Toward a Global Horizontal and Vertical Elastic Load Deformation Model Derived from GRACE and GNSS Station Position Time Series

Abstract

We model surface displacements induced by variations in continental water, atmospheric pressure, and nontidal oceanic loading, derived from the Gravity Recovery and Climate Experiment (GRACE) for spherical harmonic degrees two and higher. As they are not observable by GRACE, we use at first the degree‐1 spherical harmonic coefficients from Swenson et al. (2008, https://doi.org/10.1029/2007JB005338). We compare the predicted displacements with the position time series of 689 globally distributed continuous Global Navigation Satellite System (GNSS) stations. While GNSS vertical displacements are well explained by the model at a global scale, horizontal displacements are systematically underpredicted and out of phase with GNSS station position time series. We then reestimate the degree 1 deformation field from a comparison between our GRACE‐derived model, with no a priori degree 1 loads, and the GNSS observations. We show that this approach reconciles GRACE‐derived loading displacements and GNSS station position time series at a global scale, particularly in the horizontal components. Assuming that they reflect surface loading deformation only, our degree‐1 estimates can be translated into geocenter motion time series. We also address and assess the impact of systematic errors in GNSS station position time series at the Global Positioning System (GPS) draconitic period and its harmonics on the comparison between GNSS and GRACE‐derived annual displacements. Our results confirm that surface mass redistributions observed by GRACE, combined with an elastic spherical and layered Earth model, can be used to provide first‐order corrections for loading deformation observed in both horizontal and vertical components of GNSS station position time series.

Identification and Extraction of Seasonal Geodetic Signals Due to Surface Load Variations

“…The final step consists in removing the spherical harmonics degree‐1 contribution from the time series to allow comparison with the GRACE data set, which does not contain degree‐1 deformations (Swenson et al, ). We estimate and retrieve the degree‐1 deformation field using a data set of 689 globally distributed GNSS time series processed by NGL (Blewitt et al, ), as described in Chanard, Fleitout, Calais, Rebischung, and Avouac (). The importance of the degree‐1 deformation field and the necessity of correcting for its effect in the GNSS time series are discussed in further details in section .…”

“…The procedure we propose to extract geodetic seasonal signals aims to identify components that share the same physical mechanism in the GNSS and GRACE‐derived data sets. The step‐by‐step procedure can be summarized as follows: Generate GRACE‐derived displacement time series using the model presented in Chanard, Fleitout, Calais, Rebischung, and Avouac (). Perform vbICA with an increasing number of ICs on the GNSS data set until the ARD criterion is satisfied. Perform vbICA on the GRACE data set with the number of ICs identified in step 2). Starting with the GNSS IC with the highest weight S i , compare the temporal function V i with the remaining unmatched GRACE temporal functions by computing correlation coefficients ( ρ ). Pair GNSS IC i with the GRACE IC with which it has the highest ρ . If the correlation is higher than 0.50, consider the match a good one. …”

“…To enable comparison between the GRACE and GNSS data sets, we compute the displacements expected at the GNSS site locations from the GRACE-derived surface load distribution by using the numerical model developed by Chanard, Fleitout, Calais, Rebischung, and Avouac (2018). The model first decomposes the loads in the temporal and spatial domains and generates load Love numbers (Farrell, 1972) for an elastic Earth structure with continental crust (Bassin et al, 2000) and preliminary reference Earth model parameters (Dziewonski & Anderson, 1981).…”

“…Identifying the origin of the degree-1 deformation field as recorded by GNSS stations has major implications for reference frame definitions. If the extracted seasonal signal is meant for hydrological studies, it would be preferable to perform the analysis directly on the original GNSS time series (i.e., not corrected for degree-1) and on the GRACE-derived time series to which the degree-1 contribution has been added as described in Chanard, Fleitout, Calais, Rebischung, and Avouac (2018). The results from such analyses are presented in Figures 7 and 8 (and Figure S7) and the correlation coefficients and MAEs in Tables 1 and 2, respectively.…”

“…On one hand, a large effort has been made toward developing accurate models of the Earth's surface displacements induced by surface load variations measured by the Gravity Recovery and Climate Experiment (GRACE) satellites (Figure ). Several studies (Bettinelli et al, ; Chanard et al, ; Chanard, Fleitout, Calais, Rebischung, & Avouac, ; Davis et al, ; Fu et al, ; Fu & Freymueller, ) have demonstrated that GRACE‐based deformation models can explain a large part of the GNSS annual observations. Although such models are essential to establish the hydrological origin of seasonal geodetic signals, discrepancies remain between model and data (e.g., Figures a and b).…”