The sensitivity of ocean tide loading displacements to the structure of the upper mantle and crust of Taiwan Island

Ocean tide loading (OTL) displacements are sensitive to the shallow structure of the solid Earth; hence, the high-resolution spatial pattern of OTL displacement can provide knowledge to constrain the shallow Earth structure, especially in coastal areas. In this study, we investigate the sensitivity of the modeled M2 OTL displacement over Taiwan Island to perturbations of three physical quantities, namely, the density, bulk modulus, and shear modulus in the upper mantle and crust. Then, we compare the sensitivity of the modeled M2 OTL displacement to Earth models with the sensitivity to ocean tide models using root mean square (RMS) differences. We compute the displacement Green’s function and OTL displacement relative to the center of mass of the solid Earth (CE) reference frame, analyze the sensitivity to the three physical quantities in the CRUST1.0 model and the Preliminary Reference Earth Model (PREM), and present their spatial patterns. We find that displacement Green’s functions and OTL displacements are more sensitive to the two elastic moduli than the density in the upper mantle and crust. Moreover, their distinctive sensitivity patterns suggest that the three physical quantities might be constrained independently. The specific relationships between the perturbed structural depths and the distance ranges of peak sensitivities from the observation points to the coastline revealed by the shear modulus can mitigate the nonuniqueness problem in inversion. In particular, the horizontal tidal components observed by the Global Positioning System (GPS) can yield better results in inversions than the vertical component owing to the smaller OTL model errors and the higher structural sensitivity (except for the shear modulus in the asthenosphere).

Regional Evaluation of Minor Tidal Constituents for Improved Estimation of Ocean Tides

Satellite altimetry observations have provided a significant contribution to the understanding of global sea surface processes, particularly allowing for advances in the accuracy of ocean tide estimations. Currently, almost three decades of satellite altimetry are available which can be used to improve the understanding of ocean tides by allowing for the estimation of an increased number of minor tidal constituents. As ocean tide models continue to improve, especially in the coastal region, these minor tides become increasingly important. Generally, admittance theory is used by most global ocean tide models to infer several minor tides from the major tides when creating the tidal correction for satellite altimetry. In this paper, regional studies are conducted to compare the use of admittance theory to direct estimations of minor tides from the EOT20 model to identify which minor tides should be directly estimated and which should be inferred. The results of these two approaches are compared to two global tide models (TiME and FES2014) and in situ tide gauge observations. The analysis showed that of the eight tidal constituents studied, half should be inferred (2N2, ϵ2, MSF and T2), while the remaining four tides (J1, L2, μ2 and ν2) should be directly estimated to optimise the ocean tidal correction. Furthermore, for certain minor tides, the other two tide models produced better results than the EOT model, suggesting that improvements can be made to the tidal correction made by EOT when incorporating tides from the two other tide models. Following on from this, a new approach of merging tidal constituents from different tide models to produce the ocean tidal correction for satellite altimetry that benefits from the strengths of the respective models is presented. This analysis showed that the tidal correction created based on the recommendations of the tide gauge analysis provided the highest reduction of sea-level variance. Additionally, the combination of the EOT20 model with the minor tides of the TiME and FES2014 model did not significantly increase the sea-level variance. As several additional minor tidal constituents are available from the TiME model, this opens the door for further investigations into including these minor tides and optimising the tidal correction for improved studies of the sea surface from satellite altimetry and in other applications, such as gravity field modelling.

Simulation study on gravity field determination with small satellites in NGGM

<p>In the context of an increased public interest in climate-relevant processes, a number of studies on Next Generation Gravity Missions (NGGMs) have been commissioned to better map mass transport processes on Earth. On the basis of the successfully completed gravity field missions CHAMP, GOCE and GRACE as well as the current satellite mission GRACE-FO, different concepts were examined for their feasibility and economic efficiency. The focus is on increasing the spatiotemporal resolution while simultaneously reducing the known error effects such as the aliasing of temporal gravity fields due to under-sampling of signals and uncertainties in ocean tide models. An additional inclined pair to a GRACE-like satellite pair (Bender constellation) is the most promising solution. Since the costs for a realization of the Bender constellation are very high, this contribution focuses on alternative concepts in the form of different constellations and formations of small satellites. The latter includes both satellite pairs and chains consisting of trailing satellites. The aim is to provide a cost-effective alternative to the previous gravity field satellites while simultaneously increasing the spatiotemporal resolution and minimizing the above mentioned error effects. In numerical closed-loop simulations, various scenarios will be conducted which differ in orbit parameters like shape and number of orbits, the number of satellites per orbit and instrument performances. Additionally, the impacts from the co-parametrization of non-tidal temporal gravity field signal and ocean tides on the gravity field solutions, obtained by the different concepts, will be investigated. In particular the possibilities and limits with multiple satellites pairs for achieving the highest possible spatial and temporal resolution in (sub-)daily temporal gravity fields shall be analysed in detail.</p>

Load-Tide Sensitivity to 3-D Earth Structure

<p>Earth deformation caused by the tidal redistribution of ocean mass is governed by the material properties of Earth's interior. Surface displacements induced by ocean tidal loading can exceed several centimeters over periods of hours. The rich spectrum of elastic and gravitational responses of the solid Earth produced by the load tides are predominantly sensitive to crust and upper-mantle structure, and inverting load-tide observations for Earth structure can complement independent constraints inferred from seismic tomography and Earth's body tides. </p><p>Global Navigation Satellite Systems (GNSS) record the load-tide displacements with sub-millimeter precision and at high temporal resolution on the order of minutes. Recent studies have demonstrated agreement between predicted and GNSS-observed oceanic load tides in several regions worldwide to a similar level of accuracy. However, residuals between load-tide observations and predictions, which have been limited to spherically symmetric models for Earth structure, exhibit spatially coherent patterns that cannot be fully explained by random measurement or tide-model error and therefore present key opportunities to refine our understanding of Earth's 3-D structure at depths important to mantle convection and plate tectonics. </p><p>Here, we present a novel numerical approach based on a preconditioned conjugate-gradient solver and the spectral-element method to investigate the sensitivities of Earth's load tides to 3-D variations in elastic Earth structure, including ellipticity, topography, and lateral contrasts in elasticity, density and crustal thickness. We leverage and extend the Salvus high-performance library to include gravitational physics and to solve quasi-static problems. High-order shape transformations and adaptive mesh refinement allow us to capture the spatial heterogeneity of the ocean tides with kilometer resolution as well as the large scale of exterior domain, which is needed to model the gravitational potential at reasonable computational cost. We perform a series of benchmark tests to verify the 3-D numerical-modeling approach against established quasi-analytical methods for modeling load-induced Earth deformation (LoadDef software). We then compute the sensitivities of load-induced surface displacements to 3-D Earth structure in two ways: (1) direct comparison of predicted surface displacements computed using 1-D and 3-D Earth models, and (2) direct computation of derivatives of surface displacements with respect to density and elasticity structure using the adjoint method.</p><p>Additional high-impact applications of the surface-load modeling capabilities include: quantifying seasonal fluctuations in mountain snowpack, tracking the depletion of groundwater reservoirs during periods of drought, improving constraints on ocean-tide models and refining the load-tide corrections employed in GNSS signal processing.</p>

An Assessment of Global Ocean Barotropic Tide Models Using Geodetic Mission Altimetry and Surface Drifters

The accuracy of three data-constrained barotropic ocean tide models is assessed by comparison with data from geodetic mission altimetry and ocean surface drifters, data sources chosen for their independence from the observational data used to develop the tide models. Because these data sources do not provide conventional time series at single locations suitable for harmonic analysis, model performance is evaluated using variance reduction statistics. The results distinguish between shallow and deep-water evaluations of the GOT410, TPXO9A, and FES2014 models; however, a hallmark of the comparisons is strong geographic variability that is not well summarized by global performance statistics. The models exhibit significant regionally coherent differences in performance that should be considered when choosing a model for a particular application. Quantitatively, the differences in explained SSH variance between the models in shallow water are only 1%–2% of the root-mean-square (RMS) tidal signal of about 50 cm, but the differences are larger at high latitudes, more than 10% of 30-cm RMS. Differences with respect to tidal currents variance are strongly influenced by small scales in shallow water and are not well represented by global averages; therefore, maps of model differences are provided. In deep water, the performance of the models is practically indistinguishable from one another using the present data. The foregoing statements apply to the eight dominant astronomical tides M2, S2, N2, K2, K1, O1, P1, and Q1. Variance reduction statistics for smaller tides are generally not accurate enough to differentiate the models’ performance.

Tidal geopotential dependence on Earth ellipticity and seawater density and its detection with the GRACE Follow-On laser ranging interferometer

<p>Ocean tides produce significant gravitational perturbations that affect near-Earth orbiting spacecraft.  The gravitational potential induced by tidal mass redistribution is routinely modelled for global gravity analysis and orbit determination, although generally by assuming a spherical Earth and a uniform seawater density.  The inadequacy of these simplifications is here addressed.  We have developed an accurate yet efficient algorithm to compute the ocean tidal geopotential, allowing for Earth’s elliptical shape and variable seawater density.  Using this new computation, we find that (1) the effect of ellipticity is several percent of the tide signal over mid to high latitude regions, which is comparable to elevation error in the state-of-the-art ocean tide models; (2) the effect of seawater density variations on the potential is as large as 2-3 cm in water-height equivalent, primarily in deep water where density increases 2-3% from compressibility.  Our analysis of new GRACE Follow-On (GRACE-FO) laser ranging interferometer measurements reveals evident errors when ellipticity and density variations are ignored.  When accounted for, the GRACE-FO residual tidal gravity perturbations are reduced by half, depending on the adopted tide model; only the remaining half likely represents actual model elevation error.  The use of a spherical surface and a uniform seawater density is no longer tenable given the precision of gravity measurements from GRACE and GRACE-FO satellites.</p>