Seasonal low-degree changes in terrestrial water mass load from global GNSS measurements

Large-scale mass redistribution in the terrestrial water storage (TWS) leads to changes in the low-degree spherical harmonic coefficients of the Earth's surface mass density field. Studying these low-degree fluctuations is an important task that contributes to our understanding of continental hydrology. In this study, we use global GNSS measurements of vertical and horizontal crustal displacements that we correct for atmospheric and oceanic effects, and use a set of modified basis functions similar to Clarke et al. (2007) to perform an inversion of the corrected measurements in order to recover changes in the coefficients of degree-0 (hydrological mass change), degree-1 (center of mass shift) and degree-2 (flattening of the Earth) caused by variations in the TWS over the period January 2003 - January 2015. We infer from the GNSS-derived degree-0 estimate an annual variation in total continental water mass with an amplitude of $(3.49 \pm 0.19) \times 10^{3}$ Gt and a phase of $70 \pm 3^{\circ}$ (implying a peak in early March), in excellent agreement with corresponding values derived from the Global Land Data Assimilation System (GLDAS) water storage model that amount to $(3.39 \pm 0.10) \times 10^{3}$ Gt and $71 \pm 2^{\circ}$, respectively. The degree-1 coefficients we recover from GNSS predict annual geocentre motion (i.e. the offset change between the center of common mass and the center of figure) caused by changes in TWS with amplitudes of $0.69 \pm 0.07$ mm for GX, $1.31 \pm 0.08$ mm for GY and $2.60 \pm 0.13$ mm for GZ. These values agree with GLDAS and estimates obtained from the combination of GRACE and the output of an ocean model using the approach of Swenson et al. (2008) at the level of about 0.5, 0.3 and 0.9 mm for GX, GY and GZ, respectively. Corresponding degree-1 coefficients from SLR, however, generally show higher variability and predict larger amplitudes for GX and GZ. The results we obtain for the degree-2 coefficients from GNSS are slightly mixed, and the level of agreement with the other sources heavily depends on the individual coefficient being investigated. The best agreement is observed for $T_{20}^C$ and $T_{22}^S$, which contain the most prominent annual signals among the degree-2 coefficients, with amplitudes amounting to $(5.47 \pm 0.44) \times 10^{-3}$ and $(4.52 \pm 0.31) \times 10^{-3}$ m of equivalent water height (EWH), respectively, as inferred from GNSS. Corresponding agreement with values from SLR and GRACE is at the level of or better than $0.4 \times 10^{-3}$ and $0.9 \times 10^{-3}$ m of EWH for $T_{20}^C$ and $T_{22}^S$, respectively, while for both coefficients, GLDAS predicts smaller amplitudes. Somewhat lower agreement is obtained for the order-1 coefficients, $T_{21}^C$ and $T_{21}^S$, while our GNSS inversion seems unable to reliably recover $T_{22}^C$. For all the coefficients we consider, the GNSS-derived estimates from the modified inversion approach are more consistent with the solutions from the other sources than corresponding estimates obtained from an unconstrained standard inversion.