Basis functions for the consistent and accurate representation of surface mass loading

Inversion of geodetic site displacement data to infer surface mass loads has previously been
demonstrated using a spherical harmonic representation of the load. This method suffers from
the continent-rich, ocean-poor distribution of geodetic data, coupled with the predominance of
the continental load (water storage and atmospheric pressure) compared with the ocean bottom
pressure (including the inverse barometer response). Finer-scale inversion becomes unstable
due to the rapidly increasing number of parameters which are poorly constrained by the data
geometry. Several approaches have previously been tried to mitigate this, including the adoption
of constraints over the oceanic domain derived from ocean circulation models, the use of
smoothness constraints for the oceanic load, and the incorporation ofGRACEgravity field data.
However, these methods do not provide appropriate treatment of mass conservation and of the
ocean’s equilibrium-tide response to the total gravitational field. Instead,we propose a modified
set of basis functions as an alternative to standard spherical harmonics. Our basis functions
allow variability of the load over continental regions, but impose global mass conservation and
equilibrium tidal behaviour of the oceans.
We test our basis functions first for the efficiency of fitting to realistic modelled surface loads,
and then for accuracy of the estimates of the inferred load compared with the known model
load, using synthetic geodetic displacements with real GPS network geometry. Compared
to standard spherical harmonics, our basis functions yield a better fit to the model loads
over the period 1997–2005, for an equivalent number of parameters, and provide a more
accurate and stable fit using the synthetic geodetic displacements. In particular, recovery of the
low-degree coefficients is greatly improved. Using a nine-parameter fit we are able to model
58 per cent of the variance in the synthetic degree-1 zonal coefficient time-series, 38–41 per
cent of the degree-1 non-zonal coefficients, and 80 per cent of the degree-2 zonal coefficient.
An equivalent spherical harmonic estimate truncated at degree 2 is able to model the degree-1
zonal coefficient similarly (56 per cent of variance), but only models 59 per cent of the degree-2
zonal coefficient variance and is unable to model the degree-1 non-zonal coefficients.