The mass anomaly solution is obtained from the chaining of the partials of the KBRR data with respect to the Stokes coefficients as in a classic geopotential solution as described below. Our implementation of the formulation for mascon parameters exploits the fact that a change in potential caused by adding a small uniform layer of mass over a region at an epoch, t, can be represented as a set of (differential) potential coefficients which can be added to the mean background field. The delta coefficients can be computed as:
- l and m are the harmonic degree and order,
- kl’ is the loading Love number of degree l
- R is the mean radius and M is the mass of the Earth,
- σ is a representation of surface area, and
- Ylm is the spherical harmonic of degree and order l and m corresponding to the potential coefficient Alm and (t) is the mass of the layer over a unit of surface area at the epoch t.
Each of our mascon parameters corresponds to a small block of specified size. For each block we use equation (1) to generate a set of "differential" Stokes coefficients that correspond to 1 cm of water over the block. The estimated mascon parameter for each block is a simple scale factor on the set of differential Stokes coefficients for that block. The partial derivative of the GRACE KBRR observation with respect to a given mascon parameter is just a linear combination of the partials of the KBRR measurements with respect to standard Stokes coefficients. The multipliers are the Stokes coefficients in the base set of differential coefficients. A typical regional solution is shown over the Amazon basin in Figure 1.
The mascon solution employs spatial and temporal constraints to stabilize the solution. This constraint is accomplished by writing one constraint equation for each pair of adjusting mascons in the solution. This constraint equation "forces" a pair (i,j) of mascons to exhibit a level of correlation with one another based on the weight given to the following constraint:
exp[2-dij/D-|tij|/T] (2)
where T and D are the correlation time and distance employed to form the constraint, dij is the distance between blocks i and j, and tij is the difference in time tags for blocks i and j. In the results in Rowlands et al. [2004] over the Amazon, we used a correlation distance of 250 km and a correlation time of 10 days.
While the Rowlands et al., (2005) reference demonstrated a proof of our analysis approach, we have recently iterated and extended our solution. These results, reviewed below, were presented in Lemoine et al., (2005).
Processing Upgrades:
Table 1 below presents a summary of the current modeling we are employing in the mascon solutions reported on this site. These models are in a continuous state of improvement and new versions of mascons may be released in the future should modeling improvements warrant reiteration of this work.
Table 1
BACK
(1) 
