BOWDITCH TRAVERSE ADJUSTMENT AND A MODIFICATION: NOTES

Abstract

In the second part of the paper on this subject in the last issue (30, 483) the references to the relative angular and linear closures are rather misleading. Mr Clendinning points out that the probable angular error at a station must be considered; the mean error is clearly different.     

SOME PROBLEMS OF RESECTION AND COUNTERSECTION-I

Abstract

“A Well-Defined mountain, though miles inland and never visited by the surveyors, will often prove the very keystone of a chart which cannot be regularly and theoretically triangulated” (“Hydrographic Surveying”, by Rear-Adm. Sir Wm J. L. Wharton, K.C.B., and Rear-Adm. Mostyn Field, F.R.S. 3rd Ed. 1909, p. 128). To many the reasons prohibiting the occupation of inland stations may be unknown; it may suffice to state that, in the past, British hydrographers have mapped many coastal waters where penetration of the land was at least inadvisable. Since the charts so made were in general sold to the world, seamen of all nations have benefited from the surveys.     

Using a Grid-Based Filter to Solve InSAR Phase Unwrapping

This letter presents a phase-unwrapping (PU) algorithm for synthetic aperture radar interferometry based on a grid-based filter. The proposed PU algorithm, which is based on state-space techniques, simultaneously performs noise filtering and PU. The formulation of this technique provides independence from noise statistics and is not constrained by the nonlinearity of the problem. Results obtained with synthetic data show a significant improvement with respect to other conventional PU algorithms in some situations.     

A data-driven approach to local gravity field modelling using spherical radial basis functions

We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions (SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms that our solution is in no way inferior to NLGEO2004.     

Motion Analysis in SAR Images of Unfocused Objects Using Time–Frequency Methods

Synthetic aperture radar (SAR) image formation processing assumes that the scene is stationary, and to focus an object, one coherently sums a large number of independent returns. Any target motion introduces phases that distort and/or translate the target's image. Target motion produces a smear primarily in the azimuth direction of the SAR image. Time-frequency (TF) modeling is used to analyze and correct the residual phase distortions. An interactive focusing algorithm based on TF modeling demonstrates how to correct the phase and to rapidly focus the mover. This is demonstrated on two watercraft observed in a SAR image. Then, two time-frequency representations (TFRs) are applied to estimate the motion parameters of the movers or refocus them or both. The first is the short-time Fourier transform, from which a velocity profile is constructed based on the length of the smear. The second TFR is the time-frequency distribution series, which is a robust derivative of the Wigner-Ville distribution that works well in this SAR environment. The smear is a modulated chirp, from which a velocity profile is plotted and the phase corrections are integrated to focus the movers. The relationship between these two methods is discussed. Both methods show good agreement on the example.     

GPS tomography in the polar cap: comparison with ionosondes and in situ spacecraft data

Tomographic 4D reconstructions of ionospheric anomalies appearing in the high-latitude polar cap region are compared with plasma density measurements by digital ionosonde located near the north magnetic pole at Eureka station and with in situ plasma measurements on-board DMSP spacecraft. The moderate magnetic storm of 14–17 October 2002 is taken as an example of a geomagnetic disturbance which generates large-scale ionospheric plasma anomalies at mid-latitudes and in the polar cap region. Comparison of the GPS tomographic reconstructions over Eureka station with the ionosonde measurements of the F layer peak densities indicates that the GPS tomography correctly predicts the time of arrival and passage of the ionospheric tongue of ionization over the magnetic pole area, although the tomographic technique appears to under-estimate the value of F peak plasma density. Comparison with the in situ plasma measurements by the DMSP SSIES instruments shows that the GPS tomography correctly reproduces the large-scale spatial structure of ionospheric anomalies over a wide range of latitudes from mid-latitudes to the high-latitude polar cap region, though the tomographic reconstructions tend to over-estimate the density of the topside ionosphere at 840 km DMSP orbit. This study is essential for understanding the quality and limitations of the tomographic reconstruction techniques, particularly in high-latitude regions where GPS TEC measurements and other ionospheric data sources are limited.     

Evaluation of the first GOCE static gravity field models using terrestrial gravity,vertical deflections and EGM2008 quasigeoid heights

Recently, four global geopotential models (GGMs) were computed and released based on the first 2 months of data collected by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission. Given that GOCE is a technologically complex mission and different processing strategies were applied to real space-collected GOCE data for the first time, evaluation of the new models is an important aspect. As a first assessment strategy, we use terrestrial gravity data over Switzerland and Australia and astrogeodetic vertical deflections over Europe and Australia as ground-truth data sets for GOCE model evaluation. We apply a spectral enhancement method (SEM) to the truncated GOCE GGMs to make their spectral content more comparable with the terrestrial data. The SEM utilises the high-degree bands of EGM2008 and residual terrain model data as a data source to widely bridge the spectral gap between the satellite and terrestrial data. Analysis of root mean square (RMS) errors is carried out as a function of (i) the GOCE GGM expansion degree and (ii) the four different GOCE GGMs. The RMS curves are also compared against those from EGM2008 and GRACE-based GGMs. As a second assessment strategy, we compare global grids of GOCE GGM and EGM2008 quasigeoid heights. In connection with EGM2008 error estimates, this allows location of regions where GOCE is likely to deliver improved knowledge on the Earth’s gravity field. Our ground truth data sets, together with the EGM2008 quasigeoid comparisons, signal clear improvements in the spectral band ~160–165 to ~180–185 in terms of spherical harmonic degrees for the GOCE-based GGMs, fairly independently of the individual GOCE model used. The results from both assessments together provide strong evidence that the first 2 months of GOCE observations improve the knowledge of the Earth’s static gravity field at spatial scales between ~125 and ~110 km, particularly over parts of Asia, Africa, South America and Antarctica, in comparison with the pre-GOCE-era.     

Simulation of the Ku-band Radar altimeter sea ice effective scattering surface

A radiative transfer model is used to simulate the sea ice radar altimeter effective scattering surface variability as a function of snow depth and density. Under dry snow conditions without layering these are the primary snow parameters affecting the scattering surface variability. The model is initialized with in situ data collected during the May 2004 GreenIce ice camp in the Lincoln Sea (73/spl deg/W; 85/spl deg/N). Our results show that the snow cover is important for the effective scattering surface depth in sea ice and thus for the range measurement, ice freeboard, and ice thickness estimation.     

Software for validating parameters retrieved from satellite

A PC-based interactive software has been developed and presented here for validating geophysical data retrieved from satellite mounted sensors operating in visible, infrared and microwave frequencies. The program, coded in Visual Basic, is user interactive and runs on Windows-98 or higher platforms. The system prepares the database on a pre-selected Microsoft platform to enhance processing efficiency. Sub-setting option is also provided to reduce the processing time. Data retrieved from ‘Multi-channel Scanning Microwave Radiometer (MSMR) onboard the Indian satellites Oceansat-1 during 1999–2001 were validated using this software as a case study. The program has several added advantages over the conventional method of validation that involves strenuous efforts to incorporate subroutines to meet every minute requirement. Satellite-sea truth relationships on various space-time window combinations are determined and exhibited in matrix form to visualize the nature of correlation. User has the option to visualize the satellite-sea truth relationship through graphical representations before selecting optimum relationship for prediction.