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Bathymetry data over lake areas are not included in the current and previous NGS (National Geodetic Survey) geoid models. Lake surfaces are simply treated as land surfaces during the modeling regardless of the apparent density difference between water and rock, resulting in artificial masses that distort the model from the actual gravity field and the corresponding geoid surface. In this study, compiled high-resolution bathymetry data provided by National Centers for Environmental Information are used to identify the real volume of water bodies. Under the mass conservation principle, two strategies are deployed to properly account the water body bounded by the mean lake surface and the bathymetry indicated lake floor into the current NGS geoid modeling scheme, where the residual terrain modeling method is used to account for topographic effects. The first strategy condenses water bodies into equivalent rock masses, with the cost of changing the geometrical shape of the water body. The second one keeps the shape of the water body unchanged but replaces the water and rock densities inside each topographical column bounded by the geoid surface and the mean lake surface by an averaged density. Both strategies show up to 1-cm geoid changes when compared with the previous geoid model that does not consider bathymetric information. All three geoid models are evaluated by local GNSS/Leveling benchmarks and multi-year-multi-mission altimetry indicated mean lake surface heights. The results show that both strategies can improve the geoid model precision. And the second strategy yields more realistic results. Graphical Abstract

The primary objective of the 1-cm geoid experiment in Colorado (USA) is to compare the numerous geoid computation methods used by different groups around the world. This is intended to lay the foundations for tuning computation methods to achieve the sought after 1-cm accuracy, and also evaluate how this accuracy may be robustly assessed. In this experiment, (quasi)geoid models were computed using the same input data provided by the US National Geodetic Survey (NGS), but using different methodologies. The rugged mountainous study area (730 km × 560 km) in Colorado was chosen so as to accentuate any differences between the methodologies, and to take advantage of newly collected GPS/leveling data of the Geoid Slope Validation Survey 2017 (GSVS17) which are now available to be used as an accurate and independent test dataset. Fourteen groups from fourteen countries submitted a gravimetric geoid and a quasigeoid model in a 1′ × 1′ grid for the study area, as well as geoid heights, height anomalies, and geopotential values at the 223 GSVS17 marks. This paper concentrates on the quasigeoid model comparison and evaluation, while the geopotential value investigations are presented as a separate paper (Sánchez et al. in J Geodesy 95(3):1. https://doi.org/10.1007/s00190-021-01481-0 , 2021). Three comparisons are performed: the area comparison to show the model precision, the comparison with the GSVS17 data to estimate the relative accuracy of the models, and the differential quasigeoid (slope) comparison with GSVS17 to assess the relative accuracy of the height anomalies at different baseline lengths. The results show that the precision of the 1′ × 1′ models over the complete area is about 2 cm, while the accuracy estimates along the GSVS17 profile range from 1.2 cm to 3.4 cm. Considering that the GSVS17 does not pass the roughest terrain, we estimate that the quasigeoid can be computed with an accuracy of ~ 2 cm in Colorado. The slope comparisons show that RMS values of the differences vary from 2 to 8 cm in all baseline lengths. Although the 2-cm precision and 2-cm relative accuracy have been estimated in such a rugged region, the experiment has not reached the 1-cm accuracy goal. At this point, the different accuracy estimates are not a proof of the superiority of one methodology over another because the model precision and accuracy of the GSVS17-derived height anomalies are at a similar level. It appears that the differences are not primarily caused by differences in theory, but that they originate mostly from numerical computations and/or data processing techniques. Consequently, recommendations to improve the model precision toward the 1-cm accuracy are also given in this paper.

Daily Global Positioning System (GPS) time series provide a critical dataset for studying the Earth. In the past decade, an explosion in the number of continuously operating GPS stations combined with improved processing strategies have enabled the detection of ground motions with rates of less than 1 mm/yr. However, detecting such subtle rates in GPS time series is complicated by the presence of errors and other effects that introduce stochastic variability and increase rate uncertainty. Some of this stochastic variability is due to surface mass loading, which causes displacements in GPS time series from atmospheric pressure fluctuations, oceanic mass redistribution, and changes in hydrology. This thesis investigates the effect of surface mass loading on 2,481 GPS station time series around the Great Lakes region of the U.S. and Canada. This region is ideal for studying the effects of surface mass loading because it is covered by a dense network of GPS stations that capture ground displacements due to fluctuations in water levels within the Great Lakes. Uncorrected GPS time series are compared to time series that have been corrected with models of surface mass loading using 4 metrics: variance reduction in corrected residual time series; white, flicker, and random walk noise amplitudes; station velocity uncertainties; and average power spectra of residual time series. Common mode component (CMC) filtering is a method used to remove spatially correlated signals from GPS time series. I also compare CMC filtered time series to see if filtering methods are effective at removing surface mass loading. Finally, to understand the role that GPS station monument type plays in the stochastic variability of the time series, I compare noise amplitudes and velocity uncertainties of 5 categories of monuments: deep-drilled braced monuments, roof mounted, concrete pillars, steel towers, and any monument directly anchored in bedrock. Results show that non-tidal atmospheric and ocean loading (NTAOL) is responsible for the most significant proportion of variance in GPS time series, and correcting for NTAOL reduces the median flicker noise amplitudes by ~50%. However, median white and random walk noise amplitudes increase in NTAOL corrected time series due to a masking effect by NTAOL in the uncorrected time series. Correcting for hydrological loading reduces both variance and random walk noise amplitudes most significantly in GPS stations closest to the Great Lakes. Correcting for both NTAOL and hydrological loading decreased the median velocity uncertainty from 0.35 mm/yr to 0.18 mm/yr. There are no significant differences in variance reduction or stochastic properties between CMC filtered time series whether they have been corrected for surface mass loading or not, indicating that most of the variability due to surface mass loading is removed in the filtering process. When compared to time series that are not filtered, CMC filtering reduces both median white and flicker noise amplitudes, but median velocity uncertainty changes very little due to an increase in random walk noise amplitudes in some filtered time series. A comparison of monument types using the CMC filtered time series shows that out of the two most common monument types in the study region, roof mounted and concrete pillars, roof mounted monuments have a lower median velocity uncertainty. However, concrete pillar monuments in Michigan outperform other concrete pillar monuments and most roof mounted monuments, indicating that the design of concrete pillar monuments plays a crucial role in the stability of the station. A seasonal signal correlated to temperature was found to be present in some stations, particularly in the states of Wisconsin and Minnesota. The implications for this temperature seasonal signal and a potential method for correcting it, in order to extract only the hydrological related seasonal signal from GPS time series, is discussed.

The Mediterranean region is projected to experience severe drying trends and more extreme hydroclimate events as a consequence of anthropogenic climate change over the next century. In some places this signal may have already emerged from natural variability, but uncertainty in long-term paleoclimate reconstructions can be a significant challenge to the detection of the influence of rising CO 2 on droughts. Here we provide expanded context for recent and future hydroclimate changes with a new high-resolution (0.5 o ) spatial reconstruction of the Palmer Drought Severity Index (PDSI) using a tree-ring network that spans much of the last millennium. This network provides new perspective on the existing Old World Drought Atlas (OWDA) and allows us to characterize differences between OWDA and our reconstruction. In light of the uncertainties we identify, we also reexamine previous conclusions about the severity of recent droughts in the context of earlier centuries. We find that, in both the western Mediterranean and the Levant, recent dry periods remain the worst in at least the last 500 years, but our assessment of the significance and confidence in this finding is affected by differences in the tree-ring networks used for the reconstructions. Long millennium-length hydroclimate reconstructions in the Mediterranean do provide the opportunity to understand variability and trends in the hydroclimate of the region, but extant uncertainties arising from the existing tree-ring chronology network and methodological choices call attention to locations that require further proxy collection, chronology updates, and statistical scrutiny.

Numerical methods, like the finite element method (FEM) or finite volume method (FVM), are widely used to provide solutions in many boundary value problems. In previous studies, these numerical methods have also been applied in geodesy but demanded extensive computations because the upper boundary condition was usually set up at the satellite orbit level, hundreds of kilometers above the Earth. The relatively large distances between the lower boundary of the Earth's surface and the upper boundary exacerbate the computation loads because of the required discretization in between. Considering that many areas, such as the US, have uniformly distributed airborne gravity data just a few kilometers above the topography, we adapt the upper boundary from the satellite orbit level to the mean flight level of the airborne gravimetry. The significant decrease in the domain of solution dramatically reduces the large computation demand for FEM or FVM. This paper demonstrates the advantages of using FVM in the decreased domain in simulated and actual field cases in study areas of interest. In the simulated case, the FVM numerical results show that precision improvement of about an order of magnitude can be obtained when moving the upper boundary from 250 to 10 km, the upper altitude of the GRAV-D flights. A 2–3 cm level of accurate quasi-geoid model can be obtained for the actual datasets depending on different schemes used to model the topographic mass. In flat areas, the FVM solution can reach to about 1 cm precision, which is comparable with the counterparts from classical methods. The paper also demonstrates how to find the upper boundary if no airborne data are available. Finally, the numerical method provides a 3D discrete representation of the entire local gravity field instead of a surface solution, a (quasi) geoid model.