Methodology and use of tensor invariants for satellite gravity gradiometry

Although its use is widespread in several other scientific disciplines, the theory of tensor invariants is only marginally adopted in gravity field modeling. We aim to close this gap by developing and applying the invariants approach for geopotential recovery. Gravitational tensor invariants are deduced from products of second-order derivatives of the gravitational potential. The benefit of the method presented arises from its independence of the gradiometer instrument’s orientation in space. Thus, we refrain from the classical methods for satellite gravity gradiometry analysis, i.e., in terms of individual gravity gradients, in favor of the alternative invariants approach. The invariants approach requires a tailored processing strategy. Firstly, the non-linear functionals with regard to the potential series expansion in spherical harmonics necessitates the linearization and iterative solution of the resulting least-squares problem. From the computational point of view, efficient linearization by means of perturbation theory has been adopted. It only requires the computation of reference gravity gradients. Secondly, the deduced pseudo-observations are composed of all the gravitational tensor elements, all of which require a comparable level of accuracy. Additionally, implementation of the invariants method for large data sets is a challenging task. We show the fundamentals of tensor invariants theory adapted to satellite gradiometry. With regard to the GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite gradiometry mission, we demonstrate that the iterative parameter estimation process converges within only two iterations. Additionally, for the GOCE configuration, we show the invariants approach to be insensitive to the synthesis of unobserved gravity gradients.     

Attitude estimation based on fusion of gyroscopes and single antenna GPS for small UAVs under the influence of vibration

An attitude estimation method is presented for small unmanned aerial vehicles (UAVs) powered by a piston engine which is the major source of vibration. Vibration of the engine significantly degrades the accuracy of the inertial measurement unit, especially for low-cost sensors that are based on micro electro-mechanical system. Therefore, a vibration model for a small UAV is proposed in order to examine the influence of vibration on attitude estimation with different sensors. The model is derived based on spectrum analysis with short-time Fourier transform. The vibration is compared with the drift of the gyroscope in order to examine the impact on attitude estimation. An attitude estimation method that fuses the gyroscopes and single antenna global positioning system (GPS) is proposed to mitigate the influence of engine vibration and gyroscope drift. The quaternion-based extended Kalman filter is implemented to fuse the sensors. This filter fuses the angular rates measured by the gyroscopes and the pseudo-attitude derived from the GPS velocity to estimate the attitude of the UAV. Simulations and experiment results indicate that the proposed method performs well both in short-term and long-term accuracy even though the gyroscopes are affected by drift and vibration noise, while the pseudo-attitude contains severe noise.     

Skyline-based registration of 3D laser scans

Acquisition and registration of terrestrial 3D laser scans is a fundamental task in mapping and modeling of cities in three dimensions. To automate this task marker-free registration methods are required. Based on the existence of skyline features, this paper proposes a novel method. The skyline features are extracted from panoramic 3D scans and encoded as strings enabling the use of string matching for merging the scans. Initial results of the proposed method in the old city center of Bremen are pre-sented.     

Remotely sensed estimation of forest canopy density: A comparison of the performance of four methods

In recent years, a number of alternative methods have been proposed to predict forest canopy density from remotely sensed data. To date, however, it remains difficult to decide which method to use, since their relative performance has never been evaluated. In this study the performance of: (1) an artificial neural network, (2) a multiple linear regression, (3) the forest canopy density mapper and (4) a maximum likelihood classification method was compared for prediction of forest canopy density using a Landsat ETM+ image. Comparison of confusion matrices revealed that the regression model performed significantly worse than the three other methods. These results were based on a z-test for comparison of weighted kappa statistics, which is an appropriate statistic for analysis of ranked categories. About 89% of the variance of the observed canopy density was explained by the artificial neural networks, which outperformed the other three methods in this respect. Moreover, the artificial neural networks gave an unbiased prediction, while other methods systematically under or over predicted forest canopy density. The choice of biased method could have a high impact on canopy density inventories.     

Expanding global mapping of the foliage clumping index with multi-angular POLDER three measurements: Evaluation and topographic compensation

The clumping index measures the spatial aggregation (clumped, random and regular) of foliage elements. The global mapping of the clumping index with a limited eight-month multi-angular POLDER 1 dataset is expanded by integrating new, complete year-round observations from POLDER 3. We show that terrain-induced shadows can enhance bi-directional reflectance distribution function variation and negatively bias the clumping index (i.e. indicating more vegetation clumping) in rugged terrain. Using a global high-resolution digital elevation model, a topographic compensation function is devised to correct for this terrain effect. The clumping index reductions can reach up to 30% from the topographically non-compensated values, depending on terrain complexity and land cover type. The new global clumping index map is compared with an assembled set of field measurements from 32 different sites, covering four continents and diverse biomes.     

Evidence for the occurrence of hydrogeochemical processes in the groundwater of Khoy plain,northwestern Iran,using ionic ratios and geochemical modeling

Rapid population growth, industrialization, and agricultural expansion in the Khoy area (northwestern Iran) have led to its dependence on groundwater and degradation of groundwater quality. This study attempts to decipher the major processes and factors that degrade the groundwater quality of the Khoy plain. For this purpose, 54 groundwater samples from unconfined and confined aquifers of the plain were collected in July 2017 and analyzed for major cations and anions (Na, K, Ca, Mg, HCO₃, SO_4, and Cl), minor ions (NO₃ and F), and Al. Magnesium and bicarbonate were identified as the dominant cation and anion, respectively. Several ionic ratios and geochemical modeling using PHREEQC indicated that the most important hydrogeochemical processes to affect groundwater quality in the plain were weathering and dissolution of evaporitic and silicate minerals, mixing, and ion exchange. There were smaller effects from evaporation and anthropogenic factors (e.g., industries). Results showed that the high salinity of the groundwater in the northeast area of the plain was due to the high solubility of the evaporitic minerals, e.g., halite and gypsum. Reverse ion exchange and the contribution of mineral dissolution were more significant than ion exchange in the northeastern part of the plain. Elevated salinity of the groundwater in the southeast was attributed mostly to reverse ion exchange and somewhat to evaporation.     

Über die Verteilung der aus Gezeitenbeobachtungen bestimmten gravimetrischen Faktoren in Europa

auamaumuu am, n u a¶rt;u nuu n ¶rt;a ₂, ₂, ₁ u ₁ (u. 1–4). na ¶rt;a ¶rt;am au ¶rt;um au an¶rt;u mu naam. a n¶rt;aam unam nu nuu nna m uu u u mmu mam ¶rt; uu u a a mau n.

---

---

Vorgetragen am 2. Internationalen Symposium Geodäsie und Physik der Erde, Potsdam, Mai 1973.     

A local model for analysis of pump and treat systems with vertical barrier walls

We present a mathematical model of local, steady groundwater flow near a vertical barrier wall. Flow features represented in the model include an impermeable arc-shaped barrier wall and multiple wells; distant boundary conditions are not included explicitly, but their effects on the local flow field are modelled by specifying a uniform flow at infinity and a constant areal recharge within a local domain. We develop an explicit closed-form solution to the boundary-value problem using the analytic element method. The solution is an extension of a harmonic solution presented by Anderson and Mesa [Anderson EI, Mesa E. The effects of vertical barrier walls on the hydraulic control of contaminated groundwater. Adv Water Resourc 2006;29(1):89–98] which does not include the effects of recharge. We demonstrate that the general solution with recharge consists of the harmonic solution superposed on a special case of the harmonic solution along with two elementary one-dimensional flow solutions. The results are used to investigate the effects of areal recharge on the capture zone envelopes of the pumping wells and on the reduction in discharge that can be achieved by including a barrier wall in a pump and treat design. We find that the benefits of including an open barrier wall in a design, measured as a reduction in the pumping rate required to contain a plume, increase for higher recharge rates. Dimensionless plots of capture zone envelopes are presented for a practical well and barrier wall configuration.