An ensemble learning method to retrieve sea ice roughness from Sentinel-1 SAR images

Pengyi Chen Zhongbiao Chen Runxia Sun Yijun He

Pengyi Chen, Zhongbiao Chen, Runxia Sun, Yijun He. An ensemble learning method to retrieve sea ice roughness from Sentinel-1 SAR images[J]. Acta Oceanologica Sinica. doi: 10.1007/s13131-023-2248-9
Citation: Pengyi Chen, Zhongbiao Chen, Runxia Sun, Yijun He. An ensemble learning method to retrieve sea ice roughness from Sentinel-1 SAR images[J]. Acta Oceanologica Sinica. doi: 10.1007/s13131-023-2248-9

doi: 10.1007/s13131-023-2248-9

An ensemble learning method to retrieve sea ice roughness from Sentinel-1 SAR images

Funds: The National Key Research and Development Program of China under contract No. 2021YFC2803301; the National Natural Science Foundation of China under contract No. 41977302; the National Natural Science Youth Foundation of China under contract No. 41506199; the Natural Science Youth Foundation of Jiangsu Province under contrant No. BK20150905; the Science and Technology Project of China Huaneng Group Co., Ltd. under contract No. HNKJ20-H66.
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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  5.  Workflow of the study.

    Figure  6.  Relationship among SIR, $ \sigma_{0} $, and $ \theta $.

    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 Longitude range Latitude range
    1 L1 EW GRD 142.43°–166.67°W 75.72°–80.73°N
    2 L1 EW GRD 151.74°–169.52°W 72.40°–76.99°N
    Resolution Polarization Sensing start time Relative orbit number Incidence angle range Elevation angle range
    medium HH, HV 17:46:09 161 19.10°–46.43° 17.12°–40.69°
    medium HH, HV 17:47:13 161 19.19°–46.51° 17.20°–40.76°
    下载: 导出CSV

    Table  2.   Value of 2-D Cauchy wavelet parameters

    Parameter Default value
    A 1
    $\alpha $ π/6
    L 4
    M 4
    下载: 导出CSV
    Algorithm1 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 $H(\vec x) = \sum\limits_{i \;= \;1}^T {\ln (\frac{1}{{{w_t}}})\;f(\vec x)} .$

    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 ${e_t} \leftarrow \sum\limits_{i\;=\;1}^T { {\mathrm{Dis} }{ {\mathrm{t} }_t}({ {\vec x}_i}){e_{ti} } }$

    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 $f(\vec x)$
    下载: 导出CSV

    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.
    下载: 导出CSV

    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
    下载: 导出CSV

    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.
    下载: 导出CSV

    Table  6.   Performance metrics of training and testing set with 2-D CWT

    DatasetR2MAE/cmRMSE/cmMAPE/%
    Training0.971.241.7726.52
    Testing0.911.712.8236.37
    下载: 导出CSV

    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.
    下载: 导出CSV

    Table  8.   Sentinel-1 SAR images used in the independent test

    Image ID Product level Instrument mode Product type Longitude range Latitude range
    1 L1 EW GRD 58.89°–103.19°W 80.92°-86.11°N
    2 L1 EW GRD 51.28°–97.67°W 81.27°–86.45°N
    3 L1 EW GRD 60.61°–107.35°W 81.36°–86.54°N
    Resolution polarisation sensing start time relative orbit number incidence angle range elevation angle range
    Medium HH, HV July 16, 2017 13 18.80°–46.66° 16.86°–40.89°
    Medium HH, HV July 17, 2017 13 18.95°–46.66° 16.99°–40.88°
    Medium HH, HV July 19, 2017 13 19.19°–46.47° 17.20°–40.72°
    下载: 导出CSV

    Table  9.   Performance metrics of training and independent testing set

    DatasetR2MAE/cmRMSE/cmMAPE/%
    Training0.971.311.9210.17
    Independent test0.950.891.465.71
    下载: 导出CSV
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  • 收稿日期:  2023-06-14
  • 录用日期:  2023-08-29
  • 网络出版日期:  2024-03-08

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