David D. Rowlands

Mars Orbiter Laser Altimeter: Experiment summary after the first year of global mapping of Mars

The Mars Orbiter Laser Altimeter (MOLA), an instrument on the Mars Global Surveyor spacecraft, has measured the topography, surface roughness, and 1.064-μm reflectivity of Mars and the heights of volatile and dust clouds. This paper discusses the function of the MOLA instrument and the acquisition, processing, and correction of observations to produce global data sets. The altimeter measurements have been converted to both gridded and spherical harmonic models for the topography and shape of Mars that have vertical and radial accuracies of ~1 m with respect to the planets center of mass. The current global topographic grid has a resolution of 1/64° in latitude × 1/32° in longitude (1 × 2 km^2 at the equator). Reconstruction of the locations of incident laser pulses on the Martian surface appears to be at the 100-m spatial accuracy level and results in 2 orders of magnitude improvement in the global geodetic grid of Mars. Global maps of optical pulse width indicative of 100-m-scale surface roughness and 1.064-μm reflectivity with an accuracy of 5% have also been obtained.

Recent Greenland ice mass loss by drainage system from satellite gravity observations.

Mass changes of the Greenland Ice Sheet resolved by drainage system regions were derived from a local mass concentration analysis of NASA–Deutsches Zentrum für Luftund Raumfahrt Gravity Recovery and Climate Experiment (GRACE mission) observations. From 2003 to 2005, the ice sheet lost 101 ± 16 gigaton/year, with a gain of 54 gigaton/year above 2000 meters and a loss of 155 gigaton/year at lower elevations. The lower elevations show a large seasonal cycle, with mass losses during summer melting followed by gains from fall through spring. The overall rate of loss reflects a considerable change in trend (–113 ± 17 gigaton/year) from a near balance during the 1990s but is smaller than some other recent estimates.

Initial observations from the Lunar Orbiter Laser Altimeter (LOLA)

As of June 19, 2010, the Lunar Orbiter Laser Altimeter, an instrument on the Lunar Reconnaissance Orbiter, has collected over 2.0 × 10^9 measurements of elevation that collectively represent the highest resolution global model of lunar topography yet produced. These altimetric observations have been used to improve the lunar geodetic grid to ~10 m radial and ~100 m spatial accuracy with respect to the Moons center of mass. LOLA has also provided the highest resolution global maps yet produced of slopes, roughness and the 1064-nm reflectance of the lunar surface. Regional topography of the lunar polar regions allows precise characterization of present and past illumination conditions. LOLAs initial global data sets as well as the first high-resolution digital elevation models (DEMs) of polar topography are described herein.

An improved solution of the gravity field of Mars (GMM‐2B) from Mars Global Surveyor

A spherical harmonic solution of the Mars gravity field to degree and order 80, Goddard Mars Model 2B (GMM-2B), has been developed using X band tracking data of Mars Global Surveyor (MGS) from October 1997 to February 2000 and altimeter crossovers formed from the Mars Orbiter Laser Altimeter (MOLA) data between March and December 1999. During the mapping mission, MGS was located in a near-polar (92.9° inclination) and near-circular orbit at a mean altitude of 400 km. The tracking data from this orbit provide a detailed, global, and high resolution view of the gravity field of Mars. Mars gravity solutions are stable to 60×60 even without application of a Kaula power law constraint. The Valles Marineris is resolved distinctly with lows reaching −450 mGals. Olympus Mons and its aureole are both separately resolved, and the volcano has a peak anomaly of 2950 mGals. The global correlation of the GMM-2B gravity coefficients with MOLA-derived topography is 0.78 through degree 60, and the correlation remains above 0.6 through degree 62. The global gravity anomaly error predicted from the GMM-2B error covariance through 60×60 is 11 mGal. The global geoid error from GMM-2B through 60×60 is 1.8 m. MGS orbit quality using GMM-2B, as measured by overlapping orbital arcs, is 1 m in the radial direction and 10 m in total position.

Gravity Field and Internal Structure of Mercury from MESSENGER

Mercury Inside and Out The MESSENGER spacecraft orbiting Mercury has been in a ∼12-hour eccentric, near-polar orbit since 18 March 2011 (see the Perspective by McKinnon). Smith et al. (p. 214, published online 21 March) present the most recent determination of Mercurys gravity field, based on radio tracking of the MESSENGER spacecraft between 18 March and 23 August 2011. The results point to an interior structure that differs from those of the other terrestrial planets: the density of the planets solid outer shell suggests the existence of a deep reservoir of high-density material, possibly an Fe-S layer. Zuber et al. (p. 217, published online 21 March) used data obtained by the MESSENGER laser altimeter through to 24 October 2011 to build a topographic map of Mercurys northern hemisphere. The map shows less variation in elevation, compared with Mars or the Moon, and its features add to the body of evidence that Mercury has sustained geophysical activity for much of its history. Mercury’s outer solid shell is denser than expected, suggesting a deep reservoir of high-density material, possibly iron-sulfide. Radio tracking of the MESSENGER spacecraft has provided a model of Mercury’s gravity field. In the northern hemisphere, several large gravity anomalies, including candidate mass concentrations (mascons), exceed 100 milli-Galileos (mgal). Mercury’s northern hemisphere crust is thicker at low latitudes and thinner in the polar region and shows evidence for thinning beneath some impact basins. The low-degree gravity field, combined with planetary spin parameters, yields the moment of inertia C/MR2 = 0.353 ± 0.017, where M and R are Mercury’s mass and radius, and a ratio of the moment of inertia of Mercury’s solid outer shell to that of the planet of Cm/C = 0.452 ± 0.035. A model for Mercury’s radial density distribution consistent with these results includes a solid silicate crust and mantle overlying a solid iron-sulfide layer and an iron-rich liquid outer core and perhaps a solid inner core.

Recent glacier mass changes in the Gulf of Alaska region from GRACE mascon solutions

The mass changes of the Gulf of Alaska (GoA) glaciers are computed from the Gravity Recovery and Climate Experiment (GRACE) inter-satellite range-rate data for the period April 2003–September 2007. Through the application of unique processing techniques and a surface mass concentration (mascon) parameterization, the mass variations in the GoA glacier regions have been estimated at high temporal (10 day) and spatial (2 × 2 arc-degrees) resolution. The mascon solutions are directly estimated from a reduction of the GRACE K-band inter-satellite range-rate data and, unlike previous GRACE solutions for the GoA glaciers, do not exhibit contamination by leakage from mass change occurring outside the region of interest. The mascon solutions reveal considerable temporal and spatial variation within the GoA glacier region, with the largest negative mass balances observed in the St Elias Mountains including the Yakutat and Glacier Bay regions. The most rapid losses occurred during the 2004 melt season due to record temperatures in Alaska during that year. The total mass balance of the GoA glacier region was −84 ± 5 Gt a −1 contributing 0.23 ± 0.01 mm a −1 to global sea-level rise from April 2003 through March 2007. Highlighting the large seasonal and interannual variability of the GoA glaciers, the rate determined over the period April 2003–March 2006 is −102 ± 5 Gt a −1 , which includes the anomalously high temperatures of 2004 and does not include the large 2007 winter balance-year snowfall. The mascon solutions agree well with regional patterns of glacier mass loss determined from aircraft altimetry and in situ measurements.

A 70th Degree Lunar Gravity Model (GLGM-2) from Clementine and other tracking data

A spherical harmonic model of the lunar gravity field complete to degree and order 70 has been developed from S band Doppler tracking data from the Clementine mission, as well as historical tracking data from Lunar Orbiters 1–5 and the Apollo 15 and 16 subsatellites. The model combines 361,000 Doppler observations from Clementine with 347,000 historical observations. The historical data consist of mostly 60-s Doppler with a noise of 0.25 to several mm/s. The Clementine data consist of mostly 10-s Doppler data, with a data noise of 0.25 mm/s for the observations from the Deep Space Network, and 2.5 mm/s for the data from a naval tracking station at Pomonkey, Maryland. Observations provided Clementine, provide the strongest satellite constraint on the Moons low-degree field. In contrast the historical data, collected by spacecraft that had lower periapsis altitudes, provide distributed regions of high-resolution coverage within ±29° of the nearside lunar equator. To obtain the solution for a high-degree field in the absence of a uniform distribution of observations, we applied an a priori power law constraint of the form 15×10−5/l2 which had the effect of limiting the gravitational power and noise at short wavelengths. Coefficients through degree and order 18 are not significantly affected by the constraint, and so the model permits geophysical analysis of effects of the major basins at degrees 10–12. The GLGM-2 model confirms major features of the lunar gravity field shown in previous gravitational field models but also reveals significantly more detail, particularly at intermediate wavelengths (103 km). Free-air gravity anomaly maps derived from the new model show the nearside and farside highlands to be gravitationally smooth, reflecting a state of isostatic compensation. Mascon basins (including Imbrium, Serenitatis, Crisium, Smythii, and Humorum) are denoted by gravity highs first recognized from Lunar Orbiter tracking. All of the major mascons are bounded by annuli of negative anomalies representing significant subsurface mass deficiencies. Mare Orientale appears as a minor mascon surrounded by a horseshoe-shaped gravity low centered on the Inner and Outer Rook rings that is evidence of significant subsurface structural heterogeneity. Although direct tracking is not available over a significant part of the lunar farside, GLGM-2 resolves negative anomalies that correlate with many farside basins, including South Pole-Aitken, Hertzsprung, Korolev, Moscoviense, Tsiolkovsky, and Freundlich-Sharonov.

Crossover analysis of Mars Orbiter Laser Altimeter data

In its first 15 months of continuous operation, the Mars Orbiter Laser Altimeter (MOLA) instrument aboard Mars Global Surveyor ranged to Mars over 330 million times, generating more than 5000 orbital profiles, with a ranging precision of 0.4 m over smooth terrain. The accuracy of the profiles depends on knowledge of the spacecraft position, orientation, and observation time, which are subject to errors. We model these errors via the analysis of over 24 million altimetric crossovers. A quasiperiodic, once per revolution adjustment of the ground tracks as a function of time in three locally orthogonal directions minimizes the altimetric residuals via least-squares. Using a sparse matrix technique, computational effort scales linearly with the number of crossovers and only marginally with the number of parameters. Orbital errors mainly result from poor modeling of spacecraft thrusting events in the absence of tracking. Seasonal effects, likely due to changing thermal environment, as well as residual miscalibrations, are evident in the pointing solutions. Incorporating multiple parameters per revolution significantly improves crossover residuals, and resolves pointing aberrations during orbital transitions from night to day. Altimetry from the adjusted tracks generates a topographic model whose accuracy is typically better than 1 m vertically with respect to the center of mass of Mars. The centroid position of each MOLA shot is typically accurate to ∼100 m horizontally. Terrain models from accurately located lidar data can be gradient-shaded to illuminate geological structures with 1 in 1000 slopes that are invisible to cameras. Temporal changes in elevation (e.g., frost deposition/ablation) at decimeter levels may also be assessed using crossovers, but results must be interpreted with caution due to uncertainties in range walk correction.

The 1-Centimeter Orbit: Jason-1 Precision Orbit Determination Using GPS, SLR, DORIS, and Altimeter Data Special Issue: Jason-1 Calibration/Validation

The Jason-1 radar altimeter satellite, launched on December 7, 2001 is the follow on to the highly successful TOPEX/Poseidon (T/P) mission and will continue the time series of centimeter level ocean topography measurements. Orbit error is a major component in the overall error budget of all altimeter satellite missions. Jason-1 is no exception and has set a 1-cm radial orbit accuracy goal, which represents a factor of two improvement over what is currently being achieved for T/P. The challenge to precision orbit determination (POD) is both achieving the 1-cm radial orbit accuracy and evaluating the performance of the 1-cm orbit. There is reason to hope such an improvement is possible. The early years of T/P showed that GPS tracking data collected by an on-board receiver holds great promise for precise orbit determination. In the years following the T/P launch there have been several enhancements to GPS, improving its POD capability. In addition, Jason-1 carries aboard an enhanced GPS receiver and significantly improved SLR and DORIS tracking systems along with the altimeter itself. In this article we demonstrate the 1-cm radial orbit accuracy goal has been achieved using GPS data alone in a reduced dynamic solution. It is also shown that adding SLR data to the GPS-based solutions improves the orbits even further. In order to assess the performance of these orbits it is necessary to process all of the available tracking data (GPS, SLR, DORIS, and altimeter crossover differences) as either dependent or independent of the orbit solutions. It was also necessary to compute orbit solutions using various combinations of the four available tracking data in order to independently assess the orbit performance. Towards this end, we have greatly improved orbits determined solely from SLR+DORIS data by applying the reduced dynamic solution strategy. In addition, we have computed reduced dynamic orbits based on SLR, DORIS, and crossover data that are a significant improvement over the SLR- and DORIS-based dynamic solutions. These solutions provide the best performing orbits for independent validation of the GPS-based reduced dynamic orbits. The application of the 1-cm orbit will significantly improve the resolution of the altimeter measurement, making possible further strides in radar altimeter remote sensing.

GRGM900C: A degree 900 lunar gravity model from GRAIL primary and extended mission data

We have derived a gravity field solution in spherical harmonics to degree and order 900, GRGM900C, from the tracking data of the Gravity Recovery and Interior Laboratory (GRAIL) Primary (1 March to 29 May 2012) and Extended Missions (30 August to 14 December 2012). A power law constraint of 3.6 ×10−4/ℓ2 was applied only for degree ℓ greater than 600. The model produces global correlations of gravity, and gravity predicted from lunar topography of ≥ 0.98 through degree 638. The models degree strength varies from a minimum of 575–675 over the central nearside and farside to 900 over the polar regions. The model fits the Extended Mission Ka-Band Range Rate data through 17 November 2012 at 0.13 μm/s RMS, whereas the last month of Ka-Band Range-Rate data obtained from altitudes of 2–10 km fit at 0.98 μm/s RMS, indicating that there is still signal inherent in the tracking data beyond degree 900.