Multivariate interpolation

Abstract: Cubic convolution interpolation is a new technique for resampling discrete data. It has a number of desirable features which make it useful for image processing. The technique can be performed efficiently on a digital computer. The cubic convolution interpolation function converges uniformly to the function being interpolated as the sampling increment approaches zero. With the appropriate boundary conditions and constraints on the interpolation kernel, it can be shown that the order of accuracy of the cubic convolution method is between that of linear interpolation and that of cubic splines. A one-dimensional interpolation function is derived in this paper. A separable extension of this algorithm to two dimensions is applied to image data.

Abstract: This monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions.

Abstract: Geographical information systems Data structures for thematic maps Digital elevation models Data input, verification, storage, and output Methods of data analysis and spatial modelling Data quality, errors, and natural variation: sources of error Errors arising through processing The nature of boundaries Classification methods Methods of spatial interpolation Choosing a geographical information system Appendices Index.

Abstract: We present a European land-only daily high-resolution gridded data set for precipitation and minimum, maximum, and mean surface temperature for the period 1950-2006. This data set improves on previous products in its spatial resolution and extent, time period, number of contributing stations, and attention to finding the most appropriate method for spatial interpolation of daily climate observations. The gridded data are delivered on four spatial resolutions to match the grids used in previous products as well as many of the rotated pole Regional Climate Models (RCMs) currently in use. Each data set has been designed to provide the best estimate of grid box averages rather than point values to enable direct comparison with RCMs. We employ a three-step process of interpolation, by first interpolating the monthly precipitation totals and monthly mean temperature using three-dimensional thin-plate splines, then interpolating the daily anomalies using indicator and universal kriging for precipitation and kriging with an external drift for temperature, then combining the monthly and daily estimates. Interpolation uncertainty is quantified by the provision of daily standard errors for every grid square. The daily uncertainty averaged across the entire region is shown to be largely dependent on the season and number of contributing observations. We examine the effect that interpolation has on the magnitude of the extremes in the observations by calculating areal reduction factors for daily maximum temperature and precipitation events with return periods up to 10 years. Copyright 2008 by the American Geophysical Union.