Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain

A representation of the conformal mapping g of the interior or exterior of the unit circle onto a simply-connected domain Ω as a boundary integral in terms ofƒ|∂Ω is obtained, whereƒ :=g -l. A product integration scheme for the approximation of the boundary integral is described and analysed. An ill-conditioning problem related to the domain geometry is discussed. Numerical examples confirm the conclusions of this discussion and support the analysis of the quadrature scheme.

Approximations to the scattering of water waves by steep topography

A new method is developed for approximating the scattering of linear surface gravity waves on water of varying quiescent depth in two dimensions. A conformal mapping of the fluid domain onto a uniform rectangular strip transforms steep and discontinuous bed profiles into relatively slowly varying, smooth functions in the transformed free-surface condition. By analogy with the mild-slope approach used extensively in unmapped domains, an approximate solution of the transformed problem is sought in the form of a modulated propagating wave which is determined by solving a second-order ordinary differential equation. This can be achieved numerically, but an analytic solution in the form of a rapidly convergent infinite series is also derived and provides simple explicit formulae for the scattered wave amplitudes. Small-amplitude and slow variations in the bedform that are excluded from the mapping procedure are incorporated in the approximation by a straightforward extension of the theory. The error incurred in using the method is established by means of a rigorous numerical investigation and it is found that remarkably accurate estimates of the scattered wave amplitudes are given for a wide range of bedforms and frequencies.

Why we need new spectacles: Mapping the experiential dimension in prehistoric Cretan landscapes

The Bronze to Iron Age transition in Crete, a period of state collapse and insecurity, saw the island's rugged, high-contrast topography used in striking new ways. The visual drama of many of the new site locations has stimulated significant research over the last hundred years, with explanation of the change as the main focus. The new sites are not monumental in character: the vast majority are settlements, and much of the information about them comes from survey. Perhaps as a result, the new site map has not been much studied from phenomenological perspectives. A focus on the visual and experiential aspects of the new landscape can offer valuable insights into social structures at this period, and illuminate social developments prefiguring the emergence of polis states in Crete by c. 700 BC. To develop, share and evaluate this type of integrated study, digital reconstructive techniques are still under-used in this region. I highlight their potential value in addressing a regularly-identified shortcoming of phenomenological approaches-their necessarily subjective emphasis.

Geochemical mapping of carbonate sediments in the Makgadikgadi basin, Botswana using moderate resolution remote sensing data

This paper maps the carbonate geochemistry of the Makgadikgadi Pans region of northern Botswana from moderate resolution (500 m pixels) remotely sensed data, to assess the impact of various geomorphological processes on surficial carbonate distribution. Previous palaeo-environmental studies have demonstrated that the pans have experienced several highstands during the Quaternary, forming calcretes around shoreline embayments. The pans are also a significant regional source of dust, and some workers have suggested that surficial carbonate distributions may be controlled, in part, by wind regime. Field studies of carbonate deposits in the region have also highlighted the importance of fluvial and groundwater processes in calcrete formation. However, due to the large area involved and problems of accessibility, the carbonate distribution across the entire Makgadikgadi basin remains poorly understood. The MODIS instrument permits mapping of carbonate distribution over large areas; comparison with estimates from Landsat Thematic Mapper data show reasonable agreement, and there is good agreement with estimates from laboratory analysis of field samples. The results suggest that palaeo-lake highstands, reconstructed here using the SRTM 3 arc-second digital elevation model, have left behind surficial carbonate deposits, which can be mapped by the MODIS instrument. Copyright (c) 2006 John Wiley & Sons, Ltd.

Mapping the spatial distribution of geomorphological processes in the Okstindan area of northern Norway, using Geomorphic Process Units as derived from remote sensing and ground survey

The delineation of Geomorphic Process Units (GPUs) aims to quantify past, current and future geomorphological processes and the sediment flux associated with them. Five GPUs have been identified for the Okstindan area of northern Norway and these were derived from the combination of Landsat satellite imagery (TM and ETM+) with stereo aerial photographs (used to construct a Digital Elevation Model) and ground survey. The Okstindan study area is sub-arctic and mountainous and is dominated by glacial and periglacial processes. The GPUs exclude the glacial system (some 37% of the study area) and hence they are focussed upon periglacial and colluvial processes. The identified GPUs are: 1. solifluction and rill erosion; 2. talus creep, slope wash and rill erosion; 3. accumulation of debris by rock and boulder fall; 4. rockwalls; and 5. stable ground with dissolved transport. The GPUs have been applied to a ‘test site’ within the study area in order to illustrate their potential for mapping the spatial distribution of geomorphological processes. The test site within the study area is a catchment which is representative of the range of geomorphological processes identified.

Predictive vegetation mapping in the Mediterranean context: Considerations and methodological issues

The need to map vegetation communities over large areas for nature conservation and to predict the impact of environmental change on vegetation distributions, has stimulated the development of techniques for predictive vegetation mapping. Predictive vegetation studies start with the development of a model relating vegetation units and mapped physical data, followed by the application of that model to a geographic database and over a wide range of spatial scales. This field is particularly important for identifying sites for rare and endangered species and locations of high biodiversity such as many areas of the Mediterranean Basin. The potential of the approach is illustrated with a mapping exercise in the alti-meditterranean zone of Lefka Ori in Crete. The study established the nature of the relationship between vegetation communities and physical data including altitude, slope and geomorphology. In this way the knowledge of community distribution was improved enabling a GIS-based model capable of predicting community distribution to be constructed. The paper describes the development of the spatial model and the methodological problems of predictive mapping for monitoring Mediterranean ecosystems. The paper concludes with a discussion of the role of predictive vegetation mapping and other spatial techniques, such as fuzzy mapping and geostatistics, for improving our understanding of the dynamics of Mediterranean ecosystems and for practical management in a region that is under increasing pressure from human impact.

Why we need new spectacles: Mapping the experiential dimension in prehistoric Cretan landscapes

The Bronze to Iron Age transition in Crete, a period of state collapse and insecurity, saw the island's rugged, high-contrast topography used in striking new ways. The visual drama of many of the new site locations has stimulated significant research over the last hundred years, with explanation of the change as the main focus. The new sites are not monumental in character: the vast majority are settlements, and much of the information about them comes from survey. Perhaps as a result, the new site map has not been much studied from phenomenological perspectives. A focus on the visual and experiential aspects of the new landscape can offer valuable insights into social structures at this period, and illuminate social developments prefiguring the emergence of polis states in Crete by c. 700 BC. To develop, share and evaluate this type of integrated study, digital reconstructive techniques are still under-used in this region. I highlight their potential value in addressing a regularly-identified shortcoming of phenomenological approaches-their necessarily subjective emphasis.

Geochemical mapping of carbonate sediments in the Makgadikgadi basin, Botswana using moderate resolution remote sensing data

This paper maps the carbonate geochemistry of the Makgadikgadi Pans region of northern Botswana from moderate resolution (500 m pixels) remotely sensed data, to assess the impact of various geomorphological processes on surficial carbonate distribution. Previous palaeo-environmental studies have demonstrated that the pans have experienced several highstands during the Quaternary, forming calcretes around shoreline embayments. The pans are also a significant regional source of dust, and some workers have suggested that surficial carbonate distributions may be controlled, in part, by wind regime. Field studies of carbonate deposits in the region have also highlighted the importance of fluvial and groundwater processes in calcrete formation. However, due to the large area involved and problems of accessibility, the carbonate distribution across the entire Makgadikgadi basin remains poorly understood. The MODIS instrument permits mapping of carbonate distribution over large areas; comparison with estimates from Landsat Thematic Mapper data show reasonable agreement, and there is good agreement with estimates from laboratory analysis of field samples. The results suggest that palaeo-lake highstands, reconstructed here using the SRTM 3 arc-second digital elevation model, have left behind surficial carbonate deposits, which can be mapped by the MODIS instrument. Copyright (c) 2006 John Wiley & Sons, Ltd.

Use of a portable topographic mapping millimetre wave radar at an active lava flow

A ground-based millimetre wave radar, AVTIS (All-weather Volcano Topography Imaging Sensor), has been developed for topographic monitoring. The instrument is portable and capable of measurements over ranges up to similar to 7 km through cloud and at night. In April and May 2005, AVTIS was deployed at Arenal Volcano, Costa Rica, in order to determine topographic changes associated with the advance of a lava flow. This is the first reported application of mm-wave radar technology to the measurement of lava flux rates. Three topographic data sets of the flow were acquired from observation distances of similar to 3 km over an eight day period, during which the flow front was detected to have advanced similar to 200 m. Topographic differences between the data sets indicated a flow thickness of similar to 10 m, and a dense rock equivalent lava flux of similar to 0.20 +/- 0.08 m(3) s(-1).

LiDAR mapping of tidal marshes for ecogeomorphological modelling in the TIDE project

The European research project TIDE (Tidal Inlets Dynamics and Environment) is developing and validating coupled models describing the morphological, biological and ecological evolution of tidal environments. The interactions between the physical and biological processes occurring in these regions requires that the system be studied as a whole rather than as separate parts. Extensive use of remote sensing including LiDAR is being made to provide validation data for the modelling. This paper describes the different uses of LiDAR within the project and their relevance to the TIDE science objectives. LiDAR data have been acquired from three different environments, the Venice Lagoon in Italy, Morecambe Bay in England, and the Eden estuary in Scotland. LiDAR accuracy at each site has been evaluated using ground reference data acquired with differential GPS. A semi-automatic technique has been developed to extract tidal channel networks from LiDAR data either used alone or fused with aerial photography. While the resulting networks may require some correction, the procedure does allow network extraction over large areas using objective criteria and reduces fieldwork requirements. The networks extracted may subsequently be used in geomorphological analyses, for example to describe the drainage patterns induced by networks and to examine the rate of change of networks. Estimation of the heights of the low and sparse vegetation on marshes is being investigated by analysis of the statistical distribution of the measured LiDAR heights. Species having different mean heights may be separated using the first-order moments of the height distribution.