Low-low satellite-to-satellite tracking: a comparison between analytical linear orbit perturbation theory and numerical integration

Low-low satellite-to-satellite tracking (ll-SST) range-rate observations have been predicted by two methods: one based on a linear perturbation theory in combination with the Hill equations, and one based on solving the equations of motion of two low-flying satellites by numerical integration. The two methods produce almost equivalent Fourier spectra of the range-rate observations after properly taking into account a few resonant terms. For a typical GRACE-type configuration, where the two satellites trail each other at a distance of 300 km at an altitude of 460 km, and in the presence of the EGM96 gravity field model, complete to spherical harmonic degree and order 70, the agreement between the Fourier spectra is about 1 mm/s compared to a root-mean-square (RMS) value of more than 220 mm/s for the range-rate signal. The discrepancy of 1 mm/s can be reduced significantly when not taking into account perturbations caused by the J₂ term. Excluding the J₂ term, the agreement between the two methods improves to 0.4 mm/s compared to a RMS value of 6 mm/s for the range-rate signal. These values are 0.01 and 2.3 mm/s when ignoring the spectrum for frequencies below two cycles per orbital revolution, reducing the discrepancy even further to about 0.5% of the signal. The selected linear perturbation theory is thus capable of modeling gravity field induced range-rate observations with very high precision for a large part of the spectrum.     

Use of radio-occultation data for ionospheric imaging during the April 2002 disturbances

In 1994, Hajj et al. (1994) proposed the use of radio occultation data in ionospheric imaging. The advantages gained by including this data source are examined in this paper. Many data sources including ground-based and satellite-based observations are available for the events of the April 2002 ionospheric disturbance. This period has been chosen to study simultaneous images of the disturbed ionosphere over the USA and Europe. A 4D tomographic imaging technique known as Multi-instrument Data Analysis System (MIDAS) (Mitchell and Spencer, 2003) is applied in this study. The primary purpose of the study is to compare images produced with and without the use of radio-occultation data. The work investigates whether GPS occultation combined with ground-based GPS data improves the determination of peak height and peak density in the images. The results indicate that the occultation data improve both the peak height and the peak density in the images. The use of ionosonde data is also examined and the results are compared between the USA and Europe.     

Investigating the propagation mechanism of unmodelled systematic errors on coordinate time series estimated using least squares

The propagation of unmodelled systematic errors into coordinate time series computed using least squares is investigated, to improve the understanding of unexplained signals and apparent noise in geodetic (especially GPS) coordinate time series. Such coordinate time series are invariably based on a functional model linearised using only zero and first-order terms of a (Taylor) series expansion about the approximate coordinates of the unknown point. The effect of such truncation errors is investigated through the derivation of a generalised systematic error model for the simple case of range observations from a single known reference point to a point which is assumed to be at rest by the least squares model but is in fact in motion. The systematic error function for a one pseudo-satellite two-dimensional case, designed to be as simple but as analogous to GPS positioning as possible, is quantified. It is shown that the combination of a moving reference point and unmodelled periodic displacement at the unknown point of interest, due to ocean tide loading, for example, results in an output coordinate time series containing many periodic terms when only zero and first-order expansion terms are used in the linearisation of the functional model. The amplitude, phase and period of these terms is dependent on the input amplitude, the locations of the unknown point and reference point, and the period of the reference point's motion. The dominant output signals that arise due to truncation errors match those found in coordinate time series obtained from both simulated data and real three-dimensional GPS data.     

Estimation of ship velocities from MODIS and OCM

Detection of ships and their tracks in the atmosphere from satellites was earlier demonstrated by Porch, Noone, and Kaufman, among others. In this letter, we have gone one step further to estimate the ship speed and direction by locating them and their tracks from multisatellite imagery. Exhausts from the ships create streaks of clouds in the atmosphere that help identify the same ship from two satellites. Ship velocities are estimated from displacements of ships. We have used optical sensors data from Moderate Resolution Imaging Spectroradiometer (MODIS) and Ocean Color Monitor (OCM) to demonstrate this technique. Estimated velocities of ships are within the expected range. Application of this approach has general interest to the navy, coast guards, shipping corporations, commercial ship owners, and fishermen. More satellite observations can be used to continuously monitor the ship velocities.     

Combined Digital Photogrammetry and Time-of-Flight Laser Scanning for Monitoring Cliff Evolution

Although cliffs form approximately 75% of the world's coastline, the understanding of the processes through which they evolve remains limited because of a lack of quantitative data on the morphological changes they undergo. In this paper the combination of terrestrial time-of-flight laser scanning with high-resolution digital photogrammetry is examined to generate high-quality data-sets pertaining to the geomorphic processes governing cliff development. The study was undertaken on a section of hard rock cliffs in North Yorkshire, UK, which has been monitored over a 12-month period. High-density, laser-scanned point clouds have been used to produce an accurate representation of these complex surfaces, free from the optical variations that degrade photographic data. These data-sets have been combined with high-resolution photographic monitoring, resampled with the fixed accuracies of the terrestrial laser survey, to generate a new approach to recording the volumetric changes in complex coastal cliffs. This has led to significant improvements in the understanding of the activity patterns of coastal cliffs.     

The thermodynamic influence of subgrid orography in a global climate model

Assessments of the impacts of climate change typically require information at scales of 10 km or less. Such a resolution in global climate simulations is unlikely for at least two decades. We have developed an alternative to explicit resolution that provides a framework for meeting the needs of climate change impact assessment much sooner. We have applied to a global climate model a physically based subgrid-scale treatment of the influence of orography on temperature, clouds, precipitation, and land surface hydrology. The treatment represents subgrid variations in surface elevation in terms of fractional area distributions of discrete elevation classes. For each class it calculates the height rise/descent of air parcels traveling through the grid cell, and applies the influence of the rise/descent to the temperature and humidity profiles of the elevation class. Cloud, radiative, and surface processes are calculated separately for each elevation class using the same physical parametrizations used by the model without the subgrid orography parametrization. The simulated climate fields for each elevation class can then be distributed in post-processing according to the spatial distribution of surface elevation within each grid cell. Parallel 10-year simulations with and without the subgrid treatment have been performed. The simulated temperature, precipitation and snow water are mapped to 2.5-minute (~5 km) resolution and compared with gridded analyses of station measurements. The simulation with the subgrid scheme produces a much more realistic distribution of snow water and significantly more realistic distributions of temperature and precipitation than the simulation without the subgrid scheme. Moreover, the 250-km grid cell means of most other fields are virtually unchanged by the subgrid scheme. This suggests that the tuning of the climate model without the subgrid scheme is also applicable to the model with the scheme.