Modeling and prediction of ionospheric characteristics using nonlinear autoregression and neural network by Hendy Santosa Submitted in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF ENGINEERING at The University of Electro-Communications 非線形同定手法を用いた電離層特性のモデリングおよび予測に関する研究 ヘンデイサントーサ 論文の和文要旨 地球を取り巻く電離層は，その中を通過，反射する電磁波の伝搬特性に多大な影響 を及ぼすことが知られている。電離層の継続的な特性の観測には，電磁波による遠 隔探査（リモートセンシング）が広く用いられている。例えば，電離層中で最大の 電子密度をもつ F 層の観測には，電磁波の鉛直打ち上げ（イオノゾンデ）が用いら れ，電子密度の高度分布が得られる。一方，MLT （Mesosphere-Lower Thermosphere） 領域である電離層下端の D 層は，その電子密度の小ささゆえ，VLF 帯送信電波の受 信振幅，位相の変化がほぼ唯一の観測方法である。電離層は，その上層及び下層起 源の様々な要因（外因）により，時間空間的に複雑に変動する。例えば，上層から の外因として太陽活動の影響が挙げられる一方で，下層からの外因として大気の影 響が挙げられる。しかしながら，外因別の電離層の変動への定量的評価は，現在ま でにほとんど行われていない。そこで本研究では，非線形システム同定手法を用い て，D 層および F２層における，電離層の時間変化の予測モデルを構築し，外因別の 貢献度を導出した。特に，D 層の電離層状態を表す VLF 送信電波振幅の時間変動予 測モデルの構築は初の試みである。さらに，D 層，F 層ともに，外因別の貢献度の導 出も初めてである。今後これらの研究成果は，電離層のダイナミクスの理解，太陽 活動や大気パラメータの監視，通信障害の予測，さらには地震に関連する異常値検 出等に貢献する可能性がある。D 層に関しては，電通大 VLF 帯送信電波観測ネット ワークにより受信された様々な緯度を通過する国内外からの送信電波の電界振幅の 長期時系列観測データを解析した。まず，電界振幅データに非線形システム同定手 法の一つである NARXNN（Nonlinear AutoRegressive with eXogenous input Neural Network）を適用して，プロセスモデルを生成し，電界振幅の時間変化に対する支配 的な外因を同定した。次に，これらの支配的な外因を用いて，予測を行い構築され たモデルの評価を実施した。その結果，予測値と観測値の間に非常に高い相関係数 が得られた。また，緯度の異なる伝搬経路において支配的な外因に違いが見られ， その理由に対する物理的考察を行った。さらに，F 層に関しては，中緯度帯である 日本国内で観測された，イオノゾンデのデータを用いて，D 層と同様の解析を実施 し，予測モデルを構築するとともに，D 層と F 層間の特性の相違を調査した. Modeling and prediction of ionospheric characteristics using nonlinear autoregression and neural network Hendy Santosa Abstract The terrestrial ionosphere from D-region (60 km) to F-region (500 km) plays an important role in radio wave propagation between the Earth and ionosphere. During the last half-century, a considerable experimental, theoretical, and modeling efforts have been made to understand the physical process occurred in the ionosphere at different altitudes. Radio sensing techniques is widely used to continuously monitor the ionospheric conditions. For example, the ionospheric property in the F2 layer is obtained by a vertical sounding so-called Ionosonde. Properties of the D layer (the lower end of the ionosphere) is effectively obtained by receiving VLF/LF transmitter signals. Although, the ionospheric condition varies both in time and space due to various external forcings from the atmosphere and space weather parameters, quantitative information of contributions influencing the ionosphere from every external forcing have not understood well. In this thesis nonlinear autoregressive with exogenous input and neural network is applied first time to identify the ionospheric characteristics based on the VLF radio wave propagation and ionosonde. One step ahead prediction of the daily nighttime means of VLF electric amplitude in three different latitude paths and two receiving stations by using NARXNN has been carried out. The relative contribution to the ionospheric conditions (VLF electric amplitude variability) from every external forcing has been revealed. Moreover, the proposed model extends for multi-step ahead prediction to evaluate the performance of prediction accuracy for five and ten days ahead. The temporal dependence of F2-region critical frequency (foF2) has been predicted by using the same approach as used for the VLF signals. Physical interpretation of relative contribution to the ionospheric conditions from major external forcing parameters have been made. The results of this thesis can be used to detect anomalies in relation with severe weather, major seismic activity, and space weather to mitigate damages and human victims. Furthermore, we investigate the coupling from external sources between the D- and F-region in the middle-latitude path. Acknowledgements I am very grateful to my supervisor, Prof. Yasuhide Hobara, for his indispensable advice at every step helping me to make my work conceptually sound and also to draw my attention to even the smallest mistakes to improve my academic writing. With his great enthusiasm and efforts to explain things clearly and simply, he has guided me to the point where I have been able to complete the work of my thesis. I will remain in debt to both my co-supervisors Prof. Yanagisawa and Prof. Yoshiaki Ando, Prof. Balikhin and my laboratory assistant professor Dr. Takuo Tsuda for their priceless advice that I have progressed towards becoming a professional researcher. I would like to thank my friends, Dr. Sujay Pal, Dr. Tamal Basak, Dr. Satya Vemuri Srinivas, Mr. Tomoki Kawano, Mr. Yuma Matsui, Mr. Katsunori Suzuki and Mrs. Emiko Takahashi, for assisting me in preparing a gold standard for the evaluation of my results. I would like to thank all my colleagues for sharing their valuable experience to guide me through writing the thesis. I cannot end without thanking my parents, my wife (Fauziah Yaman) and all my family for being so patient all these years I have worked on the Ph.D. Not only have they provided constant encouragement but also compromised on several ends to allow me to complete my thesis. I would like to thank Directorate General of Resources for Science, Technology and Higher Education (DG-RSTHE) of Ministry of Research, Technology, and Higher Education of Indonesia for supporting financial expenses during my Ph.D. program. Contents 論文の和文要旨 ........................................................................................................................ 2 Abstract ..................................................................................................................................... 4 Acknowledgements .................................................................................................................. 5 Contents ..................................................................................................................................... i 1. Introduction .................................................................................................................... 1 1.1 Background ............................................................................................................. 1 1.2 Space Weather and Ionospheric Research .............................................................. 4 1.3 Nonlinear System Identification ............................................................................. 6 1.4 Objectives................................................................................................................ 8 1.5 Outline ..................................................................................................................... 9 1.6 Significance ........................................................................................................... 10 2. Radio Waves Propagating in the Ionosphere ............................................................. 12 2.1 Investigating the Ionosphere ................................................................................. 13 2.1.1 Very Low Frequency (VLF) Measurement ............................................ 13 2.1.1.1 VLF Wave Propagation in the Earth’s Ionosphere Waveguide 14 2.1.1.2 VLF Transmitter ....................................................................... 16 2.1.1.3 VLF Receiver ........................................................................... 17 2.1.1.4 VLF Technical Architecture ..................................................... 19 2.1.2 Ionosonde ................................................................................................ 19 2.2 Solar Disturbances ................................................................................................ 21 2.2.1 Ionospheric Disturbances ........................................................................ 22 2.2.2 Traveling Ionospheric Disturbances ....................................................... 22 2.3 Non-Solar Disturbances ........................................................................................ 23 2.3.1 Lightning -Induced Electron Precipitation (LEP) ................................... 23 2.3.2 Early Events ............................................................................................ 23 2.3.3 Atmospheric Gravity Waves ................................................................... 24 3. Nonlinear Autoregressive with Exogenous Input Neural Network (NARXNN) .... 26 3.1 The Concept of an Artificial Neural Networks (ANNs) ....................................... 26 i 3.2 Recurrent Neural Networks .................................................................................. 27 3.3 NARXNN Structure .............................................................................................. 30 3.4 Training a Neural Network ................................................................................... 32 3.4.1 Avoid Overfitting .................................................................................... 32 3.4.2 Training Classification ............................................................................ 34 3.4.2.1 Supervised training ................................................................... 35 3.4.2.2 Unsupervised training ............................................................... 35 3.4.2.3 Reinforcement training ............................................................. 35 3.4.3 Training Algorithm ................................................................................. 35 3.4.3.1 Bayesian regulation training algorithm .................................... 36 3.4.3.2 Levenberg-Marquardt training algorithm ................................