Table 1 Comparison of input data and post-processing methods of the two studies analysing water storage change in the Nelson River basin

GRACE data

CSR Release 04; Aug 2002 to Mar 2011; spherical harmonic degree 2 to 60

CSR Release 04; Jun 2002 to Oct 2011; spherical harmonic degree 1 to 60

De-striping filter: 3rd polynomial fitted to same parity degrees >10 from orders > 3; Isotropic Gaussian filter (340 km)

Two-step method: de-striping step and statistical test step; Apply non-isotropic Gaussian filter

Annual, 2.5 years and S2-tide (161 days); signals removed to find trend

GPS data

228 observation sites

27 continuous GPS stations and 50 Canadian Base Network (CBN) in and around the Nelson River basin

Spherical harmonic degree 2 to 60

Interpolated onto a 2 × 2 degree grid

AG data

8 stations with Absolute Gravity; 6 of them with collocated GPS stations

Methodology

Spectral inversion based on \(\dot{\sigma }_{lm}^{\mathrm{TW}}= \frac{1}{\beta _{l}}\left( \dot{u}_{lm}^{\mathrm{GPS}}+{\alpha _{l}} \Delta \dot{g}_{lm}^{\mathrm{GRACE}}\right) \)

\(\Delta \dot{g}^{\mathrm{TW}}=\Delta \dot{g}^{\mathrm{GRACE}} - \Delta \dot{g}^{\mathrm{GIA}}\) \(\Delta \dot{g}^{\mathrm{GIA}}=\left[ 1/\alpha +0.3086 \right] \dot{u}^{\mathrm{GPS}}\)

\(\alpha \) = ratio of uplift rate and gravity change rate

Theoretical value of: \(1/\alpha_{l} = 0.15\, \mu {\hbox {Gal/mm}}\)

Derived from absolute gravity measurements collocated with continuous GPS data with \(1/\alpha = -\,0.165 \pm 0.012\,\upmu {\hbox {Gal/mm}}\)