surface fitting
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A third degree polynomial surface fitting technique is adopted to compute the winds at different isobaric levels for the limited area domain from 35°E to 140°E and 30° S to 40oN for the month of June. The polynomial surfaces are fitted to the ratios of the monthly mean winds at different isobaric levels with the 850 hPa winds. The surfaces are fitted to the II and v components of the winds separately. The winds for the level are then reconstructed using the computed coefficients and observed wind at 850 hPa. The results of the technique are presented and discussed in the paper.  

Measuring, analyzing, reducing, and optimizing distortions in map projections is important in cartography. In this study, we introduced a novel image-based angular distortion metric based on the previous spherical great circle arcs-based metric. Images with predefined patterns were used to generate distorted images using mapping software. The generated distorted images with known patterns were then exploited to calculate the proposed angular distortion metric. The mapping software performed the underlying transformation of map projections. Therefore, there was no direct explicit dependence on the forward equations of the map projections in our proposed metric. However, there were fairly large computation errors in the ordinary image-based approach without special correction. To reduce the error, we introduced surface-fitting-based noise reduction in our approach. We established and solved systems of linear equations based on bivariate polynomial functions in the process of noise reduction. Sufficient experiments were made to validate the proposed image-based metric and the accompanying noise reduction approach. In the experiment, the NASA G.Projector was employed as the mapping software for evaluating more than 200 map projections. Experimental results demonstrated that the proposed image-based approach and surface fitting-based noise reduction are feasible and practical for the evaluation of the angular distortion of map projections.

The effective stress coefficient for permeability is a significant index for characterizing the variation in permeability with effective stress. The realization of its accuracy is essential for studying the stress sensitivity of oil and gas reservoirs. The determination of the effective stress coefficient for permeability can be mainly evaluated using the cross-plotting or response surface method. Both methods preprocess experimental data and preset a specific function relation, resulting in deviation in the calculation results. To improve the calculation accuracy of the effective stress coefficient for permeability, a 3D surface fitting calculation method was proposed according to the linear effective stress law and continuity hypothesis. The statistical parameters of the aforementioned three methods were compared, and the results showed that the three-dimensional (3D) surface fitting method had the advantages of a high correlation coefficient, low root mean square error, and low residual error. The principal of using the 3D surface fitting method to calculate the effective stress coefficient of permeability was to evaluate the influence of two independent variables on a dependent variable by means of a 3D nonlinear regression. Therefore, the method could be applied to studying the relationship between other physical properties and effective stress.