多标度数据轮廓相似性的度量公理与计算

为了完善轮廓相似性度量的概念和计算,拓展轮廓相似度计算公式的应用,讨论了样本几何轮廓的序结构和表示定理,修正了轮廓相似性的度量公理与计算公式.在样本几何轮廓和"轮廓优"序的定义下,证明了"轮廓优"序的"严格弱序"结构,证明了在轮廓相似性分析问题中表示定理成立,奠定了约定"轮廓相似性度量公理"的逻辑基础,进而定义了样本几何轮廓的"相似度"序,证明了"相似度"序的"严格偏序"结构,并修正了轮廓相似度计算公式.使轮廓相似分析的概念与相似度计算公式能适应不同背景下的多标度数据分析的要求.

Evaluating the Algorithm for Correction of the Bright Band Effects in QPEs with S-, C-and X-Band Dual-Polarized Radars

The bright band, a layer of enhanced radar reflectivity associated with melting ice particles, is a major source of signifi- cant overestimation in quantitative precipitation estimation （QPE） based on the Z-R （reflectivity factor-rain rate） relationship. The effects of the bright band on radar-based QPE can be eliminated by vertical profile of reflectivity （VPR） correction. In this study, we applied bright-band correction algorithms to evaluate three different bands （S-, C- and X-band） of dual-polarized radars and to reduce overestimation errors in Z-R relationship-based QPEs. After the reflectivity was corrected by the algo- rithms using average VPR （AVPR） alone and a combination of average VPR and the vertical profile of the copolar correlation coefficient （AVPR＋CC）, the QPEs were derived. The bright-band correction and resulting QPEs were evaluated in eight precipitation events by comparing to the uncorrected reflectivity and rain-gange observations, separately. The overestimation of Z-R relationship-based QPEs associated with the bright band was reduced after correction by the two schemes for which hourly rainfall was less than 5 mm. For the verification metrics of RMSE （root-mean-square error）, RMAE （relative mean absolute error） and RMB （relative mean bias） of QPEs, averaged over all eight cases, the AVPR method improved from 2.28, 0.94 and 0.78 to 1.55, 0.60 and 0.40, respectively, while the AVPR＋CC method improved to 1.44, 0.55 and 0.30, respectively. The QPEs after AVPR＋CC correction had less overestimation than those after AVPR correction, and similar conclusions were drawn for all three different bands of dual-polarized radars.

The Four Intersection-and-Difference Model for Line-Line Topological Relations

The description of line-line topological relations is still an unsolved issue although much effort has been done. The problem is involved in many practical applications such as spatial query, spatial analysis and cartographic generalization. To develop a sound and effective approach to describe line-line relations, it is first necessary to define the topology of an individual line, i.e., local topology. The concept of connective degree is used for the identification of topological differences in the geometric structure of a line. The general topological definition of a line is given, i.e., endpoints set and interior point set. This definition can be applied to the embedded spaces of different dimensions, whether co-dimension is equal to or larger than zero. On this basis, a generic model called the 4 intersection-and-difference is set up for the description of basic line-line topological relations, upon which a conceptual neighborhood graph is built with consideration of topological distance, it is concluded that the proposed model can represent the property of topological changes, and basic relations between line segments in IR^1 and IR^2.

Which Friction Factor Model Is the Best？ A Comparative Analysis of Model Selection Criteria

The ongoing research for model choice and selection has generated a plethora of approaches. With such a wealth of methods, it can be difficult for a researcher to know what model selection approach is the proper way to proceed to select the appropriate model for prediction. The authors present an evaluation of various model selection criteria from decision-theoretic perspective using experimental data to define and recommend a criterion to select the best model. In this analysis, six of the most common selection criteria, nineteen friction factor correlations, and eight sets of experimental data are employed. The results show that while the use of the traditional correlation coefficient, R2 is inappropriate, root mean square error, RMSE can be used to rank models, but does not give much insight on their accuracy. Other criteria such as correlation ratio, mean absolute error, and standard deviation are also evaluated. The AIC （Akaike Information Criterion） has shown its superiority to other selection criteria. The authors propose AIC as an alternative to use when fitting experimental data or evaluating existing correlations. Indeed, the AIC method is an information theory based, theoretically sound and stable. The paper presents a detailed discussion of the model selection criteria, their pros and cons, and how they can be utilized to allow proper comparison of different models for the best model to be inferred based on sound mathematical theory. In conclusion, model selection is an interesting problem and an innovative strategy to help alleviate similar challenges faced by the professionals in the oil and gas industry is introduced.

Validation results of NmF2 and hmF2 derived from ionospheric density profiles of GNOS on FY-3C satellite

The first Global Navigation Satellite System Occultation Sounder(GNOS) which is compatible of both Bei Dou System(BDS)and Global Positioning System(GPS) was successfully launched into orbit onboard the Feng Yun 3 C satellite(FY-3 C) on September 23, 2013, and it has already gathered a large amount of ionosphere radio occultation(RO) data so far. However, the detailed analysis and validation of GPS ionosphere RO data have not been done up to now. Therefore, this paper discusses the configuration of the FY-3 C GNOS, the methods and results of GPS ionosphere occultation processment, the quality analysis of the GPS ionosphere RO products, and the precision consistency between the GNOS GPS ionosphere RO product and ionosonde data. The peak electron density(Nm F2) correlation coefficient is 0.97, the corresponding standard deviation is 16.08%. The peak value altitude(hm F2) correlation coefficient is 0.89, and the corresponding standard deviation is 23.79 km. The in-orbit operation of GNOS provides a basis data set for the monitoring, forecasting and research of ionosphere's space weather.

An intuitive general rank-based correlation coefficient

Correlation analysis is an effective mechanism for studying patterns in data and making predictions.Many interesting discoveries have been made by formulating correlations in seemingly unrelated data. We propose an algorithm to quantify the theory of correlations and to give an intuitive, more accurate correlation coefficient.We propose a predictive metric to calculate correlations between paired values, known as the general rank-based correlation coefficient. It fulfills the five basic criteria of a predictive metric： independence from sample size,value between-1 and 1, measuring the degree of monotonicity, insensitivity to outliers, and intuitive demonstration.Furthermore, the metric has been validated by performing experiments using a real-time dataset and random number simulations. Mathematical derivations of the proposed equations have also been provided. We have compared it to Spearman＇s rank correlation coefficient. The comparison results show that the proposed metric fares better than the existing metric on all the predictive metric criteria.