Reconciling Statistical Models with Practical Experience of Reverberation Chambers

Presented are novel theoretical probability density functions (PDF) for the magnitude and phase of electromagnetic fields inside reverberation chambers (RC) operating in a dasiagood-but-imperfect regime. The derivation is based on considering two Gaussian random variables with mean values, variances and correlation between them that depart from the ideal assumptions. A multivariate approach using a complete joint Gaussian distribution of these variables is defined. Marginal distributions obtained by integration of this two-dimensional joint PDF are compared with theoretical PDFs for ideal situations, and significantly lower rejection rates are experienced for field data measured in real RCs. Additionally, these novel marginal PDFs are highly general since they are able to describe both ideal and non-ideal stirred fields

The development of the GSFC DORIS contribution to ITRF2014

AbstractThe NASA GSFC DORIS analysis center has processed data from January 1993 to December 2014 and provided 1141 weekly solutions in the form of normal equations for incorporation into the DORIS solution for ITRF2014. The solution time series, designated as gscwd26, were based on tracking data to eleven DORIS satellites divided generally into seven-day arcs. With respect to the ITRF2008 submission (Le Bail et al., 2010), the measurement model was updated to model the beacon frequency variations at certain DORIS sites, to apply the DORIS antenna phase law for the Starec and Alcatel antennae, and to apply the antenna offset corrections in the NASA GSFC orbit determination software rather than using the data-supplied corrections. We show that computing the antenna offset corrections in the orbit determination software is superior to using the offset corrections that are supplied with the DORIS data, and that this improves the RMS of fit for SPOT-2, Envisat, SPOT-4, and SPOT-5. The updates for the force model included: (1) the development of improved nonconservative force modeling for SPOT-2, SPOT-3, SPOT-5, Envisat, and HY-2A, and (2) the application of an updated static gravity model based on GRACE and GOCE data, and weekly models of the variations in the low degree gravity field deduced independently from tracking by Satellite Laser Ranging (SLR) and DORIS. The post-ITRF2008 DORIS coordinate WRMS after the launch of Envisat and SPOT-5 is improved from 11.20 to 12.45mm with ITRF2008 (Le Bail et al., 2010), to between 8.50 and 9.99mm with the gscwd26 SINEX solution. The application of the DORIS antenna phase laws shifts the DORIS scale wrt DPOD2008 by +6.0mm from 1993/01/03 to 2002/06/06, and by +11.4mm from 2002/06/13 to 2011/10/30. The application of more detailed models of time-variable gravity reduces the slopes in the Helmert transformation parameters Tx, and Ty (w.r.t. DPOD2008) after 2005. The annual amplitude in these parameters is reduced from 3.2mm (for Tx), 4.1mm (for Ty), to 1.7mm (for Tx) and 2.8mm (for Ty)

Ellipsoidal area mean gravity anomalies - precise computation of gravity anomaly reference fields for remove-compute-restore geoid determination

Gravity anomaly reference fields, required e.g. in remove-compute-restore (RCR) geoid computation, are obtained from global geopotential models (GGM) through harmonic synthesis. Usually, the gravity anomalies are computed as point values or area mean values in spherical approximation, or point values in ellipsoidal approximation. The present study proposes a method for computation of area mean gravity anomalies in ellipsoidal approximation ('ellipsoidal area means') by applying a simple ellipsoidal correction to area means in spherical approximation. Ellipsoidal area means offer better consistency with GGM quasi/geoid heights. The method is numerically validated with ellipsoidal area mean gravity derived from very fine grids of gravity point values in ellipsoidal approximation. Signal strengths of (i) the ellipsoidal effect (i.e., difference ellipsoidal vs. spherical approximation), (ii) the area mean effect (i.e., difference area mean vs. point gravity) and (iii) the ellipsoidal area mean effect (i.e., differences between ellipsoidal area means and point gravity in spherical approximation) are investigated in test areas in New Zealand and the Himalaya mountains. The impact of both the area mean and the ellipsoidal effect on quasigeoid heights is in the order of several centimetres. The proposed new gravity data type not only allows more accurate RCR-based geoid computation, but may also be of some value for the GGM validation using terrestrial gravity anomalies that are available as area mean values

The computation of the geoid model in the state of São Paulo using two methodologies and GOCE models

The purpose of this manuscript is to compute and to evaluate the geoid model in the State of São Paulo from two methodologies (Stokes' integral through the Fast Fourier Transform - FFT and Least Squares Collocation - LSC). Another objective of this study is to verify the potentiality of GOCE-based. A special attention is given to GOCE mission. The theory related to Stokes' integral and Least Squares Collocation is also discussed in this work. The spectral decomposition was employed in the geoid models computation and the long wavelength component was represented by EGM2008 up to degree and order 150 and 360 and GOCE-based models up to 150. The models were compared in terms of geoid height residual and absolute and relative comparisons from GPS/leveling and the results show consistency between them. In addition, a comparison in the mountain regions was carried out to verify the methodologies behavior in this area; the results showed that LSC is less consistent than FFT

Error sources and data limitations for the prediction ofsurface gravity: a case study using benchmarks

Gravity-based heights require gravity values at levelled benchmarks (BMs), whichsometimes have to be predicted from surrounding observations. We use EGM2008 andthe Australian National Gravity Database (ANGD) as examples of model and terrestrialobserved data respectively to predict gravity at Australian national levelling network(ANLN) BMs. The aim is to quantify errors that may propagate into the predicted BMgravity values and then into gravimetric height corrections (HCs). Our results indicatethat an approximate ±1 arc-minute horizontal position error of the BMs causesmaximum errors in EGM2008 BM gravity of ~ 22 mGal (~55 mm in the HC at ~2200 melevation) and ~18 mGal for ANGD BM gravity because the values are not computed atthe true location of the BM. We use RTM (residual terrain modelling) techniques toshow that ~50% of EGM2008 BM gravity error in a moderately mountainous regioncan be accounted for by signal omission. Non-representative sampling of ANGDgravity in this region may cause errors of up to 50 mGals (~120 mm for the Helmertorthometric correction at ~2200 m elevation). For modelled gravity at BMs to beviable, levelling networks need horizontal BM positions accurate to a few metres, whileRTM techniques can be used to reduce signal omission error. Unrepresentative gravitysampling in mountains can be remedied by denser and more representative re-surveys,and/or gravity can be forward modelled into regions of sparser gravity

Satellite altimetry and GRACE gravimetry for studies of annual water storage variations in Bangladesh

ICESat satellite laser altimetry provides an unprecedented set of global elevation measurements of the Earth, yielding great detail over ice, land and ocean surfaces. Coastal regions in particular, including seamless land-water transitions, benefit from the small footprint (50 to 90 m), high resolution (40 Hz, ~170 m along-track), and high precision (2 to 3 cm) of ICESat. We discuss the performance and character of ICESat data in three example coastal scenarios: continental coast (Louisiana-Mississippi Gulf Coast, USA, including Lake Pontchartrain), open ocean island (Funafuti, Tuvalu), and an inland river (confluence of Tapajos and Amazon rivers, Brazil). Water elevations are compared to tide gauge heights and to TOPEX and Jason-1 radar altimetry. In demonstrating the utilization of ICESat, we also present examples of: laser waveform shapes over a variety of surface types (water, land, and vegetation); vegetation canopy heights (detecting large-scale destruction from Hurricane Katrina comparing data before and after); sub-canopy surface water; measurements of waves; and examination of along-stream river slope and comparisons of river stage to hydrologically-driven GRACE geoid change