Analyzing GRAIL data: first lunar gravity field solutions at AIUB

The NASA mission GRAIL (Gravity Recovery and Interior Laboratory, Zuber et al, 2013) inherited its concept from the GRACE (Gravity Recovery and Climate Experiment) mission to determine the gravity field of the Moon. The presence of Ka-band range measurements enables data acquisition even when the spacecraft are not Doppler-tracked from the Earth, thus allowing for the first time the accurate determination of the gravity field on both the near and far side of the Moon. Such knowledge is essential to improve the understanding of the Moon's internal structure and thermal evolution (Wieczorek et al, 2013). Currently, two official GRAIL gravity field models resolve the selenopotential up to degree and order 900: GL0900D (Konopliv et al, 2014) and GRGM900C (Lemoine et al, 2014). These solutions were obtained using the software packages MIRAGE, a gravity processing version of the JPL Orbit Determination Program, and GEODYN, respectively.

The first AIUB lunar gravity fields are based on data of the GRAIL primary mission phase, covering the period March to May 2012. Gravity field recovery is realized following the Celestial Mechanics Approach (CMA, Beutler et al, 2010), using a development version of the Bernese GNSS Software along with Ka-band range-rate (KBRR) data series as observations  and GRAIL-A/B dynamic positions (GNI1B, a by-product of NASA JPL processing) as pseudo-observations. All data are freely accessible via NASA's Planetary Data System (PDS, The usage of the GNI1B positions as pseudo-observations allows for a relatively straightforward adaption of our gravity field recovery procedures from GRACE, where GPS-derived kinematic positions are available, to GRAIL without having first to implement Doppler data processing.

For the gravity field estimation we set up arc- and satellite-specific parameters (like initial state vectors and pseudo-stochastic pulses) as common parameters for all measurement types. Pseudo-stochastic pulses compensate for imperfect models of non-gravitational accelerations (indeed solar radiation pressure is not yet explicitly included in our force modeling). The gravity field recovery is designed as a generalized orbit determination process, in which both the orbits and the gravity field are improved.

Using an adequate parametrization (Arnold et al, 2015), we computed degree-200 solutions based on release 4 data of the primary mission phase. Figure 1 shows the difference degree amplitudes of the estimated degree-200 solutions w.r.t. GRGM660PRIM, a recent lunar gravity field (Lemoine et al, 2013). The red curve represents AIUB200a, the solution which was obtained using GRGM660PRIM up to degree and order (d/o) 200 as a priori field, i.e., by not making use of the American field beyond the maximum degree resolved. For reference, the difference degree amplitudes of the two pre-GRAIL gravity fields JGL165P1 (Lunar Prospector) and SGM150J (Selene) are shown, as well. The dotted lines indicate the formal errors of the respective solutions.

To assess the importance of the KBRR data for gravity field solution, a position-only solution to d/o 200 was computed, using GRGM660PRIM up to d/o 200 as a priori field (see green curve in Fig. 1). Its difference degree amplitude suggests that the solution is dominated by the dynamic GNI1B positions only at the lowest degrees. The inclusion of the KBRR data strongly improves the solution and reduces the formal errors over almost the entire spectral domain. 

Difference degree amplitudes of estimated d/o-200 solutions and of two pre-GRAIL solutions. Red: the a priori field (GRGM660PRIM) was used up to d/o 200 as well. Green: a position-only solution, showing that KBRR observations improve the solution over nearly the full spectral domain. Dotted lines: formal errors.

Figure 2 shows the free-air gravity anomalies derived from AIUB200a. It shows many details which can be correlated with surface features (a test w.r.t. LOLA topography-induced gravity fields showed a consistency above 0.98 up to degree 170) and it does not show the asymmetry in resolution between near- and far-side which was characteristic for all pre-GRAIL gravity field solutions.

Free-air gravity anomalies on a 0.5° x 0.5° grid (Mollweide projection centered around 270°, with the nearside of the Moon on the right).

In conclusion, AIUB200a represents an alternative solution for the lunar gravity field from GRAIL data obtained using an independent software. Although convenient for the initialization of GRAIL data processing, the use of the dynamic GNI1B positions is not entirely satisfactory. The ongoing implementation of DSN Doppler data processing into the Bernese GNSS Software will allow us to contribute a fully independent solution. Moreover, to further improve our gravity field models, we intend to address the explicit modeling of direct and indirect solar radiation pressure and possibly other non-gravitational forces. Furthermore, the addition of the data at lower orbital altitude from the extended mission phase will strengthen our solutions.


Arnold, D., Bertone, S., Jäggi, A., Beutler, G., Mervart, L. (2015) GRAIL gravity field determination using the Celestial Mechanics Approach. Icarus, vol. 261, pp. 182-192. doi:10.1016/j.icarus.2015.08.015

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Lemoine, F. G.; Goossens, S.; Sabaka, T. J.; Nicholas, J. B.; Mazarico, E.; Rowlands, D. D.; Loomis, B. D.; Chinn, D. S.; Caprette, D. S.; Neumann, G. A.; Smith, D. E. & Zuber, M. T. (2013) High-degree gravity models from GRAIL primary mission data. Journal of Geophysical Research (Planets), 2013, 118, 1676-1698

Lemoine, F. G.; Goossens, S.; Sabaka, T. J.; Nicholas, J. B.; Mazarico, E.; Rowlands, D. D.; Loomis, B. D.; Chinn, D. S.; Neumann, G. A.; Smith, D. E. & Zuber, M. T. (2014) GRGM900C: A degree 900 lunar gravity model from GRAIL primary and extended mission data. Geophysical Research Letters, 2014, 41, 3382-3389

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Zuber, M. T.; Smith, D. E.; Watkins, M. M.; Asmar, S. W.; Konopliv, A. S.; Lemoine, F. G.; Melosh, H. J.; Neumann, G. A.; Phillips, R. J.; Solomon, S. C.; Wieczorek, M. A.; Williams, J. G.; Goossens, S. J.; Kruizinga, G.; Mazarico, E.; Park, R. S. & Yuan, D.-N. (2013) Gravity Field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) Mission. Science, 2013, 339, 668-671