Thomas A. Herring

GPS meteorology: Remote sensing of atmospheric water vapor using the global positioning system

We present a new approach to remote sensing of water vapor based on the global positioning system (GPS). Geodesists and geophysicists have devised methods for estimating the extent to which signals propagating from GPS satellites to ground-based GPS receivers are delayed by atmospheric water vapor. This delay is parameterized in terms of a time-varying zenith wet delay (ZWD) which is retrieved by stochastic filtering of the GPS data. Given surface temperature and pressure readings at the GPS receiver, the retrieved ZWD can be transformed with very little additional uncertainty into an estimate of the integrated water vapor (IWV) overlying that receiver. Networks of continuously operating GPS receivers are being constructed by geodesists, geophysicists, government and military agencies, and others in order to implement a wide range of positioning capabilities. These emerging GPS networks offer the possibility of observing the horizontal distribution of IWV or, equivalently, precipitable water with unprecedented coverage and a temporal resolution of the order of 10 min. These measurements could be utilized in operational weather forecasting and in fundamental research into atmospheric storm systems, the hydrologic cycle, atmospheric chemistry, and global climate change. Specially designed, dense GPS networks could be used to sense the vertical distribution of water vapor in their immediate vicinity. Data from ground-based GPS networks could be analyzed in concert with observations of GPS satellite occultations by GPS receivers in low Earth orbit to characterize the atmosphere at planetary scale.

ICESat's laser measurements of polar ice, atmosphere, ocean, and land

The Ice, Cloud and Land Elevation Satellite (ICESat) mission will measure changes in elevation of the Greenland and Antarctic ice sheets as part of NASA’s Earth Observing System (EOS) of satellites. Timeseries of elevation changes will enable determination of the present-day mass balance of the ice sheets, study of associations between observed ice changes and polar climate, and estimation of the present and future contributions of the ice sheets to global sea level rise. Other scientific objectives of ICESat include: global measurements of cloud heights and the vertical structure of clouds and aerosols; precise measurements of land topography and vegetation canopy heights; and measurements of sea ice roughness, sea ice thickness, ocean surface elevations, and surface reflectivity. The Geoscience Laser Altimeter System (GLAS) on ICESat has a 1064 nm laser channel for surface altimetry and dense cloud heights and a 532 nm lidar channel for the vertical distribution of clouds and aerosols. The predicted accuracy for the surfaceelevation measurements is 15 cm, averaged over 60 m diameter laser footprints spaced at 172 m alongtrack. The orbital altitude will be around 600 km at an inclination of 94 � with a 183-day repeat pattern. The on-board GPS receiver will enable radial orbit determinations to better than 5 cm, and star-trackers will enable footprints to be located to 6 m horizontally. The spacecraft attitude will be controlled to point

GPS meteorology: mapping zenith wet delays onto precipitable water

Abstract Emerging networks of Global Positioning System (GPS) receivers can be used in the remote sensing of atmospheric water vapor. The time-varying zenith wet delay observed at each GPS receiver in a network can be transformed into an estimate of the precipitable water overlying that receiver. This transformation is achieved by multiplying the zenith wet delay by a factor whose magnitude is a function of certain constants related to the refractivity of moist air and of the weighted mean temperature of the atmosphere. The mean temperature varies in space and time and must be estimated a priori in order to transform an observed zenith wet delay into an estimate of precipitable water. We show that the relative error introduced during this transformation closely approximates the relative error in the predicted mean temperature. Numerical weather models can be used to predict the mean temperature with an rms relative error of less than 1%.

GPS Meteorology: Direct Estimation of the Absolute Value of Precipitable Water

Abstract A simple approach to estimating vertically integrated atmospheric water vapor, or precipitable water, from Global Positioning System (GPS) radio signals collected by a regional network of ground-based geodetic GPS receiver is illustrated and validated. Standard space geodetic methods are used to estimate the zenith delay caused by the neutral atmosphere, and surface pressure measurements are used to compute the hydrostatic (or “dry”) component of this delay. The zenith hydrostatic delay is subtracted from the zenith neutral delay to determine the zenith wet delay, which is then transformed into an estimate of precipitable water. By incorporating a few remote global tracking stations (and thus long baselines) into the geodetic analysis of a regional GPS network, it is possible to resolve the absolute (not merely the relative) value of the zenith neutral delay at each station in the augmented network. This approach eliminates any need for external comparisons with water vapor radiometer observation...

Modeling of nutation and precession: New nutation series for nonrigid Earth and insights into the Earth's interior

A one-piece unitary right-angle electrical contact is made by cold heading a segment of bar stock to form a cylindrical body having a flat strip thereon coplanar with the center axis of the body. The flat strip is milled transversely to form terminal posts of rectangular cross-section which are integral with the body of the contact.

Space geodetic measurement of crustal deformation in central and southern California, 1984-1992

A laboratory type of analyzer for quantitatively determining the percent third element content of a hydrocarbon sample. A unique rhodium/americium radioactive source is disclosed.

Forced nutations of the Earth: Influence of inner core dynamics: 1. Theory

Gravitational and pressure couplings between the solid inner core and the rest of the Earth give rise to torques through which the inner core influences the nutational motions of the Earth. In view of the very small magnitude of the moment of inertia of the inner core relative to that of the the Earth as a whole, one expects from physical considerations that inclusion of the inner core in the dynamics should lead to a new nutational normal mode with a natural frequency not too far from that of the free core nutation, and to an associated weak resonance in the amplitude of forced nutations. We present here a treatment of the nutation problem for an oceanless, elastic, spheroidally stratified Earth, with the dynamical role of the inner core explicitly included in the formulation. As a preliminary to the setting-up of dynamical equations, we devote some attention to a careful definition of a suitable coordinate system and of certain basic dynamical variables. We use the approach of Sasao et al. (1980), with their system of dynamical equations enlarged by the inclusion of two additional equations which are needed to describe the rotational motion of the inner core. An extension and sharpening of a line of reasoning employed by them enables us to derive expressions for the torques which couple the mantle and the fluid outer core to the solid inner core. Solving the enlarged system of equations, we show that a new nearly diurnal eigenfrequency does emerge; a rough estimate places it not very far from the prograde annual tidal excitation frequency, so that possible resonance effects on nutation amplitudes need careful consideration. Another eigenfrequency, attributable to a wobble of the inner core, is also found; its value is estimated to be a few times smaller than the wobble frequency that the inner core would have in the absence of couplings to the rest of the Earth. Considering an expansion, in terms of resonance contributions, of the amplitude of forced nutations normalized relative to that for a corresponding rigid Earth model, we indicate how the coefficients in the expansion are related to those in expansions of the type used by Wahr (1981b). Finally, we discuss the problem of comparing observed nutation amplitudes with those computed on the basis of Earth models generated from seismological data, with special reference to the fact that the dynamical ellipticity of the Earth, as computed from published Earth models which assume the condition of hydrostatic equilibrium, differs significantly from that determined from the precession constant. Numerical results, corrections for unmodeled effects, and comparison with observational results will be dealt with in accompanying papers.

Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data

We develop a formalism for parameterizing and evaluating the effects of lateral variations in the properties of Earths atmosphere on the propagation of microwave signals. A parametric form is incorporated into our analysis of very long baseline interferometry (VLBI) data, and the estimated atmospheric delay gradients are compared with those calculated from three-dimensional weather analysis fields from the National Center for Environmental Prediction (NCEP). For a 12-day series of experiments in January 1994, the VLBI and the NCEP analyses show common atmospheric gradient delays with amplitudes of up to 30 mm at 10° elevation angle. Comparison of the characteristics over a longer period of time reveals common mean north-south gradients with amplitudes up to ≈10 mm at 10° elevation at midlatitudes. No discernible mean east-west gradients were found in either data set. The root-mean-square (RMS) variations of the gradient effects, determined from the NCEP analysis, are similar in the north-south and east-west directions, with a typical RMS scatter of 6–10 mm at 10° elevation. After accounting for gradients, detailed analysis of the January 1994 VLBI data shows clearly that the residual station height variations of ≈10 mm at Westford, Massachusetts, are almost totally explained by the effects of atmospheric pressure loading.

Geodesy by radio interferometry: Water vapor radiometry for estimation of the wet delay

An important source of error in very-long-baseline interferometry (VLBI) estimates of baseline length is unmodeled variations of the refractivity of the neutral atmosphere along the propagation path of the radio signals. We present and discuss the method of using data from a water vapor radiometer (WVR) to correct for the propagation delay caused by atmospheric water vapor, the major cause of these variations. Data from different WVRs are compared with estimated propagation delays obtained by Kalman filtering of the VLBI data themselves. The consequences of using either WVR data or Kalman filtering to correct for atmospheric propagation delay at the Onsala VLBI site are investigated by studying the repeatability of estimated baseline lengths from Onsala to several other sites. The lengths of the baselines range from 919 to 7941 km. The repeatability obtained for baseline length estimates shows that the methods of water vapor radiometry and Kalman filtering offer comparable accuracies when applied to VLBI observations obtained in the climate of the Swedish west coast. For the most frequently measured baseline in this study, the use of WVR data yielded a 13% smaller weighted-root-mean-square (WRMS) scatter of the baseline length estimates compared to the use of a Kalman filter. It is also clear that the “best” minimum elevation angle for VLBI observations depends on the accuracy of the determinations of the total propagation delay to be used, since the error in this delay increases with increasing air mass. For use of WVR data along with accurate determinations of total surface pressure, the best minimum is about 20 degrees; for use of a model for the wet delay based on the humidity and temperature at the ground, the best minimum is about 35 degrees.

Forced nutations of the Earth: Influence of inner core dynamics: 2. Numerical results and comparisons

We apply the theory developed in Paper 1 (Mathews et al., this issue), which includes the solid inner core explicitly in the dynamical equations, to obtain the eigenfrequencies and other characteristics of the Earths nutational normal modes as well as the amplitudes of forced nutations at various tidal frequencies, for two commonly used Earth models, 1066A and the Preliminary Reference Earth Model (PREM). We also make an evaluation of various procedures for taking account of known deviations of the Earth from models, notably in the dynamical ellipticity e for which the two models yield values which are over 1% smaller than the value e* deduced from the precession constant. On adopting the procedure of simply replacing e by e* in the equations of our theory, the values obtained for some of the nutation amplitudes for model 1066A differ significantly from the corresponding results of Wahr (1981b). The largest of the differences, which occur in the prograde semiannual, retrograde 18.6 year, and retrograde annual nutation terms, amount to −0.59, 0.35, and −0.25 milliarcseconds (mas), respectively, while the standard errors in the very long baseline interferometry (VLBI) determinations are now only about 0.04 mas except in the long period terms. The difference in the procedures used to take account of the discrepancy between e and e* contributes −0.56, 0.81, and −0.17 mas, respectively, to the above-noted differences. For the purpose of comparison with VLBI-observed data, we use the results for a “modified PREM,” defined by a set of Earth model parameters which differ from those of PREM only in having e* for the dynamical ellipticity of the Earth as a whole and a modified value for the dynamical ellipticity eƒ of the fluid outer core. The amplitudes computed for this model, with corrections applied for the effects of ocean tides and mantle anelasticity, are in generally satisfactory agreement with observed values, when the modified eƒ is determined by matching the theoretical and observed values for the retrograde annual term. (The modified eƒ is 0.002665, about 4.6% higher than in PREM, equivalent to an increase, relative to PREM, of about 430 meters in the difference between the equatorial and the polar radii of the core-mantle boundary. We find that contributions from inner-core dynamics to the prograde semiannual and annual, and the retrograde 18.6 year and annual terms, recomputed for modified PREM, amount to −0.09, 0.03, −0.36, and −0.09 mas, respectively.) The largest residual remaining, other than in the long-period terms which still have an uncertainty of about 1 mas, is −0.25 mas in the prograde fortnightly amplitude. Consideration of possible sources of the discrepancies is facilitated by a resonance expansion of the amplitude of forced nutations, as a function of frequency, normalized relative to that for a rigid Earth model. We also provide tables which exhibit the sensitivities of various relevant quantities (the eigenfrequencies and the coefficients which appear in the resonance expansion, as well as the nutation amplitudes at important tidal frequencies) to possible errors in the Earth parameters which enter our theory. Reconciliation of theoretical and experimental values for the prograde fortnightly term, for instance, could be accomplished, without affecting significantly the comparison for other nutation terms, by a decrease of about 10% in the value of the compliance parameter k that represents, in effect, the deformability of the Earth as a whole in response to perturbations of its rotation; but this change in k would have to be produced by some mechanism which does not affect the values of the other compliances.