For each month of the observation period sets of spherical harmonic coefficients for different maximum degrees (60, 90, 120) were estimated without applying any regularization. Daily variations are co-estimated and eliminated from the normal equations. For most applications a spectral resolution of degree 60 is sufficient. In some cases a higher resolution is preferable but in some rare months the orbit configuration doesn't allow to solve for high degrees (e.g. 2004-09).

The spherical harmonic coefficients of the solutions and background models are provided in ICGEM format and can be accessed through our FTP server.

• Unconstrained monthly solutions (degree60, degree90, degree120)
• background: Monthly mean of background models (AOD1B) (atmosphere (GAA), ocean (GAB), dealiasing (GAC))

In order to recover fast gravity field variations as detailed as possible, it is reasonable to increase the temporal resolution. The goal is the calculation of daily GRACE solutions. This increase in temporal resolution results in less observations per time span and therefore a reduced redundancy in the parameter estimation process. This leads to a decreasing accuracy of the estimated parameters with decreasing time span. It can be assumed, however, that the gravity field does not change arbitrarily from one time step to the next. The information about the temporal correlation patterns can be derived from geophysical models. Utilizing this knowledge, the temporal resolution can be enhanced without losing spatial information within the framework of a Kalman smoother estimation procedure (Kurtenbach et al. 2012). The following geophysical models were used to derive the temporal correlations: the WaterGAP global hydrology model (WGHM), the atmospheric model ECMWF, and the ocean circulation model OMCT. In order to guarantee that the GRACE solutions are not biased towards the model values themselves but that only the stochastic behavior is exploited, the model output of the years 1976 - 2000 (i.e. outside the GRACE time span) was applied.

For each day of the observation period a set of spherical harmonic coefficients for degrees n=2...40 was estimated. The Kalman smoother delivers daily solutions, even if there are no GRACE data available for a specific day. These days should be handled with care, as they are predictions only and tends towards the mean trend, and annual signal of GOCO05s.

• ITSG-Grace2016_Kalman: Daily solutions using Kalman smoothing
• background: Daily mean of background models (AOD1B) (atmosphere (GAA), ocean (GAB), dealiasing (GAC))
• README_observationCount.txt: Number of GRACE observations per day