Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.     

Landscape transform and spatial metrics for mapping spatiotemporal land cover dynamics using Earth Observation data-sets

Analysis of Earth observation (EO) data, often combined with geographical information systems (GIS), allows monitoring of land cover dynamics over different ecosystems, including protected or conservation sites. The aim of this study is to use contemporary technologies such as EO and GIS in synergy with fragmentation analysis, to quantify the changes in the landscape of the Rajaji National Park (RNP) during the period of 19 years (1990–2009). Several statistics such as principal component analysis (PCA) and spatial metrics are used to understand the results. PCA analysis has produced two principal components (PC) and explained 84.1% of the total variance, first component (PC1) accounted for the 57.8% of the total variance while the second component (PC2) has accounted for the 26.3% of the total variance calculated from the core area metrics, distance metrics and shape metrics. Our results suggested that notable changes happened in the RNP landscape, evidencing the requirement of taking appropriate measures to conserve this natural ecosystem.     

Spin rate estimation of sounding rockets using GPS wind-up

Carrier phase wind-up is a well-known effect that arises from the relative rotation between a transmitting and receiving antenna. In GPS measurements at L1 frequency, this effect translates into an error of 19.029 cm per full relative rotation of antennas. Since this effect is independent of the satellite elevation for pure rotation about the antenna boresight axis, it is usually absorbed by the clock estimation in navigation algorithms. Therefore, the impact of wind-up is usually neglected for applications that do not require accuracies to the cm level like RTK. However, in receiving platforms with high rotation rate, the accumulated wind-up value can be important and actually be larger than receiver noise or even ionospheric variations. Therefore, in such scenarios, the wind-up contribution can be isolated and used as a source of information to compute the spin rate of such platforms using an appropriate combination of GPS observables. This work shows some results of a coarse, yet simple, approach to monitor the rotation angle and spin-rate of spin stabilized sounding rockets flown by DLR.     

The ionosphere: effects,GPS modeling and the benefits for space geodetic techniques

The main goal of this paper is to provide a summary of our current knowledge of the ionosphere as it relates to space geodetic techniques, especially the most informative technology, global navigation satellite systems (GNSS), specifically the fully deployed and operational global positioning system (GPS). As such, the main relevant modeling points are discussed, and the corresponding results of ionospheric monitoring are related, which were mostly computed using GPS data and based on the direct experience of the authors. We address various phenomena such as horizontal and vertical ionospheric morphology in quiet conditions, traveling ionospheric disturbances, solar flares, ionospheric storms and scintillation. Finally, we also tackle the question of how improved knowledge of ionospheric conditions, especially in terms of an accurate understanding of the distribution of free electrons, can improve space geodetic techniques at different levels, such as higher-order ionospheric effects, precise GNSS navigation, single-antenna GNSS orientation and real-time GNSS meteorology.     

Geometry and accuracy of reflecting points in bistatic satellite altimetry

The analysis of the time and space distribution of specular (reflecting) points in bistatic altimetry between GPS and CHAMP satellites or SAC-C (taken as examples) is extended from Wagner and Klokočník (2003 J. Geod 77: 128–138). We demonstrate a significantly higher number and density of reflecting points in bistatic altimetry in comparison with traditional monostatic altimetry. After an outline of our older accuracy assessment for the vertical position of the reflecting point, we add a new independent derivation and compare both approaches. We account for orbit errors of both the transmitters (GPS) and receiver (CHAMP) satellites, and the measurement (delay) error. We found that the accuracy of the vertical position of the reflecting point decreases only slowly with increasing off-nadir angle and that the orbit errors must be accounted for if decimeter and better accuracy is required. In this paper, we do not study errors such as state of the ocean, technical parameters of the receiving system, and atmospheric corrections.     

Diurnal Variation of Gravity Wave Activity at Midlatitudes in the Ionospheric F Region

We investigate the short-term fluctuations in the period range from 15 to 180 minutes in the electron density variations of the F region ionosphere. Electron density profiles obtained at the ionospheric stations of Pruhonice (49.9° N, 14.5° E) and Ebro (40.8° N, 0.5° E) at five minute time sampling have been used for this analysis. The diurnal changes of the activity of the acoustic gravity wave fluctuations (AGW) show a clear enhancement during and several hours after sunrise. The periods of such AGW's are about 60 to 75 minutes and these waves propagates vertically through the ionosphere from a source located at an altitude of 180-220 km. The most likely source for these events seems to be passage of the Solar terminator.     

Impacts of macroalgal spores on the dynamics of adult macroalgae in a eutrophic estuary: high versus low hydrodynamic seasons and long-term simulations for global warming scenarios

A model describing macroalgal early life stages and adult dynamics was used to quantify the effects of non-adult forms on the productivity of adult macroalgae in a eutrophic estuary. Predictions indicate that during years with mild winters and low rainfall, spring blooms will occur at the expense of the growth and reproduction of overwintering adults and without the contribution of the spore bank. In these circumstances, there is a positive correlation between the intensity of the blooms and the biomass of overwintering adults until a maximum threshold value. On the contrary, in years with high rainfall and low or inexistent biomass of overwintering adults, the onset of adult’s growth depends on the biomass of viable dormant spores, the growing season occurs later and adult productivity is very limited. Long-term predictions for climate change scenarios suggest that, in general, global warming will have adverse affects on Ulva intestinalis productivity, with the adults being more affected than the early life stages.     

Stress Field Estimations for Colima Volcano, Mexico, Based on Seismic Data

 For first time, during 1991, seismic activity was recorded during an eruption at Colima volcano. We analyze these data to obtain a stress pattern using a composite focal mechanism technique. From the analysis of regional seismicity, the Tamazula Fault and the Armeria River appear as active features and the dip of the slab east of the Jalisco Block is approximately 12°. Southwest of Colima volcano a vertical alignment of seismic events was observed. We estimate five different composite focal mechanism solutions from our data set, which indicate a change of the stress field at the volcano after the 1991 eruption. These solutions suggest that the stress field in the volcanic edifice was controlled by stresses related to the emplacement of magma superimposed on the regional stress field. No evidence of active local faults in the volcanic edifice was found. We propose a model for the eruptive process that involves tilting of the volcanic edifice. Received: 15 October 1995 / Accepted: 26 October 1998