Preprocessing of gravity gradients at the GOCE high-level processing facility

One of the products derived from the gravity field and steady-state ocean circulation explorer (GOCE) observations are the gravity gradients. These gravity gradients are provided in the gradiometer reference frame (GRF) and are calibrated in-flight using satellite shaking and star sensor data. To use these gravity gradients for application in Earth scienes and gravity field analysis, additional preprocessing needs to be done, including corrections for temporal gravity field signals to isolate the static gravity field part, screening for outliers, calibration by comparison with existing external gravity field information and error assessment. The temporal gravity gradient corrections consist of tidal and nontidal corrections. These are all generally below the gravity gradient error level, which is predicted to show a 1/f behaviour for low frequencies. In the outlier detection, the 1/f error is compensated for by subtracting a local median from the data, while the data error is assessed using the median absolute deviation. The local median acts as a high-pass filter and it is robust as is the median absolute deviation. Three different methods have been implemented for the calibration of the gravity gradients. All three methods use a high-pass filter to compensate for the 1/f gravity gradient error. The baseline method uses state-of-the-art global gravity field models and the most accurate results are obtained if star sensor misalignments are estimated along with the calibration parameters. A second calibration method uses GOCE GPS data to estimate a low-degree gravity field model as well as gravity gradient scale factors. Both methods allow to estimate gravity gradient scale factors down to the 10⁻³ level. The third calibration method uses high accurate terrestrial gravity data in selected regions to validate the gravity gradient scale factors, focussing on the measurement band. Gravity gradient scale factors may be estimated down to the 10⁻² level with this method.     

Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination

Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6 mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO positions.     

Efficient propagation of error covariance matrices of gravitational models: application to GRACE and GOCE

We have applied efficient methods for computing variances and covariances of functions of a global gravity field model expanded in spherical harmonics, using the full variance–covariance matrix of the coefficients. Examples are given with recent models derived from GRACE (up to degree and order 150), and with simulated GOCE derived solutions (up to degree and order 200).     

On the topographic bias in geoid determination by the external gravity field

The topographic bias is defined as the error/bias committed by continuing the external gravity field inside the topographic masses by a harmonic function. We study the topographic bias given by a digital terrain model defined by a spherical template, and we show that the topographic bias is given only by the potential of an inner-zone cap, and it equals the bias of the Bouguer shell, independent of the size of the cap. Then we study the effect on the real Earth by decomposing its topography into a template, and we show also in this case that the topographic bias is that of the Bouguer shell, independent of the shape of the terrain. Finally, we show that the topographic potential of the terrain at the geoid can be determined to any precision by a Taylor expansion outside the Earth’s surface. The last statement is demonstrated by a Taylor expansion to fourth order.     

Long term shoreline oscillation and changes of Cauvery delta coastline inferred from satellite imageries

Coastal zone is highly volatile ecosystem which is always in adjustments. Loss of shore line will cause severe impact on human life and as well as their properties. Remote sensing is a reliable technique to study the historical shoreline changes. Therefore in this paper long term shoreline oscillations of Cauvery delta shorelines at Poompuhar, Tharangambadi and Nagapattinam were studied using satellite imageries and the same was physically observed at the above three locations with the help of reference pillars and compared mutually. It was observed that the shoreline at Poompuhar is under accretion at the rate of 1.79m/ year and other shoreline stretches at Tharangambadi and Nagapattinam were under erosion at 0.4888m/ year and 0.4985m/ year respectively. It was also observed that the remote sensing study qualitatively matches with the physical observation for all the three coastal stretches of the study area.     

Using gravity and topography-implied anomalies to assess data requirements for precise geoid computation

Many regions around the world require improved gravimetric data bases to support very accurate geoid modeling for the modernization of height systems using GPS. We present a simple yet effective method to assess gravity data requirements, particularly the necessary resolution, for a desired precision in geoid computation. The approach is based on simulating high-resolution gravimetry using a topography-correlated model that is adjusted to be consistent with an existing network of gravity data. Analysis of these adjusted, simulated data through Stokes’s integral indicates where existing gravity data must be supplemented by new surveys in order to achieve an acceptable level of omission error in the geoid undulation. The simulated model can equally be used to analyze commission error, as well as model error and data inconsistencies to a limited extent. The proposed method is applied to South Korea and shows clearly where existing gravity data are too scarce for precise geoid computation.     

A hierarchical model for estimating methane emission from wetlands using MODIS data and ARIMA modeling

A three-step hierarchical Semi Automated Empirical Methane Emission Model (SEMEM) has been used to estimate methane emission from wetlands and waterlogged areas in India using Moderate Resolution Imagine Spectroradiometer (MODIS) sensor data onboard Terra satellite. Wetland Surface Temperature (WST), methane emission fluxes and wetland extent have been incorporated as parameters in order to model the methane emission. Analysis of monthly MODIS data covering the whole of India from November 2004 to April 2006 was carried out and monthly methane emissions have been estimated. Interpolation techniques were adopted to fill the data gaps due to cloudy conditions during the monsoon period. AutoRegressive Integrated Moving Average (ARIMA) model has been fitted to estimate the emitted methane for the months of May 2006 to August 2006 using SPSS software.     

An approach to aid INS using time-differenced GPS carrier phase (TDCP) measurements

This paper presents a simple and effective approach that incorporates single-frequency, L1 time-differenced GPS carrier phase (TDCP) measurements without the need of ambiguity resolution techniques and the complexity to accommodate the delayed-state terms. Static trial results are included to illustrate the stochastic characteristics and effectiveness of the TDCP measurements in controlling position error growth. The formulation of the TDCP observation model is also described in a 17-state tightly-coupled GPS/INS iterative, extended Kalman filter (IEKF) approach. Preliminary land vehicle trial results are also presented to illustrate the effectiveness of the TDCP which provides sub-meter positional accuracies when operating for more than 10 min.     

Urban cadastral mapping using very high resolution remote sensing data

With growing urban expanses, one of the pre-requisites for effective governance is Urban Information Systems (UIS) with content down to individual properties (and individuals). The basic input i.e., a map, in UIS should show individual property boundaries showing the plan outline of all structures existing within, at a scale of 1:1000 and larger with sub-metre to centimeters planimetric and geometric accuracy. With very high resolution remote sensing data of the order of 1m available in hand, it is possible to prepare maps with high resolution spatial content. The present exercise demonstrates a method of preparing a geometrically and planimetrically accurate urban cadastral map on very large scale for a small area of about 5 sq km. IKONOS merged data with 1m resolution is used for the purpose. Mapping was done in conjunction with on-site measurements and sketches. Guides are used to maintain shape symmetry and accuracy of buildings and other features. Working out cost of mapping per unit area is another objective in the present exercise. For want of fully or semi-automatic methods of information extraction from very high resolution remote sensing data, it is imperative that mapping should be carried out in conjunction with some on-site measurements wherever necessary.