Atmospheric Effects in Space Geodesy

This first part in the book on atmospheric effects in space geodesy provides a review of the basic structure, composition, and workings of the atmosphere and serves as a general background needed to help the reader understand the material in later parts. Its large diversity of topics would usually not be included in one paper, but since this work is designed as a textbook in a university geodesy course, we intentionally discuss this broad variety of topics at the outset. The reader may wish to skip this part and only revisit it as references and interest suggest. Here we cover the following topics: After an overview of atmospheric effects in space geodesy, we briefly review physical terminology and meteorological quantities. Then, we discuss gas laws and atmospheric statics, and we introduce specific topics like reference pressure, atmospheric tides, and the inverted barometer hypothesis, all of which reappear in later parts. After an overview of atmospheric layers and circulation, we concentrate on the ionosphere, highlighting ionization and recombination processes and introducing the concept of Chapman layer profiles. Finally, we discuss height- and latitude-dependent spatial variations as well as regular and non-regular temporal variations in the ionosphere.

The ionosphere is a dispersive medium for space geodetic techniques operating in the microwave band. Thus, signals traveling through this medium are—to the first approximation—affected proportionally to the inverse of the square of their frequencies. This effect, on the other hand, can reveal information about the parameters of the ionosphere in terms of Total Electron Content (TEC) of the electron density. This part of the book provides an overview of ionospheric effects on microwave signals. First, the group and phase velocities are defined along with the refractive index in the ionosphere and the ionospheric delay. Then, we focus mainly on the mitigation and elimination of ionospheric delays in the analysis of space geodetic observations, specifically for Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI) observations. In particular, we summarize existing models as well as strategies based on observations at two or more frequencies to eliminate first and higher order delays. Finally, we review various space geodetic techniques (including satellite altimetry and radio occultation data) for estimating values and maps of TEC.

This part describes the effects of the troposphere—strictly speaking the neutral atmosphere—on the propagation delay of space geodetic signals. A theoretical description of this tropospheric propagation delay is given as well as strategies for correcting for it in the data analysis of the space geodetic observations. The differences between the tropospheric effects for microwave techniques, like the Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI), and those for optical techniques, like Satellite Laser Ranging (SLR), are discussed. Usually, residual tropospheric delays are estimated in the data analysis, and the parameterization needed to do so is presented. Other possibilities of correcting for the tropospheric delays are their calculation by ray-tracing through the fields of numerical weather models and by utilizing water vapor radiometer measurements. Finally, we shortly discuss how space geodetic techniques can be used in atmospheric analysis in meteorology and climatology.

Loading of the Earth’s crust due to variations of global atmosphere pressure can displace the positions of geodetic sites by more than 1 cm both vertically and horizontally on annual to sub-diurnal time scales, and thus has to be taken into account in the analysis of space geodetic observations. This part of the book discusses methods for the calculation of the displacements. In particular, it summarizes the simple approach with regression coefficients between surface pressure and the vertical displacement and the more rigorous geophysical approach with load Love numbers and Green’s functions. Furthermore, we describe the special treatment of the thermal tides (S1 and S2), the importance of the reference pressure, as well as the inverted barometer hypothesis for the oceans. Finally, we present space geodetic results with the application of those correction models for the analysis of Very Long Baseline Interferometry observations.

The varying atmosphere exerts two disturbing forces on the gravity signal: first the so-called direct effect or Newtonian attraction, where the object in questions is attracted by the atmospheric mass itself; and second the indirect effect or atmospheric loading, where the overlying atmospheric mass has a deforming effect on the Earth’s surface, also changing the measured gravity signal. In satellite gravity missions, these short-period signals cause aliasing effects in the gravity field determination and their elimination is indispensable. For the determination of the required atmospheric gravity field coefficients, it is state of the art to use high-resolution numerical weather models, which take into account the three-dimensional distribution of the atmospheric mass. In this part of the book, we address many relevant issues, including the theoretical fundamentals of the Earth’s gravity field and its description using spherical harmonics, as well as the basics of the atmospheric pressure distribution. A short overview of the gravity satellite missions of the last decade like GRACE (Gravity Recovery and Climate Experiment) is given and the impact of the atmosphere on the satellite measurements is examined. We present a descriptions of the oceanic mass response to overlying atmospheric pressure and of the models used for de-aliasing of atmospheric effects.