### What are ‘mascons’?

Mass Concentration blocks (mascons) are essentially another form of gravity field basis functions to which GRACE’s inter-satellite ranging observations are fit. Using ‘mascons’ rather than the standard spherical harmonic approach, which has been the standard for the first decade of GRACE/GRACE-FO observations, offers several key advantages. With mascons, we can implement geophysical constraints much easier. These a priori constraints help to filter out noise from the GRACE/GRACE-FO observations at the Level-2 processing step, which is a much more rigorous approach than the empirical post-processing filtering applied to land and ocean grids derived from spherical harmonics.

The JPL RL06M Mascon solution solves for monthly gravity field variations in terms of 4,551 equal-area 3-degree spherical cap mascons placed on the surface of an elliptical Earth (go here for the placement file of these mascons). Naturally, a subset of these mascons lies on coastlines, so they contain mixed land and ocean signals. We have developed and applied a Coastline Resolution Improvement (CRI) filter (more details provided below) to separate the land and ocean portions of mass within each land/ocean mascon in a post-processing step. The final CRI-filtered version of the mascon solution is available here. The effect of this filter will be readily seen in the data, as coastlines are well defined. For more expert users who wish to do their own separation of land and ocean mass signals, a version of the data without the CRI filter implemented is available. For more details on how the mascon solution was derived, and performance metrics regarding the solution, please see Watkins et al. (2015). Note that all “Level 2 processing conventions” associated with the JPL RL06 spherical harmonic solution are also used for the JPL RL06M mascon solution.

*GRCTellus JPL-Mascons: *Data Processing Details (RL06.1Mv03)

- The JPL Mascon surface mass change fields are based on the Level-1B GRACE / GRACE-FO data, processed at JPL.
- The
**C20****C30**coefficients are replaced with the solutions from Satellite Laser Ranging via Technical Note**TN-14**[Loomis et al., 2020]. - The degree-1 coefficients (
**Geocenter**) are estimated using the methods from Sun et al., (2016); Swenson, Chambers, and Wahr (2008). - A glacial isostatic adjustment (
**GIA**) correction has been applied based on the ICE6G-D model from Peltier et al. (2017). - The JPL-RL06M uses a-priori constraints in space and time to estimate global, monthly gravity fields in terms of equal-area 3x3 spherical cap mass concentration functions to minimize the effect of measurement errors. No additional empirical destriping filter has been applied to the data. This results in better S/N ratios of the mascon fields compared to the conventional spherical-harmonic solutions.
- The data are represented on a ½ degree lon-lat grid, but they represent the 3x3 degree equal-area caps, which is the current effective
**resolution**of JPL-RL06M. - The spherical cap mascons are placed on the surface of an elliptical Earth; hence, the “ellipsoidal corrections” that are necessary to interpret spherical harmonic solutions are already made during the mascon solution process (Li et al., 2017) [https://doi.org/10.1002/2017JB014033]
- All reported data are
**anomalies relative to the 2004.0-2009.999 time-mean baseline**. Note that this baseline needs to be consistent when comparing GRACE/GRACE-FO data to other anomaly data (e.g., groundwater or sea level). Please check the FAQs regarding questions about the time-mean field. - Note that the land-grid-scaling (described below) has
**not****yet**been applied to the GRACE / GRACE-FO data fields; users must apply these optional gain factors. Note that mascon gain factors are (1) different from the harmonic-based grids, and (2) generally much smaller than those due to the better S/N ratio of the mascon fields. - For an evaluation of errors / uncertainties, please review Wiese, Landerer and Watkins (2016).
- Due to the implementation of time correlation in the solution procedure, with the addition of each consecutive month, the gravity estimate of all previous months changes very slightly. The largest changes occurr towards the end of the timeseries (the last ~4 months). To ensure that the best estimate of gravity is provided, we update and re-estimate all previous months as well when a new month is added. Any new solution is self-contained in one netcdf file, which is
*updated for all months*each time a new month is released. We recommend to use the most recent solutions available. - check out the
**README**for more details on the current release (RL06).

### A brief user guide for JPL-RL06M mascon fields

We provide the mascon surface mass changes with a spatial sampling of 1/2 degrees in both latitude and longitude (approx. 56 km at the equator). This differs from the spherical harmonic solutions, which have spatial sampling of 1 degree in latitude and longitude. The reason for the difference is that the mascons have boundaries that lie on Parallels of 0.5 degree increments. However, keep in mind that although the grid is sampled at 0.5 degree resolution, it DOES NOT mean that two neighboring cells are ‘independent’ of each other. In fact, the native resolution is the size of a single mascon, which are 3 degrees in size. The original mascon placement information is available (as a variable in the netcdf-data files) to assess how the location & placement of the mascons might impact the data analysis wiht the JPL-RL06M data.

*GRCTellus JPL-Mascons: *Grid Scaling

Using 3-degree mascons as a basis function acts as an inherent smoother on the data. As such, we can derive a set of global gain factors to aid in the interpretation of signals at sub-mascon resolution. Similar to the derivation of the gain factors for the spherical harmonic solutions (see Landerer et al., 2012), we use the CLM hydrology model at 0.5 degree resolution, and “mascon average” this, then do a least-squares fit to the “mascon-averaged” hydrology model and the original data. This mascon-set of 0.5 degree gain factors, available as a variable in the netcdf data-files, can then be applied to the data over land. Note that the gain factors for the mascon solution are much closer to 1 than for the spherical harmonic gravity solutions. ** Please note: the gain factors can be used for hydrology-related signals, but should not be used for mountain glaciers or ice sheets** (as these components are not in the CLM data that is underlying the gain factors). Also, the gain factors are suitable for application to the CRI-filtered version of the data for mascons that span coastlines. They are not suitable for expert users whom wish to use the version of the data that has not been CRI-filtered. For more information on scaling the mascon solutions, please see Wiese et al. (2016).

In a nutshell, the gain coefficient is the multiplicative factor that minimizes the difference between the model's smoothed and unfiltered monthly water storage variations ** from land hydrology **at any geographic location. The coefficients are independent of the GRACE/GRACE-FO data proper, hence they are provided as a separate file. Furthermore, the gain factors tend to be dominated by the annual cycles of land water storage variations, and may thus not be suitable to quantify trends from the GRCTellus land data. While the dependence of the gain factors on the specific land hydrology model used is generally small, please note that inter-annual trends in particular in hydrology models are very uncertain.

*GRCTellus JPL-Mascons: *Units, Format

The units of the data and error grids are centimeters of equivalent water thickness; gain factors are dimensionless. If each grid node is g(x,y,t) where x is longitude index, y is latitude index, t is time (month) index, and the scaling grid is s(x,y), then the gain-corrected time series is simply

g'(x,y,t) = g(x,y,t) * s(x,y)

The grids have 720 longitude points (0.25, 0.75, 1.25, ..., 359.75), and 360 latitude points (-89.75, -89.25, ..., 89.25, 89.75).

*GRCTellus JPL-Mascons: *Error & Uncertainty Estimates

Scaled uncertainty estimates are provided on a 0.5 degree grid in latitude and longitude. Note that the uncertainties provided are uncertainties associated with each mascon estimate, represented on this grid; as such, there are only 4,551 independent estimates of uncertainty represented on this grid. This is not the uncertainty associated with a single 0.5 degree pixel, which would be much higher! To derive the scaled uncertainty estimates, we scale the formal covariance matrix over the ocean to match the error we see when comparing the GRACE/GRACE-FO data to in-situ ocean bottom pressure data. Over quiet areas in the ocean, this amounts to approximately 1 cm of uncertainty per mascon. Over land, the formal uncertainty is scaled to roughly match uncertainty estimates that we derive using methods described in Wahr et al., (2006). The provided estimates of uncertainty are regarded to be conservative. Since we implement a Kalman filter in our solution process to link adjacent months together temporally, monthly solutions both at the very beginning and end of the time series have slightly larger uncertainties than monthly solutions in the middle of the time series.

A more detailed description is found in Wiese, Landerer and Watkins (2016).

*GRCTellus JPL-Mascons: *Acknowledgement and Citation

When using any of the *GRCTellus* data, please acknowledge.

**GRACE**/GRACE-FO** Mascon data are available at http://grace.jpl.nasa.gov.**

and cite

D. N. Wiese, D.-N. Yuan, C. Boening, F. W. Landerer, M. M. Watkins. 2018. JPL GRACE Mascon Ocean, Ice, and Hydrology Equivalent Water Height Release 06 Coastal Resolution Improvement (CRI) Filtered Version 1.0. Ver. 1.0. PO.DAAC, CA, USA. Dataset accessed [YYYY-MM-DD] at http://dx.doi.org/10.5067/TEMSC-3MJC6.

Watkins, M. M., D. N. Wiese, D.-N. Yuan, C. Boening, and F. W. Landerer (2015), Improved methods for observing Earth’s time variable mass distribution with GRACE using spherical cap mascons, J. Geophys. Res. Solid Earth, 120, doi:10.1002/2014JB011547.

Wiese, D. N., F. W. Landerer, and M. M. Watkins (2016), Quantifying and reducing leakage errors in the JPL RL05M GRACE mascon solution, Water Resour. Res., 52, 7490–7502, doi:10.1002/2016WR019344.

Landerer, F. W., Flechtner, F. M., Save, H., Webb, F. H., Bandikova, T., Bertiger, W. I., et al. (2020). Extending the global mass change data record: GRACE Follow‐On instrument and science data performance. Geophysical Research Letters, 47, e2020GL088306. https://doi.org/10.1029/2020GL088306

If you encounter any problems with the data, please use the Feedback tool to contact JPL's GRACE & GRACE-FO team.

#### Additional Useful References:

Loomis, B. D., Rachlin, K. E.,Wiese, D. N., Landerer, F. W., &Luthcke, S. B. (2020). Replacing GRACE/GRACE-FOC30with satellitelaser ranging: Impacts on Antarctic Ice Sheet mass change. Geophysical Research Letters,47, e2019GL085488.https://doi.org/10.1029/2019GL085488.

Peltier, W.R., Argus, D.F. and Drummond, R. (2018) Comment on "An Assessment of the ICE-6G_C (VM5a) Glacial Isostatic Adjustment Model" by Purcell et al. J. Geophys. Res. Solid Earth, 123, 2019-2018, doi:10.1002/2016JB013844.

Wahr, J., M. Molenaar, and F. Bryan, Time-variability of the Earth's gravity field: Hydrological and oceanic effects and their possible detection using GRACE, J. Geophys. Res., 103, 32,20530,229, doi:10.1029/98JB02844, 1998.

*Journal of Geophysical Research: Solid Earth*, 122, 9437– 9460. https://doi.org/10.1002/2017JB014033