Geodetic Refraction : Effects of Electromagnetic Wave Propagation Through the Atmosphere

With very few exceptions, geodetic measurements use electro­ magnetic radiation in order to measure directions, distances, time delays, and Doppler frequency shifts, to name the main ter­ restrial and space observables. Depending on the wavelength of the radiation and the purpose of the measurements, the follow­ ing parameters of the electromagnetic wave are measured: ampli­ tude, phase, angle-of-arrival, polarisation and frequency. Ac­ curate corrections have to be applied to the measurements in order to take into account the effects of the intervening medium between transmitter and receiver. The known solutions use at­ mospheric models, special observation programs, remote sensing techniques and instrumental methods. It has been shown that the effects of the earth's atmospheric envelope present a fundamental limitation to the accuracy and precision of geodetic measurements. This applies equally to ter­ restrial and space applications. Instrumental accuracies are al­ ready below the atmospherically induced limitations, and thus the accuracy demands on the geodetic refraction solutions are entering a new magnitude zone. This monograph is primarily devoted to the properties of the at­ mospheric effects on various geodetic measurements and to their evaluation. Ten review papers cover the most pressing aspects of the atmospheric effects on geodetic measurement~. Ttiese state­ of-the art papers were written by eminent specialists in their respective research fields.

A. Overview of Geodetic Refraction Studies.- 1. Introduction.- 2. The Challenge.- 3. Organisation.- References.- B. Two Wavelength Angular Refraction Measurement.- 1. Introduction.- 2. Theory of the Method.- 2.1 The Refraction Integral.- 2.2 Refraction Magnitudes.- 2.3 The Two Wavelength Relationship.- 2.4 Consideration of Water Vapour.- 3. Instrumental Methods.- 3.1 Instrumental Approaches.- 3.2 Khvostikov.- 3.3 Tengström.- 3.4 Vshivkov and Shilkin.- 3.5 Startsev and Tukh.- 3.6 Brein and Glissmann.- 3.7 Dyson and Williams.- 3.8 Astheimer and McHenry.- 3.9 Mikhailov.- 4. Concluding Discussion.- 4.1 Future Prospects.- 4.2 Refraction Elimination.- Appendix: Notation.- References.- C. Effects of Atmospheric Turbulence on Geodetic Interference Measurements: Methods of its Reduction.- 1. Introduction.- 2. Signal-to-Noise Ratio.- 2.1 General Remarks.- 2.2 Symmetrical Interferometer with Similar and Completely Correlated Fluctuations in Both Beams.- 2.3 Symmetrical Interferometer with Similar but Partially Correlated Fluctuations.- 2.4 Interferometers with the Reference Arm without Fluctuations.- 2.5 Discussion.- 3. Angle-of-Arrival Fluctuation: Estimation of the Effect.- 4. Linear Interference Measurements: Fluctuation Effect and its Reduction.- Appendix: Notation.- References.- D. Multiple Wavelength Electromagnetic Distance Measurement.- 1. Introduction.- 2. Instrument Design ― General Principles.- 3. Instrument Design ― Engineering Tradeoffs.- 4. Proposed Instrument Design.- 5. Current Instrument.- References.- E. Water Vapor Radiometry in Geodetic Applications.- 1. Introduction.- 2. The Problem.- 3. Formulation of the Algorithm.- 4. Determination of “Constants” in the Algorithm.- 5. Instrumentation.- 6. Vapor Effects on Baseline Determination.- 7. Summary and Conclusions.- Appendix A: Notation.- References.- F. Temperature and Humidity Structure in the Lower Atmosphere.- 1. Introduction.- 2. Broad Considerations.- 3. The Atmospheric Surface Layer.- 3.1 Turbulent Transfer Relationships.- 3.2 Diabatic Mean Profile Forms.- 3.3 Features of Temperature and Humidity Fluctuations.- 3.4 Magnitude of Temperature and Humidity Fluctuations.- 3.5 Spectrum and Structure Function.- 4. The Atmospheric Boundary Layer.- 4.1 Broad Character.- 4.2 Convective Boundary Layer.- 4.3 Stable Boundary Layer.- 5. Surface Complexities.- 5.1 Introduction.- 5.2 Small-Scale Adjustment or “Local Advection”.- 5.3 Sea Breeze.- 5.4 Hill-Valley Effects.- Notation.- References.- G. Modelling of Atmospheric Effects on Terrestrial Geodetic Measurements.- 1. Introduction.- 2. Concept of Modelling.- 3. The Atmospheric Turbulence Model.- 4. Integral Models for r?.- 4.1 Overview.- 4.2 Rectification Model.- 4.3 Operational Model.- 4.4 Discussion.- 5. Model Evaluation.- 6. Conclusion.- Appendix A: Notation.- References.- H. Refraction in Geodetic Levelling.- 1. Introduction.- 2. Investigations of Refraction by Kukkamäki.- 3. General Equation for Levelling Refraction.- 4. Temperature Gradient in the Atmospheric Boundary Layer.- 5. The Holdahl Model for Levelling.- 6. National Geodetic Survey Tests.- 7. Investigations using Angus-Leppan Equations.- 8. Statistical Analysis.- 9. Systematic and Random Effects.- 10. Conclusions.- Appendix: Notation.- I. Atmospheric Refraction Effects in Time and Latitude Observations Using Classical Techniques.- 1. Introduction.- 2. Expressions for Astronomical Refraction.- 3. Refraction Problems in VZT, PZT and Astrolabe Observations.- 4. Actual Atmospheric Structure.- 5. Refraction Effects and Meteorological Improvements for Their Corrections.- 6. Concluding Remarks.- References.- J. The Equations of Electromagnetic Wave Propagation in a Refractive Medium Corotating with the Earth.- 1. Introduction.- 2. The Variational Problem.- 2.1 Euler-Lagrange Equations.- 2.2 The Hamiltonian Complex.- 2.3 Invariant Postulates.- 2.4 Examples.- 3. The Variational Principle of the Wave Equations in an Electromagnetic Medium.- 3.1 The Faraday-Maxwell Tensors.- 3.2 Linear Constitutive Equations.- 3.3 The Variational Principles of the Wave Equation.- 4. A Discussion of the Wave Equation in an Earth-Fixed Frame.- 4.1 The Set of Wave Equations in a Medium at Rest in an Inertial Frame.- 4.2 The Set of Wave Equations in a Medium Corotating with the Earth.- 4.3 Examples.- Appendix A: Notation.- Appendix B: The Formal Structure of Electromagnetism.- References.