Fusion of Ground-Based and Spaceborne Radar Precipitation Based on Spatial Domain Regularization

基于正则化算法的地基与星载雷达降水空间域融合

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Supported by the National Natural Science Foundation of China (General Program) (41975027) and National Key Research and Development Program (2021YFC2802502).
DOI: 10.1007/s13351-024-3092-3

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    Abstract

  • Abstract

    High-quality and accurate precipitation estimations can be obtained by integrating precipitation information measures using ground-based and spaceborne radars in the same target area. Estimating the true precipitation state is a typical inverse problem for a given set of noisy radar precipitation observations. The regularization method can appropriately constrain the inverse problem to obtain a unique and stable solution. For different types of precipitation with different prior distributions, the L1 and L2 norms were more effective in constraining stratiform and convective precipitation, respectively. As a combination of L1 and L2 norms, the Huber norm is more suitable for mixed precipitation types. This study uses different regularization norms to combine precipitation data from the C-band dual-polarization ground radar (CDP) and dual-frequency precipitation radar (DPR) on the Global Precipitation Measurement (GPM) mission core satellite. Compared to single-source radar data, the fused figures contain more information and present a comprehensive precipitation structure encompassing the reflectivity and precipitation fields. In 27 precipitation cases, the fusion results utilizing the Huber norm achieved a structural similarity index measure (SSIM) and a peak signal-to-noise ratio (PSNR) of 0.8378 and 30.9322, respectively, compared with the CDP data. The fusion results showed that the Huber norm effectively amalgamate the features of convective and stratiform precipitation, with a reduction in the mean absolute error (MAE; 16.1% and 22.6%, respectively) and root-mean-square error (RMSE; 11.7% and 13.6%, respectively) compared to the 1-norm and 2-norm. Moreover, in contrast to the fusion results of scale recursive estimation (SRE), the Huber norm exhibits superior capability in capturing the localized precipitation intensity and reconstructing the detailed features of precipitation.

    摘要

    结合地基和星载雷达在同一区域的降水信息，可以获得更高质量的降水估算。对于一组有噪声的雷达降水观测值，如何估计真实降水状态是一个典型的逆问题。正则化方法可以适当地约束逆问题，以获得唯一且稳定的解。对于具有不同先验分布的降水类型，L1和L2范数分别对层状降水和对流降水的约束更有效。作为L1和L2的组合，Huber范数更适合于混合型降水。采用不同正则化范数对C波段双偏振地面雷达(CDP)和双频降水雷达(DPR)的降水数据进行融合。与单源雷达数据相比，融合图包含更多的信息。27个降水案例中，三种正则化范数的融合结果表明，基于Huber范数的融合结果更有效地融合了对流降水和层状降水的特征，平均绝对误差(MAE)分别降低了16.1%和22.6%，均方根误差(RMSE)分别降低了11.7%和13.6%。与尺度递归估计(SRE)的融合结果相比，Huber范数在捕获局域降水强度和重建降水细节特征方面表现出更强的能力。

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    Fig.  1.   Reflectivity factors of spaceborne radar and ground-based radar for a precipitation event in Nanjing on 21 June 2016. (a) CDP data at 0318 UTC, (b) DPR data at 0321 UTC, and (c) scatter density plot of reflectivity factor data comparison between the two radars.

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    Fig.  2.   Reflectivity factor images of three precipitation cases observed by radar in Nanjing and probability distribution curve after logarithmic processing. The fitted Gaussian and Laplacian distribution curves were added. (a) CDP reflectivity factor data at 1604 UTC 9 May 2016, (b) CDP reflectivity factor data at 0507 UTC 24 July 2015, (c) DPR reflectivity factor data at 1020 UTC 2 July 2016, and (d–f) comparison of the logarithmically processed probability curves and fitted Gaussian and Laplace distribution curves corresponding to the three precipitation cases.

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    Fig.  3.   Examples of L1, L2, and Huber norms (τ = 0.5).

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    Fig.  4.   Determination of λ for the precipitation case on 24 June 2016 using the L-curve criterion. Here, * indicates the optimal point of λ corresponding to this precipitation case.

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    Fig.  5.   Flow chart of the regularization fusion algorithm for CDP and DPR precipitation data.

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    Fig.  6.   Regularization fusion results of radar reflectivity factors in Nanjing on 8 July 2015. (a) Ground radar, (b) spaceborne radar, (c) fusion results of SRE, (d) L1-norm fusion results, (e) L2-norm fusion results, and (f) Huber norm fusion results, with the corresponding magnified plots in the red boxes corresponding to (g)–(i).

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    Fig.  7.   As in Fig. 6, but for 26 October 2016.

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    Fig.  8.   As in Fig. 7, but for precipitation.

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    Fig.  9.   As in Fig. 8, but for 2 May 2016.

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    Fig.  10.   Comparisons of radar data and rain gauge measurements for the precipitation case in Nanjing on 26 October 2016. (a) Ground-based radar, (b) spaceborne radar data, (c) fusion result of L1 norm, (d) fusion result of L2 norm, and (e) fusion result of Huber norm.

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    Fig.  11.   As in Fig. 10, but for 2 May 2016.

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    Table  1   Comparison between fusion results of reflectivity factors and ground-based radar data for two cases

    8 July 2015 26 October 2016
    L1 L2 Huber SRE L1 L2 Huber SRE
    RMSE 2.1634 2.2295 2.0151 2.6660 1.9565 2.0868 1.8982 2.7332
    MAE 1.0856 1.1397 0.9256 1.3907 0.9881 1.0419 0.9159 1.4460
    PSNR 26.1862 24.2788 28.7147 25.3470 27.1217 25.8067 28.3125 24.3544
    SSIM 0.8706 0.8695 0.8917 0.8389 0.8191 0.8066 0.8227 0.7803
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    Table  2   Statistical comparison between reflectivity factor fusion results and ground-based radar data for 11 precipitation events in 2016

    Date (yyyymmdd) Method RMSE MAE PSNR SSIM
    20160402 L1 2.7305 1.0844 26.8972 0.8896
    L2 2.8927 1.1625 26.4065 0.8839
    Huber 2.7066 1.0591 27.4351 0.8921
    SRE 3.6850 1.4270 25.8189 0.8385
    20160502 L1 3.2597 1.3244 29.8059 0.8728
    L2 3.4752 1.4876 29.1473 0.8589
    Huber 2.9641 1.2344 30.5181 0.8751
    SRE 4.0766 1.7369 27.9406 0.8125
    20160509 L1 2.3094 1.1104 27.5692 0.8689
    L2 2.4535 1.1706 26.1400 0.8613
    Huber 2.1938 1.0264 30.0488 0.8737
    SRE 2.9074 1.3774 24.9998 0.8072
    20160525 L1 3.1486 0.9783 27.0982 0.9025
    L2 3.2582 1.0141 26.5354 0.8952
    Huber 3.0266 0.9114 28.6628 0.9096
    SRE 3.2313 1.0584 27.3866 0.8706
    20160528 L1 2.6347 0.4051 36.4053 0.9475
    L2 2.7838 0.4301 35.7458 0.9443
    Huber 2.5831 0.3835 37.9959 0.9521
    SRE 3.5716 0.5483 33.2454 0.9437
    20160602 L1 6.3500 1.2544 35.2938 0.9259
    L2 6.3570 1.2673 35.2829 0.9268
    Huber 6.3339 1.2242 35.3722 0.9323
    SRE 7.5592 1.0619 34.0200 0.9077
    20160624 L1 2.7839 1.0000 26.1643 0.8760
    L2 3.4225 1.2463 24.3538 0.8546
    Huber 2.7656 0.9862 26.4355 0.8805
    SRE 3.3806 1.2220 24.1680 0.8521
    20160702 L1 3.6631 0.9882 32.6746 0.8931
    L2 3.8478 1.0717 31.0728 0.8862
    Huber 3.5723 0.9544 32.9729 0.8971
    SRE 4.3604 1.2624 31.0498 0.8468
    20160704 L1 1.8174 0.4288 34.3785 0.9368
    L2 1.8162 0.4278 34.5519 0.9394
    Huber 1.7532 0.4043 34.7335 0.9443
    SRE 2.6355 0.5770 33.7714 0.9375
    20161025 L1 5.9801 0.9116 33.5983 0.9205
    L2 6.2725 1.0069 29.1807 0.9141
    Huber 5.9388 0.9080 33.7727 0.9267
    SRE 6.7504 0.9821 31.1960 0.8943
    20161028 L1 1.7990 0.8557 29.0775 0.8736
    L2 2.0580 0.9886 28.8221 0.8619
    Huber 1.7159 0.8269 29.8619 0.8804
    SRE 2.3596 1.0894 27.1198 0.8274
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    Table  3   Average indexes between reflectivity factor fusion results and ground-based radar data for 27 precipitation cases

    CaseMethodRMSEMAEPSNRSSIM
    MeanL12.85231.343629.36270.8249
    L22.97251.528427.34380.8164
    Huber2.74331.225730.93220.8378
    SRE3.82762.543524.73670.7853
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    Table  4   Fusion results and ground radar observations for two precipitation cases

    26 October 2016 2 May 2016
    L1 L2 Huber SRE L1 L2 Huber SRE
    RMSE 2.0324 2.1730 1.9581 2.6205 1.7372 1.6775 1.5590 2.2724
    MAE 0.7625 0.8149 0.7092 1.3553 0.9296 0.8603 0.7047 1.1074
    PSNR 29.8554 32.0090 33.1179 29.1369 33.8526 35.0029 35.1192 32.4751
    SSIM 0.8345 0.8542 0.8898 0.8229 0.8244 0.8595 0.8871 0.8233
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    Table  5   Comparison between the regularization fusion results and ground-based radar data for 27 precipitation cases

    L1 L2 Huber SRE
    RMSE 2.7836 2.8225 2.7381 3.3748
    MAE 1.2554 1.3382 1.2086 1.8264
    PSNR 31.0857 30.1674 33.6473 27.9273
    SSIM 0.7372 0.7123 0.7622 0.7197
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    Table  6   Comparison results of radar data and rain gauge measurements for two cases

    CDP DPR L1 L2 Huber
    Correlation coefficient 0.6126 0.5590 0.6537 0.6334 0.6700
    Case 1 MAE (mm h−1) 2.2611 2.9380 2.1742 2.1821 2.0288
    RMSE (mm h−1) 3.8360 4.2820 3.0878 3.4089 3.0049
    Correlation coefficient 0.5595 0.5258 0.6304 0.5923 0.6622
    Case 2 MAE (mm h−1) 1.8874 2.4045 1.7778 2.0319 1.3397
    RMSE (mm h−1) 2.8730 3.8066 2.4610 2.5270 2.1302
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    Table  7   Average values of radar data and rain gauge measurements for 27 precipitation cases

    CDPDPRL1L2Huber
    Correlation coefficient0.53250.49020.56160.54480.5824
    MAE (mm h−1)1.87862.25621.64531.73771.4163
    RMSE (mm h−1)3.01634.05142.68992.73452.4067
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