Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

Voronoi diagrams—a survey of a fundamental geometric data structure

The authors describe the construction of a 0.58 lat‐long gridded dataset of monthly terrestrial surface climate for the period of 1901‐96. The dataset comprises a suite of seven climate elements: precipitation, mean temperature, diurnal temperature range, wet-day frequency, vapor pressure, cloud cover, and ground frost frequency. The spatial coverage extends over all land areas, including oceanic islands but excluding Antarctica. Fields of monthly climate anomalies, relative to the 1961‐90 mean, were interpolated from surface climate data. The anomaly grids were then combined with a 1961‐90 mean monthly climatology (described in Part I) to arrive at grids of monthly climate over the 96-yr period. The primary variables—precipitation, mean temperature, and diurnal temperature range—were interpolated directly from station observations. The resulting time series are compared with other coarser-resolution datasets of similar temporal extent. The remaining climatic elements, termed secondary variables,were interpolated from merged datasets comprising station observations and, in regions where there were no station data, synthetic data estimated using predictive relationships with the primary variables. These predictive relationships are described and evaluated. It is argued that this new dataset represents an advance over other products because (i) it has higher spatial resolution than other datasets of similar temporal extent, (ii) it has longer temporal coverage than other products of similar spatial resolution, (iii) it encompasses a more extensive suite of surface climate variables than available elsewhere, and (iv) the construction method ensures that strict temporal fidelity is maintained. The dataset should be of particular relevance to a number of applications in applied climatology, including large-scale biogeochemical and hydrological modeling, climate change scenario construction, evaluation of regional climate models, and comparison with satellite products. The dataset is available from the Climatic Research Unit and is currently being updated to 1998.

https://journals.ametsoc.org/doi/pdf/10.1175/1520-0442%282000%29013%3C2217%3ARTCSTC%3E2.0.CO%3B2

Representing Twentieth-Century Space-Time Climate Variability. Part II: Development of 1901-96 Monthly Grids of Terrestrial Surface Climate

The construction of a 0.5° lat × 0.5° long surface climatology of global land areas, excluding Antarctica, is described. The climatology represents the period 1961–90 and comprises a suite of nine variables: precipitation, wet-day frequency, mean temperature, diurnal temperature range, vapor pressure, sunshine, cloud cover, ground frost frequency, and wind speed. The climate surfaces have been constructed from a new dataset of station 1961–90 climatological normals, numbering between 19 800 (precipitation) and 3615 (wind speed). The station data were interpolated as a function of latitude, longitude, and elevation using thin-plate splines. The accuracy of the interpolations are assessed using cross validation and by comparison with other climatologies. This new climatology represents an advance over earlier published global terrestrial climatologies in that it is strictly constrained to the period 1961–90, describes an extended suite of surface climate variables, explicitly incorporates elevation...

/pdf/representing-twentieth-century-space-time-climate-2qzlmvmmet.pdf

Representing Twentieth-Century Space–Time Climate Variability. Part I: Development of a 1961–90 Mean Monthly Terrestrial Climatology

A framework is provided for scaling and scale issues in hydrology. The first section gives some basic definitions. This is important as researchers do not seem to have agreed on the meaning of concepts such as scale or upscaling. ‘Process scale’, ‘observation scale’ and ‘modelling (working) scale’ require different definitions. The second section discusses heterogeneity and variability in catchments and touches on the implications of randomness and organization for scaling. The third section addresses the linkages across scales from a modelling point of view. It is argued that upscaling typically consists of two steps: distributing and aggregating. Conversely, downscaling involves disaggregation and singling out. Different approaches are discussed for linking state variables, parameters, inputs and conceptualizations across scales. This section also deals with distributed parameter models, which are one way of linking conceptualizations across scales. The fourth section addresses the linkages across scales from a more holistic perspective dealing with dimensional analysis and similarity concepts. The main difference to the modelling point of view is that dimensional analysis and similarity concepts deal with complex processes in a much simpler fashion. Examples of dimensional analysis, similarity analysis and functional normalization in catchment hydrology are given. This section also briefly discusses fractals, which are a popular tool for quantifying variability across scales. The fifth section focuses on one particular aspect of this holistic view, discussing stream network analysis. The paper concludes with identifying key issues and gives some directions for future research.

/pdf/scale-issues-in-hydrological-modelling-a-review-1x61lpwqjr.pdf

Scale issues in hydrological modelling: A review

This paper provides a unified discussion of the Delaunay triangulation. Its geometric properties are reviewed and several applications are discussed. Two algorithms are presented for constructing the triangulation over a planar set ofN points. The first algorithm uses a divide-and-conquer approach. It runs inO(N logN) time, which is asymptotically optimal. The second algorithm is iterative and requiresO(N
2) time in the worst case. However, its average case performance is comparable to that of the first algorithm.

Alfred H. Thiessen

Papers

Precipitation averages for large areas

DISTRICT No. 10, GREAT BASIN

Using weather data in engineering problems