Invariant manifolds, phase correlations of chaotic orbits and the spiral structure of galaxies

In the presence of a strong   m = 2  component in a rotating galaxy, the phase-space structure near corotation is shaped to a large extent by the invariant manifolds of the short-period family of unstable periodic orbits terminating at L ₁ or L ₂. The main effect of these manifolds is to create robust phase correlations among a number of chaotic orbits large enough to support a spiral density wave outside corotation. The phenomenon is described theoretically by soliton-like solutions of a Sine–Gordon equation. Numerical examples are given in an N -body simulation of a barred spiral galaxy. In these examples, we demonstrate how the projection of unstable manifolds in configuration space reproduces essentially the entire observed bar–spiral pattern.     

Fast integration of low orbiter's trajectory perturbed by the earth's non-sphericity

A fast algorithm is proposed to integrate the trajectory of a low obiter perturbed by the earth's non-sphericity. The algorithm uses a separation degree to define the low-degree and the high-degree acceleration components, the former computed rigorously, and the latter interpolated from gridded accelerations. An FFT method is used to grid the accelerations. An optimal grid type for the algorithm depends on the trajectory's permissible error, speed, and memory capacity. Using the non-spherical accelerations computed from EGM96 to harmonic degree 360, orbit integrations were performed for a low orbiter at an altitude of 170 km. For a separation degree of 50, the new algorithm, together with the predict-pseudo correct method, speeds up the integration by 145 times compared to the conventional algorithm while keeping the errors in position and velocity below 10⁻⁴ m and 10⁻⁷ m/s for a 3-day arc. Received: 28 July 1997 / Accepted: 1 April 1998     

Reference frame stability and nonlinear distortion in minimum-constrained network adjustment

The aim of this paper is to investigate the influence of the minimum constraints (MCs) on the reference frame parameters in a free-net solution. The non-estimable part of these parameters (which is not reduced by the available data) is analysed in terms of its stability under a numerical perturbation of the constrained datum functionals. In practice, such a perturbation can be ascribed either to hidden errors in the known coordinates/velocities that participate in the MCs or to a simple change of their a priori values due to a datum switch on a different fiducial dataset. In addition, a perturbation of this type may cause a nonlinear variation to the estimable part of the reference frame parameters, since it theoretically affects the adjusted observations that are implied by the network’s nonlinear observational model. The aforementioned effects have an impact on the quality of a terrestrial reference frame (TRF) that is established via a minimum-constrained adjustment, and our study shows that they are both controlled through a characteristic matrix which is inherently linked to the MC system (the so-called TRF stability matrix). The structure of this matrix depends on the network’s spatial configuration and the ‘geometry’ of the datum constraints, while its main role is the filtering of any MC-related errors into the least-squares adjustment results. A number of examples with different types of geodetic networks are also presented to demonstrate the theoretical findings of our study.     

Applications of AnnAGNPS model for soil loss estimation and nutrient loading for Malaysian conditions

The study evaluated the performance and suitability of AnnAGNPS model in assessing runoff, sediment loading and nutrient loading under Malaysian conditions. The watershed of River Kuala Tasik in Malaysia, a combination of two sub-watersheds, was selected as the area of study. The data for the year 2004 was used to calibrate the model and the data for the year 2005 was used for validation purposes. Several input parameters were computed using methods suggested by other researchers and studies carried out in Malaysia. The study shows that runoff was predicted well with an overall R² value of 0.90 and E value of 0.70. Sediment loading was able to produce a moderate result of R² = 0.66 and E = 0.49, nitrogen loading predictions were slightly better with R² = 0.68 and E = 0.53, and phosphorus loading performance was slightly poor with an R² = 0.63 and E = 0.33. The erosion map developed was in agreement with the erosion risk map produced by the Department of Agriculture, Malaysia. Rubber estates and urban areas were found to be the main contributors to soil erosion. The simulation results showed that AnnAGNPS has the potential to be used as a valuable tool for planning and management of watersheds under Malaysian conditions.     

Comparing spatially varying coefficient models: a case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests

In this paper, we compare and contrast a Bayesian spatially varying coefficient process (SVCP) model with a geographically weighted regression (GWR) model for the estimation of the potentially spatially varying regression effects of alcohol outlets and illegal drug activity on violent crime in Houston, Texas. In addition, we focus on the inherent coefficient shrinkage properties of the Bayesian SVCP model as a way to address increased coefficient variance that follows from collinearity in GWR models. We outline the advantages of the Bayesian model in terms of reducing inflated coefficient variance, enhanced model flexibility, and more formal measuring of model uncertainty for prediction. We find spatially varying effects for alcohol outlets and drug violations, but the amount of variation depends on the type of model used. For the Bayesian model, this variation is controllable through the amount of prior influence placed on the variance of the coefficients. For example, the spatial pattern of coefficients is similar for the GWR and Bayesian models when a relatively large prior variance is used in the Bayesian model.      

Evaluation of pre-CHAMP gravity models `GRIM5-S1' and `GRIM5-C1' with satellite crossover altimetry

 The new GFZ/GRGS gravity field models GRIM5-S1 and GRIM5-C1, currently used as initial models for the CHAMP mission, have been compared with other recent models (JGM 3, EGM 96) for radial orbit accuracy (by means of latitude lumped coefficients) in computations on altimetry satellite orbits. The bases for accuracy judgements are multi-year averages of crossover sea height differences from Geosat and ERS 1/2 missions. This radially sensitive data is fully independent of the data used to develop these gravity models. There is good agreement between the observed differences in all of the world's oceans and projections of the same errors from the scaled covariance matrix of their harmonic geopotential coefficients. It was found that the tentative scale factor of five for the formal standard deviations of the harmonic coefficients of the new GRIM fields is justified, i.e. the accuracy estimates, provided together with the GRIM geopotential coefficients, are realistic. Received: 20 February 2001 / Accepted: 24 October 2001     

Reducing the draconitic errors in GNSS geodetic products

Systematic errors at harmonics of the GPS draconitic year have been found in diverse GPS-derived geodetic products like the geocenter $Z$ -component, station coordinates, $Y$ -pole rate and orbits (i.e. orbit overlaps). The GPS draconitic year is the repeat period of the GPS constellation w.r.t. the Sun which is about 351 days. Different error sources have been proposed which could generate these spurious signals at the draconitic harmonics. In this study, we focus on one of these error sources, namely the radiation pressure orbit modeling deficiencies. For this purpose, three GPS+GLONASS solutions of 8 years (2004–2011) were computed which differ only in the solar radiation pressure (SRP) and satellite attitude models. The models employed in the solutions are: (1) the CODE (5-parameter) radiation pressure model widely used within the International GNSS Service community, (2) the adjustable box-wing model for SRP impacting GPS (and GLONASS) satellites, and (3) the adjustable box-wing model upgraded to use non-nominal yaw attitude, specially for satellites in eclipse seasons. When comparing the first solution with the third one we achieved the following in the GNSS geodetic products. Orbits: the draconitic errors in the orbit overlaps are reduced for the GPS satellites in all the harmonics on average 46, 38 and 57 % for the radial, along-track and cross-track components, while for GLONASS satellites they are mainly reduced in the cross-track component by 39 %. Geocenter $Z$ -component: all the odd draconitic harmonics found when the CODE model is used show a very important reduction (almost disappearing with a 92 % average reduction) with the new radiation pressure models. Earth orientation parameters: the draconitic errors are reduced for the $X$ -pole rate and especially for the $Y$ -pole rate by 24 and 50 % respectively. Station coordinates: all the draconitic harmonics (except the 2nd harmonic in the North component) are reduced in the North, East and Height components, with average reductions of 41, 39 and 35 % respectively. This shows, that part of the draconitic errors currently found in GNSS geodetic products are definitely induced by the CODE radiation pressure orbit modeling deficiencies.     

Multifrequency algorithms for precise point positioning: MAP3

We present the new MAP3 algorithms to perform static precise point positioning (PPP) from multifrequency and multisystem GNSS observations. MAP3 represents a two-step strategy in which the least squares theory is applied twice to estimate smoothed pseudo-distances, initial phase ambiguities, and slant ionospheric delay first, and the absolute receiver position and its clock offset in a second adjustment. Unlike the classic PPP technique, in our new approach, the ionospheric-free linear combination is not used. The combination of signals from different satellite systems is accomplished by taking into account the receiver inter-system bias. MAP3 has been implemented in MATLAB and integrated within a complete PPP software developed on site and named PCube. We test the MAP3 performance numerically and contrast it with other external PPP programs. In general, MAP3 positioning accuracy with low-noise GPS dual-frequency observations is about 2.5 cm in 2-h observation periods, 1 cm in 10 h, and 7 mm after 1 day. This means an improvement in the accuracy in short observation periods of at least 7 mm with respect to the other PPP programs. The MAP3 convergence time is also analyzed and some results obtained from real triple-frequency GPS and GIOVE observations are presented.     

Use of the L2C signal for inversions of GPS radio occultation data in the neutral atmosphere

Results from processing FORMOSAT-3/COSMIC radio occultations (RO) with the new GPS L2C signal acquired both in phase locked loop (PLL) and open loop (OL) modes are presented. Analysis of L2P, L2C, and L1CA signals acquired in PLL mode shows that in the presence of strong ionospheric scintillation not only L2P tracking, but also L1CA tracking often fails, while L2C tracking is most stable. The use of L2C improves current RO processing in the neutral atmosphere mainly by increasing the number of processed occultations (due to significant reduction in the number of L2 tracking failures) and marginally by a reduction in noise in statistics. The latter is due to the combination of reduced L2C noise (compared to L2P) and increased L1CA noise in those occultations where L2P would have failed. This result suggests application of OL tracking for L1CA and L2C signals throughout an entire occultation to optimally acquire RO data. Two methods of concurrent processing of L1CA and L2C RO signals are considered. Based on testing of individual occultations, these methods allow: (1) reduction in uncertainty of bending angles retrieved by wave optics in the lower troposphere and (2) reduction in small-scale residual errors of the ionospheric correction in the stratosphere.