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.     

Comparison of ERS-SAR and spot data for sugar beet crop cover assessment

The present work was aimed to compare the abilities of radar and optical satellite data to estimate crop canopy cover, which is a key component of productivity estimates. Three ERS-1 SAR images were obtained of East Anglia (UK) in 1995 and one ERS-2 SAR image in 1996. The images covered a study area around the IACR Brooms Barn Sugar Beet Research Institute. Field data comprising radiometric and biophysical measurements of the crop canopy were collected in two fields from June 22 to August 3, 1995 to coincide with ERS-1 SAR overpass dates. In 1996, field data were collected in two fields from June 11 to July 29 on a weekly basis. A previously calibrated version of the water cloud model was inverted to estimate Leaf Area Index (LAI) from ERS-1 and ERS-2 SAR backscatter and soil moisture samples. Canopy cover was estimated from the radar-estimated LAI using a standard exponential relationship that has a well-established coefficient for sugar beet. Radio-metrically and atmospherically corrected data from three SPOT images in 1995 and one SPOT image in 1996 were used to calculate the Optimised Soil Adjusted Vegetation Index (OSAVI), from which crop canopy cover was estimated using a relationship determined previously by canopy modelling. The crop cover values estimated by satellite were in good agreement with those measured on ground with the Parkinson radiometer. Radar data may be able to provide useful estimates of canopy cover for crop production modelling, especially in the case of loss of optical data due to cloud.     

An algorithm for determination of aerosol opticalthickness from AVHRR imagery over oceans

Summary The uncertainty in aerosol size distributions is a main source of errors in aerosol optical thickness determined from satellite measurements. To reduce the errors resulting from the uncertainty in aerosol size distributions, we have performed sensitivity analyses. It is found the errors resulting from the uncertainty in aerosol size distribution can be considerably reduced by using the Junge power law to approximate the aerosol size distribution in an actual atmosphere, if the exponent value is determined at the same time. An iterative algorithm is then developed for the simultaneous determination of aerosol optical thickness and the exponent of the Junge power law over ocean areas from the upwelling radiances measured in AVHRR visible and near infrared channels. A number of numerical experiments are carried out to investigate the validity of the Junge power law approximation by assuming the aerosol size distributions in an actual atmosphere are bimodal with different mode parameters, and by using the actual aerosol size distributions determined at several places by Kaufman et al. (1994). The results show that the errors in determined aerosol optical thickness resulting from the Junge power law approach are significantly reduced. The iterative algorithm is investigated further by comparing the aerosol optical thickness deduced from satellite measurement with that observed by a sun photometer. Received October 10, 2001 Revised December 28, 2001