Determining the effect of asymmetric data on the variogram. I. Underlying asymmetry

Matheron's usual variogram estimator can result in unreliable variograms when data are strongly asymmetric or skewed. Asymmetry in a distribution can arise from a long tail of values in the underlying process or from outliers that belong to another population that contaminate the primary process. This paper examines the effects of underlying asymmetry on the variogram and on the accuracy of prediction, and the second one examines the effects arising from outliers. Standard geostatistical texts suggest ways of dealing with underlying asymmetry; however, this is based on informed intuition rather than detailed investigation. To determine whether the methods generally used to deal with underlying asymmetry are appropriate, the effects of different coefficients of skewness on the shape of the experimental variogram and on the model parameters were investigated. Simulated annealing was used to create normally distributed random fields of different size from variograms with different nugget:sill ratios. These data were then modified to give different degrees of asymmetry and the experimental variogram was computed in each case. The effects of standard data transformations on the form of the variogram were also investigated. Cross-validation was used to assess quantitatively the performance of the different variogram models for kriging. The results showed that the shape of the variogram was affected by the degree of asymmetry, and that the effect increased as the size of data set decreased. Transformations of the data were more effective in reducing the skewness coefficient in the larger sets of data. Cross-validation confirmed that variogram models from transformed data were more suitable for kriging than were those from the raw asymmetric data. The results of this study have implications for the 'standard best practice' in dealing with asymmetry in data for geostatistical analyses. (C) 2007 Elsevier Ltd. All rights reserved.

Smoothed histogram modification for image processing

The technique of constructing a transformation, or regrading, of a discrete data set such that the histogram of the transformed data matches a given reference histogram is commonly known as histogram modification. The technique is widely used for image enhancement and normalization. A method which has been previously derived for producing such a regrading is shown to be “best” in the sense that it minimizes the error between the cumulative histogram of the transformed data and that of the given reference function, over all single-valued, monotone, discrete transformations of the data. Techniques for smoothed regrading, which provide a means of balancing the error in matching a given reference histogram against the information lost with respect to a linear transformation are also examined. The smoothed regradings are shown to optimize certain cost functionals. Numerical algorithms for generating the smoothed regradings, which are simple and efficient to implement, are described, and practical applications to the processing of LANDSAT image data are discussed.

Ocean data dissemination: new challenges for data integration

In the decade since OceanObs `99, great advances have been made in the field of ocean data dissemination. The use of Internet technologies has transformed the landscape: users can now find, evaluate and access data rapidly and securely using only a web browser. This paper describes the current state of the art in dissemination methods for ocean data, focussing particularly on ocean observations from in situ and remote sensing platforms. We discuss current efforts being made to improve the consistency of delivered data and to increase the potential for automated integration of diverse datasets. An important recent development is the adoption of open standards from the Geographic Information Systems community; we discuss the current impact of these new technologies and their future potential. We conclude that new approaches will indeed be necessary to exchange data more effectively and forge links between communities, but these approaches must be evaluated critically through practical tests, and existing ocean data exchange technologies must be used to their best advantage. Investment in key technology components, cross-community pilot projects and the enhancement of end-user software tools will be required in order to assess and demonstrate the value of any new technology.

Particle swarm optimization aided orthogonal forward regression for unified data modeling

We propose a unified data modeling approach that is equally applicable to supervised regression and classification applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassification rate is adopted in two-class classification applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the efficient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting fixed-node RBF models. Another significant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classification, as well as density estimation applications.

Correlations of control variables in variational data assimilation

Variational data assimilation systems for numerical weather prediction rely on a transformation of model variables to a set of control variables that are assumed to be uncorrelated. Most implementations of this transformation are based on the assumption that the balanced part of the flow can be represented by the vorticity. However, this assumption is likely to break down in dynamical regimes characterized by low Burger number. It has recently been proposed that a variable transformation based on potential vorticity should lead to control variables that are uncorrelated over a wider range of regimes. In this paper we test the assumption that a transform based on vorticity and one based on potential vorticity produce an uncorrelated set of control variables. Using a shallow-water model we calculate the correlations between the transformed variables in the different methods. We show that the control variables resulting from a vorticity-based transformation may retain large correlations in some dynamical regimes, whereas a potential vorticity based transformation successfully produces a set of uncorrelated control variables. Calculations of spatial correlations show that the benefit of the potential vorticity transformation is linked to its ability to capture more accurately the balanced component of the flow.

Smooth Regrading of Discretized Data

Methods for producing nonuniform transformations, or regradings, of discrete data are discussed. The transformations are useful in image processing, principally for enhancement and normalization of scenes. Regradings which “equidistribute” the histogram of the data, that is, which transform it into a constant function, are determined. Techniques for smoothing the regrading, dependent upon a continuously variable parameter, are presented. Generalized methods for constructing regradings such that the histogram of the data is transformed into any prescribed function are also discussed. Numerical algorithms for implementing the procedures and applications to specific examples are described.