| 研究生: |
柯凱鈞 Kai-Jun Ke |
|---|---|
| 論文名稱: |
新中壢電離層探測儀系統特性與實高分析-演算法與資料比對 New Chung-Li Ionosonde System Description and True Height Analysis - Algorithm and Data Comparison |
| 指導教授: |
朱延祥
Yen-Hsyang Chu |
| 口試委員: | |
| 學位類別: |
博士 Doctor |
| 系所名稱: |
地球科學學院 - 太空科學與工程學系 Department of Space Science and Engineering |
| 論文出版年: | 2022 |
| 畢業學年度: | 110 |
| 語文別: | 中文 |
| 論文頁數: | 176 |
| 中文關鍵詞: | 電離層探測儀 、電離圖 、實高分析 、自動判讀 、二維自相關函數 |
| 外文關鍵詞: | Ionosonde, Ionogram, True height analysis, Automatic Scaling, Two-dimension autocorrelation fuction |
| 相關次數: | 點閱:15 下載:0 |
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目前新中壢電離層觀測儀系統(Ionosonde) 於2020年開始執行運作,由太空科學與工程研究所特高頻雷達站團隊與澳洲Genesis公司共同開發研製。系統硬體設備部分,發射機採用脈波方式發射2至30MHz,頻率間距為50kHz時,共計561組頻段,其觀測距離為70至1214.32公里,距離解析度為3.84公里,整體掃頻時間約294.13秒,且使用16位元互補碼以增強回波訊號之訊雜比(Signal-to-Noise Ratio)。發射與接收天線採用倒V型設計,且利用GPS時間同步實現雙基雷達觀測(bistatic radar),而發射機部分則利用8組諧波濾波(harmonic filter) 方式發射訊號,接收機部分則用8組帶通濾波器(band-pass filter)接收2至30MHz訊號。
本研究主要為開發電離圖參數判讀演算法,包含雜訊與訊號干擾處理、訊號辨識、機器學習、電子密度反演、實高分析與參數回歸分析等。因訊號僅由單一通道接收,經電離圖訊號處理後的正常波(O-wave)與異常波(X-wave)訊號,僅提供回波強度資訊,因此本研究首次提出二維自相關函數法(2DACF)利用影像處理方式將兩極化波成功辨識並分開,且在電離層參數與電子密度反演時也利用國際電離層參考模型(IRI)與考慮E、F1、F2層與E-F谷區的類拋物線模型(MQP-VDW),最後利用逐步線性回歸分析模型對電離層參數調整,最後取得最佳電離層參數。資料分析主要比較演算法自動判讀結果與人工判讀結果,發現foF2 與h’F2參數比較結果良好,其中平均誤差0.84%與1.82%,標準差約8.19%與4.78%。另外福爾摩沙衛星七號掩星技術(Radio Occultation)資料包含foF2與hmF2也進行參數比對,根據掩星資料與測站距離遠近(5°至2°),其結果顯示foF2相關係數約0.88至0.93,平均誤差約−0.43至−0.26 MHz,標準偏差約0.73至1.06 MHz;hmF2相關係數約0.68至0.75,平均誤差約−8.18至−5.63 km,標準偏差約23.38至29.14 km。
In spite of being interrupted several times in its long history of operation since 1950, the routine observation of the ionosphere with various ionosondes installed at the Chung-Li ionosphere station in Taiwan has been achieved successively for more than seven decades. In this study, the system characteristics of the latest Chung-Li ionosonde and algorithm developed by National Central University for ionogram scaling and true height analysis, which started to routinely operate in 2020, are introduced.
The new Chung-Li ionosonde is a pulse radar that transmits a train of short pulses with respective carrier frequencies between 2 and 30 MHz at a frequency separation of 50 kHz. The duration of an entire frequency sweep is 294.13 s, which is divided into 561 frequency channels. The 16-bit complementary code is employed to increase the signal-to-noise of the reflected echoes. The observational range is from 70 to 1221 km with a range resolution of 3.84 km.
We developed an algorithm for the Chung-Li ionosonde to automatically scale the ionogram such that the true height profile of the ionospheric electron density can be retrieved. The observed traces of the ordinary wave (O-wave) and extraordinary wave (X-wave) displayed on the ionogram were first identified and separated by using 2-dimensional autocorrelation analysis combined with the image projection method. The true height analysis used stepwise regression. With the help of the International Reference Ionosphere (IRI) model and Multiple Quasi-Parabolic model with E-F valley (MQP-VDW), we carried out true height analysis to retrieve the ionospheric electron density profile based on the O-wave trace.
An examination showed that the ionospheric parameters (i.e., foF2, h’F2) retrieved from the automatic scaling algorithm were essentially in good agreement with those obtained from manual scaling. The ionosonde-measured foF2 and hmF2 were also compared with the FORMOSAT-7 measurements made with the GPS radio occultation technique. The results show that the correlation coefficient, mean difference , and root mean squared deviation were, respectively, in ranges from 0.88 to 0.93, −0.43 to −0.26 MHz, and 0.73 to 1.06 MHz for foF2 and in ranges from 0.68 to 0.75, −8.18 to −5.63km, and 23.38 to 29.14 km for hmF2.
吳剛宏. (2015). 改進 GPS 電波掩星法反演電離層 E 層電子濃度之誤差: COSMIC 觀測與 IRI 模型模擬. 國立中央大學博士論文.
柯凱鈞. (2018). 電離層參數判讀演算法與電離圖實高分析. 國立中央大學碩士論文.
Abdu, M. (2005). Equatorial ionosphere–thermosphere system: Electrodynamics and irregularities. Advances in Space Research, 35, 771-787. https://doi.org/10.1016/j.asr.2005.03.150
Arras, C., Wickert, J., Beyerle, G., Heise, S., Schmidt, T., & Jacobi, C. (2008). A global climatology of ionospheric irregularities derived from GPS radio occultation. Geophysical research letters, 35(14).
Axford, W. (1963). The formation and vertical movement of dense ionized layers in the ionosphere due to neutral wind shears. Journal of Geophysical Research, 68(3), 769-779.
Baginyan, S., Glazov, A., Kisel, I., Konotopskaya, E., Neskoromnyi, V., & Ososkov, G. (1994). Tracking by a modified rotor model of neural network. Computer Physics Communications, 79(2), 165-178. https://doi.org/ 10.1016/0010-4655(94)90065-5
Bamford, R., Stamper, R., & Cander, L. R. (2008). A comparison between the hourly autoscaled and manually scaled characteristics from the Chilton ionosonde from 1996 to 2004. Radio Science, 43(01), 1-11.
Becker-Guedes, F., Sahai, Y., Fagundes, P., Lima, W., Pillat, V., Abalde, J., & Bittencourt, J. (2004). Geomagnetic storm and equatorial spread-F. Annales Geophysicae,
Bilitza, D., Altadill, D., Truhlik, V., Shubin, V., Galkin, I., Reinisch, B., & Huang, X. (2017). International Reference Ionosphere 2016: From ionospheric climate to real‐time weather predictions. Space weather : the international journal of research & applications., 15(2), 418-429. https://doi.org/10.1002/2016SW001593
Bilitza, D., Altadill, D., Zhang, Y., Mertens, C., Truhlik, V., Richards, P., McKinnell, L.-A., & Reinisch, B. (2014). The International Reference Ionosphere 2012 – a model of international collaboration. J. Space Weather Space Clim., 4, A07. https://doi.org/10.1051/swsc/2014004
Boswell, D. (2002). Introduction to support vector machines. Departement of Computer Science and Engineering University of California San Diego.
Bowman, G., Dunne, G., & Hainsworth, D. (1987). Mid-latitude spread-F occurrence during daylight hours. Journal of Atmospheric and Terrestrial Physics, 49(2), 165-176.
Chapman, S. (1931). The absorption and dissociative or ionizing effect of monochromatic radiation in an atmosphere on a rotating earth part II. Grazing incidence. Proceedings of the Physical Society, 43(5), 483-501. https://doi.org/10.1088/0959-5309/43/5/302
Cherniak, I., Zakharenkova, I., Braun, J., Wu, Q., Pedatella, N., Schreiner, W., Weiss, J.-P., & Hunt, D. (2021). Accuracy assessment of the quiet-time ionospheric F2 peak parameters as derived from COSMIC-2 multi-GNSS radio occultation measurements. In: EDP Sciences.
Christakis, N., Haldoupis, C., Zhou, Q., & Meek, C. (2009). Seasonal variability and descent of mid-latitude sporadic E layers at Arecibo. Annales Geophysicae,
Chu, Y.-H., Su, C.-L., & Ko, H.-T. (2010). A global survey of COSMIC ionospheric peak electron density and its height: A comparison with ground-based ionosonde measurements. Advances in Space Research, 46(4), 431-439.
Coïsson, P., Radicella, S. M., Leitinger, R., & Nava, B. (2006). Topside electron density in IRI and NeQuick: Features and limitations. Advances in Space Research, 37(5), 937-942. https://doi.org/10.1016/j.asr.2005. 09.015
Cristianini, N., & Shawe-Taylor, J. (2000). An introduction to support vector machines and other kernel-based learning methods. Cambridge university press.
Croft, T. A., & Hoogansian, H. (1968). Exact Ray Calculations in a Quasi-Parabolic Ionosphere With No Magnetic Field. Radio Science, 3, 69-74.
Dalal, N. (2006). Finding people in images and videos Institut National Polytechnique de Grenoble-INPG].
Dalal, N., & Triggs, B. (2005). Histograms of oriented gradients for human detection. 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR'05),
Davies, K. (1990). Ionospheric radio / Kenneth Davies. Peregrinus on behalf of the Institution of Electrical Engineers.
dos Santos Prol, F., Themens, D. R., Hernández-Pajares, M., de Oliveira Camargo, P., & de Assis Honorato Muella, M. T. (2019). Linear Vary-Chap topside electron density model with topside sounder and radio-occultation data. Surveys in Geophysics, 40(2), 277-293.
Enell, C.-F., Kozlovsky, A., Turunen, T., Ulich, T., Välitalo, S., Scotto, C., & Pezzopane, M. (2016). Comparison between manual scaling and Autoscala automatic scaling applied to Sodankylä Geophysical Observatory ionograms. Geoscientific Instrumentation, Methods and Data Systems, 5(1), 53-64.
Galkin, I., Reinisch, B., Grinstein, G., Khmyrov, G., Kozlov, A., Huang, X., & Fung, S. (2004). Automated exploration of the radio plasma imager data. Journal of Geophysical Research, 109. https://doi.org/10.1029/2004JA 010439
Galkin, I., Reinisch, B., Ососков, Г., Zaznobina, E., & Neshyba, S. (1996). Feedback neural networks for ARTIST ionogram processing. Radio Science - RADIO SCI, 31, 1119-1128. https://doi.org/10.1029/96RS01513
Galkin, I. A., Khmyrov, G. M., Kozlov, A. V., Reinisch, B. W., Huang, X., & Paznukhov, V. V. (2008). The Artist 5. AIP Conference Proceedings,
Galkin, I. A., & Reinisch, B. W. (2008). The new ARTIST 5 for all digisondes. Ionosonde Network Advisory Group Bulletin, 69(8), 1-8.
Ghosh, P., & Berkey, F. (2015). Autonomous identification and classification of ionospheric sporadic E in digital ionograms. Earth and Space Science, 2(7), 244-261.
Haldoupis, C. (2011). A tutorial review on sporadic E layers. Aeronomy of the Earth's Atmosphere and Ionosphere, 381-394.
Harris, T. J., & Pederick, L. H. (2017). A Robust Automatic Ionospheric O/X Mode Separation Technique for Vertical Incidence Sounders. Radio Science, 52, 1534-1543. https://doi.org/10.1002/2017rs006279
Hernández‐Pajares, M., Garcia‐Fernàndez, M., Rius, A., Notarpietro, R., von Engeln, A., Olivares‐Pulido, G., Aragón‐Àngel, À., & García‐Rigo, A. (2017). Electron density extrapolation above F2 peak by the linear Vary‐Chap model supporting new Global Navigation Satellite Systems‐LEO occultation missions. Journal of Geophysical Research: Space Physics, 122(8), 9003-9014.
Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences, 79(8), 2554-2558. https://doi.org/doi:10.1073/pnas.79.8.2554
Hu, L., Ning, B., Liu, L., Zhao, B., Li, G., Wu, B., Huang, Z., Hao, X., Chang, S., & Wu, Z. (2014). Validation of COSMIC ionospheric peak parameters by the measurements of an ionosonde chain in China. Annales Geophysicae,
Huang, X., & Reinisch, B. W. (1996). Vertical electron density profiles from the Digisonde network. Advances in Space Research, 18(6), 121-129. https://doi.org/10.1016/0273-1177(95)00912-4
Huang, X., & Reinisch, B. W. (2000). Multiple quasi-parabolic presentation of the IRI profile. Advances in Space Research, 25(1), 129-132. https://doi.org/10.1016/S0273-1177(99)00909-6
Jiang, C., Yang, G., Lan, T., Zhu, P., Song, H., Zhou, C., Cui, X., Zhao, Z., & Zhang, Y. (2015). Improvement of automatic scaling of vertical incidence ionograms by simulated annealing. Journal of Atmospheric and Solar-Terrestrial Physics, 133, 178-184. https://doi.org/10.1016/j.jastp. 2015.09.002
Jiang, C., Yang, G., Liu, J., Yokoyama, T., Komolmis, T., Song, H., Lan, T., Zhou, C., Zhang, Y., & Zhao, Z. (2016). Ionosonde observations of daytime spread F at low latitudes. Journal of Geophysical Research: Space Physics, 121(12), 12,093-012,103.
Jiang, C., Yang, G., Zhao, Z., Zhang, Y., Zhu, P., & Sun, H. (2013). An automatic scaling technique for obtaining F 2 parameters and F 1 critical frequency from vertical incidence ionograms. Radio Science, 48(6), 739-751.
Jiang, C., Yang, G., Zhao, Z., Zhang, Y., Zhu, P., Sun, H., & Zhou, C. (2014). A method for the automatic calculation of electron density profiles from vertical incidence ionograms. Journal of Atmospheric and Solar-Terrestrial Physics, 107, 20-29.
Jo, E., Kim, Y. H., Moon, S., & Kwak, Y.-S. (2019). Seasonal and local time variations of sporadic E layer over South Korea. Journal of Astronomy and Space Sciences, 36(2), 61-68.
Ke, K.-J., Su, C.-L., Kuong, R.-M., Chen, H.-C., Lin, H.-S., Chiu, P.-H., Ko, C.-Y., & Chu, Y.-H. (2022). New Chung-Li Ionosonde in Taiwan: System Description and Preliminary Results. Remote Sensing, 14(8), 1913. https://www.mdpi.com/2072-4292/14/8/1913
Kelley, M. C. (2009). The Earth's ionosphere: Plasma physics and electrodynamics. Academic press.
Krankowski, A., Zakharenkova, I., Krypiak-Gregorczyk, A., Shagimuratov, I. I., & Wielgosz, P. (2011). Ionospheric electron density observed by FORMOSAT-3/COSMIC over the European region and validated by ionosonde data. Journal of Geodesy, 85(12), 949-964. https://doi.org/ 10.1007/s00190-011-0481-z
Lan, T., Zhang, Y., Jiang, C., Yang, G., & Zhao, Z. (2018). Automatic identification of Spread F using decision trees. Journal of Atmospheric and Solar-Terrestrial Physics, 179, 389-395.
Lee, C. C., Chen, W., & Chu, F. (2013). Observation of F region irregularities near a northern equatorial anomaly crest during solar minimum using ionosonde, GPS receiver, and satellites. Journal of Geophysical Research: Space Physics, 118(6), 3613-3621.
Lynn, K. (2017). Histogram-based ionogram displays and their application to autoscaling. Advances in Space Research, 61. https://doi.org/10.1016/ j.asr.2017.12.019
Lynn, K. J. (2018). Histogram-based ionogram displays and their application to autoscaling. Advances in Space Research, 61(5), 1220-1229.
Mallick, S. (2016). Histogram of oriented gradients explained using opencv. Retrieved from LearnOpenCV: https://learnopencv.com/histogram-of-oriented-gradients.
Mathews, J., Machuga, D., & Zhou, Q. (2001). Evidence for electrodynamic linkages between spread-F, ion rain, the intermediate layer, and sporadic E: results from observations and simulations. Journal of Atmospheric and Solar-Terrestrial Physics, 63(14), 1529-1543.
Matsushita, S. (1966). Sporadic E and ionospheric currents. Radio Science, 1(2), 204-211.
Nava, B., Coïsson, P., & Radicella, S. M. (2008). A new version of the NeQuick ionosphere electron density model. Journal of Atmospheric and Solar-Terrestrial Physics, 70(15), 1856-1862. https://doi.org/10.1016/ j.jastp.2008.01.015
Norman, R. J. (2003). An inversion technique for obtaining quasi-parabolic layer parameters from VI ionograms [radar signal processing]. 2003 Proceedings of the International Conference on Radar (IEEE Cat. No.03EX695), 363-367.
Nsumei, P., Reinisch, B. W., Huang, X., & Bilitza, D. (2012). New Vary-Chap profile of the topside ionosphere electron density distribution for use with the IRI model and the GIRO real time data. Radio Science, 47(04), 1-11.
Peterson, C. (1989). Track finding with neural networks. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 279(3), 537-545. https://doi.org/ 10.1016/0168-9002(89)91300-4
Pezzopane, M., & Scotto, C. (2010). Highlighting the F2 trace on an ionogram to improve Autoscala performance. Computers & Geosciences, 36(9), 1168-1177.
Picone, J. M., Hedin, A. E., Drob, D. P., & Aikin, A. C. (2002). NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues. Journal of geophysical research., 107(A12), SIA 15-11-SIA 15-16. https://doi.org/10.1029/2002JA009430
Piggott, W., & Rawer, K. (1972). URSI handbook of ionogram interpretation and reduction, Rep. UAG-23, 15.
Pignalberi, A., Pezzopane, M., & Zuccheretti, E. (2014). Sporadic E layer at mid-latitudes: average properties and influence of atmospheric tides. Annales Geophysicae,
Pillat, V. G., Guimarães, L. N. F., Fagundes, P. R., & da Silva, J. D. S. (2013). A computational tool for ionosonde CADI's ionogram analysis. Computers & Geosciences, 52, 372-378. https://doi.org/10.1016/j.cageo.2012.11.009
Ping, B., Su, F., & Meng, Y. (2016). An Improved DINEOF Algorithm for Filling Missing Values in Spatio-Temporal Sea Surface Temperature Data. PLoS ONE, 11.
Pope, P. T., & Webster, J. T. (1972). The Use of an F-Statistic in Stepwise Regression Procedures. Technometrics, 14(2), 327-340. https://doi.org/ 10.2307/1267425
Radicella, S. M., & Leitinger, R. (2001). The evolution of the DGR approach to model electron density profiles. Advances in Space Research, 27(1), 35-40. https://doi.org/https://doi.org/10.1016/S0273-1177(00)00138-1
Rawer, K. (1982). Replacement of the present sub-peak plasma density profile by a unique expression. Advances in Space Research, 2(10), 183-190. https://doi.org/10.1016/0273-1177(82)90387-8
Reinisch, B., Bilitza, D., Huang, X., & Nsumei, P. (2012). Vary-Chap topside electron density profile for IRI and GIRO. 1607.
Reinisch, B. W., Nsumei, P., Huang, X., & Bilitza, D. K. (2007). Modeling the F2 topside and plasmasphere for IRI using IMAGE/RPI and ISIS data. Advances in Space Research, 39(5), 731-738. https://doi.org/ 10.1016/j.asr.2006.05.032
Reinisch, B. W., & Xueqin, H. (1983). Automatic calculation of electron density profiles from digital ionograms: 3. Processing of bottomside ionograms. Radio Science, 18(3), 477-492.
Roberts, L. (1963). Machine Perception of Three-Dimensional Solids.
Scotto, C. (2009). Electron density profile calculation technique for Autoscala ionogram analysis. Advances in Space Research, 44(6), 756-766.
Scotto, C., & Pezzopane, M. (2007). A method for automatic scaling of sporadic E layers from ionograms. Radio Science, 42(2).
Scotto, C., & Pezzopane, M. (2008). Removing multiple reflections from the F2 layer to improve Autoscala performance. Journal of Atmospheric and Solar-Terrestrial Physics, 70(15), 1929-1934.
Scotto, C., Pezzopane, M., & Zolesi, B. (2012). Estimating the vertical electron density profile from an ionogram: On the passage from true to virtual heights via the target function method. Radio Science, 47(01), 1-6.
Scotto, C., & Settimi, A. (2014). The calculation of ionospheric absorption with modern computers. Advances in Space Research, 54(8), 1642-1650. https://doi.org/https://doi.org/10.1016/j.asr.2014.06.017
Settimi, A., Ippolito, A., Cesaroni, C., & Scotto, C. (2014). Scientific Review on the Ionospheric Absorption and Research Prospects of a Complex Eikonal Model for One-Layer Ionosphere. International Journal of Geophysics, 2014. https://doi.org/10.1155/2014/657434
Shaikh, M., Notarpietro, R., & Nava, B. (2014). The impact of spherical symmetry assumption on radio occultation data inversion in the ionosphere: An assessment study. Advances in Space Research, 53(4), 599-608.
Shi, S., Li, W., Zhang, K., Wu, S., Shi, J., Song, F., & Sun, P. (2021). Validation of COSMIC-2-Derived Ionospheric Peak Parameters Using Measurements of Ionosondes. Remote Sensing, 13(21), 4238.
Su, F., Zhao, Z., Li, S., Yao, M., Chen, G., & Zhou, Y. (2012). Signal Identification and Trace Extraction for the Vertical Ionogram. IEEE Geoscience and Remote Sensing Letters, 9, 1031-1035. https://doi.org/ 10.1109/LGRS.2012.2189350
Sultan, P. (1996). Linear theory and modeling of the Rayleigh‐Taylor instability leading to the occurrence of equatorial spread F. Journal of Geophysical Research: Space Physics, 101(A12), 26875-26891.
Sun, J., Zhang, X., Wang, S., Gong, Z.-Q., & Guangyou, F. (2016). Multi-quasi-parabolic ionosphere model with EF-valley. Annals of Geophysics, 59. https://doi.org/10.4401/ag-6780
Thrane, E. V., & Piggott, W. R. (1966). The collision frequency in the E- and D-regions of the ionosphere. Journal of Atmospheric and Terrestrial Physics, 28(8), 721-737. https://doi.org/10.1016/0021-9169(66)90021-3
Tsai, L.-C., & Berkey, F. (2000). Ionogram analysis using fuzzy segmentation and connectedness techniques. Radio Science, 35, 1173-1186. https://doi.org/ 10.1029/1999RS002170
Tsai, L. C., & Berkey, F. T. (2000). Ionogram analysis using fuzzy segmentation and connectedness techniques. Radio Science, 35(5), 1173-1186.
Ullman, S. (2002). Structural Saliency: The Detection of Globally Salient Structures Using a Locally Connected Network.
Wakai, N., Ohyama, H., & Koizumi, T. (1987). Manual of ionogram scaling. Radio Research Laboratory, Ministry of Posts and Telecommunications, Japan.
Welch, G., & Bishop, G. (2001). An Introduction to the Kalman Filter.
Whitehead, J. (1961). The formation of the sporadic-E layer in the temperate zones. Journal of Atmospheric and Terrestrial Physics, 20(1), 49-58.
Yamashita, T., Yamashita, K., & Kamimura, R. (2007). A Stepwise AIC Method for Variable Selection in Linear Regression. Communications in Statistics - Theory and Methods, 36(13), 2395-2403. https://doi.org/ 10.1080/03610920701215639
Yang, K.-F., Chu, Y.-H., Su, C.-L., Ko, H.-T., & Wang, C.-Y. (2009). An examination of FORMOSAT-3/COSMIC ionospheric electron density profile: Data quality criteria and comparisons with the IRI model. Terrestrial, Atmospheric and Oceanic Sciences, 20(1), 193.
Yen, S.-C., & Finkel, L. H. (1998). Extraction of perceptually salient contours by striate cortical networks. Vision Research, 38(5), 719-741. https://doi.org/ 10.1016/S0042-6989(97)00197-1
Zabotin, N., Wright, J., & Zhbankov, G. (2006). NeXtYZ: Three-dimensional electron density inversion for dynasonde ionograms. Radio Science, 41(06), 1-12.