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A full introduction to geodetic data and systems written by well-known experts in their respective fields, this book is an ideal text for courses in geodesy and geomatics covering everything from coordinate and gravimetry data to geodetic systems of all types.

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.

The Exploration of energization and Radiation in Geospace (ERG) Science Center serves as a hub of the ERG project, providing data files in a common format and developing the space physics environment data analysis software and plug-ins for data analysis. The Science Center also develops observation plans for the ERG (Arase) satellite according to the science strategy of the project. Conjugate observations with other satellites and ground-based observations are also planned. These tasks contribute to the ERG project by achieving quick analysis and well-organized conjugate ERG satellite and ground-based observations.

Most bias correction algorithms used in climatology, for example quantile mapping, are applied to univariate time series. They neglect the dependence between different variables. Those that are multivariate often correct only limited measures of joint dependence, such as Pearson or Spearman rank correlation. Here, an image processing technique designed to transfer colour information from one image to another—the N-dimensional probability density function transform—is adapted for use as a multivariate bias correction algorithm (MBCn) for climate model projections/predictions of multiple climate variables. MBCn is a multivariate generalization of quantile mapping that transfers all aspects of an observed continuous multivariate distribution to the corresponding multivariate distribution of variables from a climate model. When applied to climate model projections, changes in quantiles of each variable between the historical and projection period are also preserved. The MBCn algorithm is demonstrated on three case studies. First, the method is applied to an image processing example with characteristics that mimic a climate projection problem. Second, MBCn is used to correct a suite of 3-hourly surface meteorological variables from the Canadian Centre for Climate Modelling and Analysis Regional Climate Model (CanRCM4) across a North American domain. Components of the Canadian Forest Fire Weather Index (FWI) System, a complicated set of multivariate indices that characterizes the risk of wildfire, are then calculated and verified against observed values. Third, MBCn is used to correct biases in the spatial dependence structure of CanRCM4 precipitation fields. Results are compared against a univariate quantile mapping algorithm, which neglects the dependence between variables, and two multivariate bias correction algorithms, each of which corrects a different form of inter-variable correlation structure. MBCn outperforms these alternatives, often by a large margin, particularly for annual maxima of the FWI distribution and spatiotemporal autocorrelation of precipitation fields.

Volcano geodesy often involves the use of models to explain observed surface deformation. A variety of forward models are used, from analytical point sources to numerical simulations that consider complex magma system geometries, topography, and material properties. Various inversion methods can then be used to relate observed volcano data to models. Ideally, forward models should be verified through intercomparison, to check for implementation errors and quantify the error induced by any approximations used. Additionally, forward models and inversion methods should be validated through tests with synthetic and/or real data, to determine their ability to match data and estimate parameter values within uncertainty. However, to date, there have not been comprehensive verification and validation efforts in volcano geodesy. Here, we report on the first phase of the Drivers of Volcano Deformation (DVD) exercises, which were designed to build community involvement through web-based exercises involving calculations of static elastic displacement around pressurized magma reservoirs. The forward model exercises begin with a spherical reservoir in a homogeneous half space, then introduce topography, heterogeneous elastic properties, and spheroidal geometries. The inversion exercises provide synthetic noisy surface displacement data for a spherical reservoir in a homogeneous half space and assess consistency in estimates of reservoir location and volume/pressure change. There is variability in the results from both forward modeling and inversions, which highlights the strengths and limitations of different forward models, as well as the importance of inversion method choice and uncertainty quantification. This first phase of the DVD exercises serves as a community resource and will facilitate further efforts to develop standards of reproducibility.

The station coordinates derived from GNSS (Global Navigation Satellite System) with a conventional static method underpin the study of Earth and planetary science and surveying and mapping. For the continuous provision of high-quality coordinates, it is mandatory to cope with the increasing deviation from the global standard reference frame and the launch of modern GPS (Global Positioning System) satellites. To provide coordinates agreed with ITRF2014 (International Terrestrial Reference Frame 2014) at several millimeters for GEONET (GNSS Earth Observation Network System) in Japan, we developed a new analysis strategy named F5 and assessed the reprocessed station coordinates from 1996. The major updates in F5 can be summarized as incorporating global network processing and enhancements in troposphere modeling. As for the troposphere enhancements, a modern mapping function VMF1 (Vienna Mapping Functions 1) was employed and time intervals for troposphere estimates were shortened. Station coordinates in the global network showed a great agreement with ITRF2014 at several millimeters in the recent 20 years and comparable or slightly better performance with IGS (International GNSS Services) Analysis Centers. The RMS (root mean square) averaged over all GEONET stations indicated very high accuracy of 3.2 mm (horizontal) and 7.3 mm (vertical); the latter accounts for an improvement of roughly 10% from the previous strategy. Sensitivity tests about troposphere estimates revealed that the reduced RMS was completely due to the short time intervals, not the use of VMF1, which contributed to partly suppressing the spurious vertical annual deformation. These results confirm that F5 is sufficiently accurate for the requirements of individual applications and infer the capability of detecting smaller signals the previous strategy could not resolve.

Time-variable gravity measurements from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions have opened up a new avenue of opportunities for studying large-scale mass redistribution and transport in the Earth system. Over the past 19 years, GRACE/GRACE-FO time-variable gravity measurements have been widely used to study mass variations in different components of the Earth system, including the hydrosphere, ocean, cryosphere, and solid Earth, and significantly improved our understanding of long-term variability of the climate system. We carry out a comprehensive review of GRACE/GRACE-FO satellite gravimetry, time-variable gravity fields, data processing methods, and major applications in several different fields, including terrestrial water storage change, global ocean mass variation, ice sheets and glaciers mass balance, and deformation of the solid Earth. We discuss in detail several major challenges we need to face when using GRACE/GRACE-FO time-variable gravity measurements to study mass changes, and how we should address them. We also discuss the potential of satellite gravimetry in detecting gravitational changes that are believed to originate from the deep Earth. The extended record of GRACE/GRACE-FO gravity series, with expected continuous improvements in the coming years, will lead to a broader range of applications and improve our understanding of both climate change and the Earth system.

Earth orientation parameters (EOPs) are essential in geodesy, linking the terrestrial and celestial reference frames. Due to the time needed for data processing and combining different space geodetic techniques, EOPs of the highest quality suffer latencies from several days to several weeks. However, real-time EOPs are needed for multiple geodetic and geophysical applications. Predictions of EOPs in the ultra-short term can overcome the latency of EOP products to a certain extent. Traditionally, predictions are performed using statistical methods. With the rapid expansion of computing capacity and data volume, the application of deep learning in geodesy has become increasingly promising in recent years. In particular, the Long Short-Term Memory (LSTM) neural networks, one of the most popular Recurrent Neural Network varieties, are promising for geodetic time series prediction. In this study, we investigate the potential of using LSTM to predict daily length of day (LOD) variations up to ten days in advance, accounting for the contribution of effective angular momentum (EAM). The data are first preprocessed to obtain residuals by combining physical and statistical models. Then, we employ LSTM networks to predict the LOD residuals using both LOD and EAM residuals as input features. Our methods outperform all other state-of-the-art methods in the first eight days with an improvement of up to 43% under the first EOP Prediction Comparison Campaign conditions. In addition, we assess the performance of LOD predictions using more extended time series to consider the improvements of EOP products over the last decade. The results show that extending data volume significantly increases the performance of the methods.

Monitoring and predicting fault slip behaviors in subduction zones is essential for understanding earthquake cycles and assessing future earthquake potential. We developed a data assimilation method for fault slip monitoring and the short-term prediction of slow slip events, and applied to the 2010 Bungo Channel slow slip event in southwest Japan. The observed geodetic data were quantitatively explained using a physics-based model with data assimilation. We investigated short-term predictability by assimilating observation data within limited periods. Without prior constraints on fault slip style, observations solely during slip acceleration predicted the occurrence of a fast slip; however, the inclusion of slip deceleration data successfully predicted a slow transient slip. With prior constraints to exclude unstable slip, the assimilation of data after slow slip event occurrence also predicted a slow transient slip. This study provides a tool using data assimilation for fault slip monitoring and prediction based on real observation data. Graphical Abstract