An ensemble learning method to retrieve sea ice roughness from Sentinel-1 SAR images
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Abstract: Sea ice surface roughness (SIR) affects the energy transfer between the atmosphere and the ocean, and it is also an important indicator for sea ice characteristics. To obtain a small-scale SIR with high spatial resolution, a novel method is proposed to retrieve SIR from Sentinel-1 synthetic aperture radar (SAR) images, utilizing an ensemble learning method. Firstly, the two-dimensional continuous wavelet transform is applied to obtain the spatial information of sea ice, including the scale and direction of ice patterns. Secondly, a model is developed using the Adaboost Regression model to establish a relationship among SIR, radar backscatter and the spatial information of sea ice. The proposed method is validated by using the SIR retrieved from SAR images and comparing it to the measurements obtained by the Airborne Topographic Mapper (ATM) in the summer Beaufort Sea. The determination of coefficient, mean absolute error, root-mean-square error and mean absolute percentage error of the testing data are 0.91, 1.71 cm, 2.82 cm, and 36.37%, respectively, which are reasonable. Moreover, K-fold cross-validation and learning curves are analyzed, which also demonstrate the method’s applicability in retrieving SIR from SAR images.
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Figure 1. Map of the sea ice age from the National Snow and Ice Data Center (NSIDC) (Tschudi et al., 2019) on July 15, 2016. Location of the study area is denoted as a white rectangle.
Figure 2. Preprocessed Sentinel-1 SAR image in HH-polarization sensed on July 13, 2016. The incidence angles of the three areas are marked.
Figure 3. Sentinel-1 SAR HH-polarization backscatter coefficient (σ0) image under different incidence angles. a. Small incidence angle. b. Middle incidence angle. c. Large incidence angle.
Figure 4. Spatial distribution of orthometric height (a) and surfuce ice roughness (SIR) (b) in OIB ATM data.
Figure 7. Scatter plots of the SIR measured by ATM (true value) and that estimated from SAR pixels.
Figure 8. Scatter plots of the SIR measured by ATM (true value) and that estimated from SAR with 2-D CWT.
Figure 9. Results of 2-D Cauchy CWT. a. Region with ice floes (dark path, Area 4 in Fig. 2). b. Image gradient of a. c. Peak scales. d. Peak angles.
Figure 10. Learning curves for different types of input data. Input data without 2-D CWT (a) and input data with 2-D CWT (b). The score chosen is the coefficient of determination R2. The highlighted regions demonstrate 1 standard deviation error from the mean score of each fold.
Figure 11. The spatial distribution of samples in Center Arctic. Location of the independent test area is denoted as a blue rectangle.
Figure 12. Scatter plots of the SIR in independent test region measured by ATM (true value) and that estimated from SAR with 2-D CWT.
Table 1. Related imformations of the two Sentinel-1 SAR images used in the study
Image ID Product level Instrument mode Product type Latitude range Longitude range Resolution 1 L1 EW GRD 75.72°–80.73°N 142.43°–166.67°W medium 2 L1 EW GRD 72.40°–76.99°N 151.74°–169.52°W medium Image ID Polarization Sensing start time Relative orbit number Incidence angle range Elevation angle range 1 HH, HV 17:46:09 161 19.10°–46.43° 17.12°–40.69° 2 HH, HV 17:47:13 161 19.19°–46.51° 17.20°–40.76° 
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Table 2. Value of 2-D Cauchy wavelet parameters
Parameter Default value A 1 $\alpha $ π/6 L 4 M 4
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Algorithm 1. Adaboost Regression Input: Training set $D = ({\vec x_i},{y_i})$, $i = 1,2,...,m$; $T$: number of iterations; $I$: weak learner; $L$: loss function.
Output: Strong learner $H(\vec x) = \displaystyle\sum\limits_{i \;= \;1}^T {\ln (\frac{1}{{{w_t}}})\;f(\vec x)} .$
Initialization each sample’s weight of the 1st iteration
for $i = 1$ to $m$ do
${\mathrm{Dis}}{{\mathrm{t}}_1}({\vec x_i}) \leftarrow 1/m$
end for
Training process
for $t = 1$ to $T$ do
Training weak learner ${h_t} \leftarrow I(D,{\mathrm{Dis}}{{\mathrm{t}}_t})$
for $i = 1$ to $m$ do
Updating maximum error ${E_t} \leftarrow {\mathrm{max}}({E_t},L({y_i},{\vec x_i}))$
Calculating relative error for each sample ${e_{ti}} \leftarrow L({y_i},{\vec x_i})/{E_t}$
end for
Calculating error rate ${e_t} \leftarrow \displaystyle\sum\limits_{i\;=\;1}^T { {\mathrm{Dis} }{ {\mathrm{t} }_t}({ {\vec x}_i}){e_{ti} } }$
Updating each learner’s weight ${w_t} \leftarrow {e_t}/(1 - {e_t})$
for $i = 1$ to $m$ do
Updating each learner’s weight
${\mathrm{Dis}}{{\mathrm{t}}_{t + 1}}({\vec x_i}) \leftarrow {\mathrm{Dis}}{{\mathrm{t}}_t}({\vec x_i})w_t^{1 - {e_{ti}}}$
end for
Normalize ${\mathrm{Dis}}{{\mathrm{t}}_t}({\vec x_i})$to be a proper distribution
$t = t + 1$
end for
Calculating the median of weighted predicted (${w_t}{h_t}$) value $f(\vec x)$
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Table 3. Model evaluation metrics
Metric Formula Coefficient of determination (R2) $ R^2=1-\displaystyle\frac{\displaystyle\sum_{i\;=\;1}^N(\hat{y}_i-y_i)}{\displaystyle\sum^N_{i\;=\;1}(y_i-\bar{y})^2}$ Mean absolute error (MAE) $ {\mathrm{MAE}}=\displaystyle\frac{1}{N}\sum^N_{i\;=\;1}|\hat{y}_i-y_i|$ Root mean square error (RMSE) $ {\mathrm{RMSE}}=\sqrt{\displaystyle\frac{1}{N}\sum^N_{i\;=\;1}(\hat{y}_i-y_i)^2}$ Mean absolute percentage
error (MAPE)$ {\mathrm{MAPE}}=\displaystyle\frac{1}{N}\sum^N_{i\;=\;1}\left|\frac{\hat{y}_i-y_i}{y_i}\right|\times 100{\text{%}}$ Note: N is the size of dataset, $ \hat y_i$ is the predicted value, yi is the true value and $ \bar y$ represents the average of true values.
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Table 4. Performance metrics of training and testing set
Dataset R2 MAE/cm RMSE/cm MAPE/% Training 0.91 2.11 2.80 45.24 Testing 0.74 2.93 4.85 61.98
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Table 5. Performance metrics of each fold and average performance for the selected model
Fold MAE/cm RMSE/cm R2 MAPE/% 1 2.94 4.36 0.79 59.00 2 2.84 4.39 0.79 61.50 3 3.04 4.60 0.77 65.45 4 3.07 4.41 0.79 59.77 5 2.98 4.76 0.75 61.04 2.97 4.51 0.78 61.35 Note: The bold number represent average values.
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Table 6. Performance metrics of training and testing set with 2-D CWT
Dataset R2 MAE/cm RMSE/cm MAPE/% Training 0.97 1.24 1.77 26.52 Testing 0.91 1.71 2.82 36.37
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Table 7. Performance of each fold and the average value of each metric with 2-D CWT
Fold MAE/cm RMSE/cm R2 MAPE/% 1 1.77 3.04 0.90 33.41 2 1.84 2.64 0.92 40.77 3 1.66 2.63 0.92 36.07 4 1.81 3.03 0.90 38.04 5 1.73 2.90 0.91 36.20 1.76 2.86 0.91 36.90 Note: The bold numbers represent average values.
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Table 8. Sentinel-1 SAR images used in the independent test
Image ID Product level Instrument mode Product type Latitude range Longitude range Resolution 1 L1 EW GRD 80.92°-86.11°N 58.89°–103.19°W medium 2 L1 EW GRD 81.27°–86.45°N 51.28°–97.67°W medium 3 L1 EW GRD 81.36°–86.54°N 60.61°–107.35°W medium Image ID polarisation sensing start time relative orbit number incidence angle range elevation angle range 1 HH, HV July 16, 2017 13 18.80°–46.66° 16.86°–40.89° 2 HH, HV July 17, 2017 13 18.95°–46.66° 16.99°–40.88° 3 HH, HV July 19, 2017 13 19.19°–46.47° 17.20°–40.72°
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Table 9. Performance metrics of training and independent testing set
Dataset R2 MAE/cm RMSE/cm MAPE/% Training 0.97 1.31 1.92 10.17 Independent test 0.95 0.89 1.46 5.71
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