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.     

A Ka-band backscatter model function and an algorithm for measurement of the wind vector over the sea surface

A Ka-band backscatter model and an algorithm for measurement of the wind speed and direction over the sea surface by a frequency-modulated continous-wave radar demonstrator system operated in scatterometer mode have been developed. To evaluate the proposed algorithm, a simulation of the wind vector retrieval has been performed.     

Characterization and quantification of data voids in the shuttle Radar topography mission data

The goal of this study was to characterize and quantify the occurrence of data voids in data from the Shuttle Radar Topography Mission (SRTM) for the conterminous United States. For this purpose, SRTM data and corresponding data from the national elevation data were downloaded in 21 samples spatially organized to cover the main topography of the U.S. Void locations in SRTM data were compared to terrain attributes and subsequently the area of individual data voids to the same attributes. It was found that data voids amounted to 0.3% of the total dataset. Data voids were found in all topographic settings but more often in slopes steeper than approximately 20/spl deg/ that face south (170/spl deg/), and also in flat areas such as lakes and rivers. It was also found that more than 50% of all data voids were composed of connected pixels in groups less than six pixels. The largest data voids could be attributed to water bodies, while the rest could be explained by terrain-radar interaction characteristics.     

Eddies and planetary waves in the Central Arabian Sea

Eddies and planetary waves are identified as one of the important factors that control the dynamics of the Arabian Sea. During 10–14 January 1990, Ignat, Paulyuchenkov (USSR ship) conducted an experiment in the central Arabian Sea and of late TOPEX/POSEIDON satellites collected data on sea surface height (SSH) anomalies of the Arabian Sea. These data sets give an opportunity to understand the characteristic of eddies and planetary waves in this region during winter. The geostrophic flow revealed three anticyclonic and two cyclonic eddies of diameters ranging from 75 to more than 150 km from surface to subsurface levels. Current speeds around different eddies were maximum at surface and varied from 9 cm/s to 25 cm/s (at the middle point between the center and periphery). The occurrence of eddies were further investigated with the TOPEX/POSEIDON altimetry for the years 1993–97. The analysis revealed multiple eddies of diameter 100 to 550 km occur every year with maximum number of eddies during 1997 and minimum during 1995. The calculated speed varied between 8–30 cm/s around various eddies. Longitude-Time plots showed annual Rossby waves generating at the eastern Arabian Sea and propagating westwards with a phase speed of ~ 10 cm/s along 16° N. Further, it was observed that these waves arrived in the study area by January. In addition, another positive anomaly of SSH was found generating at the western Arabian Sea simultaneously and extended up to the study region by April–June. Time series of SSH at selected locations along 16°N revealed many small-scale oscillations and their spatial variability. These oscillations were delineated using the FFT analysis. Other than the Rossby wave, the major components at the study region were 40–60 and 26–32 day oscillations. The implications of these long period waves associated with eddies are discussed.     

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.     

Observations Of Nocturnal Drainage Flow In A Shallow Gully

The formation of cold air drainage flows in a shallow gully is studied during CASES-99 (Cooperative Atmosphere-Surface Exchange Study). Fast and slow response wind and temperature measurements were obtained on an instrumented 10-m tower located in the gully and from a network of thermistors and two-dimensional sonic anemometers, situated across the gully. Gully flow formed on clear nights even with significant synoptic flow. Large variations in surface temperature developed within an hour after sunset and in situ cooling was the dominant factor in wind sheltered locations. The depth of the drainage flow and the height of the down-gully wind speed maximum were found to be largest when the external wind speed above the gully flow is less than 2 m s^-1. The shallow drainage current is restricted to a depth of a few metres, and is deepest when the stratification is stronger and the external flow is weaker. During the night the drainage flow breaks down, sometimes on several occasions, due to intermittent turbulence and downward fluxes of heat and momentum. The near surface temperature may increase by 6 ° C in less than 30 min due to the vertical convergence of downward heat flux. The mixing events are related to acceleration of the flow above the gully flow and decreased Richardson number. These warming events also lead to warming of the near surface soil and reduction of the upward soil heat flux. To examine the relative importance of different physical mechanisms that could contribute to the rapid warming, and to characterize the turbulence generated during the intermittent turbulent periods, the sensible heat budget is analyzed and the behaviour of different turbulent parameters is discussed.     

Near-Wall Flow Development After A Step Change In Surface Roughness

An experimental study of the initial flow field downstream of a step change in surface roughness is presented. The roughness length of the downstream surface was approximately tenfold that of the upstream roughness and, unlike all previous studies, attention was concentrated on the roughness sublayer region beneath the inertial (log-law) region. The experiments were conducted at a boundary layer Reynolds number of about 6 × 10⁴ (based on layer thickness andfree-stream velocity) and around a longitudinal location where the (downstream) roughness length, z_o2, was about 1% of the boundary-layer thickness atthe roughness change point.The thickness of the roughness sublayer was found for the two roughness. It was observed that the vertical profiles of mean velocity and turbulence characteristics started to show similarity after about 160z₀₂ downstream of the roughness change. The presence of a shear stress overshoot is shown to depend strongly on the precise location (with respect to the roughness elements) at which the measurements are made and the thickness of the equilibrium layer is shown to be very sensitive to the way it is defined. It is demonstrated that the growing equilibrium layer has first to encompass the roughness sublayer before any thickness of inertial sublayer can be developed. It follows that, in somepractical cases, like flows across some urban environments, the latter(log-law) region may never exist at all.