Radio Occultations Using Earth Satellites: a Wave Theory Treatment DEEP SPACE COMMUNICATIONS and NAVIGATION SERIES
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Radio Occultations Using Earth Satellites: A Wave Theory Treatment DEEP SPACE COMMUNICATIONS AND NAVIGATION SERIES Issued by the Deep Space Communications and Navigation Systems Center of Excellence Jet Propulsion Laboratory California Institute of Technology Joseph H. Yuen, Editor-in-Chief Previously Published Monographs in this Series 1. Radiometric Tracking Techniques for Deep-Space Navigation C. L. Thornton and J. S. Border 2. Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation Theodore D. Moyer 3. Bandwidth-Efficient Digital Modulation with Application to Deep-Space Communications Marvin K. Simon 4. Large Antennas of the Deep Space Network William A. Imbriale 5. Antenna Arraying techniques in the Deep Space Network David H. Rogstad, Alexander Mileant, and Timothy T. Pham Radio Occultations Using Earth Satellites: A Wave Theory Treatment William G. Melbourne Jet Propulsion Laboratory California Institute of Technology MONOGRAPH 6 DEEP SPACE COMMUNICATIONS AND NAVIGATION SERIES Radio Occultations Using Earth Satellites: A Wave Theory Treatment April 2004 The research described in this publication was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not constitute or imply its endorsement by the United States Government or the Jet Propulsion Laboratory, California Institute of Technology. Table of Contents Foreword..............................................................................................................xvii Preface...................................................................................................................xix Acknowledgments................................................................................................xxiii Chapter 1: Radio Occultation Using Earth Satellites Background and Overview ...........................................1 1.1 Introduction...................................................................1 1.1.1 History of the Occultation Technique ............................2 1.1.2 Occultations from Earth Satellites..................................3 1.1.3 The Global Positioning System ......................................8 1.1.4 Timing ...........................................................................11 1.1.5 Ephemerides ..................................................................12 1.2 Information Content in GPS Occultation Observations............................................................... 13 1.2.1 Connected Phase ...........................................................13 1.2.2 Sample Rate Versus Vertical Resolution .....................14 1.2.3 Inverting Radio Occultation Data.................................14 1.2.4 Assimilating Radio Occultation Data...........................17 1.2.5 Rays and Stationarity ....................................................18 1.2.6 Excess Doppler..............................................................21 1.3 Scientific Applications of GPS Occultation Observations............................................................... 23 1.3.1 Weather..........................................................................24 1.3.2 Climate...........................................................................27 1.4 Problems from Multipath and Some Remedies ......... 28 1.4.1 Spectral/Holographic Techniques.................................32 1.4.2 Back Propagation ..........................................................34 v vi 1.4.3 The Canonical Transform Technique...........................41 1.4.4 The Impact Parameter Space Curve .............................41 1.4.5 A Full-Spectrum Wave Theory ....................................43 1.5 Overview...................................................................... 47 1.5.1 Chapter 2 .......................................................................47 1.5.2 Chapter 3 .......................................................................48 1.5.3 Chapter 4 .......................................................................49 1.5.4 Chapter 5 .......................................................................50 1.5.5 Chapter 6 .......................................................................52 1.5.6 Appendices ....................................................................60 1.6 Limitations and Simplifications.................................. 61 1.6.1 Ionosphere .....................................................................61 1.6.2 Placing the Occulted GPS Satellite at Infinity .............61 1.6.3 Time...............................................................................63 1.6.4 Spherical Symmetry......................................................63 1.6.5 Coplanarity ....................................................................63 1.6.6 Circularity......................................................................64 1.6.7 Treating the GPS Signal as a Harmonic Wave ............64 1.7 Recommendations for the Next Chapters.................. 65 References ............................................................................ 66 Chapter 2: Scattering of Electromagnetic Waves from a Spherical Boundary Using a Thin Phase Screen Model and Scalar Diffraction Theory......................... 77 2.1 Introduction................................................................. 77 2.1.1 Multipath Scenarios ......................................................79 2.1.2 An Overview of Chapter 2............................................82 2.2 Geometric Optics in a Spherical Medium................... 83 2.2.1 Multipath, Shadow Zones, and Caustics According to Geometric Optics....................................86 2.2.2 Thin-Atmosphere Conditions .......................................90 Table of Contents vii 2.3 Thin Phase Screen Models ......................................... 92 2.3.1 The Helmholtz–Kirchoff Integral Theorem .................93 2.3.2 The Space Curve for Impact Parameter........................94 2.3.3 The Fresnel Phase Screen ...........................................100 2.3.4 Suitability of the Thin-Screen Model for Diffraction Analysis....................................................101 2.3.5 A Phase Profile for the Thin Screen...........................102 2.3.6 Bending-Angle Perturbations .....................................103 2.3.7 Case A: A Discontinuity in Refractivity ....................105 2.3.8 Case B: A Discontinuity in Scale Height ...................107 2.3.9 Case C: A Discontinuity in Lapse Rate......................109 2.4 Multipath Using a Thin Phase Screen Model ........... 109 2.5 Scalar Diffraction: The Rayleigh–Sommerfeld Integral ...................................................................... 114 2.6 The Stationary-Phase Technique ............................. 116 2.6.1 Necessary Conditions for Validity of the Geometric Optics Approach .......................................121 2.7 Numerical Results Using Thin-Screen/Scalar Diffraction.................................................................. 122 2.7.1 Fresnel Response to a Discontinuity in Lapse Rate ...................................................................125 2.7.2 Fresnel Response to a Discontinuity in Refractivity..................................................................128 2.7.3 A Boundary Layer.......................................................131 2.8 Sensing a Boundary in the Ionosphere.................... 133 2.8.1 Fresnel Effects at a Boundary.....................................136 2.8.2 Amplitude Effects at a Boundary ...............................139 2.8.3 Ray Splitting................................................................140 2.8.4 Doppler Information at a Boundary............................146 2.8.5 Fresnel Effects Using an Improved Electron Density Model.............................................................148 viii 2.9 The Error in the Recovered Refractivity Resulting from Fresnel Phase Perturbations ........................... 152 2.10 Fresnel Transform Techniques ............................... 156 2.10.1 Adjoining the Constraint Au()≡ 1.............................158 2.10.2 Diffraction Integral with Multipath ............................159 2.10.3 A Numerical Example.................................................159 2.10.4 Fresnel Aliasing...........................................................161 2.10.5 Numerical Results .......................................................162 References .......................................................................... 167 Chapter 3: Scattering from a Large Transparent Sphere Based on Maxwell’s Equations: Mie Scattering Theory ..................................................... 171 3.1 Introduction............................................................... 171 3.2 Scalar Potentials ....................................................... 174 3.2.1 Series Expansions for Scalar Potentials .....................176 3.3 Multiple Internal Reflections..................................... 179 3.4 Fresnel Formulas for Reflection and Transmission Amplitudes......................................... 181 3.4.1 Conservation Principle................................................184 3.4.2 Scattering Angles and Intensities ...............................185 3.4.3 Caustics........................................................................189