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We investigate the potential of causal inference methods (CIMs) to reveal hydrological connections from time series. Four CIMs are selected from two criteria, linear or nonlinear and bivariate or multivariate. A priori, multivariate, and nonlinear CIMs are best suited for revealing hydrological connections because they fit nonlinear processes and deal with confounding factors such as rainfall, evapotranspiration, or seasonality. The four methods are applied to a synthetic case and a real karstic case study. The synthetic experiment confirms our expectation: unlike the other methods, the multivariate nonlinear framework has a low false-positive rate and allows for ruling out a connection between two disconnected reservoirs forced with similar effective precipitation. However, for the real case study, the multivariate nonlinear method was unstable because of the uneven distribution of missing values affecting the final sample size for the multivariate analyses, forcing us to cope with the results' robustness. Nevertheless, if we recommend a nonlinear multivariate framework to reveal actual hydrological connections, all CIMs bring valuable insights into the system's dynamics, making them a cost-effective and recommendable comparative tool for exploring data. Still, causal inference remains attached to subjective choices, operational constraints, and hypotheses challenging to test. As a result, the robustness of the conclusions that the CIMs can draw always deserves caution, especially with real, imperfect, and limited data. Therefore, alongside research perspectives, we encourage a flexible, informed, and limit-aware use of CIMs without omitting any other approach that aims at the causal understanding of a system.

We employ the barotropic, data-unconstrained ocean tide model TiME to derive an atlas for degree-3 tidal constituents including monthly to terdiurnal tidal species. The model is optimized with respect to the tide gauge data set TICON-td that is extended to include the respective tidal constituents of diurnal and higher frequencies. The tide gauge validation shows a root-mean-square (RMS) deviation of 0.9–1.3 mm for the individual species. We further model the load tide-induced gravimetric signals by two means (1) a global load Love number approach and (2) evaluating Greens-integrals at 16 selected locations of superconducting gravimeters. The RMS deviation between the amplitudes derived using both methods is below $$0.5 \ $$ 0.5 nGal ($$1 \ $$ 1 nGal $$= 0.01 \frac{\text {nm}}{\text {s}^2}$$ = 0.01 nm s 2 ) when excluding near-coastal gravimeters. Utilizing ETERNA-x, a recently upgraded and reworked tidal analysis software, we additionally derive degree-3 gravimetric tidal constituents for these stations, based on a hypothesis-free wave grouping approach. We demonstrate that this analysis is feasible, yielding amplitude predictions of only a few 10 nGal, and that it agrees with the modeled constituents on a level of 63–80% of the mean signal amplitude. Larger deviations are only found for lowest amplitude signals, near-coastal stations, or shorter and noisier data sets.

The excitation of long-period signals has been reported for large eruptions such as El Chichon (1982) and Mount Pinatubo (1991).We report on series of pressure and gravity signals associated with the series of violent explosions at the Hunga-Tunga eruption, on 14-15th January 2022 at different locations and set-up configurations.We present records from various stations all over the world. Those stations have different set up and local configurations.At most stations, gravity signals records reveal clearly surface waves associated to the main eruption at ~4:30, 15th January and pressure wave up to Iceland.We analyze similarity and difference in the signals in association with the location and the station configurations

We propose a quantitative approach to search for mantle plumes in global seismic tomography models without prior assumptions on the associated mantle velocity anomalies. We design detection tests with a reasonable detection threshold while keeping false detections at a level lower than 5%. This is based on naive Bayesian clustering analysis, which is possible thanks to the varimax principal component analysis that provides components that are much more independent than the original number of depths slices in the models. We find that using such independent components greatly reduces detection errors compared to using an arbitrary number of depth slices due to correlations between the different slices.We detect a wide range of behaviour of the seismic velocity profiles underneath the hotspots investigated in this study. Moreover, we retrieve locations away from hotspots that have a similar seismic velocity profile signature to that underneath some hotspots. Hence, it is not possible to obtain a unique definition of seismic velocity anomalies that are associated with mantle plumes and thus care needs to be taken when searching for mantle plumes using prior assumptions about the velocity anomalies that might be associated with them. On the other hand, we identify a criterion that allows establishing a probability distribution of the seismic velocity profiles that is specific to a sub-list of hotspots and we show that this distribution does not occur significantly elsewhere. Overall, the mantle plume zones identified in our analysis do not appear to surround the Africa and Pacific large low shear velocity provinces (LLSVPs) but are rather within them. This supports the idea that LLSVPs may correspond to bundles of thermochemical mantle plumes rather than to compact, dense piles.

Understanding and modelling the properties of the stochastic variability -- often referred to as noise -- in geodetic time series is crucial to obtain realistic uncertainties for deterministic parameters, e.g., long-term velocities, and helpful in characterizing non-modelled processes. With the ever-increasing span of geodetic time series, it is expected that additional observations would help better understanding the low-frequency properties of the stochastic variability. In the meantime, recent studies evidenced that the choice of the functional model for the time series may bias the assessment of these low-frequency stochastic properties. In particular, the presence of frequent offsets, or step discontinuities, in position time series tends to systematically flatten the periodogram of position residuals at low frequencies and prevents the detection of possible random-walk-type variability. In this study, we investigate the ability of frequently-used statistical tools, namely the Lomb-Scargle periodogram and Maximum Likelihood Estimation (MLE) method, to correctly retrieve low-frequency stochastic properties of geodetic time series in the presence of frequent offsets. By evaluating the biases of each method for several functional models, we demonstrate that neither of these tools is reliable for low-frequency investigation. By assessing alternative approaches, we show that using Least-Squares Harmonic Estimation and Restricted Maximum Likelihood Estimation (RMLE) solves part of the problems reported by previous works. However, we evidence that, even when using those optimal methods, the presence of frequent offsets inevitably blurs the estimated low-frequency properties of geodetic time series by increasing low-frequency stochastic parameter uncertainties more than that of other stochastic parameters.2.14.0.02.14.0.0

This study proposes a method for the cross calibration of tide gauges. Based on the combination of at least three collocated sea level time series, it takes advantage of the least squares variance component estimation (LS-VCE) method to assess both sea level biases and uncertainties in real conditions. The method was applied to a multi-instrument experiment carried out on Aix Island, France, in 2016. Six tide gauges were deployed to carry out simultaneous sea level recordings for 11 h. The best results were obtained with an electrical contact probe, which reaches a 3-mm uncertainty. The method allows us to assess both the biases and the precision—that is, the full accuracy—for each instrument. The results obtained with the proposed combination method have been compared to that of a buddy-checking method. It showed that the combination of all the time series also provides more precise bias estimates.

Applying new technology rooted in quantum mechanics and relativity to terrestrial and space geodesy will sharpen our understanding of how the planet responds to natural and human-induced changes.

The Tide-Generating Potential (TGP) of the Moon is not symmetric but asymmetric with respect to the Lunar sub-orbital axis due to its relative proximity compared to astronomical length scales. This asymmetry can be described in the first order by the third-degree of the TGP expanded in Spherical Harmonic functions. Despite the tiny magnitude of this asymmetry (1/60 of the leading, second degree) several corresponding oceanic partial tides were previously detected in both tide gauge and superconducting gravimeter records. In this contribution, we present solutions with the data-unconstrained ocean tide model TiME (Sulzbach et al. 2021) for a number of partial tides of the third degree in all relevant tidal bands (long-period to terdiurnal). Tuning the model with the recently compiled TICON-td tide gauge dataset, we find the modelled ocean tide signals to agree at levels over 50 % with oceanographic data. The gravimetric impact of the oceanic load tides on 16 globally distributed gravimeter stations which amounts to only a few nGal is then modelled by 2 approaches: (1) a computation with SPOTL and (2) with an approach constrained by load Love numbers. While the gravity constituents modeled with both approaches are close to identical, comparison to the analysed constituents shows a high agreement between 63% to 80% for the degree-3 components depending on the selected partial tide solution, thereby confirming both the low noise level of state-of-the-art superconducting gravimeter recordings and the applied hydrodynamic modelling. By modeling and analyzing for additional degree-3 constituents (resulting in three partial tides in the diurnal, semidiurnal and terdiurnal band), load tide admittance functions of degree-3 can be calculated. We show that third-degree ocean and load tides exhibit a considerable admittance-dispersion that should be considered when estimating load tide contributions of other third-degree partial tides. For example, a larger number of degree-3 tides can be considered for satellite gravity when combining the presented solutions with a linear admittance approach, which might become relevant already for the upcoming MCM/MAGIC constellation currently studied by NASA and ESA.References:[1] Sulzbach, R., Dobslaw, H., & Thomas, M. (2021), JGR: Oceans., 126, 1–21, https://doi.org/10.1029/2020JC017097

The use of seismometer and gravimeter captures complementary data and brings a new understanding of the July 2021 catastrophic floods in Belgium. A sudden increase in seismic noise coincides with the testimony reporting on a “tsunami” downstream of the Membach geophysical station, along the Vesdre valley. Concurrently, the gravimeter evidenced a rising saturation of the weathered zone, thus showing less and less water accumulation. When rain re-intensified after a 3-hour break, the saturated state of the subsoil induced an accelerated increase of the runoff, as revealed by the Vesdre River flow, in a much stronger way than during the rainy episodes just before. We show that a gravimeter can detect in real-time the saturation of the catchment subsoil and soil. This saturation resulted, when the rain re-intensified, in a sudden, devastating and deadly flood. This opens perspectives to use real-time gravity for early warnings of such events

We investigate the potential of causal inference methods (CIMs) to reveal hydrological connections from time-series. Four CIMs are selected from two criteria, linear or nonlinear, and bivariate or multivariate. A priori, multivariate and nonlinear CIMs are best suited for revealing hydrological connections because they suit nonlinear processes and deal with confounding factors such as rainfall, evapotranspiration, or seasonality. The four methods are applied to a synthetic case and a real karstic study case. The synthetic experiment indicates that, unlike the other methods, the multivariate nonlinear framework has a low false-positive rate and allows for ruling out a connection between two disconnected reservoirs forced with similar effective precipitation. However, the multivariate nonlinear method appears unstable when it comes to real cases, making the overall meaning of the causal links uncertain. Nevertheless, all CIMs bring valuable insights into the system’s dynamics, making them a cost-effective and recommendable tool for exploring data. Still, causal inference remains attached to subjective choices and operational constraints while building the dataset or constraining the analysis. As a result, the robustness of the conclusions that the CIMs can draw deserves to be questioned, especially with real and imperfect data. Therefore, alongside research perspectives, we encourage a flexible, informed, and limit-aware use of CIMs, without omitting any other approach that aims at the causal understanding of a system.

International audience; Monitoring vertical land motions (VLMs) at the level of 0.1 mm/yr remains one of the most challenging scientific applications of global navigation satellite systems (GNSS). Such small rates of change can result from climatic and tectonic phenomena, and their detection is important to many solid Earth-related studies, including the prediction of coastal sea-level change and the understanding of intraplate deformation. Reaching a level of precision allowing to detect such small signals requires a thorough understanding of the stochastic variability in GNSS VLM time series. This paper investigates how the aperiodic part of non-tidal atmospheric and oceanic loading (NTAOL) deformations influences the stochastic properties of VLM time series. Using the time series of over 10,000 stations, we describe the impact of correcting for NTAOL deformation on 5 complementary metrics, namely: the repeatability of position residuals, the power-spectrum of position residuals, the estimated time-correlation properties, the corresponding velocity uncertainties, and the spatial correlation of the residuals. We show that NTAOL deformations cause a latitude-dependent bias in white noise plus power-law model parameter estimates. This bias is significantly mitigated when correcting for NTAOL deformation, which reduces velocity uncertainties at high latitudes by 70%. Therefore, removing NTAOL deformation before the statistical analysis of VLM time series might help to detect subtle VLM signals in these areas. Our spatial correlation analysis also reveals a seasonality in the spatial correlation of the residuals, which is reduced after removing NTAOL deformation, confirming that NTAOL is a clear source of common-mode errors in GNSS VLM time series.

Global seismic tomography has greatly progressed in the past decades, with many global Earth models being produced by different research groups. Objective, statistical methods are crucial for the quantitative interpretation of the large amount of information encapsulated by the models and for unbiased model comparisons. Here we propose using a rotated version of principal component analysis (PCA) to compress the information in order to ease the geological interpretation and model comparison. The method generates between 7 and 15 principal components (PCs) for each of the seven tested global tomography models, capturing more than 97 % of the total variance of the model. Each PC consists of a vertical profile, with which a horizontal pattern is associated by projection. The depth profiles and the horizontal patterns enable examining the key characteristics of the main components of the models. Most of the information in the models is associated with a few features: large low-shear-velocity provinces (LLSVPs) in the lowermost mantle, subduction signals and low-velocity anomalies likely associated with mantle plumes in the upper and lower mantle, and ridges and cratons in the uppermost mantle. Importantly, all models highlight several independent components in the lower mantle that make between 36 % and 69 % of the total variance, depending on the model, which suggests that the lower mantle is more complex than traditionally assumed. Overall, we find that varimax PCA is a useful additional tool for the quantitative comparison and interpretation of tomography models.

Data and metadata products based on intensive terrestrial gravity measurements covering the Belgian territory have been established compliant to the new ISO19115‐1 profile for gravity‐related data. A short historical introduction on gravity measurements on the Belgian territory is presented, starting with the first gravity measurement in 1892. This paper focuses on gravity data acquired after 1971, which marks the adoption of IGSN71 as a reference for the world network by the International Association of Geodesy (IAG). Next to a complete dataset containing all Belgian gravity data, the available gravity data were reduced to the corresponding measurement campaign, enabling determination of specific metadata (e.g. used gravimeter, tide system parameters, time of acquisition, etc.). New gravity and spirit levelling measurements were executed by the Royal Observatory Belgium and the National Geographic Institute (Federal Mapping Agency) to validate the g‐value at the historical reference base station ‘Carte du Ciel’ in Brussels. Taking into account the instrumental errors and the varying ground water content, the retrieved data are validated and approved for use in further research.

Global seismic tomography has greatly progressed in the past decades, with many global Earth models being produced by different research groups. Objective, statistical methods are crucial for the quantitative interpretation of the large amount of information encapsulated by the models as well as for unbiased model comparisons. We propose here to use a rotated version of the Principal Component Analysis (PCA) to compress the information, in order to ease the geological interpretation and model comparison. The method generates between 7 to 15 principal components (PC) for each of the seven tested global tomography models, capturing more than 97 % of the total variance of the model. Each PC consists of a vertical profile, to which a horizontal pattern is associated by projection. The depth profiles and the horizontal patterns enable examining the key characteristics of the main components of the models. Most of the information in the models is associated with a few features: Large Low Shear Velocity Provinces (LLSVPs) in the lowermost mantle, subduction signals and low velocity anomalies likely associated with mantle plumes in the upper and lower mantle, and ridges and cratons in the uppermost mantle. Importantly, all models highlight several independent components in the lower mantle that make between 36 % and 69 % of the total variance, depending on the model, which suggests that the lower mantle is more complex than traditionally assumed. Overall, we find that the varimax PCA is a useful additional tool for the quantitative comparison and interpretation of tomography models.

Over the past two decades, numerous studies demonstrated that the stochastic variability in GNSS position time series – often referred to as noise – is both temporally and spatially correlated. The time correlation of this stochastic variability can be well approximated by a linear combination of white noise and power-law stochastic processes with different amplitudes. Although acknowledged in many geodetic studies, the presence of such power-law processes in GNSS position time series remains largely unexplained. Considering that these power-law processes are the primary source of uncertainty for velocity estimates, it is crucial to identify their origin(s) and to try to reduce their influence on position time series. Using the Least-Squares Variance Component Estimation method, we analysed the influence of removing surface mass loading deformation on the stochastic properties of vertical land motion time series (VLMs). We used the position time series of over 10,000 globally distributed GNSS stations processed by the Nevada Geodetic Laboratory at the University of Nevada, Reno, and loading deformation time series computed by the Earth System Modelling (ESM) team at GFZ-Potsdam. Our results show that the values of stochastic parameters, namely, white noise amplitude, spectral index, and power-law noise amplitude, but also the spatial correlation, are systematically influenced by non-tidal atmospheric and oceanic loading deformation. The observed change in stochastic parameters often translates into a reduction of trend uncertainties, reaching up to -75% when non-tidal atmospheric and oceanic loading deformation is highest.

Being sensitive to any phenomena associated with mass transfer, terrestrial gravimetry allows the monitoring of many phenomena at the 10-10 g level (1 nm/s²) such as Earth tides, groundwater content, tectonic deformation, or volcanic activity. This sensitivity is richness, but also a source of problems because data interpretation requires separating the signatures from the different sources, including possible measurement artefacts associated with high precision. Separating the signal from a given source requires a thorough knowledge of both the instrument and the phenomena.At the Membach geophysical laboratory, Belgium, the same superconducting gravimeter has monitored gravity continuously for more than 24 years. Together with 300 repeated absolute gravity measurements and environmental monitoring, this has allowed us to reach an unprecedented metrological knowledge of the instrument and of its sensitivity to hydrological and geophysical signals.Separation is possible whenever the phenomena exhibit distinct time/frequency signatures, such as (pseudo)periodic phenomena or long-term processes, so that the signatures from other sources average out by stacking. For example, when performing repeated gravity measurements to evidence slow tectonic deformation, the easiest way to mitigate hydrological effects is to accumulate measurements for many years, at the same epoch of the year: the impact of seasonal variations is then minimized, and the interannual variations cancel out. Using 10 repeated absolute gravity campaigns at the same epoch of the year, we showed that the gravity rate of change uncertainty reaches on average 3–4 nm/s²/yr. Concurrently, using superconducting gravimeter time series longer than 10 years, we also investigated the time variations of tidal parameters.It is also possible to separate phenomena by observing them by both gravity and some other techniques, with a different transfer function. By using 11 year-long times series from the gravimeter and soil moisture probes, and by stacking the observations, we measured directly the groundwater mass loss by evapotranspiration in the forest above the laboratory of Membach. Always with a precision better than 1 nm/s² ( 2.5 mm of water), we also monitored ground partial saturation dynamics and combining the gravity data with a weather radar allowed measuring convective precipitation at a scale of up to 1 km².Extracting and interpreting those elusive signals could only by achieved throughout multi-instrumentation, multi-disciplinary collaborative studies, and 25 years of hard work.

One main application of electrical resistivity tomography (ERT) is the non-invasive detection of geological or hydrological structures in the shallow subsurface. This paper investigates the capability of time-series clustering to retrieve such features on real time-lapse ERT datasets considering three aspects: (1) the comparison between three clustering algorithms k-means, hierarchical agglomerative clustering (HAC), and Gaussian Mixture Model (GMM), including the question of the optimal choice of cluster number and the identification of resistivity series whose classification is uncertain, (2) the effect of adding a spatial constraint in clustering, and (3) the robustness of the approaches to various representations of resistivity values and the number of time-steps involved in the clustering. The real time-lapse ERT dataset is obtained from dipole-dipole arrays on a 48 electrodes profile installed on the top of the Rochefort cave in Belgium. It consists of resistivity time-series defined over 465 days and associated with 1558 cells of the 2D ERT models derived from a time-lapse inversion. The clustering results are appreciated using clustering validation indices and further confronted with the expert-based structural model of the site. Results show that the three clustering algorithms provide similar spatial patterns on the standardized data and reveal correlated resistivity time-series. Some clusters are, however, spatially split and regroup time-series with a wide range of mean resistivity, suggesting different geological units within these groups. Clustering on the raw resistivity time-series may also appear inconsistent as the averaged resistivity series per cluster are highly correlated, thus missing the hydrological and functional traits of the subsurface elements. Applying a spatial constraint to the clustering of standardized data increases the number of clusters in order to retrieve spatially tied clusters. The grouped series are more homogeneous in terms of mean resistivity due to their spatial proximity, but some inconsistencies may remain due to synchronous hydrological forcing. Applying the clustering to various time-series representations allows us to gain confidence about the redundant spatial patterns. However, the patterns obtained from the clustering of the full standardized dataset cannot be reproduced from continuous sub-samples up to 100 days, but well from less than 20 samples picked randomly over the 465 days. Accordingly, our study highlights the importance of time-variable parameters in the identification of structural facies and hydrofacies with ERT while demonstrating the strength of long-term monitoring.

Spring-based gravimeters are light and easy to install, with a precision around 5 μGal/√Hz. However, they are still not used for long-term gravity monitoring. The main reason for that is the non-linear drift of those instruments, which is very difficult to correct without removing geophysical signals. We will show that when the tilt is actively controlled, a gPhone spring-based gravimeter shows a quasi-linear drift and can reach a long-term stability at the µGal level.This allows experiments such as the one in the Rochefort Cave Laboratory (Belgium). Thanks to the size of the gPhone and its low facility requirements, a monitoring from inside a cave was possible. Coupled with another gravity monitoring at the surface, it reveals new information on the local hydrology of this karstic site.

In a context of global change and increasing anthropic pressure on the environment, monitoring the Earth system and its evolution has become one of the key missions of geosciences. Geodesy is the geoscience that measures the geometric shape of the Earth, its orientation in space, and gravity field. Time-variable gravity, because of its high accuracy, can be used to build an enhanced picture and understanding of the changing Earth. Ground-based gravimetry can determine the change in gravity related to the Earth rotation fluctuation, to celestial body and Earth attractions, to the mass in the direct vicinity of the instruments, and to vertical displacement of the instrument itself on the ground. In this paper, we review the geophysical questions that can be addressed by ground gravimeters used to monitor time-variable gravity. This is done in relation to the instrumental characteristics, noise sources, and good practices. We also discuss the next challenges to be met by ground gravimetry, the place that terrestrial gravimetry should hold in the Earth observation system, and perspectives and recommendations about the future of ground gravity instrumentation. Plain Language Summary: In a context of global change and increased human vulnerability to terrestrial hazard, monitoring the Earth system is one of the key challenges of geoscience. In particular, terrestrial gravimetry, with its precision at the level of one part of a billion, allows the monitoring of many phenomena, from water resource availability to volcanic activity. This paper reviews the technique, its advantages and limitations, how it has been used in the Earth monitoring, and the next challenges to be met by ground gravimetry.

The radar-based estimation of intense precipitation produced by convective storms is a challenging task and the verification through comparison with gauges is questionable due to the very high spatial variability of such types of precipitation. In this study, we explore the potential benefit of using a superconducting gravimeter as a new source of in situ observations for the evaluation of radar-based precipitation estimates. The superconducting gravimeter used in this study is installed in Membach (BE), 48 m underneath the surface, at 85 km distance from a C-band weather radar located in Wideumont (BE). The 15-year observation record 2003–2017 is available for both gravimeter and radar with 1 and 5 min time steps, respectively. Water mass increase at ground due to precipitation results in a decrease in underground measured gravity. The gravimeter integrates soil water in a radius of about 400 m around the instrument. This allows capture of rainfall at a larger spatial scale than traditional rain gauges. The precision of the gravimeter is a few tenths of nm s−2, 1 nm s−2 corresponding to 2.6 mm of water. The comparison of reflectivity and gravity time series shows that short-duration intense rainfall events produce a rapid decrease in the underground measured gravity. A remarkable correspondence between radar and gravimeter time series is found. The precipitation amounts derived from gravity measurements and from radar observations are further compared for 505 rainfall events. A correlation coefficient of 0.58, a mean bias (radar–gravimeter)/gravimeter of 0.24 and a mean absolute difference (MAD) of 3.19 mm are obtained. A better agreement is reached when applying a hail correction by truncating reflectivity values to a given threshold. No bias, a correlation coefficient of 0.64 and a MAD of 2.3 mm are reached using a 48 dBZ threshold. The added value of underground gravity measurements as a verification dataset is discussed. The two main benefits are the spatial scale at which precipitation is captured and the interesting property that gravity measurements are directly influenced by water mass at ground no matter the type of precipitation: hail or rain.

The radar-based estimation of intense precipitation produced by convective storms is a challenging task and the verification through comparison with gauges is questionable due to the very high spatial variability of such type of precipitation. In this study, we explore the potential benefit of using a superconducting gravimeter as a new source of in-situ observations for the evaluation of radar-based precipitation estimates. The superconducting gravimeter used in this study is installed in Membach (BE), 48 m underneath the surface, at 85 km distance from a C-band weather radar located in Wideumont (BE). The 15-year observation record 2003–2017 is available for both gravimeter and radar with 1-min and 5-min time steps, respectively. The gravimeter integrates soil water in a radius of about 400 m around the instrument. This allows capturing rainfall at larger spatial scale than traditional rain gauges. The precision of the gravimeter is a few nm/s2; 1 nm/s2 corresponding to 2.6 mm of water. The comparison of reflectivity and gravity time series for short duration intense rainfall events shows that reflectivity peaks larger than 40 dBZ are associated with a rapid decrease of the underground measured gravity. A remarkable correspondence between radar and gravimeter time series is found. The precipitation amounts derived from gravity measurements and from radar observations are further compared for 505 rainfall events. A correlation coefficient of 0.58, a mean bias (radar/gravimeter) of 1.24 and a mean absolute difference (MAD) of 3.19 mm are obtained. A better agreement is reached when applying a hail correction by truncating reflectivity values to a given threshold. No bias, a correlation coefficient of 0.64 and a MAD of 2.3 mm are reached using a 48-dBZ threshold. The added value of underground gravity measurements as verification dataset is discussed. The two main benefits are the spatial scale at which precipitation is captured and the interesting property that gravity measurements are directly influenced by water mass at ground no matter the type of precipitation: hail or rain.

International audience; Recharge processes of karst aquifers are difficult to assess given their strong heterogeneity and the poorly known effect of vadose zone on infiltration. However, recharge assessment is crucial for the evaluation of groundwater resources. Moreover, the vulnerability of karst aquifers depends on vadose zone behaviour because it is the place where most contamination takes place. In this work, an in situ experimental approach was performed to identify and quantify flow and storage processes occurring in karst vadose zone. Cave percolation monitoring and dye tracing were used to investigate unsaturated zone hydrological processes. Two flow components (diffuse and quick) were identified and, respectively, account for 66% and 34% of the recharge. Quickflow was found to be the result of bypass phenomenon in vadose zone related to water saturation. We identify the role of epikarst as a shunting area, most of the storage in the vadose zone occurring via the diffuse flow component in low permeability zones. Relationship between rainfall intensity and transit velocity was demonstrated, with 5 times higher velocities for the quick recharge mode than the diffuse mode. Modelling approach with KarstMod software allowed to simulate the hybrid recharge through vadose zone and shows promising chances to properly assess the recharge processes in karst aquifer based on simple physical models.

Instruments at Belgium’s Membach geophysical station set a new record for monitoring gravitational fluctuations caused by storm surges, groundwater fluctuations, and the Moon’s tidal pull.

A recent article in Reviews of Geophysics examined terrestrial techniques for measuring changes in gravity over time and their application to the geosciences.

International audience; This paper reports on different sources of errors that occur in the calibration process of a superconducting gravimeter (SG), determined by comparison with a ballistic absolute gravimeter (AG); some of them have never been discussed in the literature.We then provide methods to mitigate the impact of those errors, to achieve a robust calibration estimate at the 1 0/00 level. We demonstrate that a standard deviation at the level of 1 0/00 can be reached within 48 h by measuring at spring tides and by increasing the AG sampling rate. This is much shorter than what is classically reported in previous empirical studies. Measuring more than 5 days around a tidal extreme does not improve the precision in the calibration factor significantly, as the variation in the error as a function of 1/√N does not apply, considering the decrease in signal amplitude due to the tidal modulation. However, we investigate the precision improvement up to 120 days, which can be useful if an AG is run continuously: at mid-latitude it would require 21 days to ensure a calibration factor at the 1 0/00 level with a 99.7 % confidence interval. We also show that restricting the AG measurement periods to tidal extrema can reduce instrument demand, while this does not affect the precision on the calibration factor significantly. Then, we quantify the effect of high microseismic noise causing aliasing in the AG time series. We eventually discuss the attenuation bias that might be induced by noisy time series of the SG. When experiments are performed at the 1 0/00 level, 7 are needed to ensure that the error in the calibration estimate will be at the 1 per mille level with a 99 % confidence.

Water infiltration and recharge processes in karst systems are complex and difficult to measure with conventional hydrological methods. Especially, temporarily saturated groundwater reservoirs hosted in the vadose zone can play a buffering role in water infiltration. This results from the pronounced porosity and permeability contrasts created by local karstification processes of carbonated rocks. Analyses of time-lapse 2-D geoelectrical imaging over a period of three years at the Rochefort Cave Laboratory (RCL) site in South Belgium highlight variable hydrodynamics in a karst vadose zone. These data were compared to conventional hydrological measurements (drip discharge monitoring, soil moisture and water conductivity data sets) and a detailed structural analysis of the local geological structures providing a thorough understanding of the groundwater infiltration. Seasonal changes affect all the imaged areas leading to increases in resistivity in spring/summer attributed to enhanced evapotranspiration, whereas winter is characterised by a general decrease in resistivity associated with a groundwater recharge of the vadose zone. Three types of hydrological dynamics, corresponding to areas with distinct lithological and structural features, could be identified via changes in resistivity: (i) upper conductive layers, associated with clay-rich soil and epikarst, showing the highest variability related to weather conditions; (ii) deeper and more resistive limestone areas, characterised by variable degrees of porosity and clay contents, hence showing more diffuse seasonal variations; (iii) a conductive fractured zone associated with damped seasonal dynamics, while showing a great variability similar to that of the upper layers in response to rainfall events. This study provides detailed images of the sources of drip discharge spots traditionally monitored in caves and aims to support modelling approaches of karst hydrological processes.

International audience; Evapotranspiration (ET) controls the flux between the land surface and the atmosphere. Assessing the ET ecosystems remains a key challenge in hydrology. We have found that the ET water mass loss can be directly inferred from continuous gravity measurements: as water evaporates and transpires from terrestrial ecosystems, the mass distribution of water decreases, changing the gravity field. Using continuous superconducting gravity measurements, we were able to identify daily gravity changes at the level of, or smaller than, 10−9 nm s−2 (or 10−10 g) per day. This corresponds to 1.7 mm of water over an area of 50 ha. The strength of this method is its ability to enable a direct, traceable and continuous monitoring of actual ET for years at the mesoscale with a high accuracy.

Electrical resistivity tomography (ERT) monitoring experiments are being conducted more often to image spatiotemporal changes in soil properties. When conducting long-term ERT monitoring, the identification of suspicious electrodes in a permanent spread is of major importance because changes in electrode contact properties of a single electrode may affect the quality of many measurements on each time-slice. An automated methodology was developed to detect these temporal changes in electrode contact properties, based on a Bayesian approach called “weights of evidence.” Contrasts [Formula: see text] and studentized contrasts [Formula: see text] are estimators of the influence of each electrode in the global data quality. A consolidated studentized contrast [Formula: see text] is introduced to consider the proportion of rejected quadripoles which contain a single electrode. These estimators are computed for each time-slice using [Formula: see text]-factor (coefficient of variation of repeated measurements) threshold values, from 0 to 10%, to discriminate between selected and rejected quadripoles. An automated detection strategy is proposed to identify suspicious electrodes by comparing the [Formula: see text] to the [Formula: see text] (maximum expected [Formula: see text] values when every electrode is good for the given data set). These [Formula: see text] are computed using Monte-Carlo simulations of a hundred random draws where the distribution of [Formula: see text]-factor values follows a Weibull cumulative distribution, with [Formula: see text] and [Formula: see text], fitted on a background data set filtered using a 5% threshold on absolute reciprocal errors. The efficiency of the methodology and its sensitivity to the selected reciprocal error threshold are assessed on synthetic and field data. Our approach is suitable to detect suspicious electrodes and slowly changing conditions affecting the galvanic contact resistances where classical approaches are shown to be inadequate except when the faulty electrode is disconnected. A data-weighting method is finally proposed to ensure that only good data will be used in the inversion of ERT monitoring data sets.

We propose a method to evaluate the stress generated at the local scale by the spatial variations of the gravitational potential energy (GPE), which is related to inhomogeneous topography and mass distribution in the lithosphere. We show that it is possible to infer these local stress sources from the second spatial derivatives of a geoid height grid, used as a proxy of the GPE. The coherence of the method is validated on a passive margin, the Bay of Biscay. The result is that expected in such a geological configuration, with extensional local stress sources with the maximum horizontal principal stress parallel to the margin and compressive sources with the maximum horizontal principal stress perpendicular to the margin in the continental and oceanic lithosphere, respectively. We apply the method to Western Europe in order to provide a better understanding of the complex spatial variation of the present-day tectonic activity. Our results indicate a stress pattern from the local sources dominated by short-space-wavelength (of the order of a few tens of kilometers) variations in the tectonic style and in the direction of the maximal horizontal principal stress sigma(H). A comparison of the sigma(H) orientations and tectonic style from the local sources with the ones of the World Stress Map (WSM) data set indicates that the local stress sources can be representative of the deviatoric stress state in some regions. Our results explain 71% of the faulting styles for the earthquake fault-plane solutions in the WSM, which is better than the classical compressive NW-SE stress field model. In the central part of the Pyrenees, the agreement between earthquake fault-slip directions and the direction of shear stress from the local sources acting on the associated fault planes is compatible with the extensional stress field evidenced by recent investigations.

This paper evaluates different data-processing methods to determine the gravity rate of change, using repeated absolute gravimeter (AG) measurements and continuous monitoring by a superconducting gravimeter (SG). Based on synthetic data representative of signals observed by SGs at various station locations, we demonstrate that the addition of SG information mitigates the error in the estimation of gravity rates of change caused by the presence of long period, interannual, and annual signals in the AG data. These results are discussed as a function of the sampling rate of the absolute gravity measurements, the duration of the observations, and the uncertainties of the AGs.

We demonstrate the possibility to improve the signal-to-noise ratio of superconducting gravity time-series by correcting for local hydrological effects. Short-term atmospheric events associated with heavy rain induce step-like gravity signals that deteriorate the frequency spectrum estimates. Based on 4D modeling constrained by high temporal resolution rain gauge data, rainfall admittances for the Vienna and Membach superconducting gravity stations are calculated. This allows routine correction for Newtonian rain water effects, which reduces the standard deviation of residuals after tidal parameter adjustment by 10%. It also improves the correction of steps of instrumental origin when they coincide with step-like water mass signals.

In November 2013 an International Key Comparison, CCM.G-K2, was organized in the Underground Laboratory for Geodynamics in Walferdange. The comparison has assembled 25 participants coming from 19 countries and four different continents. The comparison was divided into two parts: the key comparison that included 10 NMIs or DIs, and the pilot study including all participants. The global result given by the pilot study confirms that all instruments are absolutely coherent to each other. The results obtained for the key comparison confirm a good agreement between the NMI instruments. Main text. To reach the main text of this paper, click on Final Report [http://www.bipm.org/utils/common/pdf/final_reports/M/G-K2/CCM.G-K2.pdf] . Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/ [http://kcdb.bipm.org/] . The final report has been peer-reviewed and approved for publication by CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

The instrumental drift of the superconducting gravimeter in Membach, Belgium, is estimated using 9 years of co-located and episodic absolute gravity measurements. We show that the best model of the long-term drift of the SG-C021 is an exponential. The thermal levelers used to compensate tilts are unlikely to induce the observed drift. Rather, the capacitance bridge, magnetic variations, gas adsorption on the levitating sphere, or helium gas pressure variations around it are most likely the possible combined causes of the observed instrumental drift. In practice, either linear or exponential drift models are equivalent as long as the record duration does not exceed 10 years. For longer records, this study demonstrates that an exponential models the drift better than a simple linear trend.

SUMMARY We report on the results of 7 yr of collocated gravity observations made with an FG5 absolute (AG) gravimeter and a GWR C-Series superconducting gravimeter (SG) located at the Membach Geophysical Station in eastern Belgium. The SG gravity residuals track changes in gravity periodically observed by the AG, at the microgal level. Further, in the SG residual signal we distinguish a quasi-seasonal term that can be mostly explained by variations in local water storage effects. In the AG time-series we observe a small trend in the gravity of −0.6 ± 0.1 µGal yr −1 perhaps indicating that the Membach Station is being displaced upwards by about 3.0 mm yr −1 . An uplift of the region is confirmed by Global Positioning System (GPS) measurements performed 3 km away. We are able to explain the features in the gravity time-series in terms of water storage variability, post-glacial rebound and tectonic activity.

International audience; Recent studies show that terrestrial and space based observations of gravity agree overEurope. In this paper, we compare time series of terrestrial gravity (including thecontribution due to surface displacement) as measured by superconducting gravimeters(SGs), space based observations from GRACE, and predicted changes in gravity derived fromtwo global hydrological models at 10 SG stations in Central Europe. Despite the fact that allobservations and models observe a maximum in the same season due to water storagechanges, there is little agreement the SG time series even when they are separated bydistances smaller than the spatial resolution of GRACE. We also demonstrate that GRACE andthe SG observations and the water storage models do not display significant correlation atseasonal periods nor at inter-annual periods. These findings are consistent with the fact thatthe SGs are sensitive primarily to mass changes in the few hundred meters surrounding thestation. Even if the hydrological models were perfect, we show that we could not correct theSGs for these local effects that would allow comparisons with GRACE.

The transfer function for the cryogenic gravimeter GWR-C021 operating at Membach (Belgium) has been experimentally determined by injecting known voltages into the control electronics of the system. The output of the gravimeter to the injected sine waves and step functions has been observed. This give a precise knowledge of the transfer function of the gravimeter. It allows one to reach a precision of better than 0.01 second in the phase response of the instrument, in agreement with the Global Geodynamics Project (GGP) requirements.

SUMMARY This paper investigates the precision of the estimation of geophysical fluid load deformation computed from GRACE space gravity, GPS vertical displacement and geophysical fluids models [Global Circulation Models (GCMs) for ocean, atmosphere and hydrology], using the three-cornered hat method. This method allows the estimation of the variance of the errors of each technique, when the same quantity is monitored by three instruments with independent errors.Appliedonanetworkofstations,severalpointsofviewcanbeconsidered:thetechnique level(inordertodeterminetheerrorofeachtechnique:GRACE,GPSandGCMs),thesolution level(allowingtocomparetheprecisionofthesametechniquewhendifferentstrategies/models are used), and the station level (in order to emphasize local anomalies and geographical patterns). In particular, our results show a precision of the loading vertical displacement at the level of 1 mm when using GRACE or the fluid models, and of 2 mm using GPS. We do not find significant differences between the precision of different solutions of the same techniques, even when there are strong differences in the data processing.

Michel Van Camp and Olivier de Viron are attracted to the fluctuations in the Earth's gravitational pull.

In continental plate interiors, ground surface movements are at the limit of the noise level and close to or below the accuracy of current geodetic techniques. Absolute gravity measurements are valuable to quantify slow vertical movements, as this instrument is drift free and, unlike GPS, independent of the terrestrial reference frame. Repeated absolute gravity (AG) measurements have been performed in Oostende (Belgian coastline) and at 8 stations along a southwest-northeast profile across the Belgian Ardennes and the Roer Valley Graben (Germany), in order to estimate the tectonic deformations in the area. The AG measurements, repeated once or twice a year, can resolve elusive gravity changes with a precision better than 3.7 nm/s²/yr (95% confidence interval) after 11 years, even in difficult conditions. After 8-15 years (depending on the station), we find that the gravity rates of change lie in the [-3.1, 8.1] nm/s²/yr interval and result from a combination of anthropogenic, climatic, tectonic, and Glacial Isostatic Adjustment (GIA) effects. After correcting for the GIA, the inferred gravity rates and consequently, the vertical land movements, reduce to zero within the uncertainty level at all stations except Julich (due to man-induced subsidence) and Sohier (possibly, an artifact due to the shortness of the time series at that station).