefficients of training, validation and testing data for wind speed inversion from radar first-order peaks during the Fedje experiment
During the training of the network, the network automatically verifies its performances.
For the application of the network, the trained network is used independently (only the new input data is used). So the capability of the generalization is an important issue. In order to verify the trained network, we manually select some data for testing. In the anemometer measurement, we have 929 valid wind records. The first 200 wind records are selected for manual testing and the last 729 data for the network training, validation and testing. The 729 data wind records consist of high and low wind speeds, which are sufficient and variable
for the network training. Figure 5.24 shows the time series of the wind record.
0 100 200 300 400 500 600 700 800 900
0 5 10 15 20 25
Time Record(1-929)
Wind Speed [m/s]
Wind speed measurement by anemometer, Fedje,2000
Manual Test For training, validation, testing in network
Figure 5.24: Records for manual testing and the network training
The scatter plot of the network output and the anemometer measurement for the 729 samples is given in Figure 5.25a, which gives a correlation coefficient of 0.8484. After the training, the network net1 is generated and saved. We use the first 200 samples as the input data for the network net1, they are the new input data. The scatter plot of the network output and anemometer measurement for the manual selected testing data is given in Figure 5.25b, the correlation coefficient value is 0.8366, which is acceptable for wind speed inversion.
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 20
Wind Speed (anemometer) [m/s]
Wind Speed (neural network output) [m/s]
Scatter plot of wind speed; CC = 0.84841
(a) Scatter plot of last 729 samples
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 20
Wind Speed (anemometer) [m/s]
Wind Speed (neural network output) [m/s]
Scatter plot of wind speed; CC = 0.83656
(b) Scatter plot of first 200 sample
Figure 5.25: Scatter plots of the wind speed, (a) is the result of network training, (b) is the result using the trained network for the new data set.