Tessellations in GIS: Part II–making changes

Abstract

We attempt to describe the role of tessellated models of space within the discipline of Geographic Information Systems (GIS) – a speciality coming largely out of Geography and Land Surveying, where there was a strong need to represent information about the land’s surface within a computer system rather than on the original paper maps. We look at some of the basic operations in GIS, including dynamic and kinetic applications. We examine issues of topology and data structures, and produced a tessellation model that may be widely applied both to traditional “object” and “field” data types. The Part I of this study examined object and field spatial models, the Voronoi extension of objects, and the graphs that express the resulting adjacencies. The required data structures were also briefly described, along with 2D and 3D structures and hierarchical indexing. The importance of graph duality was emphasized. Here, this second paper builds on the structures described in the first, and examines how these may be modified: change may often be associated with either viewpoint or time. Incremental algorithms permit additional point insertion, and applications involving the addition of skeleton points, for map scanning, contour enrichment or watershed delineation and simulation. Dynamic algorithms permit skeleton smoothing, and higher order Voronoi diagram applications, including Sibson interpolation. Kinetic algorithms allow collision detection applications, free-Lagrange flow modeling, and pen movement simulation for map drawing. If desired these methods may be extended to 3D. Based on this framework, it can be argued that tessellation models are fundamental to our understanding and processing of geographical space, and provide a coherent framework for understanding the “space” in which we exist.     

Airborne vector gravimetry using precise,position-aided inertial measurement units

Vector gravimetry using a precise inertial navigation system continually updated with external position data, for example using GPS, is studied with respect to two problems. The first concerns the attitude accuracy requirement for horizontal gravity component estimation. With covariance analyses in the space and frequency domains it is argued that with relatively stable uncompensated gyro drift, the short-wavelength gravity vector can be estimated without the aid of external attitude updates. The second problem concerns the state-space estimation of the gravity signal where considerable approximations must be assumed in the gravity model in order to take advantage of the ensemble error estimation afforded by the Kalman filter technique. Gauss-Markov models for the gravity field are specially designed to reflect the attenuation of the signal at a specific altitude and the omission of the long-wavelength components from the estimation. With medium accuracy INS/GPS systems, the horizontal components of gravity with wavelengths shorter than 250 km should be estimable to an accuracy of 4–6 mgal (µg); while high accuracy systems should yield an improvement to 1–2 mgal.     

Non-stationary Approaches for Mapping Terrain and Assessing Prediction Uncertainty

It is well known that terrain may vary markedly over small areas and that statistics used to characterise spatial variation in terrain may be valid only over small areas. In geostatistical terminology, a non-stationary approach may be considered more appropriate than a stationary approach. In many applications, local variation is not accounted for sufficiently. This paper assesses potential benefits in using non-stationary geostatistical approaches for interpolation and for the assessment of uncertainty in predictions with implications for sampling design. Two main non-stationary approaches are employed in this paper dealing with (1) change in the mean and (2) change in the variogram across the region of interest. The relevant approaches are (1) kriging with a trend model (KT) using the variogram of residuals from local drift and (2) locally-adaptive variogram KT, both applied to a sampled photogrammetrically derived digital terrain model (DTM). The fractal dimension estimated locally from the double-log variogram is also mapped to illustrate how spatial variation changes across the data set. It is demonstrated that estimation of the variogram of residuals from local drift is worthwhile in this case for the characterisation of spatial variation. In addition, KT is shown to be useful for the assessment of uncertainty in predictions. This is shown to be true even when the sample grid is dense as is usually the case for remotely-sensed data. In addition, both ordinary kriging (OK) and KT are shown to provide more accurate predictions than inverse distance weighted (IDW) interpolation, used for comparative purposes.     

Can Plant Competition and Diversity Reduce the Growth and Survival of Exotic <Emphasis Type="Italic">Phragmites australis</Emphasis> Invading a Tidal Marsh?

The rapid proliferation of Phragmites australis in North America has challenged resource managers to curb its expansion and reduce the loss of functional tidal marsh. We investigated whether native plant competition could reduce the ability of Phragmites to invade a tidal marsh, and if plant diversity (species richness, evenness, and composition) altered the competitive outcome. Immature Phragmites shoots and four native halophytes were transplanted to small but dense field plots (~1,200 shoots m⁻²) comprising three community structure types (Phragmites alone, Phragmites + 1 native species, and Phragmites + 4 native species). Interspecific competition significantly reduced Phragmites aboveground biomass, shoot length production, density, and survival by approximately 60%. Additionally, plots planted with greater native diversity contained Phragmites with the lowest growth and survival, potentially indicating diversity-enhanced resource competition. Competition consistently reduced the growth of Phragmites even under favorable conditions: lack of strong tidal flooding stresses as well as elevated nutrient pools.     

Analysis of sustained long-period activity at Etna Volcano, Italy

Following the installation of a broadband network on Mt. Etna, sustained Long-Period (LP) activity was recorded accompanying a period of total quiescence and the subsequent onset of the 2004–2005 effusive episode. From about 56000 events detected by an automatic classification procedure, we analyse a subset of about 3000 signals spanning the December 17th, 2003–September 25th, 2004, time interval. LP spectra are characterised by several, unevenly-spaced narrow peaks spanning the 0.5–10 Hz frequency band. These peaks are common to all the recording sites of the network, and different from those associated with tremor signals. Throughout the analysed time interval, LP spectra and waveforms maintain significant similarity, thus indicating the involvement of a non-destructive source process that we interpret in terms of the resonance of a fluid-filled buried cavity. Polarisation analysis indicates radiation from a non-isotropic source involving large amounts of shear. Concurrently with LP signals, recordings from the summit station also depict Very-Long-Period (VLP) pulses whose rectilinear motion points to a region located beneath the summit craters at depths ranging between 800 and 1100 m beneath the surface. Based on a refined repicking of similar waveforms, we obtain robust locations for a selected subset of the most energetic LP events from probabilistic inversion of travel-times calculated for a 3D heterogenous structure. LP sources cluster in a narrow volume located beneath the summit craters, and extending to a maximum depth of ≈ 800 m beneath the surface. No causal relationships are observed between LP, VLP and tremor activities and the onset of the 2004–2005 lava effusions, thus indicating that magmatic overpressure played a limited role in triggering this eruption. These data represent the very first observation of LP and VLP activity at Etna during non-eruptive periods, and open the way to the quantitative modelling of the geometry and dynamics of the shallow plumbing system.     

Key Design Elements of Building Pressure Cycling for Evaluating Vapor Intrusion—A Literature Review

Building pressure cycling (BPC) is becoming an increasingly important tool for studying vapor intrusion. BPC has been used to distinguish subslab and indoor sources of vapor intrusion as well as to define reasonable worst case volatile organic compound mass discharge into a structure. Analyses have been performed both semi-quantitatively with concentration trends and quantitatively with more rigorous flux calculation and source attribution methods. This paper reviews and compares the protocols and outcomes from multiple published applications of this technology to define the key variables that control performance. Common lessons learned are identified, including those that help define the range of building size and type to which BPC is applicable. Differences in test protocols are discussed, recognizing that the complexity of the test protocol required depends on the particular objectives of each project. Research gaps are identified and tabulated for future validation studies and applications.     

High resolution imaging of the Hubble Deep and Flanking Fields

42 hours of A-array VLA data and 18 days MERLIN data at 1.4 GHz have been combined to image a 10 arcminute field centred on the Hubble Deep Field (HDF). This area encloses both the Hubble Deep and Flanking Fields. A complete sample of 87 sources have been detected with flux densities above 40 μJy. All these have been imaged with the MERLIN+VLA combination to produce images with 0.2, 0.3 and 0.5 arcsecond resolution. These are the most sensitive 1.4 GHz images yet made with rms noise levels of 3.3 μJy/beam in the 0.2 arcsecond images. About 70% of the microJy sources are found to be starburst type systems associated with major disk galaxies in the redshift range 0.4–1. Some 20% are found to be low-luminosity AGN systems identified with field ellipticals at redshifts close to 1. The remaining 10% are associated with optically faint systems close to or beyond the HDF limit; many of these may be dust-shrouded starbursts at high redshift. We propose to extend this study to include VLBI data of comparable sensitivity to investigate the compact radio structures found in the microJy source population.