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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.

ICESat-2 science requirements are dependent on the accurate real-time pointing control (i.e. geolocation control) and post-processed geolocation knowledge of the laser altimeter surface returns. Pre-launch pointing alignment errors and post-launch pointing alignment variation result in large geolocation errors that must be calibrated on orbit. In addition, the changing sun-orbit geometry causes thermal-mechanical forced laser frame alignment variations at the orbit period and trends from days, weeks and months. Early mission analysis computed precise post-launch laser beam alignment calibration. The alignment calibration was uploaded to the spacecraft and enabled the pointing control performance to achieve 4.4 ± 6.0 m, a significant improvement over the 45 m (1 σ) mission requirement. Laser frame alignment calibrations are used to reduce the alignment bias and time variation, as well as the orbital variation contributions to geolocation knowledge error from 6 m to 1.7 m (1 σ). Relative beam alignment of the six beams is calibrated and shown to contribute between 0.5 ± 0.1 m and 2.4 ± 0.2 m of remaining geolocation knowledge error. Independent geolocation assessment based on comparison to high-resolution digital elevation models agrees well with the calibration geolocation error estimates. The analysis demonstrates the ICESat-2 mission is performing far better than its geolocation knowledge requirement of 6.5 m (1 σ) after the laser frame alignment bias variation and orbital variation calibrations have been applied. Remaining geolocation error is beam dependent and ranges from 2.5 m for beam 6 to 4.4 m for beam 2 (mean + 1 σ).

The differences between mass concentration (mas con) parameters and standard Stokes coefficient parameters in the recovery of gravity infonnation from gravity recovery and climate experiment (GRACE) intersatellite K-band range rate data are investigated. First, mascons are decomposed into their Stokes coefficient representations to gauge the range of solutions available using each of the two types of parameters. Next, a direct comparison is made between two time series of unconstrained gravity solutions, one based on a set of global equal area mascon parameters (equivalent to 4deg x 4deg at the equator), and the other based on standard Stokes coefficients with each time series using the same fundamental processing of the GRACE tracking data. It is shown that in unconstrained solutions, the type of gravity parameter being estimated does not qualitatively affect the estimated gravity field. It is also shown that many of the differences in mass flux derivations from GRACE gravity solutions arise from the type of smoothing being used and that the type of smoothing that can be embedded in mas con solutions has distinct advantages over postsolution smoothing. Finally, a 1 year time series based on global 2deg equal area mascons estimated every 10 days is presented.

We present the results on precision orbit determination from the radio science investigation of the Lunar Reconnaissance Orbiter (LRO) spacecraft. We describe the data, modeling and methods used to achieve position knowledge several times better than the required 50–100 m (in total position), over the period from 13 July 2009 to 31 January 2011. In addition to the near-continuous radiometric tracking data, we include altimetric data from the Lunar Orbiter Laser Altimeter (LOLA) in the form of crossover measurements, and show that they strongly improve the accuracy of the orbit reconstruction (total position overlap differences decrease from ~70 m to ~23 m). To refine the spacecraft trajectory further, we develop a lunar gravity field by combining the newly acquired LRO data with the historical data. The reprocessing of the spacecraft trajectory with that model shows significantly increased accuracy (~20 m with only the radiometric data, and ~14 m with the addition of the altimetric crossovers). LOLA topographic maps and calibration data from the Lunar Reconnaissance Orbiter Camera were used to supplement the results of the overlap analysis and demonstrate the trajectory accuracy.

A new spherical harmonic solution of the lunar gravity field to degree and order 100, called SGM100h, has been developed using historical tracking data and 14.2 months of SELENE tracking data (from 20 October 2007 to 26 December 2008 plus 30 January 2009). The latter includes all usable 4‐way Doppler data collected which allowed direct observations of the farside gravity field for the first time. The new model successfully reveals farside features in free‐air gravity anomalies which are characterized by ring‐shaped structures for large impact basins and negative spots for large craters. SGM100h produces a correlation with SELENE‐derived topography as high as about 0.9, through degree 70. Comparison between SGM100h and LP100K (one of the pre‐SELENE models) shows that the large gravity errors which existed in LP100K are drastically reduced and the asymmetric error distribution between the nearside and the farside almost disappears. The gravity anomaly errors predicted from the error covariance, through degree and order 100, are 26 mGal and 35 mGal for the nearside and the farside, respectively. Owing to the 4‐way Doppler measurements the gravity coefficients below degree and order 70 are now determined by real observations with contribution factors larger than 80 percent. With the SELENE farside data coverage, it is possible to estimate the gravity field to degree and order 70 without applying any a priori constraint or regularization. SGM100h can be used for global geophysical interpretation through degree and order 70.

In the convolutional retinex approach to image lightness processing, an image is filtered by a centre/surround operator that is designed to mitigate the effects of shading (illumination gradients), which in turn compresses the dynamic range. Typically, the parameters that define the shape and extent of the filter are tuned to provide visually pleasing results, and a mapping function such as a logarithm is included for further image enhancement. In contrast, a statistical approach to convolutional retinex has recently been introduced, which is based upon known or estimated autocorrelation statistics of the image albedo and shading components. By introducing models for the autocorrelation matrices and solving a linear regression, the optimal filter is obtained in closed form. Unlike existing methods, the aim is simply to objectively mitigate shading, and so image enhancement components such as a logarithmic mapping function are not included. Here, the full mathematical details of the method are provided, along with implementation details. Significantly, it is shown that the shapes of the autocorrelation matrices directly impact the shape of the optimal filter. To investigate the performance of the method, we address the problem of shading removal from text documents. Further experiments on a challenging image dataset validate the method.

As of June 19, 2010, the Lunar Orbiter Laser Altimeter, an instrument on the Lunar Reconnaissance Orbiter, has collected over 2.0 × 109 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 Moon's 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. LOLA's initial global data sets as well as the first high‐resolution digital elevation models (DEMs) of polar topography are described herein.

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 mi Hi-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 CIMR² = 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 CJC = 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.

It is well known that a quantum correlated probe can yield better precision in estimating an unknown parameter than classically possible. However, how such a quantum probe should be measured remains somewhat elusive. We examine the role of measurements in quantum metrology by considering two types of readout strategies: coherent, where all probes are measured simultaneously in an entangled basis; and adaptive, where probes are measured sequentially, with each measurement one way conditioned on the prior outcomes. Here we firstly show that for classically correlated probes the two readout strategies yield the same precision. Secondly, we construct an example of a noisy multipartite quantum system where coherent readout yields considerably better precision than adaptive readout. This highlights a fundamental difference between classical and quantum parameter estimation. From the practical point of view, our findings are relevant for the optimal design of precision-measurement quantum devices.