R. Klees

Assessment of Gravity Recovery and Climate Experiment (GRACE) temporal signature over the upper Zambezi

The temporal signature of terrestrial storage changes inferred from the Gravity Recovery and Climate Experiment (GRACE) has been assessed by comparison with outputs from a calibrated hydrological model (lumped elementary watershed (LEW)) of the upper Zambezi and surroundings and an inspection of the within?month ground track coverage of GRACE together with spatial?temporal rainfall patterns. The comparison of the hydrological model with GRACE reveals temporal inconsistencies between both data sets. Because the LEW model has been calibrated and validated with independent data sources, we believe that this is a GRACE artifact. The within?month ground track coverage shows an irregular orbit behavior which may well cause aliasing in the GRACE monthly deconvolutions. This aliasing is the most probable cause of observed temporal inconsistencies between GRACE and other data sets.

Deformation measurements using SAR interferometry: potential and limitations

Most applications of Synthetic Aperture Radar (SAR) make only use of the amplitude information in just one image. Interferometric SAR (InSAR) makes use mainly of the phase measurements in two or more SAR images of the same scene, acquired at two different moments and/or at two slightly different locations. By interference of the two images, very small slant-range changes of the same surface can be inferred. These slant-range changes can be related to topography and/or surface deformations. InSAR thus has the potential of mapping centimeter-scale ground displacements over a region many tens of kilometers in size at a resolution of a few meters making it one of the most promising space-geodetic techniques for monitoring Earths surface deformations. The goal of this paper is to discuss some of the potential new applications of InSAR for the monitoring of deformations, and to show its major limitations. Some potential new applications of InSAR related to surface-change detection including earthquake and crustal studies, the monitoring of volcanoes and anthropogenic effects, and the monitoring of glaciers and ice sheets are presented. The discussion on the limitations of InSAR for surface-change detection focuses on atmospheric perturbations and the problem of temporal decorrelation.

Comparison of Precipitable Water Vapor Observations by Spaceborne Radar Interferometry and Meteosat 6.7-μm Radiometry

Abstract Satellite radar interferometry (InSAR) can be applied to study vertically integrated atmospheric refractivity variations with a spatial resolution of 20 m and an accuracy of 2 mm, irrespective of cloud cover or solar illumination. The data are derived from the difference between the radar signal delay variations within the imaged area during two acquisitions with a temporal separation of one or more days. Hence, they reflect the superposition of the refractivity distribution during these two acquisitions. On short spatial scales, integrated refractivity variations are dominantly caused by spatial heterogeneities in the water vapor distribution. Validation of the radar interferometric results can be difficult, since conventional imaging radiometers do not provide quantitative measures for water vapor content over the entire tropospheric column and are lacking in spatial resolution. Moreover, comparable quantitative data such as signal delay observed by Global Positioning System (GPS) receivers are...

The spherical Slepian basis as a means to obtain spectral consistency between mean sea level and the geoid

The mean dynamic topography (MDT) can be computed as the difference between the mean sea level (MSL) and a gravimetric geoid. This requires that both data sets are spectrally consistent. In practice, it is quite common that the resolution of the geoid data is less than the resolution of the MSL data, hence, the latter need to be low-pass filtered before the MDT is computed. For this purpose conventional low-pass filters are inadequate, failing in coastal regions where they run into the undefined MSL signal on the continents. In this paper, we consider the use of a bandlimited, spatially concentrated Slepian basis to obtain a low-resolution approximation of the MSL signal. We compute Slepian functions for the oceans and parts of the oceans and compare the performance of calculating the MDT via this approach with other methods, in particular the iterative spherical harmonic approach in combination with Gaussian low-pass filtering, and various modifications. Based on the numerical experiments, we conclude that none of these methods provide a low-resolution MSL approximation at the sub-decimetre level. In particular, we show that Slepian functions are not appropriate basis functions for this problem, and a Slepian representation of the low-resolution MSL signal suffers from broadband leakage. We also show that a meaningful definition of a low-resolution MSL over incomplete spherical domains involves orthogonal basis functions with additional properties that Slepian functions do not possess. A low-resolution MSL signal, spectrally consistent with a given geoid model, is obtained by a suitable truncation of the expansions of the MSL signal in terms of these orthogonal basis functions. We compute one of these sets of orthogonal basis functions using the Gram–Schmidt orthogonalization for spherical harmonics. For the oceans, we could construct an orthogonal basis only for resolutions equivalent to a spherical harmonic degree 36. The computation of a basis with a higher resolution fails due to inherent instabilities. Regularization reduces the instabilities but destroys the orthogonality and, therefore, provides unrealistic low-resolution MSL approximations. More research is needed to solve the instability problem, perhaps by finding a different orthogonal basis that avoids it altogether.

Lowest Astronomical Tide in the North Sea Derived from a Vertically Referenced Shallow Water Model, and an Assessment of its Suggested Sense of Safety

Water level reduction with global navigation satellite systems in bathymetric surveying requires knowledge of the ellipsoidal heights of lowest astronomical tide (LAT). The traditional approach uses tidal water levels of an ocean tide model, which are subtracted from mean sea level (MSL). This approach has two major drawbacks: the modeled water levels refer to an equipotential surface, which differs from MSL, and MSL may not be known close to the coast. Here, we propose to model LAT directly relative to an equipotential surface (geoid). This is conceptually consistent with the flow equations and allows the inclusion of temporal MSL variations into the LAT definition. Numerical experiments for the North Sea show that significant differences between the traditional and the pursued approach exist if average monthly variations in MSL are included. A validation of the modeled LAT using tide gauge records reveals systematic errors, which we attribute to both the model and the tidal analysis procedure. We also show that the probability that water levels drop below LAT is high, with maximum frequency of once per week in the eastern North Sea. Therefore, we propose to reconsider the deterministic concept of LAT by a probabilistic chart datum concept, and we quantified the differences between them.

Using Satellite Constellations for Improved Determination of Earth's Time-Variable Gravity

The spatiotemporal resolution of the time-variable gravity field models derived from current dedicated gravity field missions is inherently limited by their ground-track coverage. Furthermore, the results are subject to aliasing effects caused by submonthly mass transport signals, such as those caused by atmospheric and ocean processes. To address these issues, this study explores the feasibility of using nondedicated satellite constellations, such as those from commercial communication networks or a low-cost array of custom-built microsatellites, as a complementary data source. The positioning receivers onboard the constellation’s satellites would ideally provide a high density of observations in the form of derived accelerations that, while much less accurate than those obtained from dedicated gravitymissions, are still sufficient to observe the longest wavelength gravity signals at even subdaily intervals. Using a series of simulated mission scenarios, as well as a limited amount of real-data analysis, it is shown that such constellations, acting either independently or when combined with dedicated gravity field missions, may offer a noticeable improvement in the recovery of the large-scale (greater than 1000 km) high-frequency (less than 1month) components of the global gravity field.

A Comparison of Different Integral-Equation-Based Approaches for Local Gravity Field Modelling: Case Study for the Canadian Rocky Mountains

We compare the accuracy of local gravity field modelling in rugged mountains using three different discretised integral equations; namely (1) the single layer approach, (2) Poisson’s integral approach, and (3) Green’s integral approach. The study area comprises a rough part of the Canadian Rocky Mountains with adjacent plains. The numerical experiment is conducted for gravity disturbances and for topographically corrected gravity disturbances. The external gravity field is parameterized by gravity disturbances (Poisson’s integral approach) and disturbing potential values (Green’s integral approach), both discretised below the data points at the same depth beneath the Bjerhammar sphere. The point masses in the single layer approach are discretised below the data points on a parallel surface located at the same depth beneath the Earth’s surface. The accuracy of the gravity field modelling is assessed in terms of the STD of the differences between predicted and observed gravity data. For the three chosen discretisation schemes, the most accurate gravity field approximation is attained using Green’s integral approach. However, the solution contains a systematic bias in mountainous regions. This systematic bias is larger if topographically corrected gravity disturbances are used as input data.

History Matching Time-Lapse Surface-Gravity and Well-Pressure Data With Ensemble Smoother for Estimating Gasfield Aquifer Support--A 3D Numerical Study

Water influx is an important factor influencing production of gas reservoirs with an active aquifer. However, aquifer properties such as size, porosity, and permeability are typically uncertain and make predictions of field performance challenging. The observed pressure decline is inherently nonunique with respect to water influx, and large uncertainties in the actual reservoir state are common. Time-lapse (4D) gravimetry, which is a direct measure of a subsurface mass redistribution, has the potential to provide valuable information in this context. Recent improvements in instrumentation and data-acquisition and -processing procedures have made time-lapse gravimetry a mature monitoring technique, both for land and offshore applications. However, despite an increasing number of gas fields in which gravimetric monitoring has been applied, little has been published on the added value of gravity data in a broader context of modern reservoir management on the basis of the closed-loop concept. The way in which gravity data can contribute to improved reservoir characterization, production-forecast accuracy, and hydrocarbon-reserves estimation is still to be addressed in many respects. In this paper, we investigate the added value of gravimetric observations for gasfield-production monitoring and aquifer-support estimation. We perform a numerical study with a realistic 3D gasfield model that contains a large and complex aquifer system. The aquifer support and other reservoir parameters (i.e., porosity, permeability, reservoir top and bottom horizons) are estimated simultaneously using the ensemble smoother (ES). We consider three cases in which gravity only is assimilated, pressure only is assimilated, and gravity and pressure data are assimilated jointly. We show that a combined estimation of the aquifer support with the permeability field, porosity field, and reservoir structure is a very challenging and nonunique history-matching problem, in which gravity certainly has an added value. Pressure data alone may not discriminate between different reservoir scenarios. Combining pressure and gravity data may help to reduce the nonuniqueness problem and provide not only an improved gas- and water-production forecast and gas-in-place evaluation, but also a more-accurate reservoir-state description

Parallel Setup of Galerkin Equation System for a Geodetic Boundary Value Problem

A particular problem in setting up large Galerkin equation systems in the 3D-BEM is the huge number of offdiagonal elements, which are mainly regular integrals over pairs of boundary elements. The numerical effort of cubature depends strongly on the distance between these elements. Therefore, the polynomial degree of exactness of the cubature formula may be chosen based on an estimate of the distance. In a straightforward implementation on a parallel computer, this may lead to severe imbalances of workload, which considerably reduces the speedup. To overcome this difficulty, a dynamic load balancing scheme is applied. It is shown how this works in the solution of the classical oblique boundary value problem (BVP) of potential theory (which results from the linearization of the fixed BVP of Physical Geodesy) on a IBM 9076 SP/2.

An approach for estimating time-variable rates from geodetic time series

There has been considerable research in the literature focused on computing and forecasting sea-level changes in terms of constant trends or rates. The Antarctic ice sheet is one of the main contributors to sea-level change with highly uncertain rates of glacial thinning and accumulation. Geodetic observing systems such as the Gravity Recovery and Climate Experiment (GRACE) and the Global Positioning System (GPS) are routinely used to estimate these trends. In an effort to improve the accuracy and reliability of these trends, this study investigates a technique that allows the estimated rates, along with co-estimated seasonal components, to vary in time. For this, state space models are defined and then solved by a Kalman filter (KF). The reliable estimation of noise parameters is one of the main problems encountered when using a KF approach, which is solved by numerically optimizing likelihood. Since the optimization problem is non-convex, it is challenging to find an optimal solution. To address this issue, we limited the parameter search space using classical least-squares adjustment (LSA). In this context, we also tested the usage of inequality constraints by directly verifying whether they are supported by the data. The suggested technique for time-series analysis is expanded to classify and handle time-correlated observational noise within the state space framework. The performance of the method is demonstrated using GRACE and GPS data at the CAS1 station located in East Antarctica and compared to commonly used LSA. The results suggest that the outlined technique allows for more reliable trend estimates, as well as for more physically valuable interpretations, while validating independent observing systems.