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The Rotational and Gravitational Effect of Earthquakes

The static displacement field generated by an earthquake has the effect of rearranging the Earth's mass distribution and will consequently cause the Earth's rotation and gravitational field to change. Although the coseismic effect of earthquakes on the Earth's rotation and gravitational field have been modeled in the past, no unambiguous observations of this effect have yet been made. However, the Gravity Recovery And Climate Experiment (GRACE) satellite, which is scheduled to be launched in 2001, will measure time variations of the Earth's gravitational field to high degree and order with unprecedented accuracy. In this presentation, the modeled coseismic effect of earthquakes upon the Earth's gravitational field to degree and order 100 will be computed and compared to the expected accuracy of the GRACE measurements. In addition, the modeled second degree changes, corresponding to changes in the Earth's rotation, will be compared to length-of-day and polar motion excitation observations.

Gross, Richard↗

Space Science Reference Guide, 2nd Edition

This Edition contains the following reports: GRACE: Gravity Recovery and Climate Experiment; Impact Craters in the Solar System; 1997 Apparition of Comet Hale-Bopp Historical Comet Observations; Baby Stars in Orion Solve Solar System Mystery; The Center of the Galaxy; The First Rock in the Solar System; Fun Times with Cosmic Rays; The Gamma-Ray Burst Next Door; The Genesis Mission: An Overview; The Genesis Solar Wind Sample Return Mission; How to Build a Supermassive Black Hole; Journey to the Center of a Neutron Star; Kepler's Laws of Planetary Motion; The Kuiper Belt and Oort Cloud ; Mapping the Baby Universe; More Hidden Black Hole Dangers; A Polarized Universe; Presolar Grains of Star Dust: Astronomy Studied with Microscopes; Ring Around the Black Hole; Searching Antarctic Ice for Meteorites; The Sun; Astrobiology: The Search for Life in the Universe; Europa and Titan: Oceans in the Outer Solar System?; Rules for Identifying Ancient Life; Inspire ; Remote Sensing; What is the Electromagnetic Spectrum? What is Infrared? How was the Infrared Discovered?; Brief History of Gyroscopes ; Genesis Discovery Mission: Science Canister Processing at JSC; Genesis Solar-Wind Sample Return Mission: The Materials ; ICESat: Ice, Cloud, and Land Elevation Satellite ICESat: Ice, Cloud, and Land; Elevation Satellite ICESat: Ice, Cloud, and Land Elevation Satellite ICESat: Ice, Cloud, and Land Elevation Satellite ICESat: Ice, Cloud, and Land Elevation Satellite Measuring Temperature Reading; The Optical Telescope ; Space Instruments General Considerations; Damage by Impact: The Case at Meteor Crater, Arizona; Mercury Unveiled; New Data, New Ideas, and Lively Debate about Mercury; Origin of the Earth and Moon; Space Weather: The Invisible Foe; Uranus, Neptune, and the Mountains of the Moon; Dirty Ice on Mars; For a Cup of Water on Mars; Life on Mars?; The Martian Interior; Meteorites from Mars, Rocks from Canada; Organic Compounds in Martian Meteorites May be Terrestrial Contaminants; Bands on Europa;Big Mountain, Big Landslide on Jupiter's Moon, Io; Cratering of the Moon; Europa's Salty Surface; The Europa Scene in the Voyager-Galileo Era; Explosive Volcanic Eruptions on the Moon; Ice on the Bone Dry Moon; Jupiter's Hot, Mushy Moon; The Moon Beyond 2002 ; Phases of the Moon; The Ph-D Project: Manned Expedition to the Moons of Mars; and Possible Life in a Europan Ocean.

Dotson, Renee↗

Earth System Dynamics: The Determination and Interpretation of the Global Angular Momentum Budget using the Earth Observing System

The objective of this investigation has been to examine the mass and momentum exchange between the atmosphere, oceans, solid Earth, hydrosphere, and cryosphere. The investigation has focused on changes in the Earth's gravity field, its rotation rate, atmospheric and oceanic circulation, global sea level change, ice sheet change, and global ground water circulation observed by contemporary sensors and models. The primary component of the mass exchange is water. The geodetic observables provided by these satellite sensors are used to study the transport of water mass in the hydrological cycle from one component of the Earth to another, and they are also used to evaluate the accuracy of models. As such, the investigation is concerned with the overall global water cycle. This report provides a description of scientific, educational and programmatic activities conducted during the period July 1, 1999 through June 30,2000. Research has continued into measurements of time-varying gravity and its relationship to Earth rotation. Variability of angular momentum and the related excitation of polar motion and Earth rotation have been examined for the atmosphere and oceans at time-scales of weeks to several years. To assess the performance of hydrologic models, we have compared geodetic signals derived from them with those observed by satellites. One key component is the interannual mass variability of the oceans obtained by direct observations from altimetry after removing steric signals. Further studies have been conducted on the steric model to quantify its accuracy at global and basin-scales. The results suggest a significant loss of water mass from the Oceans to the land on time-scales longer than 1-year. These signals are not reproduced in any of the models, which have poorly determined interannual fresh water fluxes. Output from a coupled atmosphere-ocean model testing long-term climate change hypotheses has been compared to simulated errors from the Gravity Recovery and Climate Experiment (GRACE) mission. Results indicate that GRACE will be able to observe seasonal signals at half-wavelengths ranging from 1000 to 10000 km, and may be able to observe secular trends at half- wavelengths of greater than 2000-3000 km for soil moisture and snow depth if they are as large as some of the climate experiments predict.

Source record↗

Moving water to South America as observed from space

The approximate balance of the mass change rate measured by the Gravity Recovery and Climate Experiment (GRACE) with the moisture influx across the entire coastline less climatological river discharge for South America (SA), in agreement with the conservation principle, bolsters not only the credibility of the spacebased measurements, but supports the characterization of ocean's influence on the annual variation of continental water balance. The moisture transport integrated over the depth of the atmosphere is estimated using measurements by QuikSCAT and Special Sensor Microwave/Imager. The large-scale geographic patterns of precipitation from the Tropical Rain Measuring Mission (TRMM) and the mass change rate were found to follow similar annual changes over South America.

monsoon↗

Thermal Band Atmospheric Correction Using Atmospheric Profiles Derived from Global Positioning System Radio Occultation and the Atmospheric Infrared Sounder

This Rapid Prototyping Capability study explores the potential to use atmospheric profiles derived from GPS (Global Positioning System) radio occultation measurements and by AIRS (Atmospheric Infrared Sounder) onboard the Aqua satellite to improve surface temperature retrieval from remotely sensed thermal imagery. This study demonstrates an example of a cross-cutting decision support technology whereby NASA data or models are shown to improve a wide number of observation systems or models. The ability to use one data source to improve others will be critical to the GEOSS (Global Earth Observation System of Systems) where a large number of potentially useful systems will require auxiliary datasets as input for decision support. Atmospheric correction of thermal imagery decouples TOA radiance and separates surface emission from atmospheric emission and absorption. Surface temperature can then be estimated from the surface emission with knowledge of its emissivity. Traditionally, radiosonde sounders or atmospheric models based on radiosonde sounders, such as the NOAA (National Oceanic & Atmospheric Administration) ARL (Air Resources Laboratory) READY (Real-time Environmental Application and Display sYstem), provide the atmospheric profiles required to perform atmospheric correction. Unfortunately, these types of data are too spatially sparse and too infrequently taken. The advent of high accuracy, global coverage, atmospheric data using GPS radio occultation and AIRS may provide a new avenue for filling data input gaps. In this study, AIRS and GPS radio occultation derived atmospheric profiles from the German Aerospace Center CHAMP (CHAllenging Minisatellite Payload), the Argentinean Commission on Space Activities SAC-C (Satellite de Aplicaciones Cientificas-C), and the pair of NASA GRACE (Gravity Recovery and Climate Experiment) satellites are used as input data in atmospheric radiative transport modeling based on the MODTRAN (MODerate resolution atmospheric TRANsmittance) radiative transport software to separate out the atmospheric component of measured top of atmosphere radiance. Simulated water bodies across a variety of MODTRAN model atmospheres including desert, mid-latitude, tropical and sub-artic conditions provide test bed conditions. Atmospherically corrected radiance and surface temperature results were compared to those obtained using traditional radiosonde balloon data and models. In general, differences between the different techniques were less than 2 percent indicating the potential value satellite derived atmospheric profiles have to atmospherically correct thermal imagery.

Pagnutti, Mary↗

Spacebased Observations of Oceanic Influence on the Annual Variation of South American Water Balance

The mass change of South America (SA) continent measured by the Gravity Recovery and Climate Experiment (GRACE) imposes a constraint on the uncertainties in estimating the annual variation of rainfall measured by Tropical Rain Measuring Mission (TRMM) and ocean moisture influx derived from QuikSCAT data. The approximate balance of the mass change rate with the moisture influx less climatological river discharge, in agreement with the conservation principle, bolsters not only the credibility of the spacebased measurements, but supports the characterization of ocean's influence on the annual variation of continental water balance. The annual variation of rainfall is found to be in phase with the mass change rate in the Amazon and the La Plata basins, and the moisture advection across relevant segments of the Pacific and Atlantic coasts agrees with the annual cycle of rainfall in the two basins and the Andes mountains.

rainfall annual cycle↗

Spaceborne Autonomous and Ground Based Relative Orbit Control for the TerraSAR-X/TanDEM-X Formation

TerraSAR-X (TSX) and TanDEM-X (TDX) are two advanced synthetic aperture radar (SAR) satellites flying in formation. SAR interferometry allows a high resolution imaging of the Earth by processing SAR images obtained from two slightly different orbits. TSX operates as a repeat-pass interferometer in the first phase of its lifetime and will be supplemented after two years by TDX in order to produce digital elevation models (DEM) with unprecedented accuracy. Such a flying formation makes indeed possible a simultaneous interferometric data acquisition characterized by highly flexible baselines with range of variations between a few hundreds meters and several kilometers [1]. TSX has been successfully launched on the 15th of June, 2007. TDX is expected to be launched on the 31st of May, 2009. A safe and robust maintenance of the formation is based on the concept of relative eccentricity/inclination (e/i) vector separation whose efficiency has already been demonstrated during the Gravity Recovery and Climate Experiment (GRACE) [2]. Here, the satellite relative motion is parameterized by mean of relative orbit elements and the key idea is to align the relative eccentricity and inclination vectors to minimize the hazard of a collision. Previous studies have already shown the pertinence of this concept and have described the way of controlling the formation using an impulsive deterministic control law [3]. Despite the completely different relative orbit control requirements, the same approach can be applied to the TSX/TDX formation. The task of TDX is to maintain the close formation configuration by actively controlling its relative motion with respect to TSX, the leader of the formation. TDX must replicate the absolute orbit keeping maneuvers executed by TSX and also compensate the natural deviation of the relative e/i vectors. In fact the relative orbital elements of the formation tend to drift because of the secular non-keplerian perturbations acting on both satellites. The goal of the ground segment is thus to regularly correct this configuration by performing small orbit correction maneuvers on TDX. The ground station contacts are limited due to the geographic position of the station and the costs for contact time. Only with a polar ground station a contact visibility is possible every orbit for LEO satellites. TSX and TDX use only the Weilheim ground station (in the southern part of Germany) during routine operations. This station allows two scheduled contact per day for the nominal orbit configuration, meaning that the satellite conditions can be checked with an interval of 12 hours. While this limitation is usually not critical for single satellite operations, the visibility constraints drive the achievable orbit control accuracy for a LEO formation if a ground based approach is chosen. Along-track position uncertainties and maneuver execution errors affect the relative motion and can be compensated only after a ground station contact.

Ardaens, J. S.↗

Annual Variations in Water Storage and Precipitation in the Amazon Basin: Bounding Sink Terms in the Terrestrial Hydrological Balance using GRACE Satellite Gravity Data

We combine satellite gravity data from the Gravity Recovery and Climate Experiment (GRACE) and precipitation measurements from the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center's (CPC) Merged Analysis of Precipitation (CMAP) and the Tropical Rainfall Measuring Mission (TRMM), over the period from mid-2002 to mid-2006, to investigate the relative importance of sink (runoff and evaporation) and source (precipitation) terms in the hydrological balance of the Amazon Basin. When linear and quadratic terms are removed, the time series of land water storage variations estimated from GRACE exhibits a dominant annual signal of 250 mm peak-to-peak, which is equivalent to a water volume change of approximately 1800 cubic kilometers. A comparison of this trend with accumulated (i.e., integrated) precipitation shows excellent agreement and no evidence of basin saturation. The agreement indicates that the net runoff and evaporation contributes significantly less than precipitation to the annual hydrological mass balance. Indeed, raw residuals between the detrended water storage and precipitation anomalies range from plus or minus 40 mm. This range is consistent with streamflow measurements from the region, although the latter are characterized by a stronger annual signal than ow residuals, suggesting that runoff and evaporation may act to partially cancel each other.

Crowley, John W.↗

Ongoing Development of NASA's Global Land Data Assimilation System

NASA's Global Land Data Assimilation System (GLDAS) produces global fields of land surface states (e.g., soil moisture and temperature) and fluxes (e.g., latent heat flux and runoff) by driving offline land surface models with observation-based inputs, using the Land Information System (LIS) software. Since production began in 2001, GLDAS has supported more than 100 scientific investigations and applications. Some examples are GEWEX and NASA Energy and Water Cycle Study (NEWS) global water and energy budget analyses, interpretations of hydrologic data derived from the Gravity Recovery and Climate Experiment (GRACE) satellite mission, and forecast model initiation studies at NOAA and NASA. At the same time, the GLDAS team has continued improve results through the development of new modeling and data assimilation techniques. Here we describe several recent and ongoing innovations. These include global implementation of a runoff routing procedure, GRACE data assimilation, advanced snow cover assimilation, and irrigation modeling.

Rodell, Matthew↗

Greenland Ice Sheet Surface Temperature, Melt, and Mass Loss: 2000-2006

Extensive melt on the Greenland Ice Sheet has been documented by a variety of ground and satellite measurements in recent years. If the well-documented warming continues in the Arctic, melting of the Greenland Ice Sheet will likely accelerate, contributing to sea-level rise. Modeling studies indicate that an annual or summer temperature rise of 1 C on the ice sheet will increase melt by 20-50% therefore, surface temperature is one of the most important ice-sheet parameters to study for analysis of changes in the mass balance of the ice-sheet. The Greenland Ice Sheet contains enough water to produce a rise in eustatic sea level of up to 7.0 m if the ice were to melt completely. However, even small changes (centimeters) in sea level would cause important economic and societal consequences in the world's major coastal cities thus it is extremely important to monitor changes in the ice-sheet surface temperature and to ultimately quantify these changes in terms of amount of sea-level rise. We have compiled a high-resolution, daily time series of surface temperature of the Greenland Ice Sheet, using the I-km resolution, clear-sky land-surface temperature (LST) standard product from the Moderate-Resolution Imaging Spectroradiometer (MODIS), from 2000 - 2006. We also use Gravity Recovery and Climate Experiment (GRACE) data, averaged over 10-day periods, to measure change in mass of the ice sheet as it melt and snow accumulates. Surface temperature can be used to determine frequency of surface melt, timing of the start and the end of the melt season, and duration of melt. In conjunction with GRACE data, it can also be used to analyze timing of ice-sheet mass loss and gain.

Hall, Dorothy K.↗

Models of Active Glacial Isostasy Roofing Warm Subduction: Case of the South Patagonian Ice Field

Modern geodetic techniques such as precise Global Positioning System (GPS) and high-resolution space gravity mapping (Gravity Recovery and Climate Experiment, GRACE) make it possible to measure the present-day rate of viscoelastic gravitational Earth response to present and past glacier mass changes. The Andes of Patagonia contain glacial environments of dramatic mass change. These mass load changes occur near a tectonically active boundary between the Antarctic and South American plates. The mechanical strength of the continental side of this boundary is influenced by Neogene ridge subduction and by the subduction of a youthful oceanic slab. A ridge of young volcanos parallels the Pacific coastline. Release of volatiles (such as water) at depth along this ridge creates a unique rheological environment. To assess the influence of this rheological ridge structure on the observational land uplift rate, we apply a two dimensional viscoelastic Earth model. A numerical study is presented which examines the sensitivity of the glacial loading-unloading response to the complex structure at depth related to the subducting slab, the viscous wedge between slab and continental lithosphere, and the increase of elastic thickness from oceanic to continental lithosphere. A key feature revealed by our numerical experiments is a continuum flow wherein the slab subdues the material transport toward oceanic mantle and crust. The restricted flow is sensitive to the details of slab mechanical strength and penetration into the upper mantle. The reduced viscosity within the mantle wedge, however, enhances the load-induced material transport everywhere within the asthenosphere.

crustal mass changes↗

Assimilation of GRACE Terrestrial Water Storage Data into a Land Surface Model

The NASA Gravity Recovery and Climate Experiment (GRACE) system of satellites provides observations of large-scale, monthly terrestrial water storage (TWS) changes. In. this presentation we describe a land data assimilation system that ingests GRACE observations and show that the assimilation improves estimates of water storage and fluxes, as evaluated against independent measurements. The ensemble-based land data assimilation system uses a Kalman smoother approach along with the NASA Catchment Land Surface Model (CLSM). We assimilated GRACE-derived TWS anomalies for each of the four major sub-basins of the Mississippi into the Catchment Land Surface Model (CLSM). Compared with the open-loop (no assimilation) CLSM simulation, assimilation estimates of groundwater variability exhibited enhanced skill with respect to measured groundwater. Assimilation also significantly increased the correlation between simulated TWS and gauged river flow for all four sub-basins and for the Mississippi River basin itself. In addition, model performance was evaluated for watersheds smaller than the scale of GRACE observations, in the majority of cases, GRACE assimilation led to increased correlation between TWS estimates and gauged river flow, indicating that data assimilation has considerable potential to downscale GRACE data for hydrological applications. We will also describe how the output from the GRACE land data assimilation system is now being prepared for use in the North American Drought Monitor.

Reichle, Rolf H.↗

Remote Sensing of Terrestrial Water Storage and Application to Drought Monitoring

Terrestrial water storage (TWS) consists of groundwater, soil moisture and permafrost, surface water, snow and ice, and wet biomass. TWS variability tends to be dominated by snow and ice in polar and alpine regions, by soil moisture in mid-latitudes, and by surface water in wet, tropical regions such as the Amazon (Rodell and Famiglietti, 2001; Bates et al., 2007). Drought may be defined as a period of abnormally dry weather long enough to cause significant deficits in one or more of the TWS components. Thus, along with observations of the agricultural and socioeconomic impacts, measurements of TWS and its components enable quantification of drought severity. Each of the TWS components exhibits significant spatial variability, while installation and maintenance of sufficiently dense monitoring networks is costly and labor-intensive. Thus satellite remote sensing is an appealing alternative to traditional measurement techniques. Several current remote sensing instruments are able to detect variations in one or more TWS variables, including the Advanced Microwave Scanning Radiometer (AMSR) on NASA's Aqua satellite and the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA's Terra and Aqua. Future satellite missions have been proposed to improve this capability, including the European Space Agency's Soil Moisture Ocean Salinity mission (SMOS) and the Soil Moisture Active Passive (SMAP), Surface Water Ocean Topography (SWOT), and Snow and Cold Land Processes (SCLP) missions recommended by the US National Academy of Science's Decadal Survey for Earth Science (NRC, 2007). However, only one remote sensing technology is able to monitor changes in TWS from the land surface to the base of the deepest aquifer: satellite gravimetry. This paper focuses on NASA's Gravity Recovery and Climate Experiment mission (GRACE; http://www.csr.utexas.edu/grace/) and its potential as a tool for drought monitoring.

Rodell, Matt↗

Recent Changes in the Greenland Ice Sheet as Seen from Space

Many changes in the Greenland Ice Sheet have been reported in the recent scientific literature and have been attributed to various responses of the ice sheet due to regional (and global) warming. Because melting of the ice sheet would contribute approximately 7 m to sea-level rise, the lives and habitat of hundreds of millions of people worldwide would be directly and indirectly affected if continued ice-sheet melting occurs. As mean-annual global temperatures have increased, there has been an increasing focus on studying the Greenland Ice Sheet using available satellite data, and numerous expeditions have been undertaken. Regional "clear-sky" surface temperature increases since the early 1980s in the Arctic, measured using Advanced Very High Resolution Radiometer (AVHRR) infrared data, range from 0.57+/-0.02 C to 0.72+/-0.10 C per decade. Arctic warming has important implications for ice-sheet mass balance because much of the periphery of the Greenland Ice Sheet is already near O C during the melt season, and is thus vulnerable to more extensive melting if temperatures continue to increase. An increase in melting of the ice sheet would accelerate sea-level rise, an issue of increasing concern to billions of people worldwide. The surface temperature of the ice sheet has been studied in even greater detail using Moderate-Resolution Imaging Spectroradiometer (MODIS) data in the six individual drainage basins as well as for the ice sheet as a whole. Surface temperature trends in the decade of the 2000s have not been strong, according to the MODIS measurements. In addition to surface-temperature increases over the last few decades as measured by AVHRR, other changes have been observed such as accelerated movement of many of Greenland's outlet glaciers and sudden draining of supraglacial lakes. Decreasing mass of the ice sheet since (at least) 2002 has been measured using Gravity Recovery and Climate Experiment (GRACE) data, along with an build-up of ice at the higher elevations and a decrease of ice at the lower elevations as measured using airborne Lidar and Ice, Cloud and Land Elevation Satellite (ICESat) data. The seminar will address the above issues using a variety of NASA satellite data and ground observations.

Hall, Dorothy K.↗

Towards Improved Snow Water Equivalent Estimation via GRACE Assimilation

Passive microwave (e.g. AMSR-E) and visible spectrum (e.g. MODIS) measurements of snow states have been used in conjunction with land surface models to better characterize snow pack states, most notably snow water equivalent (SWE). However, both types of measurements have limitations. AMSR-E, for example, suffers a loss of information in deep/wet snow packs. Similarly, MODIS suffers a loss of temporal correlation information beyond the initial accumulation and final ablation phases of the snow season. Gravimetric measurements, on the other hand, do not suffer from these limitations. In this study, gravimetric measurements from the Gravity Recovery and Climate Experiment (GRACE) mission are used in a land surface model data assimilation (DA) framework to better characterize SWE in the Mackenzie River basin located in northern Canada. Comparisons are made against independent, ground-based SWE observations, state-of-the-art modeled SWE estimates, and independent, ground-based river discharge observations. Preliminary results suggest improved SWE estimates, including improved timing of the subsequent ablation and runoff of the snow pack. Additionally, use of the DA procedure can add vertical and horizontal resolution to the coarse-scale GRACE measurements as well as effectively downscale the measurements in time. Such findings offer the potential for better understanding of the hydrologic cycle in snow-dominated basins located in remote regions of the globe where ground-based observation collection if difficult, if not impossible. This information could ultimately lead to improved freshwater resource management in communities dependent on snow melt as well as a reduction in the uncertainty of river discharge into the Arctic Ocean.

Forman, Bart↗

Estimation and Validation of Oceanic Mass Circulation from the GRACE Mission

Since the launch of the Gravity Recovery And Climate Experiment (GRACE) in March 2002, the Earth's surface mass variations have been monitored with unprecedented accuracy and resolution. Compared to the classical spherical harmonic solutions, global high-resolution mascon solutions allows the retrieval of mass variations with higher spatial and temporal sampling (2 degrees and 10 days). We present here the validation of the GRACE global mascon solutions by comparing mass estimates to a set of about 100 ocean bottom pressure (OSP) records, and show that the forward modelling of continental hydrology prior to the inversion of the K-band range rate data allows better estimates of ocean mass variations. We also validate our GRACE results to OSP variations modelled by different state-of-the-art ocean general circulation models, including ECCO (Estimating the Circulation and Climate of the Ocean) and operational and reanalysis from the MERCATOR project.

Boy, J.-P.↗

Time-Transfer System for Two Orbiting Spacecraft

A report describes the time-transfer system of the Gravity Recovery and Climate Experiment (GRACE), in which information on the distribution of Earth mass is extracted from position and time measurements for two spacecraft about 200 km apart in a circular, nearly polar orbit. Each spacecraft carriers a Global Positioning System (GPS) receiver, a K/Ka-band ranging (KBR) instrument, and an ultra-stable oscillator (USO) that serves as a clock for the GPS and KBR units. The long-term errors of the USOs are cancelled by use of a technique, called dual-one-way phase measurements, in which the phases of the KBR signals from spacecraft A as measured at spacecraft B are added to the phases of the KBR signals from spacecraft B as measured at spacecraft A. GPS data are used to synchronize time between the USOs to within approximately 150 ps as needed to enable the dual-one-way phase measurements: For each spacecraft, the GPS data are used to solve for orbital positions, and the difference between the onboard clocks and a ground clock every 5 minutes. The relative clock rate between the spacecraft is then determined from the difference between the two solutions.

Bertiger, William↗