Forward Simulation and Comparative Experiment Analysis of Polarimetric GNSS Radio Occultations Detecting Rainfall Events
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摘要: 研究证明,全球导航卫星系统(GNSS)极化无线电掩星(PRO)技术可以用于探测降雨。利用GPM DPR降雨率数据与PAZ卫星极化相移观测数据匹配,筛选出代表性降雨事件。通过选用TB等7种雨滴形状和MP等5种雨滴谱模型,采用T矩阵法对各事件进行正演,并分析PAZ极化相移的线性校正值、天线相位校正值与正演模拟值之间的关系。对比分析得出线性校正值、相位校正值与模拟值的相关系数分别为0.9994和0.9933,均方根差分别为0.3429和1.2765。模拟值与实测值之间高度相关,且更接近线性校正值。进一步的研究表明,模拟降雨率在1 mm·h–1以下的事件时,雨滴谱采用MP或JD分布,雨滴形状采用SC或PB的模拟精度更高;降雨率在1 mm·h–1以上的事件,雨滴谱采用MP或 SS分布,雨滴形状采用TB的模拟结果最优。Abstract: Studies have proved that the Global Navigation Satellite System (GNSS) Polarimetric Radio Occultation (PRO) technology has the possibility of detecting rainfall. This study uses GPM DPR products as rainfall rate data to collocate with the latest PAZ satellite observation data, and selects representative rainfall events with a wide range of rainfall and matching with RO events. By selecting 7 raindrop shapes such as TB, and 5 raindrop size distribution models such as MP, the T-matrix method is used to simulate these rainfall events. The Pearson correlation coefficient, root mean square error, and other parameters between the simulated polarimetric phase shift and the observation data calibrated using linear trend, or the observation data calibrated using antenna pattern are calculated respectively. The Pearson correlation coefficients between the simulated value and the calibrated value using linear trend, or the calibrated value using antenna pattern are 0.9994 and 0.9933, respectively. The root mean square error between the simulated value and the calibrated value using linear trend, or the calibrated value using antenna pattern are 0.3429 and 1.2765, respectively. The comparative analysis results show that there is a high correlation between the simulated value and the polarimetric phase shift measured by PAZ and the simulated results are closer to the polarimetric phase shift calibrated using linear trend. The results show that adopting MP or JD as the raindrop size distribution model and SC or PB as the raindrop shape can get higher accuracy when simulating events with a small rainfall rate (below 1 mm·h–1). For events with high rainfall rates (above 1 mm·h–1), selecting the MP or SS raindrop size distribution model and the TB raindrop shape can simulate the best results.
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Key words:
- Polarimetric phase shift /
- Polarimetric radio occultation /
- Rainfall /
- Forward simulation
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图 7
$ \Delta \varPhi $ 与$ \Delta {\varPhi }_{\mathrm{l}\mathrm{i}\mathrm{n}} $ 和$ \Delta {\varPhi }_{\mathrm{a}\mathrm{n}\mathrm{t}} $ 的关系Figure 7. Relationship between
$ \Delta \varPhi $ and$ \Delta {\varPhi }_{\mathrm{l}\mathrm{i}\mathrm{n}} $ ,$ \Delta {\varPhi }_{\mathrm{a}\mathrm{n}\mathrm{t}} $ 表 1 正演所用雨滴模型
Table 1. Raindrop models used in forwarding performance
雨滴模型 模型公式 BC (Beard-Chuang) $b/a=1.0048+5.7\times 1{0}^{-4}D-2.628\times 1{0}^{-2} {D}^{2}$
$+3.682\times 1{0}^{-3} {D}^{3}-1.677\times 1{0}^{-4} {D}^{4}$
($ D\leqslant 7\;\mathrm{m}\mathrm{m} $)obA (Oguchi) $b/a=1-0.1 \dfrac{D}{2}$ (较大雨滴) obB (Oguchi) $b/a=1-\dfrac{0.41}{9} D$ (较大雨滴) PB (Pruppacher-Beard) $b/a=1.03-0.062 D$ ($ 1\leqslant D\leqslant 9\;\mathrm{m}\mathrm{m} $) TB (Thurai-Bringi) $b/a=1.065-6.25\times 1{0}^{-2} D-3.99\times 1{0}^{-3} {D}^{2}$
$ +7.66\times 1{0}^{-4}{D}^{3}-4.095\times 1{0}^{-5} {D}^{4} $
($ \text{1.5}\leqslant D\leqslant 9\;\mathrm{m}\mathrm{m} $)SC (Steinert-Chandra) ${b}/{a}=1-10^{-2}\;{D^2}$ GR (Green) $b/a=1.0148-2.0465\times 1{0}^{-2} D-2.0048\times 1{0}^{-2} {D}^{2}$
$+3.09\times 1{0}^{-3} {D}^{3}-1.543\times 1{0}^{-4} {D}^{4}$表 2 正演所用雨滴谱分布
Table 2. Raindrop size distribution models used in forwarding performance
分布模型 表达式$/({\rm{m}}^{-3} \cdot {\rm{mm}}^{-1}) $ 经验参数 Marshall–Palmer (MP)分布 $N\left(D\right)={N}_{0}{{\rm{e}}}^{-\varLambda D}$ $ {N}_{0}=8000 $,$ \varLambda =4.1{R}^{-0.21} $ Laws-Parsons (LP)分布 $ {N}_{0}=5100{R}^{-0.03} $,$ \varLambda =3.8{R}^{-0.2} $ Sekhon-Srivastava (SS)分布 $ {N}_{0}=7000{R}^{0.37} $,$ \varLambda =3.8{R}^{-0.14} $ Joss分布 毛毛雨 (JD) $ {N}_{0}=30000 $,$ \varLambda =5.7{R}^{-0.21} $ 广布雨 (JW) $ {N}_{0}=7000 $,$ \varLambda =4.1{R}^{-0.21} $ 雷暴雨 (JT) ${N}_{0}=1400 $,$ \varLambda =3.0{R}^{-0.21} $ 表 3 2018年12月19日降雨事件正演结果
Table 3. Forward results of the rain event on 19 December 2018
雨滴形状 雨滴谱分布模型 $ {\Delta }{\varPhi }_{\mathrm{l}\mathrm{i}\mathrm{n}} $ $ {\Delta }{\varPhi }_{\mathrm{a}\mathrm{n}\mathrm{t}} $ MP LP SS JD JW BC 9.7285 9.5550 13.2806 8.8738 17.0256 4.7228 6.0154 obA 21.6714 19.6496 27.9718 31.0749 37.9248 obB 19.7122 17.8684 25.4371 28.2774 34.4919 PB 14.5598 13.9813 19.5714 14.0450 25.4842 TB 2.1843 3.7085 4.5574 –12.0205 3.8248 SC 5.6636 5.5146 7.6781 5.8649 9.9055 GR 11.7102 11.4385 15.9314 10.5048 20.4895 表 4 2019年12月19日降雨事件正演结果
Table 4. Forward results of the rain event on 19 December 2019
雨滴形状 雨滴谱分布模型 $ {\Delta }{\varPhi }_{\mathrm{l}\mathrm{i}\mathrm{n}} $ $ {\Delta }{\varPhi }_{\mathrm{a}\mathrm{n}\mathrm{t}} $ MP LP SS JD JW BC 42.6748 37.3830 54.7560 42.6554 74.6939 50.2430 52.8257 obA 74.6919 62.0340 98.3237 106.8904 130.7056 obB 67.8809 56.3753 89.3715 97.2678 118.7923 PB 58.8645 50.5148 76.3712 65.3379 103.0087 TB 26.9562 26.0200 32.9855 –3.6220 47.1618 SC 24.6297 21.6835 31.5413 25.3906 43.1193 GR 50.1853 43.6986 64.6629 51.3756 87.8163 表 5 降雨事件信息以及模型最优选择统计
Table 5. Statistics of rainfall events information and optimal model selection
RO事件 RO范围 GPM经过
时刻(UT)沿射线路径平均
降雨率/(mm·h–1)正演最优组合 日期 时间(UT) 纬度/(°) 经度/(°) 雨滴谱 最优雨滴模型 最大粒径/mm 2018-06-01 10:44 –20-–18 122-125 11:15 0.8353 JD SC 5.6 2018-06-10 08:02 –47-–44 168-171 06:47 0.4297 LP obA 5.6 2018-07-16 03:22 6-10 52-56 01:56 1.5094 MP TB 5.6 2018-08-24 22:14 –3-2 98-103 23:19 8.0735 LP TB 1.6 2018-10-16 06:14 3-8 158-165 04:10 14.3313 SS TB 1.6 2018-12-19 16:54 34-38 –147-–144 16:16 1.4317 SS TB 5.6 2018-12-25 11:21 –8-–4 113-116 10:29 1.4509 SS TB 5.6 2019-02-09 16:05 51-59 –172-–166 19:12 2.9561 LP TB 1.9 2019-02-15 14:43 –20-–17 –148-–143 12:08 5.1476 LP TB 1.9 2019-03-19 19:48 –30-–29 139-142 21:11 1.2528 JD GR 5.6 2019-03-21 12:48 –13-–8 –121-–116 13:13 2.3603 SS TB 2 2019-03-23 16:08 4-9 42-46 13:49 0.5395 MP SC 5.6 2019-04-18 01:34 –7-–4 74-77 03:51 0.3570 SS PB 5.6 2019-04-18 03:06 3-6 54-57 05:26 0.5205 SS PB 5.6 2019-05-07 07:49 –30-–22 135-141 06:58 1.8151 LP TB 2 2019-07-13 09:04 –43-–39 122-128 12:53 0.2626 SS obA 5.6 2019-07-16 02:47 9-12 60-64 03:13 1.4592 MP TB 5.6 2019-07-24 02:43 –47-–44 –112-–109 01:57 0.6810 JD SC 5.6 2019-07-28 11:02 –52-–50 98-104 10:54 1.9016 SS SC 5.6 2019-08-26 10:41 –31-–29 123-126 09:30 1.9969 JW TB 2 2019-10-18 01:53 –7-–1 –136-–130 00:28 0.3141 MP SC 5.6 2019-12-19 21:14 0-3 142-145 23:39 3.9332 MP GR 5.6 2019-12-21 00:51 –8-–2 –87-–83 02:40 1.3798 MP TB 2.5 2019-12-21 02:24 –11-–4 –108-–105 04:14 2.0559 MP TB 2 2019-12-26 08:10 –7-–2 –20-–16 08:23 1.8006 JW TB 2 2019-12-31 11:26 –2-4 –67-–63 10:18 1.3038 MP TB 5.6 -
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