Asthenospheric anelasticity effects on ocean tide loading in the East China Sea region observed with GPS

Anelasticity may decrease the shear modulus of the asthenosphere by 8-10% at semi-diurnal tidal 10 periods compared with the reference 1 s period of seismological Earth models. We show that such anelastic effects are likely to be significant for ocean tide loading displacement at the M2 tidal period around the East China Sea. By comparison with tide gauge observations, we establish that NAO99Jb is the most accurate numerical ocean tide model in this region, and that related errors in the predicted M2 vertical ocean tide loading displacements will be 0.2-0.5 mm. In contrast, GPS observations on 15 the Ryukyu Islands (Japan), with uncertainty 0.2-0.3 mm, show discrepancies of over 1.5 mm with respect to ocean tide loading displacements predicted using the purely elastic radial Preliminary Reference Earth Model. We show that the use of an anelastic PREM-based Earth model reduces these discrepancies to no more than 0.8 mm, which is of the same order as the sum of the remaining errors due to uncertainties in the ocean tide model and the GPS observations. Use of a regional Earth model 20 based on the laterally-varying S362ANI, with or without further empirical tuning, results in minor additional improvements in fit.


Introduction
The periodic redistribution of ocean mass around the Earth's surface due to ocean tides deforms the 25 solid Earth, a phenomenon known as ocean tide loading (OTL).The resulting OTL displacements can reach several centimetres in the vertical component and more than one centimetre in the horizontal components, with the Earth's response to the OTL depending strongly on the material properties within its interior (Farrell, 1972).In the past two decades, Global Positioning System (GPS) data analysis techniques have been developed to directly measure OTL displacements with millimetre 30 accuracy, and even sub-millimetre accuracy at some frequencies (e.g., Allinson et al., 2004;Thomas et al., 2007;Yuan et al., 2009;Penna et al., 2015).With parallel substantial advancements in the accuracy of global ocean tide models (Stammer et al, 2014;Ray et al., 2019), comparisons of GPSobserved and predicted (modelled) OTL displacements have several times revealed the deficiencies of using spherically symmetric, non-rotating, elastic and isotropic (SNREI) Earth models.One of the 35 reasons for these deficiencies is that these models have been derived from seismic data and represent the Earth's elastic properties at a reference period of 1 s, but have typically been assumed to be directly applicable at tidal frequencies.Ito et al. (2009) analysed the average amplitude ratio between GPS tidal displacement observations and an Earth tidal model (including OTL and Earth body tide) across Japan, finding that the positive trend of amplitude agreed with predictions from inelastic Earth models.Ito and Simons (2011) further attempted to invert GPS-observed displacements for one-dimensional profiles of the elastic moduli and density beneath the western United States, demonstrating the limitations of the Preliminary 5 Reference Earth Model (PREM) (Dziewonski and Anderson, 1981).Also, Yuan and Chao (2012) and Yuan et al. (2013) reported continental-scale spatially coherent differences between GPS-observed and predicted OTL displacements at sites located more than 150 km inland from the coastline, and attributed these differences to elastic and inelastic deficiencies in the a priori Earth body tide model.More recently, Bos et al. (2015) showed for western Europe that large discrepancies exist between 10 GPS-observed and modelled OTL displacements, arising from disregarding anelastic dispersion in the asthenosphere that occurs when the elastic constants of the Earth model are modified to be applicable at tidal periods.Such an effect could bring about a reduction of around 8-10% of the shear modulus in the asthenosphere at tidal frequencies.In addition, Martens et al. (2016) observed spatial coherence among residual M2 OTL displacements across South America, postulating deficiencies in 15 the a priori SNREI Earth models.Bos et al. (2015) showed the feasibility of representing the behaviour of the asthenosphere across an absorption band from seismic to tidal frequencies by a constant quality factor Q, which provides a rough transformation to account for the anelastic dispersion effect.Hence, it can be postulated that 20 the asthenosphere should always produce ~8.5% OTL displacement discrepancies with respect to a purely elastic PREM-based Earth model, not only in western Europe where Bos et al. demonstrated this effect, but all over the world.However, these discrepancies will not be equally observable in all localities, either because ocean tide amplitudes are too small within the 50-250 km distance range from the analysis point that samples asthenospheric behaviour, or because regional uncertainties in 25 ocean tide models are too large to be able to attribute any observed discrepancy to the Earth model.To identify regions where the findings of Bos et al. (2015) are testable, we have examined the global distribution of a 'detectability ratio'.This is defined as the ratio between the elastic-anelastic OTL displacement discrepancy (taken to be the difference between OTL predicted using a purely elastic PREM Green's function, as described in Section 3, and that using Bos et al.'s anelastic S362ANI(M2) 30 Green's function) as the numerator, and the combination of expected GPS observational and ocean tide model related errors as the denominator.For the latter, the ocean tide model related error is characterised as the standard deviation (STD) of the predicted elastic OTL displacements at each location, using each of the DTU10, EOT11a, FES2014b, GOT4.10c,HAMTIDE11a, NAO99b, OSU12, and TPXO9-Atlas numerical ocean tide models (see Table 1 for references), and the GPS 35 observational error is assigned a STD of 0.3 mm following Penna et al. (2015).
Figure 1a shows a global 1/8° grid of detectability ratio for the M2 vertical OTL displacement, which is unfavourable (less than one) for most inland and deep ocean regions.Many of the areas where it exceeds one, such as off the coasts of southern Greenland, eastern Africa and central America, are 40 poorly sampled with continuously-operating GPS networks.However, the East China Sea (ECS) region exhibits a favourable combination of large OTL displacements and fairly consistent ocean tide models across much of it, so the detectability ratio here exceeds three across a wide area, and contains a healthy distribution of long-running GPS sites (Figure 1b shows the 102 GPS sites used).Accordingly, we have selected this as a suitable region for an independent test of Bos et al.'s (2015) https://doi.org/10.5194/se-2019-133Preprint.Discussion started: 10 September 2019 c Author(s) 2019.CC BY 4.0 License.conclusions.A further attraction of this region for the testing of Earth models is that its position overlying a subduction zone means that it represents a very different tectonic setting to the mature passive margin in western Europe studied by Bos et al.
Figure 1c shows the predicted M2 vertical OTL displacements across the ECS region using the 5 FES2014b ocean tide model (Carrère et al., 2016) and an elastic PREM Green's function.It can been seen that the M2 vertical OTL displacement amplitudes are as large as 20-25 mm around the Ryukyu Islands and on the southeast coast of China, so the anelastic OTL displacement discrepancies would be expected to be about 2 mm and therefore detectable using GPS.Overall, the accuracy of recent ocean tide models is believed to be good, e.g.Stammer et al. (2014) show sub-centimetre M2 root 10 mean square (RMS) agreement between bottom pressure observations and seven recent models in the deep oceans globally and additionally, the FES2014b model has been suggested as providing a clear advancement in global ocean tide modelling (Ray et al., 2019).However, the fact that the tides in the ECS are large and complex owing to the irregular geometry of the basin (Lefèvre et al., 2000) implies that careful evaluation of the ocean tide models is still necessary in this region to ascertain the optimal 15 model, and thus minimise the effect of errors in ocean tide models on the OTL predictions.
In this paper, we first assess the accuracy of a selection of up-to-date ocean tide models in the ECS, and quantify their contribution to the predicted OTL error budget.We then describe the kinematic GPS analysis approach for obtaining the observed OTL displacements.Finally, we examine the 20 evidence of asthenospheric anelasticity effects in the ECS region based on the GPS-observed OTL displacements.We consider the M2 constituent and the vertical component of OTL displacement, as these are dominant in the ECS region.

Ocean tide model accuracy assessment using tide gauges
A pre-requisite for using GPS measurements of OTL displacement for evaluating the Earth's interior material properties is that the impact of ocean tide model errors on the predicted OTL displacement is understood and found to be near negligible.Therefore, we first evaluate the quality of ocean tide models in the ECS region (considered throughout this paper as 116° to 133° east in longitude and 23° 5 to 42° north in latitude) by assessing their consistency with each other and by comparing them with tide gauge observations.To date, no single ocean tide model has been demonstrated as optimal in all regions of the world (Stammer et al., 2014;Ray et al., 2019), so we selected eight recent global (DTU10, EOT11a, 10 FES2014b, GOT4.10c,HAMTIDE11a, NAO99b, OSU12, TPXO9-Atlas) models and one regional (NAO99Jb) model for the quality assessment.The key features of the models are listed in Table 1.All models, except for GOT4.10c,directly assimilate TOPEX/Poseidon (T/P) altimeter data plus, for some of the models, data from one or more of the ERS-1/2, Geosat Follow-on (GFO), Jason-1/2, Envisat and ICESat altimetry satellites, as well as tide gauge data.FES2014b, HAMTIDE11a, 15 NAO99b and TPXO9 are barotropic data-assimilative models.DTU10 and EOT11a are both based on an empirical correction to the global hydrodynamic tide model FES2004 (Lyard et al., 2006), while the a priori model for GOT4.10c is a collection of global and regional models blended at mutual boundaries.OSU12 is a purely empirical model determined by analysis of multi-mission satellite altimeter measurements.TPXO9-Atlas is obtained by combining the base global TPXO9 and local 20 solutions for all coastal areas including around Antarctica and the Arctic Ocean.The regional model, NAO99Jb, covers the area from 110° to 165° east in longitude and from 20° to 65° north in latitude, including the whole area of the ECS, and assimilates more local tide gauge data than do the other models.To evaluate the consistency among the different ocean tide models for the dominant M2 constituent, 30 all models were bilinearly interpolated on to a common 1/16° grid across the ECS region and the STDs of the phasor differences from the mean were computed per grid point, as shown in Figure 2.
It can be seen that away from the coastlines, all models are quite similar with the STD no more than 1 cm, which likely arises because they have more or less assimilated the same altimeter data, albeit To ascertain which models are the cause of the large STDs in some sub-areas, and to assess their accuracy, we compared each model with observations from 75 coastal tide gauges (58 from the Japan Oceanographic Data Centre and 17 from the University of Hawaii Sea Level Center) in the ECS region, as shown in Figure 2. Using the UTide package (Codiga, 2011), the tidal constants observed at these locations were deduced from hourly sea level time series spanning 4 to 69 years, with a median time-series length of 26 years.For time series shorter than 18.6 years, we applied nodal corrections at exact times during the harmonic tidal analysis (Foreman et al., 2009), instead of regarding them as constant values.
In order to investigate in detail the problematic areas of eastern China, western Korea and the Seto 20 Inland Sea, the region is divided into the separate sub-areas shown in Figure 2, basically in accordance with the zones of inter-model discrepancy.Moreover, for the sake of describing the ocean tide model errors as precisely as possible in the next section, the sub-area denoted as Kyushu is further divided.The M2 phasor difference between each model and each tide gauge was computed, and the RMS of these differences per model for all tide gauges in each sub-area are listed in Table 2.
For eastern China, FES2014b and NAO99Jb perform quite well (RMS of 10-12 cm), whereas DTU10 and EOT11a are the worst models (RMS of 47-59 cm).This could be explained by the fact that the FES2004 model, on which DTU10 and EOT11a are both based, has several grossly incorrect tidal 5 values in this area owing to insufficient satellite altimetry data available at the time.RMS agreements of better than 4 cm between tide gauge observations and each of the models are obtained for the Ryukyu Islands sub-area, except for TPXO9-Atlas.This is despite TPXO9-Atlas having the finest resolution among the models of 1/30°, whereas the coarser (1/2°) GOT4.10c and NAO99b models have better than 4 cm RMS agreement.Around the island of Kyushu, the observations compare 10 consistently well with FES2014b and NAO99Jb (RMS lower than 4 cm), while the comparisons are poor for DTU10, EOT11a, HAMTIDE11a, OSU12 and TPXO9-Atlas along the west coast of Kyushu, and for GOT4.10c and NAO99b along the north coast of Kyushu.NAO99Jb exhibits the best agreement with the observations in the Ariake Sea and Seto Inland Sea, which is expected as it assimilates data from 219 local tide gauges (Matsumoto et al., 2000).This also results in NAO99Jb 15 being more accurate than NAO99b in most parts of the ECS region.However, the agreement between NAO99Jb and the tide gauges is no better than the other models in the Kanmen Straits, because the tide gauges there were installed in 2011, after the release of NAO99Jb, and hence none of their data have been assimilated.Nonetheless, NAO99Jb is the most accurate ocean tide model in the ECS region as a whole. 20 Table 2 The root mean square (in cm) of the M2 phasor differences between each of the nine ocean tide models and the tide gauge observations in each defined sub-area of the East China Sea region.In this section we assess the impact of ocean tide model errors on the predicted OTL displacements, which is needed to ensure the confident geophysical interpretation of the GPS-observed OTL displacement residuals considered thereafter.For a particular tidal constituent, the OTL displacement u at a point r on the Earth's surface may be computed (predicted) with the following convolution integral (Farrell, 1972): where Ω represents the global water areas, ρ is the density of seawater, G is a Green's function that describes the displacement at r from a unit point load, and Z is the tide height at r ′ , written as a complex number to include both the amplitude and varying phase-lag.Here, the convolution integral is determined by numerical integration, and may be written as: where Gi here is the integrated Green's function for the ith element of Ω, as per Agnew (1997), and 5 the tidal heights Zi are represented over Ω by inputting a global ocean tide model.Bos et al. (2015) took the STD of predicted OTL displacements computed per point for a set of ocean tide models as the error contribution of the ocean tide models in western Europe, assuming that there were no systematic biases shared by the models.However, we have shown in Section 2 that for the 10 ECS region, the STD among the models is not always a good indicator of their accuracy.To check this, M2 vertical OTL displacements were computed for a 1/8° grid across the ECS region for each of the nine ocean tide models (NAO99Jb was augmented globally outside its boundary by FES2014b) using the SPOTL (NLOADF) software version 3.3.0.2 (Agnew, 1997).A Green's function computed based on the isotropic, purely elastic version of PREM was input (as for all elastic PREM-generated 15 results in this paper) and is provided in Appendix A. As the GPS sites considered in this study are on land, the upper 3 km water layer in PREM was replaced with the density and elastic properties from the underlying rock layer.The OTL displacement STDs among the models per point are shown in Figure 3a, and it can be seen that the distribution of the STDs is similar to those shown for the ocean tide models in Figure 2, with large STDs of up to 2.5 mm arising around eastern China, western Korea 20 and the Seto Inland Sea.However, as shown in Section 2, these large STDs arise from large errors in some (but not all) of the nine ocean tide models and NAO99Jb was shown to be the most accurate model across the ECS region.Therefore, it is unreasonable to use the inter-model STD as an indicator of OTL displacement accuracy for the ECS region.Instead, we now present an approach which allows us to quantify (to first order) the resulting OTL displacement prediction error individually for a 25 particular ocean tide model.
Assuming the ocean is divided into k specified water areas Ωk (e.g., as per Table 2), and that the ocean tide model error magnitude per area is δ k , the corresponding OTL accuracy δu k is: Then, assuming no correlation between each of the k areas, the total OTL displacement prediction error may be computed as: To evaluate the OTL error using equation 4 for NAO99Jb, the most accurate ocean tide model in the

35
ECS region, we define the ocean tide model errors for the separate sub-areas (as per Figure 2) as the RMS difference between NAO99Jb and the tide gauge observations within the sub-area (Table 2).
For the Korea sub-area, although no tide gauge data source is available, the error of NAO99Jb for Korea can be estimated as the mean value of the RMS of the areas around Kyushu excluding the Kanmen Straits, considering the fact that NAO99Jb also assimilated the tide gauge data around Korea. each sub-area to both the OTL displacement and its accompanying error are shown in Table 3, which provides further clarification that the local ocean tides are the principal contributor to the OTL displacements, as well as the OTL errors.The large effect from the 'other water areas' is mainly due to their vast area, although most of this is far from our study area and will have no impact on regional comparison of Earth models.The Kanmen Straits and eastern China, where NAO99Jb performs 5 relatively poorly, have little effect on the OTL displacements at these sites, with contributions to the OTL amplitude and error of only 1.0-1.5 mm and less than 0.1 mm, respectively.Furthermore, the effect of the ocean tide model errors from these two sub-areas is no more than 0.13 mm for all three sites.These computations were repeated for all the GPS sites, and only three of the 102 GPS sites had a total OTL prediction error greater than 0.5 mm.It can therefore be concluded that the OTL 10 displacements computed using the NAO99Jb ocean model are suitable for investigating possible anelasticity effects in the ECS region.

Kinematic GPS estimation of OTL displacement
Using the NASA GNSS-Inferred Positioning System (GIPSY) software in kinematic precise point positioning (PPP) mode, Penna et al. (2015) showed for sites in western Europe with at least 2.5 years 20 of GPS data (4 years recommended), that vertical OTL displacements may be estimated with a precision of about 0.2-0.4mm.We apply the same approach for GPS sites in the ECS region.In order to assess the accuracy and precision of the OTL displacements, particularly to check that the tuned coordinate and tropospheric delay process noise values for western Europe are applicable for the ECS region, we insert an artificial harmonic displacement per GPS site.We then assess how well it is 25 recovered from the kinematic PPP GPS processing, as per Penna et al. (2015) but in the time series used for the final OTL displacement estimation rather than as a preliminary investigation step.

GPS data source
All available continuous GPS data in the ECS region were collated for the window 2013.0-2017.0, with the distribution of the 102 sites used shown in Figure 1.These comprised 96 sites from the GPS Earth Observation Network (GEONET), which all had at least 95% data availability throughout the 4-year window considered, and are located mainly on the Ryukyu Islands and Kyushu.We also collated data from six International GNSS Service (IGS) sites in China and Korea, although two sites (SHAO and YONS) only had 2.5 years of data.On the Ryukyu Islands and along the coast of Kyushu, 5 the sites exhibit detectability ratios of greater than one, with the median value being 2.1, although close to the Seto Island Sea the ratio reduces to less than one.The data spans of at least 2.5 and typically 4 years are sufficient to separate the different major tidal constituents robustly according to the Rayleigh criterion.

Data analysis strategy
Full details of the GPS data processing strategy used are provided in Penna et al. (2015): in summary it is as follows.Daily, 30-hour, kinematic PPP GPS solutions were generated for each site using GIPSY version 6.4 software with Jet Propulsion Laboratory (JPL) reprocessed version 2.1 fiducial satellite orbits, Earth orientation parameters and 30 s satellite clocks held fixed in the IGb08 reference 15 frame.A priori hydrostatic and wet zenith tropospheric delays from the European Centre for Medium-Range Weather Forecasts reanalysis product were used, with residual zenith tropospheric delays estimated every 5 min (applying a process noise of 0.1 mm √s ⁄ ), together with north-south and eastwest tropospheric gradients.The VMF1 gridded mapping function was used with an elevation cutoff of 10°, and corrections were applied for solid Earth and pole tides according to the IERS 20 Conventions 2010 (Petit and Luzum, 2010), along with IGS satellite and receiver antenna phase centre variation corrections.Ambiguities were fixed to integers according to the approach of Bertiger et al. (2010).Receiver coordinates were estimated every 5 min, with a coordinate process noise of 3.2 mm √s ⁄ applied.OTL displacement was modelled using the IERS Conventions (2010) hardisp routine, based on amplitudes and phase lags generated using the NLOADF software with the 25NAO99Jb model (augmented in the rest of the world with the FES2014b model) and a PREM elastic Green's function, computed in the centre of mass of the solid Earth and oceans (CM) frame to be compatible with the JPL orbits.In each daily solution, an artificial 13.96 hour harmonic signal of 3.0 mm amplitude was introduced in each of the east, north and vertical components, with the phase referenced to zero defined at GPS time frame epoch J2000.30 The estimated coordinates at 5 min resolution within the central 24 hours of the daily 30-hour kinematic PPP GPS solutions (which ran from 21:00 the previous day to 03:00 the next day) were averaged in non-overlapping, 30 min bins, then concatenated to form coordinate time series.Harmonic analysis was then undertaken using UTide to estimate the residual M2 vertical OTL 35 displacement signal per site, and also a 13.96 hour harmonic was estimated to assess how well the introduced 3.0 mm amplitude artificial signal could be recovered.The resulting UTide formal errors were 0.1-0.2mm.

40
The M2 vertical OTL residual phasors extracted from the harmonic analysis are shown in Figure 4, as well as the artificial 13.96 hour harmonic signal residual phasors.It can be seen from Figure 4 that on the Ryukyu Islands and in the west coastal area of Kyushu the M2 vertical OTL GPS-observed minus model discrepancies (residuals) can reach over 1.5 mm, corresponding to about 7% of the total loading signal.The typical magnitudes of phasor differences between the recovered and original https://doi.org/10.5194/se-2019-133Preprint.Discussion started: 10 September 2019 c Author(s) 2019.CC BY 4.0 License.artificial 13.96 hour harmonic signals are 0.2-0.3mm, providing an indication of the accuracy level of our GPS-observed M2 vertical OTL displacements, and indicating that the optimal process noise values found for western Europe by Penna et al. (2015) are also applicable to the ECS region.Since the ocean tide error of NAO99Jb maps to only an error of 0.2-0.5 mm for the predicted M2 vertical OTL displacement values across the Ryukyu Islands and Kyushu (Figure 3b), it can be concluded that 5 the 1.5 mm discrepancies must be dominated by errors in the elastic PREM Green's function.
Figure 4 Phasor differences (in blue) between the GPS-observed M2 vertical OTL displacements and the predictions computed using the NAO99Jb regional ocean tide model (augmented elsewhere globally with FES2014b) and an 10 elastic PREM Green's function.Also shown (in green) are the phasor differences between the recovered and original artificial ~13.96 hour harmonic vertical displacement signal of 3.0 mm amplitude.

Optimal Green's function for the East China Sea region
As Green's functions essentially depend on the material properties of the adopted Earth models, the 15 improvement of the agreement between GPS-observed and predicted OTL values could be expected by modifying these properties, and those of the asthenosphere have been demonstrated to be important (Bos et al. 2015).In order to compute an optimal Green's function for the ECS region, instead of PREM we consider the more recent S362ANI Earth model (Kustowski et al. 2008), which is a transversely isotropic seismic tomographic model for the upper mantle.For the computation, the 20 mean shear velocity of S362ANI was prepared using an area centred on the oceanic region of interest, between longitudes 122° and 133° east and latitudes 23° and 35° north.For the density and compressional velocity, S362ANI only provides global mean profiles.In our work, the asthenosphere is defined a priori to be between depths of 80 and 220 km with a Q of 70.Following a similar method to Bos et al. (2015), we vary the depths of the top (D1) and bottom (D2) of the asthenosphere of S362ANI, and the amount of anelastic dispersion (Q) in this layer.For each combination of these three parameters, a new Green's function was computed via the load Love number formulation.While computing the load Love numbers, we transformed the shear modulus from the reference period (1 s) to the period of harmonic M2 using the relation formula given by Dahlen and Tromp (1998), with the 5 Q value assumed constant over this range of periods.The Q value in the other layers is at least twice that of the asthenosphere so the frequency dependence will be smaller, but to be consistent the elastic properties were also transformed to the period of harmonic M2.However, these Q values were not varied in our inversion.New Green's functions were then derived and used to predict the M2 vertical OTL values using the NAO99Jb ocean tide model.This transformation produces complex-valued 10 shear moduli and therefore complex-valued Green's functions but the imaginary part is less than 5% of the real part, see Bos et al. (2015), and can be neglected.The optimal Green's function is considered to be that which minimises the sum of the squared misfits between the observed and predicted OTL phasor values using all the GPS sites. 15 The optimal Green's function has been obtained when Q is 90 (corresponding to a reduction of the shear modulus of about 7.6% at the M2 period), and the estimated values of D1 and D2 are 40 and 220 km, respectively, implying an asthenosphere extending to shallower depths than its original definition for this region in S362ANI.To indicate that the optimal Green's function refers to the period of M2, the label "M2" is added to the S362ANI name, along with the prefix 'mod' to denote 20 that it has been modified.Figure 5 compares the phasor differences of the predicted M2 vertical OTL displacements computed using NAO99Jb and the Green's functions PREM and mod_S362ANI_M2, with respect to the GPS-observed values.It can be seen that for mod_S362ANI_M2 the discrepancies have been substantially reduced on the Ryukyu Islands, where the ~1.5 mm discrepancies typically reduce to less than 0.8 mm, and the RMS agreement has been improved by about 0.3 mm (~0.7 mm 25 reducing to ~0.4 mm) compared to the elastic PREM Green's function (Table 4).Therefore, the large influence of the asthenosphere has been validated.

Figure 5
Phasor differences between our GPS-observed M2 vertical OTL displacements and the predictions computed using the NAO99Jb regional ocean tide model (augmented elsewhere globally with FES2014b) and the elastic PREM (blue phasors) and mod_S362ANI_M2 (red phasors) Green's functions. 5 For completeness, we also compare the GPS-observed M2 vertical OTL displacements with the predictions computed using the Green's function based on the a priori definition of S362ANI for the ECS region, as well as the ones based on PREM and S362ANI with their anelastic dispersion effect directly corrected, termed PREM_M2 and S362ANI_M2, respectively.The RMS, minimum and maximum values of the M2 vertical OTL phasor differences per Green's function are shown in Table 10 4. It can be seen that using the elastic S362ANI Green's function reduces the overall RMS by about 0.1 mm compared to the elastic PREM Green's function, which could be explained by applying the regional mean shear velocity.The RMS agreement can be further improved by correcting the anelastic dispersion effect (PREM_M2 and S362ANI_M2), and their results are quite similar to the optimal mod_S362ANI_M2 Green's function, which provides a simple way to improve predicted OTL 15 displacements instead of performing the complex numerical optimisation scheme each time.Table 4 Statistics (in mm) of the phasor differences between the GPS-observed and predicted M2 vertical OTL displacements using the NAO99Jb regional ocean tide model (augmented elsewhere globally with FES2014b) and various Green's functions.

Conclusions
By introducing the detectability ratio for the asthenospheric anelasticity effects and considering the distribution of the available GPS sites, the ECS region was selected as a potential area to observe the anelastic dispersion in the asthenosphere.Using an inter-comparison of eight recent global (DTU10, EOT11a, FES2014b, GOT4.10c,HAMTIDE11a, NAO99b, OSU12, TPXO9-Atlas) and one regional 10 (NAO99Jb) models and a validation with tide gauges, NAO99Jb has been demonstrated to be the most accurate tide model in the region.In the open sea areas NAO99Jb is slightly worse than the other ocean tide models, due to the assimilation of more satellite altimetry data in the latter, but this does not outweigh the benefits of forcing the NAO99Jb model to fit a large amount of tide gauge observations.We quantified the impact of the errors in NAO99Jb on the predicted OTL values, based 15 on the RMS difference between NAO99Jb and the tide gauge observations.Compared to the approach of using the STD of predicted OTL displacements as the error contribution of the ocean tide models, this method can allow for systematic biases shared by the models, so the outputs are more realistic.
For the GPS sites located in Japan, the errors in NAO99Jb result in M2 vertical OTL displacement errors of 0.2-0.5 mm.

20
We then estimated the M2 vertical OTL displacements for 102 sites around the ECS using GPS with typical accuracy of 0.2-0.3mm.On the Ryukyu Islands and in the west coastal area of Kyushu, the discrepancies between GPS-observed and predicted values can reach over 1.5 mm when using the NAO99Jb tide model and the purely elastic PREM Green's function.However, the discrepancies 25 cannot be explained by the sum of the remaining errors due to ocean tide models and the uncertainty in the GPS observations themselves.Given that the observations are sensitive to the elastic properties of the asthenosphere, we estimated an optimal Green's function by varying the depth and thickness of the asthenosphere of the S362ANI Earth model and its Q values, which were used to model the anelastic dispersion effect during the computations.A reduction of about 7.6% of the shear modulus 30 has been confirmed to produce the best agreement, which reduces the discrepancies to no more than 0.8 mm on the Ryukyu Islands, clearly demonstrating the importance of considering the anelastic properties of the asthenosphere.

Figure 1
Figure 1 (a) Global distribution (1/8° grid) of M2 'detectability ratio' of difference between vertical OTL displacements predicted using purely elastic and anelastic Green's functions to uncertainty in residual OTL displacements predicted using eight ocean tide models and the GPS observational error.(b) Detectability ratio in the East China Sea (ECS) region, showing as triangles the GPS sites used in this study.(c) The M2 vertical OTL displacement amplitudes and Greenwich 5

5 Figure 2
Figure2The M2 standard deviations for nine ocean tide models (DTU10, EOT11a, FES2014b, GOT4.10c,HAMTIDE11a, NAO99Jb, NAO99b, OSU12 and TPXO9-Atlas).(a) shows the whole East China Sea (ECS) region, while (b) is an enlargement of the Kyushu sub-area of (a).The white labelled polygons define the sub-areas for which the quality of the ocean tide models has been evaluated, and the white dots represent the locations of coastal tide gauges.

5 Figure 3
Figure 3 (a) The standard deviation of M2 vertical OTL displacements, computed using the nine ocean tide models and an elastic PREM Green's function.(b) The M2 vertical OTL errors per grid point according to equation (4), using the RMS errors in NAO99Jb based on comparisons with tide gauges, and an elastic PREM Green's function.10 https://doi.org/10.5194/se-2019-133Preprint.Discussion started: 10 September 2019 c Author(s) 2019.CC BY 4.0 License.

25 Table 1 Summary of the selected ocean tide models.
a T/P, TOPEX/Poseidon; GFO, Geosat Follow-on; TG, tide gauge.b E, empirical adjustment to an adopted a priori model; H, assimilation into a barotropic hydrodynamic model.

Table 3
The contribution of the defined water sub-areas in Figure2to the M2 vertical OTL displacement amplitudes and the resulting errors at GPS sites 0487, 0706 and 1094 according to equation 4 and using the NAO99Jb model and its RMS